MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Miljø- og Fødevareudvalget 2017-18
MOF Alm.del Bilag 35
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Questions from the panel to the researchers

Introduction

The panel members have all read the report, and commented individually on it. In these first appraisals, all

panel members have stressed the points that they thought were most important for the review. They have also

raised a number of questions, that ranged from general discussion points to very specific questions asking for

clarification, and details in need of closer examination.

Subsequently, the panel members have received the questions from the stakeholders. These questions also

range from very general discussion points to detailed questions and comments. The general discussion points

raised by the stakeholders corresponded well to the points already identified by the panel members. Some

remarks are outside of the scope of the review (e.g. legal and economic issues) and will not be commented

upon by the panel. Other issues are very local and also outside of the scope, as the panel members have

insufficient knowledge to comment on them in detail. The final report of the panel will follow the structure of

the scientific report and be formulated in general terms, but the panel intends to indicate in an appendix

whether and how it responded to each of the stakeholder questions, and where this response is to be found in

its report.

In this document the panel formulates a number of questions and discussion points to the researchers. A long

and complicated report naturally raises questions and discussion points, as a large number of decisions have

had to be made regarding the set-up of the study, choice of variables, indicators and processes, choice of policy

measures etc. With the

general questions

formulated in this document we want to give the researchers the

opportunity to better explain the reasoning behind these choices, where that was not clear to us in the report,

or to justify the choices made. The panel wants to take into account these justifications wherever possible in its

assessment. We consider these general questions to be the most important part of this document. In addition

to these general questions, we also formulated a number of

detailed questions.

Sometimes these concern

simple questions for clarification, sometimes they concern details that form part of the more general

questions. We would appreciate a simple answer to these detailed questions, but expect that in many

instances a reference to the answers to the general questions will suffice.

This document with questions, and the answers given to them, will not be published as part of the panel

report. However, both documents will be archived as part of the underlying documentation of the panel report.

The panel may cite (parts of) the answers in its final report, and will refer to these answers in an appropriate

way.

General questions

land-

Exclusive focus on reducing land-based N load to obtain good ecological status

Both the panel and the stakeholders miss a justification of the fundamental choice to focus exclusively on

reduction of (diffuse) N sources as the main means to improve water quality. The situation is complex, as there

is ample evidence that in many systems there is co-limitation of phytoplankton growth by N and P, with some

seasonal pattern in most systems. In addition, N fixation in the Baltic may aggravate the problem and undo N

reduction measures where ample P is available. But it is also true that the N:P ratio of winter loadings is biased

towards N, and that historical reductions have affected P loadings much more than N loadings.

Questions:

We are in need of a thorough literature-based justification of the choices made, as this is a key aspect of the

whole study and the policy.

In addition, we would like the researchers to answer the following questions:

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

What data and evidence (published) exists that indicate which nutrient is limiting (N or P)?. This

may vary with season and location (e.g. Baltic/North Sea). How does this address diverse water

bodies?

Nitrogen loading may be manageable, but is phosphorus in view of sediment exchange and large

past efforts?

In most systems, there is a gradual decrease in N loading that is not synchronous with the

historical decrease in P loading. Which factors or policies have caused this decrease, and what is

the expected autonomous trend in N loading under existing policies? Is there any quantitative

information on this?

How important is the

interaction

between N and P reductions and does the exclusive focus on N

jeopardize the chances of reaching good status by the methods proposed here?

Has N:P stoichiometry as a determining factor for phytoplankton composition been considered?

Very important for the societal discussion: is the exclusive focus on (diffuse) N loading leading to

the economically and societally optimal solution for the water quality problems? Is there evidence

that it leads to the best results in comparison with the costs of the measures? Have any analyses

been made of the cost aspects of the efforts required?

apart from N-runoff from land (chosen as the primary concern) there are other factors that may

affect Ecological Status. P loading has been mentioned. Also fisheries, habitat modification,

change in the species composition of benthos have been mentioned in the literature, especially as

influences on seagrass distribution. Have these factors been considered somehow, and is there

evidence they are unimportant compared to land-based N runoff?

The adopted strategy to derive regionalized reduction targets for nutrient loading

In principle, nutrient reduction scenarios in a country can vary from a general, country-wide reduction target,

over regionalized targets to water system specific targets. This document leads in the end to the definition of

regional targets, but that comes as a surprise to the reader. The statistical modelling chapters suggested that

water body specific targets would be defined, while the mechanistic model, based on country-wide reduction

scenarios, suggested that one would arrive at a single national target. In the end, a regionalisation based on a

set of aggregation rules were derived.

In general, there are arguments in favour of one national target (e.g. setting a level playing field for agriculture,

simplicity of control, simplicity of communication, incorporating mutual influences between systems through

coastal waters) but also in favour of specific targets (e.g. not overdoing efforts, optimal economic strategy). In

the document, however, these arguments have not been made explicit and have not been the subject of

extensive discussion.

Questions:

procedural: when was it decided to adopt this regionalized strategy? Who decided this? Were the

current scientific results used as a basis for this strategy? If so, how was this done precisely?

How sure can we be that the regions are sufficiently homogeneous in their water bodies? In

particular, when a regional target is low because most water bodies are open with short

freshwater residence time, the region may also contain some sensitive, more isolated water

bodies that would suffer from the low targets. Is this the case? How was it controlled?

The scenarios used for the mechanistic modeling use boundary values that are (in part)

determined by nation-wide reductions of nutrient loading with a certain percentage. If there are

regions with mostly open water bodies and low reduction targets, the actual boundary conditions

for all of these water bodies may differ from the modelled ones, since the reductions in the

coastal area will be less. There is, thus, a discrepancy between the modeled policy and the actual

policy. Will this affect the results of the study? Is it possible that the reduction strategy for these

regions is too low, because it is the regional rather than the local reduction percentage that will

influence the ecological status?

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

The statistical modeling only focuses on within-system temporal trends and the causality in these

trends. As far as we understand, no cross-system analysis, relating the hydrographical

characteristics of the systems to their vulnerability to nutrient loading has been performed. Why

hasn’t this been done? It could have formed a scientific basis for the regionalisation, as well as a

basis for investigating the sensitivity of the approach to within-region differences in water body

characteristics?

Choice of indicators and their sensitivity to nutrient loading

Compared to the requirements of the WFD, only a limited set of indicators have been used. Only two of them

(chlorophyll a and Kd) have been used across the two modelling approaches. This leaves a number of unstudied

indicator variables with respect to the good ecological status:

chl-a only gives an indication of phytoplankton biomass, not of composition. Thus it may miss

occurrence of toxic blooms

Kd is probably insufficient as an indicator of habitat quality for eelgrass. In particular, herbicide

concentrations may be missed as an alternative explanatory variable. The literature on eelgrass in

Denmark frequently mentions hysteresis and the occurrence of alternative stable states. It may be

the case that low nutrient loading and high water transparency are necessary but insufficient

conditions for eelgrass restoration - it would be very useful to bring forward quantitative

arguments proving this point. However, it would still be needed to know what other factors

contribute and how.

The benthic index seems to be unresponsive and should be examined more closely or replaced

nutrient stoichiometry (N:P in particular) is not considered

toxic substances, in particular herbicides, might be needed as supporting physico-chemical

variables

Questions:

why are additional variables (e.g. days with nutrient limitation) used in the statistical modeling

but not in the mechanistic modeling, especially as it appears that these variables correlate closely

with chl-a and do not give much independent information?

Could additional reference value targets be developed for TN and TP, using the same

methodology as for chl-a? Presumably, these would be more directly related to loads and simpler

to understand than the supplementary indicators used at present.

None of the models has been able to show a strong influence of nutrient loading on Kd, except

when going from hypertrophic to eutrophic conditions. Why is Kd nevertheless given more weight

(at least with the statistical modeling) than other variables?

what justifies the apparently arbitrary translation of calculated needed reductions (of N load in

order to obtain target Kd) in the order of 200% to 25 %? Why 25 and not any other arbitrary

number? Is the fact that unrealistic needed reductions are obtained, not a reason to decrease

confidence in the models and downweight the importance of the variable in the final conclusions?

What is the impact of the (doubtful) Kd calculations on the final results? Would the results have

been essentially similar without these calculations or is the dependency (and thus the

uncertainty) on Kd results large? This is important to estimate the robustness of the results!

Can you derive supporting evidence from the literature that shows that nutrient loadings affect

eelgrass independent of Kd, or that nutrients and Kd are necessary but insufficient conditions for

eelgrass restoration?

Have you considered other measures than nutrient load reduction in order to restore eelgrass

beds?

Basic strategy of the statistical modeling

The statistical modeling focuses on within-system short-term models, resolving both long-term trends,

seasonal variation and year-to-year variation that correlates with freshwater discharge. This is a choice, but

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

alternatives could have been chosen. One could have concentrated on long-term trends only, e.g. by correcting

yearly values for freshwater discharge as is often done in Danish literature. One could also have chosen to

model the cross-system differences as a function of hydrographic conditions (e.g. fraction freshwater in some

form, stratification,…), thus enabling an evidence-based typology of systems, rather than the current (and

unclear) basis for the typology. It would also have given an evidence base underlying the meta-modeling. At

first sight, a long-term and cross-system approach would have fitted the purposes of the study better.

A second basic choice has been to detrend all independent variables, except the nutrient loadings, and not to

detrend the response variables. This necessarily inflates the correlation between nutrient loadings and

response variable, in case the latter shows trend: the trend can only be attributed to the nutrient loadings, also

when in fact it would have been caused by climate change, increased freshwater extraction or other causes.

A third basic choice has been to select independent variables on MLS, and then apply regression models using

PLS. This combines the sensitivity of MLS to colinearity in independent variables, and the bias in slope

estimators (when applied for prediction) of PLS. The most important consequence of this choice is that only

one nutrient loading can be selected, and combined effects of N and P loading, or their interaction, cannot be

resolved by the models. Another consequence is that in some systems neither nutrient is selected as affecting

the response variable, thus leading to a logical problem in estimating needed levels of reduction. Given the

large knowledge on aquatic ecological processes, one wonders why variable selection has been needed in the

first place, and why the modeling was not based on more advanced models that could have taken into account

colinearity.

A final basic choice has been not to perform an explicit sensitivity analysis, or to report on the uncertainty of

the results. Several methods to do this properly exist, both for within-system studies (e.g. based on Bayesian

approach) and especially for between-system studies in a metamodeling or typology-based grouping of

systems. Lack of communication about uncertainty of the findings hampers communication with stakeholders

and induces risks of economic or ecological damage (in cases of overdoing, resp. underdoing).

Questions:

Why has the choice been made for short-term, within-system models? Why are these better than

alternatives?

What justifies the choice for models that exclude the probing of interaction between different

nutrients, one of the major problems in the current study?

What justifies the variable selection procedure, given that the emphasis was not on proving the

effects of nutrients on water quality, but the estimation of the regression coefficients?

How reliable are the estimates of influence of nutrient loadings, given the strategy of detrending

applied?

Why have no measures of uncertainty been formally derived and presented in a way that is easy

to understand for stakeholders? This could make the recommendations clearer and more

acceptable. (e.g.https://www.ipcc.ch/pdf/supporting-material/uncertainty-guidance-note.pdf)

(most important): What are consequences of all these choices for the conclusions?

set-

Basic set-up and validation of the mechanistic models

In general, the model set-up is clear, but details of the processes and parameters are not easy to find,

especially as some of the referred documents in the model description are not publicly available. In the general

set-up, it is not entirely clear why in the end four different models were set up, especially as the use of a

flexible mesh would have allowed to use a single model with spatially differing resolution. You mention in the

description that the IDW model differs from the estuarine models in some process formulations and variable

settings, and you give arguments why that has been done. We assume that you split the estuarine models in

different models for practical reasons, but would like to know why. More importantly, we do not know if these

models were the same in variables and parameters, and thus only differ from one another in bathymetry and

boundary conditions. If settings differed, we would need details on the how and why.

Model validation was presented based on average values per month and water type. However, in the present

setting a crucial validation element for the models is whether the models have been able to capture the long-

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

term trends in water quality as related to reductions in nutrients. Evidence showing the model behaviour in this

respect should be easily obtainable from model output.

Questions:

can you provide us with a copy of the documents you refer to in the model description?

can you give more details on the four models, and what are their differences and similarities?

can you specify details on the atmospheric forcing: was only a single year used, whereas Denmark

reports on atmospheric deposition to Helcom for longer periods? How was the atmospheric N

deposition divided over different species? Was atmospheric P deposition considered?

can you provide us with the validation data showing that the models have been able to capture

the essential effects of nutrient reduction on target variables chl-a and Kd?

no estimates of model uncertainty were given. Do you have any estimate, what is it based on and

what is the order of magnitude of the estimated error on the variables of interest (in particular

the derived nutrient reduction need)?

Consistency between target values in statistical and mechanistic modeling

Both the statistical model chapters and the mechanistic model chapters describe how reference conditions and

target values were defined. In the ‘ensemble modeling’, as well as in the meta-modeling, the targets from both

model approaches are considered sufficiently consistent to be used in averaging procedures.

Questions:

are these target and reference values conceptually consistent across the two modelling

approaches? As far as we understand, the statistical modelling extrapolates back from the present

situation in a particular water body to the situation that would be present if the

local

nutrient

loading would be reduced to 1900 levels. This does not take into account the reduction in

background marine values, nor the effect of local Danish reductions in other waters that reach the

system of interest through the sea. It also does not take into account regional (e.g. BSAP) efforts.

This reference value, therefore, must be significantly higher than the reference value calculated

with the mechanistic model (which assumes both N and P reduction to 1900 levels, in both the

system of interest and the whole world around). The reference value of the statistical model

would be much closer to the ‘target

obtainable through Danish land-based N reduction’

in the

mechanistic model. In terms of fig. 8.14: the intersection of the orange slope line with the upper

dotted horizontal orange line, and not the point with the red cross. Can this relation between the

definitions of the reference and target values be clarified, and can arguments be given why the

approaches from both model strategies are nevertheless conceptually similar enough to be

averaged?

Meta-

Meta-modeling

While in general the strategy for meta-modeling is clear, there is a question regarding the North Sea waters on

the Jutland coast, and a request from the panel for more supporting data.

Questions:

can you explain how ‘meta-modeled’ results for North Sea waters could be derived, when none of

the underlying models has considered this type of waters, which differ from all other water bodies

in tidal range, temperature regime, sediment loading, nutrient concentration, stoichiometry and

possibly a suite of other characteristics? Have the same indicators and criteria been used for

North Sea and Baltic estuaries, and is this justified?

A serious weakness of the report is that the input data basis is not sufficiently presented. Tables

are lacking that show spatially resolved values for present and past atmospheric deposition,

spatially resolved emission data from land, concrete concentrations in all rivers and estuaries for

both N and P, and hydrographic data (e.g. % freshwater, residence time, tide, depth) for all

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

systems. The lack of area specific data does not allow a critical evaluation of regional MAI nor a

comparison with data and results from other countries. The panel would greatly appreciate if such

a table could be produced, preferably electronically.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

que

Specific questions

Page

Report

Fig. 3.2

20 /

“In addition to the Danish land-based loadings, the

mechanistic models also include N and P loadings at a

regional scale, i.e. loadings to the entire Baltic Sea, and

atmospheric deposition, see chapter 7.”

and P 58:

“An

important input to the setup of the mechanistic models is

the external supply of nutrients. Apart from Danish land-

based nutrient loadings, the mechanistic models include

nutrient input to the Baltic Sea from other countries and

atmospheric deposition. In section 4.2, Danish land-based

nutrient loadings and atmospheric deposition are

described, both based on data from the Danish monitoring

programme DNAMAP.”

Time series of observatio

ns (including Kd)

“only time series with a minimum of 15 years were used”

“… refrained from doing so” (Log transformation)

“daily values gained from interpolation were used to

construct monthly average values”

“… we defined the following rules for predictor

variables”

Question

It seems formally strange to attribute F as

“index” when it is a dimensional quantity

(dimension L^3/T^2) and it does not appear

very logical to divide runoff with residence

time, that is, wouldn’t a longer residence

time imply larger runoff influence? Why not

use a more straightforward parameter

around specific freshwater content:

f=R/(Q+R) = (Sm – S)/Sm

Type 1 subtypes represent different

nitrogen and phosphorus regimes, ranging

from the quite Baltic Sea influenced to

quite North Sea influenced, should perhaps

this be taken into account in the model

validation? On the other hand, the number

of Type 1 areas that are both critically

dependent on Danish nutrient inputs and

significantly deviating from GES are

probably limited.

In shallow waters assumptions with respect

to atmospheric deposition input can be

crucial and potentially allow a manipulation

of the MAI. Was the deposition data

spatially resolved? If not, how was it taken

into account in the model? Were gradients

between land and sea taken into account?

Which atmospheric N fractions were

considered as bio-available in the model

and how were they calculated? Was the

atmospheric input of P fractions

considered, as well?

How was Kd measured?

What is the statistical justification?

How much data are omitted?

Are data normally distributed?

Do you have a statistical reference for this

procedure?

Do you have statistical criteria or a

reference for this?

There are robust

& complete time series analysis theories

and methodologies available

What was the final weight of this exercise

in the selection of variables?

Why did you not estimate error variances

and confidence limits which are

preconditions for evidence based, adaptive

management, policy and decision making?

Your justification conflicts with your

observation of significant autocorrelation,

doesn’t it?

calculation of Chl-a and KD is critical in this

study. Thus, more information on how Chl-

“The half saturation coefficients (Ks) for phosphorus and

nitrogen were chosen to be 0.2 uM and 2 uM”

“… quantification of autocorrelation , this effect was not

included in the models”

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

„However, an important difference between the national

data and the data adopted by AU for the mechanistic

modelling is the resolution in time. Whereas the national

data are reported on an annual basis, the data used for

the modelling were provided on a daily basis, both for

water discharges and nutrient loadings.“

„The loadings were estimated as discharges of total

nitrogen (TN) and total phosphorus (TP). Since the

mechanistic models differentiate between the different

chemical forms (inorganic/organic, dissolved/particulate,

nitrogen and phosphorous species), the data were

subsequently transformed into nutrient forms required by

the modelling. Through an assessment of available

observations on nutrients in water discharged from

Danish catchments, monthly relations between inorganic

and organic nutrients were developed and applied to split

TN and TP into an inorganic and an organic fraction. By

combining TOC and COD/BOD observations, the organic

part was further split to separate the organic nutrients

into the three forms adopted in the modelling process.“

„Hence, the data are those officially reported by the

various countries. Differentiation of TN and TP loadings

was done according to Stepanauskas et al. (2002).“

Stepanauskas et al. (2002): „We estimate that the input of

summer riverine N to the Baltic Sea consists of 48%

dissolved inorganic N, 41% DON, and 11% particulate N.

Corresponding values for phosphorus are 46%, 18%, and

36% of dissolved inorganic P, DOP, and particulate P,

respectively.“

“… data were lumped according to topology…” Fig. 7.6

a is calculated from phytoplankton carbon

and on the optical model parameterization

relating model state-variables to KD would

be interesting.

How was this done?

Skills of biogeochemical models

“seasonal anoxia in these areas, inducing release of

phosphorus from the sediments”

Since the assumptions with respect of the

model input are crucial for the later results,

I like some clarifications. Am I right that you

used (with respect to N) DIN and a part of

TON as bio-available fractions in the

model? How did you calculate it from

biological and chemical oxygen demands

(COD/BOD)? Did you take into account

DON, as well? Was this calculated for every

river separately or as an average for all

Danish rivers? Could you give numbers

about the relative share of each fraction for

N and P?

Is this the same approach that you used for

Danish rivers? Stepanauskas et al. (2002)

quantify DIN and DON and these are the

fraction you used as input for all other

Baltic areas, is this right? In some areas the

model seems not to cover the entire coast

and nutrient retention may take place

between river input and onset of the model

domain. How did you deal with it?

Did you calibrate models by water body?

Evaluation by type does not reveal accuracy

and precision of water body specific

models, does it? Would it be possible to

estimate error variances and confidence

limits (e.g. 0,95) for water body specific

models?

What are the estimated mean, covariance

and variance of model parameters and

error variances of water body specific

models?

Is it true that all data was used for model

calibration and that a model validation

using an independent data set (year) was

not carried out?

In addition to regression coefficients

demonstrating similar trends in model and

data, can you also indicate that the actual

values corresponded?

Could you provide non-aggregated time

series showing the model performance and

data for concrete monitoring stations in

comparison?

Have the sorption-desorption on

suspended sediment particles been taken

into consideration?

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

You attribute the decrease due to UWWT in Copenhagen,

population about 600 000

“In order to reduce the influence of model bias, we used

… ensemble models …” & “… most robust chlorophyll-a

estimates were achieved using ensemble model”

“ … status values are converted into water body averages

by relating the observed status to the modelled status at

the actual observation point and applying the ratio

between the two (model and observation) to correct the

modelled water body average”

“The purpose of averaging … is to reduce uncertainty”

What is the point of validation based on

water body Type? Type 1 waters seem to

include as diverse areas as the ones inside

the sills to rather marine areas in Kattegat,

why not use the different sub-categories of

Type 1, Figure 3.2 and Table 8.1?

How is the aggregation done into Type

averages in e.g. Figure 7.6? Just mean value

water bodies (model/observed data)?

The quantitative assessment (page 65-66) is

done on monthly mean time-series. That

implies a mixture of validation of seasonal

cycle and inter-annual variability. At least

for the non-open water Types, it would

make sense to explicitly look at the

interannual variability that probably gives

more information on the model’s

capabilities of resolving the response to

load reductions.

The sediment pools are reduced for the

reference simulation in the Baltic Sea and

IDW based on literature values. But it is not

explicitly stated whether this adaption

resulted in a new quasi-steady-state in the

model when forced with reference loads,

which could be influential on several of the

Type 1 water bodies. Is this the case?

What management measures in the same

time period have been implemented to

treat the manure of the approx. 25million

pigs? Each pig represents 3 person

equivalents, so approximately 75 million

people.

How can you justify this without proper

error variance/uncertainty estimates?

Could you clarify? Are you correcting model

results?

“This choice is based on our wish from a management

perspective to emphasise intercalibrated indicators and

has no scientific basis”

“we chose a half saturation coefficient (Ks) for nitrogen

limitation of 2 µM”

“… Kd indicator … are assigned double weight”

“… light attenuation indicator has beem giving double

weight”

“… we have transformed the estimated PLR values into

categories when above 25 %”

Can you justify? Is average any more

certain than either of the models?

What is the method to estimate the

weights?

Could it be possible to use error variances

of models as weights?

Does this mean the WFD intercalibration?

Why does intercalibration not provide a

scientific basis for the chosen indicators?

On what basis (published) was this

concentration chosen? This is difficult for a

mix of diatoms, cyanobacteria and

dinoflagellates.

All of these choices sound arbitrary and

cursory. Can you justify?

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102

“…due to the time constraints … we chose not to develop

models” & “… the demand was assigned as 25 %..”

“… values above one trigger a demand 25%”

“we used categorization … as demonstrated in Table 8.7”

“… the target values are rounded …”

111

124

125

“With respect to the North Sea water bodies, the data

basis does not support the methodology described for

mechanistic model-based meta model since

biogeochemical modelling was not included in the study.

However, GES has not been reached in any of the Danish

water bodies in the North Sea and Skagerrak, and an

approach taking limitation and differences into account

has therefore been developed

The described approach is subject to uncertainty.

The scenarios have the basis that BSAP

nutrient load reductions are implemented.

These comprise of massive P-load

reductions (e.g., 60% for Baltic Proper that

eventually should lead to halving winter DIP

concentrations there), but all published

scenarios show that the response time is

quite slow with typical e-folding time of say

20 years. How is this time-delay handled in

the model?

It is surprising that massive load reductions

to Baltic Sea do not give more response to

basin 217. The export of phosphorus from

the Baltic proper should decrease

substantially given that DIP concentrations

should be reduced to 50% of present day

concentrations in BSAP. Could you explain?

What is meant by this statement? It is

unclear

129

“…95% confidence interval at +/- 13.5 % reduction”

130

141

“the methods presented here basically violate the one-out-

all-out principle, which is defined when evaluating the

ecological status and not when estimating measures to

ensure GES”; “When reductions based on chlorophyll-a

or Kd are averaged instead of choosing the maximum

reductions,we do, in theory, not obtain GES for both

indicators”

Can the uncertainty be expressed in a way

that it is easily understoon by decision

makers and stakeholders?

What can you say about model error

variances and confidence limits based on

the comparison of mechanistic and

statistical models? Is this 13.5% the overall

confidence interval of loading reduction?

Does the observation that for area 44 the

statistical model fails because it does not

take regional reductions into account imply

that the statistical approach would fail for

all Type 1 water bodies?

Is the method therefore WFD compliant? If

not, what is necessary to make it WFD

compliant?

What management measures are necessary

to obtain GES for BOTH indicators?

It is stated that the basis is to obtain GES in

2027. This is fine, but it also has

consequences on how to handle effects

from regional reductions (BSAP), see the

comment above on scenarios (page 102). It

would be relevant to discuss the time

aspect already in the beginning of the

report as well, because we know the

ecosystem responds slowly, and differently

across the water bodies.

141

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

142

“… focused on reducing uncertainties, for instance by

averaging … and applying a type-specific approach

142

“The ensemble model results reveal good agreement

between the two very different model approaches …, thus

indicating that the estimated MAIs are reliable”

You lose information at the same time. Can

you guarantee reduction of uncertainties

without proper statistical error analysis,

that is, comparison on error variances of

models based on actual and averaged data?

How can you say so without proper

statistical error analysis?

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DHI 3 Algae and Sediment Model

ECO Lab Template

Scientific Description

MIKE

2016

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PRINTING HISTORY

October 2013 ........................................................... Release 2014

July 2015 ................................................................... Release 2016

DHI headquarters

Agern Allé 5

DK-2970 Hørsholm

Denmark

+45 4516 9200 Telephone

+45 4516 9333 Support

+45 4516 9292 Telefax

[email protected]

www.mikepoweredbydhi.com

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DHI

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CONTENTS

DHI 3 Algae and Sediment Model

ECO Lab Template

Scientific Description

3.1

3.2

3.3

3.3.1

3.3.2

3.3.3

3.3.4

3.3.5

3.3.6

3.3.7

3.3.8

3.3.9

3.3.10

3.3.11

3.3.12

3.3.13

3.3.14

3.3.15

3.3.16

3.3.17

3.3.18

3.3.19

3.3.20

3.3.21

3.3.22

3.3.23

3.3.24

3.3.25

3.3.26

3.3.27

3.3.28

3.4

3.4.1

3.4.2

3.4.3

3.4.4

3.4.5

3.4.6

3.4.7

Introduction .......................................................................................................................1

Applications ......................................................................................................................3

Mathematical Formulations..............................................................................................5

Vertical light penetration....................................................................................................................... 8

Production of autotrophs ...................................................................................................................... 9

Differential equations pelagic state variables .................................................................................... 12

-3

PC1: Flagellate C, g C m ................................................................................................................. 12

-3

PC2: Diatom C, g C m ..................................................................................................................... 15

-3

PC3: Cyanobacteria C, g C m .......................................................................................................... 17

-3

PN1: Flagellate N, g N m ................................................................................................................. 20

-3

PN2, Diatom N, g N m ..................................................................................................................... 22

-3

PN3, Cyanobacteria N, g N m .......................................................................................................... 23

-3

PP1, Flagellate P, g P m .................................................................................................................. 25

-3

PP2, Diatom P, g P m ...................................................................................................................... 26

-3

PP3, Cyanobacteria P, g P m .......................................................................................................... 28

-3

PSi2, Diatom Si, g Si m .................................................................................................................... 29

-3

CH, Chlorophyll, g m ........................................................................................................................ 31

-3

ZC, zooplankton, g C m ................................................................................................................... 33

-3

DC, Detritus C, g C m ...................................................................................................................... 34

-3

DN, Detritus N, g N m ...................................................................................................................... 36

-3

DP, Detritus P, g P m ....................................................................................................................... 38

-3

DSi, Detritus Si, g Si m .................................................................................................................... 40

-3

NH4, Total ammonia, g N m ............................................................................................................ 41

-3

NO3, Nitrate, g N m ......................................................................................................................... 45

-3

H2S, Hydrogen Sulphide, g S m ...................................................................................................... 47

-3

IP, Phosphate (PO4-P), g P m ......................................................................................................... 49

-3

IP, Phosphate (PO4-P), g P m ......................................................................................................... 52

-3

DO, Oxygen, g O2 m ....................................................................................................................... 53

-3

CDOC, Coloured refractory DOC, g C m ......................................................................................... 57

-3

CDON, Coloured refractory DON, g N m ......................................................................................... 58

-3

CDOP, Coloured refractory DOP, g P m ......................................................................................... 59

-3

LDOC, Labile DOC, g C m ............................................................................................................... 60

-3

LDON, Labile DON, g N m ............................................................................................................... 62

-3

LDOP, Labile DOP, g P m ............................................................................................................... 63

Differential Equation Sediment State Variables ................................................................................. 65

SSi, Sediment, bio-available Silicate, g Si m .................................................................................. 65

KDOX, depth of NO3 penetration in sediment, m .............................................................................. 66

KDO2, DO penetration in sediment, m .............................................................................................. 67

-2

SOC, Sediment organic C, g C m .................................................................................................... 68

-2

SON, Bio-available organic N in sediment, g N m ........................................................................... 70

-2

SOP, Bio-available organic P in sediment, g P m ............................................................................ 72

-2

FESP, PO4 adsorbed to oxidised ion in sediment, g P m ............................................................... 74

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DHI 3 Algae and Sediment Model

3.4.8

3.4.9

3.4.10

3.4.11

3.4.12

3.4.13

3.4.14

3.5

3.5.1

3.5.2

SNH, Sediment pore water NH4, g N m .......................................................................................... 75

-2

SNO3, NO3 in sediment pore water, layer (0 - kdo2), g N m .......................................................... 76

-2

SIP, PO4 in sediment pore water, g P m ......................................................................................... 79

-2

SH2S, Reduced substances in sediment, g S m ............................................................................. 80

-2

SPIM, Immobilised sediment P, g P m ............................................................................................ 82

-2

SNIM, Immobilised sediment N by denitrification & burial, g N m ................................................... 83

-2

SNIM, Immobilised sediment N by denitrification & burial, g N m ................................................... 84

Help Processes .................................................................................................................................. 85

The P1 processes listed in alphabetic order ...................................................................................... 85

Auxiliary (A) processes listed in alphabetic order .............................................................................. 91

-2

Data Requirements ...................................................................................................... 131

References.................................................................................................................... 133

ECO Lab Template - © DHI

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Introduction

ECO Lab is a numerical lab for Ecological Modelling. It is a generic and open tool for

customising aquatic ecosystem models to describe for instance water quality and

eutrophication. DHI’s expertise and know how concerning ecological modelling has been

collected in predefined ecosystem descriptions (ECO Lab templates) to be loaded and

used in ECO Lab. So the ECO Lab templates describe physical, chemical and biological

processes related to environmental problems and water pollution. The following is a

description of the DHI 3 algae and sediment model.

The DHI 3 algae and sediment template is used in investigations of eutrophication effects

where different algae species and sediment pools of nutrients are essential and as an

instrument in environmental impact assessments for such ecosystems. The 3 algae and

sediment modelling can be applied in environmental impact assessments considering:

•

Pollution sources such as domestic and industrial sewage and agricultural run-off

Cooling water outlets from power plants resulting in excess temperatures

Physical conditions such as sediment loads and change in bed topography affecting

especially the benthic vegetation

Evaluation of action plans related to nutrient reductions

Risk evaluation in connection to potential harmful algae blooms

The aim of using 3 algae and sediment modelling as an instrument in environmental

impact assessment studies is to obtain, most efficiently in relation to economy and

technology, the optimal solution with regards to ecology and the human environment.

The 3 algae and sediment model describes nutrient cycling including internal loadings

from sediment pools of nutrient, phytoplankton and zooplankton growth, in addition to

simulating oxygen conditions.

The model results describe the concentrations of phytoplankton, chlorophyll-a,

zooplankton, organic matter (detritus), organic and inorganic nutrients, oxygen and the

area-based sediment pools of nitrogen and phosphorous over time. In addition to this, a

number of derived variables are stored: primary production, total nitrogen and phosphorus

concentrations, sediment oxygen demand and Secchi disc depth.

The 3 algae and sediment template is integrated with the advection-dispersion module,

which describes the physical transport processes at each grid-point covering the area of

interest. Other data required are concentrations at model boundaries, flow and

concentrations from pollution sources, water temperature and influx of light, etc.

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DHI 3 Algae and Sediment Model

ECO Lab Template - © DHI

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Applications

The eutrophication template can be applied in a range of environmental investigations:

•

Studies where the effects of alternative nutrient loading situations are compared

and/or different waste water treatment strategies are evaluated.

Studies of oxygen depletion.

Studies of the effects of the discharge of cooling water.

Comparisons of the environmental consequences of different construction concepts

for harbours, bridges, etc.

Evaluation of the environmental consequences of developing new urban and

industrial areas.

Evaluation of action plans related to nutrient reductions and long term effects of

reduction scenarios.

Risk evaluation in connection to potential harmful algae blooms.

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DHI 3 Algae and Sediment Model

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

The MIKE 21/3 ECO Lab is coupled to the MIKE 21/3 AD module in order to simulate the

simultaneous processes of transport, dispersion and biological/biochemical processes.

The 3 algae and sediment model includes state variables for 3 pelagic algae groups,

nutrients, oxygen, hydrogen sulphide and sediment pools of C, N and P as well as a

number of sediment state variables..

Table 3.1

Name

PC1

PC2

PC3

PN1

PN2

PN3

PP1

PP2

PP 3

Psi

DSi

NH4

NO3

H2S

CDOC

CDON

CDOP

LDOC

LDON

LDOP

Pelagic state variables

Comment

Flagellate C

Diatom C

Cyanobacteria C

Flagellate N

Diatom N

Cyanobacteria N

Flagellate P

Diatom P

Cyanobacteria P

Diatom Si

Chlorophyll-a

Zooplankton C

Detritus C

Detritus N

Detritus P

Detritus Si

Total ammonia (NH

)

Nitrate+ nitrite

Hydrogen Sulphide (H

Inorganic Phosphorous (PO

)

Silicate Si

Dissolved Oxygen

Coloured refractory DOC

Coloured refractory DON

Coloured refractory DOP

Labile DOC

Labile DON

Labile DOP

Unit

gCm

gNm

gPm

-3

g Si m

g Chl m

gCm

gNm

gPm

-3

g Si m

gNm

gSm

gPm

-3

g Si m

g O

gCm

gNm

gPm

-3

gCm

gNm

gPm

-3

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DHI 3 Algae and Sediment Model

Table 3.2

Name

SSi

KDOX

KDO2

SOC

SON

SOP

FESP

SNH

SNO3

SIP

SH2S

SPIM

SNIM

SCIM

Sediment state variables

Comment

Sediment biological available Silicate

Oxidised layer, depth of NO3 penetration in sediment

DO penetration into sediment

Sediment organic C

Sediment organic N

Sediment organic P

Sediment iron adsorbed PO4

Sediment pore water NH4

NO3-N in Surface sediment pore water, layer (0 - kdo2)

Sediment pore water PO4

Sediment reduced substances as (H2S)

Immobilised P in sediment

Sediment immobilised N by denitrification & burial

Sediment immobilised C by mineralisation & burial of SOC

Unit

g Si m-2

g C m-2

g N m-2

g P m-2

g N m-2

g P m-2

g S m-2

g P m-2

g N m-2

g C m-2

Table 3.3

Name

sum_PRPC

sum_CminW

Additional State variables for mass considerations

Comment

Sum of PC production

Sum of pelagic C mineralisation

Sum of SOC mineralisation

Sum of atmospheric deposition of N

Sum of cyanobaterial N fixation

Sum of denitrification in water column

Sum of N flux sediment- water

Sum of sediment denitrification

Sum of atmospheric deposition of P

Sum of P flux sediment-water

Sum of reaeration

Sum of sediment O2 respiration

Sum of H2S production in sediment

Unit

g C m-2

g N m-2

g P m-2

g O2 m-2

g S m-2

sum_minSOC

sum_DEPON

Sum_Nfix

sum_DENW

sum_Nflux

sum_rdenit

sum_DEPOP

sum_Pflux

sum_rear

sum_ODSC

sum_RSH2S

ECO Lab Template - © DHI

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Mathematical Formulations

The first 28 components or state variables (pelagic system) are moveable and treated in

both the MIKE 21/3 AD and the MIKE 21/3 ECO Lab module. The additional components

have a fixed nature belonging to the benthic system.

The processes and transfer of carbon, nitrogen and phosphorus in the Eutrophication

model system is illustrated in Figure 3.1. Also included in the model is an oxygen balance.

The processes describing the variations of the components in time and space are

dependent on external factors such as the salinity, water temperature, the light influx, and

the discharges.

The salinity and water temperature can be results of MIKE 21/3 AD simulations or be user

specified values. The first possibility is especially relevant for cooling water investigations

whereas the latter possibility often is used in areas where only natural variations in

temperature are seen.

The mathematical formulations of the biological and chemical processes and

transformations for each state variable are described one by one below. The differential

equations are 1st order, ordinary and coupled.

State variables & processes

Photosynthesis

inorganic

N,P, Si

Grazing

of algae

Mineralization

& Respiration

Zooplankton

C(N,P)

Diss Oxygen

Defae. Zoopl. Dead Zoopl.

Dead algae

Part. org matter

C,N,P

Mineralization & Respiration

in sediment (CO

, N,P)

Algae

C,N,P

SEDIMENT

Processes

Sources & Sinks

Immobile N,P

State variables

Figure 3.1

The simplified flow diagram of the fluxes of carbon, nitrogen and phosphorus in the

eutrophication model.

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DHI 3 Algae and Sediment Model

3.1

Vertical light penetration

Light is essential for growth of all plants, including the pelagic. The vertical light

penetration can be described by an exponential decay with depth which is dependent on

a light extinction K

, which either can be described as with light extinction constants (k

)

-3

multiplied by concentrations of light extinction concentration (Chlorophyll (CH, g m )),

-3

detritus (DC, g C m ), dissolved organic matter (CDOC, g C m ), inorganic matter (SS, g

-3

-1

m ) and water(k

bla,

m ) or it can be described as a function of scattering (b, m ) and

-1

absorption (a, m ) of light.

Vertical light penetration with depth (z, m) in the water column:

Where K

can be either K

or K

Or:

∗

−��

��

∗

The absorption of light is mainly associated to particulate and dissolved organic matter

whereas the scattering is mainly associated to particulate inorganic matter.

Light absorption, where the notation Kx

stand for light absorption constant of

component x:

=√

ℎ

+ .

∗ �� +

⁡mol⁡photons⁡�� ⁡

∗ ��+

−

(3.1)

∗

∗ ⁡, ��

−

∗��

��+

∗ �� +

⁡, ��

−

(3.2)

(3.3)

Light scattering form phytoplankton and fine suspended inorganic matter can be

describes as power functions of CH and SS:

ℎ

��

∗ �� +

ℎ

��

∗ ��+

∗ ��

��

∗��

��+

��

∗ �� +

⁡

⁡, ��

−

(3.4)

Where the light scattering constants (bkch, bkss in m g ) and exponents (ekch, ekss) are

for chlorophyll and inorganic suspended matter, respectively.

The present ecological model do not simulate resuspensition of (fine) sediment, therefore

SS is not dynamically simulated. Resuspension is most pronounced on shallow waters

below 5-10 m. The user should therefore consider the need for either including measured

SS concentrations or modelled concentrations of SS by a sediment transport model

(MIKE by DHI 2011a). On shallow waters (like lagoons) the EU-MT ECO Lab template

can be used. This template includes resuspension of and transport of fine sediment and

combine it with a description of nutrients (N, P) one phytoplankton group, one

macroalgae, one rooted macrophyte (eelgrass) and microbenthic algae (Rasmussen E. K.

et al. 2009).

The present model however calculates dynamically the concentration of chlorophyll (CH),

detritus carbon (DC) and refractory or coloured dissolved organic C (CDOC). The missing

resuspension of SS is minimal if used on set up with waters above 10 m depth, like the

Baltic Sea.

ℎ ∗ ��

⁡, ��

−

(3.5)

2 -1

ECO Lab Template - © DHI

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Mathematical Formulations

3.2

Production of autotrophs

The template includes 3 pelagic autotrophs (flagellates, diatoms and cyanobacteria). The

production is based on daily dose of photosynthetic active light (PAR, mol photons m

-1

)

light resulting in a net production.

The differential equation includes a net production, sedimentation, buoyancy (flagellate

& cyanobacteria) and mortality by grazing and nutrient limitation (nutrient stress).

��

The net production is determined by light (flight(i)), temperature (ftemp(T)) and nutrient

availability (fnut(N,P,

(Si diatoms))).

is the temperature corrected max specific growth

-1

-3

-2

(d ) and X is the biomass (g C m or g C m )

⁡

��

�� = �� ∗ �� ℎ �� ∗ ��

∗��

(��, , �� ) ∗ �� ∗

∗

(3.7)

�� ⁡

��

�� − ��

��

−

��

�� + ⁡ ��

(3.6)

Where:

Name

N,P, Si

FAC

Comment

Max specific net growth rate (12 h light/12 h dark) at 20 °C

Light (PAR) dose

Temperature

Internal concentrations of N, P and SI in algae

Correction of dark reaction (growth)

Relative day length, function of latitude, 1 at 12 h light

Unit

-1

-2

-1

mol photon m d

°C

g nutrient g C

n.u.

n.u

-1

Temperature is an important direct or indirect regulator of many processes. Two types of

temperature functions are used, Arrhenius or Lassiter functions.

The Arrhenius function increases the process exponentially with temperature; whereas

the Lassiter function have an optimum temperature from which the process decline

towards zero.

In the present template Arrhenius relations are used to describe the max specific growth

rates, as the template is used in waters where the temperature rarely exceeds 20 °C.

Further at increasing temperatures the plankton community will have a tendency to adapt

to the higher temperature by change of species composition.

The user is encouraged to consider the feasibility to change from Arrhenius to a Lassiter

temperature regulation of the max specific growth rates if needed. Both Arrhenius and

Lassiter expressions are bullied in function in ECO Lab see (MIKE by DHI 2011b).

Lassiter functions are used to temperature regulate the max specific growth rates. In

contrast to the Arrhenius function The Lassiter function include an optimum temperature

above which the function will decline. Arrhenius functions are used to regulate the specific

growth of phytoplankton or macrophytes in areas normally having summer temperatures

well above 20 °C.

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DHI 3 Algae and Sediment Model

It is still recommended to use Arrhenius functions for temperature regulation of respiration

processes; however the user might consider to increase the reference temperature for 20

°C, if data or references justify this.

Lassiter:

=⁡

��

∗

−

∗

(

−

��

)

∗

(

��

−

��

−

��

)

∗

(

��

−

��

)

−

(3.8)

Arrhenius 20 °C:

��

=��

−

(3.9)

Where:

ρopt:

Topt:

Tmaxt:

Ɵ:

K2:

Temperature °C

max growth at Topt, d-1

Optimum temperature °C

Maximum temperature° C

Teta constant Arrhenius function

constant

Figure 3.2

Arrhenius at 5 and 20 °C (Ɵ 1.04) and Lassiter function at T

opt

at 12 and 18 °C

max

30 °C, K2 0.4)

The nutrient regulates the growth of all autotrophs. Two different nutrient regulators of the

growth are used. A Droop kinetic (Droop 1973, Droop 1975) is used for autotrophs having

internal nutrient pools (flagellates, diatoms, cyanobacteria). A Monod kinetics (Monod J.

1949) is used to describe the uptake of inorganic N, P and Si from the water into plankton.

ECO Lab Template - © DHI

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Mathematical Formulations

Further cyanobacteria has the ability to N fixation in situation where the internal N:C ratio

is low and the internal P:C is above average.

Nutrient regulation of primary production of phytoplankton (flagellates and cyanobacteria):

��

��,

��

(3.10)

In the expression for diatoms Si is included:

��

��, , ��

��

(3.11)

Droop kinetics used for N modified after (Nyholm1978, Nyholm 1979) is used to regulate

growth of phytoplankton:

��

The same formulation is used for diatoms.

Droop kinetics used for P modified after (Nyholm1978, Nyholm 1979) is used to regulate

growth of phytoplankton:

��

�� − �� ⁡

(3.12)

��

Where:

Name

PNmin

PNmax

PPmin

PPmax

��−

�� −

��

∗

+ ��−

�� −

�� ⁡

(3.13)

Comment

Phytoplankton C

Phytoplankton N

Phytoplankton P

Minimum N:C ratio for phytoplankton

Maximum N:C ratio for phytoplankton

Minimum P:C ratio for phytoplankton

Maximum P:C ratio for phytoplankton

Unit

g C m-3

g N m-3

g P m-3

g N g C-1

g P g C-1

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DHI 3 Algae and Sediment Model

3.3

3.3.1

Differential equations pelagic state variables

PC1: Flagellate C, g C m

-3

�� /�� =

Process

PRPC1

GRPC1

DEPC1

SEPC1

BUOYC

Where:

�� −

�� −��

�� −

��

Unit

gCm d

-3

-1

(3.14)

Comment

Net production flagellate carbon

Grazing of flagellate carbon

Death of flagellate carbon

Settling of flagellate carbon

Flagellate upward movement

-1

PRPC1: Net Production flagellate carbon, g C m d

Where:

Name

mntp1

myfi1

fac

�� =��

∗ �� ∗ ��

∗

∗ ��

-3

-1

(3.15)

Comment

N, P & temperature corrected max. net growth rate

Light function Flagellate,

Phytoplankton, Correction for dark reaction

Relative daylength, f(latitude, day,month,year)

Unit

-1

Type*)

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

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Mathematical Formulations

GRPC1: Grazing of phytoplankton (Flagellate) carbon, g C m d

�� =

��

∗��

��

∗ ��

∗ �� +

�� − .

�� ∗ �� +

��

∗ ��

-3 -1

∗��

(3.16)

Where:

Name

Kedib1

Kedib2

Kedib3

PC1

PC2

PC3

mgpc

Comment

Edible fraction of Flagellate

Edible fraction of Diatoms

Edible fraction of Cyanobacteria

Flagellate C

Diatom C

Cyanobacterie C

Temperature & food corrected grazing rate

Zooplankton C

Unit

n.u.

gCm

-1

-3

Type*)

-3

gCm

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

DEPC1: Death of phytoplankton (flagellate) carbon, g C m d

Where:

Name

kdma

mnl1

�� =

�� ∗��

∗ ��

-3 -1

(3.17)

Comment

Specific death rate phytoplankton

Nutrient dependent death factor, flagellate

Unit

-1

Type*)

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

SEPC1: Settling of phytoplankton (flagellate) carbon, g C m d

Phytoflagellates has the ability of vertical movement in the water column optimising their

ability to pick up nutrient and gain light. During nutrient limitation the flagellates is

assumed to seek down to the pycnocline to pick up nutrient, and in case they are not

nutrient limited they are assumed to stay in the photic zone.

In the present model nutrient limitation, in term of a low PN/PC and or PP/PC ratio,

enhance the sedimentation rate. PN/PC and PP/PC ratios close to maximum N and P

content in the algae result in a reduction of the sedimentation rate. The nutrient regulation

of the sedimentation rate is expressed in the auxiliary

sed1.

Light is also regulating the sedimentation rate. At high light dozes the sedimentation is

accelerated at medium light dozes sedimentation is

mspc1

and at low light dozes the

sedimentation decreases. This light regulation is expressed in the auxiliary

fiz.

-3 -1

Where:

Name

mspc1

sed1

Fiz

��

�� =

��

∗

∗ �� ∗ ��

(3.18)

Comment

Sedimentation rate flagellate phytoplankton

Height of actual water layer

N & P regulation of sedimentation. flagellate

Light factor for PC1 & PC3 sedimentation

Unit

n.u.

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

BUOYC1: Flagellate upward movement, g C m d

The vertical upward movement by the phytoflagellates is described as a function of light

doze and the algae’s nutrient condition expressed in the auxiliary

buoy1.

An upward

vertical movement is enhanced by a good nutrient condition and a low light doze.

-3 -1

Where:

Name

mspc1

buoy1

�� =

��

∗

��

∗ ��

(3.19)

Comment

Sedimentation rate flagellate phytoplankton

N & P & light upward movement function, flagellate

Height of actual water layer

Unit

n.u.

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

3.3.2

PC2: Diatom C, g C m

-3

��

Process

PRPC2

GRPC2

DEPC2

SEPC2

Where:

�� +

Comment

�� −

�� −��

��

Unit

gCm d

-3

-1

(3.20)

Net production diatom carbon

Grazing of diatom carbon

Death of diatom carbon

Settling of diatom carbon

-1

PRPC2: Net Production phytoplankton carbon, g C m d

Where:

Name

mntp2

myfi2

fac

�� =��

∗ �� ∗ ��

∗

∗ ��

-3 -1

(3.21)

Comment

N, P, Si & temperature corrected max. net growth rate

Light function Diatom

Phytoplankton, correction for dark reaction

Relative daylength, f(latitude, day,month,year)

Unit

-1

Type*)

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

GRPC2: Grazing of

phytoplankton (Diatom)

carbon, g C m d

�� =

��

∗��

��

∗ ��

∗ �� +

�� − .

�� ∗ �� +

��

-3 -1

∗ ��

∗��

(3.22)

Where:

Name

Kedib1

Kedib2

Kedib3

PC1

PC2

PC3

mgpc

Comment

Edible fraction of Flagellate

Edible fraction of Diatoms

Edible fraction of Cyanobacteria

Flagellate C

Diatom C

Cyanobacterie C

Temperature & food corrected grazing rate

Zooplankton C

Unit

n.u.

gCm

-1

-3

Type*)

-3

gCm

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

DEPC2: Death of diatom carbon, g C m d

Where:

Name

kdma

mnl2

�� =

�� ∗��

∗ ��

-3 -1

(3.23)

Comment

Specific death rate phytoplankton

Nutrient dependent death factor, diatom

Unit

-1

Type*)

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

SEPC2: Settling ofdiatom carbon, g C m d

Where:

Name

mspc2

mnl2

��

�� =��

∗

��

-3 -1

��

∗ ��

(3.24)

Comment

Sedimentation rate diatom phytoplankton

Nutrient function, sedimentation & death, diatom

Height of actual water layer

Unit

n.u.

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.3

PC3: Cyanobacteria C, g C m

-3

�� /�� =

Process

PRPC3

GRPC3

DEPC3

SEPC3

BUOYC3

Where:

�� −

�� −��

�� −

��

Unit

(3.25)

Comment

Net production cyanobacteria carbon

Grazing of cyanobacteria carbon

Death of cyanobacteria carbon

Settling of cyanobacteria carbon

Cyanobacteria upward movement

g C m-3 d-1

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

PRPC3: Net Production cyanobacteria carbon, g C m d

Where:

Name

mntp3

myfi3

fp3sal

fac

�� =��

∗ �� ∗ ��

∗��

∗

∗ ��

-3 -1

(3.26)

Comment

N, P & temperature corrected max. net growth rate

Light function Cyanobacteria,

Function for cyanobacteria dependency of salinity

Cyanobacteria, Correction for dark reaction

Relative daylength, f(latitude, day,month,year)

Unit

-1

Type*)

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

GRPC3: Grazing of

cyanobacteria (Flagellate)

carbon, g C m d

�� =

Where:

Name

Kedib1

Kedib2

Kedib3

PC1

PC2

PC3

mgpc

-3 -1

��

∗��

��

∗ ��

∗ �� +

�� − .

�� ∗ �� +

��

∗ ��

∗��

(3.27)

Comment

Edible fraction of Cyanobacteria

Edible fraction of Diatoms

Edible fraction of Cyanobacteria

Flagellate C

Diatom C

Cyanobacteria C

Temperature & food corrected grazing rate

Zooplankton C

Unit

n.u.

gCm

-1

-3

Type*)

-3

gCm

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

DEPC3: Death of cyanobacteria carbon, g C m d

Where:

Name

kdma

mnl3

fp3sal

�� =

�� ∗

��

-3 -1

∗ ��

(3.28)

Comment

Specific death rate cyanobacteria

Nutrient dependent death factor, cyanobacteria

Function for cyanobacteria dependency of salinity

Unit

-1

Type*)

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

SEPC3: Settling of cyanobacteria carbon, g C m d

Cyanobacteria has the ability of vertical movement in the water column optimising their

ability to pick up nutrient and gain light. During nutrient limitation the cyanobacteria seek

down to the pycnocline to pick up P nutrients, and in case they are not nutrient limited (P)

they are assumed to stay in the photic zone.

In the present model nutrient limitation, in term of a low PN/PC and or PP/PC ratio,

enhance the sedimentation rate. PN/PC and PP/PC ratios close to maximum N and P

content in the algae result in a reduction of the sedimentation rate. The nutrient regulation

of the sedimentation rate is expressed in the auxiliary

sed3.

Light is also regulating the sedimentation rate. At high light dozes the sedimentation is

accelerated at medium light dozes sedimentation is

mspc3

and at low light dozes the

sedimentation decreases. This light regulation is expressed in the auxiliary

fiz.

-3 -1

Where:

Name

mspc3

sed3

Fiz

��

�� =

��

∗

∗ �� ∗ ��

(3.29)

Comment

Sedimentation rate cyanobacteria

Height of actual water layer

N & P regulation of sedimentation. cyanobacteria

Light factor for PC1 & PC3 sedimentation

Unit

n.u.

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

BUOYC3: Cyanobacteria upward movement, g C m d

The vertical upward movement by the cyanobacteria is described as a function of light

doze and the algae’s nutrient condition expressed in the auxiliary

buoy3.

An upward

vertical movement is enhanced by a good nutrient condition and a low light doze.

-3 -1

Where:

Name

mspc3

�� =

��

∗

��

∗ ��

(3.30)

Comment

Sedimentation rate cyanobacteria

N & P & light upward movement function,

cyanobacteria

Height of actual water layer

Unit

-1

Type*)

Buoy3

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.4

PN1: Flagellate N, g N m

-3

��

Process

UPNH1

UPN31

GRPN1

DEPN1

SEPN1

BUOYN1

Where:

�� +

Comment

��

−

�� −

�� −��

�� −

��

Unit

gNm d

-3

-1

(3.31)

Uptake of NH

into flagellates N

Uptake of NO

into flagellates N

Grazing of flagellates N

Death of flagellates N

Settling of flagellates N

Upward movement flagellate N

-1

UPNH1: Uptake of NH

into flagellate N, g N m d

�� =

��

ℎ ,

�� ∗

��

-3

-1

(3.32)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

UPN31: Uptake of NO

into flagellate N, g N m d

��

�� ∗

�� −

-1

-3

��

-1

(3.33)

GRPN1: Grazing of flagellate N, g N m d

�� =

∗

��

-3

(3.34)

DEPN1: Death of flagellate N, g N m d

�� =

∗

��

-3

-1

(3.35)

SEPN1: Settling of flagellate N, g N m d

��

�� =

∗��

��

-3

-1

(3.36)

BUOYN1: Upward movement of PN1, g N m d

�� =

∗

��

-3

-1

(3.37)

Where:

Name

pnma

unh1

un31

Comment

Max. intracellular algae N

potential NH

uptake by flagellate

potential NO

uptake by flagellate

Flagellate N:C ration

Flagellate C

Grazing of flagellate C

Death of flagellate C

Settling of flagellate C

Upwared movement of flagellate C

Unit

gNgC

-3

-1

Type*)

-1

gNm d

gNgC

gC m

-1

-3

-1

pn1pc1

PC1

GRPC1

DEPC1

SEPC1

BUOYC1

-3

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.3.5

PN2, Diatom N, g N m

-3

��

�� +

Comment

Uptake of NH

into diatoms N

Uptake of NO

into diatoms N

Grazing of diatoms N

Death of diatoms N

Settling of diatoms N

Where:

��

−

�� −

�� −��

��

Unit

gNm d

-3

-1

(3.38)

Process

UPNH2

UPN32

GRPN2

DEPN2

SEPN2

-1

UPNH2: Uptake of NH

into diatom N, g N m d

�� =

��

ℎ ,

�� ∗

��

-3

-1

(3.39)

UPN32: Uptake of NO

into diatom N, g N m d

��

�� ∗

�� −

-3

-1

��

(3.40)

GRPN2: Grazing of dioatom N, g N m d

�� =

∗

��

-3

-1

(3.41)

DEPN2: Death of diatom N, g N m d

�� =

∗

��

-3

-1

(3.42)

SEPN2: Settling ofdiatom N, g N m d

��

�� =

∗��

��

-3

-1

(3.43)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Where:

Name

pnma

unh2

un32

pn2pc2

PC2

GRPC2

DEPC2

SEPC2

Comment

Max. intracellular algae N

potential NH

uptake by diatom

potential NO

uptake by diatom

Diatom N:C ration

Diatom C

Grazing of diatom C

Death of diatom C

Settling of diatom C

Unit

gNgC

-3

-1

Type*)

-1

gNm d

gNgC

gC m

-1

-3

-1

-3

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.6

PN3, Cyanobacteria N, g N m

-3

��

�� +

��

+��

−

�� −

�� −��

�� −

��

(3.44)

Where:

Process

UPNH3

UPN33

NFIX

GRPN3

DEPN3

SEPN3

BUOYN3

Comment

Uptake of NH

into cyanobacteria N

Uptake of NO

into cyanobacteria N

N fixation cyanobacteria

Grazing of cyanobacteria N

Death of cyanobacterias N

Settling of cyanobacterias N

Upward movement cyanobacteria N

Unit

gNm d

-3

-1

UPNH3: Uptake of NH4 into cyanobacteria N, g N m d-

�� =

��

ℎ ,

�� ∗

��

-3

(3.45)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

UPN33: Uptake of NO3 into cyanobacteria N, g N m d-

��

�� ∗

�� −

-3

��

-3

(3.46)

NFIX: N fixation by cyanobacteria N, g N m d-

��

⁡

−

knfix1*

∗

��

−

��

, ��

−

��⁡ �� ⁡ ⁡ ��

∗ �� ∗ ��

-3

(3.47)

GRPN3: Grazing of cyanobacteria N, g N m d-

�� =

��

(3.48)

DEPN3: Death of cyanobacteria N, g N m d-

�� =

∗

��

-3

(3.49)

SEPN3: Settling of cyanobacteria N, g N m d-

��

�� =

∗��

��

-3

(3.50)

BUOYN3: Upward movement of PN3, g N m d-

�� =

∗

��

-3

(3.51)

Where:

Name

Pnma

unh3

un33

Comment

Max. intracellular algae N

potential NH

uptake by cyanobacteria

potential NO

uptake by cyanobacteria

Cyanobacteria N:C ration

Redfield ratio N:C

Max. N fixation, 20 °C, cyanobacteria

Ɵ in Arrhenius temperature function

Temperature

Half saturation constant, N fixation

Function for N fixation (1 if PSU≤12 else 0)

Unit

gNgC

-3

-1

Type*)

-1

gNm d

gNgC

-1

-3

-1

pn3pc3

krednc

knfix1

Tppc

Kqppn

nfix1

-1

gNgC d

n.u.

°C

gNgC

n.u.

-1 -1

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Name

nfix2

PC3

GRPC3

DEPC3

SEPC3

BUOYC3

Comment

Function for N fixation (1 if

0≤PSU≤10 else 0-1)

Cyanobacteria C

Grazing of cyanobacteria C

Death of cyanobacteria C

Settling of cyanobacteria C

Upwared movement of cyanobacteria C

Unit

n.u.

gC m

-3

Type*)

-1

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.7

PP1, Flagellate P, g P m

-3

��

−

Comment

Uptake of PO

into flagellates P

Grazing of flagellates P

Death of flagellates P

Settling of flagellates P

Upward movement flagellate

Where:

−

−��

−

Unit

gPm d

-3

-1

(3.52)

Process

UPPP1

GRPP1

DEPP1

SEPP1

BUOYP1

-1

UPPP1: Uptake of PO4 into flagellate P, g P m d-

��

�� ,

�� ∗

��

-3

(3.53)

GRPP1: Grazing of flagellate P, g P m d-

∗

��

-3

(3.54)

DEPP1: Death of flagellate P, g P m d

∗

��

-3

-1

(3.55)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

SEPP1: Settling of flagellate P, g P m d

��

∗��

��

-3

-1

(3.56)

BUOYP1: Upward movement of PP1, g P m d

∗

��

-3

-1

(3.57)

Where:

Name

pnma

upo1

pp1pc1

PC1

GRPC1

DEPC1

SEPC1

BUOYC1

Comment

Max. intracellular algae P

Potential PO

uptake by flagellate

Flagellate P:C ration

Flagellate C

Grazing of flagellate C

Death of flagellate C

Settling of flagellate C

Upward movement of flagellate C

Unit

gPgC

-3

-1

Type*)

-1

gPm d

gPgC

gC m

-1

-3

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.8

PP2, Diatom P, g P m

-3

��

−

Comment

Uptake of PO

into diatoms P

Grazing of diatoms P

Death of diatoms P

Settling of diatoms P

Where:

−

−��

Unit

gPm d

-3

-1

(3.58)

Process

UPPP2

GRPP2

DEPP2

SEPP2

-1

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

UPPP2: Uptake of PO4 into diatom P, g P g P m d

��

�� ,

�� ∗

��

-3

-1

(3.59)

GRPP2: Grazing of diatom P, g P m d

∗

��

-3

-1

(3.60)

DEPP2: Death of diatom P, g P m d

∗

��

-3

-1

(3.61)

-3

-1

SEPP2: Settling of diatom P, g P m d

��

∗��

��

(3.62)

Where:

Name

pnma

upo2

pp2pc2

PC2

GRPC2

DEPC2

SEPC2

Comment

Max. intracellular algae P

Potential PO

uptake by diatom

Diatom P:C ration

Diatom C

Grazing of diatom C

Death of diatom C

Settling of diatom C

Unit

gPgC

-3

-1

Type*)

-1

gPm d

gPgC

gC m

-1

-3

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

3.3.9

PP3, Cyanobacteria P, g P m

-3

��

Comment

Uptake of PO

into cyanobacteria P

Cyanobacteria uptake of LDOP

Grazing of cyanobacteria P

Death of cyanobacteria P

Settling of cyanobacteria P

Upward movement cyanobacteria

Where:

−

−��

−

Unit

gPm d

-3

-1

(3.63)

Process

UPPP3

UPLDOPP3

GRPP3

DEPP3

SEPP3

BUOYP3

-1

UPPP3: Uptake of PO

into cyanobacteria P, g P m d

��

�� ,

�� ∗

��

-3

-1

(3.64)

UPLDOPP3: Cyanobacteria uptake of LDOP, g P m d

⁡ (

�� −

��

�� ⁡

)⁡<

⁡

��, , ��

< .

�� ∗

⁡ ��

-3

-1

∗ . ∗

+ℎ

∗

∗ .

∗ ��

(3.65)

GRPP3: Grazing of cyanobacteria P, g P m d

∗

��

-3

-1

(3.66)

DEPP3: Death of cyanobacteria P, g P m d

∗

��

-3

-1

(3.67)

SEPP3: Settling of cyanobacteria P, g P m d

��

∗��

��

-3

-1

(3.68)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

BUOYP3: Upward movement of PP3, g P m d

∗

��

-3

-1

(3.69)

Where:

Name

ppma

upo3

epsi

maxupip

LDOP

pda3

pdb3

pp3pc3

PC3

PP3

GRPC3

DEPC3

SEPC3

BUOYC3

Comment

Max. intracellular algae P

Potential PO

uptake by cyanobacteria

Small value

Max. PO

uptake by flagellates during P

Labile DOP

Ratio, nutrient uptake cyanobacteria:flagellates

Halfsaturation conc. Cyanobacteria:flagellates

Cyanobacteria P:C ratio

Cyanobacteria C

Cyanobacteria P

Grazing of cyanobacteria C

Death of cyanobacteria C

Settling of cyanobacteria C

Upwared movement of cyanobacteria C

Unit

gPgC

-3

-1

Type*)

-1

gPm d

n.u.

gPgC

gP m

n.u.

gPgC

gC m

-1

-3

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.10 PSi2, Diatom Si, g Si m

-3

��

�� −

�� − ��

��

(3.70)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Where:

Process

UPSi2

GRPSi2

DEPSi2

SEPSi2

Comment

Uptake of Si into diatoms Si

Grazing of diatoms Si

Death of diatoms Si

Settling of diatoms Si

Unit

g Si m d

-3

-1

UPSi2: Uptake of Si into diatom Si, g Si m d

�� =

��

��,

�� ∗

��

-3

-1

(3.71)

GRPSi2: Grazing of diatomSiP, g Si m d

�� =

∗

-3

-1

(3.72)

DEPSi2: Death of diatom Si, g Si m d

�� =

��

∗

��

-3

-1

(3.73)

SEPSi2: Settling of diatom Si, g Si m d

��

�� =

��

∗��

��

-3

-1

(3.74)

Where:

Name

psma

usi2

psi2pc2

PC2

GRPC2

DEPC2

SEPC2

Comment

Max. intracellular algae Si

potential Si uptake by diatom

Diatom Si:C ration

Diatom C

Grazing of diatom C

Death of diatom C

Settling of diatom C

Unit

g Si g C

-3

-1

Type*)

-1

g Si m d

Si P g C

gC m

-3

-1

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

3.3.11 CH, Chlorophyll, g m

-3

��

�� −

Comment

Net production phytoplankton chlorophyll

Settling of phytoplankton chlorophyll

Death of phytoplankton chlorophyll

Upward movement of CH

Zooplankton grazing on CH

Where:

�� − �� −

�� −

��

Unit

(3.75)

Process

PRCH

SECH

DECH

BUOYCH

GRCH

g Chl m d

-3

-1

PRCH: Net production phytoplankton chlorophyll, g Chl m d

The production of chlorophyll

�� =

�� ∗

ℎ

∗

-3

-1

ℎ��

∗

��

�� ∗

ℎ��

∗

��

ℎ

∗

⁡

-3

�� ∗

-1

ℎ��

∗

��

ℎ

∗

(3.76)

SECH: Settling of phytoplankton chlorophyll, g Chl m d

�� =

��

∗ ��

�� + �� + ��

��

∗

�� + �� + ��

�� +��

�� +

-3

�� +��

�� +

��

(3.77)

DECH: Death of phytoplankton chlorophyll, g Chl m d

�� =

��

-3

-1

(3.78)

GRCH: ZC Grazing on CH, g Chl m d

�� =

��

∗

�� + �� + ��

�� +

-1

�� +

��

(3.79)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Where:

Name

PC1

PC2

PC3

chmi

chma

myn1

myn2

ik1

Ik2

PRPC1

SEPC1

DEPC1

GRPC1

PRPC2

SEPC2

DEPC2

GRPC2

PRPC3

SEPC3

DEPC3

GRPC3

Comment

Flagellate C

Diatom C

Cyanobacteria C

Min. chlorophyll-a production

Max. chlorophyll-a producti

Nitrogen function Flagellate

Nitrogen function Diatom

Nitrogen function Cyanobacteria

Light saturation temp. corrected, PC1, PC3

Light saturation temp. corrected, PC2

Net production of flagellate C

Sedimentation of flagellate C

Death of flagellate C

Grazing of flagellate C

Net production of diatom C

Sedimentation of diatom C

Death of diatom C

Grazing of diatom C

Net production of cyanobacteria C

Sedimentation of cyanobacteria C

Death of cyanobacteria C

Grazing of cyanobacteria C

Unit

gC m

-3

Type*)

-1

-2 -1

-3

mol photon m d

n.u.

mol photon m d

gCm d

-3

-1

-2 -1

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

3.3.12 ZC, zooplankton, g C m

-3

��

��−

Comment

Net production of zooplankton carbon

Death of zooplankton carbon

Where:

��

Unit

gCm d

-3

-1

(3.80)

Process

PRZC

DEZC

-1

PRZC: Production of zooplankton carbon, g C m d

��=

�� ∗

�� +

��

-3

-1

(3.81)

DEZC: Death of zooplankton carbon, g C m d

��=

��∗��

�� ∗��

-3

-1

(3.82)

Where:

Name

vefo

kdz

kdzb

GRPC1

GRPC2

GRPC3

Comment

Zooplankton growth efficiency

Zooplankton death rate 2nd order,

Zooplankton death rate 1st order

Grazing of flagellate C

Grazing of diatom C

Grazing of cyanobacteria C

Unit

gCgC

-1

Type*)

-1

m (g C*d)

-1

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

3.3.13 DC, Detritus C, g C m

-3

��

��+

��

��−

��

−��

��−��

��

(3.83)

Where:

Process

EKZC

DEZC

DEPC2DC

REDC

deDCw

SREDC

SEDC

Comment

Excretion by zooplankton carbon

Death of zooplankton carbon

Death phytoplankton to detritus carbon

DO mineralisation of detritus carbon

DC anaerobic respiration with NO

DC anaerobic oxidation with SO

Settling of detritus carbon

Unit

gCm d

-3

-1

EKZC: Excretion by zooplankton carbon, g C m d

��=

−

�� −

�� ∗

�� +

-3

-1

��

(3.84)

DEZC: Death of zooplankton carbon, g C m d

-1

DEZC: see processes for zooplankton C, ZC, Equation (3.82)

DEPC2DC: Death phytoplankton to detritus carbon, g C m

��

��=

− ��−

−

∗

�� +

-3

-1

-3

-1

�� +

-3

��

(3.85)

REDC: DO mineralisation of detritus carbon, g C m d

�� = �� ∗ ��∗

��

∗

−

-1

∗

��

∗ .

+��

∗

��+

��

(3.86)

deDCw: DC respiration with NO

, g C m d

+ ��

(3.87)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

SREDC: DC oxidation with SO

, g C m d

=��

∗

��∗

��

-3

-1

(3.88)

SEDC: Settling of detritus carbon, g C m d

��

��=

∗

��

-3

-1

(3.89)

Where:

Name

vefo

refo

GRPC1

GRPC2

GRPC3

DEPC1

DEPC2

DEPC3

kmdm

tere

ndo2

Comment

Zooplankton growth effency

Zooplankton, respiration

Grazing of flagellate C

Grazing of diatom C

Grazing of cyanobacteria C

Death of flagellate C

Death of diatom C

Death of cyanobacteria C

Fraction of PC mineralised at PC death

Fraction of PC to CDOC-N&P at PC death

Fraction of PC to LDOC-N&P at PC death

DC mineralisation rate at 20 ° C

Ɵ in Arrhenius function, DC

mineralisation

Temperature

Oxygen

DC & LDOC:Coefficient, DO mineralisation

DO half-saturation constant, DC & LDOC

mineralisation

Denitrificaion in water using DC+LDOC

C:N ratio denitrification

Anammox, NO

+NH



Unit

gCgC

-3

-1

Type*)

-1

gCm d

n.u.

-1

-3

-1

n.u.

°C

g O

n.u.

-3

mdo2

DENW

vn3

ANAMOX

n.u

gNm d

gCgN

-3

-1

-3

-1

gNm d

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Name

LDOC

SRED

vso

ksd

Comment

Labile DOC

Respiration of DC+LDOC

C:S ratio C mineralisation SO

to H

Sedimentation rate detritus

Height of actual water layer in model

Unit

gCm

-3

Type*)

-1

gSm d

gCgS

-1

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.14 DN, Detritus N, g N m

-3

��

��+

��

��−

��−��

��−

��

−��

��

(3.90)

Where:

Process

EKZN

DEZN

DEPN2DN

REDN

deDNw

SREDN

SEDN

Comment

Excretion by zooplankton N

Death of zooplankton N

Death phytoplankton to detritus N

DO mineralisation of detritus N to NH

Anaerobic respiration of DN with NO

to NH

Anaerobic oxidation of DN with SO

to NH

Settling of detritus N

Unit

gNm d

-3

-1

EKZN: Excretion by zooplankton N, g N m d

��=

−

�� −

��

�� ∗

�� +

-3

-1

�� +

-3

-1

��

(3.91)

DEZN

��= �� ∗

Death of zooplankton N, g N m d

(3.92)

DEPN2DN: Death phytoplankton to detritus N, g N m d

-3

-1

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

��

��=

− ��−

∗

−

��

∗

�� +

-3

-1

�� +

��

(3.93)

REDN: DO mineralisation of detritus N, g N m d

��= ��

(3.94)

deDNw: DN respiration with NO3, g N m d

��

�� ∗

��∗

-3

-1

(3.95)

SREDN: DN oxidation with SO4, g N m d

��

=��

-3

-1

(3.96)

-3

-1

SEDN: Settling of detritus N, g N m d

��

=��

��∗

(3.97)

Where:

Name

vefo

refo

GRPN1

GRPN2

GRPN3

DEPN1

DEPN2

DEPN3

vzn

kmdn

dndc

REDC

Comment

Zooplankton growth effency

Zooplankton, respiration

Grazing of flagellate N

Grazing of diatom N

Grazing of cyanobacteria N

Death of flagellate N

Death of diatom N

Death of cyanobacteria N

N:C ratio Zooplankton

Fraction of PC mineralised at PC death

Fraction of PC to CDOC-N&P at PC death

Fraction of PC to LDOC-N&P at PC death

Factor N mineralisation of DN

N:C ration, detritus

DO mineralisation of detritus carbon

Unit

gCgC

-3

-1

Type*)

-1

gNm d

gNgC

n.u.

gNgC

-3

-1

-3

-1

gCm d

-1

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Name

deDCw

SREDC

SEDC

Comment

Anaerobic DC respiration with NO

Anaerobic DC oxidation with SO

Settling of detritus carbon

Unit

gCm d

-3

-1

Type*)

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.15 DP, Detritus P, g P m

-3

��

−

−��

−

−��

(3.98)

Where:

Process

EKZP

DEZP

DEPP2DNP

REDP

deDPw

SREDP

SEDP

Comment

Excretion by zooplankton P

Death of zooplankton P

Death phytoplankton to detritus P

DO mineralisation of detritus P to PO

Anaerobic respiration of DP with NO

to PO

Anaerobic oxidation of DP with SO

to PO

Settling of detritus P

Unit

gPm d

-3

-1

EKZP: Excretion by zooplankton P, g P m d

−

�� −

��

�� ∗

-3

-1

(3.99)

DEZP: Death of zooplankton P, g P m d

= �� ∗

-3

-1

(3.100)

DEPP2DP: Death phytoplankton to detritus P, g P m d

− ��−

−

∗

-3

-1

(3.101)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

REDP: DO mineralisation of detritus P, g P m d

= ��

∗

��

-3

-1

(3.102)

-3

-1

deDPw: DP respiration with NO

, g P m d

��

∗

(3.103)

SREDP: DP oxidation with SO

, g P m d

��

=��

��∗

-3

-1

(3.104)

SEDP: Settling of detritus P, g P m d

=��

��∗

-3

-1

(3.105)

Where:

Name

vefo

refo

GRPP1

GRPP2

GRPP3

DEPP1

DEPP2

DEPP3

vzp

kmdp

dpdc

REDC

deDCw

Comment

Zooplankton growth effency

Zooplankton, respiration

Grazing of flagellate P

Grazing of diatom P

Grazing of cyanobacteria P

Death of flagellate P

Death of diatom P

Death of cyanobacteria P

P:C ratio Zooplankton

Fraction of PC mineralised at PC death

Fraction of PC to CDOC-N&P at PC death

Fraction of PC to LDOC-N&P at PC death

Factor P mineralisation of DP

P:C ration, detritus

DO mineralisation of detritus carbon

Anaerobic DC respiration with NO

Unit

gCgC

-3

-1

Type*)

-1

gPm d

gPgC

n.u.

gPgC

-3

-1

-3

-1

gCm d

-3

-1

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Name

SREDC

SEDC

Comment

Anaerobic DC oxidation with SO

Settling of detritus carbon

Unit

gCm d

-3

-1

Type*)

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.16 DSi, Detritus Si, g Si m

-3

��

�� +

�� −

�� − ��

��

(3.106)

Where:

Process

DEPSi2

GRPSi2

REDSi

SEDSi

Comment

Death phytoplankton Si to detritus Si

Grazing of Diatom Si

DO mineralisation of detritus Si to Si

Settling of detritus Si

Unit

g Si m d

-3

-1

DEPSi2: Death phytoplankton Si to detritus Si, g Si m d

�� =

�� ∗

��

-3

-1

(3.107)

GRPSi2: Grazing of Diatom Si, g Si m d

�� =

�� ∗

��∗

��

-3

-1

(3.108)

REDSi: DO mineralisation of detritus Si to Si, g Si m d

�� =

��

∗ ��

-3

-1

(3.109)

SEDSi: Settling of detritus Si, g Si m d

��

�� = ��

��∗

��

-3

-1

(3.110)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Where:

Name

DEPC2

psi2pc2

GRPC2

REDC

dsidc

kmds

SEDC

Comment

Death of diatom C

Si:C ration, Diatom

Grazing of diatom C

DO mineralisation of detritus carbon

Si:C ration, detritus

Factor Si mineralisation of DSi

Settling of detritus carbon

Unit

gCm d

g Si g C

-3

-1

Type*)

-3

-1

gCm d

g Si g C

n.u.

gCm d

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.17 NH4, Total ammonia, g N m

-3

��

Where:

Process

REDN

REZN

deDNw

SREDN

reLDON

deLDON

sreLDON

feunh4m3

fsnb

NH4dep

DEPN2NH

��+

− ��

��+

��+��

− ��

��

+��

ℎ �� +��

+ ��

��

−

�� −

��

��+

��

(3.111)

Comment

DNNH

via DO oxidation of DC

Respiration of zooplankton nitrogen

DNNH

denitrification mineralisation of DC

NH

via SO

mineralisation of DC

LDONNH

via DO oxidation of LDOC

LDON

NH

via denitrification mineralisation of LDOC

LDON

NH

via SO

mineralisation of LDOC

flux between sediment pore water and water

Mineralisation of newly settled organic N

Atmospheric NH

deposition

Fraction of DEPN1-3 to NH

Unit

gNm d

-3

-1

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Process

RNIT

ANAMOX

UPNH1

UPNH2

UPNH3

Comment

Nitrification in water column

Anammox, NO

+NH



uptake by flagellate

uptake by diatom

uptake by cyanobacteria

Unit

gNm d

-3

-1

g NH

-N m d

gNm d

-3

-1

-3

-1

REDN: NH4 production via mineralisation of DC, DN & DP with DO, g N m d

Please see under DN, Equation (3.94)

REZN: Respiration of zooplankton nitrogen, g N m d

�� = GRPN + GRPN + GRPN

��=

∗ �� −

��

-3

-1

-3

-1

(3.112)

Where:

EKZN: Excretion of N by zooplankton

− vefo − refo ∗ GRPN + GRPN + GRPN

(3.113)

deDNw: NH4 production via denitrificatiation (NO3 mineralisation) of DC, DN & DP,

-3 -1

gNm d

Pease see under DN, Equation (3.95)

SREDN: NH4 production via anaerobic SO4 mineralisation of DC, DN & DP, g N m

-1

Please see under DN, Equation (3.96)

-3

reLDON: NH4 production via mineralisation of LDOC, LDON & LDOP with DO, g N

-3 -1

m d

Please see under LDON (Section 3.3.27).

deLDON: NH4 production via denitrificatiation, (mineralisation) of LDOC, LDON &

-3 -1

LDOP, g N m d

Please see under LDON (Section 3.3.27).

sreLDON: NH4 production via anaerobic SO4 mineralisation of LDOC, LDON &

-3 -1

LDOP, g N m d

Please see under LDON (Section 3.3.27).

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

feunh4m3: NH4 flux between sediment pore water and water, g N m d

��

ℎ �� =��

ℎ / ��

-3

-1

(3.114)

fsnb: Mineralisation of newly settled organic N, g N m d

∗ ��

−

�� −

�� ∗

�� +��

��/ �� ∗

�� +��

−

�� −

-3

-1

�� +��

-3

��

-1

(3.115)

NH4dep: Atmospheric N deposition as NH4 to surface layer, g N m d

��

�� = ��

/ ��

−

(3.116)

RNIT: Nitrification in water column, g N m d

= knitw ∗

⁡

��

∗ sqdo ∗

ANAMOX: Anammox, NO3+NH4



N2, , g NH4-N m d

��

��∗

−

��

∗ NH

�� + ℎ��

-3

-1

(3.117)

�� ⁡

∗

< .

��

�� + ℎ

⁡ �� ⁡

-3

-1

∗

��

�� +ℎ

∗

��+

��

��+ℎ

⁡

(3.118)

UPNH1-3: NH4 uptake by phytoplankton, g N m d

-3

-1

UPNH1, UPNH2 & UPNH3 see under PN1 (Section 3.3.4), PN2 (Section 3.3.5) and PN3

(Section 3.3.6)

Where:

Name

vzn

GRPN1

GRPN2

GRPN3

EKZN

vefo

Comment

N to C ratio in zooplankton,

Grazing of flagellate N

Grazing of diatom N

Grazing of cyanobacteria N

Excretion of N by zooplankton

Zooplankton growth effency

Unit

gNgC

-3

-1

Type*)

-1

gNm d

gCgC

-1

-3

-1

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Name

refo

feunh4

SEPN1

SEPN2

SEPN3

BUOYN1

BUOYN3

depoC

knim

tetn

NHdep

knitw

tnit

hmt

sqdo

kanam

NO3

Comment

Zooplankton, respiration

Flux of NH

from sediment to water

Settling of flagellate N

Settling of diatom N

Settling of cyanobacteria N

Upward movement of flagellate N

Upward movement of cyanobacteria N

Deposition of organic C to sediment

Sediment: N:C ratio of immobile N

Ɵ value in Arrhenius equation for N

Temperature Deg. Celsius

Atmospheric N deposition

Specific nitrification water at 20 C

Ɵ value in Arrhenius equation for nitrification

Halfsaturation NH

nitrification

DO function

max anammox NO

-N or NH

-N concumption

–N

half satutation conc., anammox &

thiodenitrification

half saturation concentration, anammox

Detrituc C

Labile DOC

DC+LDC Half saturation concentration, anammox

Unit

gCgC

-2

-1

Type*)

-1

gNm d

gCm d

gNgC

n.u.

°C

gNm d

-1

-2

-1

-2

-3

-1

n.u.

gNm d

n.u.

gNm d

gNm

-3

-1

-3

-1

hun4

hun3

LDOC

hudc1

gNm

gCm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

3.3.18 NO3, Nitrate, g N m

-3

��

Where:

Process

RNIT

feuno3m3

NO3dep

DENW

ANAMOX

UPN31

UPN32

= ��

+��

−

��

�� +��

−

��

−

��

−

��

− ��

(3.119)

Comment

Nitrification in water column

Flux of NO

between water & sediment

Atmospheric deposition of NO

at the water surface

Denirification water

Thiodenitification, 4NO

+3H



+3SO

Anammox, NO

+NH



uptake by flagellate

uptake by diatom

uptake by cyanobacteria

Unit

gNm d

-3

-1

g NO

-N m d

gNm d

-3

-1

-3

-1

RNIT: Nitrification in water column, g N m d

Please see under NH4, Equation (3.117)

-3

-1

feuno3m3: Flux of NO3 between water & sediment, g N m d

��

�� =��

=��

�� / ��

��/ ��

-3

-1

(3.120)

NO3dep: Atmospheric deposition of NO3 at the water surface, g N m d

��

-3

-1

(3.121)

DENW: Denirification water, g N m d

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡

= IF⁡

< mdo ⁡THEN⁡

∗

−

-3

-1

ELSE⁡

+ .

∗

+ . ��

��+

��

∗

��+

�� +ℎ

∗

��

+ℎ

(3.122)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

DENWS: Thiodenitification, 4NO3+3H2S2N2+3SO4, g N m d

��

∗

⁡

< .

∗

��

�� +ℎ

⁡ �� ⁡

∗

��

�� +ℎ

∗

ℎ

-3

-1

ANAMOX: Anammox, NO3+NH4



N2 , g NO3-N m d

��

��∗

−

�� ⁡

−

��+

��+ℎ

-1

⁡

(3.123)

⁡

�� ⁡

∗

< .

��

�� + ℎ

⁡ �� ⁡

-3

∗

��

�� +ℎ

∗

��+

��

��+ℎ

⁡

(3.124)

UPN31, UPN32, UPN33: NO3 uptake flagellates, diatoms and cyanobacteria,

-3 -1

gNm d

Please see under PN1 (Section 3.3.4), PN2 (Section 3.3.5) and PN3 (Section 3.3.6)

Where:

Name

feuno3

NO3depo

Comment

Nitrate flux between sediment and water column

Atmospheric NO

-N deposition to water surface

DO limit for denitrification in water column & half

saturation concentration in sqdo

Max. denitrification at 20 °C in water column

Half saturation DO conc. for denitrification

Ɵ in Arrhenius function, denitrifications temperature

dependency

half saturation concentration for denitrification

DC+LDOC Half saturation concentration for SO

reduction & denitrification

Detritus C

Labile fraction of DOC

Ɵ value

in Arrhenius equation for N

Unit

gNm d

-3

-2

-1

Type*)

-1

mdo3

Kdenw

ksb

g O

-1

gNm d

g O

-3

tetn

hun3

n.u

gNm

-3

hudc

LDOC

tetn

gCm

n.u.

-3

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Name

H2S

hs1

NH4

Comment

Temperature

S-S

H2S half saturation thiodenitirfication

-N

half satutation conc., anammox &

thiodenitrification

DC+LDC Half saturation concentration, anammox

Unit

°C

gSm

-3

Type*)

-3

gNm

-3

hun4

hudc1

gNm

gCm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.19 H2S, Hydrogen Sulphide, g S m

-3

��

=��

��

+��

ℎ

�� −��

−��

��

(3.125)

Where:

Process

SRED

fwsh2sm3

SOXI

Comment

Anaerobic SO

Respiration of DC+LDOC

S flux from sediment to water

Oxidation of H

production by thiodenitrification, 4NO

+3H

S2N

+3SO

Unit

gSm d

-3

-1

SRED: SO

Respiration of DC+LDOC, g S m d

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡

��

ℎ

��

⁡

∗��

< . ⁡ �� ⁡

∗

ℎ

∗

-3

-1

fwsh2sm3: H

S flux from sediment to water, g S m d

�� =�� ℎ

/ ��

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡

�� ⁡

−

��

+ℎ

��+

-3

��

��+ℎ

-1

(3.126)

(3.127)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

SOXI: Oxidation of H

S, g S m d

��

∗

��

−

SOXI

: SO

production by thiodenitrification, 4NO

+3H

S-->2N

+3SO

, g S m d

��

Where:

Name

Ksc

��

∗ .

∗�� ∗

-3

-1

��

(3.128)

-3

-1

(3.129)

Comment

Max. anoxic DC +LDOC respiration rate with SO

Salinity function for reduction of SO4 to H2S

half saturation concentration for denitrification

DC+LDOC Half saturation concentration for SO

reduction & denitrification

Detritus C

Labile fraction of DOC

Ɵ value in Arrhenius function for SO

reductions

temperature dependency.

Flux of reduced H

S equialents from sediment to

water

Max. specific oxidation rate of H2S, 20 deg. °C

Ɵ value in Arrhenius function for SO

oxidations

temperature dependency.

DO function

Thiodenitification. 4NO

+3H

S2N

+3SO

Unit

gSm d

n.u.

gNm

-3

-1

Type*)

Fsa

hun3

Hudc

LDOC

gCm

-3

ts4r

n.u.

-2 -1

fwh2s

Kse

gSm d

-1

Ksf

Sqdo

DENW

n.u.

gNm d

-3 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

3.3.20 IP, Phosphate (PO4-P), g P m

-3

��

Where:

Process

REDP

REZP

reLDOP

deLDOP

sreLDOP

deDPw

SREDP

DEPP2IP

fspb

fsipm3

Pdep

UPPP1

UPPP2

UPPP3

−

+��

+�� +

−

+��

(3.130)

Comment

DPPO

via DO oxidation of DC

Respiration of zooplankton P

LDOPPO

via DO oxidation of LDOC

LDOP

PO

via denitrification mineralisation of LDOC

LDOP

PO

via SO

mineralisation of LDOC

DPPO

denitrification mineralisation of DC

PO

via SO

mineralisation of DC

Dead Plankton P to PO

Mineralisation of newly settled organic P

flux between sediment pore water and water

Atmospheric P deposition

uptake by flagellates

uptake by Diatoms

uptake by cyanobacteria

Unit

gPm d

-3

-1

REDP: PO

production via mineralisation of DC, DN & DP with DO, g P m d

Please see under state variable DP, Section 3.3.15

REZP: Respiration of zooplankton phosphorus, g P m d

= MAX , GRPP + GRPP + GRPP − PRZC ∗ �� −

-3

-1

-3

-1

(3.131)

reLDOP: PO4 production via mineralisation of LDOC, LDON & LDOP with DO,

-3 -1

gPm d

��

∗

��

(3.132)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

deLDOP: PO4 production via denitrificatiation ( mineralisation) of LDOC, LDON &

-3 -1

LDOP, g P m d

��

∗

��

(3.133)

sreLDOP: PO4 production via anaerobic SO4 mineralisation of LDOC, LDON &

-3 -1

LDOP, g P m d

��

∗s

��

(3.134)

deDPw: PO4 production via anaerobic denitrificatiation (mineralisation) of DC, DN

-3 -1

& DP, g P m d

Please see under DP, Section 3.3.15

SREDP: PO4 production via anaerobic SO4 mineralisation of DC, DN & DP,

-3 -1

gPm d

Please see under DP, Section 3.3.15

DEPP2IP: Dead Plankton P to PO4 , g P m d

DEPP IP = DEPP + DEPP + DEPP

��

∗ ��

∗

−

∗ vm

-3

-1

(3.135)

fspb: Mineralisation of newly settled organic P, g P m d

−

+��

−

-3

-1

+��

-3

-1

(3.136)

fsipm3: PO4 flux between sediment pore water and water, g P m d

�� =�� / ��

��/ ��

(3.137)

-3

-1

Pdep: Atmospheric P deposition as PO4 to surface layer, g P m d

(3.138)

UPPP1-3: PO4 uptake by flagellates, diatoms and cyanobacteria, g P m d

-3

-1

Please see under PP1 (Section 3.3.7), PP2 (Section 3.3.8), and PP3 (Section 3.3.9)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Where:

Name

GRPP1

GRPP2

GRPP3

PRZC

vzp

EKZP

reLDOC

LDOP

LDOC

deLDOC

sreLDOC

DEPP1

DEPP2

DEPP3

krsp0

SEPP1

SEPP2

SEPP3

BUOYP1

BUOYP3

SEDP

tetp

fsip

Pdep

Comment

Grazing of phytoplankton (Flagellate) P

Grazing of phytoplankton (diatom) P

Grazing of cyanobacteria P

Net production of zooplankton C

P:C ratio in zooplankton

Excretion by zooplankton P

DO respiration LDOC

Labile DOP

Labile DOC

Anaerobic mineralisation of LDOC via denitrification

Anaerobic mineralisation of LDOC via SO

reduction

Death of flagellate P

Death of diatom P

Death of cyanobacteria P

Fraction of PC mineralised at PC death

Fraction of newly settled P to mineralisation

Sedimentation of flagellates P

Sedimentation of diatom P

Sedimentation of cyanobacteria P

Upward movement of flagellates P

Upward movement of cyanobacteria P

Sedimentation detritus P

Ɵ value in Arrhenius equation for P

Temperature Deg. Celsius

flux between pore water and water

Atmospheric P deposition

Height of actual water layer in model

Unit

gPm d

-3

-1

Type*)

-1

gCm d

gPgC

-3

-1

gPm d

-3

gCm d

gPm

-3

gCm

gCm d

gPm d

n.u.

gPm d

n.u.

°C

gPm d

-2

-3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

3.3.21 IP, Phosphate (PO4-P), g P m

-3

��

�� + �� −

��

(3.139)

Where:

Process

REDSi

RSSi2Si

UPSi2

Comment

DO mineralisation of detritus DSi to Si

Si release fom sediment

Uptake of Si into diatom Si

Unit

g Si m d

-3 -1

DEPSi2: Death phytoplankton Si to detritus Si, g Si m d

Please see under DSi, Section 3.3.16

RSSi2Si: Si release fom sediment, g Si m d

�� = ��/ ��

-3

-1

-3

-1

(3.140)

UPSi2: Uptake of Si into diatom Si, g Si Si m d

Please see under Psi2, Section 3.3.10

Where:

Name

RSSi

-3

-1

Comment

Si release form sediment

Height of actual water layer in model

Unit

g Si m d

-2

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

3.3.22 DO, Oxygen, g O2 m

-3

��

��+

�� +

−

��

−

��

��−

��−��

− ��

−

��

(3.141)

Where:

Process

ODPC

REAR

REAR1

ODDC

ODZC

SOXI2DO

RNIT2DO

reLDOC2DO

DEPC2DO

ODSC

Comment

Net O

production by phytoplankton

Reaeration

Reaeration shallow water

DO consumption by mineralisation of DC

Zooplankton respiration

DO consumption due to H

S oxidation

DO consumption due to nitrification

DO consumption by mineralisation of LDOC

DO consumption by mineralisation during PC death

Sediment DO consumption

Unit

g O

m d

g O

m d

g O

m d

g O

m d

g O

m d

g O

m d

g O

m d

g O

m d

g O

m d

g O

m d

-3

-1

ODPC: Net O

production/consumption by phytoplankton, g O

m d

��=

�� +

��

∗ ��

-3 -1

(3.142)

REAR: Reaeration, surface layer only, g O

m d

�� =

IF depth<5 THEN 0 ELSE

√ℎ

��ℎ

��

-3 -1

( 3.93*

+ .

∗

*(csair-DO)/dz

(3.143)

REAR1: Reaeration, shallow water all layers, g O

m d

��

IF depth<5 THEN

��

√ℎ

. ,

��

��ℎ

-3 -1

( 3.93*

ELSE 0

+ .

∗

*(csair-DO)*dz/depth

(3.144)

ODDC: DO consumption by mineralisation of DC, g O

m d

��=

��∗ ��

-3 -1

(3.145)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

ODZC: Zooplankton respiration, g O

m d

��=

��∗ ��

�� +

-3 -1

(3.146)

Where:

��=

�� +

ℎ

��

∗

��

-3 -1

(3.147)

SOXI2DO: DO consumption due to H

S oxidation, g O

m d

��

=��

∗

(3.148)

RNIT2DO: DO consumption due to nitrification, g O

m d

��

= ��

��=

∗

ℎ

-3 -1

(3.149)

reLDOC2DO: DO consumption by mineralisation of LDOC, g O

m d

��

��∗ ��

-3 -1

(3.150)

DEPC2DO: DO consumption by mineralisation during PC death, g O

m d

��

�� +

��

∗ ��∗ ��

-3 -1

(3.151)

ODSC: Sediment DO consumption, g O

m d

From the sediment-water intreface oxygen (DO) can penetrat into the sediment pore

water by diffusion or actively being transportet into the sediment by ventilation pumping

and sediment mixing by the benthic fauna. Further microbenthic algae through

photosynthetis can produce DO in the sediment-waterinterface. DO is consumed in the

sediment by bacterial respiration and chemical oxidation of reduced substances (Fe ,

S) resulting in the O

concentration becomes 0 (normally 0-2 cm) below the sediment

surface. In the model this depth is defined as KDO2. Assuming the DO produced by the

microbenthic algae is delivered to the water, the below differential equation can be set up

assuming a steady state condition:

= − �� ∗

��

(3.152)

Where 0<y<(KDO2), which by integration becomes:

��⁡

��

∗

��

(3.153)

Where a is a constant, which by using the border condition (��O

��y

=0 at y=KDO2)) can be

defined as:

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

��⁡

Which by yet an integration gives:

∗ ��

∗

��

∗

−

��

=−

��

∗

−

��

Where b is a constant, which by using the border condition (O

=0 at y=KDO2) can be

defined as:

∗ ��

��

∗

��

∗

(3.154)

∗

(3.155)

∗ ��

∗

−

⁡

��

∗

��

∗

⁡

(3.156)

At the sediment surface y=0 the O

= DO =>

= √ ∗ �� ∗

∗ ��

��

∗

−

��

∗ √ ∗ �� ∗

��

∗

+∗ ∗

(3.157)

The flux of DO from the water into the sediment can be described using Fick’s 1. Law at

depth y=0

�� = − �� ∗

(3.158)

is found by differentiation of the above expression for O

in the sediment and

determaine the flux of DO into the sediment at Y=0.

�� = − �� ∗ −

��

�� =√ ∗

∗ �� ∗

∗ √ ∗ �� ∗

��

(3.159)

The DO consumption in the model is the sum of bacterial respiration (reKDO2),

nitrification (rsnit) and a flux of reduced substances from the under laying sediment

(fsh2s) to the layer with O

. All the mentioned DO consuming processes has the unit (g m

2 -1

d ) and therefore has to be divided with the DO penetration (KDO2). A conversion factor

for O

:N of 4.57 g O

:g NH

-N is used and a conversion factor for O

:S of 2 g O

: H

S-S

is used.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

The diffusion or rather transport of oxygen into the sediment is dependent of the activity of

the benthic infauna. Their activity is linked to the DO concentration, at low DO (below 2 g

-3

m ) the activity will decrease caused by increased mortality. The constant

difO2

therefore multiplied by an oxygen function (1+sqdo).

The final equation for (ODSC, g O

m d ) in the template therefore becomes:

√ ∗ ��

�� =

IF KDO2>0.001 THEN

∗

�� ∗

∗

�� ℎ

∗

�� ∗ .

⁡∗⁡

��

-3 -1

(3.160)

ELSE 0

Where:

Name

PRPC1

PRPC2

PRPC3

hcur

wsp

CSAIR

depth

REDC

REZC

GRPC1

GRPC2

GRPC3

refo

SOXI

vsh

RNIT

Comment

Production flagellate carbon

Production diatom carbon

Production cyanobacteria carbon

:C ratio for Production & respiration

Horizontal current

Wind speed, 10 m above sea

saturation in water, relative to PSU & temp.

Oxygen in water

Depth of water column

Height of actual water layer

Respiration detritus

Respiration zooplankton

Grazing of

phytoplankton (Flagellate)

carbon

Grazing of

phytoplankton (diatom)

carbon

Grazing of cyanobacteria carbon

Zooplankton, respiration

S oxidation to SO

:S ratio for oxidation of H

S to SO

Nitrification

Unit

gCm d

g O

g C

-1

-3

-1

Type*)

-3

-1

g O

-3

gCm d

gCgC

-2

-1

-3

-1

gSm d

g O

g S

-3

-1

gNm d

-1

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Name

vnh

reLDOC

DEPC1

DEPC2

DEPC3

difO2

DOconsum

sqdo

fsh2s

rsnit

reKDO2

KDO2

Comment

:N ratio nitrification

Respiration LDOC

Death of flagellate C

Death of diatom C

Death of cyanobacteria C

Fraction of DEPC1-3 respired at once

Diffusion of O2 in sediment

Sediment O

consumption, layer (0-KDO2)

Depth below sediment surface

DO dependend auxiliary

S flux from under laying anoxic sediment layer

Nitrification in sediment in oxic sediment layer

Respiration in oxic sediment layer

Oxic layer in sediment

Unit

g O

g N

-3

-1

Type*)

-1

gCm d

n.u.

m s

-3

-1

-3 -1

g O

m d

n.u.

gSm d

-2

-1

gNm d

-2

-1

gOm d

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.23 CDOC, Coloured refractory DOC, g C m

-3

��

�� − ℎ��

��

(3.161)

Where:

Process

depc2CDOC

phoxCDOC

Comment

Fraction of depc to CDOC

UV Photo oxidation of CDOC to LDOC

Unit

gCm d

-3

-1

depc2CDOC: Fraction of depc to CDOC, g C m d

��

��=

�� +

��

∗

-3

-1

(3.162)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

phoxCDOC: UV photo oxidation of CDOC to LDOC, g C m d

ℎ��

��=��

��∗ ��

∗

∗ ��

-3

-1

(3.163)

Where:

Name

DEPC1

DEPC2

DEPC3

Comment

Death of flagellate C

Death of diatom C

Death of cyanobacteria C

Fraction of DEPC, DEPN & DEPP to CDOC, CDON &

CDOP

Max relative photo oxidation rate

Relative daylength, f(latitude, day,month,year)

UV radiation Monod relation for photo oxidation

Unit

gCm d

-3

-1

Type*)

-1

doc

maxde

doc

monod

n.u.

-1

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.24 CDON, Coloured refractory DON, g N m

-3

��

�� − ℎ��

��

(3.164)

Where:

Process

depc2CDON

phoxCDON

Comment

Fraction of depn to CDON

UV Photo oxidation of CDON to LDON

Unit

gNm d

-3

-1

Depc2CDON: Fraction of depn to CDON, g N m d

��

��=

�� +

∗

��

∗

-3

-1

(3.165)

phoxCDON: UV photo oxidation of CDON to LDON, g N m d

ℎ��

��=��

��∗ ��

∗ ��

-3

-1

(3.166)

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

Where:

Name

DEPN1

DEPN2

DEPN3

doc

maxde

doc

monod

Comment

Death of flagellate N

Death of diatom N

Death of cyanobacteria N

Fraction of depc, depn, depp to CDOC, CDON, CDOP

Relative daylength, f(latitude, day,month,year)

Max relative photo oxidation rate

UV radiation Monod relation for photo oxidation

Unit

gNm d

n.u.

-1

-3

-1

Type*)

-1

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.25 CDOP, Coloured refractory DOP, g P m

-3

��

− ℎ��

(3.167)

Where:

Process

Comment

Fraction of depp to CDOP

UV Photo oxidation of CDOP to LDOP

Unit

gPm d

-3

-1

depc2CDOP

phoxCDOP

-1

depc2CDOP: Fraction of depp to CDOP, g P m d

��

∗

-3

-1

(3.168)

phoxCDOP: UV photo oxidation of CDOP to LDOP, g P m d

ℎ��

=��

∗ ��

∗

∗ ��

-3

-1

(3.169)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

DHI 3 Algae and Sediment Model

Where:

Name

DEPP1

DEPP2

DEPP3

doc

maxde

doc

monod

Comment

Death of flagellate P

Death of diatom P

Death of cyanobacteria P

Fraction of depc, depn, depp to CDOC, CDON, CDOP

Relative daylength, f(latitude, day,month,year)

Max relative photo oxidation rate

UV radiation Monod relation for photo oxidation

Unit

gPm d

n.u.

-1

-3

-1

Type*)

-1

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.26 LDOC, Labile DOC, g C m

-3

��

= ℎ��

��+

��−

��

(3.170)

Where:

Process

Comment

UV Photo oxidation of CDOC to LDOC

Fraction of depc to LDOC

Aerobic respiration of LDOC using O

Anaerobic respiration of LDOC using NO

Anaerobic respiration of LDOC using SO

Unit

gCm d

-3

-1

phoxCDOC

depc2LDOC

reLDOC

deLDOC

sreLDOC

-1

phoxCDOC: UV photo oxidation of CDOC to LDOC, g C m d

See under CDOC, Section 3.3.23.

depc2CDPC: Fraction of depc to LDOC, g C m d

��

��=

�� +

��

∗

-3

-1

-3

-1

(3.171)

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Mathematical Formulations

reLDOC: Aerobic respiration of LDOC using O

, g C m d

��=

��∗ �� ∗

��

∗

−

-3

-1

∗

+��

-3

-1

(3.172)

deLDOC: Anaerobic respiration of LDOC using NO

, g C m d

��=

��+

��

∗

+ ��

∗ .

(3.173)

sreLDOC: Anaerobic respiration of LDOC using SO

, g C m d

��=

��

∗��

∗

��

-3

-1

(3.174)

Where:

Name

DEPC1

DEPC2

DEPC3

tere

ndo2

Comment

Death of flagellate C

Death of diatom C

Death of cyanobacteria C

Fraction of depc, depn, depp to LDOC, LDON, LDOP

Ɵ in Arrhenius function, DC mineralisation

DC & LDOC:Coefficient, DO mineralisation

DO half-saturation constant, DC & LDOC

mineralisation

Specific mineralisation rate of LDOC at 20 °C

Detritus C

Denitrification in water

C:N ratio denitrification

Anoxic C mineralisation via SO

H

C:S ratio, SO

respiration

Unit

gCm d

n.u.

-3

-1

Type*)

-1

mdo2

kmLC

DENW

vn3

sred

vso

n.u

-1

-3

gCm

-1

gNm d

gCgN

-3

-1

-3

gSm d

gCgS

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.3.27 LDON, Labile DON, g N m

-3

��

= ℎ��

��+

��−

��

(3.175)

Where:

Process

Comment

UV Photo oxidation of CDON to LDON

Fraction of depn to LDON

Aerobic respiration of LDON using O

Anaerobic respiration of LDON using NO

Anaerobic respiration of LDON using SO

Unit

gNm d

-3

-1

phoxCDON

depc2LDON

reLDON

deLDON

sreLDON

-1

phoxCDON: UV photo oxidation of CDON to LDON, g N m d

See under CDON, Section 3.3.24.

depc2LDON: Fraction of depn to LDON, g N m d

��

��=

�� +

��

∗

-3

-1

-3

-1

(3.176)

reLDON: Aerobic respiration of LDON using O

, g N m d

��=

��

∗

��

-3

-1

(3.177)

deLDON: Anaerobic respiration of LDON using NO

, g N m d

��=

��

∗

��

-3

-1

(3.178)

sreLDON: Anaerobic respiration of LDON using SO

, g N m d

��=

��

∗

��

-3

-1

(3.179)

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Mathematical Formulations

Where:

Name

DEPN1

DEPN2

DEPN3

reLDOC

deLDOC

sreLDOC

Comment

Death of flagellate P

Death of diatom N

Death of cyanobacteria N

Fraction of depc, depn, depp to LDOC, LDON, LDOP

Aerobic respiration of LDOC using O

Anaerobic respiration of LDOC using NO

Anaerobic respiration of LDOC using SO

Unit

gNm d

n.u.

gCm d

-3

-1

-3

-1

Type*)

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.3.28 LDOP, Labile DOP, g P m

-3

��

= ℎ��

−

(3.180)

Where:

Process

phoxCDOP

depp2LDOP

UPLDOPP3

reLDOP

deLDOP

sreLDOP

Comment

UV Photo oxidation of CDOP to LDOP

Fraction of depp to LDOP

Cyanobacteria uptake of LDOP

Aerobic respiration of LDOP using O

Anaerobic respiration of LDOP using NO

Anaerobic respiration of LDOP using SO

Unit

gPm d

-3

-1

phoxCDOP: UV photo oxidation of CDOP to LDOP, g P m d

See under CDOP, Section 3.3.25.

depp2LDOP: Fraction of depp to LDOP, g P m d

��

∗

-3

-1

-3

-1

(3.181)

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DHI 3 Algae and Sediment Model

UPLDOPP3: Cyanobacteria uptake of LDOP, g P m d

Please see under state variable PP3, Section 3.3.9.

-3

-1

reLDOP: Aerobic respiration of LDOP using O

, g P m d

��

∗

��

-3

-1

(3.182)

deLDOP: Anaerobic respiration of LDOP using NO

, g P m d

∗

��

-3

-1

(3.183)

sreLDOP: Anaerobic respiration of LDOP using SO

, g P m d

��

∗

��

-3

-1

(3.184)

Where:

Name

DEPP1

DEPP2

DEPP3

reLDOC

deLDOC

sreLDOC

Comment

Death of flagellate P

Death of diatom P

Death of cyanobacteria P

Fraction of depc, depn, depp to LDOC, LDON, LDOP

Aerobic respiration of LDOC using O

Anaerobic respiration of LDOC using NO

Anaerobic respiration of LDOC using SO

Unit

gNm d

n.u.

gCm d

-3

-1

-3

-1

Type*)

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

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Mathematical Formulations

3.4

3.4.1

Differential Equation Sediment State Variables

SSi, Sediment, bio-available Silicate, g Si m

��

= �� − ��

��

Comment

Deposition of Diatom & Detritus Si

Flux of Si from sediment

Unit

g Si m d

-2 -1

(3.185)

Where:

Process

SESi

RSSi

-2 -1

SESi: Deposition of Diatom & Detritus Si, g Si m d

�� = ��

�� =

�� + ��

∗

�� ∗ ��

∗

-2 -1

(3.186)

RSSi: Flux of Si from sediment, g Si m d

−

��

�� + ℎ

-2 -1

∗

��

��( ,

)

(3.187)

Where:

Name

SEPSi2

SEDSi

krss

trss

hss1

KDOX

Comment

Sedimentation of diatom Si

Sedimentation of detritus Si

Height of actual water layer

Max Si release rate from sediment at 20 °C

Ɵ value in Arrhenius temperature function, Si

Temperature

Half saturation constant for SSi

penetration depth in sediment

Unit

g Si m d

n.u.

°C

g Si m

-2

-2 -1

-3 -1

Type*)

-3 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.4.2

KDOX, depth of NO3 penetration in sediment, m

KDOX is the NO

penetration into the sediment. NO

is denitrified in the anoxic part of the

sediment and therefore normally only penetrate 0-10 cm into the sediment. Normally, DO

only penetrates a few mm into the sediment and therefore KDO2 (the DO penetration) will

be smaller than KDOX. In a simulation, a situation may occur where KDOX is smaller than

KDO2, which at least in theory may happen in nature. In this case, the increase in KDOX

is set to a fixed fraction of the difference between KDO2 and KDOX.

��

(3.188)

Where:

Process

Dkdox

Comment

change oxidised layer sediment, KDOX

Unit

-1

Change oxidised layer sediment, KDOX:

�� =IF

KDOX<KDO2

THEN

−

∗

��

ELSE

dkdox_no3

(3.189)

Where:

Name

KDO2

Comment

DO penetration into sediment

penetration rate constant into sediment,

KDOX<KDO2

penetration rate sediment, analytical solution

Unit

-1

Type*)

kkdox

dkdox_no3

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

3.4.3

KDO2, DO penetration in sediment, m

��

(3.190)

Where:

Process

dkdo2

Comment

change in DO penetration in sediment

Unit

-1

dkdo2: Change in DO penetration in sediment, m d

�� =IF

(kds-KDO2)<epsi

THEN

��

�� −

∗

�� ,

ELSE

(kdo2i-KDO2)*kkdo2

-1

(3.191)

Where:

Name

KDO2

kds

epsi

Comment

DO penetration into sediment

Depth of modelled sediment layer

Constant small value also used for PC nutrient uptake

New steady state condition for KDO2, function of DO

and respiration, analytical solution

Rate constant for DO penetration into sediment

Unit

n.u.

Type*)

kdo2i

kkdo2

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.4.4

SOC, Sediment organic C, g C m

-2

��

�� − �� −

��

(3.192)

Where:

Process

depoC

minSOC

Rscim

Comment

Deposition of C

Mineralisation of SOC

Burial of sediment organic C

Unit

gCm d

-2 -1

Deposition of C on sediment surface:

Where:

Name

�� =(SEPC1-BUOYC1+SEP2+SEPC3-BUOYC3+SEDC)*dz

Comment

Sedimentation of flagellate C

Sedimentation of diatom C

Sedimentation of cyanobacteria C

Flagellate upward movement

Cyanobacteria upward movement

Sedimentation of detritus C (DC) to sediment

Height of actual water layer

Unit

gCm d

-3

-1

(3.193)

Type*)

SEPC1

SEPC2

SEPC3

BUOYC1

BUOYC3

SEDC

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

minSOC: Mineralisation of SOC, g C m d

�� =krsc1*SOC*

Comment

−

-2 -1

+fscb*dz

(3.194)

Where:

Name

krsc1

Unit

-1

Type*)

Specific mineralisation rate of SOC 20 °C

Ɵ in Arrhenius temperature equation, SON

mineralisation

Temperature

Mineralisation of newly settled organic C

Height of actual layer= layer above sediment

tetn

temp

fscb

n.u.

°C

gCm d

-3 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

rscim: Burial of sediment organic C, g C m d

�� =

�� − ��

∗ �� ∗

��

-2 -1

(3.195)

Where:

Name

depoC

Fscb

Comment

Deposition of C

Mineralisation of newly settled organic C

Burial of organic sediment N (SON), see SON

(Section 3.4.5)

Burial of organic sediment N (SON), see SON

(Section 3.4.5)

Height of actual layer= layer above sediment

Unit

gCm d

-2 -1

Type*)

-3 -1

Rsnim

gNm d

-2 -1

Rson

gNm d

-2 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.4.5

SON, Bio-available organic N in sediment, g N m

-2

��

�� −

��

ℎ−

��

(3.196)

Where:

Process

Rson

Rsonnh

Rsnim

Comment

Settling of organic N to SON

Mineralisation of SON to pore water NH

Burial of organic sediment N (SON)

Unit

gNm d

-2 -1

rson: Settling of organic N to SON

�� = ��

�� −

��

+ ��

∗ ��

�� +��

�� −

��

+ ��

��−��

(3.197)

Where:

Name

SEPN1

SEPN2

SEPN3

BUOYN1

BUOYN3

SEDN

Comment

Sedimentation of flagellate N

Sedimentation of diatom N

Sedimentation of cyanobacteria N

Flagellate upward movement N

Cyanobacteria upward movement N

Sedimentation of detritus N, (DN), see DN

Mineralisation of newly settled organic N on sed.

surface

Height of actual layer= layer above sediment

Unit

gNm d

-3

-1

Type*)

-1

Fsnb

gNm d

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

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Mathematical Formulations

rsonnh: Mineralisation of SON to pore water NH

�� ℎ=

∗�� ∗

−

(3.198)

Where:

Name

krsn1

Comment

Specific mineralisation rate of SON 20 °C

Ɵ in Arrhenius temperature equation, SON

mineralisation

Temperature

Unit

-1

Type*)

Tetn

n.u.

°C

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

rsnim: Burial of organic sediment N (SON), g N m d

-2 -1

The mineralisation of SOC and SON is assumed to a function of the sediment SON:SOC

ratio. At low SON:SOC ratios close to

knim

the mineralisation is assumed to small or

close to 0. The fraction of organic N settled to the sediment (rson) to buried or

immobilised is set to be

knim

multiplied with settled organic C to sediment. If N:C ration of

the settled N is below

knim

all settled N (rson) is buried.

�� =

��

�� ∗

ELSE

Rson

⁡

�� − ��

�� ∗

∗ ��

�� − ��

∗ �� <

��n

(3.199)

Where:

Name

knim

depoC

fscb

rson

Comment

Sediment: N:C ratio of immobile N

Deposition of C, see SOC

Mineralisation of newly settled organic C

Settling of organic N to SON

Unit

gNgC

-1

Type*)

gCm d

gNm d

-2 -1

-3 -1

-2 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.4.6

SOP, Bio-available organic P in sediment, g P m

-2

��

�� − ��

�� −

��

(3.200)

Where:

Process

rsop

ropsip

rspim

Comment

Settling of organic P to SOP

Mineralisation of SOP to pore water PO

Burial

–

immobilisation of organic sediment P (SOP)

Unit

gPm d

-2 -1

rsop: Settling of organic P to SOP, g P m d

�� = ��

−

��

+ ��

∗ ��

+��

-2 -1

−

��

+ ��

−��

(3.201)

Where:

Name

SEPP1

SEPP2

SEPP3

BUOYP1

BUOYP3

Comment

Sedimentation of flagellate P

Sedimentation of diatom P

Sedimentation of cyanobacteria P

Flagellate upward movement P

Cyanobacteria upward movement P

Mineralisation of newly settled organic P on sed.

Surface

Height of actual layer= layer abowe sediment

Unit

gPm d

-3

-1

Type*)

-1

Fspb

gPm d

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

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Mathematical Formulations

ropsip: Mineralisation of SOP to pore water PO

, g P m d

��

�� =

∗��

∗

−

-2 -1

(3.202)

Where:

Name

krsp1

Comment

Specific mineralisation rate of SOP 20 °C

Ɵ in Arrhenius temperature equation, SOP

mineralisation

Temperature

Unit

-1

Type*)

tetp

n.u.

°C

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

rspim: Burial and immobilisation of organic sediment P (SOP), g P m d

-2 -1

P is able to be incorporated into hydroxyapatite (chalk) or adsorbed to reduced Fe (in

fresh waters) or simply it is incorporated into inert organic C. The processes are not well

known and therefore a fixed fraction of the settled organic P is immobilised. In sediments

(typical marine) where the pool of H2S (reduced substances) exceeds a fixed value of

0.01 g S m-2 immobilisation to Fe++ is reduced to 1/10.

The user may change the process if new information is available, or information on

sediment type prescribes another formulation.

�� =

⁡�� > .

⁡ �� ⁡⁡⁡

��

∗

�� ⁡

�� ∗

��

(3.203)

Where:

Name

knim

rsop

Comment

Sediment: P:C ratio of immobile P

Settling of organic P to SOP

Unit

gPgC

-1

Type*)

gNm d

-2 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

3.4.7

FESP, PO4 adsorbed to oxidised ion in sediment, g P m

-2

��

= ��

��

Comment

Flux between pore water PO

and iron-absorped P

Unit

gPm d

-2 -1

(3.204)

Where:

Process

rfesip

rfesip: Flux between pore water PO

and iron-absorped P, g P m d

+++

-2 -1

The exchange of PO

-P between oxidised ion (Fe ) is calculated as a rate constant

(krap) multiplied with the difference between a new steady state sorption of PO

to Fe+++

(FESP_f(KDOX)

∞

)

and the last calculated pool of sorbed PO

-P (FESP

An approximation of

FESP_f(KDOX)

∞

is estimated using a Monod kinetic for PO

in the

pore water combined with information of sediment ion conten, dry matter sediment,

density and finaly multiplied with the oxidised layer (KDOX), which is a state variable in

the model.

�� =

Where:

Name

krap

kfe

Kfepo

SIPm3

khfe

KDOX

FESP

�� =

∗

−

�� ∗ ��

��

�� _��

��∗

��

∗ ��∗ ��∗

�� + ℎ��

∞

−

��

∗

(3.205)

Comment

Rate constant for iron absorption

–

desorption of PO

Oxidable ion content in sediment

Maximum Fe-P sorption capacity

Pore water PO

concentration

Half saturation constant, adsorption-desorption

Sediment density

Dry weight sediment

Depth of No3 penetration ~oxidised layer with Fe

Ion(FE

+++

Unit

-1

Type*)

-1

g Fe g dw

g P g Fe

gPm

-3

-1

-3

g WW cm

-3

-1

g DM g WW

gPm

-2

) bound PO4 in sediment

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ECO Lab Template - © DHI

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Mathematical Formulations

3.4.8

SNH, Sediment pore water NH4, g N m

-2

��

ℎ−

�� −��

ℎ

(3.206)

Where:

Process

rsonnh

rsnit

feunh4

Comment

Mineralisation of SON to pore water NH

Nitrification of NH

in sediment

Flux between sediment pore water and water

Unit

gNm d

-2 -1

rsonnh: mineralisation of SON to pore water NH

, g N m d

Please see under the state variable SON, Section 3.4.5.

rsnit: Nitrification of NH

in sediment, g N m d

-2 -1

The nitrification of NH4 in sediment pore water (SNHm3) is described as the product

between a specific nitrification rate (knit), SNHm3, a Monod relation of

SNHm3

a Monod

relation for DO (sqdo), the DO penetration in the sediment (KDO2) and a temperature

relation.

�� =

IF DO>0

THEN

�� ∗ �� ∗

��

�� +

∗

��∗

∗

ELSE

ℎ

−

(3.207)

Where:

Name

Knit

SNHm3

ksnh0

Sqdo

KDO2

Tetn

Comment

Specific nitrification rate at 20 C in sediment

concentration in pore water

half saturation concentration for nitrification

DO Mond function

DO penetration in sediment

Ɵ in Arrhenius temperature equation, SON

mineralisation

Temperature

Unit

-1

-3

Type*)

gNm

n.u.

°C

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DHI 3 Algae and Sediment Model

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

feunh4: NH

Flux between sediment pore water and water, g N m d

-2 -1

The flux between pore water NH

(SNHm3) and NH

in the water (NH4) is described as a

product of a vertical diffusion constant (difnh) and concentration difference divided with

the the NO

penetration depth in the sediment (KDOX).

��

ℎ = �� ℎ ∗

�� − ��

��

(3.208)

Where:

Name

difnh

Comment

Vertical diffusion for ammonia

concentration in pore water

concentration in water

Depth of modelled sediment layer

penetration in sediment~oxidised layer

Unit

2 -1

Type*)

-3

SNHm3

NH4

kds

KDOX

gNm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.4.9

SNO3, NO3 in sediment pore water, layer (0 - kdo2), g N m

-2

��

�� −

�� −��

��

(3.209)

Where:

Process

rsnit

Rdenit

feuno3

Comment

Nitrification of pore water NH

in sediment

Denitrification of NO

in sediment

Flux between sediment pore water and water

Unit

gNm d

-2 -1

rsnit: Nitrification of pore water NH

in sediment, g N m d

Please see state variable SNH, Section 3.4.8.

rdenit: Denitrification of NO

in sediment, g N m d

-2 -1

ECO Lab Template - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Mathematical Formulations

rdenit is expressed as flux of NO

into the anoxic zone of the sediment where only

diffusion and denitrification are the driving processes. An analytical solution is used

assuming steady state conditions.

From the surface layer of the sediment with DO (KDO2), NO

in the pore water with

concentration SNO3m3 will penetrate deeper into the anoxic sediment layer while being

denitrified to N

. At a sudden depth below the surface (KDOX) NO

concentration will be

0. Assuming a constant denitrification and under steady state condition the NO

concentration (NO3x) in the pore water at depth x below the surface layer with DO can be

described with:

= − �� ∗

��

Which by integration becomes:

��⁡��

��

∗��+

��

=−

��

Where 0<x<(KDOX-KDO2)

(3.210)

Where a is a constant, which by using the border condition (��NO3x/

��

x=0

at x=(KDOX-

KDO2))

can be defined as:

��⁡��

(3.211)

Which by yet an integration gives:

��

��=

��

∗

Where b is a constant, which by using the border condition (SNO3m3=0 at x=(KDOX-

KDO2))

can be defined as:

��

��=

∗ ��

��

∗�� ∗−

∗

∗ ��

��

∗

−

∗ ��−

−

(3.212)

−

∗��+

(3.213)

∗ ��

∗�� −

��

∗

−

∗��+

∗ ��

∗

−

(3.214)

At depth x=0 in the anoxic zone (which is at depth KDO2 below sediment surface)

NO3x=SNO3m3.

−

= √ ∗ �� ∗

��

∗ ��

��

(3.215)

��

��=

Assuming the flux of NO

into the anoxic sediment solely being created by denitrification

2 -1

the NO

-flux=denitrification pr. m d = rdenit.

��

∗�� −

∗ √ ∗ �� ∗

∗��+

∗ ��

��

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Using Fick’s 1. law for a flux at depth x=0.

�� = − �� ∗

��

(3.216)

��

for x=0. The final equation used in the template:

�� = √ ∗ �� ∗

Comment

Vertical diffusion for NO

in sediment

denitrification in sediment, corrected for temperature

in pore water surface sediment, layer (0-kdo2)

DO penetration into the sediment

penetration into the sediment

concentration in pore water at depth x

Depth below zone with DO

��

is found by differentiation of the above expression for

NO3x

and determine the flux

�� ∗ ��

��

(3.217)

Where:

Name

difno3

dnm3

Unit

2 -1

Type*)

-3 -1

gNm d

gNm

-3

SNO3m3

KDO2

KDOX

NO3x

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

feuno3: NO

Flux between sediment pore water and water, g N m d

-2 -1

The flux between pore water NO

(SNO3m3) and NO

in the water (NO3) is described as

a product of a vertical diffusion constant (difno3) and concentration difference divided with

the the DO penetration depth in the sediment (KDO2).

��

�� = �� ∗

��

�� −��

(3.218)

Where:

Name

difno3

NO3

Comment

Vertical diffusion for NO

in sediment

concentration in water

in pore water surface sediment, layer (0-kdo2)

DO penetration into the sediment

Unit

2 -1

Type*)

-3

gNm

SNO3m3

KDO2

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

3.4.10 SIP, PO4 in sediment pore water, g P m

-2

��

=− �� + ��

��

Comment

Flux between pore water PO

and iron-adsorbed P

Mineralisation of SOP to pore water PO

Flux between PO

in pore water and water above sediment

Where:

�� −��

(3.219)

Process

rfesip

ropsip

fsip

Unit

gPm d

-2 -1

rfesip: Flux between pore water PO

and iron-absorped P, g P m d

-2 -1

Please see under the stat variable FESP, sediment ion adsorbed PO

, Section 3.4.7.

ropsip: Mineralisation of SOP to pore water PO

, g P m d

-2 -1

Please see under the stat variable SOP, bio-available organic P in sediment. Section

3.4.6.

fsip: Flux between PO

in pore water and water above sediment, g P m d

-2 -1

The flux between pore water PO

(SIPm3) and PO

in the water (IP) is described as a

product of a vertical diffusion constant (kfip) and concentration difference divided with the

penetration depth in the sediment (KDOX).

�� = �� ∗

�� −

(3.220)

Where:

Name

kfip

Comment

Vertical diffusion for PO

in sediment

concentration in water

in pore water of the sediment

penetration into the sediment

Unit

2 -1

Type*)

-3

gNm

SIPm3

KDOX

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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3.4.11 SH2S, Reduced substances in sediment, g S m

-2

��

= �� − �� ℎ

��

Comment

Sediment H2S production in anaroxic layer: mineralisation of SOC

–

denitrification

flux of SH2S from reduced sediment (below KDOX) to oxidised

sediment.

flux of reduced H2S equivalents from sediment to water

Where:

−��

ℎ

(3.221)

Process

Unit

RSH2S

gSm d

-2 -1

fsh2s

fwsh2

gSm d

-2 -1

RSH2S: Sediment H2S production in anaroxic layer: mineralisation of SOC minus

denitrification

The production of H2S (reduced substances in sediment expressed as H

S-S) is

calculated as the mineralisation of SOC (minSOC) minus the a fraction of the minSOC

being oxidised by DO in layer KDO2 minis a fraction of minSOC being oxidised by NO

denitrification in the anoxic zone penetrated by NO

(KDOX-KDO2). A C:N ratio of 1.07

is used to convert denitrified NO

-N to C, and a C:S ratio of 1.33 is used to convert

mineralised C to S.

�� = (�� −

��

−

�� ∗ .

)∗ .

(3.222)

Where:

Name

Comment

mineralisation SOC

Sediment mineralisation of SOC by DO, in layer KDO2

: C ratio used in production & consumption

processes

Denitrification in anoxic sediment layer

Unit

gCm d

-2 -1

Type*)

minSOC

reKDO2

g O

m d

-2 -1

Rdenit

g O

g C

gNm d

-1

-2 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

fsh2s: flux of SH2S from reduced sediment (below KDOX) to oxidised sediment,

-2 -1

gSm d

The flux of reduced substances expressed as H

S-S from sediment below the oxidised

zone of the sediment (below KDOX) is expressed as a diffusion constant multiplied by a

S concentration difference between the H

S concentration (calculated from SH2S) and

the H2S concentration in the water above the sediment divided by the distance from the

reduced zone in the sediment to the depth of DO penetration (KDO2).

�� ℎ =

��

⁡

> .

⁡

��

�� (

−��

ELSE 0

Where:

Name

difh2s

SH2S

kds

KDO2

KDOX

H2S

��ℎ

∗

− �� ∗ ��∗

−

)

⁡

(3.223)

Comment

Vertical diffusion of SH2S in sediment

Reduced substances in sediment as H

Sediment density

Dry weight sediment

Depth of modelled sediment layer

DO penetration into the sediment

penetration into the sediment

Hydrogen sulphide in water above sediment (H

Unit

2 -1

Type*)

-2

gSm

-3

g WW cm

-1

g DM g WW

gSm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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fwsh2s: flux of reduced H2S equivalents from sediment to water, g S m d

In case the DO penetration in the sediment (KDO2) is below 1 mm the flux of H

S go

directly from the reduced zone of the sediment into the water above the sediment.

��

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ ��ℎ

ℎ =

��

⁡

∗

��

−�� ∗��∗ ��−��

-2

-1

ELSE 0

Where:

Name

difh2s

SH2S

Kds

KDO2

KDOX

H2S

��

⁡

��

−��

(3.224)

Comment

Vertical diffusion of SH2S in sediment

Reduced substances in sediment as H

Sediment density

Dry weight sediment

Depth of modelled sediment layer

DO penetration into the sediment

penetration into the sediment

Hydrogen sulphide in water above sediment (H

Unit

2 -1

Type*)

-2

gSm

-3

g WW cm

-1

g DM g WW

gSm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.4.12 SPIM, Immobilised sediment P, g P m

-2

��

(3.225)

Where:

Process

Rspim

Comment

Immobilisation of sediment P

Unit

gPm d

-2 -1

rspim: Immobilisation of sediment P, g P m d

-2 -1

The immobilisation of P in the sediment is set to be a constant fraction of the organic P

settling to the sediment surface. In water bodies with permanently or semi permanent

-3

anoxia having a H

S concentration above 0.01 g S m the immobilisation is set to be 10%

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Mathematical Formulations

��

�� =

∗

Where:

Name

H2S

kpim

rsop

�� ⁡⁡

�� ∗

�� ⁡

⁡�� > .

��

⁡ �� ⁡

(3.226)

Comment

S in the water above the sediment

Fraction of settled P to immobilisation

Supply of organic P to sediment

Unit

gSm

n.u.

gPm d

-2 -1

-3

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.4.13 SNIM, Immobilised sediment N by denitrification & burial, g N m

-2

��

�� +

��

(3.227)

Where:

Process

rspim

rdenit

Comment

Immobilisation of sediment N by burial

Denitrification of NO

in sediment

Unit

gNm d

-2 -1

rsnim: Immobilisation of sediment N by burial, g N m d

-2 -1

Please see under state variable sediment organic N (SON), Section 3.4.5.

rdenit: Denitrification of NO

in sediment, g N m d

-2 -1

Please see under state variable sediment NO3 (SN03), Section3.4.9.

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DHI 3 Algae and Sediment Model

3.4.14 SNIM, Immobilised sediment N by denitrification & burial, g N m

-2

��

= �� +

��

(3.228)

Where:

Process

minSOC

rscim

Comment

Mineralisation of SOC

Burial of sediment organic C

Unit

gCm d

-2 -1

minSOC: Mineralisation of SOC, g C m d

-2 -1

Please see under state variable sediment organic C (SOC), Section 3.4.4.

rscim: Burial of sediment organic C, g C m d

-2 -1

Please see under state variable sediment organic C (SOC), Section 3.4.4.

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Mathematical Formulations

3.5

Help Processes

The help processes are divided into processes not included into differential equations

(P1) and auxiliary processes (A). The distinction between is unimportant and relay on P1

processes in ECO Lab being able to be defined exclusively for bottom layer, surface layer

and all layers in a 3D model. This distinction is not possible for auxiliary processes.

3.5.1

The P1 processes listed in alphabetic order

dkdox_no3: Change in NO3 penetration rate sediment, analytical solution, m d

-1

in the pore water of the sediment is caused by penetration of NO

form water above

the sediment and by nitrification of NH

in the uppermost layer (KDO2) with DO in the

pore water. The NO

concentration in this layer (0 to KDO2) has in the model the average

concentration SNO3m3. From this layer NO

penetrates deeper into the anoxic sediment

layer while being denitrified to N

. Provided there is no outflow of NO

enriched ground

water the NO

concentration at a sudden depth below the surface (KDOX) will be 0.

Assuming a constant denitrification and under steady state condition the NO

concentration (NO3x) in the pore water at depth x below the surface layer with DO can be

described with:

= − �� ∗

��

Which by integration becomes:

��⁡��

��

∗��+

��

=−

��

Where 0<x<(KDOX

∞

-KDO2)

(3.229)

Where a is a constant, which by using the border condition (��NO3x/

��

x=0

at x=(KDOX-

KDO2))

can be defined as:

��⁡��

(3.230)

Which by yet an integration gives:

��

��=

∗ ��

��

∗

∗ ��−

∞

−

∞

Where b is a constant, which by using the border condition (SNO3m3=0 at x=(KDOX

∞

KDO2))

can be defined as:

∗ ��

∗�� −

∞

��

∗

−

(3.231)

∞

−

∗��+

(3.232)

��

��=

∗ ��

∗

∗�� −

−

��

∗

∞

−

∗��+

∗ ��

∗

∞

−

(3.233)

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At depth x=0 in the anoxic zone (which is at depth KDO2 below sediment surface)

NO3x=SNO3m3.

∞

= √ ∗ �� ∗

−

= √ ∗ �� ∗

��

(3.234)

KDOX

∞

in the above equation is the NO

peneteration in the sediment under steady state

condition. Assuming KDO2

~KDO2

t+1

the change in the change in in KDOX ( kdox_no3)

from time step t to time step t+1 can the be defined as:

��

∞

��

Where:

Name

difno3

dnm3

= √ ∗ �� ∗

−

��

∗

��

−

��

∗

��

(3.235)

Comment

Vertical diffusion for NO

in sediment

denitrification in sediment, corrected for temperature

in pore water surface sediment, layer (0-kdo2)

DO penetration into the sediment

DO penetration into the sediment , time step t

penetration into the sediment, same as KDOX

Rate constant NO

penetration into sediment

penetration into the sediment, time step t

penetration into the sediment, steady state

concentration in pore water at depth x

Depth below zone with DO

Unit

2 -1

Type*)

-3 -1

gNm d

gNm

-1

-3

SNO3m3

KDO2

KDOX

kkdox

KDOX

∞

NO3x

gNm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

fscb: Mineralisation of newly settled organic C, g C m d

-3 -1

A fraction of newly settled particulate organic C (plankton and detritus) on the sediment

surface is assumed to be mineralised at once. The fraction mineralised is dependent on

the N:C ratio.

��

�� −

Comment

Mineralisation of newly settled organic N

Deposition of particulate organic C

Sedimentation of flagellate N

Sedimentation of diatom N

Sedimentation of cyanobacteria N

Flagellate upward movement N

Cyanobacteria upward movement N

Deposition of detritus N

Height of actual layer

Where:

Name

fsnb

depoC

�� +��

��

�� +��

�� −

�� +��

��

∗

��

(3.236)

Unit

gNm d

gCm d

-3

-3 -1

Type*)

-2 -1

SEPN1

SEPN2

SEPN3

BUOYN1

BUOYN3

SEDN

gNm d

-3

-1

-3 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

fsnb: Mineralisation of newly settled organic N, g N m d

-3 -1

A fraction of newly settled particulate organic N (plankton, detritus and dead eelgrass) on

the sediment surface is assumed to be mineralised at once. The fraction mineralised is

dependent on the N:C ratio.

��

∗ (��

−

�� −

�� ∗

��

�� +��

)∗

��

�� +��

−

�� −

�� +��

��

(3.237)

Where:

Name

krsn0

depoC

SEPN1

Comment

Fraction of deposited N mineralised

Deposition of particulate organic C

Sedimentation of flagellate N

Unit

-1

Type*)

-2 -1

gCm d

-3

gNm d

-1

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DHI 3 Algae and Sediment Model

Name

SEPN2

SEPN3

BUOYN1

BUOYN3

SEDN

knim

tetn

temp

Comment

Sedimentation of diatom N

Sedimentation of cyanobacteria N

Flagellate upward movement N

Cyanobacteria upward movement N

Deposition of detritus N

Height of actual layer

Sediment N:C ratio of immobile N

Ɵ value in Arrhenius temperature function

Temperature

Unit

gNm d

gNgC

n.u.

°C

-1

-3

-1

Type*)

-1

-3 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

fspb: Mineralisation of newly settled organic P, g P m d

-3 -1

A fraction of newly settled particulate organic P (plankton and detritus) on the sediment

surface is assumed to be mineralised at once. The fraction mineralised is not set to be

dependent on the N:C ratio, because mineralised P as PO

can be adsorbed to

+++

resuspended fine sediment containing Fe . The user⁡should therefore consider this

problem and set the constant

krsp0

accordingly, from model set up to model set up.

��

∗ ��

∗

��

−��

−

+��

−

+��

(3.238)

Where:

Name

krsp0

SEPP1

SEPP2

SEPP3

BUOYP1

BUOYP3

SEDP

tetp

temp

Comment

Fraction of deposited N mineralised

Sedimentation of flagellate P

Sedimentation of diatom P

Sedimentation of cyanobacteria P

Flagellate upward movement P

Cyanobacteria upward movement P

Deposition of detritus P

Ɵ value in Arrhenius temperature function

Temperature

Unit

-1

-3

-1

Type*)

gPm d

n.u.

°C

-3 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

kdo2i: new steady state condition for KDO2, function of DO & respiration, analytical

solution

From the sediment-water intreface oxygen (DO) can penetrat into the sediment pore

water by diffusion or actively being transportet into the sediment by ventilation pumping

and sediment mixing by the benthic fauna. Further microbenthic algae through

photosynthetis can produce DO in the sediment-water interface. DO is consumed in the

sediment by bacterial respiration and chemical oxidation of reduced substances (Fe ,

S) resulting in the O

concentration becomes 0 (normally 0-2 cm) below the sediment

surface. In the model this depth is defined as KDO2. Assuming the DO produced by the

microbenthic algae is delivered to the water, the below differential equation can be set up

assuming a steady state condition:

= − �� ∗

��

Which by integration becomes:

��⁡

��

∗

��

∗

��

Where 0<y<(KDO2

∞

)

(3.239)

(3.240)

Where a is a constant, which by using the border condition (��O

��y

=0 at y=KDO2

∞

))

can

be defined as:

��⁡

Which by yet an integration gives:

∗ ��

∗

��

∗

−

��

=−

��

∗

−

∞

��

Where b is a constant, which by using the border condition (O

=0 at y=KDO2

∞

) can be

defined as:

∗ ��

��

∗

��

∗

∞

(3.241)

∞

∗

(3.242)

At the sediment surface y=0 the O

= DO =>

∞

∗ ��

∗

−

∞

⁡

��

∗

∞

∗

��

∗

∞

⁡

(3.243)

= √ ∗ �� ∗

(3.244)

KDO2

∞

is identical to

ko2i

in the model, however the DO consumption in the model is the

sum of bacterial respiration (reKDO2), nitrification (rsnit) and a flux of reduced substances

from the under laying sediment (fsh2s) to the layer with O

. All the mentioned DO

-2 -1

consuming processes has the unit (g m d ) and therefore has to be divided with the DO

penetration from the previous time step t (KDO2

). A conversion factor for O

:N of 4.57 g

:g NH

-N is used and a conversion factor for O

:S of 2 g O

: H

S-S is used.

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DHI 3 Algae and Sediment Model

The diffusion or rather transport of oxygen into the sediment is dependent of the activity of

the benthic infauna. Their activity is linked to the DO concentration, at low DO (below 2 g

-3

m ) the activity will decrease caused by increased mortality. The constant

difO2

therefore multiplied by an oxygen function (1+sqdo).

�� =√ ∗

Where:

Name

Comment

Vertical diffusion for O

in sediment, low fauna

activity

Sediment O

consumption, layer (0-KDO2)

Depth below sediment surface

DO penetration into the sediment, steady

state=kdo2i

DO penetration into the sediment time step t=KDO2

DO penetration into the sediment

DO dependend auxiliary

Nitrification in sediment layer (0-KDO2)

DO consumption by bacteria layer (0-KDO2)

Flux of SH2S from reduced sediment to layer (0-

KDO2)

in water above sediment

∗

�� ∗ +

�� ∗ . +

�� ∗

+�� ℎ

��

∗

(3.245)

Unit

Type*)

difo2

DOconsum

2 -1

-3 -1

g O

m d

KDO2

∞

KDO2

sqdo

rsnit

reKDO2

n.u.

gNm d

-2 -1

g O

m d

-2 -1

fsh2s

gSm d

g O

-3

-2 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

reKDO2: Sediment mineralisation of SOC by DO, in layer KDO2, g O

m d

∗ �� ∗ �� ∗

��

-2

-1

(3.246)

Where:

Name

KDO2

kds

minSOC

sqdo

Comment

DO penetration depth in sediment

Depth of modelled sediment layer

Mineralisation of organic in sediment

: C ration production, respiration, mineralisation

Oxygen function

Unit

gCm d

g O

g C

n.u.

-2

-1

Type*)

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

3.5.2

Auxiliary (A) processes listed in alphabetic order

buoy1: N & P & light upward movement function, flagellate, n.u.

The upward movements of phytoflagellates are a function of the light regime and nutrient

condition of the algae. If the internal N and P pools (N/C and P/C ratios in the algae) are

small the function powNP1 will have a small but positive value resulting in an in

sedbouNP1 being negative and the buoy1 becoming 0. At low powNP1 there will be no

upward movements. At high powNP1values (high N/C and P/C ratio in the algae)

sedbouNP1 become positive and the algae will move upward provided the light doze is

below a value of kiz3.

buoy1=IF

i≤kiz3

THEN MAX (0,sedbouNP1)

ELSE 0

Where:

��

�� ∗

��

�� + ��

,��

��

(3.247)

��

− .

(3.248)

And:

��

(3.249)

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DHI 3 Algae and Sediment Model

Figure 3.3

Figure Flagellates upward movement is dependent of positive values of sedboy1, which is

dependent on a good N and P condition myn1 and myp1

Where:

Name

Comment

Unit

mol photon

-2 -1

m d

mol photon

-2 -1

m d

n.u.

Type*)

kiz3

Light limit, buoyancy for PC1 & PC 3

k1NP

k2NP

k3NP

powNP1

myn1

myp1

Photosynthetic Active Light (PAR) at top of layer

Exponent, sedimentation & buoyancy, PC1&PC3

Factor, sedimentation & buoyancy, PC1 & PC3

Shift from sedimentation to buoyancy, PC1 & PC3

Power function limiting nutrient, Flagellate (PC1)

Nitrogen function flagellates

Phosphorous function flagellates

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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buoy3: N & P & light upward movement function, cyanobacteria, n.u.

The upward movement of cyanobacteria is a function of the light regime and nutrient

condition of the bacteria. If the internal N and P pools (N/C and P/C ratios in the bacteria)

are small the function powNP3 will have a small but positive value resulting in an in

sedbouNP3 being negative and the buoy1 becoming 0. At low powNP3 there will be no

upward movements. At high powNP3 values (high N/C and P/C ratio in the bacteria)

sedbouNP3 become positive and the algae will move upward provided the light doze is

below a value of

kiz3.

Where:

buoy

=IF⁡⁡i kiz ⁡THEN⁡MAX ,sedbouNP ⁡ELSE⁡

��

�� ∗

��

Comment

(3.250)

And:

Where:

Name

��

,��

��

�� + ��

��

− .

(3.251)

(3.252)

Unit

mol photon

-2 -1

m d

mol photon

-2 -1

m d

n.u.

Type*)

kiz3

Light limit, buoyancy for PC1 & PC 3

k1NP

k2NP

k3NP

powNP3

myn3

myp3

Photosynthetic Active Light (PAR) at top of layer

Exponent, sedimentation& buoyancy, PC1&PC3

Factor, sedimentation & buoyancy, PC1 & PC3

Shift from sedimentation to buoyancy, PC1 & PC3

Power function limiting nutrient, cyanobacteria

Nitrogen function cyanobacteria

Phosphorous function cyanobacteria

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

Figure 3.4

Cyanobaterial upward movement is dependent of positive values of sedboy3, which is

dependent on a good N and P condition myn3 and myp3.

CSAIR: O

saturation in water, relative to PSU & temp., g O

-3

A built in function in ECO Lab calculates the O

saturation relative to salinity and

temperature. In this template the O2 saturation defined by (Weiss 1970) is used:

CSAIR=

OXYGENSATURATION_WEISS(S,T)

(3.253)

Or:

CSAIR=

Where:

. 999

��

(3.254)

a=-173.4292+249.6339+

In other templates the below equation is used.

CSAIR=

OXYGENSATURATION(S,T)

+��∗ − .

+ .

⁡

∗

∗ log

− .

∗

−

∗

(3.255)

(3.256)

Or:

0.0000374*S -0. 000077774*T ) )

CSAIR=

14. 65

–

0 0841

⋅

S + T*(0. 00256

⋅

–

0. 41022 + T*( 0.007991-

(3.257)

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Where:

Name

Comment

Salinity

Temperature

Unit

PSU

°C

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

dndc: N:C ration, detritus, g N g C

��

-1

(3.258)

Where:

Name

Comment

Detritus N

Detritus C

Unit

gNm

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

dnm3: denitrification in sediment, corrected for temperature

�� =

�� ∗

−

(3.259)

Where:

Name

Comment

Max. denitrification rate in sediment at 20 °C

Ɵ value in Arrhenius temperature function

Temperature

Unit

gNm d

n.u

°C

-2 -1

Type*)

Demax

Tetn

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

doc

monod

: UV radiation Monod relation for photo oxidation, n.u

��

��− ��

��

��− ��

��

+ ��

��

(3.260)

Where:

Name

Comment

Unit

μmol photon

-2 -1

m s

μmol photon

-2 -1

m s

μmol photon

-2 -1

m s

Type*)

Solar radiation (PAR) in actual water column layer

doc

min PAR light, CDOC photo oxidation

doc

PAR half saturation photo oxidation of CODC

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

dpdc: P:C ration, detritus, g P g C

��

Comment

Detritus P

Detritus C

-1

(3.261)

Where:

Name

Unit

gPm

-3

Type*)

gCm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

dsidc: Si:C ration, detritus, g Si g C

��

-1

(3.262)

Where:

Name

DSi

Comment

Detritus Si

Detritus C

Unit

g Si m

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

day

: AD time step (and not HD time step!) in days, d step

-1

(3.263)

Where:

Name

Comment

Time step in sec.

Unit

Sec. step

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

eta: Vertical light attenuation, m

-1

It is possible to calculate the vertical light attenuation based on light extinction constants

or use the expression formulated by (Effer 1988; Kirk 2000) splitting the light attenuation

into a light absorption and a scattering of light.

The surface area of the particles are important for the optical properties, as small particle

have a larger surface area, they also have a higher vertical light extinction constant or a

higher light scattering constant. In general the optical properties of particulate matter are

proportional to the surface area of the particles in the water. In the equation for

eta1

and

-3

scattering

scatw

3 size classes of inorganic matter (ss1-ss3) are defined in g m . The

mass is not an ideal measure for inorganic matter in relation to the optical properties;

therefore the mass of ss1-ss3

is related to a particle size with a diameter of 10 μm, by

multiplication of a factor (10/diass

). Small particles

below 10 μm thereby will be assigned

a higher light extinction constant, or absorption and scattering constants, whereas larger

particles will be assigned smaller constants.

The shape of the particles may be anything from a ball to spherical cone; therefore the

correction factor (10/diass

) should only be regarded as guidelines to be used if no

measured data exists.

In the present ECO Lab template resuspension is not included therefore the light

extinction not included dynamically in the model often is put into the background light

extinction (bla) and the light extinction form suspended matter is the light extinction from

marine earth works. The user should in this case be aware that the background extinction

varies in time and space especially in coastal waters.

eta=

Where:

eta

��

⁡

eta

= √

∗ �� +

> ⁡ �� ⁡

+ .

∗ ��+

∗

⁡

�� ⁡

(3.264)

∗

∗��

��+

∗

��

(3.265)

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And:

absw=

��

scatw=

The scatter of light (scatw) is defined as a power function of phytoplankton chlorophyll,

(Morel A. 1980, Prieur L. & S. Sathyendranath 1981). The authours found a value range

-1

for bkch of 0.12-0.4 m mg & ekch 0.63. The scatter by phytoplankton is dependent on

cell size. The cell size tends to be smaller at low chlorophyll concentrations, where the

plankton typically is nutrient limited (Yentsch C.S., D. A. Phinney 1989).

Lund-Hansen L.C. 2004 found chlorophyll in average to be responsible for 41% of the

scattering in the nearby Århus Bay using a fixed specific chlorophyll scattering of 0.239

-1

m mg measured in New Zeland coastal waters (Pfannkuche F. 2002).

Please note that the mentioned scatter constants should be converted from m mg to

2 -1

m g before being used in this model.

Where:

Name

Keta

eta1

Comment

Constant for choice of eta estimate

Function vertical light attenuation, extinction constants

Function vertical light attenuation, absorption &

scattering

Chlorophyll light extinction constant

Chlorophyll concentration

Detritus light extinction constant

Detritus C

CDOC light extinction constant

Coloured refractory DOC

Inorganic matter light extinction constant (Ɵ=10 μm)

Inorganic matter, s e class 1

Inorganic matter, size class 2

Inorganic matter, size class 3

Diameter of inorganic matter, size class 1

Diameter of inorganic matter, size class 2

Unit

n.u.

-1

ℎ ∗ ��

∗ �� +

ℎ

∗ ��+

∗

��

∗

∗��

��

∗

��+

��

∗

��

(3.266)

-1

Type*)

eta2

pla

dla

cla

CDOC

sla

ss1

ss2

ss3

diass1

diass2

-1

m g

-3

m g

-1

-3

m g

-1

-3

m g

μm

-1

-3

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Name

diass2

bla

absw

scatw

pla

dla

cla

sla

bla

bkch

ekch

bkss

ekss

Comment

Diameter of inorganic matter, size class 2

Background light extinction

Light absorption in layer

Light scattering in layer

Chlorophyll light absorption constant

Detritus light absorption constant

CDOC light absorption constant

Inorganic matter light

absorption constant (Ɵ=10 μm)

Background light absorption

Chlorophyll scattering constant

Chlorophyll scattering exponent

Inorganic matter scattering constant

Inorganic matter scattering exponent

Unit

μm

-1

Type*)

-1

m g

-1

m g

n.u.

m g

n.u.

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

fiz: Light factor for flagellates and cyanobacteria (PC1 & PC3) sedimentation, n.u.

�� = �� ∗ ��

�� =

(3.267)

Where:

⁡�� > �� ⁡ �� ⁡ ⁡

Comment

�� ⁡

Unit

n.u.

mol photon m d

-2 -1

(3.268)

Where:

Name

fiz1

fiz2

kiz1

kiz2

Type*)

1. Help factor for PC1 & PC3 sedimentation

2. Help factor for PC1 & PC3 sedimentation

Light at top of actual water layer

Light limit for 3 X sedimentation rate of PC1 & PC3

Light limit for 1 X sedimentation rate of PC1 & PC3

-2 -1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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fiz1: 1. Help factor for PC1 & PC3 sedimentation, n.u.

See under auxiliary fiz, Equation (3.18) and Equation (3.29).

fiz2: 2. Help factor for PC1 & PC3 sedimentation, n.u.

See under auxiliary fiz, Equation (3.18) and Equation (3.29).

fn3a: Denitrification, DO dependency in water column, n.u.

��

Comment

Denitrification Half saturation conc. DO

Oxygen concentration

Unit

g O

-3

(3.269)

Where:

Name

ksb

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

fp3sal: Function for cyanobacteria dependency (death & growth) of salinity, n.u.

��

⁡�� <

�� ⁡ �� ⁡ ⁡

�� ⁡

−

∗ −

(3.270)

Where:

Name

kp3opti

kp3sal1

kp3sal2

Comment

Highest salinity for optimum cyanobacteria growth

Cyanobacteria growth salinity dependency coefficient

Cyanobacteria growth salinity dependency constant

Salinity

Unit

PSU

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

100

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fsa: Salinity function for reduction of SO

to H

S, n.u.

��

⁡�� >

⁡ �� ⁡ ⁡

�� ⁡

(3.271)

Where:

Name

ksa

Comment

Minimum salinity for SO

reduction

Salinity

Unit

PSU

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

i: Solar radiation (PAR) in actual water column layer (j), mol photon m d

-2 -1

If the surface water temperature >0.2 °C the water is assumed ice free and i

will be the

light (PAR) reaching the surface of the water.

If the temperature is below 0.2 °C ice is assume on the water and only 10% of i

assumed to penetrate the ice cover.

In a more general form the light (PAR) distribution in the different water layer can be

expressed as:

��=�� ∗

∑ − ��

−

∗

⁡ −

(3.272)

ECO Lab has an builtin function (LAMBERT_BEER_1) calculate the light (PAR) at the top

of each water layer.

The average light (PAR) in a water layer can be expressed as:

��=

−

− �� ∗

Where:

Name

∗ ��

_ �� , ��,

(3.273)

Comment

Unit

mol photon

-2 -1

m d

-1

Type*)

eta

0-j

eta

Solar (PAR) radiation at water surface

Light attenuation (Kd) in layers 0 to j

Height of layer 0 to j

Light attenuation (Kd) in actual layer

Height of actual water layer

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

101

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ik1: Temperature corrected Light saturation for flagellates, mol photon m d

��

∗

��

−

-2 -1

(3.274)

Where:

Name

Comment

Unit

mol photon

-2 -1

m d

n.u

°C

Type*)

alfa1

teti

Light saturation at 20 °C for flagellates

Ɵ value Arrhenius expression

temperature

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ik2: Temperature corrected Light saturation for diatoms, mol photon m d

��

∗

��

−

-2 -1

(3.275)

Where:

Name

Comment

Unit

mol photon

-2 -1

m d

n.u

°C

Type*)

Alfa2

teti

Light saturation at 20 °C for diatoms

Ɵ value Arrhenius expression

temperature

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

ik3: Temperature corrected Light saturation for cyanobacteris, mol photon m d

��

∗

��

−

-2 -1

(3.276)

Where:

Name

Comment

Unit

mol photon

-2 -1

m d

n.u

°C

Type*)

Alfa3

teti

Light saturation at 20 °C for cyanobacteria

Ɵ value

Arrhenius expression

temperature

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

102

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ksd: Sedimentation rate detritus, d

-1

The sedimentation of a particle is not allowed to pass through several water layers in one

time step (DT

day

time step in d). The sedimentation in one times step is therefore

restricted to a maximum of dz. This is valid for ECO Lab version 2011 and earlier.

This restriction may led to an underestimation of sedimentation in 3-D set ups with a fine

vertical resolution using small dz. However by not imposing the below restriction in

sedimentation will potentially generate mass balance errors.

⁡ ��

∗

⁡ �� ⁡

��

⁡

�� ⁡

(3.277)

Where:

Name

day

sevd

Comment

Height of actual water layer

AD time step

Sedimentation rate

Unit

d step

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mgpc: Temperature, O

& food corrected max. grazing rate by zooplankton, d

��

∗

��

−

Where:

Name

kgrb

tetz

sqdo

∗

�� −

�� ∗

��

∗

��

-1

��

∗

��

∗

⁡

(3.278)

Comment

Max. specific grazing rate, zooplankton

Ɵ in Arrhenius temp. relation of zooplankton grazing

Temperature

DO function

Zooplankton 0. order dependency of grazing on

plankton

Zooplankton 1. order dependency of grazing on

plankton

Edible fraction of Flagellate

Unit

-1

Type*)

n.u.

°C

n.u.

kgrm

n.u.

kgrs

kedib1

kedib2

n.u.

103

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DHI 3 Algae and Sediment Model

Name

kedib3

PC1

PC2

PC3

Comment

Edible fraction of Flagellate

Flagellate C

Diatom C

Cyanobacteria C

Unit

n.u.

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mnl1: Nutrient dependent death factor, flagellate,

n.u.

The death factor is 1 with flagellate having high internal N:C and P:C ratios, but up to 5 in

a nutrient stressed condition ( low N:C and P:C ratios).

��

(3.279)

Where:

Name

myn1

myp1

Comment

Nitrogen function flagellate

Phosphorous function flagellate

Unit

n.u

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mnl2: Nutrient dependent death factor, diatoms,

n.u.

The death factor is 1 with diatoms having high internal N:C, P:C and Si:C ratios, but up to

5 in a nutrient stressed condition ( low N:C, P:C or Si:C ratios).

��

(3.280)

Where:

Name

myn2

myp2

mys2

Comment

Nitrogen function diatoms

Phosphorous function diatoms

Si function, diatoms

Unit

n.u

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

104

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Mathematical Formulations

mnl3: Nutrient dependent death factor, cyanobacteria, n.u.

The death factor is 1 with cyanobacteria having high internal N:C and P:C ratios, but up to

5 in a nutrient stressed condition ( low N:C and P:C ratios).

��

(3.281)

Where:

Name

myn3

myp3

Comment

Nitrogen function cyanobacteria

Phosphorous function cyanobacteria

Unit

n.u

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mntp1: N, P & temperature corrected max. net growth rate, flagellates d

��

=��

∗

��

Unit

n.u.

-1

(3.282)

Where:

Name

myte1

myn1

myp1

Comment

Specific growth ,temperature regulated, flagellates

Nitrogen function flagellates

Phosphorous function flagellates

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

105

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mntp2: N, P & temperature corrected max. net growth rate, diatoms d

��

=��

∗

��

Unit

n.u.

-1

(3.283)

Where:

Name

myte2

myn2

myp2

mys2

Comment

Specific growth ,temperature regulated, diatoms

Nitrogen function diatoms

Phosphorous function diatoms

Silicate function diatoms

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mntp3: N, P & temperature corrected max. net growth rate, cyanobacteria d

��

=��

∗

��

Unit

n.u.

-1

(3.284)

Where:

Name

myte3

myn3

myp3

Comment

Specific growth ,temperature regulated, cyanobacteria

Nitrogen function cyanobacteria

Phosphorous function cyanobacteria

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mspc1: Sedimentation rate flagellate phytoplankton, d

-1

The sedimentation of a particle is not allowed to pass through several water layers in one

time step (DT

day

time step in d). The sedimentation in one times step is therefore

restricted to a maximum of dz. This is valid for ECO Lab version 2011 and earlier.

��

⁡ ��

∗

⁡ ��

��

⁡

�� ⁡

(3.285)

This restriction may lead to an underestimation of sedimentation in 3D set-ups with a fine

vertical resolution using small dz. However, by not imposing the above restriction in

sedimentation will potentially generate mass balance errors.

106

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Mathematical Formulations

Where:

Name

seve1

day

Comment

Sedimentation rate flagellate

time step (and not HD time step!) in days

Height of actual water layer

Unit

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mspc2: Sedimentation rate diatom phytoplankton, d

-1

The sedimentation of a particle is not allowed to pass through several water layers in one

time step (DT

day

time step in d). The sedimentation in one times step is therefore

restricted to a maximum of dz. This is valid for ECO Lab version 2011 and earlier.

��

⁡ ��

∗

⁡ ��

��

⁡

�� ⁡

(3.286)

This restriction may lead to an underestimation of sedimentation in 3D set-ups with a fine

vertical resolution using small dz. However, by not imposing the above restriction in

sedimentation will potentially generate mass balance errors.

Where:

Name

seve2

day

Comment

Sedimentation rate diatoms

time step (and not HD time step!) in days

Height of actual water layer

Unit

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mspc3: Sedimentation rate cyanobacteria, d

-1

The sedimentation of a particle is not allowed to pass through several water layers in one

time step (DT

day

time step in d). The sedimentation in one times step is therefore

restricted to a maximum of dz. This is valid for ECO Lab version 2011 and earlier.

��

⁡ ��

∗

⁡ ��

��

⁡

�� ⁡

(3.287)

This restriction may lead to an underestimation of sedimentation in 3D set-ups with a fine

vertical resolution using small dz. However, by not imposing the above restriction in

sedimentation will potentially generate mass balance errors.

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DHI 3 Algae and Sediment Model

Where:

Name

seve3

day

Comment

Sedimentation rate cyanobacteria

time step (and not HD time step!) in days

Height of actual water layer

Unit

-1

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myfi1: Light function Flagellate, n.u.

Equation (3.288) is an analytical solution of the integrated light available for production of

flagellates in the water column.

Where:

�� = ��

��

∗

−

/ ��

Where:

Name

zk1

��

− �� ∗

(3.288)

Comment

Light availability flagellate production

Unit

mol photon

-2 -1

m d

-1

Type*)

ik1

eta

Light saturation flagellate temperature corrected

Vertical light attenuation

Photosynthetic Active Light (PAR) of layer

Height of actual layer

mol photon

-2 -1

m d

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myfi2: Light function diatom, n.u.

Equation (3.289) is an analytical solution of the integrated light available for production of

flagellates in the water column.

�� = ��

��

∗

− �� ∗

−

− �� ∗

/ ��

(3.289)

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Mathematical Formulations

Where:

Name

zk2

Comment

Light availability diatom production

Unit

mol photon

-2 -1

m d

-1

Type*)

ik2

eta

Light saturation diatome temperature corrected

Vertical light attenuation

Photosynthetic Active Light (PAR) of layer

Height of actual layer

mol photon

-2 -1

m d

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myfi3: Light function cyanobacteria, n.u.

Equation (3.290) is an analytical solution of the integrated light available for production of

flagellates in the water column.

�� = ��

��

∗

− �� ∗

Where:

Name

zk3

−

− �� ∗

/ ��

(3.290)

Comment

Light availability cyanobacteria production

Unit

mol photon

-2 -1

m d

-1

Type*)

ik3

eta

Light saturation cyanobacteria temp. corrected

Vertical light attenuation

Photosynthetic Active Light (PAR) of layer

Height of actual layer

mol photon

-2 -1

m d

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

myn1: Nitrogen function flagellates, n.u.

��

�� / �� − ��

�� − ��

Comment

Flagellate phytoplankton C

Flagellate phytoplankton N

Minimum N:C ratio in phytoplankton

Maximum N:C ratio in phytoplankton

(3.291)

Where:

Name

PC1

PN1

pnmi

pnma

Unit

gCm

gNm

-3

Type*)

-1

-3

gNgC

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myn2: Nitrogen function Diatoms, n.u.

��

− �� ∗

��

�� − �� ∗

��

Unit

gCm

gNm

-3

(3.292)

Where:

Name

PC2

PN2

psmi

pnsi

pnma

Comment

Diatom phytoplankton C

Diatom phytoplankton N

Minimum Si:C ratio in diatoms

Minimum N:Si ratio in diatoms

Maximum N:C ratio in phytoplankton

Type*)

-1

-3

g Si g C

g N g Si

gNgC

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myn3: Nitrogen function cyanobacteria, n.u.

��

�� / �� − ��

�� − ��

(3.293)

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Mathematical Formulations

Where:

Name

PC3

PN3

pnmi

pnma

Comment

Cyanobacteria C

Cyanobacteria N

Minimum N:C ratio in phytoplankton / cyanobacteria

Maximum N:C ratio in phytoplankton / cyanobacteria

Unit

gCm

gNm

-3

Type*)

-1

-3

gNgC

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myp1: Phosphorous function flagellates, n.u.

��

Where:

Name

PC1

PP1

ppmi

ppma

�� −

�� ∗

��

−

��

(3.294)

Comment

Flagellate phytoplankton C

Flagellate phytoplankton P

Minimum P:C ratio in phytoplankton

Maximum P:C ratio in phytoplankton

Half saturation concentration for phytoplankton P

Unit

gCm

gPm

-3

Type*)

-1

-3

gPgC

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myp2: Phosphorous function diatoms, n.u.

��

Where:

Name

PC2

PP2

ppmi

�� −

�� ∗

��

−

��

(3.295)

Comment

Flagellate phytoplankton C

Flagellate phytoplankton P

Minimum P:C ratio in phytoplankton

Unit

gCm

gPm

-3

Type*)

-1

-3

gPgC

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DHI 3 Algae and Sediment Model

Name

ppma

Comment

Maximum P:C ratio in phytoplankton

Half saturation concentration for phytoplankton P

Unit

gPgC

-1

Type*)

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myp3: Phosphorous function cyanobacteria, n.u.

��

Where:

Name

PC3

PP3

ppmi

ppma

p3pma

p3pmi

��

�� −

∗

�� +

�� ∗

�� −

��

∗

�� ∗

�� +

��

−

��

(3.296)

Comment

Cyanobacteria C

Cyanobacteria P

Minimum P:C ratio in phytoplankton

Maximum P:C ratio in phytoplankton

Half saturation conc. for phytoplankton

Maximum P:C ratio in cyanobacteria

Minimum P:C ratio in cyanobacteria

Unit

gCm

gPm

-3

Type*)

-1

-3

gPgC

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

mys2: Si function, diatoms, n.u

��

−

��

�� +

��

(3.297)

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Mathematical Formulations

Where:

Name

PC2

PSi2

psmi

psma

Comment

Diatom phytoplankton C

Diatom phytoplankton Si

Minimum Si:C ratio in diatoms

Maximum Si:C ratio in diatoms

Unit

gCm

-3

Type*)

-1

g Si m

-3

g Si g C

-1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myte1: Flagellate specific temperature corrected growth, d

��

=�� ∗

−

-1

(3.298)

Where:

Name

mym1

tet1

Comment

Max. specific net growth at 20 °C, flagellates

Ɵ value in Arrhenius relation, flagellate temp. relation

Temperature

Unit

-1

Type*)

n.u.

°C

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myte2: Diatom specific temperature corrected growth, d

-1

Smoot_T is a function that makes a smoothing or rolling average of the daily surface

insolation (PAR) over a number of days (T2

days

) defined by the user, see auxiliary

Smoot_T, Equation (3.318). This smoothing or rolling average is used to adjust the

reference temperature of the max. specific growth rate of the diatoms.

The seasonal variation of temperature in the water follow the seasonal variation of the

light (PAR) with a delay (1 month) depending of the amount of water (depth) to be heated

up. In spring the temperature will be low compared to the daily PAR doze whereas in fall

the temperature will be high compared to the daily PAR doze. The diatom reference

temperature therefor has to change over the season.

In spring the diatoms blooms at low temperatures and disappear when the silicate is used

up. During summer some silicate will be available however the diatom community has

changed and another higher reference temperature is needed. In fall a secondary diatom

bloom is sometimes seen after the erosion of the pycnocline. The diatom community is

again adapted to lower temperatures and decreasing PAR.

Introducing Smoot_T is an attempt to make a seasonal adjustment of the specific growth

with the water temperature and light as forcing.

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DHI 3 Algae and Sediment Model

Where:

Name

mym2

tet2

��

=�� ∗

Comment

− −

��_

(3.299)

Unit

-1

Type*)

Max. specific net growth at 6-10 °C, Diatoms

Ɵ value in Arrhenius relation, diatom temp. relation

Correction of reference temp. for diatoms

Temperature

n.u.

°C

Smoot_T

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

myte3: Cyanobacteria specific temperature corrected growth, d

��

=�� ∗

−

-1

(3.300)

Where:

Name

mym3

Comment

Max. specific net growth at 20 °C, cyanobacteria

Ɵ value in Arrhenius relation, cyanobacteria temp.

relation

Temperature

Unit

-1

Type*)

tet3

n.u.

°C

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

nfix1: Function for N fixation (1 if PSU≤12 else 0), n.u.

�� =

⁡��

⁡ �� ⁡ ⁡

�� ⁡

(3.301)

Where:

Name

Comment

Salinity

Unit

PSU

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

nfix2: Function for N fixation (1 if 0≤PSU≤10 else 0-1),

n.u.

�� =

⁡�� ≥

⁡ �� ⁡

−

��−

−

⁡

�� ⁡

(3.302)

Where:

Name

Comment

Salinity

Unit

PSU

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

pn1pc1: N:C ration flagellates g N g C

��

-1

(3.303)

Where:

Name

PN1

PC1

Comment

Flagellate phytoplankton N

Flagellate phytoplankton C

Unit

gNm

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

pn2pc2: N:C ration diatomes g N g C

��

-1

(3.304)

Where:

Name

PN2

PC2

Comment

Diatom phytoplankton N

Diatom phytoplankton C

Unit

gNm

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

pn3pc3: N:C ration cyanobacteria g N g C

��

-1

(3.305)

Where:

Name

PN3

PC3

Comment

Cyanobacteria N

Cyanobacteria C

Unit

gNm

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

powNP1: Power function for limiting nutrient, Flagellate (PC1), n.u.

See under auxiliary sed1, Equation (3.18).

powNP3: Power function for limiting nutrient, cyanobacteria (PC3), n.u.

See under auxiliary sed3, Equation (3.29).

pp1pc1: P:C ration flagellates g P g C

��

Comment

Flagellate phytoplankton P

Flagellate phytoplankton C

Unit

gPm

-3

-1

(3.306)

Where:

Name

PP1

PC1

Type*)

gCm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

pp2pc2: P:C ration diatomes g P g C

��

-1

(3.307)

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Mathematical Formulations

Where:

Name

PP2

PC2

Comment

Diatom phytoplankton P

Diatom phytoplankton C

Unit

gPm

-3

Type*)

gCm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

pp3pc3: P:C ration cyanobacteria g P g C

��

Comment

Cyanobacteria P

Cyanobacteria C

-1

(3.308)

Where:

Name

PP3

PC3

Unit

gPm

-3

Type*)

gCm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

psi2pc2: Si:C ration diatomes g Si g C

��

-1

(3.309)

Where:

Name

PSi2

PC2

Comment

Diatom Si

Diatom phytoplankton C

Unit

g Si m

gCm

-3

Type*)

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

rd: Relative daylength, f(month, day,latitude), n.u.

A built in function in ECO Lab that returns a value for relative day length. The value

equals 1 at equinox (when day and night have same length).

�� _ ��

��

�� ⁡�� ℎ,

��

(3.310)

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DHI 3 Algae and Sediment Model

sedbouNP1: sedimentation & buoyance N&P function, Flagellate, n.u

Please see auxiliary sed1, Equation (3.18), or buoy1, Equation (3.19)

sedbouNP3: sedimentation & buoyance N&P function, cyanobacteria, n.u

Please see auxiliary sed3, Equation (3.29), or buoy3, Equation (3.30).

sed1: N&P sedimentation function, Flagellate, n.u.

The sedimentation (downward movement) of the algae is increased by low internal N/C

and P/C ratios of the algae. powNP1 will be positive but small and sedbuoNP1 becomes

negative resulting in a positive value of sed1, see Figure 3.3, under auxiliary buoy1.

��

,−

��

(3.311)

Where:

And:

��

�� ∗

��

Where:

Name

k1NP

K2NP

k3NP

��

,��

��

�� + ��

��

− .

(3.312)

(3.313)

Comment

Exponent, sedimentation& buoyancy, PC1&PC3

Factor for sedimentation & buoyancy, PC1 & PC3

Shift from sedimentation to buoyancy, PC1 & PC3

Power function for limiting nutrient, Flagellate (PC1)

Nitrogen function flagellates

Phosphorous function flagellates

Unit

n.u.

Type*)

powNP1

myn1

myp1

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

Sed3: N&P sedimentation function, cyanobacteria, n.u.

The sedimentation (downward movement) of the bacteria is increased by low internal N/C

and P/C ratios of the bacteria. powNP3 will be positive but small and sedbuoNP3

becomes negative resulting in a positive value of sed3, see Figure 3.4 under auxiliary

buou3.

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Mathematical Formulations

Where:

��

,−

�� ∗

��

(3.314)

And:

Where:

Name

k1NP

K2NP

k3NP

��

,��

��

�� + ��

��

− .

(3.315)

(3.316)

Comment

Exponent, sedimentation& buoyancy, PC1&PC3

Factor for sedimentation & buoyancy, PC1 & PC3

Shift from sedimentation to buoyancy, PC1 & PC3

Power function for limiting nutrient, cyanobacteria

(PC3)

Nitrogen function cyanobacteria

Phosphorous function cyanobacteria

Unit

n.u.

Type*)

powNP3

myn3

myp3

n.u.

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

SIPm3: PO

-P in pore water, g P m

��

�� =

��

− �� ∗ ��∗

-3

(3.317)

Where:

Name

SIP

Kds

Comment

Sediment PO

-P pool

Sediment dry matter

Sediment bulk density

Depth of modelled sediment layer

Unit

gPm

-2

Type*)

-1

g DM gWW

g ww cm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

Smoot_T: Correction of reference temperature for diatoms, °C

Smoot_T is a function that makes a smoothing or rolling average of the daily insolation

(PAR) on surface over a number of days (T2

days

) defined by the user. This smoothing or

rolling average is used to adjust the reference temperature of the max. specific growth

rate of the diatoms, see auxiliary

myte2,

Equation (3.299).

The seasonal variation of temperature in the water follow the seasonal variation of the

light (PAR) with a delay (1 month) depending of the amount of water (depth) to be heated

up. In spring the temperature will be low compared to the daily PAR doze whereas in fall

the temperature will be high compared to the daily PAR doze. The diatom reference

temperature therefor has to change over the season.

In spring the diatoms blooms at low temperatures and disappear when the silicate is used

up. During summer some silicate will be available however the diatom community has

changed and another higher reference temperature is needed. In fall a secondary diatom

bloom is sometimes seen after the erosion of the pycnocline. The diatom community is

again adapted to lower temperatures and decreasing PAR.

Introducing Smoot_T is an attempt to make a seasonal adjustment of the specific growth

with the water temperature and light as forcing.

One of two builtin functions can be used SMOOTING_AVERAGE or MOVING_AVERAGE

can be used, see (MIKE by DHI 2011b). The latter function demands more memory and

increases the CPU time slightly.

�� _ =

��

∗��

�� _��

��

�� ,

(3.318)

Where:

Name

difT2

Comment

Max variation in reference temp., diatom production

Unit

°C

mol photon

-2 -1

m d

mol photon

-2 -1

m d

Type*)

maxI

Max average monthly i

of year (July or Jan.)

day

days

Light (PAR) at surface

AD time step in days, (normally between 5 min. to 1 h)

No. of days in smoothing or rolling average function

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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Mathematical Formulations

SNHm3: NH4-N in sediment pore water, g N m

�� =

��

− �� ∗ ��∗

-3

(3.319)

Where:

Name

SNH

Kds

Comment

Sediment NH

-N pool

Sediment dry matter

Sediment bulk density

Depth of modelled sediment layer

Unit

gNm

-2

Type*)

-1

g DM gWW

g ww cm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

SNO3m3: NO

-N in pore water of surface sediment layer (0-KDO2) , g N m

��

�� =

��

− �� ∗ ��∗

(3.320)

Where:

Name

SNO3

KDO2

Comment

Sediment NO

-N pool

Sediment dry matter

Sediment bulk density

Depth of O

penetration in sediment

Unit

gNm

-2

Type*)

-1

g DM gWW

g ww cm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

sqdo: Oxygen function, n.u.

��=

+��

Comment

Oxygen

Exponent for DO in sqdo

Half-saturation constant DO

Unit

g O

n.u.

g O

-3

(3.321)

Where:

Name

ndo3

mdo3

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

zk1: Light penetration (availability) in actual layer for flagellate production, m

��

��,

��

ln �� − ln ��

(3.322)

Where:

Name

Comment

Unit

mol photon

-2 -1

m d

mol photon

-2 -1

m d

-1

Type*)

Light (PAR) in actual layer

ik1

eta

Light saturation temp. corrected, Flagellate

Vertical light extinction in layer

Height of actual water layer

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

zk2: Light penetration (availability) in actual layer for diatom production, m

��

��,

��

ln �� − ln ��

(3.323)

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Mathematical Formulations

Where:

Name

Comment

Unit

mol photon

-2 -1

m d

mol photon

-2 -1

m d

-1

Type*)

Light (PAR) in actual layer

Ik2

eta

Light saturation temp. corrected, diatoms

Vertical light extinction in layer

Height of actual water layer

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

zk3: Light penetration (availability) in actual layer for cyanobacteria production, m

��

��,

��

ln �� − ln ��

(3.324)

Where:

Name

Comment

Unit

mol photon m

2 -1

mol photon m

2 -1

-1

Type*)

Light (PAR) in actual layer

Ik3

eta

Light saturation temp. corrected, cyanobacteria

Vertical light extinction in layer

Height of actual water layer

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

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DHI 3 Algae and Sediment Model

unh1: potential NH

uptake by flagellates, g N m d

ℎ = �� ∗��

ℎ∗

��

�� + ℎ

ℎ

-3

-1

(3.325)

Where:

Name

PC1

Comment

Flagellate C

Max. N uptake by phytoplankton during N limitation

Half-saturation constant for NH

, phytoplankton uptake

-N in water

Unit

gCm

-3

Type*)

-1 -1

maxupnh

hupnh

NH4

gNgC d

gNm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

unh2: potential NH

uptake by diatoms, g N m d

ℎ = �� ∗

∗��

ℎ∗

��

�� + ℎ

ℎ∗

-3

-1

(3.326)

Where:

��

(3.327)

And:

Where:

Name

PC2

��

(3.328)

Comment

Diatom C

Max. N uptake by flagellates during N limitation

Half-saturation constant for NH

, phytoplankton uptake

-N in water

Ratio, nutrient uptake, Diatom : Flagellate

Ratio, half saturation conc. Diatom: Flagellate

Equivalent spherical diameter, flagellates

Unit

gCm

-3

Type*)

-1 -1

maxupnh

hupnh

NH4

pda2

pdb2

esd1

gNgC d

gNm

n.u.

μm

-3

124

ECO Lab Template - © DHI

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Mathematical Formulations

Name

esd2

kbet1

kbet2

Comment

Equivalent spherical diameter, Diatom

Exponent 1 for potential uptake of nutrients

Exponent 2 for half saturation conc.

Unit

μm

n.u.

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

unh3: Potential NH4 uptake by cyanobacteria, g N m d

ℎ = �� ∗

∗��

ℎ∗

��

�� + ℎ

ℎ∗

-3

-1

(3.329)

Where:

��

(3.330)

And:

Where:

Name

PC3

��

(3.331)

Comment

Cyanobacteria C

Max. N uptake by flagellates during N limitation

Half-saturation constant for NH

, phytoplankton uptake

-N in water

Ratio, nutrient uptake, Cyanobacteria : Flagellate

Ratio, half saturation conc. Cyanobacteria: Flagellate

Equivalent spherical diameter, flagellates

Equivalent spherical diameter, Cyanobacteria

Exponent 1 for potential uptake of nutrients

Exponent 2 for half saturation conc.

Unit

gCm

-3

Type*)

-1 -1

maxupnh

hupnh

NH4

pda3

pdb3

esd1

esd3

kbet1

kbet2

gNgC d

gNm

n.u.

μm

n.u.

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

un31: Potential NO

uptake by flagellate, g N m d

-3

-1

125

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DHI 3 Algae and Sediment Model

Where:

Name

PC1

= �� ∗��

∗

��

+ℎ

Unit

g C m-3

gNgC d

gNm

-3

-1 -1

(3.332)

Comment

Flagellate C

Max. NO3 uptake by phytoplankton during N limitation

Half-saturation constant for NO3, phytoplankton uptake

NO3-N in water

Type*)

maxupn3

hupnh3

NO3

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

un32: Potential NO

uptake by diatoms, g N m d

= �� ∗

∗��

∗

��

+ℎ

∗

-3

-1

(3.333)

Where:

��

(3.334)

And:

Where:

Name

PC2

��

(3.335)

Comment

Diatom C

Max. NO

uptake by flagellates during N limitation

Half-saturation constant for NO

, phytoplankton uptake

-N in water

Ratio, nutrient uptake, Diatom : Flagellate

Ratio, half saturation conc. Diatom: Flagellate

Equivalent spherical diameter, flagellates

Equivalent spherical diameter, Diatom

Unit

gCm

-3

Type*)

-1 -1

maxupn3

hupn3

NO3

pda2

pdb2

esd1

esd2

gNgC d

gNm

n.u.

μm

-3

126

ECO Lab Template - © DHI

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Mathematical Formulations

Name

kbet1

kbet2

Comment

Exponent 1 for potential uptake of nutrients

Exponent 2 for half saturation conc.

Unit

n.u.

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

un33: Potential NH

uptake by cyanobacteria, g N m d

= �� ∗

∗��

∗

��

+ℎ

∗

-3

-1

(3.336)

Where:

And:

Where:

Name

PC3

��

(3.337)

(3.338)

Comment

Cyanobacteria C

Max. NO

uptake by flagellates during N limitation

Half-saturation constant for NO

, phytoplankton uptake

-N in water

Ratio, nutrient uptake, Cyanobacteria : Flagellate

Ratio, half saturation conc. Cyanobacteria: Flagellate

Equivalent spherical diameter, flagellates

Equivalent spherical diameter, Cyanobacteria

Exponent 1 for potential uptake of nutrients

Exponent 2 for half saturation conc.

Unit

gCm

-3

Type*)

-1 -1

maxupn3

Hupn3

NO3

pda3

pdb3

esd1

esd3

kbet1

kbet2

gNgC d

gNm

n.u.

μm

n.u.

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

127

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DHI 3 Algae and Sediment Model

upo1: Potential PO

uptake by flagellate, g P m d

�� = �� ∗��

�� ∗

+ℎ

-3

-1

(3.339)

Where:

Name

PC1

Comment

Flagellate C

Max. P uptake by phytoplankton during P limitation

Half-saturation constant for PO

, phytoplankton uptake

-P in water

Unit

gCm

-3

Type*)

-1 -1

maxupip

hupip

PO4

gPgC d

gPm

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

upo2: Potential PO

uptake by diatoms, g P m d

�� = �� ∗

∗��

�� ∗

+ℎ

∗

-3

-1

(3.340)

Where:

��

(3.341)

And:

Where:

Name

PC2

��

(3.342)

Comment

Diatom C

Max. PO

uptake by flagellates during P limitation

Half-saturation constant for PO

, phytoplankton uptake

-P in water

Ratio, nutrient uptake, Diatom : Flagellate

Ratio, half saturation conc. Diatom: Flagellate

Equivalent spherical diameter, flagellates

Unit

gCm

-3

Type*)

-1 -1

maxupip

hupp

PO4

pda2

pdb2

esd1

gPgC d

gPm

n.u.

μm

-3

128

ECO Lab Template - © DHI

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Mathematical Formulations

Name

esd2

kbet1

kbet2

Comment

Equivalent spherical diameter, Diatom

Exponent 1 for potential uptake of nutrients

Exponent 2 for half saturation conc.

Unit

μm

n.u.

Type*)

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

upo3: Potential PO

uptake by cyanobacteria, g P m d

�� = �� ∗

∗��

�� ∗

+ℎ

∗

-3

-1

(3.343)

Where:

��

(3.344)

And:

��

(3.345)

Where:

Name

PC3

Comment

Cyanobacteria C

Max. PO

uptake by flagellates during P limitation

Half-saturation constant for PO

, phytoplankton uptake

-P in water

Ratio, nutrient uptake, Cyanobacteria : Flagellate

Ratio, half saturation conc. Cyanobacteria: Flagellate

Equivalent spherical diameter, flagellates

Equivalent spherical diameter, Cyanobacteria

Exponent 1 for potential uptake of nutrients

Exponent 2 for half saturation conc.

Unit

gCm

-3

Type*)

-1 -1

maxupip

hupp

PO4

pda3

pdb3

esd1

esd3

kbet1

kbet2

gPgC d

gPm

n.u.

μm

n.u.

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

129

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DHI 3 Algae and Sediment Model

usi2: Potential Si uptake by diatoms, g Si m d

�� = �� ∗��

��∗

��

�� + ℎ

��

-3

-1

(3.346)

Where:

Name

PC2

�� = �� − ��

Comment

Flagellate C

(3.347)

Unit

gCm

-3

Type*)

-1 -1

maxupsi

hupsi

Max. Si uptake by phytoplankton during Si limitation

Half-saturation constant for Si, diatom uptake

available Si for diatoms, (Si-Simin) >=0, Si for uptake

PC2

Si in water

Si not available for PC2

g Si g C d

g Si m

-3

Six

Simin

g Si m

-3

S: State variable, F: Forcing, C: Constant, P: Process in differential equation, P1: Help process,

A: Auxiliary help process.

130

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Data Requirements

•

Basic Model Parameters

Model grid size and extent

Time step and length of simulation

Type of output required and its frequency

Bathymetry and Hydrodynamic Input

Combined Advection-Dispersion Model

Dispersion coefficients

Initial Conditions

Concentration of parameters

Boundary Conditions

Concentration of parameters

Pollution Sources

Discharge magnitudes and concentration of parameters

Process Rates

Size of coefficients governing the process rates. Some of these coefficients can

be determined by calibration. Others will be based on literature values or found

from actual measurements and laboratory tests.

Forcings

Data sets of photosynthetic active light (PAR) (E/m /day)

•

131

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DHI 3 Algae and Sediment Model

132

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References

/1/

/2/

/3/

/4/

/5/

Droop M.R. 1973. Some thoughts on nutrient limitation in algae. J. Phycol. 9

P:264-272.

Droop M.R. 1975. The nutrient status of algae cells in bach cultures. J. Mar.

Biol. Ass. U.K. 55 P:541-555.

Effer S.W. 1988. Secchi disk transparency and turbidity. Journal of

environmental engineer-ing. 1988 vol. 114 no. 6 pp. 1436-1447.

Kirk J.T.O. 2000. Light and photosynthesis in aquatic ecosystems. Cambridge

University Press 2. Edition 2000. ISBN 0521453534, ISBN 052145459664

Lund-Hansen L.C. 2004. Diffuse attenuation coefficients Kd(PAR) at estuarine

North Sea-Baltic Sea transition: time-series, partitioning, absorption, and

scattering. Estuarine, Coastal and Shelf Science 61 (2004) pp:251-259.

MIKE by DHI 2011a. MIKE 21 & MIKE 3 Flow Model. Mud Transport module

Scientific Description. DHI water environment health, Hørsholm Denmark

MIKE by DHI 2011b. ECO Lab User guide. DHI water environment health,

Hørsholm Denmark

Monod J. 1949. The Growth of Bacterial Cultures. Annual Review of

Microbiology, v. 3, p. 371.

Morel A. 1980. In water and remote measurements of ocean color. Boundary-

Layer Meteor-ology 18 (1980) pp 177-201.

Nyholm N. 1977 Kinetics of phosphate-limited algae growth. Biotechn.

Bioengineering 19 P:467-492.

Nyholm N. 1978 A simulation model for phytoplankton growth cycling in

eutrophic shallow lakes. Ecological Modelling. Vol. 4, P:279-310.

Nyholm N. 1979 The use of management models for lakes at the Water Quality

Institute. Denmark. Ste

–of-the-art

in Ecological Modelling. Vol. 7. P:561-577.

Pfannkuche F. 2002. Optical properties of Otago Shelf Waters: South Island

New Zealand. Estuarine, Coastal and Shelf Science 55 (2002) pp:613-627.

Prieur L., S. Sathyendranath 1981. An optical classification of coastal and

oceanic waters based on the specific spectral absorption curves of

phytoplankton pigments, dissolved or-ganic matter, and other particulate

materials. Limnol. Oceanogr. 26(4) PP 671-689.

Rasmussen Erik Kock, O.S. Petersen, J.R. Thomsen, R. J. Flower, F. Aysche,

M. Kraiem, L. Chouba 2009. Model analysis of the future water quaity of the

eutrophicated Ghar EL Melh lagoon (Northern Tunesia). Hydrobiologia (2009)

622:173-193

Tett P., A. Edvards & K. Jones 1986. A model for the growth of shelf-sea

phytoplankton in summer. Estuar. Coast. Shelf Sci. 23 P:641-672.

/6/

/7/

/8/

/9/

/10/

/11/

/12/

/13/

/14/

/15/

/16/

133

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DHI 3 Algae and Sediment Model

134

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ECO Lab

Short Scientific Description

MIKE

2016

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PLEASE NOTE

This document refers to proprietary computer software which is pro-

tected by copyright. All rights are reserved. Copying or other repro-

duction of this manual or the related programs is prohibited without

prior written consent of DHI. For details please refer to your 'DHI

Software Licence Agreement'.

The liability of DHI is limited as specified in Section III of your 'DHI

Software Licence Agreement':

'IN NO EVENT SHALL DHI OR ITS REPRESENTATIVES

(AGENTS AND SUPPLIERS) BE LIABLE FOR ANY DAMAGES

WHATSOEVER INCLUDING, WITHOUT LIMITATION, SPECIAL,

INDIRECT, INCIDENTAL OR CONSEQUENTIAL DAMAGES OR

DAMAGES FOR LOSS OF BUSINESS PROFITS OR SAVINGS,

BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMA-

TION OR OTHER PECUNIARY LOSS ARISING OUT OF THE

USE OF OR THE INABILITY TO USE THIS DHI SOFTWARE

PRODUCT, EVEN IF DHI HAS BEEN ADVISED OF THE POSSI-

BILITY OF SUCH DAMAGES. THIS LIMITATION SHALL APPLY

TO CLAIMS OF PERSONAL INJURY TO THE EXTENT PERMIT-

TED BY LAW. SOME COUNTRIES OR STATES DO NOT ALLOW

THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSE-

QUENTIAL, SPECIAL, INDIRECT, INCIDENTAL DAMAGES AND,

ACCORDINGLY, SOME PORTIONS OF THESE LIMITATIONS

MAY NOT APPLY TO YOU. BY YOUR OPENING OF THIS

SEALED PACKAGE OR INSTALLING OR USING THE SOFT-

WARE, YOU HAVE ACCEPTED THAT THE ABOVE LIMITATIONS

OR THE MAXIMUM LEGALLY APPLICABLE SUBSET OF THESE

LIMITATIONS APPLY TO YOUR PURCHASE OF THIS SOFT-

WARE.'

PRINTING HISTORY

November 2003

June 2004

April 2006

...

September 2012

October 2013

July 2015

LIMITED LIABILITY

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ECO Lab - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

CONTENTS

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Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

What Is Behind ECO Lab?

. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

ECO Lab Set of Ordinary Differential Equations

. .

3.1

Special handling of settling process

. . . . . . . . .

3.2

Special handling of light penetration in ECO Lab

. .

3.3

Handling of built-in constants and forcings

. . . . .

3.4

Handling of site specific processes

. . . . . . . . .

3.5

Example of ordinary ECO Lab differential equation:

Integration Methods

. . . . . . . . . . . . . .

5.1

Euler integration method

. . . . . . . . . .

5.2

Runge Kutta 4th order

. . . . . . . . . . .

5.3

Runge Kutta 5th order with quality check

. .

Integration With AD Engines

. . . . . . . . . . . . . . . . . . . . . . . . . 15

ECO Lab - © DHI

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Introduction

ECO Lab is a piece of numerical simulation software for Ecological Modelling

developed by DHI. It is an open and generic tool for customising aquatic eco-

system models to simulate for instance water quality, eutrophication, heavy

metals and ecology.

ECO Lab functions as a module in the MIKE simulation software.

The module is developed to describe processes and interactions between

chemical and ecosystem state variables. Also the physical process of sedi-

mentation of state variables can be described (moves the state variable phys-

ically down the water column).

The module is coupled to the Advection-Dispersion Modules of the DHI

hydrodynamic flow models, so that transport mechanisms based on advec-

tion-dispersion can be integrated in the ECO Lab simulation.

The description of the ecosystem state variables in ECO Lab is formulated as

a set of ordinary coupled differential equations describing the rate of change

for each state variable based on processes taking place in the ecosystem. All

information about ECO Lab state variables, processes and their interaction

are stored in a so-called generic ECO Lab template.

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Introduction

ECO Lab - © DHI

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What Is Behind ECO Lab?

ECO Lab uses a so-called ECO Lab COM

(1)

object to perform the ECO Lab

calculations. The ECO Lab object is generic and shared with a number of dif-

ferent DHI flow model systems. It consists of an interpreter that first translates

the equation expressions in the ECO Lab template

(2)

to lists of instructions

that enables the object to evaluate all the expressions in the template. During

simulation the model system integrates one time step by simulating the trans-

port of advective state variables based on hydrodynamics. Initial concentra-

tions or updated AD concentrations, coefficients/constants and updated

forcing functions are loaded into the ECO Lab object and then the ECO Lab

object evaluates all the expressions, integrates one time step, and returns

updated concentration values to the general flow model system that

advances one time step. An illustration of the data flow is shown in

Figure 2.1.

Figure 2.1

Data flow between the hydrodynamic flow model, in this case MIKE 3,

and ECO Lab.

1 Microsoft COM standard

2 An ECO Lab template contains the mathematical definition of an ECO Lab model. It contains information about

the included state variables, constants, forcings, processes and the state variables' rate-of-change differential

equations.

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What Is Behind ECO Lab?

ECO Lab - © DHI

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ECO Lab Set of Ordinary Differential Equations

In general an ordinary differential equation is specified for each state variable.

The ordinary differential equation summaries the processes involved for the

specific state variable. If a process affect more than one state variable, or the

state variables affect each other, the differential equations are said to be cou-

pled with each other.

The processes contain mathematical expressions using arguments such as

numbers, constants, forcings and state variables. Processes always describe

the rate at which something changes. In this context constants are values

always constant in time, and forcings are values that can be varying in time.

= ----- =



= 1

process

(3.1)

The concentration of the ECO Lab state variable

Number of processes involved for specific state variable

The Unit for ‘Rate of change’ of P

can be specified as 3 types:



g/m

mg/l/d

Undefined

In general the part of the unit that relates to time shall always be specified as

‘per day’ in the template.

In ECO Lab there are two kinds of processes: transformation and settling pro-

cesses. Transformation is a point description of a process not dependent on

neighbouring points. Settling is a process transporting state variables to

neighbouring points down the water column. The calculation of a state varia-

ble with a settling process is therefore dependent on information from neigh-

bouring points. Also, the light forcing needs special handling to calculate the

light penetration in the water column. A special built-in function can be used

for this purpose. ECO Lab can also handle that some processes only take

place at specific positions in the water column. For instance should reaeration

(exchange with the atmosphere) only take place in the water surface. In other

parts of the water column the reaeration is not active.

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ECO Lab Set of Ordinary Differential Equations

3.1

Special handling of settling process

The calculation of vertical movements need information from the layer below

or above in multi layered systems. It is possible to in ECO Lab to specify one

type of process with vertical movement: settling. This process is transporting

the state variable vertically towards the bottom. As for transformation pro-

cesses an expression must be specified describing the ‘concentration

change’ from actual cell to cell below [mg/l/d]. When looking at a ‘Settling’

process directly in output from an ECO Lab simulation the output will show

the result of the specified expression (the same as if it was a transformation

process). The difference between a ‘Settling’ and a ‘Transformation’ process

will appear in output of the affected state variable. This is because the numer-

ical solution of a state variable affected by a ‘Settling’ process is different than

if it was a ’Transformation’ process. The definition of sign for a settling pro-

cess is so that it should be specified as minus in the differential equation in

order to transport the state variable correctly down the water column. The

solution of a state variable with a settling process in a multilayered system

takes into account that a contribution to the state variable is received from the

layer above ( if not top layer). Any variation in vertical discretization is also

included in the numerical solution of differential equation involving a settling

process. When solving a differential equation containing a settling process,

ECO Lab substitutes the settling process expression in the differential equa-

tion with the following expression;

–

settling

– 1



– 1

settling



-------- = -------------------------------------------------------------------------------------------------

where



(3.2)



settling

n-1

is the userspecified expression for ‘rate of change’ of the state

variable concentration in layer n caused by a settling process transport-

ing from layer n-1 to layer n [g·m-3·d-1]. It is usually a function of the

concentration in layer n -1.

settling

is the userspecified expression for ‘rate of change’ of the state

variable concentration in layer n caused by a settling process transport-

ing from layer n to layer n+1 [g·m-3·d-1]. It is usually a function of the

concentration in layer n.

is the thickness of layer

[m] and

n-1

is the thickness of layer

n–1

[m].

ECO Lab - © DHI

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Special handling of light penetration in ECO Lab

Figure 3.1

Schematic illustration of settling process

3.2

Special handling of light penetration in ECO Lab

Light penetration in the water column can be solved with a Lambert Beer

built-in function in ECO Lab. In multi-layered systems with vertical varying

extinction coefficients, the Lambert Beer expression must be calculated for

each layer, and therefore, the Lambert Beer expression as argument uses

the result of the Lambert Beer expression in the layer above.

– 1







(3.3)

where

is the light available for primary production in the actual layer

n, I

n-1

is the irradiance in the layer above,



is the extinction coefficient and

the

layer thickness.

The way ECO Lab handles this problem is by using a so-called built-in func-

tion that is special designed to handle this ‘Lambert Beer’ problem. The func-

tions are called:



LAMBERT_BEER_1(surface radiation, layer height, light extinction coef-

ficient). The function returns the solar radiation in top of each layer of the

water column.

LAMBERT_BEER_2(surface radiation, layer height, light extinction coef-

ficient). The function returns the solar radiation in bottom of each layer of

the water column.

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ECO Lab Set of Ordinary Differential Equations

3.3

Handling of built-in constants and forcings

Forcings such as for instance temperature can be specified in different ways.

They can be user specified, as constant values or as timeseries, map series,

or volume series. As an alternative to using user specified values of con-

stants and forcings, it is also possible to use built-in forcing and constants.

Built-in constants and forcings can be picked from a list in the dialog and they

are already estimated in the hydrodynamic model, and they can be used as

arguments in ECO Lab expressions. During simulation the built-in forcings

and constants will be updated with the calculations in the hydrodynamic sim-

ulation. Examples of built-in forcings are temperature, flow velocities, salinity,

wind velocity.

3.4

Handling of site specific processes

Some processes only take place in specific layers of the water column, and

such processes are handled by calculating the process at the relevant layer

where the process takes place and setting the process to zero in other layers.

Examples of this could be a process such as re-aeration.

3.5

Example of ordinary ECO Lab differential equation:

Cyanide is assumed only to be affected by one temperature dependent decay

process in this simple example;

cyanide

---------------------- = –

decay

 



temperature

– 20





cyanide

Decay coefficient (day

-1

)

Arrhenius temperature coefficient



The scientific descriptions of specific ECO Lab differential equations and pro-

cess equations in DHI supported ECO Lab templates has a PDF file attached

containing scientific description of the template in question. For DHI projects

with tailor-made ECO Lab templates for specific projects, the scientific

description of the used ECO Lab equations typically will be described in the

project report.

ECO Lab - © DHI

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Example of ordinary ECO Lab differential equation:

Integration With AD Engines

The dynamics of advective ECO Lab state variables can be expressed by a

set of transport equations, which in non-conservative form can be written as:



----- +

----- =

------- +



(4.1)

u, v, w:

Dx, Dy,

Dz:

Sc:

Pc:

The concentration of the ECO Lab state variable

Flow velocity components

Dispersion coefficients

Sources and sinks

ECO Lab processes

The state variables may be coupled linearly or non-linearly to each other

through the ECO Lab source term P

The transport equation can be rewritten as



----- =



(4.2)

where the term AD

represents the rate of change in concentration due to

advection, dispersion (including sources and sinks).

The ECO lab numerical equation solver makes an explicit time-integration of

the above transport equations, when calculating the concentrations to the

next time step.

An approximate solution is obtained in ECO Lab by treating the advection-

dispersion term as AD

as constant in each time step.

The coupled set of ordinary differential equations defined in ECO Lab are

solved by integrating the rate of change due to both the ECO Lab processes

themselves and the advection-dispersion processes.

















(4.3)

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Integration With AD Engines

The advection-dispersion contribution is approximated by







–





= -------------------------------------------------



(4.4)

where the intermediate concentration c* is found by transporting the ECO

Lab state variable as a conservative substance over the time period

t

using

the AD module.

The main advantage of this approach is that the explicit approach resolve

coupling and non-linearity problems resulting from complex source ECO Lab

terms P

, and therefore the ECO Lab and the advection-dispersion part can

be treated separately.

An implicit approach of solving the transport equations is not possible yet in

ECO Lab.

ECO Lab - © DHI

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Euler integration method

Integration Methods

The following integration methods are available in ECO Lab: Euler, Runge

Kutta 4, Runge Kutta with quality check.

5.1

Euler integration method

A very simple numerical solution method for solving ordinary differential

equations.

The formula for the Euler method is:

+ 1









which advances a solution

from

n+1

(5.1)

5.2

Runge Kutta 4th order

A classical numerical solution method for solving ordinary differential equa-

tions. It has usually higher accuracy than the Euler method, but requires

longer simulation times. The fourth order Runge-Kutta method requires four

evaluations of the right hand side per time step.

+ 1

= rk4















The function is solved this way:













+ --



+ ----











+ --



+ ----















+ 1

+ ---- + ---- + ---- + ---- –





3 3 6

which advances a solution

from

n+1

(5.2)

(5.3)

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Integration Methods

5.3

Runge Kutta 5th order with quality check

A numerical solution method for solving ordinary differential equations. The

accuracy is evaluated and the time step is adjusted if results are not accurate

enough.

+ 1













 

yscale



The function is solved this way:

First take two half steps:

= 0.5



+ �½

= rk4















= rk4









+ �½



+ �½





Compare with one full time step:

= rk4















Then estimate error:

–

err =MAX



ABS



/yscale

 /

If the error is small (err <= 1.0) the function returns

+ 1

+ -----

which advances a solution

from

n+1

or else the time step is reduced and the function tries again.

(5.12)

(5.10)

(5.11)

(5.9)

(5.5)

(5.6)

(5.7)

(5.8)

(5.4)

ECO Lab - © DHI

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data flow

integration

. . . . . . . . . . . . . . . 9

. . . . . . . . . . . . . 17

light penetration . . . . . . . . . . . 13

process . . . . . . . . . . . . . . . 11

re-aeration

settling

. . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . 12

. . . . . . . . . 15

transport equation

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ECO Lab - © DHI

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Answers to expert

pa el ased o

uestio s f o the pa el to the esea he s

researchers from 16/8-2017 through an e-mail from Implement.

ade a aila le to the

General questions

Exclusive focus on reducing land-based N load to obtain good ecological status

Both the panel and the stakeholders miss a justification of the fundamental choice to focus exclusively on

reduction of (diffuse) N sources as the main means to improve water quality.

Comment:

We did not choose to focus exclusively on N reductions. The focus on nitrogen was a

consequence of the agreement with the authorities to focus on the intercalibrated quality element

indicators summer chlorophyll-and eelgrass depth limit (the latter described by the proxy-indicator K

Both the statistical and mechanistic models include N and P as well as several climatic factors known to

affect the parameters chlorophyll-a and K

. However, the modelling work showed that these included

indicators were most sensitive towards nitrogen reductions whereas reductions in phosphorous did not

significantly affect the indictors. Hence, we cannot document that phosphorous reductions will affect the

indicators

–

whereas we can document that nitrogen reductions will. Currently, a research project is trying

to identify P-sensitive indicators that could be included in a more holistic assessment of marine water

quality.

The situation is complex, as there is ample evidence that in many systems there is co-limitation of

phytoplankton growth by N and P, with some seasonal pattern in most systems.

Comment:

We agree, and we observe this seasonality in most estuaries and coastal Danish marine waters

as well, with P limitation in spring and N limitation during summer/autumn. This seasonality in N versus P

limitation in DK waters, and especially N limitation during summer, is supported by several studies (Hansen

2016), (Timmermann et al., 2010), (Carstensen et al., 2007), (Pedersen 1995), (Nielsen et al., 2002b),

(Møhlenberg et al., 2007). Although, we fully recognize the importance of P for water quality (in a broad

sense), we could not document P sensitivity for the applied indicators in most Danish water bodies covered

by the developed models.

In addition, N fixation in the Baltic may aggravate the problem and undo N reduction measures where

ample P is available. But it is also true that the N:P ratio of winter loadings is biased towards N, and that

historical reductions have affected P loadings much more than N loadings.

Comment:

Large occurrences of cyanobacteria in Danish waters are rare and limited to the southern part of

Øresund/western Baltic Sea properly due to the high salinity (>10 psu). Figure 1 (from Lyngsgaard PhD

thesis 2013) shows the contribution of cyanobacteria and other phytoplankton groups at three sites

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The figure show that cyanobacteria only occur in measureable numbers in The Sound in June to August.

These occurrences (mean over decades) reflect that cyanobacteria irregularly flow into the south-eastern

part of the Danish waters from the Baltic Sea. Although they can represent a significant problem for water

quality, the population is decaying and the N-fixation rates are low or absent as they are not growing.

As cyanobacteria only may occur in a few Danish water bodies N fixation in Danish waters is neghlegtable

as N source (Jorgensen et al., 2014) and in-situ N fixation in DK waters is not likely to counteract any

future N load reduction. In the central Baltic Sea, N fixation is, however, an important N source, which

potentially may result in increased TN concentration in the central Baltic Sea and consequently impact

especially the more open part of the Danish water bodies, and thus potentially counteract (some of) the N

reduction efforts from Danish catchments for these areas. It is, however, a prerequisite for the performed

scenarios and following reduction targets that the BSAP have been implemented, and this plan is expected

to reduce the problem with cyanobacteria in the central Baltic Sea over time. For water bodies dominated

by Danish catchments, and less affected by Baltic Sea water, riverine concentrations of bioavailable TN is

generally 25-30 times higher than in Baltic Sea waters and hence slightly increased Baltic Sea TN

concentrations is not likely to influence the environmental conditions of most Danish estuaries.

Questions and answers

Q: We are in need of a thorough literature-based justification of the choices made, as this is a key aspect

of the whole study and the policy.

As mentioned above, focus on N reduction was not a choice per se, but an emergent property when

focusing on the indicators pre-determined to be the focus of the performed study. Whether N and/or P is

limiting primary production and act as bottom up control of phytoplankton biomass varies with location

and season (Tamminen and Andersen 2007; Hrustic et al., 2017; Burson et al., 2016). In Danish marine

waters, P is often found to be limiting in the spring whereas N becomes limiting during late spring/early

summer and remains the limiting nutrient (Hansen 2016; Timmermann et al., 2010; Carstensen et al., 2007;

Pedersen 1995; Nielsen et al., 2002b) and also the results from the present study show that N loading (and

not P loading) is controlling the addressed indicators in the dominant part of the examined water bodies. It

must be noticed that in the statistical as well as the mechanistic model approach, both N and P input are

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included (from Danish catchment: both approaches and from atmosphere, sediment and via exchange with

North Sea and Baltic Sea: mechanistic model approach). Furthermore several climatic parameters known to

influence the indicators directly (e.g.light) or indirectly (e.g. via influence on water temperature and

hydrodynamic properties) are included. The choice of including N and P as potential controlling factors is

based on a vast amount of literature documenting that eutrophication (due to excess of nutrient loadings,

mainly N and P) affect primary production and subsequent chlorophyll-a and Kd (e.g. (Nixon 1995; Cloern

2001; Ryther and Dunstan 1971; Smith et al., 2006; Smith 2003; Carpenter et al., 1998; Herbert 1999;

Duarte 2009; Duarte 1995; Nielsen et al., 2002b; Kemp et al., 2005).

We chose to focus on N input from Danish catchments (including both diffuse and point sources) in the

scenarios, keeping atmospheric N deposition and Baltic sea waters nutrient concentrations unchanged (or

implementing Gothenburg Protocol and BSAP for the mechanistic models). However, it is possible that part

of the esti ated edu tio i i e i e N i put pote tiall ould e epla ed

reduction in e.g.

atmospheric N deposition.

Q: What data and evidence (published) exists that indicate which nutrient is limiting (N or P)? This may

vary with season and location (e.g. Baltic/North Sea). How does this address diverse water bodies?

Published data on nutrient limitation in different Danish water bodies include analysis of DIN/DIP ratios

(e.g. (Hansen 2016), ecological modelling (e.g. (Timmermann et al., 2010) , statistical modelling (Carstensen

et al., 2007; Carstensen and Henriksen 2009, Møhlenberg et al. 2007) and nutrient enrichment experiments

(Pedersen and Borum 1996; Pedersen 1995). These different publications also assess nutrient limitations

supporting that N is the main limiting nutrient during summer across a wide range of the Danish water

bodies.

Q: Nitrogen loading may be manageable, but is phosphorus in view of sediment exchange and large past

efforts?

It has not been part of our assignment to analyse possible technical measures to achieve the calculated

requirements to reduction of nutrient loadings; nor have the associated costs for managing nutrients (both

N and P) been part of our assignment. Internal loading (of both N and P) is of course influencing the actual

environmental condition. The Danish water bodies are relatively well flushed, and according to model

results a new steady state between riverine loadings and nutrient pools in the sediment will be established

over time resulting in lower benthic nutrient fluxes as a result of reduced riverine loadings

Q: In most systems, there is a gradual decrease in N loading that is not synchronous with the historical

decrease in P loading. Which factors or policies have caused this decrease, and what is the expected

autonomous trend in N loading under existing policies? Is there any quantitative information on this?

Begi i g i the

s a d a ele ati g th ough

sa d

s i eased appli atio of N fe tilize s

and effective removal of P from wastewater and ban of P in detergents in mid-

s i so e ou t ies

earlier) lead to high N:P ratios in streams and coastal waters potentially resulting in P-limitation in some

estuaries

–

especially during spring. So, yes, there are factors (implementation of measures, changes in

agricultural practice, waste water treatment etc.) explaining the historical decline in Danish nutrient loading

as well as influencing the expected autonomous trend and predictions of future loadings resulting from

different potential nutrient management scenarios. Past and future development in nutrient loading is,

however, not within our area of expertise but we can recommend the following literature (in Danish):

(Thodsen et al., 2016).

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In the present study we have assessed the reductions targets compared to the average 2007-2012 loadings.

The implementation of the Danish RBMP 2015-2021 include estimations on the trend in N loadings under

existing policies, and the reduction targets has been corrected accordingly by the authorities. This is,

however, not a part of the present study.

Q: How important is the interaction between N and P reductions and does the exclusive focus on N

jeopardize the chances of reaching good status by the methods proposed here?

The model scenarios have mainly focused on N reductions (as the indicators were mainly N sensitive)

keeping other factors (including P loading) constant. According to the model results, Danish marine systems

will approach (and most of them also reach) GES under current conditions (climate, P loading, fishery etc.) if

N loadings from Danish catchment is reduced. However, e.g. increased P loadings or changes in other

factors (climate, nutrient from other sources, fishery etc.) may potentially challenge the ability to reach

GES. If the current situation changes significantly, recalculations have to be made.

It should also be noticed that the implementation of BSAP, as a minimum, is a prerequisite for the

possibilities to reach GES in the more open parts of the Danish waters. Here we do not expect that

reduction in Danish N loadings alone is sufficient to reach GES.

Q: Has N:P stoichiometry as a determining factor for phytoplankton composition been considered?

Phytoplankton composition can be important for assessing water quality, especially if blooms of toxic

algae or cyanobacteria are occurring. However, despite the comprehensive data records on phytoplankton

composition in Danish waters, it has not been possible to develop a meaningful operational WFD indicator

for phytoplankton composition. Due to the lack of a suitable indicator, and since neither toxic algae nor N

fixating cyanobacteria are important in the majority of the Danish marine waters (Jorgensen et al., 2014),

we have not tried to link N:P stoichiometry and/or nutrient loading to phytoplankton composition but

focused on chlorophyll-a as the only intercalibrated phytoplankton indicator.

Q: Very important for the societal discussion: is the exclusive focus on (diffuse) N loading leading to the

economically and societally optimal solution for the water quality problems? Is there evidence that it

leads to the best results in comparison with the costs of the measures? Have any analyses been made of

the cost aspects of the efforts required?

This is an important question, but it has not been a part of the present project.

Q: Apart from N-runoff from land (chosen as the primary concern) there are other factors that may affect

Ecological Status. P loading has been mentioned. Also fisheries, habitat modification, change in the

species composition of benthos have been mentioned in the literature, especially as influences on

seagrass distribution. Have these factors been considered somehow, and is there evidence they are

unimportant compared to land-based N runoff?

As described above the addressed indicators are known to be sensitive towards eutrophication and the

mechanisms are well established. Furthermore, in the present study N load turned out to be the main

eutrophication factor controlling the applied indicators. Although the list of hypothetical pressures is very

long, the ranking of pressures (with regard to their quantitative effects) is limited by the lack of evidence

based and quantified link between the pressure and a certain indicator (not the least lack of spatially and

temporally resolved data is a main obstacle to the required multi-pressure studies). E.g. one might

speculate that fishery may affect chlorophyll-a concentration due to trophic cascade effects, but this is very

hard to document and the link between chlorophyll-a and fishery have not been demonstrated in Danish

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coastal waters. Model sensitivity tests have shown that changes in zooplankton influence chlorophyll-a

concentrations in inner Danish waters (Petersen et al., 2017). However, to our knowledge changes in

zooplankton biomass/composition have not been linked to fishery in Danish waters. Likewise, trend

analysis have indicated a shift in benthic fauna from filter feeders towards deposit feeders in Danish waters

perhaps as a response to decreased phytoplankton concentrations (Riemann et al., 2016), but it is unclear

if, or to what extent, this might influence e.g. chlorophyll-a concentration. During the last decades,

potential pressures hampering eelgrass re-establishment have been studied extensively revealing a suite of

factors affecting eelgrass growth and distribution depending on the local environment (Flindt et al., 2016;

Canal-Verges et al., 2016; Valdemarsen et al., 2010; Pedersen et al., 2004; Koch 2001). However, light

availability is documented to be one of the main factors controlling eelgrass depth limit (Duarte 1991;

Duarte et al., 2007; Ralph et al., 2007; Nielsen et al., 2002a), which has been adopted as the indicator by

the Danish Authorities. It is very likely that extensive studies may document and quantify additional

pressures (besides eutrophication) that, at least to some extend may affect long term changes in e.g.

chlorophyll-a concentration or light climate, but it is not likely that other factors may be more important

than eutrophication given the vast amount of evidence of the importance of excess nutrient supply for

these indicators. Future climate changes will likely exacerbate effects of eutrophication and induce changes

in marine ecosystem functioning and structure. However, we do not expect this to be of great importance

towards year 2027, and have not analysed this in more details as part of this project.

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The adopted strategy to derive regionalized reduction targets for nutrient loading

In principle, nutrient reduction scenarios in a country can vary from a general, country-wide reduction

target, over regionalized targets to water system specific targets. This document leads in the end to the

definition of regional targets, but that comes as a surprise to the reader. The statistical modelling

chapters suggested that water body specific targets would be defined, while the mechanistic model,

based on country-wide reduction scenarios, suggested that one would arrive at a single national target.

In the end, a regionalisation based on a set of aggregation rules were derived.

In general, there are arguments in favour of one national target (e.g. setting a level playing field for

agriculture, simplicity of control, simplicity of communication, incorporating mutual influences between

systems through coastal waters) but also in favour of specific targets (e.g. not overdoing efforts, optimal

economic strategy). In the document, however, these arguments have not been made explicit and have

not been the subject of extensive discussion.

Questions and answers

Comment:

The aim of the project was to develop water body specific reduction targets to ensure the

fulfilment of GES for all Danish water bodies. Hence, we have tried to estimate these reduction targets as

individual targets for as many individual water bodies, and corresponding catchments, as we find possible

from a model perspective, both taking into account the specific estuary characteristics and exchange with

surrounding waters. The WFD operate with typology (which could be interpret as some kind of

regionalization) and the Danish authorities has also divided the Danish water bodies in different types,

which we have adopted in a modified version, as described in the scientific documentation. We are

presently discussing a project description with the Danish EPA on an update of the typology applied

towards the RBMP 2021-2027.

Q: Procedural: When was it decided to adopt this regionalized strategy? Who decided this? Were the

current scientific results used as a basis for this strategy? If so, how was this done precisely?

We believe this question reflects some kind of misunderstanding, which indicate that our description

does not fully describe the final procedure. Both during the development of the statistical models and the

mechanistic models, we aim at setting up specific models for specific water bodies in order to provide

water body specific nutrient reduction targets. For the statistical models, this is obvious, as it is the site-

specific monitoring data that forms the input data to the model development, whereas we use the

surrogate model approach (section 8.4.5) to calculate similar water body specific cause and effect relations

when applying the mechanistic model approach. The nationwide N-load reductions (15%, 30% and 60%

reductions) applied to the mechanistic models is solely to develop site-specific responses to N-load

reductions (i.e. the surrogate models). The site specific surrogate models also depend on reductions in the

boundary water bodies. However, we assume that the surrogate models can be used individually for

enclosed local models. For the open waters, we use a kind of regionalization since open water bodies are

highly interrelated and connected. The regionalization of reduction targets in open waters builds on

calculated water body specific reduction targets, which have then been averaged over several connected

water bodies (regions) such as the area around Samsø and Århus (blue area in Figure 8.19). In this area, K

reduction targets based on the individual water bodies are 15% for Ebeltoft Vig, 19% for Kalø Vig (inner

part), 13% for Århus Bay and 35% for the area around Samsø. However, this area is well flushed and well

connected and surface waters mixes greatly, why we do not find any reasoning for dividing the open

(regional) waters in to specific water bodies. This was based on a DHI decision and was formed while

developing the methods to move from mechanistic model scenario results to final reduction targets.

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Hence, for all water bodies upstream the open waters shown in Figure 8.19 we aim at water body specific

reduction targets. Hence, we do neither adopt to a country-wide reduction target or regionalized reduction

targets. We have tried to develop water body specific reduction targets where ever possible, however,

adopting some kind of regional reduction targets for open waters. This should also be evident from Figure

8.23. Here the different reductions are shown on a catchment scale.

Q: How sure can we be that the regions are sufficiently homogeneous in their water bodies? In particular,

when a regional target is low because most water bodies are open with short freshwater residence time,

the region may also contain some sensitive, more isolated water bodies that would suffer from the low

targets. Is this the case? How was it controlled?

We believe that this question reflects the same misunderstanding as mentioned above. As mentioned

above, we only apply the regional approach in open waters where freshwater residence time is short and

presumable well flushed and well mixed with boundary water bodies. For enclosed and more isolated

water bodies we apply water body specific reductions. The procedure for setting specific reduction targets

is described in section 8.7.1.

Q: The scenarios used for the mechanistic modeling use boundary values that are (in part) determined by

nation-wide reductions of nutrient loading with a certain percentage. If there are regions with mostly

open water bodies and low reduction targets, the actual boundary conditions for all of these water

bodies may differ from the modelled ones, since the reductions in the coastal area will be less. There is,

thus, a discrepancy between the modeled policy and the actual policy. Will this affect the results of the

study? Is it possible that the reduction strategy for these regions is too low, because it is the regional

rather than the local reduction percentage that will influence the ecological status?

It is correct that some discrepancy between the modelled policy and the actual policy exists. The

adaptation of surrogate models leads to different individual reductions targets, whereas the development

of the surrogate models assumed uniform reductions. For the open waters, we see lower needs for

reductions than for enclosed and isolated water bodies, where we generally find the largest needs for

reductions, and the resulting effects have not been assessed due to time constraints. However, DHI and

MST are presently working on a project that will look into this as well.

The modelling of the accumulated reduction targets may suggests local adjustment to the reduction

requirements originating from the surrogate modelling approach, but it is not expected to reveal

substantial underestimations in any waters. Considering e.g. the estimated requirements for open waters,

obviously reductions in one region influences reductions in neighboring regions but generally, the largest

open water reductions are found in most southern water bodies, like the Little Belt region (39%), Great Belt

region (20%) and the Sound region (18%) (see Figure 8.19). As surface water primarily is northbound the

larger reductions in the southern regions influences the more northern parts with lower reduction needs.

Hence, when reducing more in the southern parts we do not expect that the reductions in the more

northern parts of the open waters are insufficient.

Furthermore, applying the strategy in section 8.7.1, the estimated reduction targets in coastal areas or

upstream estuaries, that are less restrict than the down-stream reduction targets, have been substituted by

the down-stream reduction targets.

It is also correct that the results from the open waters constitute the boundaries for the local models

–

and

as the target reductions in the open waters are generally lower than for the estuaries and isolated water

bodies, the effects from boundary reductions are less pronounced. Consequently, there is a much closer

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link to the local nutrient loads, assuming that the boundary condition is not of decisive importance. This is

an assumption, and can be challenged, but as we generally do not see large changes in absolute, modelled

values in the open waters we do not expect this assumption to change upstream reduction targets

significantly.

The generally larger reduction targets in estuaries and isolated water bodies does on the other hand impact

downstream water bodies and locally open water bodies will be imposed by larger reductions than the

overall targets set for that specific region.

Q: The statistical modeling only focuses on within-system temporal trends and the causality in these

trends. As far as we understand, no cross-system analysis, relating the hydrographical characteristics of

the syste s to thei ul e a ility to ut ie t loadi g has ee pe fo ed. Why has ’t this ee do e? It

could have formed a scientific basis for the regionalisation, as well as a basis for investigating the

sensitivity of the approach to within-region differences in water body characteristics?

We agree that it will be beneficial to expand the analysis of the systems across the different types based

on both hydrographical and hydrodynamic characteristics. This will increase the understanding of the

systems and reduce the uncertainties of estimates of MAI outside the monitored estuaries. That said, the

meta - analysis is a cross system analysis primarily based on hydrodynamic characteristics. However, it is

very likely that a future revision of the adopted typology as well a cross-system analysis would improve our

understanding of system sensitivity and functioning.

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Choice of indicators and their sensitivity to nutrient loading

Compared to the requirements of the WFD, only a limited set of indicators have been used. Only two of

them (chlorophyll a and Kd) have been used across the two modelling approaches. This leaves a number

of unstudied indicator variables with respect to the good ecological status:



Chl-a only gives an indication of phytoplankton biomass, not of composition. Thus it may miss

occurrence of toxic blooms

Kd is probably insufficient as an indicator of habitat quality for eelgrass. In particular, herbicide

concentrations may be missed as an alternative explanatory variable. The literature on eelgrass

in Denmark frequently mentions hysteresis and the occurrence of alternative stable states. It

may be the case that low nutrient loading and high water transparency are necessary but

insufficient conditions for eelgrass restoration - it would be very useful to bring forward

quantitative arguments proving this point. However, it would still be needed to know what other

factors contribute and how.

The benthic index seems to be unresponsive and should be examined more closely or replaced

Nutrient stoichiometry (N:P in particular) is not considered

Toxic substances, in particular herbicides, might be needed as supporting physico-chemical

variables



Comment:

As agreed with the authorities, the development of models and methods has been focused on

two (out of three) indicators adopted by the Danish authorities: Chlorophyll-a and eelgrass depth limit. The

depth limit has been transformed into K

as described in the scientific documentation prepared for the

international evaluation.

As the expert panel states, eelgrass development is dependent on a number of other conditions than light

availability. Especially, the abundance and coverage are shown to be controlled by other factors than light

availability (Koch 2001). However, the official indicator defined by the Danish authorities is the eelgrass

depth limit and it has often been demonstrated that light penetration/water clarity is the most important

factor controlling the depth limit (Duarte 1991; Dennison 1987; Nielsen et al., 2002a; Ralph et al., 2007).

Therefore, it has been evaluated that Kd is a reliable proxy for the Danish bottom flora indicator.

Other indicators

–

intercalibrated or not

–

could be included towards the development of RBMP 2021-2027,

and DHI and AU are presently having a dialogue with the authorities about including additional indicators.

Questions and answers

Q: Why are additional variables (e.g. days with nutrient limitation) used in the statistical modeling but

not in the mechanistic modeling, especially as it appears that these variables correlate closely with chl-a

and do not give much independent information?

The statistical models link external drivers (e.g. nutrients) to a single variable (e.g. chl a) but do not

explicit include indirect effects of nutrient loading (e.g. primary production and oxygen depletion) which

also affect chl a concentration. These interactions are more explicit included in the mechanistic models. In

order to capture more of the complexity of the ecological functioning and provide a more holistic picture of

ecological status several additional indicato

s e e i luded i the statisti al app oa h. The i di ato da s

ith ut ie t li itatio is a i di ato fo the deg ee of otto up o t ol of the s ste a d a p o fo

pelagic primary production. Although there is a link between primary production and e.g. chl a, primary

production (or days with nutrient limitation) provide information of ecosystem functioning that is not

captured by the chl a indicator although the indicators are often correlated.

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Q: Could additional reference value targets be developed for TN and TP, using the same methodology as

for chl-a? Presumably, these would be more directly related to loads and simpler to understand than the

supplementary indicators used at present.

It is obvious to continue applying the developed models and set targets for e.g. TN and TP. We are sure

this is doable, and we are presently having a dialogue with the authorities focusing on targets for TN and TP

and potentially winter concentrations of DIN and DIP. How this will be effectuated and potentially

implemented towards RBMP 2021-2027 is not entirely clear yet, but we are presently working on

describing different methodologies.

Q: None of the models has been able to show a strong influence of nutrient loading on Kd, except when

going from hypertrophic to eutrophic conditions. Why is Kd nevertheless given more weight (at least with

the statistical modeling) than other variables?

In the statistical model approach, Kd has been given same weight as the chlorophyll-a indicator and

double weight relative to the additional indicators used in the statistical approach. The Kd and Chl a

indicators have been given double weight in order to reflect the importance of these indicators in the

official ecological classification where only intercalibrated indicators are used. In addition, they are both of

fundamental importance for ecological systems. In the calculation of total nutrient reduction requirement,

the Kd indicator has a weight of 2/7.

In the mechanistic model approach the two indicators chlorophyll-a and Kd have similarly been given equal

weight.

Q: What justifies the apparently arbitrary translation of calculated needed reductions (of N load in order

to obtain target Kd) in the order of 200% to 25 %? Why 25 and not any other arbitrary number? Is the fact

that unrealistic needed reductions are obtained, not a reason to decrease confidence in the models and

downweight the importance of the variable in the final conclusions?

We fully acknowledge that the estimated slopes for nitrogen reductions versus Kd are low, leading to

sometimes very high estimates for load reductions. However, for some areas, the slopes are higher and

overall there is plenty of evidence that reduction in nitrogen loadings leads to a decrease in Kd (e.g.

Lyngsgaard et al. 2014, Riemann et al. 2016). We also believe that we have a good hypothesis

(accumulation of organic matter both in the form of DOM and particles leading to a considerable time lag)

for the low slope values as explained in the report (section 8.3).

We do not find that our intervals for categorization of Kd-slope reductions are arbitrary at all, as suggested

by the panel. The values for the categories (25-50, 50-75, and 75) are chosen given that fact that inter

annual variation in N-loadings are in the order of 25% and the hypothesis that a change larger than then

inter annual variation is needed in order to change the status of the ecosystems. We admit that values in

the range of 20-30 % could also have been used, but we believe that values outside this range are

unreasonable. This is an example were expert judgement is part of the overall analysis; something there is

recommend in the WFD. In fact it illustrate our strategy for this project

–

to use objective statistical

methods on observed data as far as it can be done and then supplement with expect judgement.

The suggestion of decreasing the weight or remove Kd as an indicator from the analysis was not an option.

In the former WFD plan period, the depth limit of eelgrass was the only indicator used, based on an

assumption with Kd and N-loadings. This was heavily criticized by the agricultural organizations. In this

analysis, we have a much more diverse approach for evaluating the status of marine systems. However, as

explained in the report (section 8.3) there are pro and cons for all indicators, and one of the strengths of Kd

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indicator is the coupling to depth limits of eelgrass, which is the only indicator for which we have

trustworthy observations for the reference conditions. In contrast, for chlorophyll-a concentration the

reference conditions are based on estimates on loadings at the year 1900 and model estimates that

necessarily are extrapolation far beyond the validation range.

Q: What is the impact of the (doubtful) Kd calculations on the final results? Would the results have been

essentially similar without these calculations or is the dependency (and thus the uncertainty) on Kd

results large? This is important to estimate the robustness of the results!

The governing assumption behind the estimated reduction targets is; when a water body (based on

observations) does not fulfil the indicator targets, some actions are required. The modelling

–

supported by

literature

–

suggest that the Danish indicators reacts to N loadings, why we estimate a reduction target

when at least one of the two indicators does not fulfil the targets.

Based on the official water body classification, the chlorophyll-a target alone is not met in 18 water bodies,

the depth limited (transferred into K

) target alone is not met in 27 water bodies, and for 45 water bodies

neither of the two targets are met

. Consequently, reduction targets for 27 out of the 119 water bodies are

solely defined by the Kd target (averaged with a zero-target for chlorophyll-a).

As described in the scientific documentation prepared to the expert panel we carried out a sensitivity test.

This test revealed that the reduction targets were most sensitive to the status and the targets, and less

sensitive to the slopes. Varying the slopes by ±10% lead to changes in N-load reductions of ±2-3% on

average, whereas changes in status and target values of ±10% lead to changes in load reductions of ± 10-

11% on average. The Kd targets were based on historical observations of eelgrass depth limit and have not

been assessed further in this report. Hence, we do not consider the overall reductions largely dependent on

Kd, and the sensitivity does not indicate otherwise.

Q: Can you derive supporting evidence from the literature that shows that nutrient loadings affect

eelgrass independent of Kd, or that nutrients and Kd are necessary but insufficient conditions for eelgrass

restoration?

Light availability is a necessary but not sufficient factor for eelgrass growth and distribution. Whereas the

maximum depth limit is often explained by light (Duarte 1991; Dennison 1987; Nielsen et al., 2002; Ralph et

al., 2007; Duarte et al., 2007) several other pressures not necessarily linked to light (Kd) and nutrients

including physical stress, frequent resuspension, epiphytes, sediment composition , hypoxia/anoxia etc.

may affect eelgrass growth and restoration (Koch 2001; Canal-Verges et al., 2016; Flindt et al., 2016;

Pedersen et al., 2004). The combination of realised pressures depends on the local conditions and even at

sites optimal for eelgrass growth, recolonization may take years.

Q: Have you considered other measures than nutrient load reduction in order to restore eelgrass beds?

Eelgrass restauration is difficult, and research is ongoing (e.g. in the Danish research project

NOVAGRASS,

http://www.novagrass.dk/en).

In this project we have not assessed measures for

restauration, but assessed reduction targets to obtain sufficient light to support the depth limit indicator.

Over the past 3-5 decades anthropogenic activities have been affecting seagrass ecosystems globally

leading to major loss of valuable habitats (Schmidt et al. 2012). In temperate seas, eelgrass historically

For 17 water bodies no observations were available, and potential reduction targets are set according to

downstream reduction targets

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covered large areas in protected bays and estuaries, but because of eutrophication affecting light

availability and epiphyte growth the extent of present eelgrass beds are only a fraction of healthy beds

experienced around 1900 and in the 1960-ies (Krause-Jensen & Rasmussen 2009). In Denmark nutrient

reduction load targets (80% for phosphorus and 50% for nitrogen) adopted in 1988 were met about 15

years ago but recovery of eelgrass beds is yet to be seen (Carstensen et al. 2013). Other pressures such as

increasing summer temperature, changed sediment texture and organic content, or impacts from toxic

chemicals such as herbicides have been suggested as potential pressures preventing eelgrass recovery

(Koch 2001, Kaldy 2014, Krause-Jensen et al. 2011, Roca et al. 2016, Pulido & Borum 2010, Devault &

Pascaline 2013).

The expert panel specifically requested information about potential impacts of pesticides (herbicides) on

eelgrass health. Present use of herbicides (including desiccation products) in Denmark amounts to ca. 2.000

tons active substance per year (Miljøstyrelsen 2017). Most herbicides (and their degradation products) are

rather water soluble and there is a risk that excess herbicides are transported to ground water or to

streams draining agricultural fields. Herbicides are routinely monitored in Danish streams with Glyphosate

(including the degradation product AMPA) and 2-6-dichlorbenzamid (BAM), being the degradation product

of the banned 2,6-Dichlorobenzonitrile (Dichlorobenil) with highest occurrences and concentrations (Table

. Co pa ed to a e age a d e t e e

-percentile) herbicide concentrations measured in freshwater

streams (Table 1) we must expect even lower concentrations in coastal waters because of dilution. With

that in mind and combined with estimated no-effect concentration (PNEC) at 398 µg/l (Maycock et al.

2010) impact of Glyphosate/AMPA on seagrass in Danish estuaries and coastal waters is highly unlikely.

Besides AMPA, 2-6-dichlorbenzamid (BAM) occurs regularly in streams but in low concentrations 0.012-

0.12 µg/l (Table 1). Although no EQS or PNEC values have been estimated for BAM, the 90-percentile

freshwater concentrations are 4-to-6 orders of magnitudes lower than the concentrations known to cause

toxic effects in aquatic organisms, including primary producers (Björklund et al. 2011). Hence, impacts on

eelgrass population are unlikely.

Some abandoned herbicides such as TCAA are still present in the aquatic environment in measurable

concentrations while others such as Atrazine must be regarded as a past phenomenon in Danish streams

(Table 1). Compared to impact concentrations of in TCAA the mg/l-range the 90-percentile is 10-100.00

times lower in Danish streams. Therefore, TCAA-induced impact on eelgrass in Danish estuaries is not likely.

Two Danish studies addressing potential impacts of herbicides on eelgrass are worth to mention;



Dahllöf et al. (2008) using passive samplers found 20 different herbicides in Nissum Fjord during the

autumn 2007. The most freshwater-influenced (2-5 ppt) part of Nissum Fjord had the highest

he i ide o e t atio s . Appl i g f esh ate uptake ates to the sa ple s o e t atio s of

t o old he i ides diu o a d isop otu o

ot sold fo

-7 years) were estimated between 0.14

and 1.76 µg/l (diuron) and 0.02 and 0.13 µg/l (isoproturon). Especially diuron is toxic to seagrass

with increased mortality at 7.2 µg/l and sublethal effects at 1.7 µg/l measured after 79 days

exposure (Negri et al. (2015). Compared to other estuaries the inner part of Nissum Fjord is not a

typical eelgrass habitat because of low and fluctuating salinities. Low salinity imply low level of

dilution of freshwater with seawater.

Nielse & Dahllöf

o pa ed i pa t o eelg ass g o th leaf-elongation)

after short term

(3 d) exposures to herbicides (Glyphosate, Bentazone, MCPA), applied as single toxicants or in

mixtures. Single toxicant applications did not differ from controls even at the highest

o e t atio s Gl phosate:

µg/l; Be tazo : 4 µg/l; MCPA:

µg/l , hile g o th as

a out hal ed o pa ed to o t ols he he i ides e e applied i

i tu es at lo



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concentration (A: 170 µg Glyphosate/l + 2.4 µg Bentazon/l + 2 µg MCPA/l) thereby indicating

synergistic effects. Compared to recent concentration levels measured in streams (Table 1) the

experimental concentrations are highly unrealistic and it is questionable if such observations can be

used to predict impact of herbicides in Danish estuaries and coastal waters.

To conclude, apart for nutrient loads most probable sediment quality (including H

S) and high temperatures

stimulating respiration are those factors preventing fast recovery of eelgrass.

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Table 1. Overview of results from Danish monitoring for herbicides in streams

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Basic strategy of the statistical modeling

The statistical modelling focuses on within-system short-term models, resolving both long-term trends,

seasonal variation and year-to-year variation that correlates with freshwater discharge. This is a choice,

but alternatives could have been chosen.

Comment:

It is not correct that our method is resolving seasonal variation. On the contrary, we are

deliberately avoiding this because we think that would be unsound for two reasons. First, only in very small

estuaries with a large inflow, we can expect significant effects of short time (days, weeks or up to a few

month) events in freshwater and hence nutrient inputs. Almost all Danish estuaries are likely to integrate

the pressure over a longer period. Secondly, in the evaluation of status in a WFD context, the criteria are

annual or several years values of an indicator.

One could have concentrated on long-term trends only, e.g. by correcting yearly values for freshwater

discharge as is often done in Danish literature.

Comment:

For small estuaries like the Danish, most (about 90%, see e.g. Thodsen et al. 2016) of the

interannual variation on a five-year scale, in nutrient input comes from inter annual changes in freshwater

discharge. Thus, by normalizing an indicator to freshwater input, most of the variability in nutrient loadings

is removed. It is very unlikely that freshwater in itself has an effect on eutrophication. Only over a longer

time scale, changes in freshwater-specific loadings become important. Ideally, e.g. with a 100-year time

series, normalization to freshwater discharge could probably work, but we are far from having that long

time series. The often used practice to normalize a marine variable to freshwater runoff is a short cut to

take into account the effect of nitrogen loadings (before mid-1990s) or the combined effect of nitrogen and

phosphorous loadings (after mid-1990s where most of both N and P come from the open land). The fact

that this practice often works, further support the dominating effect of nutrient loadings for the ecology of

Danish estuaries.

One could also have chosen to model the cross-system differences as a function of hydrographic

conditio

s e.g. f a tio f esh ate i so e fo , st atifi atio ,… , thus e a li g a e ide e-based

typology of systems, rather than the current (and unclear) basis for the typology. It would also have given

an evidence base underlying the meta-modeling. At first sight, a long-term and cross-system approach

would have fitted the purposes of the study better.

Comment:

The typology was a given precondition as it is the official typology reported to the EU under the

WFD. We agree that the assessment work could most likely benefit from a revision of the typology/a more

cross-system-based approach as we also state in the report. MST, AU and DHI have initiated a project with

the aim to evaluate and revise the typology, which could support the MAI estimations especially for meta

water bodies and estimation of chlorophyll a reference values. Relevant criteria could be

at h e t/ olu e atio , ea depth et . Ho e e , the la k of ele a t data espe iall fo the eta

ate odies as ell as suffi ie t ause-effect

relations will most likely constrain the approach.

A second basic choice has been to detrend all independent variables, except the nutrient loadings, and

not to detrend the response variables. This necessarily inflates the correlation between nutrient loadings

and response variable, in case the latter shows trend: the trend can only be attributed to the nutrient

loadings, also when in fact it would have been caused by climate change, increased freshwater extraction

or other causes.

A third basic choice has been to select independent variables on MLS, and then apply regression models

using PLS. This combines the sensitivity of MLS to colinearity in independent variables, and the bias in

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slope estimators (when applied for prediction) of PLS. The most important consequence of this choice is

that only one nutrient loading can be selected, and combined effects of N and P loading, or their

interaction, cannot be resolved by the models. Another consequence is that in some systems neither

nutrient is selected as affecting the response variable, thus leading to a logical problem in estimating

needed levels of reduction. Given the large knowledge on aquatic ecological processes, one wonders why

variable selection has been needed in the first place, and why the modeling was not based on more

advanced models that could have taken into account colinearity.

A final basic choice has been not to perform an explicit sensitivity analysis, or to report on the uncertainty

of the results. Several methods to do this properly exist, both for within-system studies (e.g. based on

Bayesian approach) and especially for between-system studies in a metamodeling or typology-based

grouping of systems. Lack of communication about uncertainty of the findings hampers communication

with stakeholders and induces risks of economic or ecological damage (in cases of overdoing, resp.

underdoing).

Questions and answers

Q: Why has the choice been made for short-term, within-system models? Why are these better than

alternatives?

The basic argument

ithi

-s

ste

odels is that this is e ui ed i the WFD. I ou i te p etatio ,

which is supported by legal experts (see e.g. Anker 2016 and citations in Altinget 26-02-2016), the

obligation for the member states is to ensure GES for each individual water body. In principle, this requires

an analysis of the status and the pressures on each water body, and then an estimation of the combined

reduction of one or several of the pressures in order to bring the individual water bodies in GES.

Denmark has reported 119 marine water bodies in the WFD. In principle, the above-mentioned analysis

should therefore have been made 119 times. This is a very ambitious task, which is hampered by the fact

that we do not have monitoring data for the majority of the water bodies. As mentioned in our report,

long-term data (more than 15 years with annual sampling) are available for 29 stations covering 23 water

bodies. For the remaining about 81% of the water bodies, there is either no or only sporadic monitoring

data. As far as we understand, this situation with limited data coverage is similar to the situation in most

member states.

The lack of sufficient monitoring data for several water bodies poses a challenge and we have used a

typology approach to extrapolate model results to adjacent water bodies with similar typology. The WFD is

typology based (e.g. for establishing reference values) and as such there is consistency between WFD

indicator target setting and e.g. the meta-model approach. However, a revised typology/cross-system

analysis could potentially improve the cause-effect relations provided that we have sufficient monitoring

data to derive the models and meta-data. As aforementioned the long term analyses are constrained by the

length of the data series and as stated in the report (p 46-47) we consider the next logical step in the

statistical modelling approach to be a Bayesian hierarchical modelling of cross-system data as seen in e.g.

(Borsuk et al., 2004).

T o se o da

a gu e ts fo a

ithi

-s

ste

app oa h :

From a scientific point of view, the Danish water bodies are highly diverse spanning large gradients in

depth, salinity, and impact from the catchments and from other press factors, e.g. mussel dredging. Thus, it

is necessary to treat each water body individually. That said, there are similarities, which is why we have

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grouped the water bodies into e.g. the estuaries on the east coast of Jutland (see also below about

typologies).

The last a gu e t fo the ithi

-s

ste app oa h is the o i atio of histo i al easo s a d ti e

constraints. The technique was first undertaken in the late 1990s, specifically for Mariager Fjord, after an

event in 1997 where the estuary went completely anoxic emitting free H

S to the atmosphere. The

technique was further developed and applied during the 00s but only for individual estuaries. When the

Danish government initiated the project in 2013, with a time frame of 1.5 years and a limited budget, we

had to rely on existing data and techniques.

Q: What justifies the choice for models that exclude the probing of interaction between different

nutrients, one of the major problems in the current study?

The technique as such does not exclude probing the interactions between the nutrients nitrogen and

phosphorus. In fact, the technique has successfully been used for that purpose in an earlier study about the

estuary Limfjorden published in 2006 in the report Markager et al. (2006). However, this report used data

from 1985 to 2003, where there was a clear decoupling of changes in loading of phosphorous and nitrogen

in the data. The successful reduction in phosphorous loadings from sewage treatments plants (about 90 %)

means that today

–

and in the data from 1990 to 2012 used for this analysis - both phosphorous and

nitrogen are predominantly coming from the diffuse sources and therefore co-vary with each other and

with freshwater run-off (see also section about N and P). Separating co-varying variables is always a

challenge in statistical modelling and in order to overcome this and qualify the parameter selection in

water bodies where N and P loadings are co-varying, we have performed an analysis of nutrient limitation .

Q: What justifies the variable selection procedure, given that the emphasis was not on proving the effects

of nutrients on water quality, but the estimation of the regression coefficients?

We are somewhat puzzled about this question. In our view, any regression technique involves a selection

of explanatory variables, one or in the case of MLR several variables. The strength of MLR is that it allow

probing interactions between explanatory variables, and that is what we believe we have achieved for

nutrient loading versus the other variable. However, even with the PLS-technique a high degree of co-

variation poses a problem. Thus, simultaneous estimation of coefficients for N and P loadings can be

problematic. In the report (page 35), we have described how we have used accepted and well-described

statisti al te h i ues a d also that e ha e o pa ed f ee a d u o st ai ed solutio s ith solutio s

with N and P as preselected explanatory variables. See also section about N versus P in general. As stated

the e, e disag ee ith the ie that diffe e tiati g the effe ts of N a d P is o e the ajo p o le s .

Q: How reliable are the estimates of influence of nutrient loadings, given the strategy of detrending

applied?

It is clear that the detrending of other variables than N and P will relate trends to put more weight on

the effects of changes in N and P versus indicators that show a trend. However, a choice of not detrending

would mean that a trend in a climate variable, in this case wind, will get a substantial effect and take part of

the effect away from decreasing N-loading and put it on the observed decrease in wind (This was realised

during the development of the models). Given our knowledge about marine systems, we find it less likely

that wind will have a large effect on e.g. TN concentrations. However, it is not impossible to come up with a

mechanistic hypothesis where wind does affect TN concentrations; but it is likely less likely than the

hypothesis that N-loadings are the main driver of the observed TN-concentrations.

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Q: Why have no measures of uncertainty been formally derived and presented in a way that is easy to

understand for stakeholders? This could make the recommendations clearer and more acceptable.

(e.g.https://www.ipcc.ch/pdf/supporting-material/uncertainty-guidance-note.pdf)

We have used several traditional statistical measures (R

, RMSEP etc.) in order to assess model

uncertainty/model reliability. These measures are focused on the ability of the model to predict individual

indicators (Chl a, Kd etc.) which is important, but these measures are not assessing the uncertainty related

to predictions of MAI. Dealing with uncertainties related to complex calculations such as MAI, which

involves status values and reference/target values for several indicators, expert judgements as well as

models and extrapolations etc. are far from trivial and there is no formal way to estimate the uncertainty.

In addition, it is not possible to compare model predicted MAI-values with observations which further

hamper a traditional uncertainty analysis. Instead, we have applied sensitivity tests and ensemble

modelling where possible. This approach is also used in e.g. climate predictions and weather forecasts

where traditional uncertainty analysis is difficult/impossible. The rationale behind the ensample modelling

is that if predictions of MAI using two independent model approaches are almost similar and significantly

correlated, then it is unlikely that the uncertainty of the individual models is large (assuming no model bias

in both model approaches). In addition to the more quantitative assessments of model uncertainty that we

have performed (using statistical measures, ensample modelling and sensitivity tests), we have indeed tried

to convey the uncertainties in the text and on many meetings during the process.

We totally agree with the panel about the importance and the desirable in trying to convey uncertainties to

managers and stakeholders. However, we also find this the most difficult part to communicate. The panel

refers to the IPCC material. However, reading it reveal a statement like:

Be p epa ed to ake e pe t judg e ts i de elopi g ke fi di gs, a d to e plai those judg e ts

p o idi g a t a ea le a ou t:

We actually find that this is precisely what we tried to do in both our original report in Danish, in popular

articles, in countless interviews in TV, radio and new papers and on meetings, but communicating

uncertainties (whether they are quantified or more qualitative) is challenging.

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Basic set-up and validation of the mechanistic models

In general, the model set-up is clear, but details of the processes and parameters are not easy to find,

especially as some of the referred documents in the model description are not publicly available. In the

general set-up, it is not entirely clear why in the end four different models were set up, especially as the

use of a flexible mesh would have allowed to use a single model with spatially differing resolution. You

mention in the description that the IDW model differs from the estuarine models in some process

formulations and variable settings, and you give arguments why that has been done. We assume that

you split the estuarine models in different models for practical reasons, but would like to know why.

More importantly, we do not know if these models were the same in variables and parameters, and thus

only differ from one another in bathymetry and boundary conditions. If settings differed, we would need

details on the how and why.

Model validation was presented based on average values per month and water type. However, in the

present setting a crucial validation element for the models is whether the models have been able to

capture the long-term trends in water quality as related to reductions in nutrients. Evidence showing the

model behavior in this respect should be easily obtainable from model output.

Questions and answers

Can you provide us with a copy of the documents you refer to in the model description?

We assume it is the DHI documents you are referring to. Hence, these have been attached. If you also

were referring to other documents detailing the model description, please get back to us. For practical

reasons we have included the 2016 version of the references, but differences between the latest and

earlier version are insignificant.

Can you give more details on the four models, and what are their differences and similarities?

Basically, we have adopted two different biogeochemical models (i.e. two different sets of state

variables and processes); one for the IDW model and one for the estuarine models. In the DHI references

forwarded to the panel as part of the answers to this group of questions, the state variables and processes

are described for the IDW biogeochemical model (DHI 2016). The differences between the two models are

highlighted in Table 7.1. This table highlights the functional differences between the two different

biogeochemical models. The functionalities not highlighted are more or less identical formulations in the

two models.

Setting up four different models in the end instead of having one model including both estuaries and the

IDW model is based on combinations of different arguments:

1. A practical argument is that the CPU demands would raise, and time for each model run would

increase significantly. The models are based on flexible mesh and in the IDW model the resolution

varies between approx. 300 m to >6 km, whereas the estuarine models have grid cells less than 100

m for the finer grids, and down to less than 30 m in e.g. Odense Fjord. We did try to increase

resolution in the IDW model to less than 300 m locally, but the increase in CPU time did not allow

for this approach.

2. A process and data argument is that the estuarine models includes a tighter coupling between the

benthic and the pelagic compartments and also include inorganic sediments subject to

resuspension, and adsorption/desorption of PO

to inorganic sediments. These processes can be

equally important in the IDW model, but the demand for sediment data for this benthic-pelagic

interaction calls for more data than what is available in the open waters. Hence, especially the

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sediment interactions are described in less details in the IDW model compared to the estuarine

models.

In the three estuarine models, identical biogeochemical model formulations are used. Due to local

differences (system and data), the set of calibration constants are not entirely identical for all three setups.

However, the model consists of approx. 275 different constants, and less than 10 of those constants differs

between the estuarine setups. All the constants that differ are associated with the sediment.

Can you specify details on the atmospheric forcing: Was only a single year used, whereas Denmark

reports on atmospheric deposition to Helcom for longer periods? How was the atmospheric N deposition

divided over different species? Was atmospheric P deposition considered?

With respect to atmospheric depositions, we apply modelled N depositions for each single year of the

period 2002-2011 (i.e. monthly averages for 2002 to perform biogeochemical modelling of year 2002, etc.).

The atmospheric model is developed by AU and they were responsible for delivery of the required data.

The model was first applied in 2007 and have been used since then for estimation of national atmospheric

inventories, e.g. to HELCOM. All years have been executed based on specific emissions and meteorology of

the specific year. For the ecological modelling, we only considered the inorganic nitrogen fractions (NH

and NOx) of the wet and dry deposition, which is delivered as output of the atmospheric modelling. The dry

and wet depositions of each species are lumped and applied as input to the surface concentrations of NH

and NOx in the model.

In shallow waters assumptions with respect to atmospheric deposition input can be crucial and

potentially allow a manipulation of the MAI. Was the deposition data spatially resolved? If not, how was

it taken into account in the model? Were gradients between land and sea taken into account? Which

atmospheric N fractions were considered as bio-available in the model and how were they calculated?

Was the atmospheric input of P fractions considered, as well?

The atmospheric model was executed with a grid resolution of 16 km in order to handle the land-sea

gradients. In order to handle gradients in the deposition velocities at the different surface types the model

have different deposition velocities for the different surface types (different forest types, different crops,

grass etc, and open water). It is only the total deposition to open waters (with a spatial resolution of 16km),

which have been used as input to the mechanistic biogeochemical model.

The yearly reports (in Danish) also include some indication on resolution and spatial distribution of the N

depositions, see

http://www.dmu.dk/pub/fr708.pdf, http://www.dmu.dk/pub/fr761.pdf,

http://www2.dmu.dk/pub/fr801.pdf, http://www2.dmu.dk/Pub/SR2.pdf

and

http://www2.dmu.dk/pub/sr30.pdf

for the specific years: 2007 to 2011.

Can you provide us with the validation data showing that the models have been able to capture the

essential effects of nutrient reduction on target variables chl-a and Kd?

We have run the models for a period of 10 years: 2002-2011. During that period no significant trend in

loads are observed, why we cannot, through verification data, show that the model is able to capture the

essential effects of nutrient reduction. However, as we find similar cause-effects (slopes) compared to the

statistical models, we conclude that the models respond to the loadings, as has been observed historically.

To be able to evaluate the models comparing to the historical load reductions we should have modelled at

least 10 more years.

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No estimates of model uncertainty were given. Do you have any estimate, what is it based on and

what is the order of magnitude of the estimated error on the variables of interest (in particular the

derived nutrient reduction need)?

As for the statistical models, we have used traditional statistical measures in order to assess model

uncertainty/model reliability for the mechanistic models. These measures are focused on the ability of the

model to predict individual indicators (chlorophyll-aa, Kd etc.) which is important, but these measures are

not assessing the uncertainty related to predictions of MAI. Dealing with uncertainty of predictions in

complex ecosystem models is far from trivial, because of potential errors and uncertainty associated with

input data, the initial conditions, data used for calibration and model structure. With 10 years input data

including > 300 nutrient sources in Denmark alone, more than 275 model constants and 60 state variables it

will be impossible, due to computationally capacity, to apply proper uncertainty analysis (Monte-Carlo)

similar to what is often done for simpler hydraulic river models.

As an alternative approach multi-model ensemble modelling to determine model prediction uncertainties

may be used as in the climate change community (Weigel et al. 2008). Application of a

t uth

ensemble

approach will require multiple models covering the same area, time period, each using the same set of

input data and preferentially also use comparable model resolution (Pogson & Smith 2015). Previously,

post-ho

e se le odelli g 4 diffe e t odels ha e ee used to assess p o le a eas due to

eutrophication in the North Sea and the Baltic Sea (Almroth & Skogen 2010).

True ensemble modelling has not been possible in this project, however, as described in the scientific

documentation we did introduce some reduced ensemble approach. Having very different and

independent model approaches covering overlapping water bodies did result in quite similar reduction

targets. Hence, it is unlikely that the individual model uncertainties are large.

In addition, we have compared the slopes between nitrogen load and response variables (summer

chlorophyll-and Kd) estimated with the mechanistic models and the statistical models. During the 10 years

of modelling carried out as part of this project, we do not see any significant trends in measured

concentrations of either N, P or chlorophyll-a. This is also expected as the loads from Denmark (Figure 2.2

in the scientific documentation) and from neighboring countries (HELCOM 2011) during that period is fairly

uniform. However, as the response in the mechanistic models (based on N load reduction scenarios) show

similar slopes as compared to the statistical models using historical load reductions going back to the

period before significant nutrient load reduction are introduced, we find it most likely that the dose-

response in the different water bodies is reflected in the mechanistic models.

At present both AU and DHI participate in a Danish research project (http://seastatus.dhigroup.com/)

where one keyaim is to define methodologies for estimation of model uncertainties. If anyone in the expert

panel has some advice on how to proceed with estimating model uncertainties, this will be highly

appreciated.

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Consistency between target values in statistical and mechanistic modeling

Both the statistical model chapters and the mechanistic model chapters describe how reference

o ditio s a d target alues ere defi ed. I the e se le odeli g , as ell as i the eta-modeling,

the targets from both model approaches are considered sufficiently consistent to be used in averaging

procedures.

Questions and answers

Are these target and reference values conceptually consistent across the two modelling approaches?

As far as we understand, the statistical modelling extrapolates back from the present situation in a

particular water body to the situation that would be present if the

local

nutrient loading would be

reduced to 1900 levels. This does not take into account the reduction in background marine values, nor

the effect of local Danish reductions in other waters that reach the system of interest through the sea. It

also does not take into account regional (e.g. BSAP) efforts. This reference value, therefore, must be

significantly higher than the reference value calculated with the mechanistic model (which assumes both

N and P reduction to 1900 levels, in both the system of interest and the whole world around). The

refere e alue of the statisti al odel ould e u h loser to the

target obtainable through Danish

land-based N reduction

in the mechanistic model. In terms of fig. 8.14: the intersection of the orange

slope line with the upper dotted horizontal orange line, and not the point with the red cross. Can this

relation between the definitions of the reference and target values be clarified, and can arguments be

given why the approaches from both model strategies are nevertheless conceptually similar enough to

be averaged?

In contrast to the mechanic models, the statistical models do not take non-Danish N loadings into

account and therefor these models are only applied in water bodies where N load from Danish catchments

are assumed to be dominant. For these water bodies the intersection of the orange slope is approximately

in line with the point marked by a red cross for the mechanistic models, indicating that non-Danish N load is

of minor importance. For areas where local Danish N loads are dominating the two model approaches will

be simulating the same reference-scenario (although the methods are different).

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Meta-modelling

While in general the strategy for meta-modeling is clear, there is a question regarding the North Sea

waters on the Jutland coast, and a request from the panel for more supporting data.

Questions and answers

Ca ou e plai ho

eta- odeled results for

North Sea waters could be derived, when none of the

underlying models has considered this type of waters, which differ from all other water bodies in tidal

range, temperature regime, sediment loading, nutrient concentration, stoichiometry and possibly a suite

of other characteristics? Have the same indicators and criteria been used for North Sea and Baltic

estuaries, and is this justified?

For the North Sea area, only the chlorophyll indicator is involved in investigation of needs for nitrogen

reduction as the environment along the North Sea coast does not support eelgrass meadows. As

determined by the EU intercalibration procedure, this indicator evaluate the 90-percential chlorophyll-a

concentration from Marts to September. In the present project we assume that the meta-model effect

from N on chlorophyll-a are similar in the North Sea as within the Kattegat and Baltic Sea area, and we

apply the meta-slopes developed for this study. This is an assumption that allows for estimation of a

reduction target. We fully acknowledge that using meta-slopes developed for the Inner Danish waters is an

assumption associated with uncertainties, both because the indicator is defined differently, and due to the

ecosystem differences mentioned by the expert panel. We are presently in the process of initiating a

project focusing on the finalization of a mechanistic biogeochemical model for the North Sea that can

consolidate reduction targets in these water bodies.

A serious weakness of the report is that the input data basis is not sufficiently presented. Tables are

lacking that show spatially resolved values for present and past atmospheric deposition, spatially

resolved emission data from land, concrete concentrations in all rivers and estuaries for both N and P,

and hydrographic data (e.g. % freshwater, residence time, tide, depth) for all systems. The lack of area

specific data does not allow a critical evaluation of regional MAI nor a comparison with data and results

from other countries. The panel would greatly appreciate if such a table could be produced, preferably

electronically.

We apologies for the lack of input data. The evaluation report has focused on models and methodologies

behind the Danish MAIs. We have prepared and sent a xls-spread-sheet with the data we have readily

available.

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Detailed questions

Page

Question

It seems formally strange to attribute F

as i de

he it is a di e sio al

quantity (dimension L^3/T^2) and it

does not appear very logical to divide

runoff with residence time, that is,

ould t a lo ge eside e ti e i pl

larger runoff influence? Why not use a

more straightforward parameter around

specific freshwater content: f=R/(Q+R) =

(Sm

–

S)/Sm

The applied F index was adopted from the Dahl et al. 2005 and has originally been used

to make a typology for Danish marine waters as part of the initial Danish implementation of

WFD. It has not been a part of the present study to evaluate or revise the F index.

Type 1 subtypes represent different

nitrogen and phosphorus regimes,

ranging from the quite Baltic Sea

influenced to quite North Sea

influenced, should perhaps this be taken

into account in the model validation? On

the other hand, the number of Type 1

areas that are both critically dependent

on Danish nutrient inputs and

significantly deviating from GES are

probably limited.

The verification presented in the scientific documentation summarizes the model results

between the different water body regimes ranging from eutrophied closed estuaries to

open waters.

Fig. 3.2

Report

While working with the different models they have all been calibrated/verified separately

applying a number of monitoring stations across the model domains. During this process,

we did include monitoring stations scattered across the Danish marine waters, but for the

scientific documentations we did not provide more information on the differences between

the open waters. In Annex 1 we did include a few examples for various Type 1 water bodies,

Figure 34 to Figure 45.

20 / 58

“In addition to the Danish land

-based loadings, the

mechanistic models also include N and P loadings at a

regional scale, i.e. loadings to the entire Baltic Sea, and

atmospheric deposition, see chapter 7.”

and P 58:

“An

important input to the setup of the mechanistic models is the

external supply of nutrients. Apart from Danish land-based

nutrient loadings, the mechanistic models include nutrient

input to the Baltic Sea from other countries and atmospheric

deposition. In section 4.2, Danish land-based nutrient

loadings and atmospheric deposition are described, both

based on data from the Danish monitoring programme

DNAMAP.”

In shallow waters, assumptions with

respect to atmospheric deposition input

can be crucial and potentially allow a

manipulation of the MAI. Was the

deposition data spatially resolved? If

not, how was it taken into account in the

model? Were gradients between land

and sea taken into account? Which

atmospheric N fractions were

considered as bio-available in the model

and how were they calculated? Was the

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atmospheric input of P fractions

considered, as well?

As mentiond earlier, the atmospheric model was executed with a grid resolution of 16 km

in order to handle the land-sea gradients, and the model has different deposition velocities

for the different surface types (different forest types, different crops, grass etc, and open

water) in order to handle gradients in the deposition velocities to the different surface

types. It is only the total deposition to open waters (with a spatial resolution of 16 km),

which have been used as input to the mechanistic biogeochemical model.

The model entails a chemical model including the transformation from NO and NO2 to

NHO3 and nitrate aresols, as well as the chemical transformation of NH3 to NH4 (via acids

like H2SO4 og HNO3), and through a dry and wet deposition those nutrients are allocated to

different surface types, like the water surface of the Baltic Sea. Thus, output of the model is

two species of nitrogen for wet and dry deposition, respectively. After summation per

species of wet and dry deposition, the data is applied as input in the biogeochemical

modelling.

Atmospheric deposition of P was not considered.

Time series of observatio

ns (including Kd)

How was Kd measured?

Before 1998, water transparency was in general measured as Secchi depth by the

counties. The exception was monitoring performed by the National Environmental Research

Institute, Denmark, that had CTD equipped with light sensors (4π PAR). After 1998, the

cou

ties o ito i g essels e e also e uipped ith CTD s i ludi g se so s fo su fa e

light and 4π PAR censors on the CTD. Kd was estimated from light readings every 0.2 m

according to common technical guidelines (Kaas and Markager, 1998, in Danish). For the

current project, the Secchi depth data were converted to Kd-values as described in Murray

and Markager (submitted to Frontiers in Marine Science). This analysis is based on more the

61,000 paired observations and Secchi depth and Kd and take into account the seasonal and

spatial variability in the Kd*Sd factor.

What is the statistical justification?

How much data are omitted?

The length of the time series determines the number of data points used for the regression.

Statistical theory dictates that the confidence of a regression decreases with the number of

data points as the residual degree of freedom decreases, and similarly when the number of

explanatory variables increases. As a rule of thumb, the residual degree of freedom is

calculated as the number of observations

–

(number of explanatory variables + 1)

(though

dependent on the collinearity in the explanatory variables in PLSR).

There is no objective way

to determine the minimum number of data points and the choice of 15 years as threshold

value was based on our experience with the data analysis. This is a compromise between

representing as many waterbodies as possible and avoiding poorly monitored waterbodies,

with few observations and hence increased uncertainty in the coefficients or erroneously

selected variables.

“… refrained from doing so” (Log transformation)

“only time series with a minimum of 15 years were used”

Are data normally distributed?

Not all data are normally distributed, nor is this required in the PLSR assumptions.

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“daily values gained from interpolation were used to

construct monthly average values”

Do you have a statistical reference for

this procedure?

The problem arises from the fact that the observations are unevenly distributed in time.

More samples have been taken during the growing season, in order to monitor the

environmental situation more closely during the most critical time of the year. In some

cases, technical problems or conditions at sea have caused loss of data. Basically this is just

a way to make a time weighted mean. The interpolation method has been widely used and

has been used for these types of data for decades. We are aware of other techniques, e.g.

GLM-procedures. However, we have found that such procedures generate other problems

(e.g. GLM does not account for variable month lengths).

“… we defined the following rules for predictor variables”

Do you have statistical criteria or a

reference for this? There are robust &

complete time series analysis theories

and methodologies available

The first part is a question, and, no, we do not have a reference. The rules have been

developed for the specific purpose of this analysis, given the nature of the data and the aim

of the analysis. We have sought to explain the reasoning behind the rules in the report (p.

33). As there are no specific question to these, we find it difficult to go into a more detailed

explanation. We are familiar we other approaches, e.g. Box-Jenkins Time-series analysis and

Fourier transformations. However, we have found that they are less suited for the problem.

This is not to say that they cannot be applied. However, it was not possible to do a

systematic comparison of several methodological approaches with the framework of this

project.

“The half saturation coefficients (Ks) for phosphorus and

nitrogen were chosen to be 0.2 uM and 2 uM”

What was the final weight of this

exercise in the selection of variables?

We have not assessed the weight of this for the variable selection.

Why did you not estimate error

variances and confidence limits which

are preconditions for evidence based,

adaptive management, policy and

decision making?

We have applied several statistical measures in order to quantify the applicability of the

models to describe the indicators (Chla, Kd etc.) of which e.g. the empirical standard error

of the cross-validated model (RMSECV) can be easily converted to variance and confidence

limits. However, there is no formal parametric way of calculating error variance for the

slope in PLSR nor for the final model. The variance of the PLSR slopes could perhaps be

estimated empirically using jack-knifing but the computational time to do this for approx.

100 models poses a challenge. Likewise there is no formal way of calculating confidence

limits for the MAI estimates. Instead we have used ensemble modelling and sensitivity tests

as a surrogate for a more formal assessment of model uncertainty and to assess the

consequences of uncertainty in input parameters (status values, target values and models)

for the MAI estimate. Hence, because of the complexity in the calculations, which hinder

formal uncertainty analysis, we have used other measures in order to quantify the

uncertainty related to the models and MAI calculations.

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“… quantification of autocorrelation , this effect was not

included in the models”

Your justification conflicts with your

observation of significant

auto o elatio , does t it?

We are not sure what the evaluation panel mean by this question. The occurrence of

autocorrelation, particular for TN and TP is described in the paragraph om page 42 and a

possible explanation. In essence; yes, autocorrelation occur in the time series for TN and TP,

and means that the slope in the models are underestimated. However, at present, the time

series are too short to quantify this and therefore we refrain from including this in the

models.

In relation to this and to some of the other questions raised about the technical details, we

kindly ask the evaluation panel to consider that the framework for the analysis was subject

to tight constrains in time and resources. Thus, the task was to obtain the best possible

estimates under these conditions and with the data available.

Calculation of Chl-a and KD is critical in

this study. Thus, more information on

how Chl-a is calculated from

phytoplankton carbon and on the optical

model parameterization relating model

state-variables to KD would be

interesting.

This is be available in the DHI references forwarded to you as part of the answers. See fx.

Section 3.1. and 3.3.11 in DHI (2014).

„However, an important difference between the national

data and the data adopted by DHI for the mechanistic

modelling is the resolution in time. Whereas the national

data are reported on an annual basis, the data used for the

modelling were provided on a daily basis, both for water

discharges and nutrient loadings.“

How was this done?

The national yearly inventory of Q, N and P loads to Danish marine waters is based on a

model taking precipitation and down-stream observations from a number of Danish

catchments into account. For the national reporting, data are aggregated in both time and

space to yearly loadings on a water body level. For this study, we received the data without

this aggregation, meaning that we received daily catchment model output for this study.

The daily data were delivered by AU.

„The loadi

ngs were estimated as discharges of total

nitrogen (TN) and total phosphorus (TP). Since the

mechanistic models differentiate between the different

chemical forms (inorganic/organic, dissolved/particulate,

nitrogen and phosphorous species), the data were

subsequently transformed into nutrient forms required by

the modelling. Through an assessment of available

observations on nutrients in water discharged from Danish

catchments, monthly relations between inorganic and

organic nutrients were developed and applied to split TN

and TP into an inorganic and an organic fraction. By

combining TOC and COD/BOD observations, the organic

part was further split to separate the organic nutrients into

the three forms adopted in the modelling process.“

Since the assumptions with respect of

the model input are crucial for the later

results, I like some clarifications. Am I

right that you used (with respect to N)

DIN and a part of TON as bio-available

fractions in the model? How did you

calculate it from biological and chemical

oxygen demands (COD/BOD)? Did you

take into account DON, as well? Was this

calculated for every river separately or

as an average for all Danish rivers? Could

you give numbers about the relative

share of each fraction for N and P?

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For sure, the assumptions with respect of the model input are crucial for the later results,

and we did spent some time trying to come up with a method for transferring river TN to

the five different N-species included in the model (NH4, NOx, DN, CDON and LDON) and the

4 different P species (PO4, DP, CDOP and LDOP). During this process we developed an

internal working paper describing the applied method. This is not an official document but

we have included this paper as part of the answers to the expert panel.

„Hence, the data are those officially reported by the various

countries. Differentiation of TN and TP loadings was done

according to Stepanauskas et al. (2002).“ Stepanauskas et

al. (2002): „We estimate that the input of summer riverine N

to the Baltic Sea consists of 48% dissolved inorganic N,

41% DON, and 11% particulate N. Corresponding values

for phosphorus are 46%, 18%, and 36% of dissolved

inorganic P, DOP, and particulate P, respectively.“

Is this the same approach that you used

for Danish rivers? Stepanauskas et al.

(2002) quantify DIN and DON and these

are the fraction you used as input for all

other Baltic areas, is this right? In some

areas the model seems not to cover the

entire coast and nutrient retention may

take place between river input and

onset of the model domain. How did you

deal with it?

The differences in how we handle N and P loadings from Danish respectively Baltic Sea

rivers is described briefly in the attached internal working paper.

It is correct that we do not resolve the entire coast

–

within the Danish waters we include

the effects from retention for Odense Fjord, Roskilde Fjord and Limfjorden by applying local

model results from the three estuaries in the IDW model. A number of the other estuaries

are resolved in the IDW model but for the water bodies not resolved, and we do not include

retention.

For areas in the remaining part of the Baltic Sea, which is not resolved, we likewise do not

include a retention.

“… data were lumped according to topology…” Fig. 7.6

Did you calibrate models by water body?

Evaluation by type does not reveal

accuracy and precision of water body

specific models, does it?

Would it be

possible to estimate error variances and

confidence limits (e.g. 0,95) for water

body specific models?

What are the estimated mean,

covariance and variance of model

parameters and error variances of water

body specific models?

For the study, the models have been calibrated one-by-one and not lumped.

Furthermore, the models have been calibrated according to specific monitoring stations and

specific parameters for the individual stations. The lumping in e.g. Fig. 7.6. is an attempt to

summaries the model across the different water body types. Examples of observations and

model results are included in Annex 1:



Limfjord observations and model results: Figure 1 to Figure 13



The Odense Fjord observations and model results: Figure 14 to Figure 23



The Roskilde Fjord observations and model results: Figure 24 to Figure 33



The IDW model observations and model results: Figure 34 to Figure 45

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During the development of the scientific documentation, we did lump according to types

trying to summaries the overall quality and highlighting the variation between the different

types covered by the individual models. We did not estimate error variances and confidence

limits but worked with BIAS and R

Is it true that all data was used for model

calibration and that a model validation

using an independent data set (year)

was not carried out?

In addition to regression coefficients

demonstrating similar trends in model

and data, can you also indicate that the

actual values corresponded?

Could you provide non-aggregated time

series showing the model performance

and data for concrete monitoring

stations in comparison?

It is correct that we used all observations available as part of the calibration process. Due

to the limited amount of data available, setting data aside for verification would have left

too few data for both calibration and validation. Therefore, with respect to the three

estuarine models, identical data are used during the calibration process and the final

verification. With regard to the IDW model, we did - in addition to monitoring data from

inside the water bodies - calibrate the model against a number of monitoring stations

outside the water body areas (open water stations), and these stations were not part of the

final evaluation . When doing the more overall verification presented in the documentation

report prepared for the panel, the majority of the monitoring stations/data included was

not used for calibrations. Besides the regression coefficients demonstrating similar trends in

model and data, we also included BIAS in the evaluation of the individual models.

Skills of biogeochemical models

As requested by the expert panel, we have prepared some specific examples from the

different models as part of this Q&As, these being presented in Annex 1 of this document

(see figure numbers below). Not all monitoring stations in the different estuaries and open

waters contain biogeochemistry and/or data covering all years. In Annex 1, we have

included one monitoring station for each of the two models Odense Fjord and Roskilde

Fjord, two stations for Limfjorden and three stations for IDW. The monitoring stations are

chosen to reflect differences in water bodies. A criterion has been that data from the station

cover a larger part of the modelled years. We have also included salinity and water

temperature examples, but data has not necessarily been prepared for the exact same

stations as for the biochemistry (not all data have been stored for all monitoring stations).

The example figures included in Annex 1 are:

Limfjord observations and model results: Figure 1 to Figure 13

The Odense Fjord observations and model results: Figure 14 to Figure 23

The Roskilde Fjord observations and model results: Figure 24 to Figure 33

The IDW model observations and model results: Figure 34 to Figure 45

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Have the sorption-desorption on

suspended sediment particles been

taken into consideration?

The estuarine models include sorption-desorption to inorganic sediment particles and

hence is impacted by e.g. resuspension. The IDW model does not include the same

interaction, as data on inorganic sediment for the IDW model area was insufficient for the

model development.

What is the point of validation based on

water body Type? Type 1 waters seem

to include as diverse areas as the ones

inside the sills to rather marine areas in

Kattegat, why not use the different sub-

categories of Type 1, Figure 3.2 and

Table 8.1?

How is the aggregation done into Type

averages in e.g. Figure 7.6? Just mean

value water bodies (model/observed

data)?

The quantitative assessment (page 65-

66) is done on monthly mean time-

series. That implies a mixture of

validation of seasonal cycle and inter-

annual variability. At least for the non-

open water Types, it would make sense

to explicitly look at the interannual

variability that probably gives more

i fo atio o the odel s apa ilities

of resolving the response to load

reductions.

We notice the point raised by the expert panel and have included some examples of

modelled time series in Annex 1, Figure 34 to Figure 45. The model calibration has been

performed on individual monitoring stations and not by aggregating for specific water body

types.

The aggregation in Figure 7.6 are mean values per water body (model and monitoring.

“seasonal anoxia in these areas, inducing release of

phosphorus from the sediments”

The sediment pools are reduced for the

reference simulation in the Baltic Sea

and IDW based on literature values. But

it is not explicitly stated whether this

adaption resulted in a new quasi-steady-

state in the model when forced with

reference loads, which could be

influential on several of the Type 1 water

bodies. Is this the case?

The model did not reach a new quasi-steady-state in all sub-areas of the IDW model after

adopting the reductions in the sediment based on literature values. In some areas, the

sediment seems to build up some additional nutrients pools following the reductions. We

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do not observe a visual trend in surface concentrations but cannot rule out some long-term

effects.

What management measures in the

same time period have been

implemented to treat the manure of the

approx. 25million pigs? Each pig

represents 3 person equivalents, so

approximately 75 million people.

We have not assessed any management measures

–

the comment to the figure is merely

an observation and an explanation to the data representing the Northern Sound.

You attribute the decrease due to UWWT in Copenhagen,

population about 600 000

“In order to reduce the influence of model bias, we used …

ensemble mode

ls …” & “… most robust chlorophyll

-a

estimates were achieved using ensemble model”

How can you justify this without proper

error variance/uncertainty estimates?

For both the mechanistic and statistical models error variance/uncertainty estimates

would require e.g. Monte Carlo simulation and Jack-knifing which was not practically

doable. Since we have no a priori knowledge of model performance in a low nutrient

situation -

a ea of the t o odels is elie ed to e the est esti ate of the t ue alue.

It is also the ost si ple app oa h a d the fi st hoi e he o othe i fo atio a e

available.

“ … status values are converted into water body averages

by relating the observed status to the modelled status at the

actual observation point and applying the ratio between the

two (model and observation) to correct the modelled water

body average”

Could you clarify? Are you correcting

model results?

We are using the model results to estimate a water body average based on the

observations conducted in the specific water body. Hence, we assume the observations

provide the best estimate of the status in the observation point, but use the model to

extrapolate the observations to a water body average.

“The purpose of averaging … is to reduce uncertainty”

Can you justify? Is average any more

certain than either of the models?

Averaging the reduction need for the individual indicators is believed to provide a more

robust and precise estimate of MAI for a given water body since 1) we do not have a priori

knowledge that one indicator is better than others and 2) consistently choosing the

indicator with the highest reduction need (in order to ensure that all indicators reach GES)

ould i ease u e tai t si e it is a e t e e alue ith a i he e t highe isk of

being influenced by both model - and observational errors.

What is the method to estimate the

weights?

Could it be possible to use error

variances of models as weights?

Yes in principle it could be possible to use error variances as weights, and we

acknowledge that this is a sound approach in an analysis with several parameters were the

main difference is the uncertainty of the data/models. However, in this case the differences

(outlined page 91-101) are not related to the uncertainty in the data but should reflect the

formal

–

or juridical

–

difference; is the indicator intercalibrated in the WFD context? For

these reason Kd and chlorophyll-a is given double weight. Secondly, the two indicators for

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ecological signs of hypoxia are merged into one indicator, to obtain the same weight as the

others.

Does this mean the WFD

intercalibration? Why does

intercalibration not provide a scientific

basis for the chosen indicators?

Yes, hat is ea t

i te ali ated i di ato s is the p o edu e i the WFD. Ho e e ,

this is not to say that the intercalibrated indicators are not sound indicators describing the

environmental status. On the contrary, we find that both Kd and chlorophyll-a

concentrations are highly relevant parameters. Our intentions with the sentence quoted

a o e is just to e phasise that the dou le eight to these pa a ete s Ta le .

argued in the fact that they are intercalibrated, which is a formal or juridical argument and

not a scientific argument.

On what basis (published) was this

concentration chosen? This is difficult

for a mix of diatoms, cyanobacteria and

dinoflagellates.

The K

-value (K

is a mistake in the report, it is the half-saturation constant in a Michaelis-

Menten kinetic there is meant, which usually is denoted K

) is taken from the literature

cited in the paragraph. This aspect of the analysis was published in Hydrology and Earth

System Sciences (Hindsby et al. 2012). Different values for K

can be found in the literature,

but often in the range 1-3 µM DIN on system scale. It is clear that a K

-value of 2 µM only is

indicative as the affinity vary between species and also might depends if DIN is represented

by ammonium or nitrate. It is also shown in the literature (¤ref.¤) that DON can be a source

of nitrogen for phytoplankton. Rather than taxonomic group, size is clearly a factor that

systematically affect K

, with smaller cells having a higher affinity (¤ref.¤). This is also

reflected in the observation for Danish marine areas, where cell size increase with

chlorophyll concentration (Stæhr et al. 2004, Stæhr and Markager 2004). However, in a

situation with low DIN-concentrations the phytoplankton community will adapt toward

species with higher affinity

–

as stated

–

often smaller species. Thus, even that some types

of phytoplankton clearly display much higher K

-values; they will likely be replaced under

nutrient poor conditions, meaning that a general value for K

under 2 µM is meaningful for

lo DIN o ditio s. Although, e ha e t ade a o plete se siti it a al sis, e e pe t

that values in the range is 1-3 µM DIN will produce about the same results with respect to

number of days with nutrient limitation, given that the change for high to low DIN

concentrations in the spring is often occur within a few days. It should also be emphasized

that we have not just used the K

values as a rigid threshold but

–

as described in the report

–

we have analysed the relationship between the number of days with DIN and DIP

concentration under these thresholds (2 and 0.2 µM respectively) and the observed Chl. a

concentration with another K

value the number of days would change, but so would the

eak poi t a d he e the goal. The efo e o l la ge ha ges i the K

or a varying K

would result in significant changes in MAI based on this supporting indicator alone.

“… Kd indicator … are assigned double weight”

“… light attenuation indicator has beem giving double

weight”

“… we have transformed the estimated PLR values into

categories when above 25 %”

“we chose a half saturation coefficient (Ks) for nitrogen

limitation of 2 µM”

“This choice is b

ased on our wish from a management

perspective to emphasise intercalibrated indicators and has

no scientific basis”

All of these choices sound arbitrary and

cursory. Can you justify?

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“…due to the time constraints … we chose not to develop

models” & “… the demand was assigned as 25 %..”

“… values above one trigger a demand 25%”

“we used categorization … as demonstrated in Table 8.7”

“… the target values are rounded …”

The hoi es a e ot ade u so

ut a e all a efull o side ed e pe t judge e ts.

The alues a e the esults of dis ussio s a d a eful o side atio s ased o the a

results from the analysis and our knowledge of the system and the development over the

last decades combined with literature studies. We have sought to argue for the choices in

section 8.3. As the question is not specific, we find it difficult to supplement this

argumentation.

To this poi t, e fi d it i po ta t to ef esh the ai of the a al sis; To gi e the

best

possible estimate of the reduction in press factors the can result in GES for Danish marine

areas and hence compliance with the WFD. As the environmental statuses of Danish marine

areas are quite far away from GES, the result can only be an estimate. The choices in

question reflect our aim to find a balance and minimize the risk of both over and

underestimation of the reduction in nutrient loadings.

102

The scenarios have the basis that BSAP

nutrient load reductions are

implemented. These comprise of

massive P-load reductions (e.g., 60% for

Baltic Proper that eventually should lead

to halving winter DIP concentrations

there), but all published scenarios show

that the response time is quite slow with

typical e-folding time of say 20 years.

How is this time-delay handled in the

model?

We have not assessed the time-delay. We have assessed the impact as we expect them

to be over the coming decade. Our focus has been on evaluating the reduction targets that

will ensure that Denmark fulfil Danish obligations towards WFD in all water bodies given

that the loadings from other countries comply with BASP.

It is surprising that massive load

reductions to Baltic Sea do not give

more response to basin 217. The export

of phosphorus from the Baltic proper

should decrease substantially given that

DIP concentrations should be reduced to

50% of present day concentrations in

BSAP. Could you explain?

Since the adaptation of the BSAP significant reductions (although especially the Baltic

Proper still lack significant P reductions) in both N and P loads have been implemented and

observed (HELCOM 2011). However, when assessing the impact in observed concentrations

of both DIN, DIP, TN and TP in the Baltic Proper, and even more evident in the Arkona Basin

and Bornholm Basin (HELCOM 2013), the reductions in concentrations does not reflect the

reductions in loads. Hence, scenario results behind BSAP show that eventually significant

111

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reductions in e.g. DIP is expected, but the observations indicate that this could be impacted

by climate and, as mentioned by the expert panel, time-lag.

Our modelling has the BASP loading reductions as a prerequisite and the modelling result

provide the expected impact of reductions for the coming decade (and not several

decades). In this period, the model do not indicate a significant impacts on e.g. summer

chlorophyll-a and Kd even when implementing BSAP fully.

124

“With respect to the North Sea water bodies, the data basis

does not support the methodology described for mechanistic

model-based meta model since biogeochemical modelling

was not included in the study. However, GES has not been

reached in any of the Danish water bodies in the North Sea

and Skagerrak, and an approach taking limitation and

differences into account has therefore been developed

What is meant by this statement? It is

unclear

As we did not develop a mechanistic biogeochemical model for the North Sea, we could

not assess the reduction targets in a similar way as for the water bodies in the Kattegat and

Baltic Sea area. However, since the status assessment showed there is a need for

improvement of the environmental status (GES is not reached), we developed a method (a

meta-model) to circumvent the missing data from biogeochemical modelling. As mention in

the general Q&As we are working with the Danish EPA to develop a biogeochemical model

for the RBMP 2021-2027.

125

Can the uncertainty be expressed in a

way that it is easily understood by

decision makers and stakeholders?

This is basically a very interesting question. Especially, as it is extremely difficult for all

parts to understand what to do about the uncertainties.

The described approach is subject to uncertainty.

129

“…95% confidence interval at +/

13.5 % reduction”

What can you say about model error

variances and confidence limits based on

the comparison of mechanistic and

statistical models? Is this 13.5% the

overall confidence interval of loading

reduction?

The 13.5% is a calculated confidence interval for the percentage load reduction. This can

be translated to a confidence interval of approx. +/- 20% on the estimated MAI. This is not a

esult of a t aditio al u e tai t a al sis hi h is ot possi le to pe fo , ut a esult of

ensample modelling in 11 water bodies covered by both a statistical and mechanistic model.

Does the observation that for area 44

the statistical model fails because it does

not take regional reductions into

account imply that the statistical

approach would fail for all Type 1 water

bodies?

We have developed statistical models for several Type 1 water bodies (including area 44),

but not applied these in the final calculations of MAI (page 125 in report). This is because

the statistical approach is best suited for estuaries were local nutrient loadings dominate

over the nutrient exchange. Area 44 (Hjelm Bay) is on open bay on the south side of the

island Møn. The location means that the catchment in Denmark is small and the connection

130

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to the Western Baltic Sea is significant. Thus, it is an area were the statistical approach

probably only could work when based on data for regional nutrient loadings or maybe not

at all as the distance from nutrient loadings to effect is large. The statistical approach might

work better for other Type 1 water bodies, especially those located in the inner Danish

water where Danish land based loadings are more important. However, since the statistical

models do not operate with non-Danish nutrient sources as explanatory variables we

decided not to use this approach for Type 1 water bodies.

141

“the methods presented here basically violate the one

-out-

all-out principle, which is defined when evaluating the

ecological status and not when estimating measures to

ensure GES”; “When reductions based on chlorophyll

-a or

Kd are averaged instead of choosing the maximum

reductions,we do, in theory, not obtain GES for both

indicators”

Is the method therefore WFD

compliant? If not, what is necessary to

make it WFD compliant?

What management measures are

necessary to obtain GES for BOTH

indicators?

Our hypothesis is the GES for both Kd and chlorophyll-a will be reached after reductions

in nutrient loadings. However, the time scale in the response will probably be different, with

chlorophyll-a reacting faster than Kd. The reason is that chlorophyll-a respond to the

nutrient input to the system as well as the nutrient pool stored after decades with high

loadings (see e.g. Jørgensen at al. 2014 and Knudsen-Leerbeck et al (2017). In contract, Kd is

only for a small part related to the chlorophyll-a concentration (see e.g. Pedersen et al. 2014

and Carstensen 2013) but closely correlated with the total amount of organic matter in the

systems. This difference in response has also been described in Timmermann et al. 2010.

The use of an average reduction target instead of the calculated maximum reduction target

will, at least formally, indicate that at least one parameter will not reach GES but it will also

reduce the risk of overestimating the reduction target. Therefore, we suggest an adaptive

management strategy where the effects of the suggested nutrient reductions (based on

average, instead of maximum reduction targets) are evaluated after some years and then, if

necessary, additional measures can be implemented. It should be noticed that even if the

light climate is sufficient for eelgrass (i.e. the Kd indicator has reached GES), it is very likely

that the offi ial i di ato eelg ass depth li it has ot ea hed GE“.

141

It is stated that the basis is to obtain GES

in 2027. This is fine, but it also has

consequences on how to handle effects

from regional reductions (BSAP), see the

comment above on scenarios (page

102). It would be relevant to discuss the

time aspect already in the beginning of

the report as well, because we know the

ecosystem responds slowly, and

differently across the water bodies.

We acknowledge that the ecosystem responds slowly, and especially the expected

impacts from the actions taken according to BSAP and the Gothenburg Protocol. We believe

that the estimated reduction targets should be seen as the reductions needed to obtain GES

in Danish water bodies, but we cannot guarantee that observations will support this in

2027.

“… focused on reducing uncertainties,

for instance by

averaging … and applying a type

-specific approach

142

You lose information at the same time.

Can you guarantee reduction of

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uncertainties without proper statistical

error analysis, that is, comparison on

error variances of models based on

actual and averaged data?

Information might be lost when data is aggregated (averaged and/or type-specific)

provided that the uncertainty is low. However, this is not likely the case especially for

estimating reference chlorophyll-a concentrations where the models are used far from the

calibration area. Whenever individual values were considered too uncertain, we have

prioritized robust (but aggregated) values with the risk of individual value deviating from

the average/type-specific value.

142

“The

ensemble model results reveal good agreement

between the two very different model approaches …, thus

indicating that the estimated MAIs are reliable”

How can you say so without proper

statistical error analysis?

The rationale behind the statement is that since to independent methods obtain fairly

similar predictions of MAI, it support the confidence in the result. It is not possible to

perform traditional statistical error analysis on the MAI estimates. Instead we have used an

ensemble approach when possible and although we cannot rule out the risk that the both

models are biased or the error/uncertainty for each of the approaches is much higher than

the difference between the approaches, it is highly unlikely (P<0.0001) that the two

methods just by chance coincide for 11 independent areas and are highly correlated

(R2=0.85).

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Pedersen, O., T. Binzer, and J. Borum 2004. Sulphide intrusion in eelgrass (Zostera marina L.). Plant Cell and

Environment

27:

595-602.

Pedersen, T.M., K. Sand-Jensen, S. Markager & S. L. Nielsen (2014) Optical changes in a eutrophic estuary

during reduced nutrient loadings. Estuaries and Coast 37, 880-892. doi: 10.1007/s12237-013-9732-y.

Petersen, M. E., M. Maar, J. Larsen, E. F. Moller, and P. J. Hansen 2017. Trophic cascades of bottom-up and

top-down forcing on nutrients and plankton in the Kattegat, evaluated by modelling. Journal of Marine

Systems

169:

25-39.

Pogson M & P Smith (2015) Effect of spatial data resolution on uncertainty. Environmental Modelling &

Software 63: 87-96

Pulido Pérez C & J Borum (2010) Eelgrass (Zostera marina) tolerance to anoxia. JEMBE 385(1-2): 8-13.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Ralph, P. J., M. J. Durako, S. Enriquez, C. J. Collier, and M. A. Doblin 2007. Impact of light limitation on

seagrasses. Journal of Experimental Marine Biology and Ecology

350:

176-193.

Riemann, B., J. Carstensen, K. Dahl, H. Fossing, J. W. Hansen, H. H. Jakobsen, A. B. Josefson, D. Krause-

Jensen, S. Markager, P. A. Staehr, K. Timmermann, J. Windolf, and J. H. Andersen 2016. Recovery of Danish

Coastal Ecosystems After Reductions in Nutrient Loading: A Holistic Ecosystem Approach. Estuaries and

Coasts

39:

82-97.

Roca G, Alcoverro T, Krause-Jensen D, Balsby TJS, van Katwijk MM, Marba N, Santos R, Arthur R, Mascaró O,

Fernández-Torquemada Y, Pérez M, Duarte C & J Romero (2016) Response of seagrass indicators to shifts in

environmental stressors: A global review and management synthesis. Ecological Indicators 63: 310-323.

Ryther, J. H., and W. M. Dunstan 1971. Nitrogen,Phosphorus, and Eutrophication in Coastal Marine

Environment. Science

171:

1008-&.

Smith, V. H. 2003. Eutrophication of freshwater and coastal marine ecosystems - A global problem.

Environmental Science and Pollution Research

10:

126-139.

Smith, V. H., S. B. Joye, and R. W. Howarth 2006. Eutrophication of freshwater and marine ecosystems.

Limnology and Oceanography

51:

351-355.

Schmidt AL, Wysmyk JKC, Craig SE & HK Lotze (2012) Regional-scale effects of eutrophication on ecosystem

structure and services of seagrass beds. Limnol Oceanogr 57(5). 1389–1402

Tamminen, T., and T. Andersen 2007. Seasonal phytoplankton nutrient limitation patterns as revealed by

bioassays over Baltic Sea gradients of salinity and eutrophication. Marine Ecology Progress Series

340:

121-

138.

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Vandløb 2015. NOVANA. 206. 2016.

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–

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Ref Type: Generic

Timmermann, K., S. Markager, and K. E. Gustafsson 2010. Streams or open sea? Tracing sources and effects

of nutrient loadings in a shallow estuary with a 3D hydrodynamic-ecological model. Journal of Marine

Systems

82:

111-121.

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Vulnerability of Zostera marina seedlings to physical stress. Marine Ecology-Progress Series

418:

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134: 241–260.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Annex 1

The Limfjord model

Figure 1: Monitoring stations applied within the Limfjord. Red dots indicate a monitoring station with at

least 5 years of data within the period year 2000 to year 2012. Blue areas indicate the

different Danish water bodies. The red circles indicate the locations of the time series

included in this Annex.

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Figure 2: Comparison of measured surface (red markings) and bottom (black markings) salinity with

modelled salinity at the surface (orange line) and at the bottom (green line) at 3708-1 and

3727-1.

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Figure 3: Comparison of measured surface (red dots) and bottom (black dots) water temperature with

modelled water temperature at the surface (orange line) and at the bottom (green line) at

3708-1. Data from 3727-1 were not processed.

Figure 4: Measurements of nitrogen at station 3708-1 in the surface (black markings) and bottom (blue

markings) compared to modelled surface nitrogen (orange line) and bottom nitrogen (red

line). At the top measurements and modelling results of DIN are shown, and at the bottom of

TN.

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Figure 5: Measurements of nitrogen at station 3727-1 in the surface (black markings) and bottom (blue

markings) compared to modelled surface nitrogen (orange line) and bottom nitrogen (red

line). At the top measurements and modelling results of DIN are shown, and at the bottom of

TN.

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Figure 6: Measurements of nitrogen at station 3708-1 in the surface (black markings) and bottom (blue

markings) compared to modelled surface phosphorous (orange line) and bottom

phosphorous (red line). At the top measurements and modelling results of DIP are shown,

and at the bottom of TP.

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Figure 7: Measurements of nitrogen at station 3727-1 in the surface (black markings) and bottom (blue

markings) compared to modelled surface phosphorous (orange line) and bottom

phosphorous (red line). At the top measurements and modelling results of DIP are shown,

and at the bottom of TP.

Figure 8: Measurements of chlorophyll-a at station 3727-1 in the surface (black markings) and bottom

(blue markings) compared to modelled surface chlorophyll-a (orange line) and bottom

chlorophyll-a (red line).

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Figure 9: Measurements of chlorophyll-a at station 3708-1 in the surface (black markings) and bottom

(blue markings) compared to modelled surface chlorophyll-a (orange line) and bottom

chlorophyll-a (red line).

Figure 10: Measurements of dissolved oxygen at station 3727-1 in the surface (black markings) and

bottom (blue markings) compared to modelled surface dissolved oxygen (orange line) and

bottom dissolved oxygen (red line).

Figure 11: Measurements of dissolved oxygen at station 3708-1 in the surface (black markings) and

bottom (blue markings) compared to modelled surface dissolved oxygen (orange line) and

bottom dissolved oxygen (red line).

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Figure 12: Measurements K

dPAR

at station 3708-1 (blue markings) and modelled K

dPAR

(red line).

Figure 13: Measurements K

dPAR

at station 3727-1 (blue markings) and modelled K

dPAR

(red line).

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Odense Fjord Model

Figure 14: Monitoring stations applied for the Odense Fjord model performance. Biogeochemical data

exists for two of the four stations in the map, and here we include the data from the central

station FYN6900017.

Figure 15: Comparison of measured and calculated salinity in the surface (upper) and on the bottom

(lower) at station 69100017 in the outer fjord.

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Figure 16: Comparison of measured and calculated water temperature in the surface (upper) and on the

bottom (lower) at station 69100017 in the outer fjord.

Figure 17: Measurements (blue markings) and model results (red lines) of DIN at station 6910017. Surface

concentrations are shown in the top figure and bottom concentrations in the bottom figure.

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Figure 18: Measurements (blue markings) and model results (red lines) of TN at station 6910017. Surface

concentrations are shown in the top figure and bottom concentrations in the bottom figure.

Figure 19: Measurements (blue markings) and model results (red lines) of DIP at station 6910017. Surface

concentrations are shown in the top figure and bottom concentrations in the bottom figure.

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Figure 20: Measurements (blue markings) and model results (red lines) of TP at station 6910017. Surface

concentrations are shown in the top figure and bottom concentrations in the bottom figure.

Figure 21: Measurements (blue markings) and model results (red lines) of chlorophyll-a at station

6910017. Surface concentrations are shown in the top figure and bottom concentrations in

the bottom figure.

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Figure 22: Measurements (blue markings) and model results (red lines) of dissolved oxygen at station

6910017. Surface concentrations are shown in the top figure and bottom concentrations in

the bottom figure.

Figure 23: Measurements K

dPAR

at station 6900017 (blue markings) and modelled K

dPAR

(red line).

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Roskilde Fjord Model

Figure 24: Monitoring stations applied for the Roskilde Fjord model performance. Continuous

biogeochemical data exists for two of the stations in the map, and here we include the data

from FBR65.

Figure 25: Comparison of measured and calculated salinity in the surface (upper) and on the bottom

(lower) at station FRB65.

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Figure 26: Comparison of measured and calculated water temperature in the surface (upper) and on the

bottom (lower) at station FRB65.

Figure 27: Surface measurements (blue markings) and model results (black line) of DIN at station FRB65.

Red line indicate modelled bottom concentrations.

Figure 28: Surface measurements (blue markings) and model results (black line) of TN at station FRB65.

Red line indicate modelled bottom concentrations.

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Figure 29: Surface measurements (blue markings) and model results (black line) of DIP at station FRB65.

Red line indicate modelled bottom concentrations.

Figure 30: Surface measurements (blue markings) and model results (black line) of TP at station FRB65.

Red line indicate modelled bottom concentrations.

Figure 31: Surface measurements (blue triangles) and model results (black line) of chlorophyll-a at station

FRB65. Red line indicate modelled bottom concentrations and blue circles indicate

corresponding measured bottom concentrations.

Figure 32: Surface measurements (blue markings) and model results (black line) of dissolved oxygen at

station FRB65. Surface concentrations are shown in the top figure and bottom

concentrations in the bottom figure. Red line indicate modelled bottom concentrations and

green dots indicate measured bottom concentrations.

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Figure 33: Measurements of Secchi disc depth at station FRB65 (blue and red markings

–

green markings

show the water depth) and modelled Secchi disc depth (black line).

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IDW Model

Figure 34: Monitoring stations applied for the IDW model performance analysis. Red dots indicate a

monitoring station with at least 5 years of data within the period: Year 2000 to year 2012.

Blue areas indicate the different Danish water bodies. Red circles show the biogeochemical

monitoring stations included in this annex. Salinity and temperature are shown for the two

station with blue circles. The differences between the locations of the salinity/temperature

stations and biogeochemistry stations is due to which data is readily available from the

model runs.

Figure 35: Measured surface (black dots) and bottom (blue dots) salinity compared to modelled salinity at

surface (orange line) and at the bottom (red lines), respectively, at the monitoring station

Ven (431).

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Figure 36: Measured surface (black dots) and bottom (blue dots) salinity concentrations compared to

modelled salinity at surface (orange line) and at the bottom (red lines) at the monitoring

station at Gniben (925).

Figure 37: Measured surface (black dots) and bottom (blue dots) water temperature compared to modelled

temperature at surface (orange line) and at the bottom (red lines) at the monitoring station

Ven (431).

Figure 38: Measured surface (black dots) and bottom (blue dots) water temperature compared to modelled

temperature at surface (orange line) and at the bottom (red lines) at the monitoring station

Gniben (925).

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Figure 39: Measurements of surface chlorophyll-a concentrations (green dots) and modelled

concentrations (black line). Top panel is from south of Funen, middle panel is from the

Sound and bottom panel is from Aarhus Bay.

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Figure 40: Measurements of surface nitrate concentrations (green dots) and modelled concentrations

(black line). Red dots indicate measurements at the bottom and blue line indicated modelled

concentrations at the bottom. Top panel is from south of Funen, middle panel is from the

Sound and bottom panel is from Aarhus Bay.

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Figure 41: Measurements of surface phosphorous concentrations (green dots) and modelled

concentrations (black line). Red dots indicate measurements at the bottom and blue line

indicated modelled concentrations at the bottom. Top panel is from south of Funen, middle

panel is from the Sound and bottom panel is from Aarhus Bay.

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Figure 42: Measurements of surface TN concentrations (green dots) and modelled concentrations (black

line). Red dots indicate measurements at the bottom and blue line indicated modelled

concentrations at the bottom. Top panel is from south of Funen, middle panel is from the

Sound and bottom panel is from Aarhus Bay. The sudden drops at the beginning of each

years is an ‘artificial’ model output due to initialisation, and they are not a result of the

modelling.

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Figure 43: Measurements of surface TP concentrations (green dots) and modelled concentrations (black

line). Red dots indicate measurements at the bottom and blue line indicated modelled

concentrations at the bottom. Top panel is from south of Funen, middle panel is from the

Sound and bottom panel is from Aarhus Bay.

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Figure 44: Measurements of surface dissolved oxygen concentrations (green dots) and modelled

concentrations (black line). Red dots indicate measurements at the bottom and blue line

indicated modelled concentrations at the bottom. Top panel is from south of Funen, middle

panel is from the Sound and bottom panel is from Aarhus Bay. No oxygen concentrations

exists at the stations in the Sound.

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Figure 45: Measurements of Secchi depth (green dots) and modelled Secchi depth (black line). Top panel

is from south of Funen and bottom panel is from Aarhus Bay. Data for the Sound station was

not available.

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MIKE 21 & MIKE 3 Flow Model FM

Hydrodynamic and Transport Module

Scientific Documentation

MIKE

2016

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DHI headquarters

Agern Allé 5

DK-2970 Hørsholm

Denmark

+45 4516 9200 Telephone

+45 4516 9333 Support

+45 4516 9292 Telefax

[email protected]

www.mikepoweredbydhi.com

mike_321_fm_scientific_doc.docx/OSP/ORS/2015-10-22 -

DHI

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PLEASE NOTE

This document refers to proprietary computer software, which is

protected by copyright. All rights are reserved. Copying or other

reproduction of this manual or the related programmes is

prohibited without prior written consent of DHI. For details please

refer to your

‘DHI

Software Licence Agreement’.

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‘DHI

Software Licence Agreement’:

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NO EVENT SHALL DHI OR ITS REPRESENTATIVES

(AGENTS AND SUPPLIERS) BE LIABLE FOR ANY DAMAGES

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PRINTING HISTORY

June 2004 ................................................................... Edition 2004

August 2005 ............................................................... Edition 2005

April 2006 ................................................................... Edition 2007

December 2006 ........................................................... Edition 2007

October 2007 .............................................................. Edition 2008

January 2009............................................................... Edition 2009

February 2010 ............................................................. Edition 2009

July 2010 ..................................................................... Edition 2011

August 2012 ................................................................ Edition 2012

October 2013............................................................... Edition 2014

October 2015............................................................... Edition 2016

LIMITED LIABILITY

MIKE

2016

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MIKE 21 & MIKE 3 Flow Model FM

Hydrodynamic and Transport Module - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

CONTENTS

MIKE 21 & MIKE 3 Flow Model FM

Hydrodynamic and Transport Module

Scientific Documentation

2.1

2.1.1

2.1.2

2.1.3

2.1.4

2.1.5

2.2

2.3

2.3.1

2.3.2

2.3.3

2.4

2.5

2.6

2.7

2.8

2.9

2.10

2.10.1

2.10.2

2.10.3

2.10.4

Introduction .......................................................................................................................1

Governing Equations........................................................................................................3

3D Governing Equations in Cartesian Coordinates ............................................................................. 3

Shallow water equations ...................................................................................................................... 3

Transport equations for salt and temperature ...................................................................................... 5

Transport equation for a scalar quantity .............................................................................................. 6

Turbulence model ................................................................................................................................ 6

Governing equations in Cartesian and sigma coordinates .................................................................. 9

3D Governing Equations in Spherical and Sigma Coordinates ......................................................... 11

2D Governing Equations in Cartesian Coordinates ........................................................................... 13

Shallow water equations .................................................................................................................... 13

Transport equations for salt and temperature .................................................................................... 14

Transport equations for a scalar quantity........................................................................................... 14

2D Governing Equations in Spherical Coordinates ........................................................................... 14

Bottom Stress ..................................................................................................................................... 15

Wind Stress ........................................................................................................................................ 16

Ice Coverage ...................................................................................................................................... 17

Tidal Potential .................................................................................................................................... 18

Wave Radiation .................................................................................................................................. 19

Heat Exchange ................................................................................................................................... 20

Vaporisation ....................................................................................................................................... 20

Convection ......................................................................................................................................... 22

Short wave radiation .......................................................................................................................... 23

Long wave radiation ........................................................................................................................... 26

3.1

3.1.1

3.1.2

3.1.3

3.2

3.3

3.3.1

3.3.2

3.3.3

Numerical Solution .........................................................................................................29

Spatial Discretization .......................................................................................................................... 29

Vertical Mesh ..................................................................................................................................... 31

Shallow water equations .................................................................................................................... 34

Transport equations ........................................................................................................................... 37

Time Integration ................................................................................................................................. 38

Boundary Conditions .......................................................................................................................... 40

Closed boundaries ............................................................................................................................. 40

Open boundaries ................................................................................................................................ 40

Flooding and drying ............................................................................................................................ 40

4.1

4.2

Infiltration and Leakage ..................................................................................................43

Net Infiltration Rates ........................................................................................................................... 43

Constant Infiltration with Capacity ...................................................................................................... 44

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MIKE 21 & MIKE 3 Flow Model FM

5.1

5.1.1

5.1.2

5.1.3

Validation ........................................................................................................................ 47

Dam-break Flow through Sharp Bend ............................................................................................... 47

Physical experiments ......................................................................................................................... 47

Numerical experiments ...................................................................................................................... 48

Results ............................................................................................................................................... 49

References...................................................................................................................... 53

Hydrodynamic and Transport Module - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Introduction

This document presents the scientific background for the new MIKE 21 & MIKE 3 Flow

Model FM modelling system developed by DHI Water & Environment. The objective is to

provide the user with a detailed description of the flow and transport model equations,

numerical discretization and solution methods. Also model validation is discussed in this

document.

The MIKE 21 & MIKE 3 Flow Model FM is based on a flexible mesh approach and it has

been developed for applications within oceanographic, coastal and estuarine

environments. The modelling system may also be applied for studies of overland flooding.

The system is based on the numerical solution of the two/three-dimensional

incompressible Reynolds averaged Navier-Stokes equations invoking the assumptions of

Boussinesq and of hydrostatic pressure. Thus, the model consists of continuity,

momentum, temperature, salinity and density equations and it is closed by a turbulent

closure scheme. For the 3D model the free surface is taken into account using a sigma

coordinate transformation approach.

The spatial discretization of the primitive equations is performed using a cell-centred finite

volume method. The spatial domain is discretized by subdivision of the continuum into

non-overlapping elements/cells. In the horizontal plane an unstructured grid is used while

in the vertical domain in the 3D model a structured mesh is used. In the 2D model the

elements can be triangles or quadrilateral elements. In the 3D model the elements can be

prisms or bricks whose horizontal faces are triangles and quadrilateral elements,

respectively.

Including the MIKE 21 Flow Model FM (two-dimensional flow) and MIKE 3 Flow Model FM (three-

dimensional flow)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MIKE 21 & MIKE 3 Flow Model FM

Hydrodynamic and Transport Module - © DHI

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

Governing Equations

2.1

2.1.1

Governing Equations

3D Governing Equations in Cartesian Coordinates

Shallow water equations

The model is based on the solution of the three-dimensional incompressible Reynolds

averaged Navier-Stokes equations, subject to the assumptions of Boussinesq and of

hydrostatic pressure.

The local continuity equation is written as





�½



(2.1)

and the two horizontal momentum equations for the x- and y-component, respectively









�½























�½ 









 









  







 



 







 





 





(2.2)











  



 









 



 







 





 





(2.3)

is the still water depth;

�½





is the total water depth;

u, v

and

are the velocity

components in the

x, y

and

direction;

�½

2 sin



is the Coriolis parameter (



is the

angular rate of revolution and



the geographic latitude);

is the gravitational

acceleration;



is the density of water;

and

are components of the

radiation stress tensor;

atmospheric pressure;

discharge due to point sources and





is the velocity by which the water is

where

is the time;

x, y

and

are the Cartesian coordinates;



is the surface elevation;



is the vertical turbulent (or eddy) viscosity;

is the



is the reference density of water.

is the magnitude of the

discharged into the ambient water. The horizontal stress terms are described using a

gradient-stress relation, which is simplified to

�½

  

    



 







  



 

 

  



 





(2.4)

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MIKE 21 & MIKE 3 Flow Model FM

�½

   



    











  



  

 











(2.5)

where

is the horizontal eddy viscosity.

The surface and bottom boundary condition for

u, v

and

are

�½



�½ 













 











�½



 �½















(2.6)



 









�½



 �½



 









where

bottom stresses.







and







are the

and

components of the surface wind and





(2.7)

The total water depth,

can be obtained from the kinematic boundary condition at the

surface, once the velocity field is known from the momentum and continuity equations.

However, a more robust equation is obtained by vertical integration of the local continuity

equation

 





�½







(2.8)



where

and

are precipitation and evaporation rates, respectively, and

and

are

the depth-averaged velocities

The fluid is assumed to be incompressible. Hence, the density,



, does not depend on

the pressure, but only on the temperature,

and the salinity,

via the equation of state

�½



udz





�½



vdz





(2.9)



�½



(

)

(2.10)

Here the UNESCO equation of state is used (see UNESCO, 1981).

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Governing Equations

2.1.2

Transport equations for salt and temperature

The transports of temperature,

and salinity,

follow the general transport-diffusion

equations as



 







�½

 

 











 









�½

 

 











(2.11)

(2.12)

where

is the vertical turbulent (eddy) diffusion coefficient.

is a source term due to

heat exchange with the atmosphere.

and

are the temperature and the salinity of

the source.

are the horizontal diffusion terms defined by







�½  



 

  





  













 







 



(2.13)

where

is the horizontal diffusion coefficient. The diffusion coefficients can be related

to the eddy viscosity

�½

where



is the Prandtl number. In many applications a constant Prandtl number can be

used (see Rodi (1984)).

The surface and bottom boundary conditions for the temperature are

�½





and

�½





(2.14)

�½ 



�½









(2.15)



the water. A detailed description for determination of

and

is given in Section 2.10.

where

is the surface net heat flux and

�½

4217

 

)

is the specific heat of



�½



(2.16)

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MIKE 21 & MIKE 3 Flow Model FM

The surface and bottom boundary conditions for the salinity are

�½



�½ 



�½



�½



(2.17)

(2.18)

When heat exchange from the atmosphere is included, the evaporation is defined as









�½ 









where

is the latent heat flux and

water.

(2.19)

�½

2.5



is the latent heat of vaporisation of

2.1.3

Transport equation for a scalar quantity

The conservation equation for a scalar quantity is given by



  





�½

 

 











where

is the concentration of the scalar quantity,

is the linear decay rate of the

(2.20)

scalar quantity,

is the concentration of the scalar quantity at the source and

is the

vertical diffusion coefficient.

is the horizontal diffusion term defined by

 

 

  

�½  

  

 







 







 



where

is the horizontal diffusion coefficient.

(2.21)

2.1.4

Turbulence model

The turbulence is modelled using an eddy viscosity concept. The eddy viscosity is often

described separately for the vertical and the horizontal transport. Here several turbulence

models can be applied: a constant viscosity, a vertically parabolic viscosity and a

standard k- model (Rodi, 1984). In many numerical simulations the small-scale

turbulence cannot be resolved with the chosen spatial resolution. This kind of turbulence

can be approximated using sub-grid scale models.

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Governing Equations

Vertical eddy viscosity

The eddy viscosity derived from the log-law is calculated by









 







�½





 





 





(2.22)

where



�½

max







and

are two constants.



and



are the

friction velocities associated with the surface and bottom stresses,

�½ 

0.41

give the standard parabolic profile.

�½

0.41

and

In applications with stratification the effects of buoyancy can be included explicitly. This is

done through the introduction of a Richardson number dependent damping of the eddy

viscosity coefficient, when a stable stratification occurs. The damping is a generalisation

of the Munk-Anderson formulation (Munk and Anderson, 1948)

where



is the undamped eddy viscosity and

is the local gradient Richardson number





  

  

 

     

�½ 





  

  

 









�½





aRi

)



(2.23)

(2.24)

In the k- model the eddy-viscosity is derived from turbulence parameters

and



�½

and

�½

0.5

are empirical constants.



�½





(2.25)

where

is the turbulent kinetic energy per unit mass (TKE),

and



is an empirical constant.

The turbulent kinetic energy,

and the dissipation of TKE,

following transport equations



is the dissipation of TKE



, are obtained from the



 

















�½

 































�½





(2.26)

 











 







 

























(2.27)

where the shear production,

and the buoyancy production,

are given as

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MIKE 21 & MIKE 3 Flow Model FM

  



 















     



�½

  

  

 













�½

(2.28)





(2.29)

with the Brunt-Väisälä frequency,

defined by

�½ 









(2.30)

is the turbulent Prandtl number and

constants.

are the horizontal diffusion terms defined by





and



are empirical

 

 

  

(



)

�½  

  



(



)



 

 

 









The horizontal diffusion coefficients are given by

respectively.

(2.31)

�½



and

�½





Several carefully calibrated empirical coefficients enter the k-e turbulence model. The

empirical constants are listed in (2.47) (see Rodi, 1984).

Table 2.1

Empirical constants in the k- model.



0.09



1.44



1.92





0.9



1.0





1.3

At the surface the boundary conditions for the turbulent kinetic energy and its rate of

dissipation depend on the wind shear,



z =



�½





(2.32)



�½









�½







�½

for











�½

3/ 2

for



(2.33)

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Governing Equations

where



=0.4 is the von Kármán constant,

�½ 

�½

0.07

is and empirical constant and



is the distance from the surface where the boundary condition is imposed. At the seabed

the boundary conditions are

�½

where







�½







(2.34)



is the distance from the bottom where the boundary condition is imposed.

Horizontal eddy viscosity

In many applications a constant eddy viscosity can be used for the horizontal eddy

viscosity. Alternatively, Smagorinsky (1963) proposed to express sub-grid scale

transports by an effective eddy viscosity related to a characteristic length scale. The

subgrid scale eddy viscosity is given by

�½

(2.35)

where

is a constant,

is a characteristic length and the deformation rate is given by

 



�½ 



 





2.1.5





(

�½

1,2)





(2.36)

Governing equations in Cartesian and sigma coordinates

The equations are solved using a vertical

-transformation



�½

where



varies between 0 at the bottom and 1 at the surface. The coordinate

transformation implies relations such as



 �½

(2.37)

     

 



  

 



  





�½

 







 







 



  





 







 



 





 

 







In this new coordinate system the governing equations are given as



�½



z h





(2.38)

(2.39)







�½



 



(2.40)

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MIKE 21 & MIKE 3 Flow Model FM



hvu













�½

fvh

































huv













�½ 

fuh

























 









 









 

 

 

 









 









(2.41)



huT



hvT







�½





























 

 



 













 











 









(2.42)



huk



hvk







�½























hus



hvs





 







�½



 





















 









 















(2.43)

(2.44)



















�½

































 

(







)











(2.45)

 







huC



hvC





�½



 































The modified vertical velocity is defined by















 



























(2.46)

(2.47)



�½

 















 







 

















 





(2.48)

The modified vertical velocity is the velocity across a level of constant

.

The horizontal diffusion terms are defined as



 



    



 

  

   









 

  



 



 

(2.49)

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Governing Equations



(



)







   



   



     









  



  









 

(2.50)

 

   

 

 

 

(



)

 





 





 

 



(2.51)

The boundary condition at the free surface and at the bottom are given as follows

 







�½



 �½



 















=1:





(2.52)

 







�½





�½



















=0:



(2.53)

The equation for determination of the water depth is not changed by the coordinate

transformation. Hence, it is identical to Eq. (2.6).

2.2

3D Governing Equations in Spherical and Sigma Coordinates

In spherical coordinates the independent variables are the longitude,



, and the latitude,



. The horizontal velocity field (u,v) is defined by

�½

cos





�½



(2.54)

where

is the radius of the earth.

In this coordinate system the governing equations are given as (all superscripts indicating

the horizontal coordinate in the new coordinate system are dropped in the following for

notational convenience)

 



cos



 







 



 



  



�½



t R

cos







(2.55)

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MIKE 21 & MIKE 3 Flow Model FM

 



hvu

cos



 











�½ 



tan















cos



 







 



 









cos



 

 



 

















 















 

 





 



cos



  









 



 



(2.56)

 

huv



cos



 











�½  



tan















cos



 







 



 









 

 



 







 

huT



hvT

cos



 







  



�½

cos



 











 









 

























 

















 

















 





cos











(2.57)

(2.58)



 

hus



hvs

cos



 





  



�½



t R

cos



 















 

huk



hvk

cos



 







�½















cos



 







 









 

(







)





















 







 













(2.59)

(2.60)





 







cos



 





  



�½





cos



 

















 

huC



hvC

cos



 





  



�½





cos



 























 



























(2.61)

 







 















(2.62)

The modified vertical velocity in spherical coordinates is defined by

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Governing Equations



�½

 





h v







d v









 





 

t R

cos

















cos















(2.63)

The equation determining the water depth in spherical coordinates is given as

 



cos









 �½







t R

cos



 











(2.64)

2.3

2.3.1

2D Governing Equations in Cartesian Coordinates

Shallow water equations

Integration of the horizontal momentum equations and the continuity equation over depth

�½





the following two-dimensional shallow water equations are obtained



hvu









�½

fvh









 



 





















 









�½



(2.65)

















(2.66)



huv









�½ 

fuh









 



 





















 



















(2.67)

The overbar indicates a depth average value. For example,

and

are the depth-

averaged velocities defined by

�½



udz





�½



vdz





(2.68)

The lateral stresses

include viscous friction, turbulent friction and differential

advection. They are estimated using an eddy viscosity formulation based on of the depth

average velocity gradients

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MIKE 21 & MIKE 3 Flow Model FM

�½

 







�½



 

�½

 











(2.69)

2.3.2

Transport equations for salt and temperature

Integrating the transport equations for salt and temperature over depth the following two-

dimensional transport equations are obtained



hu s



hvs



�½









hu T



hvT



�½





(2.70)

(2.71)

where

and

is the depth average temperature and salinity.

2.3.3

Transport equations for a scalar quantity

Integrating the transport equations for a scalar quantity over depth the following two-

dimensional transport equations are obtained



hu C



hvC



�½







where

is the depth average scalar quantity.

(2.72)

2.4

2D Governing Equations in Spherical Coordinates

In spherical coordinates the independent variables are the longitude,



,and the latitude,



. The horizontal velocity field (u,v) is defined by

�½

cos





�½



(2.73)

where

is the radius of the earth.

In spherical coordinates the governing equation can be written

 



cos









�½







t R

cos



 











(2.74)

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Governing Equations



 



hvu

cos



 





�½ 



tan













cos



 





 



 

 







 





 



cos



  







 

cos



 

 









 

 































(2.75)



 

huv



cos











�½  



tan













cos



 







 











 

 





 









 

 

 









 



cos











 

hu T



hvT

cos









 �½









cos



 









 

hu s



hvs

cos







 �½



 











cos

































(2.76)

(2.77)

(2.78)



 

hu C



hvC

cos







 �½













cos



 







(2.79)

2.5

Bottom Stress

The bottom stress,



�½

(



)

, is determined by a quadratic friction law





 

�½



(2.80)

where

is the drag coefficient and



�½

(

)

is the flow velocity above the bottom.

The friction velocity associated with the bottom stress is given by



�½

(2.81)

For two-dimensional calculations

is the depth-average velocity and the drag coefficient

can be determined from the Chezy number,

, or the Manning number,



�½

(2.82)

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MIKE 21 & MIKE 3 Flow Model FM

�½





1/ 6 2

(2.83)

For three-dimensional calculations

is the velocity at a distance



bed and the drag coefficient is determined by assuming a logarithmic profile between the

seabed and a point



above the seabed



above the sea

�½

where



=0.4 is the von Kármán constant and

is the bed roughness length scale.

When the boundary surface is rough,

, depends on the roughness height,



 















(2.84)

�½

where m is approximately 1/30.

(2.85)

Note, that the Manning number can be estimated from the bed roughness length using

the following

�½

25.4

/ 6







(2.86)

The wave induced bed resistance can be determined from



�½ 





(2.87)

where

is the friction velocity calculated by considering the conditions in the wave

boundary layer. For a detailed description of the wave induced bed resistance, see

Fredsøe (1984) and Jones et.al. (2014).

2.6

Wind Stress

In areas not covered by ice the surface stress,



�½

(



)

, is determined by the winds



above the surface. The stress is given by the following empirical relation



�½



(2.88)

where

is the density of air,

is the drag coefficient of air, and



�½

(

)

is the

wind speed 10 m above the sea surface. The friction velocity associated with the surface

stress is given by

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Governing Equations



�½



(2.89)

The drag coefficient can either be a constant value or depend on the wind speed. The

empirical formula proposed by Wu (1980, 1994) is used for the parameterisation of the

drag coefficient.





















�½ 











(2.90)

where

, c

, w

and

are empirical factors and

is the wind velocity 10 m above the

-3

sea surface. The default values for the empirical factors are

= 1.255·10 ,

= 2.425·10

= 7 m/s and

= 25 m/s. These give generally good results for open sea

applications. Field measurements of the drag coefficient collected over lakes indicate that

the drag coefficient is larger than open ocean data. For a detailed description of the drag

coefficient see Geernaert and Plant (1990).

2.7

Ice Coverage

It is possible to take into account the effects of ice coverage on the flow field.

In areas where the sea is covered by ice the wind stress is excluded. Instead, the surface



stress is caused by the ice roughness. The surface stress,



�½

(



)

, is determined

by a quadratic friction law



 

�½



(2.91)

where

is the drag coefficient and



�½

(

)

is the flow velocity below the surface.

The friction velocity associated with the surface stress is given by



�½

(2.92)

For two-dimensional calculations

is the depth-average velocity and the drag coefficient

can be determined from the Manning number,



�½





1/ 6 2

(2.93)

The Manning number is estimated from the bed roughness length using the following

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MIKE 21 & MIKE 3 Flow Model FM

�½

25.4

/ 6



(2.94)

For three-dimensional calculations

is the velocity at a distance

and the drag coefficient is determined by assuming a logarithmic profile between the

surface and a point



below the surface



below the surface

�½

where



=0.4 is the von Kármán constant and

is the bed roughness length scale.

When the boundary surface is rough,

, depends on the roughness height,



 















(2.95)

�½

where m is approximately 1/30.

(2.96)

2.8

Tidal Potential

The tidal potential is a force, generated by the variations in gravity due to the relative

motion of the earth, the moon and the sun that act throughout the computational domain.

The forcing is expanded in frequency space and the potential considered as the sum of a

number of terms each representing different tidal constituents. The forcing is implemented

as a so-called equilibrium tide, which can be seen as the elevation that theoretically would

occur, provided the earth was covered with water. The forcing enters the momentum

equations (e.g. (2.66) or (2.75)) as an additional term representing the gradient of the

equilibrium tidal elevations, such that the elevation



can be seen as the sum of the actual

elevation and the equilibrium tidal potential.



�½



ACTUAL





(2.97)

The equilibrium tidal potential



is given as



�½



cos(2





)

(2.98)

where



is the equilibrium tidal potential,

refers to constituent number (note that the

constituents here are numbered sequentially),

is a correction for earth tides based on

Love numbers,

is the amplitude,

is a nodal factor,

is given below,

is time,

is the

period of the constituent,

is the phase and

is the longitude of the actual position.

The phase

is based on the motion of the moon and the sun relative to the earth and can

be given by

�½

(



)



(



)



sin(

)

(2.99)

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Governing Equations

where

is the species,

are Doodson numbers,

is a nodal modulation factor (see

Table 2.3) and the astronomical arguments

s, h, p, N

and

are given in Table 2.2.

Table 2.2

Astronomical arguments (Pugh, 1987)

Mean longitude of the moon

Mean longitude of the sun

Longitude of lunar perigee

Longitude of lunar ascending node

Longitude of perihelion

277.02+481267.89T+0.0011T

280.19+36000.77T+0.0003T

334.39+4069.04T-0.0103T

259.16-1934.14T+0.0021T

281.22+1.72T+0.0005T

In Table 2.2 the time, T, is in Julian century from January 1 1900 UTC, thus T = (365(y

–

1900) + (d

–

1) +

i)/36525

and

int

(y-1901)/4),

is year and

is day number

depends on species number

and latitude

�½

3sin

(

)



�½

sin(2

)

�½

cos

(

)

The nodal factor

represents modulations to the harmonic analysis and can for some

constituents be given as shown in Table 2.3.

Table 2.3

Nodal modulation terms (Pugh, 1987)





, N

, M

1.000 - 0.130 cos(N)

1.043 + 0.414 cos(N)

1.009 + 0.187 cos(N)

1.006 + 0.115 cos(N)

1.000 - 0.037 cos(N)

1.024 + 0.286 cos(N)

-23.7 sin(N)

10.8 sin(N)

-8.9 sin(N)

-2.1 sin(N)

-17.7 sin(N)

2.9

Wave Radiation

The second order stresses due to breaking of short period waves can be included in the

simulation. The radiation stresses act as driving forces for the mean flow and can be used

to calculate wave induced flow. For 3D simulations a simple approach is used. Here a

uniform variation is used for the vertical variation in radiation stress.

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MIKE 21 & MIKE 3 Flow Model FM

2.10

Heat Exchange

The heat exchange with the atmosphere is calculated on basis of the four physical

processes

•

Latent heat flux (or the heat loss due to vaporisation)

Sensible heat flux (or the heat flux due to convection)

Net short wave radiation

Net long wave radiation

Latent and sensible heat fluxes and long-wave radiation are assumed to occur at the

surface. The absorption profile for the short-wave flux is approximated using

Beer’s law.

The attenuation of the light intensity is described through the modified Beer's law as

(

)

�½













(2.100)

where

(d )

is the intensity at depth

below the surface;

is the intensity just below the

water surface;



is a quantity that takes into account that a fraction of light energy (the

constants. The default values are



�½

0.3

and

energy that is absorbed near the surface is

infrared) is absorbed near the surface;



is the light extinction coefficient. Typical values

for



and



are 0.2-0.6 and 0.5-1.4 m

-1

, respectively.



and



are user-specified



. The net short-wave radiation,

net

, is



�½

1.0



. The fraction of the light

attenuated as described by the modified Beer's law. Hence the surface net heat flux is

given by

�½





net



net

(2.101)



For three-dimensional calculations the source term

is given by



 

net













(





)



net









�½

�½ 

















(





)



(2.102)

For two-dimensional calculations the source term

is given by





net



net

�½



(2.103)

The calculation of the latent heat flux, sensible heat flux, net short wave radiation, and net

long wave radiation as described in the following sections.

In areas covered by ice the heat exchange is excluded.

2.10.1 Vaporisation

Dalton’s law yields the following relationship for the vaporative heat loss (or latent flux),

see Sahlberg, 1984

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Governing Equations

�½

(



)



water



air



where

�½

2.5



is the latent heat vaporisation (in the literature

(2.104)

�½

2.5





2300

water

is commonly used);

�½

1.32





is the moisture transfer

coefficient (or Dalton number);

is the wind speed 2 m above the sea surface;

water

is the water vapour density close to the surface;

air

is the water vapour density in the

atmosphere;

and

�½

0.9

and

are user specified constants. The default values are

�½

0.5

Measurements of

water

and

air

are not directly available but the vapour density can

be related to the vapour pressure as

�½

0.2167



(2.105)

in which subscript

refers to both water and air. The vapour pressure close to the sea,

water

, can be expressed in terms of the water temperature assuming that the air close to

the surface is saturated and has the same temperature as the water

where

�½

5418



and

relative humidity, R



water

�½

6.11

 



T T

water





�½

273.15



is the temperature at 0 C. Similarly the







(2.106)

vapour pressure of the air,

air

, can be expressed in terms of the air temperature and the



air

�½



6.11

 



T T



air



�½ 















(2.107)

Replacing

water

and

air

with these expressions the latent heat can be written as



 



 

exp



 



exp



 





 



 

water



  

 

air



  





water



air















(2.108)

where all constants have been included in a new latent constant

�½

4370

 

During cooling of the surface the latent heat loss has a major effect with typical values up

to 100 W/m

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MIKE 21 & MIKE 3 Flow Model FM

The wind speed, W

, 2 m above the sea surface is calculated from the from the wind

speed, W

, 10 m above the sea surface using the following formula:

Assuming a logarithmic profile the wind speed,

u(z),

at a distance

above the sea surface

is given by

(

)

�½

where

is the wind friction velocity,

is the sea roughness and



=0.4 is von

Karman's constant.

and

are given by

�½

Cha rnock





log

 











(2.109)

(2.110)

�½

where

Cha rnock

is the Charnock parameter. The default value is

Cha rnock

�½

0.01

4. The

wind speed,

, 2 m above the sea surface is then calculated from the from the wind

speed,

, 10m above the sea surface by first solving Eq. (2.114) and Eq. (2.115)

iteratively for z

with

z=10m

and

u(z)=W

. Then

is given by



(

)





log

 









(2.111)

�½





log

 









�½





log

 











0.5



0.5

(2.112)

The heat loss due to vaporization occurs both by wind driven forced convection by and

free convection. The effect of free convection is taken into account by the parameter

Eq. (2.104). The free convection is also taken into account by introducing a critical wind

speed

critical

so that the wind speed used in Eq. (2.112) is obtained as

=max(W

critical

)

. The default value for the critical wind speed is 2 m/s.

2.10.2 Convection

The sensible heat flux,

(

)

, (or the heat flux due to convection) depends on the

type of boundary layer between the sea surface and the atmosphere. Generally this

boundary layer is turbulent implying the following relationship





air

heating

(

air



water

)

air





�½ 





air

cooling

(

air



water

)

air





(2.113)

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Governing Equations

air;

heating

�½

0.0011

and

cooling

�½

0.0011

, respectively, is the sensible transfer

where



air

is the air density 1.225 kg/m

;

air

�½

1007

 

)

is the specific heat of

coefficient (or Stanton number) for heating and cooling (see Kantha and Clayson, 2000);

is the wind speed 10 m above the sea surface;

water

is the temperature at the sea

surface;

air

is the temperature of the air.

The convective heat flux typically varies between 0 and 100 W/m

The heat loss due to convection occurs both by wind driven forced convection by and free

convection. The free convection is taken into account by introducing a critical wind speed

critical

so that the wind speed used in Eq. (2.113) is obtained as

=max(W

critical

)

The default value for the critical wind speed is 2 m/s.

2.10.3 Short wave radiation

Radiation from the sun consists of electromagnetic waves with wave lengths varying from

1,000 to 30,000 Å. Most of this is absorbed in the ozone layer, leaving only a fraction of

the energy to reach the surface of the Earth. Furthermore, the spectrum changes when

sunrays pass through the atmosphere. Most of the infrared and ultraviolet compound is

absorbed such that the solar radiation on the Earth mainly consists of light with wave

lengths between 4,000 and 9,000 Å. This radiation is normally termed short wave

radiation. The intensity depends on the distance to the sun, declination angle and latitude,

extraterrestrial radiation and the cloudiness and amount of water vapour in the

atmosphere (see Iqbal, 1983)

The eccentricity in the solar orbit,

, is given by





�½ 

 �½

1.000110



0.034221cos(



)



0.001280 sin(



)







0.000719 cos(2



)



0.000077 sin(2



)

(2.114)

where

is the mean distance to the sun,

is the actual distance and the day angle



(rad )

is defined by

�½



(



365

(2.115)

and

is the Julian day of the year.

The daily rotation of the Earth around the polar axes contributes to changes in the solar

radiation. The seasonal radiation is governed by the declination angle,



(rad )

, which

can be expressed by



�½

0.006918



0.399912 cos(



)



0.07257sin(



)



0.006758cos(2



)



0.000907sin(2



)



0.002697 cos(3



)



0.00148sin(3



)

(2.116)

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MIKE 21 & MIKE 3 Flow Model FM

The day length,

, varies with



. For a given latitude,



, (positive on the northern

hemisphere) the day length is given by

�½



arccos





tan(



) tan(



)



(2.117)

and the sunrise angle,



�½

arccos





tan(



) tan(



)



and



(rad )

, and the sunset angle



(rad )



�½ 



are

(2.118)

The intensity of short wave radiation on the surface parallel to the surface of the Earth

changes with the angle of incidence. The highest intensity is in zenith and the lowest

during sunrise and sunset. Integrated over one day the extraterrestrial intensity,

(

day

)

, in short wave radiation on the surface can be derived as

�½

where

�½

4.9212 (

)

is the solar constant.



cos







cos







sin











cos







(2.119)

For determination of daily radiation under cloudy skies,

(

day

)

, the following

relation is used

�½



in which

hours.

(2.120)

and

are user specified constants. The default values are

�½

0.295

and

�½

0.371

. The user-specified clearness coefficient corresponds to

. Thus the





�½ 







cos







3600





is the number of sunshine hours and

is the maximum number of sunshine

solar radiation,

(

)

, can be expressed as

(2.121)

where







�½

0.6609



0.4767 sin





 











�½

0.4090



0.5016 sin





 





(2.122)

(2.123)

The extraterrestrial intensity,

(

)

and the hour angle



is given by

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Governing Equations





�½



sin







sin









cos







cos







cos















(2.124)



�½

the standard longitude for the time zone.



displacement

and

are user specified

constants. The default values are



displacement

�½

0 (

)

and

varying during the year. It is given by



displacement

is the displacement hours due to summer time and the time meridian





 

displacement











local











(2.125)

�½

0 (deg)

is the

local longitude in degrees.

(

)

is the discrepancy in time due to solar orbit and is



0.000075



0.001868 cos(



)



0.032077 sin(



)



 

229.18

�½ 



 

0.014615 cos(2



)



0.04089 sin(2



)





Finally,

local

is the local time in hours.

(2.126)

Solar radiation that impinges on the sea surface does not all penetrate the water surface.

Parts are reflected back and are lost unless they are backscattered from the surrounding

atmosphere. This reflection of solar energy is termed the albedo. The amount of energy,

which is lost due to albedo, depends on the angle of incidence and angle of refraction. For

a smooth sea the reflection can be expressed as

where

is the angle of incidence,

the refraction angle and



the reflection coefficient,

which typically varies from 5 to 40 %.



can be approximated using



sin

(



) tan

(



)







�½ 



sin (



)



tan

(



)







(2.127)



altitude

0.48

altitude







altitude



0.48



0.05





altitude





�½



altitude





0.05





(2.128)

where the altitude in degrees is given by



180



altitude

�½

 

arccos(sin(



) sin(



)



cos(



) cos(



) cos(



))









Thus the net short wave radiation,

net

�½









(2.129)

net

(

)

, can possibly be expressed as

(2.130)

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MIKE 21 & MIKE 3 Flow Model FM

The net short wave radiation,

sr,net

, can be calculated using empirical formulae as

described above. Alternatively, the net short wave radiation can be calculated using Eq.

(2.130) where the solar radiation,

, is specified by the user or the net short wave

radiation,

sr,net

, can be given by the user.

2.10.4 Long wave radiation

A body or a surface emits electromagnetic energy at all wavelengths of the spectrum. The

long wave radiation consists of waves with wavelengths between 9,000 and 25,000 Å.

The radiation in this interval is termed infrared radiation and is emitted from the

atmosphere and the sea surface. The long wave emittance from the surface to the

atmosphere minus the long wave radiation from the atmosphere to the sea surface is

called the net long wave radiation and is dependent on the cloudiness, the air

temperature, the vapour pressure in the air and the relative humidity. The net outgoing

long wave radiation,

net

(

Falkenmark, 1972)

)

, is given by

Brunt’s equation (See Lind and







net

�½ 





air







b e













where

is the vapour pressure at dew point temperature measured in

mb;

number of sunshine hours,

is the maximum number of sunshine hours;





(2.131)

is the



�½

5.6697





 

)

is Stefan Boltzman's constant;

air

(



)

is the air

temperature. The coefficients

a, b, c

and

are given as

�½

0.56;

�½

0.077



�½

;

�½

0.10;

�½

.90

The vapour pressure is determined as

(2.132)

�½



R e

saturated

(2.133)

100 % relative humidity in the interval from

–51

to 52

C

can be estimated by

saturated

�½

3.38639





where

is the relative humidity and the saturated vapour pressure,

saturated

(kPa )

, with



7.38



air



0.8072





1.9





1.8



air



1.316







(2.134)

The net long wave radiation,

lr,net

, can be calculated using empirical formulae as

described above. Alternatively, the net long wave radiation can be calculated as

net

�½

net



(2.135)

where the net incident atmospheric radiation, q

ar,net

, is specified by the user and the back

radiation, q

, is given by

�½



)



(2.136)

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Governing Equations

where r=0.03 is the reflection coefficient and ε=0.985 is the

emissivity factor of the

atmosphere. The net long wave radiation can also be specified by the user.

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MIKE 21 & MIKE 3 Flow Model FM

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Numerical Solution

3.1

Numerical Solution

Spatial Discretization

The discretization in solution domain is performed using a finite volume method. The

spatial domain is discretized by subdivision of the continuum into non-overlapping

cells/elements.

In the two-dimensional case the elements can be arbitrarily shaped polygons, however,

here only triangles and quadrilateral elements are considered.

In the three-dimensional case a layered mesh is used: in the horizontal domain an

unstructured mesh is used while in the vertical domain a structured mesh is used (see

Figure 3.1). The vertical mesh is based on either sigma coordinates or combined sigma/z-

level coordinates. For the hybrid sigma/z-level mesh sigma coordinates are used from the

free surface to a specified depth and z-level coordinates are used below. The different

types of vertical mesh are illustrated in Figure 3.2. The elements in the sigma domain and

the z-level domain can be prisms with either a 3-sided or 4-sided polygonal base. Hence,

the horizontal faces are either triangles or quadrilateral element. The elements are

perfectly vertical and all layers have identical topology.

Figure 3.1

Principle of meshing for the three-dimensional case

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MIKE 21 & MIKE 3 Flow Model FM

Figure 3.2

Illustrations of the different vertical grids. Upper: sigma mesh, Lower: combined

sigma/z-level mesh with simple bathymetry adjustment. The red line shows the

interface between the z-level domain and the sigma-level domain

The most important advantage using sigma coordinates is their ability to accurately

represent the bathymetry and provide consistent resolution near the bed. However, sigma

coordinates can suffer from significant errors in the horizontal pressure gradients,

advection and mixing terms in areas with sharp topographic changes (steep slopes).

These errors can give rise to unrealistic flows.

The use of z-level coordinates allows a simple calculation of the horizontal pressure

gradients, advection and mixing terms, but the disadvantages are their inaccuracy in

representing the bathymetry and that the stair-step representation of the bathymetry can

result in unrealistic flow velocities near the bottom.

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Numerical Solution

3.1.1

Vertical Mesh

For the vertical discretization both a standard sigma mesh and a combined sigma/z-level

mesh can be used. For the hybrid sigma/z-level mesh sigma coordinates are used from

the free surface to a specified depth,

, and z-level coordinates are used below. At least

one sigma layer is needed to allow changes in the surface elevation.

Sigma

In the sigma domain a constant number of layers,

σ,

are used and each sigma layer is a

fixed fraction of the total depth of the sigma layer,

, where

ℎ

��

= − max⁡ �� , ��

��

. T

discretization in the sigma domain is given by a number of discrete σ-levels

{��

��

,⁡⁡⁡�� =

, ��

��

+ }.⁡

Here σ varies from

�� =

at the bottom interface of the lowest sigma layer

��

at the free surface.

Variable sigma coordinates can be obtained using a discrete formulation of the general

vertical coordinate (s-coordinate) system proposed by Song and Haidvogel (1994). First

an equidistant discretization in a s-coordinate system

(-1≤ s

≤0)

is defined

��

The discrete sigma coordinates can then be determined by

=−

��

+ − ��

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡�� = , ��

��

(3.1)



�½



















�½









where

(3.2)

−

Here

is a weighting factor between the equidistant distribution and the stretch

distribution,

is the surface control parameter and

is the bottom control parameter. The

range for the weighting factor is

0<σ

≤1

where the value 1 corresponds to equidistant

distribution and 0 corresponds to stretched distribution. A small value of

can result in

linear instability. The range of the surface control parameter is

0<θ≤20

and the range of

the bottom control parameter is

0≤b≤1.

θ<<1

and

b=0

an equidistant vertical resolution

is obtained. By increasing the value of the

θ,

the highest resolution is achieved near the

surface. If

θ>0

and

b=1

a high resolution is obtained both near the surface and near the

bottom.

Examples of a mesh using variable vertical discretization are shown in Figure 3.3 and

Figure 3.4.

sinh ��

tanh ��

tanh⁡

��

− tanh⁡

��

(3.3)

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MIKE 21 & MIKE 3 Flow Model FM

Figure 3.3

Example of vertical distribution using layer thickness distribution. Number of layers:

10, thickness of layers 1 to 10: .025, 0.075, 0.1, 0.01, 0.02, 0.02, 0.1, 0.1, 0.075,

0.025

Figure 3.4

Example of vertical distribution using variable distribution. Number of layers: 10, σ

0.1, θ = 5,

b = 1

Combined sigma/z-level

In the z-level domain the discretization is given by a number of discrete z-levels

{��

��

,⁡⁡⁡�� =

, �� + },⁡

where

is the number of layers in the z-level domain.

is the minimum z-

level and

��

is the maximum z-level, which is equal to the sigma depth,

. The

corresponding layer thickness is given by

The discretization is illustrated in Figure 3.5 and Figure 3.6.

Using standard z-level discretization the bottom depth is rounded to the nearest z-level.

Hence, for a cell in the horizontal mesh with the cell-averaged depth,

, the cells in the

corresponding column in the z-domain are included if the following criteria is satisfied

Δ��

��

= ��

��+

− ��

��

⁡⁡⁡⁡⁡⁡⁡⁡⁡�� = , ��

(3.4)

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Numerical Solution

The cell-averaged depth,

, is calculated as the mean value of the depth at the vortices

of each cell. For the standard z-level discretization the minimum depth is given by

. Too

take into account the correct depth for the case where the bottom depth is below the

minimum z-level (

�� > ��

)

a bottom fitted approach is used. Here, a correction factor,

for the layer thickness in the bottom cell is introduced. The correction factor is used in the

calculation of the volume and face integrals. The correction factor for the bottom cell is

calculated by

− z

/ ≥ �� ⁡⁡⁡⁡�� = , ��

(3.5)

The corrected layer thickness is given by

∆��

∗

= �� ∆��

The simple bathymetry

adjustment approach is illustrated in Figure 3.5.

�� =

�� −��

∆��

(3.6)

For a more accurate representation of the bottom depth an advanced bathymetry

adjustment approach can be used. For a cell in the horizontal mesh with the cell-averaged

depth,

, the cells in the corresponding column in the z-domain are included if the

following criteria is satisfied

A correction factor,

, is introduced for the layer thickness

> �� ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡�� = , ��

��

= �� (

��

��+

− ��

∆��

��

(3.7)

A minimum layer thickness,

∆��

��

, is introduced to avoid very small values of the

correction factor. The correction factor is used in the calculation of the volume and face

integrals. The corrected layer thicknesses are given by

{∆��

��∗

= ��

��

∆��

��

, �� = , �� }.⁡

The

advanced bathymetry adjustment approach is illustrated in Figure 3.6.

��

= ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡�� ≥ ��

��

)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡��

��

< �� < ��

��+

⁡⁡�� ⁡⁡�� > ��

∆��

��

(3.8)

Figure 3.5

Simple bathymetry adjustment approach

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MIKE 21 & MIKE 3 Flow Model FM

Figure 3.6

Advanced bathymetry adjustment approach

3.1.2

Shallow water equations

The integral form of the system of shallow water equations can in general form be written



  

(

)

�½

(

)



(3.9)

where

is the vector of conserved variables,

is the flux vector function and

is the

vector of source terms.

In Cartesian coordinates the system of 2D shallow water equations can be written



















�½



(3.10)

where the superscripts

and

denote the inviscid (convective) and viscous fluxes,

respectively and where

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Numerical Solution





�½ 



 





 





















  





�½ 



(



)



, F

�½ 















 





huv



  



 













  



 

























  



 





, F

�½ 





y I

�½ 

hvu





 











(



)



  



















  





(3.11)













 





 



 









fvh







 











 















�½





















 



 







fuh





 



 











 









































�½











In Cartesian coordinates the system of 3D shallow water equations can be written

(3.12)

where the superscripts

and

denote the inviscid (convective) and viscous fluxes,

respectively and where

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MIKE 21 & MIKE 3 Flow Model FM





�½ 



 





 









�½ 



(



)









huv















y I

�½ 

hvu







(



)











�½













































  



 

�½ 

   

  



 

  

















 















  

 

�½ 



 

  

 

  



 



   

  



 





(3.13)









�½ 

























 

�½ 





fvh





 









fuh



 









 



















 





 















 

























y dz





 

 

 











Integrating Eq. (3.9) over the

ith

cell

and using Gauss’s theorem to rewrite the flux integral

gives

where

is the area/volume of the cell



is the integration variable defined on







t d

 





(



)

�½



(

)



(3.14)



is the boundary of the

ith

cell and

is the integration variable along the boundary.

the unit outward normal vector along the boundary. Evaluating the area/volume integrals

by a one-point quadrature rule, the quadrature point being the centroid of the cell, and

evaluating the boundary intergral using a mid-point quadrature rule, Eq. (3.14) can be

written

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Numerical Solution











�½



(3.15)

Here

and

, respectively, are average values of

and

over the

ith

cell and stored

at the cell centre, NS is the number of sides of the cell,

is the unit outward normal

vector at the

jth

side and



the length/area of the

jth

interface.

Both a first order and a second order scheme can be applied for the spatial discretization.

For the 2D case an

approximate Riemann solver (Roe’s scheme, see Roe, 1981) is used

to calculate the convective fluxes at the interface of the cells.

Using the Roe’s scheme the

dependent variables to the left and to the right of an interface have to be estimated.

Second-order spatial accuracy is achieved by employing a linear gradient-reconstruction

technique. The average gradients are estimated using the approach by Jawahar and

Kamath, 2000. To avoid numerical oscillations a second order TVD slope limiter (Van

Leer limiter, see Hirch, 1990 and Darwish, 2003) is used.

For the 3D case an

approximate Riemann solver (Roe’s

scheme, see Roe, 1981) is used

to calculate the convective fluxes

at the vertical interface of the cells (x’y’-plane).

Using

the Roe’s scheme the dependent variables to the left and to the right of an interface have

to be estimated. Second-order spatial accuracy is achieved by employing a linear

gradient-reconstruction technique. The average gradients are estimated using the

approach by Jawahar and Kamath, 2000. To avoid numerical oscillations a second order

TVD slope limiter (Van Leer limiter, see Hirch, 1990 and Darwish, 2003) is used. The

convective fluxes at the horizontal interfaces (vertical line) are derived using first order

upwinding for the low order scheme. For the higher order scheme the fluxes are

approximated by the mean value of the fluxes calculated based on the cell values above

and below the interface for the higher order scheme.

3.1.3

Transport equations

The transport equations arise in the salt and temperature model, the turbulence model

and the generic transport model. They all share the form of Equation Eq. (2.20) in

Cartesian coordinates. For the 2D case the integral form of the transport equation can be

given by Eq. (3.9) where

�½

�½ 

huC

hvC













�½ 









�½ 



For the 3D case the integral form of the transport equation can be given by Eq. (3.9)

where

(3.16)

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�½



huC

hvC













�½ 











�½ 



(3.17)

The discrete finite volume form of the transport equation is given by Eq. (3.15). As for the

shallow water equations both a first order and a second order scheme can be applied for

the spatial discretization.

In 2D the low order approximation uses simple first order upwinding, i.e., element

average values in the upwinding direction are used as values at the boundaries. The

higher order version approximates gradients to obtain second order accurate values at

the boundaries. Values in the upwinding direction are used. To provide stability and

minimize oscillatory effects, a TVD-MUSCL limiter is applied (see Hirch, 1990, and

Darwish, 2003).

In 3D the low order version uses simple first order upwinding. The higher order version

approximates horizontal gradients to obtain second order accurate values at the

horizontal boundaries. Values in the upwinding direction are used. To provide stability and

minimize oscillatory effects, an ENO (Essentially Non-Oscillatory) type procedure is

applied to limit the horizontal gradients. In the vertical direction a 3 order ENO procedure

is used to obtain the vertical face values (Shu, 1997).

3.2

Time Integration

Consider the general form of the equations



�½







(3.18)

For 2D simulations, there are two methods of time integration for both the shallow water

equations and the transport equations: A low order method and a higher order method.

The low order method is a first order explicit Euler method

where



is the time step interval. The higher order method uses a second order Runge

Kutta method on the form:



�½

 

(

)

(3.19)



�½





(

)



�½

 

(



)

(3.20)

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Numerical Solution

For 3D simulations the time integration is semi-implicit. The horizontal terms are treated

implicitly and the vertical terms are treated implicitly or partly explicitly and partly implicitly.

Consider the equations in the general semi-implicit form.



�½

(

)



(

)

�½

(

)



(

)



(

)



(3.21)

where the

and

subscripts refer to horizontal and vertical terms, respectively, and the

superscripts refer to invicid and viscous terms, respectively. As for 2D simulations, there

is a lower order and a higher order time integration method.

The low order method used for the 3D shallow water equations can written as









(



)



(

)



�½

 

(

)

(3.22)

The horizontal terms are integrated using a first order explicit Euler method and the

vertical terms using a second order implicit trapezoidal rule. The higher order method can

be written



1 2







(



1 2

)



(

)



�½





(

)



 



(



)



(

)



�½

 

(



1 2

)

(3.23)

The horizontal terms are integrated using a second order Runge Kutta method and the

vertical terms using a second order implicit trapezoidal rule.

The low order method used for the 3D transport equation can written as









(



)



(

)



�½

 

(

)

 

(

)

(3.24)

The horizontal terms and the vertical convective terms are integrated using a first order

explicit Euler method and the vertical viscous terms are integrated using a second order

implicit trapezoidal rule. The higher order method can be written



1 2







(



1 2

)



(

)



�½





(

)





(

)



 



(



)



(

)



�½

(3.25)

 

(



1 2

)

 

(



1/ 2

)

The horizontal terms and the vertical convective terms are integrated using a second

order Runge Kutta method and the vertical terms are integrated using a second order

implicit trapezoidal rule for the vertical terms.

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3.3

3.3.1

Boundary Conditions

Closed boundaries

Along closed boundaries (land boundaries), normal fluxes are forced to zero for all

variables. For the momentum equations, this leads to full-slip along land boundaries. For

the shallow water equations, the no slip condition can also be applied where both the

normal and tangential velocity components are zero.

3.3.2

Open boundaries

For the shallow water equations a number of different boundary conditions can be applied

The flux, velocity and Flather boundary conditions are all imposed using a weak

approach. A ghost cell technique is applied where the primitive variables in the ghost cell

are specified. The water level is evaluated based on the value of the adjacent interior cell,

and the velocities are evaluated based on the boundary information. For a discharge

boundary, the transverse velocity is set to zero for inflow and passively advected for

outflow. The boundary flux is then calculated using an approximate Riemann solver.

The Flather (1976) condition is one of the most efficient open boundary conditions. It is

very efficient in connection with downscaling coarse model simulations to local areas (see

Oddo and Pinardi (2007)). The instabilities, which are often observed when imposing

stratified density at a water level boundary, can be avoided using Flather conditions

The level boundary is imposed using a strong approach based on the characteristic

theory (see e.g. Sleigh et al., 1998).

The discharge boundary condition is imposed using both a weak formulation using ghost

cell technique described above and a strong approach based on the characteristic theory

(see e.g. Sleigh et al., 1998).

Note that using the weak formulation for a discharge boundary the effective discharge

over the boundary may deviate from the specified discharge.

For transport equations, either a specified value or a zero gradient can be given. For

specified values, the boundary conditions are imposed by applying the specified

concentrations for calculation of the boundary flux. For a zero gradient condition, the

concentration at the boundary is assumed to be identical to the concentration at the

adjacent interior cell.

3.3.3

Flooding and drying

The approach for treatment of the moving boundaries problem (flooding and drying fronts)

is based on the work by Zhao et al. (1994) and Sleigh et al. (1998). When the depths are

small the problem is reformulated and only when the depths are very small the

elements/cells are removed from the calculation. The reformulation is made by setting the

momentum fluxes to zero and only taking the mass fluxes into consideration.

The depth in each element/cell is monitored and the elements are classified as dry,

partially dry or wet. Also the element faces are monitored to identify flooded boundaries.

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Numerical Solution

•

An element face is defined as flooded if the following two criteria are satisfied: Firstly,

the water depth at one side of face must be less than a tolerance depth,

d r y

, and

the water depth at the other side of the face larger than a tolerance depth,

flood

Secondly, the sum of the still water depth at the side for which the water depth is less

than

dr y

and the surface elevation at the other side must be larger than zero.

•

An element is dry if the water depth is less than a tolerance depth,

d r y

, and no of

the element faces are flooded boundaries. The element is removed from the

calculation.

•

An element is partially dry if the water depth is larger than

d r y

and less than a

tolerance depth,

wet

, or when the depth is less than the

d r y

and one of the

element faces is a flooded boundary. The momentum fluxes are set to zero and only

the mass fluxes are calculated.

•

An element is wet if the water depth is greater than

wet

. Both the mass fluxes and

the momentum fluxes are calculated.

The wetting depth,

wet

, must be larger than the drying depth,

d r y

, and flooding depth,

flood

, must satisfy

dry



flood



wet

(3.26)

The default values are

dr y

�½

0.005

flood

�½

0.05

and

wet

�½

0.1

Note, that for very small values of the tolerance depth,

wet

, unrealistically high flow

velocities can occur in the simulation and give cause to stability problems.

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MIKE 21 & MIKE 3 Flow Model FM

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Infiltration and Leakage

The effect of infiltration and leakage at the surface zone may be important in cases of

flooding scenarios on otherwise dry land. It is possible to account for this in one of two

ways: by Net infiltration rates or by constant infiltration with capacity.

j-1

j+1

Surface zone

Infiltration

Infiltration zone

Figure 4.1

Leakage

Illustration of infiltration process

4.1

Net Infiltration Rates

The net infiltration rate is defined directly. This will act as a simple sink in each element in

the overall domain area.

The one-dimensional vertical continuity equation is solved at each hydrodynamic time

step after the two-dimensional horizontal flow equations have been solved. The

calculation of the new water depth in the free surface zone for each horizontal element is

found by

Where

��

element.

��

= ⁡��

− ⁡ ��

��

becomes marked as

dry

then element

will be taken out of the two-dimensional

horizontal flow calculations and no infiltration can occur until the element is flooded again.

��

is the infiltrated volume in element

/��

(4.1)

and A(j) the area of the

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MIKE 21 & MIKE 3 Flow Model FM

In summary: when using Net infiltration rate an unsaturated zone is never specified and

thus has no capacity limits, so the specified infiltration rates will always be fully

effectuated as long as there is enough water available in the element.

4.2

Constant Infiltration with Capacity

Constant infiltration with capacity describes the infiltration from the free surface zone to

the unsaturated zone and from the unsaturated zone to the saturated zone by a simplified

model. The model assumes the following:

•

The unsaturated zone is modelled as an infiltration zone with constant porosity over

the full depth of the zone.

The flow between the free surface zone and the infiltration zone is based on a

constant flow rate, i.e.

��

= ��

��

∙ ∆

where

��

is the prescribed flow rate.

The flow between the saturated and unsaturated zone is modelled as a leakage

��

having a constant flow rate, i.e.

��

=�� ∙∆

The simplified model described above is solved through a one-dimensional continuity

equation. Feedback from the infiltration and leakage to the two-dimensional horizontal

hydrodynamic calculations is based solely on changes to the depth of the free surface

zone

–

the water depth.

Note that the infiltration flow cannot exceed the amount of water available in the free

surface water zone nor the difference between the water capacity of the infiltration zone

and the actual amount of water stored there. It is possible that the infiltration flow

completely drains the free surface zone from water and thus creates a dried-out point in

the two-dimensional horizontal flow calculations.

The one-dimensional vertical continuity equation is solved at each hydrodynamic time

step after the two-dimensional horizontal flow equations have been solved. The solution

proceeds in the following way:

Calculation of the volume from leakage flow in each horizontal element

–

��

∶= ⁡��

=⁡��

= min⁡ ��

−��

∙ ∆⁡ ∙ ��

, ��

(4.2)

(4.3)

(4.4)

Where

��

⁡is

the total amount of water in the infiltration zone and

��

leakage flow rate.

��

∙ ∆⁡ ∙ ��

⁡

is the

Calculation of the volume from infiltration flow in each horizontal element

–

��

∶= ⁡��

+ ⁡ ��

��

min

(��

��

⁡, ��

��

− ��

,��

∙��

(4.5)

(4.6)

(4.7)

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Infiltration and Leakage

Where

��

is the infiltration rate,

��

depth of the free surface.

��

= ⁡��

− ⁡ ��

��

/��

)

is the water storage capacity and

��

the

Calculation of the new water depth in the free surface zone for each horizontal

element

��

becomes marked as

dry

then element

(j)

will be taken out of the two-dimensional

horizontal flow calculations. The element can still

leak

but no infiltration can occur until the

element is flooded again.

The water storage capacity of the infiltration zone is calculated as

��

(4.8)

Where

In summary, when using Constant infiltration with capacity there can be situations where

the picture is altered and the rates are either only partially effectuated or not at all:

•

= ⁡��

<��

��

is the depth of the infiltration zone and

��

∙��

⁡∙ ��

(4.9)

is the porosity of the same zone.

on the surface (dry surface) => infiltration rate is not effectuated

If: the water volume in the infiltration zone reaches the full capacity => infiltration rate

is not effectuated

If: the water volume is zero in the infiltration zone (the case in many initial conditions)

=> leakage rate is not effectuated

Leakage volume must never eclipse the available water volume in the infiltration

zone, if so we utilise the available water volume in infiltration zone as leakage

volume

Infiltration volume must never eclipse the available water volume on the surface, if so

we utilise the available water on the surface as infiltration volume

•

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Validation

The new finite-volume model has been successfully tested in a number of basic, idealised

situations for which computed results can be compared with analytical solutions or

information from the literature. The model has also been applied and tested in more

natural geophysical conditions; ocean scale, inner shelves, estuaries, lakes and overland,

which are more realistic and complicated than academic and laboratory tests. A detailed

validation report is under preparation.

This chapter presents a comparison between numerical model results and laboratory

measurements for a dam-break flow in an L-shaped channel.

Additional information on model validation and applications can be found here

http://www.mikepoweredbydhi.com/download/product-documentation

5.1

Dam-break Flow through Sharp Bend

The physical model to be studied combines a square-shaped upstream reservoir and an

L-shaped channel. The flow will be essentially two-dimensional in the reservoir and at the

angle between the two reaches of the L-shaped channel. However, there are numerical

and experimental evidences that the flow will be mostly unidimensional in both rectilinear

reaches. Two characteristics or the dam-break flow are of special interest, namely

•

The "damping effect" of the corner

The upstream-moving hydraulic jump which forms at the corner

The multiple reflections of the expansion wave in the reservoir will also offer an

opportunity to test the 2D capabilities of the numerical models. As the flow in the reservoir

will remain subcritical with relatively small-amplitude waves, computations could be

checked for excessive numerical dissipation.

5.1.1

Physical experiments

A comprehensive experimental study of a dam-break flow in a channel with a 90 bend has

been reported by Frazão and Zech (2002, 1999a, 1999b). The channel is made of a 3.92

and a 2.92 metre long and 0.495 metre wide rectilinear reaches connected at right angle

by a 0.495 x 0.495 m square element. The channel slope is equal to zero. A guillotine-

type gate connects this L-shaped channel to a 2.44 x 2.39 m (nearly) square reservoir.

The reservoir bottom level is 33 cm lower that the channel bed level. At the downstream

boundary a chute is placed. See the enclosed figure for details.

Frazão and Zech performed measurements for both dry bed and wet bed condition. Here

comparisons are made for the case where the water in the reservoir is initially at rest, with

the free surface 20 cm above the channel bed level, i.e. the water depth in the reservoir is

53 cm. The channel bed is initially dry. The Manning coefficients evaluated through

1/3

steady-state flow experimentation are 0.0095 and 0.0195 s/m , respectively, for the bed

and the walls of the channel.

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MIKE 21 & MIKE 3 Flow Model FM

The water level was measured at six gauging points. The locations of the gauges are

shown in Figure 5.1 and the coordinates are listed in Table 5.1.

Figure 5.1

Set-up of the experiment by Frazão and Zech (2002)

Table 5.1

Location of the gauging points

Location

x (m)

1.19

2.74

4.24

5.74

6.56

y (m)

1.20

0.69

1.51

3.01

5.1.2

Numerical experiments

Simulations are performed using both the two-dimensional and the three-dimensional

shallow water equations.

An unstructured mesh is used containing 18311 triangular elements and 9537 nodes. The

minimum edge length is 0.01906 m and the maximum edge length is 0.06125 m. In the

3D simulation 10 layers is used for the vertical discretization. The time step is 0.002 s. At

the downstream boundary, a free outfall (absorbing) boundary condition is applied. The

wetting depth, flooding depth and drying depth are 0.002 m, 0.001 m and 0.0001 m,

respectively.

A constant Manning coefficient of 105.26 m /s is applied in the 2D simulations, while a

constant roughness height of 510

-5

m is applied in the 3D simulation.

1/3

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Validation

5.1.3

Results

In Figure 5.2 time series of calculated surface elevations at the six gauges locations are

compared to the measurements. In Figure 5.3 contour plots of the surface elevations are

shown at T = 1.6, 3.2 and 4.8 s (two-dimensional simulation).

In Figure 5.4 a vector plot and contour plots of the current speed at a vertical profile along

the centre line (from (x,y)=(5.7, 0.69) to (x,y)=(6.4, 0.69)) at T = 6.4 s is shown.

Figure 5.2

Time evolution of the water level at the six gauge locations. (blue) 3D calculation,

(black) 2D calculation and (red) Measurements by Frazão and Zech (1999a,b)

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MIKE 21 & MIKE 3 Flow Model FM

Figure 5.3

Contour plots of the surface elevation at T = 1.6 s (top), T = 3.2 s (middle) and T = 4.8

s (bottom).

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Validation

Figure 5.4

Vector plot and contour plots of the current speed at a vertical profile along the centre

line at T = 6.4 s

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References

/1/

/2/

/3/

/4/

/5/

/6/

Darwish M.S. and Moukalled F. (2003), TVD schemes for unstructured grids, Int.

J. of Heat and Mass Transfor, 46, 599-611)

Fredsøe, J. (1984), Turbulent boundary layers in Combined Wave Current

Motion. J. Hydraulic Engineering, ASCE, Vol 110, No. HY8, pp. 1103-1120.

Geernaert G.L. and Plant W.L (1990), Surface Waves and fluxes, Volume 1

–

Current theory, Kluwer Academic Publishers, The Netherlands.

Hirsch, C. (1990). Numerical Computation of Internal and External Flows,

Volume 2: Computational Methods for Inviscid and Viscous Flows, Wiley.

Iqbal M. (1983). An Introduction to solar Radiation, Academic Press.

Jawahar P. and H. Kamath. (2000). A high-resolution procedure for Euler and

Navier-Stokes computations on unstructured grids, Journal Comp. Physics, 164,

165-203.

Jones, O., Zyserman, J.A. and Wu, Yushi (2014), Influence of Apparent

Roughness on Pipeline Design Conditions under Combined Waves and Current,

Proceedings of the ASME 2014 33rd International Conference on Ocean,

Offshore and Arctic Engineering.

Kantha and Clayson (2000). Small Scale Processes in Geophysical Fluid flows,

International Geophysics Series, Volume 67.

Lind & Falkenmark (1972), Hydrology: en inledning till vattenressursläran,

Studentlitteratur (in Swedish).

Munk, W., Anderson, E. (1948), Notes on the theory of the thermocline, Journal

of Marine Research, 7, 276-295.

Oddo P. and N. Pinardi (2007), Lateral open boundary conditions for nested

limited area models: A scale selective approach, Ocean Modelling 20 (2008)

134-156.

Pugh, D.T. (1987), Tides, surges and mean sea-level: a handbook for engineers

and scientists. Wiley, Chichester, 472pp

Rodi, W. (1984), Turbulence models and their applications in hydraulics, IAHR,

Delft, the Netherlands.

Rodi, W. (1980), Turbulence Models and Their Application in Hydraulics - A

State of the Art Review, Special IAHR Publication.

Roe, P. L. (1981), Approximate Riemann solvers, parameter vectors, and

difference-schemes, Journal of Computational Physics, 43, 357-372.

Sahlberg J. (1984). A hydrodynamic model for heat contents calculations on

lakes at the ice formation date, Document D4: 1984, Swedish council for

Building Research.

/7/

/8/

/9/

/10/

/11/

/12/

/13/

/14/

/15/

/16/

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MIKE 21 & MIKE 3 Flow Model FM

/17/

Shu C.W. (1997), Essentially Non-Oscillatory and Weighted Essenetially Non-

Oscillatory Schemes for Hyperbolic Conservation Laws, NASA/CR-97-206253,

ICASE Report No. 97-65, NASA Langley Research Center, pp. 83.

Sleigh, P.A., Gaskell, P.H., Bersins, M. and Wright, N.G. (1998), An

unstructured finite-volume algorithm for predicting flow in rivers and estuaries,

Computers & Fluids, Vol. 27, No. 4, 479-508.

Smagorinsky (1963), J. General Circulation Experiment with the Primitive

Equations, Monthly Weather Review, 91, No. 3, pp 99-164.

Soares Frazão, S. and Zech, Y. (2002), Dam-break in channel with 90 bend,

Journal of Hydraulic Engineering, ASCE, 2002, 128, No. 11, 956-968.

Soares Frazão, S. and Zech, Y. (1999a), Effects of a sharp bend on dam-break

flow, Proc., 28th IAHR Congress, Graz, Austria, Technical Univ. Graz, Graz,

Austria (CD-Rom).

Soares Frazão, S. and Zech, Y. (1999b), Dam-break flow through sharp bends

–

Physical model and 2D Boltzmann model validation, Proc., CADAM Meeting

Wallingford, U.K., 2-3 March 1998, European Commission, Brussels, Belgium,

151-169.

UNESCO (1981), The practical salinity scale 1978 and the international

equation of state of seawater 1980, UNESCO technical papers in marine

science, 36, 1981.

Wu, Jin (1994), The sea surface is aerodynamically rough even under light

winds, Boundary layer Meteorology, 69, 149-158.

Wu, Jin (1980), Wind-stress Coefficients over sea surface and near neutral

conditions

–

A revisit, Journal of Physical. Oceanography, 10, 727-740.

Zhao, D.H., Shen, H.W., Tabios, G.Q., Tan, W.Y. and Lai, J.S. (1994), Finite-

volume two-dimensional unsteady-flow model for river basins, Journal of

Hydraulic Engineering, ASCE, 1994, 120, No. 7, 863-833.

/18/

/19/

/20/

/21/

/22/

/23/

/24/

/25/

/26/

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MarineVandplanVærktøjer

Principles for distribution of loads

Author(s)

V1 date

Review

Quality

Assurance

Anders Erichsen

Distributed to:

1 Objective

In order to do mechanistic modelling, loads must be allocated to specific positions (grids)

in the models and have an associated freshwater source. The methodology for

distributing the freshwater is described in /2/ and this note describes the methodology of

distributing the nutrient loads.

Data used

Load (N & P) data from NST via DCE has been delivered (primo July 2013) and imported

in an Access database for further processing.

Furthermore, GIS data for water bodies, catchments (ID15) and streams have been

delivered by NST, as well as measured data of nutrients, suspended solids, dry matter

etc. within the streams.

repository

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

folder

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q & load\GIS

project\Farvandsområder

Q & load\GIS

project\Belastninger

Q & load\GIS

project\Belastninger

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q & load\GIS

project\Arealanvendelse

Q & load\GIS

project\Arealanvendelse

Q & load\GIS

project\Arealanvendelse

File names

qp_dogn2579235_5jul13.txt (DCE)

qn_dogn2579235_5jul13.txt (DCE)

4.ordens belastninger.accdb (-)

Farvandsinddeling.shp (NST)

oplande_id15.shp (NST)

vandlob_vp1.shp (NST)

Vandkemi_dokumentation.docx

(NST)

Vandkemi1.csv

Vandkemi.xls (NST)

Fordelingsnøgler - uorganiske

næringssalte (-)

kemi.txt (NST)

Skov.shp (NST)

Søer.shp (NST)

Vådområder.shp (NST)

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MarineVandplanVærktøjer

Principles for distribution of loads

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

\\dkcph1-

stor.dhi.dk\Projects\11811187-1

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Q and loads - Acquired data -

DCE

Stepanauskas_PON.POC.xls

C.N.P Denmark.xls

SSin_pr.mdr_Limfjorden.xls

Landuse-relationer_v2.xls

3 General principles

Nutrient load data from Danish catchments to 4

order water body levels has been

delivered by DCE. Loads are calculated according to the methodology of the national

load calculations but with finer spatial resolution than estimated previously, see /1/, /7/

and Appendix B for methodology.

Figure 1: Loading (red line) and concentrations (blue line) of total nitrogen (top figure) and

total phosphorus (bottom figure) to Hjarbæk Fjord, 4

order water body no.

3745.

An example of load data for Hjarbæk Fjord (the Limfjord) is shown in

Error! Reference

source not found..

The loads are delivered as a total load per day. The corresponding

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MarineVandplanVærktøjer

Principles for distribution of loads

concentrations of total nitrogen (TN), and total phosphorus (TP) in streams are estimated

from total discharge (Q)

and total load, see

Error! Reference source not found..

A thorough description of monitoring stations and method for estimating the loads can be

found in /7/.

In addition to N and P, mechanistic modelling needs information on total organic carbon

(TOC) loads and their fractions (dissolved and particulate organic carbon), as well as

information on silica loads (Si) and inorganic suspended sediments (SSin). These data

are rarely measured and not estimated as part of the national nutrient budgets. Hence,

for these loads other strategies has to be implemented, and this note also includes

descriptions of methodologies for deriving these parameters.

As freshwater primarily is discharged through stream outfalls, it has been decided in

general to allocate almost all loads to these stream outfalls

–

including direct sewage

outfalls and discharge from marine aquacultures. Exceptions are, potentially, the major

sewage outfalls (like Lynetten in Copenhagen and Marselisborg in Århus). Such direct

loads will be handled as separate sources if evaluated critical to the modelled distribution

of nutrients in the recipient.

As described in /2/ the loads are generally ascribed to one single source per 4

order

water body and introduced into the models at a location corresponding to the outfall of the

largest stream within that water body.

The estimated total daily load of nutrients constitutes the baseline of the nutrient input to

the mechanistic marine models. However, the mechanistic marine models developed for

this project require nutrient input that is distributed between different species. The

different nutrient species simulated (described) by the mechanistic models are listed in

Table 1.

Table 1: Pelagic state variables related to nutrients

Name

NH4

NO3

IPss

CDOC

CDON

CDOP

LDOC

LDON

LDOP

SSi

Comment

Detritus C

Detritus N

Detritus P

Total ammonium (NH

-N + NH

-N)

Nitrate+ nitrite, (NO

-N + NO

-N)

Dissolved inorganic phosphorous (PO

-P)

Inorganic phosphorous (PO

-P) adsorbed to inorganic

sediments

Silicate (SiO

-Si)

Coloured refractory dissolved organic carbon, DOC

Coloured refractory dissolved organic nitrogen, DON

Coloured refractory dissolved organic phosphorus, DOP

Labile DOC

Labile DON

Labile DOP

Inorganic Solids

Unit

g C m

-3

g N m

-3

g P m

-3

g N m

-3

g N m

-3

g P m

-3

g P m

-3

g Si m

-3

g C m

-3

g N m

-3

g P m

-3

g C m

-3

g N m

-3

g P m

-3

g m

-3

Distribution of discharge is described in /2/.

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MarineVandplanVærktøjer

Principles for distribution of loads

The methodology for distributing total N and total P into the different N- respectively P-

species are described in the following sections, and summarised in Table 2.

Table 2: Overview of strategies for fractionation of TN and TP into inorganic and organic

species required by the marine model (see Table 1)

State variable

Detritus C

Detritus N

Detritus P

Detritus Si

Measurements

(Not measured)

(NM)

Note

Estimated and scaled to detritus N

Estimated (from LOI and DC:DN) and

scaled to TN

Estimated (from LOI and DC:DP) and

scaled to TP

Not assumed to be an important part of

Total Si loadings, and hence neglected.

Estimated based on monthly

relationships between measured NH

-N

and TN in the stream, see section 0.

Estimations based on monthly

relationships between measured NOx-N

and TN in the stream, see section 0.

Estimations based on monthly

relationships between measured PO

-P

and TP in the stream, see section 0.

Can be significant for phosphor

transport to the coast. Especially in

connection to heavy rain. This

parameter has not been measured.

Concentration time series constructed

from sporadic measurement as part of

NOVA/NOVANA, see section

Error!

Reference source not found..

Literature

Can be important for light attenuation.

For some model relations to Q has been

applied whereas other models does not

include SSi.

NOx (NO

+NO

)

NOx

IPss

(NM)

SiO

CDOC

CDON

CDOP

LDOC

LDON

LDOP

SSi

0.80 × DOC

0.69 × DON

0.25 × DOP

0.20 × DOC

0.31 × DON

0.75 × DOP

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Principles for distribution of loads

4 Determining the dissolved inorganic fractions of TN and TP

In order to determine the dissolved inorganic fraction of the total N and P loads,

monitoring data from a number of

stations in the “measured

catchments” have been

analysed as basis for the distribution. As guidance

, only stations with extended time

series are included, see /7/ for details on monitoring stations included.

The analyses of the fraction of dissolved inorganic nutrients are made per 4

order water

body, as is the resolution of the load data, and thus each monitoring station has been

associated with a catchment of a 4

order water body. The links between monitoring

stations, the stream they are located in and the associated 4

order water bodies are

listed in Appendix A. Figure 2 illustrates some of the monitoring stations included in the

load estimation, with focus on the catchments of the Limfjord.

The breakdown of TN and TP into inorganic and organic nutrients is exemplified by the

analysis of the Limfjord.

Figure 2: Example of all NOVANA monitoring stations (green dots) and the monitoring

stations (red dots) applied for the load calculations reported in /1/ and /7/.

For the main part of monitoring stations in streams discharging to Limfjorden (see red dots in Figure 2) data has

been collected frequently and since

the beginning of the 1990’ties with one to two water quality samples collected

every month. The stations selected for the analyses have over the last approximately 20 years 20 or more

datasets of corresponding measurements of total N and inorganic N and similar with P. For other water bodies

sampling may be less complete

–

this will show when we start to analyse these data and we may have to

compromise.

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Principles for distribution of loads

4.1 Determining the inorganic fractions (NO

and NH

) of TN

For the main part of monitoring stations shown in red dots in Figure 2, data has been

collected

frequently since the beginning of the 1990’ties.

These monitored data are used

to determine the inorganic fractions (NO

and NH

) of TN, as described below and in

Figure 3.

Monitoring

data

•

Assign monitoring station to stream(s)

Fraction

•

Calculate fraction of dissolved inorganic nutrient

concentration to total nutrient

Concentration

•

Use fractions to estimate concentrations of NO

and PO

based on TN and TP

Figure 3: Schematic figure of the method for determining the dissolved inorganic fractions

nutrients of total nutrients.

At first, each monitoring station is assigned to one or more streams within the vicinity of

the location of the monitoring. Only downstream stations are used. Obviously the stream

where the monitoring stations is located is included, and e.g. in the model four streams

are included for Hjarbæk fjord, and they all have one unique monitoring station assigned,

see Appendix A for more details.

At Mors, on the other hand, only one monitoring stations exists, why this stations is

assigned to all streams on Mors and hence represents inorganic fractions (NO

and NH

)

of TN for streams from Mors to the 4

order water bodies: Agerø Bredning/Nees Sund

and Visby Bredning/ Vilsund. Likewise, all monitoring stations within the Limfjord

catchment have been assigned to stream outlets to the Limfjord, and the method is

applied for all other mechanistic models.

For each sampling occasion (usually monthly intervals), the fractions of NH

-N to TN, and

-N to TN has been estimated for each monitoring station. In case that the sum of

inorganic N fractions is larger than the measured TN, the data set has been discarded.

Based on the estimated fractions per date, monthly means (averaged over 20 years) and

StDev’s are calculated.

Figure 4 shows an example of the yearly variation in the NOx-fraction from a monitoring

station located in the catchment to Hjarbæk Fjord (4

order water body no. 3745).

Furthermore, ± StDev is included to illustrate variation between the years of monitoring.

For this station the nitrate fraction constitute about 90% ± 10-15% SD of total nitrogen

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MarineVandplanVærktøjer

Principles for distribution of loads

with minor seasonal variation. Figure 5 shows the fractions of inorganic N to TN and the

shares by NH

and NO

for all 4 streams discharging in the model to the 4

order water

body 3745, Hjarbæk Ford. The fraction of DIN is about 80-90% whith NO

majorly

dominating. At 3 of the 4 stations there is a tendency to a little higher share of NOx in late

spring-early summer and a lower share in late summer- autumn. Table xx in section

Error! Reference source not found.

gives the statistics for all 4

order water bodies and

here the overall patterns are also discussed.

This method is carried out and applied for each monitoring station included in this study

and associated loadings on a 4

order water body level.

Figure 4: Annual variation in monthly means of the fraction of NO

-N to TN, including ± 1

StDev for an upstream monitoring station (17000007) in Simested Å

discharging to 4

order water body 3745, Hjarbæk Fjord. Data covers 20

years with ca. 24 sampling per year. Data sets where the fraction of DIN

exceeded 100% have been omitted from the following analysis.

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MarineVandplanVærktøjer

Principles for distribution of loads

Figure 5: Annual variation in the fraction of inorganic N and P. Also showing the

distribution of inorganic N between NH

-N (blue area), and NO

-N (red area).

The stream and monitoring stations all associate with Hjarbæk Fjord, 4

order water body no. 3745.

4.2 Determining the inorganic P fraction of total P

A similar approach as for nitrogen has been applied to estimate the fraction of phosphate

(DIP) to total P. Based on data from the same stream monitoring stations monthly data

sets are compiled and the monthly means and StDev’s

has been calculated.

The results of the calculation for the station in Simested Å discharging to Hjarbæk Fjord

order water body 3745), Limfjorden, are shown in Figure 6. Compared to DIN the

fraction of DIP is generally lower and with more seasonal variation. Some differences are

observed between the stations. Figure 5 shows the mean of the 4 monitoring stations in

the catchment of Hjarbæk Fjord. In Fiskebæk Å the fraction of DIP is lowest, constituting

about 40% of TP. The highest fraction is measured in Simested Å, up to 80% during

autumn. All stations showed an increase in late summer-autumn but only Simested and

Skals Å showed pronounced seasonal variation with noticeable decrease in late spring-

early summer (around April) and increase in autumn. .

Figure 6: Annual variation in monthly means of the fraction of PO

-P (DIP) to TP,

including ± 1 StDev for an upstream monitoring station (17000007) in

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Principles for distribution of loads

Simested Å discharging to 4

order water body 3745, Hjarbæk Fjord. Data

covers 20 years with ca. 24 sampling per year..

4.3 Uncertainties

Some uncertainties do of course exist as we do not have measurements from all streams

included in the model. Using Figure 2 as an example it is obvious that the water quality

monitoring stations does not represent all streams and catchments and for some areas

only few stations are included.

As the inorganic nutrient fraction versus the organic fraction depends on soil type, land

use etc. any variations occurring within catchments are not accounted for in the applied

approach.

4.3.1 Inorganic nutrients versus total nutrients

We have chosen to include measurements over the past 20 years (if available) when

evaluating the fraction of inorganic nutrients versus total nutrients to have a larger

amount of monthly data to support the seasonal distribution. However, land use and

agricultural practice has changed over the last 20 year which might have influenced the

relation between inorganic nutrients and total nutrients.

4.3.2 Retention downstream observations

The estimated loads is based on measurements taken somehow upstream in the

respectively rivers. From the measurement station to the marine waters some N retention

is taken place, a retention that is estimated in the load calculations, see /7/. However, that

down-stream retention has not verified and is uncertain.

4.3.3 Inorganic P

In contrast to nitrogen, a larger part of phosphorous is known to be transported in pulses

as PO

adsorbed to inorganic suspended particles, bound in organic particles and partly

as bed-load. Therefore, load estimates based on weekly or bi-weekly water samples of

total P inherently will be uncertain and most likely will underestimate the total P load

(because bed-load transport will not be represented in water samples). In the loads

provided by DCE the P load from monitored catchments are based on single samples

whereas the P load from non-monitored catchments includes some estimates from small

catchments based on continuous measurements. Hence, the P loads from non-monitored

catchments are generally larger than from monitored catchments, and we expect the P

load from monitored catchments to be underestimated.

If we during modelling discover a miss-match between the P load and the P

concentrations in the recipient, we might need to address this by introducing of some

relationship between discharge and land-use (agricultural area or forest areas

dominating) or the amount of downstream lakes within the catchment in question.

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Principles for distribution of loads

5 Organic matter and nutrients

Where section

Error! Reference source not found.

handles the method for separating

dissolved inorganic N and P this section handles the remaining part: The organic fraction

of TN respectively TP as well as the organic carbon fraction. The overall method is

schematically described in Figure 7 and during the follow sections

•Estimation

of the total amount of organic carbon (TOC)

Total organic

carbon

Particulate

organic carbon

•Estimating

the fraction of particulate organic carbon (DC) to TOC

Total organic N

•Estimation

of total organic fraction of N (TON) and P (TOP)

•TON:

TN - NOx - NH4

•TOP:

TP - PO4

•Seperation

of dissolved and particulate organic material (C, N and P)

Seperation

Figure 7: Schematic figure of the method for determining the organic fractions of the total

nutrients.

5.1 Total organic N and P

The fraction of total N bound in organic material is estimated as the total N minus

inorganic N (NH

+ NO

), see section 4.1. Organic bound nitrogen can exist in a

particulate fraction (detritus N, DN) and in a dissolved fraction (DON). Unfortunately,

these fractions are not measured but must be estimated indirectly from the corresponding

concentrations of particulate organic carbon, i.e. detritus C (DC) and dissolved organic

carbon (DOC).

Phosphorus and its speciation are more complicated because the particulate fraction can

include both inorganic P and organic P. Initially, we will estimate the

“unreactive”

(organic) P fraction as the difference between TP and PO

but most likely we will refine

this issue in more details when modelling commence.

5.2 Organic carbon

The data collected under the national monitoring program NOVA/NOVANA include a

limited number of measurements of organic carbon and other data that can be converted

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to organic carbon. The measurements relevant to this modelling exercise are listed in

Table 3.

Because of the limited number of measurements (Table 3) it is not possible to estimate

both fractions (DC and DOC) on a temporal (monthly) and on a spatial (catchment) scale.

Figure 8: Location of applied monitoring stations for estimations of DC/TOC. Markings

represents monitoring stations with TOC (red triangles (notice the figure

includes two stations very close, why this is not visible)), NVOC (green dots)

and COD (yellow dots) measurements.

Both TOC and NVOC are direct measurements of total organic carbon, and hence, can

be used directly. However, TOC and NVOC measurements are few and sporadic and

time series cannot be constructed for neither of the two measurements. Hence, for TOC

and NVOC estimations are lumped without analysing locations, seasons nor years of the

measurements. The number of samples shown in Table 3 indicates the total amount of

measurement from ODA, however, to be used for this analysis we seek sets of data

where both LOI and one of the three other measurements (TOC, NVOC or COD) exists.

This procedure reduces the amount of measurements dramatically, see Table 5.

As a supplement total Chemical Oxygen Demand (COD) is applied as an indirect

measurement of TOC. A larger amount of data exist for COD, and few monthly mean

time series have been constructed where sets of COD and LOI exists, see Figure 8 and

Figure 9.

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Table 3: Number of samples where organic carbon or indicators of organic carbon has

been measured in streams.

Organic carbon or indicators of organic carbon

Chemical Oxygen demand (COD) (Total)

Total Organic Carbon (TOC)

Non Volatile Organic Carbon (NVOC)

Loss on Ignition (Suspended solids)

Number of samples

21270

757

2057

29213

Figure 9: Time series of COD at four different monitoring stations, see Figure 8 for

locations. Solid line is average concentrations and shaded area illustrates ±

1×StDev.

In Figure 9 time series of COD is shown and in Table 4 average conversion factors to

estimate organic carbon from COD and from LOI are listed.

Table 4: Figures for converting COD and LOI to organic carbon.

Variables

Total organic carbon

(dissolved & particulate) to

COD

Particulate organic carbon to

LOI

Value

0.28 g C/g O

Reference

0.30 g C/g LOI (range 0.2-0.37)

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We assume that Loss on Ignition (LOI) is an accurate measurement of organic content in

suspended solids. Hence, LOI is used to estimate the fraction of particulate carbon

content, corresponding to the fraction of detritus C (see Table 1).

As for COD, time series of LOI are constructed, see Figure 10, and converted to

particulate organic carbon using Table 4. Finally, the fraction of DC to TOC is estimated,

see Figure 11.

Figure 10: Time series of LOI at four different monitoring stations, see Figure 8 for

locations. Solid line is average concentrations and shaded area illustrates ±

1×StDev.

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Figure 11: Time series of the DC to TOC fraction at four different monitoring stations, see

Figure 8 for locations.

As can be seen from Figure 11 differences in time and between locations exists, but with

no clear seasonal patterns and with only few stations to support regional/local patterns all

measurements are used to estimate one lumped fraction of DC to TOC. Hence, COD as

well as TOC and NVOC are used to estimate one fraction, see Table 5.

In Table 5 the StDev is comparable to the average values indicating some variation not

accounted for in this relatively simple method. However, as the fraction of organic to total

nutrients is low, as seen in section 0, and as we have only limited amount of

measurements to ensure a uniform and

repeatable

method on a nationwide scale and for

later scenarios, the lumped value of 28% in Table 5 is adopted for estimating the fraction

of DC to TOC.

Table 5: Fraction of DC to TOC based on different direct or indirect measurements of

TOC.

TOC origin

DC/TOC

DC/NVOC

DC/COD

DC/ Avr. (TOC, NVOC & COD)

Average

StDev

128

167

342

637

0.21

0.29

0.23

0.25

0.22

0.23

5.3 Organic nitrogen and phosphorous

To estimate detritus N (DN, i.e. particulate organic nitrogen), dissolved organic N (DON),

detritus P (DP) and dissolved organic P (DOP) we will assume C:N:P ratios for both

detritus as well as dissolved organic matter. The ratios applied primarily came from an

extensive USGS data set encompassing 28400 water samples (from ca. 500 streams

each sampled between 6 and 1440 times during the period 1991-1997) analysed for

organic carbon and nutrients (dissolved, particulate, inorganic, organic) along with basic

hydrological parameters such as discharge. Prior to analysis stream data were selected

“match”

(represent) Danish conditions, i.e. data with high ammonia (> 3 µm NH4-N)

indicating sewer discharge were eliminated and only data with seasonal NOx peaks

All estimates of detritus C (DC) are based on LOI measurements.

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between 0.8 and 10 µM were included. Monthly averages of nutrient concentrations and

ratios were estimated for each stream, analysed for seasonal variation and the yearly

averages (C:N:P ratios) were plotted against Q to examine if size of water course

affected the ratios. Data used for this study is listed in Table 6

Table 6: C:N:P ratios for detritus respectively dissolved organic matter.

Variables

Detritus

C:N:P [g C:g N:g P]

DCx:DNx:DPx

32:5.5:1

Dissolved organic matter

DOCx:DONx:DOPx

625:41:1

Appendix B

Reference

Appendix B

Based on the values in Table 6 and the following equations the relation between DN and

DON respectively DP and DOP are estimated. In the following, the relations are solved

for N as example, but same procedure is applicable for P. We know that

��

where TOC is total organic C, DC is detritus C, DOC is dissolved organic C, TON is total

organic N, DN is detritus N and DON is dissolved organic N. Also, we know that

��

Where DCx, DNx, DOCx and DONx are from Table 6.

Finally, from section 5.2 we estimated that

= 0.

×��

��

Solving these sets of equations allow us to estimate the different fractions, see Table 7.

Table 7: Fraction of particulate organic nutrients (DN and DP) and dissolved organic

nutrients (DON and DOP)

Nitrogen

0.44 × ON

DON

0.56 × ON

0.85 × OP

Phosphorous

DOP

0.15 × OP

DN×5.8

Carbon

DOC

DON×15.2

= 0.77 × ��

5.4 CDOM versus LDOM

Based upon /6/ the fraction distribution of CDOM and LDOM has been adopted, see

Table 8. Table 8 also includes estimated fractions of particulate nutrients to dissolved

nutrients. These fractions are different compared to Table 7, but land-use is also different

between Danish land-use and Baltic country land-use. We still apply the estimated

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relation between labile dissolved organics and coloured dissolved organics, as described

in Table 8.

Table 8: Distribution between particulate and dissolved organic material and splitting of

the dissolved organics into labile dissolved organics and coloured dissolved

organics. Estimations based on /6/.

Organic P

DOP

66.7%

33.3%

LDOP

CDOP

Organic N

DON

21.2%

78.8%

LDON

CDON

Organic C

DOC

=TOC-DOC

LDOC

CDOC

20%

80%

31%

69%

75%

25%

6 Concentrations of Silicate

Silicate (SiO

-Si) is also an important nutrient to some primary producers like diatoms and

in the open waters silicate can be a limiting nutrient to the pelagic algae in some periods

(spring bloom). Hence, Silicate is a part of the mechanistic models setup for the North

Sea as well as the inner Danish waters (including the Baltic Sea), why we need to

estimate realistic concentrations of inorganic silicate for the models applied for this study,

where diatoms as single species is included.

In contrast to N and P loads of silicate is not calculated on a nationwide scale why the

same approach as for N and P (see section

Error! Reference source not found.)

is not

applicable.

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Figure 12: Illustration of monitoring stations with more than 20 measurements of Si from

the period 1999-2012. These monitoring stations have been used to

estimate the Si concentrations for all associated 4

order water bodies.

From ODA reported concentrations of silicate, where the monitoring stations include more

than 20 measurement over the period from 1990-2012, has been identified, see Figure

12. The coverage and continuity of the measurements varies significantly over the

stations included in Figure 12. However, the differences in concentrations seems to be

somehow related to regions and from the few long-term time series identified there

seems not to be an development in time, see Figure 13.

From Figure 13 it might be argued that some development does occur in the early

1990’ties but we do not find any evidence for this –

nor explanation

–

and from the period

of the modeling (year 2002 and forward) there are no clear trends, except for some

seasonal variation.

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Figure 13: Time series of Si measurements from 5 different monitoring stations (Source:

ODA)

For each of the stations included in Figure 12 monthly averaged concentrations are

constructed, see Figure 14. These constructed time series are then appointed a number

of streams for each 4

order water body in the inner Danish waters as well as for the

North Sea, according to the stream described in /2/.

Figure 14: Monthly averages ± 1×StDev of Si at 5 different monitoring stations, see

Figure 13.

The monitoring stations included in Figure 14 are located in Jutland (14000020,

21000487 and 21000707 and Zealand (50000045 and 50000046) and as can be seen

the three stations in Jutland has concentrations between 6-9 g SiO

-Si/m

with only little

or no seasonality whereas the concentrations in Zealand is between 1-5 g SiO

-Si/m

but

with more pronounced seasonality.

The variability expressed as ± StDev is more or less to constant 1 g SiO

-Si/m

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As for N and P each monitoring stations identified having sufficient amount of data will be

appointed a number of streams corresponding to the area of the different monitoring

stations, see Appendix A for details.

7 Inorganic Solids

As a final component in (some of) the mechanistic models inorganic solids (SSin) has to

be included. SSin is an important parameter as the concentration of SSin has an impact

on the light attenuation in the receiving waters (4

order water body). Furthermore, SSin

is known to be potential important for transport of adsorbed inorganic P (IPss) as

mentioned in section

Error! Reference source not found..

Concentrations of SSin have previously been described as a function of discharge /8/ and

for this study we adopt this concept for monitoring stations where relations can be

developed.

In the stations shown in Figure 15 sets of data on both suspended solids (SS) and loss

on ignition (LoI) exists, and hence, by subtracting SS with LoI the amount of inorganic

suspended solids (SSin) can be estimated. In the following these data are used to

estimate relations between daily discharge (as delivered by DCE and described in /2/)

and estimations of SSin (SS-LoI).

Figure 15: Illustration of monitoring stations where measurements of inorganic suspended

solids (SSin) exists. Downstream stations have been used to estimate

relations between SSin and discharge.

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As described in previous sections each monitoring stations is appointed to a number of

streams to cover all 4

order water bodies depending on locations of monitoring stations

and streams included in the modelling, see /2/.

However, these relations cannot be transformed directly from one catchment to another

before some

uniformity has been adopted. To obtain uniformity we build the relations to

discharge by calculating discharge divided by catchments area: Q (m

/s) / Area (1000

Only monitoring stations with sufficient amount of measurements are included, and here

we define sufficient monitoring as an estimated average concentration per month is not

estimated based on less than 4 measurements per month over a period of 20 years.

As an example, four stations from the Limfjord has been included in this paper, see

Figure 16.

Figure 16: Monthly averages ± 1×StDev of inorganic suspended solids (SSin) at 4

different monitoring stations within the Limfjord. (Blue line) is average

monthly concentrations of SSin, (blue shaded area) is ± StDev and (purple

line) is average monthly discharge.

For SSin clear seasonality is observed. Especially for station 9000001 (north of Thiested

bredning) the concentrations of SSin are high in fall and winter and low during summer.

This is also the case for stations 17000007 (Hjarbæk fjord) and 10000238 (Halkær

bredning) although not that strong as for station 9000001.

What is also clear, is the StDev being larger in autumn and winter (station 9000001 and

17000007) which indicate some relation to discharge as the discharge in these periode s

can be larger, and very variable due to weather conditions (precipitation, snow and snow

melt).

In Hjarbæk bredning the variance is equally large during the entire year and

concentrations vary between 4-15 g/m

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Station 11000011 (north of Nissum bredning) is included in this description as the relation

to discharge is opposite to normal picture: Low discharge results in high concentrations of

SSin and high discharge results in low concentrations of SSin.

For now, we have no obvious explanation for this, but the relation is adopted for streams

close to this monitoring stations. In Figure 17 relations between SSin and discharge on

four different monitoring stations within the Limfjord catchment is included. These kind of

relations ships makes it for the F(Q/area) for the SSin estimations adopted for the

mechanistic models.

Figure 17: Relations between SSin and discharge on four different monitoring stations

within the Limfjord catchment.

In Figure 17 relations between SSin and discharge (Q/area) is included. Where R

larger than

0.15

the relation is adopted for the mechanistic models whereas e.g. relation

for station 10000237 does almost not exist why the average monthly concentrations is

adopted instead of a relation to discharge.

Adopting the above relations results in SSin concentrations as illustrated in Figure 18.

The relations build and associated statistical measures (R

) are included in Appendix A.

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Figure 18: Examples of estimated concentrations of SSin based on relations to discharge

/s)

–

upper panel: To average monthly concentrations (lower left panel)

and a relation to discharge with opposite relationship (lower right panel).

8 References

/1/

/2/

Windolf et al

Q-distribution note

/3/ Vere, D. (2002): A Comparative Study between Loss on Ignition and Total Carbon

analysis on Minerogenic Sediments. Studia Universitatis Babebolyai, Geologia, XLVII, 1,

2002, 171-182

/4/

/5/

Markager et al. 1992

Stedmon et al 2006

/6/ Ramûnas Stepanauskas, Niels O. G. Jørgensen, Ole R. Eigaard, Audrius, Vikas,

Lars Tranvik, and Lars Leonardson (2002). Summer inputs of riverine nutrients to the

Baltic Sea: bioavailability and eutrophication relevance. Ecological Monographs 72:579–

597.

/7/

/8/

/9/

Windolf

–

beskrivelse af load til typefjorde

Hans T

–

Odense og ??

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Appendix A: Monitoring stations and associated streams and 4

order water bodies.

North Sea

WQ station

90000001

–

Storå

11000011

–

Kastet Å

90000001

–

Storå

90000001

–

Storå

90000001

–

Storå

22000062

–

Storå

25000086

–

Tim Å

25000086

–

Tim Å

25000086

–

Tim Å

25000086

–

Tim Å

25000097

–

Skjern Å

25000078

–

Omme Å

31000032

–

Frisvad

Møllebæk

31000027

–

Varde Å

35000011

–

Sneum Å

39000001

–

Brøns Å

31000027

–

Varde Å

38000024

–

Ribe Å

36000009

–

Kongeåen

35000011

–

Sneum Å

Name

Klitmøller Å

Thyborøn

Dybe Å

Bækmarksbro Å

Damhus Å

Storå

Thorsminde

Von Å

Venner Å

Velling Stauning Landkanal

Skjern Å

Hvide Sande

Henne Mølleå

Kallesmærsk

Fanø

Rømø

Varde Å

water body

1110

1200

1210

1241

1242

1243

1250

1310

1321

1322

1323

1330

1410

1510

1520

1530

1610

1620

1651

(Catchment

1630)

Ribe Å

Kongeåen

Sneum Å

Brøns Å

39000001

–

Brøns Å

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WQ station

42000021

–

Vidå

40000001

–

Brede Å

30000002

–

Uggerby Å

30000002

–

Uggerby Å

90000001

–

Storå

60000001

–

Ry Å

40000005

–

Liver Å

90000021

–

Tranum Å

90000001

–

Storå

Name

Vide Å

Brede Å

Skagen

Uggerby Å

Lild Strand

Nybæk

Liver Å

Slette Å

Esdal Vandløb

water body

1651

2100

2110

2200

2213

2216

2310

Kattegat

WQ station

5000003

–

Voer Å

5000003

–

Voer Å

5000003

–

Voer Å

23000087

–

Hevring Å

48000007

–

Højbro Å

48000007

–

Højbro Å

51000020

–

Lammefjordens

Pumpekanaler

24000061

–

Feldbæk

24000061

–

Feldbæk

23000087

–

Hevring Å

23000087

–

Hevring Å

23000087

–

Hevring Å

Name

Lundbæk

Filstrøm

Læsø Nord

Anholt

Hesselø

Højbro Å

Klintsø-Landkanal

water body

3011

3012

3013

3020

3102

3110

3310

Hoed Å

Koldingsand Nordkanal

Brøndstrup Mølleå

Hevring Å

Lindbjerg Bæk

Gudenå

3410

3420

3510

3520

3531

3532

21000467

–

Gudenå

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WQ station

21000413

–

Alling Å

15000002

–

Kastbjerg Å

15000002

–

Kastbjerg Å

15000035

–

Villestrup Å

15000042

–

Onsild Å

Name

Allinge Å

Store Vejle Pumpekanal

Kastbjerg Å

Villestrup Å

Onsild Å

water body

3533

3540

3611

3612

3613

3623

3626

3812

3814

3816

3910

3920

15000032

–

Haslevgårds Å

80000001

–

Gerå

80000001

–

Gerå

50000003

–

Voer Å

20000005

–

Elling Å

20000005

–

Elling Å

Haslevgårds Å

Hals

Gerå

Voer Å

Søby Å

Elling Å

Nordlige Bælthav

WQ station

27000035

–

Odder Å

27000035

–

Odder Å

27000035

–

Odder Å

27000035

–

Odder Å

27000035

–

Odder Å

27000035

–

Odder Å

27000035

–

Odder Å

51000020

–

Lammefjordens

pumpekanaler

51000020

–

Lammefjordens

pumpekanaler

51000020

–

Lammefjordens

Name

Sørende

Stavns Fjord

Samsø Nordvest

Sælvig

Dallebæk

Vester kanal

Tunø

water body

4011

4012

4021

4022

4023

4025

Fuglebæks Å

4110

Bølerenden

Revesgrøften

4115

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WQ station

pumpekanaler

51000020

–

Lammefjordens

pumpekanaler

51000020

–

Lammefjordens

pumpekanaler

51000020

–

Lammefjordens

pumpekanaler

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

Name

water body

Bregninge Å

4120

Tangmoserenden

4120

Vestre Landkanal

Nordskov

Fyns Hoved

Sørenden

Hindsholm

Ålekisterenden

Gabet

Odense Fjord

4120

4210

4221

4222

4223

4224

4225

4231

4232

4250

4260

4270

4310

4320

4331

4332

4333

43000003

–

Ringe Å

43000003

–

Ringe Å

43000003

–

Ringe Å

43000003

–

Ringe Å

43000003

–

Ringe Å

29000009

–

Rohden Å

28000001

–

Bygholm Å

28000001

–

Bygholm Å

27000045

–

Hansted Å

28000001

–

Bygholm Å

27000045

–

Hansted Å

27000045

–

Hansted Å

27000045

–

Hansted Å

Storskov

Ringe Å

Afløb fra Tørresø

Lungrenden

Jesore Byrende

As-Rårup Skelbæk

Skjold Å

Hjarnø

Vl. S. f. Lerdrup

Glud Bæk

Åkær Å

Møllebæk

Haldrup Mølleå

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WQ station

28000001

–

Bygholm Å

27000045

–

Hansted Å

28000001

–

Bygholm Å

27000035

–

Odder Å

27000035

–

Odder Å

24000061 - Feldbæk

26000080

–

Århus Å

24000061 - Feldbæk

26000080

–

Århus Å

24000061 - Feldbæk

Name

Skelbækken

Hansted Å

Klokkedal Å

Malskær Å

Odder Å

Egå

Skæring Bæk

Skødstrup Bæk

Balskov Bæk

Knubbro Baek

Kolå

Stenbæk

Sletterhage

Giberå

Vadbro Bæk

Århus Å

Femmøller Mølleå

–

Skovmølle

Bro - udløb

water body

4333

4334

4340

4360

4411

4111

4412

4420

4440

4450

4460

4510

Lillebælt

WQ station

43000003

–

Ringe Å

43000003

–

Ringe Å

43000003

–

Ringe Å

43000001

–

Stor Å

43000001

–

Stor Å

29000009

–

Rohden Å

29000009

–

Rohden Å

Name

Kragelund Møllebæk

Ålebækken

Fogense Eng

Stor Å

Aulby Mølleå

5131_nn

Rosenvold Å

water body

5110

5120

5131

5132

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

33000004

–

Spang Å

33000004

–

Spang Å

29000009

–

Rohden Å

29000009

–

Rohden Å

33000004

–

Spang Å

32000001

–

Vejle Å

43000007

–

Viby Å

33000004

–

Spang Å

43000007

–

Viby Å

37000011

–

Binderup

Mølleå

37000011

–

Binderup

Mølleå

34000019

–

Kolding Å

34000019

–

Kolding Å

33000004

–

Spang Å

43000007

–

Viby Å

43000007

–

Viby Å

46000001

–

Brende Å

46000001

–

Brende Å

37000036

–

Kærmølle Å

37000038

–

Vejle Å

37000011

–

Binderup

Mølleå

37000038

–

Vejle Å

46000020

–

Puge Mølle Å

37000039

–

Fjeldstrup Å

46000020

–

Puge Mølle Å

46000001

–

Brende Å

46000001

–

Brende Å

Name

Spangs Å

Hede Å

Rohden Å

Tirsbæk

Sellerupskov Bæk

Vejle Å

Afløb fra Staurby Skov

Erritsø Bæk

Føns Vang

Tilløb Kolding Fjord_5261

Tilløb Kolding Fjord_5262

Dalby Møllebæk

Kolding Å

Gudsø Mølleå

Fønsskov

Laven Bæk

Afløb fra Grevindeskov

Moserenden

Hejlsminde Strand

Aller Å

Binderup Mølleå

Brandsø

Bågø

Årø

Kærum Å

Brende Å

Ålebækken

water body

5132

5133

5134

5135

5200

5240

5261

5262

5263

5264

5310

5320

5330

5340

5341

5350

5401

5402

5403

5410

5411

5412

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

46000020

–

Puge Mølle Å

46000020

–

Puge Mølle Å

37000034

–

Haderslev

Møllestrøm

37000034

–

Haderslev

Møllestrøm

37000039

–

Fjeldstrup Å

37000039

–

Fjeldstrup Å

37000038

–

Vejle Å

46000017

–

Hårby Å

41000016

–

Strømmen

37000034

–

Haderslev

Møllestrøm

37000034

–

Haderslev

Møllestrøm

46000017

–

Hårby Å

46000017

–

Hårby Å

46000017

–

Hårby Å

46000017

–

Hårby Å

47000001

–

Hundstrup Å

47000001

–

Hundstrup Å

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000014

–

Fiskbæk

41000014

–

Fiskbæk

41000014

–

Fiskbæk

41000014

–

Fiskbæk

41000014

–

Fiskbæk

41000014

–

Fiskbæk

Name

Puge Mølle Å

Torø

Årøsund

Haderslev Fjord

Ørby Strand

Knudbæk og Fjeldstrup Å

Tilb Lillebælt_5470

Damrenden

Havnbjerg

Flovt Strand

Bankel

Helnæs

Hattebækken

Hårby Å

Møllebækken

Duereds Vaenge

Lyø

Eskebæk

Melved Bæk

Humbæk

Kruså

Flensborg Fjord

Marbæk

Nybøl Nor

Broager Vig

Krambæk

water body

5413

5414

5430

5440

5450

5460

5470

5510

5520

5530

5531

5610

5621

5622

5630

5640

5650

5660

5711

5721

5722

5723

5730

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

41000014

–

Fiskbæk

41000016

–

Strømmen

41000016

–

Strømmen

41000012

–

Elsted Bæk

41000016

–

Strømmen

41000012

–

Elsted Bæk

41000012

–

Elsted Bæk

41000020

–

Blå Å

41000012

–

Elsted Bæk

41000012

–

Elsted Bæk

41000012

–

Elsted Bæk

41000012

–

Elsted Bæk

37000034

–

Haderslev

Møllestrøm

37000034

–

Haderslev

Møllestrøm

41000020

–

Blå Å

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000016

–

Strømmen

41000020

–

Blå Å

Name

Vemmingbugt

Vibæk

Kvl. 1, Broager

Barsø

Nordborg Bæk

Bøgelunds Bæk

Slotsmølle Å

Grensbæk

Møllebæk

Tilb Lillebælt_5840

Elsted Bæk

Hoptrup Å

Tilb Lillebælt_5860

Halk Strand

Blå Å

Holmbæk

Stegsvig

Stolbæk Bro

Tilb. Augustb Fj_5920

Sandvig

Tilb. Augustb Fj_5922

Augustenborg Fjord

Tilb. Augustb Fj_5924

Snogbæk

water body

5731

5732

5740

5801

5810

5820

5830

5840

5841

5850

5860

5870

5910

5911

5913

5920

5921

5922

5923

5924

5930

Storebælt

WQ station

Name

water body

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

54000002

–

Fladmose Å

54000002

–

Fladmose Å

44000021

–

Vindinge Å

55000015

–

Nedre Halleby

55000015

–

Nedre Halleby

55000015

–

Nedre Halleby

56000005

–

Tude Å

56000002

–

Seerdrup Å

56000001

–

Bjerge Å

64000025

–

Nældevads Å

64000025

–

Nældevads Å

62000012

–

Halsted Å

54000002

–

Fladmose Å

56000001

–

Bjerge Å

56000001

–

Bjerge Å

57000055

–

Saltø Å

54000002

–

Fladmose Å

54000002

–

Fladmose Å

54000002

–

Fladmose Å

57000055

–

Saltø Å

57000058

–

Nedre Suså

57000052

–

Fladså

57000052

–

Fladså

57000052

–

Fladså

60000032

–

Næs Å

60000029

–

Køng Å

61000011

–

Sørup Å

Name

Agersø

Omø

Sprogø

Kærby Å

Nedre Halleby Å

Råmosegrøften

Tude Å

Hulbyrenden

Kobæk Rende

Femø

Askø

Fejø

Stigsnæs

Spegerborgrenden

Noret

Møllerende

Tjærebyrenden

Fladmose Å

Tørremølle rende

Saltø Å

Nedre Suså

Fladså

Kyllebæk

Basnæs Grøften

Næs Å

Køng Å

Langkærrende

water body

6100

6110

6120

6130

6140

6201

6202

6203

6210

6211

6212

6220

6221

6222

6223

6224

6225

6230

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

61000011

–

Sørup Å

61000011

–

Sørup Å

36000007

–

Saksløbing Å

36000007

–

Saksløbing Å

61000011

–

Sørup Å

61000012

–

Tingsted Å

61000012

–

Tingsted Å

61000015 - Nordkanalen

63000007

–

Sakskøbing Å

63000007

–

Sakskøbing Å

63000007

–

Sakskøbing Å

63000007

–

Sakskøbing Å

63000007

–

Sakskøbing Å

64000025

–

Nældevads Å

62000012

–

Halsted Å

62000012

–

Halsted Å

64000025

–

Nældevads Å

62000015

–

Marrebæksrende

60000031

–

Mern Å

60000031

–

Mern Å

61000011

–

Sørup Å

60000031

–

Mern Å

60000034

–

Sømose Bæk

60000034

–

Sømose Bæk

60000034

–

Sømose Bæk

61000013

–

Fribrødre Å

61000013

–

Fribrødre Å

Name

T.T.Smålandshavet_6232

T.T.Guldborgsund_6251_a

T.T.Guldborgsund_6251_b

Ny Krog Vandløb

Sørup Å

Tingsted Å

Marbæk Kanal

Flintinge Å

Rørmose Bæk

T.T.Smålandshavet_6261

Låge Å

Sakskøbing Å

T.T.Smålandshavet_6262

Lomose Å

Nældemose Å

Kasbæk

Ørby Å

Stokkemarkeløbet

Uterslevløbet

Vintersebølle Bæk

Bakkesbølle Bæk

Orenæs

T.T.storstrømmen_6313

Askeby Landkanal

Bækrenden

Damme Vandløb

Gundslev Å

Fribrødre Å

water body

6232

6251

6252

6253

6261

6262

6263

6264

6311

6312

6313

6322

6323

6330

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

61000013

–

Fribrødre Å

62000015

–

Marrebæksrende

62000017

–

Ryde Å

62000017

–

Ryde Å

62000012

–

Halsted Å

62000017

–

Ryde Å

47000036

–

Vejstrup Å

47000033

–

Lillebæk

47000035

–

Syltemae Å

47000035

–

Syltemae Å

47000035

–

Syltemae Å

47000001

–

Hundstrup Å

47000001

–

Hundstrup Å

47000001

–

Hundstrup Å

47000001

–

Hundstrup Å

47000036

–

Vejstrup Å

47000036

–

Vejstrup Å

47000036

–

Vejstrup Å

47000036

–

Vejstrup Å

47000036

–

Vejstrup Å

47000036

–

Vejstrup Å

47000035

–

Syltemae Å

47000035

–

Syltemae Å

47000035

–

Syltemae Å

47000036

–

Vejstrup Å

47000035

–

Syltemae Å

47000035

–

Syltemae Å

47000037

–

Name

Søborgkanalen

Marrebæksrende

Vestkanalen

Hovedkanalen

Branderslev Å

Søndernor

Akkemoserenden

Troldebjerggrøften

Skelbækken

Syltemae Å

Lehnskov Bæk

Rislebæk

Bjerne Bæk

Hundstrup Å

Møllebækken

Kobberbækken

Halling Skov

Egemadsafløbet

Thurø

Lindelse Nor

Langeland

Tåsinge

Kløven

Landgrøften

Skattebøllerenden

Vemmenæs

Nørreskov Bæk

Kongshøj Å

water body

6330

6420

6421

6422

6430

6440

6510

6511

6512

6520

6521

6522

6531

6532

6533

6541

6542

6610

6620

6630

6650

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

Stokkebækken

47000037

–

Stokkebækken

47000036

–

Vejstrup Å

47000033

–

Lillebæk

47000037

–

Stokkebækken

44000021

–

Vindinge Å

44000021

–

Vindinge Å

44000021

–

Vindinge Å

44000021

–

Vindinge Å

44000021

–

Vindinge Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

Stokkebækken

Vejstrup Å

Tange Å

Tåsinge Strand

Ladegårds Å

Ørbæk Å

Grønholt afløbet

Lysemoseafløbet

Kauslunde Å

Tårup Inddæmmede Strand

Vejlebækken

Skjoldmoserenden

Ålebækken

Hindsholm

6650

6710

6721

6722

6740

6751

6752

6753

6760

Name

water body

Øresund

WQ station

59000010

–

Stevns Å

59000008

–

Vedskølle Å

59000006

–

Tryggevælde

58000047

–

Køge Å

53000010

–

Lille Vejle Å

53000054

–

Skensved Å

53000054

–

Skensved Å

53000054

–

Skensved Å

Name

Møllerende

Vedskølle Å

Tryggevælde Å

Køge Å

Lille Vejle Å

Skensved Å

Solrød Bæk

Karlstrup Mosebæk

water body

7110

7122

7124

7126

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

53000010

–

Lille Vejle Å

53000011

–

Store Vejle Å

53000028

–

Harrestrup Å

53000028

–

Harrestrup Å

53000028

–

Harrestrup Å

53000028

–

Harrestrup Å

53000028

–

Harrestrup Å

50000051

–

Mølle Å

50000051

–

Mølle Å

50000048

–

Kighanerenden

50000057

–

Nive Å

50000048

–

Kighanerenden

50000057

–

Nive Å

50000057

–

Nive Å

50000057

–

Nive Å

50000056

–

Nive Å

48000011

–

Østerbæk

48000004

–

Esrum Å

48000004

–

Esrum Å

48000011

–

Østerbæk

48000011

–

Østerbæk

48000010

–

Søborg Kanal

Name

Olsbæk

Store Vejle Å

Harrestrup Å

Hovedgrøften

Enghave Å

Saltholm

Kastrup

Tårbæk Rende

Mølle Å

Kighanerenden

Nive Å

Ulvemoserenden

Humlebækken

Krogerup vandløb

Egebæk

Helsingør Red

Knudemoseløbet

Esrum Å

Pandehave Å

Vesterbæk

Østerbæk

Søborg Kanal

water body

7126

7127

7128

7130

7201

7210

7220

7230

7240

7310

7320

7330

Sydlige Bælthav

WQ station

47000035

–

Syltemae Å

Name

Magleby Nors Pumpekanal

water body

8110

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

65000001

–

Rødby Fjord

61000015

–

Nordkanalen

61000015

–

Nordkanalen

61000015

–

Nordkanalen

61000015

–

Nordkanalen

61000015

–

Nordkanalen

61000015

–

Nordkanalen

61000015

–

Nordkanalen

Name

Rødby Fjord

Ålholmløbet

Egeholmløbet

T.T.Lambo Farvand_8220_a

Strognæs Bæk

Pumpekanal Strognæs Enge

T.T.Lambo Farvand_8220_b

T.T.Lambo Farvand_8220_c

water body

8210

8220

Østersø

WQ station

66000014

–

Bagge Å

66000014

–

Bagge Å

66000014

–

Bagge Å

66000014

–

Bagge Å

66000014

–

Bagge Å

66000014

–

Bagge Å

61000012

–

Tingsted Å

60000034

–

Sømosebæk

60000036

–

Tubæk

60000034

–

Sømosebæk

60000034

–

Sømosebæk

60000034

–

Sømosebæk

60000031

–

Mern Å

60000026

–

Herredsbæk

60000036

–

Tubæk

60000024

–

Fakse Å

Name

Vase Å

Byå

Blykobbe Å

Kobbe Å

Øle Å

Læså

Askehaveløbet

Nyhåndsbæk

Brønsvig

Sømosebæk

Ulvshale Bækken

Landsledgrøft

Mern Å

Herredsbæk

Tubæk

Fakse Å

water body

9100

9110

9120

9130

9140

9150

9210

9220

9300

9310

9320

9321

9330

9350

9360

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

60000037

–

Vivede Mølleå

Name

Vivede Mølleå

water body

9360

Limfjord:

Estimating the fraction of dissolved inorganic nutrients to total nutrient is based on

monitoring data from following water quality stations. Also, the streams covered by each

station and corresponding 4

order water body in included.

WQ station

17000007 - Simested

18000077 - Skals Å

19000011 - Fiskbæk Å

19000012 - Jordbro Å

13000005 - Lerckenfeld Å

13000010 - Trend Å

Name

Simested Å

Skals Å

Fiskbæk Å

Jordbro Å

Lerkenfeld Å

Trend Å

Stistrup Å

water body

3745

3743

3741

3742

3747

3764

3763

3754

3771

3772

3751

3734

3752

16000030 - Lyby-Gronning

Grøft

20000024 - Karup Å

12000001 - Vejerslev Bæk

Astrup Bæk

Karup Å

Mygdam Å

Spang Å

Lyngbro Bæk

16000023 - Bredkær Bæk

Skærbæk Å

Hellegård Å

Hummelmose Å

16000024 - Fold Å

Fold Å

Østergård Bæk

16000070 - Vium Mølleå

Vium Mølleå

Hinnerup Å

Rødding Å

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

9000001 - Storå

Name

Sundby Å

Storå

Sløjkanal

Ørebro Kanal

10000013 - Dybvad Å

Dybvad Å

Vaar Å

11000011 - Hvidbjerg Å

Kastet Å

Serup Å

Borregår Bæk

13000065 - Bjørnsholm Å

7000002 - Lindholm Å

Bjørnsholm Å

Ry å

Lindenholm Å

Lerbæk

Stae Bæk

9000021 - Tranum Å

10000009 - Herreds Å

10000014 - Binderup Å

10000010 - Kærs Mølleå

10000011 - Romdrup Å

14000016 - Lindenborg Å

Tranum Å

Halkær Å

Binderup Å

Kærs Mølleå

Romdrup Å

Lindenborg Å

Hyllebrors Bæk

water body

3762

3761

3733

3732

3731

3728

3773

3753

3733

3722

3721

3719

3717

3726

3724

3723

3721

3715

3713

3711

Estimating the concentration of inorganic suspended sediments (SSin) is based on

monitoring data from following water quality stations. Also, the streams covered by each

station and corresponding 4

order water body in included.

WQ station

17000007 - Simested

Name

Simested Å

water body

3745

SSin estimations

y = 326276x

1.5548

(R² = 0.2491)

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

Name

Lerkenfeld Å

18000077 - Skals Å

19000012 - Jordbro Å

Skals Å

Jordbro Å

Fiskbæk Å

20000024 - Karup Å

Karup Å

water body

3743

3745

(R² = 0.1621)

3745

y = 20795x1.1814

3747

(R² = 0.1568)

16000030 - Lyby-Gronning

Grøft

y = 3E+08x

2.5228

Astrup Bæk

3742

(R² = 0.3743)

y = 5124.8x

1.0339

13000010 - Trend Å

Trend Å

Stistrup Å

Bjørnsholm Å

16000070 - Vium Mølleå

Vium Mølleå

Hinnerup Å

Rødding Å

Mygdam Å

Spang Å

Lyngbro Bæk

16000024 - Fold Å

Fold Å

Østergård Bæk

Skærbæk Å

Hellegård Å

Hummelmose Å

11000011 - Hvidbjerg Å

Kastet Å

3741

(R² = 0.1452)

3742

3733

y = 1.8945e

683.09x

3751

(R² = 0.3582)

3734

3752

3764

3763

y = 20795x

1.1814

3771

(R² = 0.1568)

3772

3754

3773

y = 0.018x

-0.909

Monthly mean

y = 166938x

1.453

SSin estimations

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

Name

water body

SSin estimations

(R² = 0.6171)

Serup Å

Borregår Bæk

9000001 - Storå

Sundby Å

Storå

Sløjkanal

Ørebro Kanal

9000021 - Tranum Å

10000237 - Halkær Å

Tranum Å

Halkær Å

Dybvad Å

Vaar Å

Binderup Å

7000002 - Lindholm Å

Ry å

Lindenholm Å

Lerbæk

Stae Bæk

14000016 - Lindenborg Å

Lindenborg Å

Romdrup Å

Kærs Mølleå

Hyllebrors Bæk

3753

y = 3894x

0.9437

3762

(R² = 0.4167)

3761

3733

3732

y = 2.2915e

554.03x

3726

(R² = 0.4087)

3724

3731

3728

3723

y = 3.1223e

505.58x

3722

(R² = 0.179)

3721

3719

3717

3713

3715

3721

3711

Monthly mean

Odense Fjord:

WQ station

Name

water body

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

43000003

–

Ringe Å

43000003

–

Ringe Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

45000058

–

Geels Å

Name

fj_n

fj_s

u28

u29

u46

Geel

lu_n

water body

4231

4232

45000002

–

Odense Å

45000002

–

Odense Å

45000005

–

Stavis

oden

Odense_A_Discharge

stav

u27

u48

45000048

–

Vejrup

vejr

Roskilde/Ise Fjord

WQ station

49000054

–

Arresø Kanal

49000054

–

Arresø Kanal

52000025

–

Græse Å

52000029

–

Havelse

52000025

–

Græse Å

52000033

–

Mademose

52000035 - Udesundby

52000039

–

Værebro

52000063

–

Hove

52000199

–

Maglemose

52000199

–

Maglemose

52000068

–

Langvad

Name

Arresø

Melby

Græse

Havelse

Hornsherred

Mademose

Sillebro

Værebro

Hove

Maglemose

Sønderby

Langvad

water body

3221

3222

3223

3224

3226

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17

MOF, Alm.del - 2017-18 - Bilag 35: Rapporten fra det internationale ekspertpanel om evaluering af de danske marine modeller

MarineVandplanVærktøjer

Principles for distribution of loads

WQ station

52000068

–

Langvad

52000068

–

Langvad

52000068

–

Langvad

52000068

–

Langvad

52000068

–

Langvad

52000068

–

Langvad

Name

Honepil

Lejrerende

Lejre Å

Lundby

Ørbæk

Selsø

water body

3227

- mvv_documentation_load_distribution_evaluation / aer / 2014-03-17