university of gdaŃsk - model...

UNIVERSITY OF GDAŃSK INSTITUTE OF OCEANOGRAPHY

Marek Kowalewski, Jan Jędrasik, Bogdan Ołdakowski, Jacek Nowacki

The impact of the Vistula river on the coastal water of the Gulf of Gdańsk

Ecohydrodynamic modeling

GDYNIA 2003

Contents

INTRODUCTION.........................................................................................................................3

1. DESCRIPTION OF THE MODEL.....................................................................................5 1.1. PRODEMO MODEL............................................................................................................5 1.2. INTEGRATION WITH HYDRODYNAMIC MODEL...................................................................7 1.3. DATA USED FOR MODEL SIMULATIONS .............................................................................9

2. METHODOLOGY OF RESEARCH..................................................................................9 2.1. CALIBRATION OF THE MODEL ...........................................................................................9

3. COMPARISON OF THE SIMULATIONS VERSUS MEASUREMENTS..................13 3.1. VERTICAL DISTRIBUTION OF VARIABLES IN SEASONAL FORMULATION...........................13

4. STATISTIC CHARACTERISTICS OF THE MODEL QUALITY..............................25

5. DEFINITION OF SCENARIOS........................................................................................29 5.1. METHOD OF ANALYSIS ...................................................................................................30 5.2. RESULTS.........................................................................................................................31

6. CONCLUSIONS..................................................................................................................46

LITERATURE ............................................................................................................................46

APPENDIX I................................................................................................................................50

APPENDIX II ..............................................................................................................................51

APPENDIX III. EQUATIONS OF THE MODEL ..................................................................54 PHYTOPLANKTON.......................................................................................................................54 ZOOPLANKTON...........................................................................................................................55 MINERALIZATION OF CARBON, NITROGEN, PHOSPHORUS AND SILICON ......................................55 CARBON .....................................................................................................................................56 CARBON IN DETRITUS.................................................................................................................56 NITROGEN ..................................................................................................................................56 PHOSPHORUS..............................................................................................................................57 SILICON......................................................................................................................................58 DISSOLVED OXYGEN...................................................................................................................59

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Introduction

Permanent inflow of contaminates from land into the sea caused their significant accumulation and even marine ecosystems transformation. Main deliverance comes from rivers which carry huge polluted loads gathered at their catchments. A necessity of deep studies occurred considering dependence of inflowing loads of nutrients to marine fertility processes. Presently the sea waters are over eutrophicated what is a consequence of inadequate agricultural and industrial activities. The socio-economical changes need to be introduced to reverse disadvantageous processes.

The EUROCAT project was undertaken to investigate the influence of delivered contaminants from chosen seven European rivers to the coastal waters. One of them is the Vistula river which carries polluted waters from its catchment (over 100 000 square kilometers area) to the Gulf of Gdansk. These riverine waters rich with nitrogen and phosphorus compounds have an effect on the coastal waters, particularly on the Gulf of Gdansk. A research of response of marine ecosystem to inflowing contaminates has been undertaken by using of mathematical modeling. The ecohydrodynamic model has been developed and applied for investigation of biogeochemical processes at the water environment of the Gulf of Gdansk. Detailed examinations were conducted for period 1994 – 2002. However, forecasts for the gulf ecosystem behavior were evaluated according to three scenarios. The last ones assumed the riverine loads of nitrogen and phosphorous reduction resulted in expected policy targets.

Mathematical modeling is a method of research which enables quantitative and qualitative analysis of processes taking place in natural environment. Mathematical model of ecosystem may also be used as a tool for the prognoses of estimated influence of man’s activity or the analysis of future changes in ecosystem, which may take place under the influence of external factors.

Ecological modelling involves physical, chemical and biological processes in marine environment and their interaction (Nihoul, 1975; Jorgensen, 1988; Fransz et al., 1991). Physical processes involve a continuous complex movement of water described with equations of momentum, mass and energy flow. Chemical processes involve reactions of chemical compounds in water and sediment as well as on their contact area, and biological processes reveal behaviour of biological “agents” on various trophic levels on the physical-biological stage (Shuert and Walsh, 1993).

The interest in ecological modelling started in the nineteen twenties last centaury (Streeter-Phelps, 1925) when ecology did not articulate threats as clearly as it does nowadays. The methodology of research was propelled by the increasingly endangered marine environment due to the influx of pollution, as well as by the need to understand how the ecosystem worked in order to predict directions and effects of its transformation. The fundamental methodological works were written in the 70s and 80s (Odum, 1970; Nihoul, 1977; Jorgensen, 1988). Modern ecological modelling involves a wide range of issues from a short-term bloom of phytoplankton to long-term changes, and from local research to the studies of vast seawater regions (Lauenroth et al., 1983, Fransz et al., 1991) This was illustrated in particular with the modelling describing the circulation of biogeochemical fluxes in the coastal zone. Modelling of carbon, nitrogen and phosphorus cycles in the sea-land interaction zone is a “prerequisite for the arising problems and targets of LOICZ programme” (Gordon et al., 1995).

Many pioneering works concerning the North Sea ecosystem modelling were written in the 90s (Baretta et al., 1995; Blackford and Radford,1995; Radch and Lenhart, 1995; Varela et al., 1995; Moll, 1997; Moll, 1998; Delhez, 1998; Hoch and Garreau, 1998). Fransz (1991) reviewed the models applied in the research of for this region. One of the key works presents ERSEM model (Baretta et al., 1995) describing the dynamics of seasonal variation of organisms on various trophic levels of food chain from bacteria to fish and the related nutrients circulation.

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The need to understand in more depth the processes of ecosystem transformation was implicated by the endangered sea environment in various water regions e.g. the Mediterranean (Levy et al., 1998; Skrilis et al., 2001). The large oxygen deficit in the Black Sea was particularly of interest for many works (Gregoire et al., 1998; Sokołowa et al., 2002; Stanew et al., 2001; Iwanow et al., 2002). Biogeochemical processes have not only been modelled in the temperate climate zone but in sub-polar regions as well (Nihoul et al, 1993; Shuert and Walsh, 1993). The last two decades were marked by the tendency to join three-dimensional hydrodynamic models with ecological ones (Nihoul, 1975; Fransz et al., 1991; Shuert and Walsh, 1993; Blackford and Radford, 1995; Baretta et al., 1995).

The Baltic Sea as a region particularly endangered by eutrophication processes was also an object of a number of research works in the area of ecosystem modelling (Suursaar and Astok, 1996; Savchuk and Wulff, 1996; Tamsalu, 1996; Fennel and Neumann, 1996; Elken, 1996; Jędrasik, 1997; Ołdakowski and Renk, 1997; Mamerfelt and Hansen, 2000; Fennel et al., 2001). There were even earlier works describing selected aspects of ecosystem and applying ecological modelling e.g. concerning nitrogen cycles and oxygen conditions in the Baltic Proper (Stigebrandt and Wulf, 1987). Savchuk and Wulff (1993) developed a model describing auto- and heterotrophs interactions in a pelagic zone. Assimilation of the satellite data from the North Atlantic and the Baltic Sea for the ecological model was made in Semowski and Woźniak (1995). A similar work concerning the bloom of phytoplankton in the Gulf of Gdańsk was presented by Semowski (1994). Model DELWAQ was also adapted for the Gulf of Gdańsk by van der Vat (1994). The same water region observation data was compared with a simulation of Sjöberg model by Witek et al. (1993). They demonstrated the impact of water temperature on the rate of primary production and zooplankton decay.

High increase of pollution contamination transported from the land to the Baltic waters, especially in the coastal zone, inspired works, which indicated the need to resolve this issue (Renk, 1990; Cyberski and Jędrasik,1991). Conferences and symposiums were held to search for solutions to such issues as pollution, effective water renewal and methods of handling sea environment (Błażejowski and Schuller, 1994; Szymelfenig, 1997). A number of monograph studies of selected water regions was carried out to investigate the problem in a comprehensive and thorough manner (Łomniewski et al., 1975; Majewski and Łazarienko, 1970; Majewski, 1980; Korzeniewski, 1993; Renk, 1997). There also appeared some works on the ecosystem modelling of coastal zone waters (the Gulf of Gdańsk in particular) (Jędrasik and Kowalewski, 1993; Ołdakowski et al., 1994). A three-dimensional hydrodynamic model TRISULA coupled with the water quality model DELWAQ served to develop works concerning the Gulf of Gdańsk with the radiation condition on the open boundary (Van der Vat, 1994; Robakiewicz and Karelse, 1994).

Considering the present state of research on ecological modelling one can notice that most classical ecological models assume a particular behaviour of each individual in a functional group (e.g. phytoplankton group) to be identical (e.g. they all react identically to sunlight). Functional groups are represented by chlorophyll or organic carbon concentration. In the beginning of the 90s a trend in modelling appeared which assumed that all individuals vary in size and age and that they can choose “their own way” (Judson, 1994). Babovic and Barreta (1996) investigated the impact of the dynamics of processes on local and seasonal interactions of three groups: phytoplankton, the omnivorous and predators.

The aim of the paper is to present a model describing the dynamics of production and destruction of organic matter (ProDeMo) The model is a further development of the previous modelling attempts (Ołdakowski et al.,1994; Ołdakowski and Renk, 1997, Kowalewski, Jędrasik, Oładkowski, 2003).

The present version of the ProDeMo model contains developed description of the biogeochemical processes. It has been an increased number of the phytoplankton groups from two (diatoms and non-diatoms) to five: spring and autumn diatoms, dinoflagellate, green algae and blue-green algae. Also nitrogen fixation by the blue-green algae from atmosphere during

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suitable conditions was taken into account. Another modification of the algorithm referred to deposition of nutrients with splitting of the process in two phases: their accumulation into active layer as well as burring in the passive one of the sediment.

Introduced changes have entailed necessity of new calibration of the ProDeMo model. Drawing a conclusion from the former calibration of the model and using the statistics measures, it has been elaborated new favourable calibration. That approach resulted in new set of coefficients to be completed the equations biogeochemical processes. The outcome obtained from comparison between model simulations and measured data as high coefficients of effectiveness gave evidence that the processes have been described accurately as well as the model has got better quality. However, the model was subjected to validation using measurements taken from coast waters in front of the mouth of the Vistula river. The obtained compliance with the observations confirmed that the model was a tool for reliable prediction of ecosystem behavior in the Southern Baltic.

The new calibrated model ProDeMo has been used to evaluations of ecological changes in the waters of the Gulf of Gdansk due to anticipated reductions of the nutrient loads from the Vistula River catchment. Expected changes were caused by three separate introduced scenarios: low, high and deep green. Due to them, prognosis for 13 years beginning from year 2002 as a basic were performed. Concentration of nutrients, values of the primary production, times and duration of the phytoplankton blooms were consequences displayed response for reduced nutrient loads. The results were investigated according to appointed indicators to designate the level of eutrophicated marine waters of the Gulf of Gdansk.

The paper includes a detailed description of the algorithm, procedure of calibration, whole application procedure and results of the model taking into account the scenarios. The results of modelling contain indexes of impact for examined scenarios e.g. budget of nutrients, residential times and eutrophication in the Gulf of Gdańsk.

1. Description of the model

1.1. ProDeMo model The mathematical model of production and destruction of organic matter (ProDeMo)

describes basic biological and chemical processes taking place in the sea environment. The ProDeMo model includes 18 state variables (Appendix I), which can be divided into several functional groups: phytoplankton, zooplankton, nutrients, detritus, dissolved oxygen and nitrogen, phosphorus and silicon compounds in sediment (Fig. 1.1). The present version of the ProDeMo is a further development of the previous towards complex marine ecosystem model (Kowalewski et al., 2003).

Phytoplankton includes autotrophic organisms divided into five groups: spring diatoms, dinoflagellate, green algae, blue-green algae and autumn diatoms. Zooplankton was restricted to a group of organisms feeding on phytoplankton. Detritus includes all dead matter (dead phytoplankton and zoological plankton and excrements), which undergo mineralization. Inorganic forms of nutrients include: nitrate nitrogen (N-NO3), ammonium nitrogen (N-NH4), phosphate phosphorus (P-PO4) and silicate silicon (Si-SiO4). Inorganic forms of carbon were not included in the ProDeMo model structure because they do not limit the growth of phytoplankton. That is also why the ProDeMo model involves only partial carbon cycle including phytoplankton, zoological plankton and detritus. Nitrogen, phosphorus and silicon cycles are closed with regard to exchange with bottom sediment and atmosphere. It is similar with the case of dissolved oxygen (O2) where mass balance equations includes processes taking place in water column, as well as the use of oxygen for mineralization of compounds included in bottom sediment and the exchange through the sea surface. Moreover, the ProDeMo model describes penetration of sunlight inside the sea depth in relation to concentration of phytoplankton and detritus.

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NUTRIENTS

N-NO3

P-PO4

Si-SiO4

N-NH4

DETRITUS CDETR

PDETR

SiDETR

NDETR

ZOOPLANKTON

Zooplankton C:N:P

PHYTOPLANKTON

Dinoflagellate

NSED PSED SiSED

DISSOLVEDOXYGEN

Water

Atmosphere

Sediment

1

2

3

4 53

6

7

8

7

10

11

12

13

1617

18

1920

21

22

23

Spring diatoms

Autumn diatoms

Blue-green algae

Green algae

Inactive layer

Active layer

14

15 15 15

Fig. 1.1. Scheme of the ProDeMo Model

The following processes are included in the ProDeMo: 1) nutrient uptake by phytoplankton, 2) phytoplankton grazing by zooplankton, 3) phytoplankton respiration, 4) phytoplankton decay, 5) sedimentation, 6) nutrients release from sediment, 7) atmospheric deposition, 8) denitrification, 9) mineralization, 10) zooplankton respiration, 11) sedimentation of phosphorus adsorbed on particles, 12) detritus sedimentation, 13) zooplankton decay 14) nitrogen fixation 15) nutrient deposition. The model also describes processes influenced the dissolved oxygen: 16) reaeration, 17) flux to atmosphere due to the over saturated conditions, 18) zooplankton respiration, 19) phytoplankton respiration, 20) assimilation, 21) mineralization, 22) nitrification, 23) denitrification

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Phytoplankton includes autotrophic organisms divided into five groups: spring diatoms, dinoflagellate, green algae, blue-green algae and autumn diatoms. Zooplankton was restricted to a group of organisms feeding on phytoplankton. Detritus includes all dead matter (dead phytoplankton and zoological plankton and excrements), which undergo mineralization. Inorganic forms of nutrients include: nitrate nitrogen (N-NO3), ammonium nitrogen (N-NH4), phosphate phosphorus (P-PO4) and silicate silicon (Si-SiO4). Inorganic forms of carbon were not included in the ProDeMo model structure because they do not limit the growth of phytoplankton. That is also why the ProDeMo model involves only partial carbon cycle including phytoplankton, zoological plankton and detritus. Nitrogen, phosphorus and silicon cycles are closed with regard to exchange with bottom sediment and atmosphere. It is similar with the case of dissolved oxygen (O2) where mass balance equations includes processes taking place in water column, as well as the use of oxygen for mineralization of compounds included in bottom sediment and the exchange through the sea surface. Moreover, the ProDeMo model describes penetration of sunlight inside the sea depth in relation to concentration of phytoplankton and detritus.

Processes affecting the change of concentration of particular state variables were given parameters in the shape of proper mathematical formulae. The result was a set of equations including about 100 coefficients whose values were established in course of calibration process (Appendix II). The full set of mathematical formulae describing all process under consideration is included in Appendix III.

1.2. Integration with hydrodynamic model The mathematical definition of biogeochemical processes taking place in the sea allows for

the coupling of ecological and hydrodynamic models in order to include processes of diffusion and advection (Vested et al., 1996). The ecological model (ProDeMo) was joined with three-dimensional hydrodynamic model of the Baltic Sea (Kowalewski,1997). The connection of the two models was made through the solution of advection-diffusion equation in the Cartesian coordinate system (x, y, z) for an arbitrary state variable (Ci):

)S(KKK)(+)(+)( ii

Zi

Hi

Hiiii C

zC

zyC

yxC

xwC

zvC

yuC

xtC

+

∂∂

∂∂

+

∂

∂∂∂

+

∂∂

∂∂

=∂∂

∂∂

∂∂

+∂

∂ (1)

Components of velocity of flow: u, v, w and coefficients of horizontal and vertical diffusion of mass KH and KZ were calculated in the hydrodynamic model. Biogeochemical processes, which cause changes of concentrations of particular state variables (Ci) were represented in the equation above as a function of sources S(Ci) The solution of the equation (1) consists in determining a local change of concentration Ci in time t∂ which is represented by the first term of the equation (1), and also allows for simultaneous inclusion of diffusion and advection processes as well as biological and chemical processes taking place in water depth.

The hydrodynamic model is based on the Blumberg and Mellor model (1987) POM (Princeton Ocean Model) and the changes necessary for its application on the area of the Baltic were connected with modification of the numerical scheme for computation of advection (Kowalewski, 1997).

The area where calculations were made included the Baltic Sea and the Danish Straits. The open boundary was located between Kattegat and Skagerrak where the exchange of waters with the North Sea took place. A radiation boundary condition was applied for averaging vertical flows with the assumption of stable sea level in Skagerrak. If the momentary value of the free surface elevation is larger than the adopted constant value, the outflow of waters from the Baltic occurs proportionally to the difference of these values. In the contrary case, that is when the sea level in Kattegatt is lower – the inflow of waters from Skagerrak takes place. On the open boundary the constant condition for salinity was applied, which means that the waters flowing from the North Sea to the Baltic have a constant vertical distribution of salinity. However, the salinity of the waters flowing from the Baltic varies in time i.e. the accepted value of salinity is

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calculated in the grid points neighbouring with the open boundary. The assumption was made for the ProDeMo model temperature and its state variables, that the horizontal gradient in the normal direction of the border equals zero, as a coastal condition on the open boundary. It means that both, the water flowing out of the calculation area and the water flowing into it, have the same temperature or value of state variable, which was calculated as a result of model simulation near the open boundary.

The model includes two areas of different spatial steps: the Baltic, of 5 NM step and the Gulf of Gdańsk of 1 NM step (Fig. 1.2). Calculations in those two areas are parallel and the exchange of information on the common boundary takes place on each time step. All the model variables calculated on the border of one area serve as a boundary condition for the other area. The algorithm which realises the connection ensures conservation mass and energy conservation.

A “sigma transformation” approach was applied in the model, making it possible to divide the vertical profile in each point of the sea, irrespectively of its depth, into equal number of layers (Fig. 1.3). It enabled better mapping of the bottom boundary layer, as well as simplified numerical calculation scheme. On the other hand, however, particular layers are not located exactly horizontally, which causes horizontal diffusion and inaccuracies in calculating horizontal pressure gradients (Haney, 1991), which may in turn result in calculation errors. In order to minimise this type of errors a technique was applied consisting in subtracting the area-averaged climatic value before calculating the horizontal gradient of a given parameter (Gary, 1973; Mellor et al., 1994). This method has relaxation character, i.e. in case no other factors occurred, the three-dimensional fields of state variables would approach its climatic distribution after a long period of simulation. A division into 18 layers of unequal thickness was made. In order to better map the surface and bottom boundary layer, the layers of smaller thickness were adopted.

P140

P39P5 P63 Baltic Sea

KNP

P1

P101P110

ZN2Vistula

Gulf of Gdańsk

Gdańsk

Fig. 1.2. Modelled areas (the Baltic and the Gulf of Gdańsk ) with marked observation stations

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Fig.1.3

1.3. DMo

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The(heightbalancedata anof the amodel adoptedOnce tvariablassimil

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H

δ = 0

δ =-1

. Division of depth (H) into layers in sigma transformation

ata used for model simulations del simulations were carried out for the years 1994–1996 and 1998–2000. 125 rivers into the Baltic Sea were considered. For the Vistula River daily observed values of ge and temperature were considered as well as the measurements of the concentrations of , ammonia, phosphorus, total nitrogen, total phosphorus and dissolved oxygen made week with daily values coming from interpolation. For the other rivers the discharge and ature of water for each day of the year were calculated from trigonometric series ing seasonal variation of river outflow established on the basis of the data gathered for ears (Cyberski,1997). Nutrient concentrations and dissolved oxygen were assumed to be

on the basis of available data (Stalnacke, 1996). The influx of nitrogen and phosphorus unds from the atmosphere was assumed from Falkowska (1985). solar energy input were calculated for each time step on the basis of astronomical data of the sun) and meteorological conditions (Krężel, 1997). The other components of heat on the sea surface were given parameters (Jędrasik, 1997) on the basis of meteorological d simulated temperature of the sea surface. Meteorological data: wind field, temperature ir, atmospheric pressure and vapour pressure came form a mezoscale operational weather UMPL (Herman-Iżycki et al., 2002). The initial conditions for hydrodynamic fields were on the basis of climate temperature distribution and salinity of the Baltic Sea waters.

he model was started, the changes of temperature and salinity were shaped as a result of es function during weather conditions and water inflows exclusively without any ation of hydrological data being made.

ethodology of research

alibration of the model mer calibration of the ProDeMo model (Kowalewski, Jędrasik, Ołdakowski, 2002) d the set of complementary coefficients to equations describing biogeochemical es at the southern Baltic with particular stress on the Gulf of Gdansk environment. The was based on a comparative analyses of sequential model results as well as analyses of eness of state variables. Another advantage of that calibration was using statistic es for evaluation of effectiveness modelled simulation in comparison with the ements. However, that approach was found as time-consuming. ent development of biogeochemical processes description caused essential changes of the algorithm. There were as following: extension number of phytoplankton groups to five, ng nitrogen fixation process, splitting of nutrients deposition on two phases: their lation into active layer and burring in the deeper passive one. Due to the changes in the m, the necessity of new calibration of the model ProDeMo was found.

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2.1.1. Assumptions for the calibration Based on the experience, new assumptions for the calibration have been made. Assessment of the model quality ought to be based on statistical measures, particularly on the

effectiveness coefficient evaluated between observed and modelled values of state variables (Appendix IV). The basic compared quantities were the modelled and observed values. The differences between them were defined as a model error, which has risen to the square became the mean quadratic error. To investigate what degree the modelled values were underestimated or overestimated in relation to the observed ones, difference of averages called absolute bias were calculated. The correlation coefficient as a product of calculated and observed standard quantities as well as the standard deviation of the differences between observed and modelled values were evaluated. Relationship between correlation coefficient and biases contained in the mean quadratic error, allowed to deduce the coefficient of effectiveness, which was assumed as a basic one for optimization of model calibration. Another important statistical measure was the special coefficient of correlation which was a result of the relation between the correlation coefficient and a total quadratic error. This coefficient was assumed for estimation of the model’s quality. These formulas were taken as an algorithm in calibrating database for judgment of the simulations during calibration’s processes.

The assumptions included comparison of sequential simulations to basic one. All of them referred to the same set of measured data. Simulations in the next runs of the model ought to be affected by changes of calibrating coefficients.

Distinction of marine aquatories was another assumption during investigation of the simulations. There were three areas: coastal, open boundary of the Gulf of Gdansk and the southern Baltic that have been taken into account. Stations: ZN2, NP, K and P101 which were located in front of the mouth of the Vistula river belonged to the coastal area. The open boundary waters contained P1 and P110 stations, the others: P5, P39, P63 and P140 were located at the third area.

Analyses of effectiveness were also made in vertical direction dividing waters into three layers: surface (0 – 30 m), intermediate (30 – 70 m) and bottom ones (beneath 70 m). Calibration’s processes need to be based on time stages - three and nine years ones – using different horizontal resolutions for the Baltic and the Gulf of Gdansk. The first period (1994 - 1996) and the second one (1994 – 2002) referred to the model of the whole Baltic. The third period (1994 – 1996) concerned both areas with their resolutions.

2.1.2. Calibration’s description The interactive database in the computer program access was formulated due to mentioned

assumptions. It referred to both areas, the Baltic and the Gulf of Gdansk, for period between 1994 – 2002. The database contained of measured data and modelled simulations. The effectiveness of the new simulation was analysed and evaluated for three groups of state variables: nutrients (NO3, NH4, PO4, SiO4), total forms of nitrogen and phosphorus (NTOT, PTOT) as well as for oxygen dissolved (O2) (Tab. 2.1).

Table 2.1. Coefficients of effectiveness for nutrients (EB), total forms of N,P (ETOT) and oxygen (EO2) for basic and final model

effectiveness Basic Final ChangeEB 0.37 0.42 0.05

ETOT 0.20 0.31 0.10 EO2

0.74 0.76 0.02 The effectiveness was also estimated for each state variables separately as well as for

temperature T and salinity S (Tab. 2.2).

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Table 2.2. Coefficients of effectiveness of state variables for basic and final model

Parameter Basic Final ChangeNH4 0.29 0.32 0.03 NO3 0.53 0.52 -0.01

NTOT 0.00 0.05 0.05 O2 0.74 0.76 0.02

PO4 0.46 0.58 0.12 PTOT 0.41 0.57 0.16

S 0.82 0.79 -0.03 SiO4 0.21 0.28 0.07

T 0.91 0.92 0.00

The following step was the research of effectiveness in layers. It was compared between the basic model and the present one. It was observed clearly which variables were simulated better or worse (Fig. 2.1). The effectiveness coefficients for compared the basic and present models were illustrated on the left panel and differences between them on the right one.

Some additional analyses have been undertaken to change the effectiveness coefficient for new simulation. The bias were considered for state variables to evaluate whether they were underestimated or overestimated in relation to the observed ones. The simulation was compared to observations at the chosen depth of a particular station. The next steps were following: the observation of the simulated sequences of five groups of phytoplankton blooms, primary production, phyto- and zooplankton sedimentation as well as detritus. Then both the rate of deposition and the structure of sediments, the results of fixation and nitrification processes have been analysed. Due to this analyses it was indicated which coefficients ought to be modified before next simulation. Each simulation provided arguments whether the progress appeared comparing to the basic model. The necessity of introducing the new basic model has occurred to obtain better results of calibration.

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

PO4 Ptot SiO4 O2 T S NO3 Ntot NH4

layer IIBASICPRESENT

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


layer II

Fig. 2.1. Coefficients of effectiveness for state variables at layer II in 1994 - 2002

2.1.3. Stages of the calibration process The first stage of calibration referred to the whole Baltic with simulations for 1994 – 1996.

Obtained coefficients presented changes in phytoplankton, nutrients and oxygen. Decreasing of maximum temperature of phytoplankton growth (Tmax) for dinoflagellates improved the simulation. For blue green algae the optimum and minimum temperatures (Topt Tmin) as well as sedimentation rate (Vs) were decreased. However, optimum light intensity (Is) was increased. The maximum temperature has been decreased and optimum light intensity was increased for autumn diatoms. Their phytoplankton mortality rate (L) slightly increased. For green algae optimum light intensity was increased. The nitrification coefficient (KnN) has been increased for nitrogen. For phosphorus the phosphorus mineralization rate in water (KmP) and sediments (KmPS) were increased but the silicon mineralization rate (KmSi) was decreased. The parameter

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for oxygen flux in case of over saturation conditions (BDO) was increased what implied for decreasing of the reaeration coefficient (BDOW).

In the second stage of calibration the simulations were extended from three to nine years (1994 – 2002) and still referred to the whole Baltic area. Sequential changes of coefficients referred to the phytoplankton contained increasing of the sedimentation rate for both the spring diatoms and the green algae as well as the optimum light intensity for autumn diatoms. Considering a slow growth of the blue green algae, the parameter of food availability (Paval) has been increased. The phosphorus and silicon mineralization rate were lowered in the water but has been risen in the sediments.

The third stage comprised both the Baltic and the Gulf of Gdansk for period of three years (1994-1996). Despite the differences in resolutions of numerical grids the same coefficients were used for both areas. Except for zooplankton coefficients the changes have been made in each group of remaining ones. The sedimentation rate for the spring diatoms has been decreased. For blue green algae the optimum and minimum temperatures as well as the parameter of food availability were decreased. The optimum light intensity rose for dinoflagellates and blue green algae. Oxygen parameter for carbon mineralization rate was decreased while the nitrification coefficient increased. Quite a number of changes have been registered for phosphorus e.g. the phosphorus mineralization rate in water and sediments also fraction of phosphorus adsorbed on inorganic particles have been lowered. The parameter for oxygen flux in case of over saturation conditions was decreased, too. Oxygen to carbon ratio during photosynthesis (aOC) grew up.

On account of long computing time the forth stage of calibration (1994 – 2002) including both areas, it was only initiated. The phytoplankton calibration coefficients were identical as at the previous stage. The only differences referred to values for sedimentation rate of dinoflagellates as well as silicon mineralization rate for the autumn diatoms. Moreover, the detritus sedimentation rate (VsDE) was decreased but the nitrogen mineralization rate in sediments (KmNS) rose.

There were adequate numbers of simulations for each particular calibration stage: 42 (first stage - I), 11 (second stage - II), 4 (third stage – III) 1 (forth stage - IV). Increasing or decreasing of three effectiveness coefficients EB (nutrients), EC (total forms of N,P), EO2 (oxygen) was a result of its comparison at the beginning and the end of each calibration stage (Tab. 2.3). A significant improvement for EC, EO2 and a slight one occurred during the first stage. The second widen calibration stage effectiveness for oxygen was constant, little improved for total forms but slightly decreased for nutrients. The calibration performed for both areas with different resolutions of numerical grids, caused lower effectiveness. However, its little improvement appeared for oxygen and total forms. Due to this calibration obtained a new set of complementary coefficients (Appendix II) to equations describing biogeochemical processes at the southern Baltic with particular stress on the Gulf of Gdansk environment.

Table 2.3. Coefficients of effectiveness for stages (I – IV) of the model’s calibration

I II III IV Effectiveness Basic Final Basic Final Basic Final Basic Final EB 0.37 0.38 0.38 0.36 0.28 0.27 0.28 0.25 EC 0.20 0.45 0.45 0.48 0.18 0.15 0.18 0.35 EO2 0.74 0.79 0.79 0.79 0.68 0.74 0.68 0.76

Most often published scientific literature presents similar investigations limited to one or few

stations. This calibration was based on all measurements at the available monitoring stations during period 1994 – 2002. Due to such a number of measurements the results of calibrations coefficients are statistically essential. They contribute to the increase of the model’s simulations quality. This kind of calibration is an important procedural step in ecological modelling and renders the model as a reliable scientific research tool.

12

3. Comparison of the simulations versus measurements

Here are the results after calibration process to define the relationship between observations and simulations of the selected variables: concentrations of nitrate nitrogen [N-NO3], ammonium nitrogen [N-NH4], total nitrogen [N-Tot], phosphate phosphorus [P-PO4], total phosphorus [P-Tot], silicate silicon [Si-SiO4], dissolved oxygen [O2], temperature [T] and salinity [S] of water in the southern part of the Baltic Sea mainly at the Gulf of Gdansk. The modelled values were compared with those measured on standard levels of depth in selected observation stations.

3.1. Vertical distribution of variables in seasonal formulation Vertical distribution of selected calculated and measured parameters was analysed on the

example of station P1 for two seasons winter and summer in 2000 (Fig. 3.1 a, b). The modelled values of the vertical distribution both nitrate nitrogen and ammonium nitrogen were overstated. Phosphate and total phosphorus simulations down to 70 m (halocline) were described well and those below slightly underrated (Fig. 3.1a). Silicate silicon values modelling for the winter period showed convergence with the observations down to 80 meters but they were underrated in the bottom layers. The best described distribution of dissolved oxygen was to the halocline depth – 70 m. Beneath measured values indicated for its budget deficit in opposite to model (Fig. 3.1a). The weak permanent thermocline was showed more clearly by measured winter profiles of the water temperature and salinity than model simulation (Fig. 3.1a).

N-NO3 [g m -3]

Dep

th [m

]

0.00 0.05 0.10 0.15

-100

-80

-60

-40

-20

0OBSMOD

15.02.2000

N-NH4 [g m -3]

-0.00 0.03 0.06 0.09

-100

-80

-60

-40

-20

0OBSMOD

15.02.2000

N-NTOT [g m -3]

0.00 0.10 0.20 0.30 0.40

-100

-80

-60

-40

-20

0OBSMOD

15.02.2000

P-PO4 [g m -3]

Dep

th [m

]

0.00 0.05 0.10 0.15

-100

-80

-60

-40

-20

-0OBSMOD

15.02.2000

P-PTOT [g m -3]

0.00 0.05 0.10 0.15

-100

-80

-60

-40

-20

0OBSMOD

15.02.2000

Si-SiO4 [g m -3]

0.00 0.50 1.00 1.50

-100

-80

-60

-40

-20

-0OBSMOD

15.02.2000

O-O2 [g m -3]

Dep

th [m

]

-0.40 3.00 6.40 9.80 13.20

-100

-80

-60

-40

-20

-0OBSMOD

15.02.2000

T [oC] 0.00 2.00 4.00 6.00

-100

-80

-60

-40

-20

-0OBSMOD

15.02.2000

S [PSU]

0.00 4.00 8.00 12.00

-100

-80

-60

-40

-20

-0OBSMOD

15.02.2000

Fig. 3.1a. Winter variability in 2000 of vertical distributions of the observed (OBS) and

modelled (MOD) chemical and physical parameters at the Gdańsk Deep, station P1

13

In surface layer for summer the modeled nitrate concentrations were in accordance with the measurements. The summer period observations indicated, however, that model simulations indicated much shallower nitrate depletion than the observations would show. Their full depletion down to 60 meters while the model simulations only down to 20 meters (Fig. 3.1b). The calculated distribution of ammonium nitrogen concentration in particular season of 2000 was in conformity with the measured values. The phosphate phosphorus concentrations reached the values approaching those measured during the summer in the layer to 70 meters. Comparing vertical distribution of total forms of nitrogen to phosphorus has been noticed much favourable in the water column for phosphorous. It was similar with silicate silicon and dissolved oxygen. In the bottom layer below halocline the calculated values of concentrations of silicates and phosphates were underrated, and concentration of oxygen was overstated in relation to the observed ones. Vertical distributions of salinity demonstrated better consistence with observations than water temperature (Fig. 3.1b).

N-NO3 [g m -3]

Dep

th [m

]

0.00 0.05 0.10 0.15

-100

-80

-60

-40

-20

0OBSMOD

17.08.2000

N-NH4 [g m -3]

0.00 0.03 0.06 0.09 0.12

-100

-80

-60

-40

-20

0OBSMOD

17.08.2000

N-NTOT [g m -3]

0.00 0.10 0.20 0.30 0.40

-100

-80

-60

-40

-20

0OBSMOD

17.08.2000

P-PO4 [g m -3]

Dep

th [m

]

0.00 0.05 0.10 0.15 0.20

-100

-80

-60

-40

-20

-0OBSMOD

17.08.2000

P-PTOT [g m -3]

0.00 0.07 0.14 0.21 0.28

-100

-80

-60

-40

-20

-0OBSMOD

17.08.2000

Si-SiO4 [g m -3]

0.00 0.50 1.00 1.50 2.00 2.50

-100

-80

-60

-40

-20

-0OBSMOD

17.08.2000

O-O2 [g m -3]

Dep

th [m

]

-3.00 0.00

3.00 6.00

9.00 12.00

-100

-80

-60

-40

-20

-0OBSMOD

17.08.2000

T [oC] 0.00 5.00 10.00 15.00 20.00

-100

-80

-60

-40

-20

-0OBSMOD

17.08.2000

S [PSU]

0.00 4.00 8.00 12.00

-100

-80

-60

-40

-20

-0OBSMOD

17.08.2000

Fig. 3.1b. Summer variability in 2000 of vertical distributions of the observed (OBS) and modelled (MOD) chemical and physical parameters at the Gdańsk Deep, station P1

Apart from vertical variability, surface runs of parameters were analyzed. Modeled and measured surface values of state variables have been compared at mentioned stations as well as the bottom one (z = 100 m) at the station P1. The best correlations between simulations and observations at the surface station P1 for temperature (r =0.97), oxygen (r = 0.85) phosphates (r = 0.76) and nitrates (r = 0.66) were obtained. In contrary ammonium and silicon were modeled inadequately (r = -0.06 and r = 0.15). Highest correlation of coefficients were received as follows: nitrates (r = 0.68), ammonium (0.53), phosphates (r = 0.0.76) silicon (r = 0.21), oxygen

14

(r = 0.85) temperature (r = 0.98) and salinity (r = 0.63) adequately at stations K, ZN2, P1, ZN2, P1 and NP (Fig. 3.2 a – d). The parameter which has been best described by the model up till now is the sea water temperature. The values of the ammonium and silicon differentiated between the stations P1 and ZN2 (at the 50 km distance) by one order (Fig. 3.2a and c). It was observed similar relationship for total nitrogen and phosphates. The salinity was the most stable parameter at the station P1 and very highly changeable at the ZN2 (because of the Vistula river influence).

In the Gdansk Deep at station P1 the analysis of parameter fluctuation was made at the bottom on 100 meters. Correlation for each variables fell regularly e.g., for temperature from r = 0.98 at the surface to r = 0.19 at the bottom (Fig. 3.3). Observations showed the deficit of dissolved oxygen while simulations do not describe this phenomenon. Despite of that, the oxygen was the best modeled parameter at the bottom (r = 0.35). The next important feature was underestimating of values especially in the deeper layers, which is confirmed by vertical distributions (Fig. 3.1 a, b).

Comparison of variables at stations P1, NP, ZN2 and K during 1994–2002, demonstrated recurrence of annual cycles without any definite trend (Fig. 3.2a-d). This testifies good functioning of the model. Each of the researched stations showed a regularity of the summer depletion of mineral forms of nitrogen and phosphorus. In this period silicate silicon exhibited a lowered level of concentration. Variability of oxygen, which was in counter phase to water temperature showed characteristic cycle. The rise of temperature corresponded to lowered values of dissolved oxygen concentrations. It should be emphasized that the values modeled for the period 1994–2002 departed from the measurements reasonably.

NO

3 [g

m-3

]

0.00

0.10

0.20

0.30

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NO3_OBS NO3_MOD

P1 z = 0m r = 0.662

NH

4 [g

m-3

]

0.00

0.02

0.04

0.06

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NH4_OBSNH4_MOD

P1 z = 0m r = -0.061

NTO

T [g

m-3

]

0.00

0.20

0.40

0.60

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NTOT_OBSNTOT_MOD

P1 z = 0m r = 0.581

Fig. 3.2a The run of surface variability of the observed (OBS) and modelled (MOD) chemical and physical parameters: nitrates NO3, ammonia NH4, total nitrogen (NTOT), phosphates PO4, total phosphorus (PTOT), silicates SiO4, dissolved oxygen O2, water temperature Tw on the Gdańsk Deep (station P1, depth – 0 m) in 1994–2002

15

PO4

[gm

-3]

0.00

0.01

0.02

0.03

0.04

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PO4_OBSPO4_MOD

P1 z = 0m r = 0.759

P TOT

[gm

-3]

0.00

0.02

0.04

0.06

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PTOT_OBSPTOT_MOD

P1 z = 0m r = 0.245

SiO

4 [g

m-3

]

0.00

0.20

0.40

0.60

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

SiO4_OBSSiO4_MOD

P1 z = 0m r = 0.143

O2

[gm

-3]

8.00

12.00

16.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

O2_OBSO2_MOD

P1 z = 0m r = 0.852

T [o C

]

0.00

10.00

20.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Tw_OBSTw_MOD

P1 z = 0m r =0.979

S [g

m-3

]

5.00

6.00

7.00

8.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

S_OBSS_MOD

P1 z = 0m r = 0.527

Fig. 3.2a (continuation)

16

NO

3 [g

m-3

]

0.00

0.50

1.00

1.50

2.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NO3_OBS NO3_MOD

NP z = 0m r = 0.374

NH

4 [g

m-3

]

0.00

0.05

0.10

0.15

0.20

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NH4_OBSNH4_MOD

NP z = 0m r = 0.372

NTO

T [gm

-3]

0.00

1.00

2.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NTOT_OBSNTOT_MOD

NP z = 0m r = 0.545

PO4

[gm

-3]

0.00

0.05

0.10

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PO4_OBSPO4_MOD

NP z = 0m r = 0.159

P TOT

[gm

-3]

0.00

0.04

0.08

0.12

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PTOT_OBSPTOT_MOD

NP z = 0m r = 0.475

SiO

4 [g

m-3

]

0.00

0.30

0.60

0.90

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

SiO4_OBSSiOP4_MOD

NP z = 0m r = 0.204

Fig. 3.2b The run of surface variability of the observed (OBS) and modelled (MOD) chemical and physical parameters: nitrates NO3, ammonia NH4, total nitrogen (NTOT), phosphates PO4, total phosphorus (PTOT), silicates SiO4, dissolved oxygen O2, water temperature Tw (station NP, depth 0 m) in 1994–2002

17

O2

[gm

-3]

8.00

12.00

16.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

O2_OBSO2_MOD

NP z = 0m r = 0.825

NH

4 [g

m-3

]

4.00

6.00

8.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

S_OBSS_MOD

NP z = 0m r = 0.627

Fig. 3.2b (continuation)

NO

3 [g

m-3

]

0.00

0.70

1.40

2.10

2.80

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NO3_OBS NO3_MOD

ZN2 z = 0m r = 0.662

NH

4 [g

m-3

]

0.00

0.15

0.30

0.45

0.60

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NH4_OBSNH4_MOD

ZN2 z = 0m r = 0.525

NTO

T [g

m-3

]

0.00

1.00

2.00

3.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NTOT_OBSNTOT_MOD

ZN2 z = 0m r = 0.427

PO4

[gm

-3]

0.00

0.05

0.10

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PO4_OBSPO4_MOD

ZN2 z = 0m r = 0.344

Fig. 3.2c The run of surface variability of the observed (OBS) and modelled (MOD) chemical and physical parameters: nitrates NO3, ammonia NH4, total nitrogen (NTOT), phosphates PO4, total phosphorus (PTOT), silicates SiO4, dissolved oxygen O2, water temperature Tw (station ZN2, depth 0 m) in 1994–2002

18

P TOT

[gm

-3]

0.00

0.05

0.10

0.15

0.20

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PTOT_OBSPTOT_MOD

ZN2 z = 0m r = 0.115

SiO

4 [g

m-3

]

0.00

2.00

4.00

6.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

SiO4_OBSSi4_MOD

ZN2 z = 0m r = 0.211

O2

[gm

-3]

8.00

12.00

16.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

O2_OBSO2_MOD

ZN2 z = 0m r = 0.681

T [o C

]

0.00

10.00

20.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Tw_OBSTw_MOD

ZN2 z = 0m r =0.966

S [g

m-3

]

0.00

2.00

4.00

6.00

8.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

S_OBSS_MOD

ZN2 z = 0m r = 0.358

Fig. 3.2c (continuation)

19

NO

3 [g

m-3

]

0.00

0.50

1.00

1.50

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NO3_OBS NO3_MOD

K z = 0m r = 0.679

NH

4 [g

m-3

]

0.00

0.04

0.08

0.12

0.16

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NH4_OBSNH4_MOD

K z = 0m r = 0.325

NTO

T [g

m-3

]

0.00

0.50

1.00

1.50

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NTOT_OBSNTOT_MOD

K z = 0m r = 0.293

PO4

[gm

-3]

0.00

0.02

0.04

0.06

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PO4_OBSPO4_MOD

K z = 0m r = 0.659

P TOT

[gm

-3]

0.00

0.04

0.08

0.12

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PTOT_OBSPTOT_MOD

K z = 0m r = 0.387

Fig. 3.2d The run of surface variability of the observed (OBS) and modelled (MOD) chemical and physical parameters: nitrates NO3, ammonia NH4, total nitrogen (NTOT), phosphates PO4, total phosphorus (PTOT), silicates SiO4, dissolved oxygen O2, water temperature Tw (station ZN2, depth 0 m) in 1994–2002

20

SiO

4 [g

m-3

]

0.00

0.50

1.00

1.50

2.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

SiO4_OBSSi4_MOD

K z = 0m r = 0.185

O2

[gm

-3]

10.00

15.00

20.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

O2_OBSO2_MOD

K z = 0m r = 0.666

T [o C

]

0.00

10.00

20.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Tw_OBSTw_MOD

K z = 0m r =0.972

S [g

m-3

]

0.00

2.00

4.00

6.00

8.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

S_OBSS_MOD

K z = 0m r = 0.331

Fig. 3.2d (continuation)

21

NO

3 [g

m-3

]

0.00

0.10

0.20

0.30

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NO3_OBS NO3_MOD

P1 z = 100m r = -0.175

NH

4 [g

m-3

]

0.00

0.10

0.20

0.30

0.40

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NH4_OBSNH4_MOD

P1 z = 100m r = 0.259

NTO

T [g

m-3

]

0.00

0.20

0.40

0.60

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

NTOT_OBSNTOT_MOD

P1 z = 100m r = 0.574

PO4

[gm

-3]

0.00

0.10

0.20

0.30

1995 1996 1997 1998 1999 2000 2001 2002 2003

PO4_OBSPO4_MOD

P1 z = 100m r = 0.259

P TOT

[gm

-3]

0.00

0.10

0.20

0.30

0.40

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

PTOT_OBSPTOT_MOD

P1 z = 100m r = 0.337

Fig. 3.3 The run of surface variability of the observed (OBS) and modelled (MOD) chemical and physical parameters: nitrates NO3, ammonia NH4, total nitrogen (NTOT), phosphates PO4, total phosphorus (PTOT), silicates SiO4, dissolved oxygen O2, water temperature Tw on the Gdańsk Deep (station P1, depth – 100 m) in 1994–2002

22

SiO

4 [g

m-3

]

0.00

1.00

2.00

3.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

SiO4_OBSSiO4_MOD

P1 z = 100m r = 0.264

O2

[gm

-3]

-4.00 0.00 4.00 8.00 12.00 16.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

O2_OBSO2_MOD

P1 z = 100m r = 0.354

T w [O

C]

0.00

4.00

8.00

12.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Tw_OBSTw_MOD

P1 z = 100m r = 0.188

O2

[gm

-3]

8.00

12.00

16.00

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

S_OBSS_MOD

P1 z = 100m r = 0.273

Fig. 3.3 (continuation)

To evaluate the simulation quality of the state variables the correlation and effectiveness coefficients as well as the bias were applied. The simulations from all stations were subjected to these measures. The parameter which has been best described in the whole profiles was the water temperature (Tab. 3.1), similarly as at the surface. The oxygen was another parameter that obtained high correlation coefficient (0.72 – 0.91). Modeled and measured values of phosphates and ammonium have agreed quite well at the station P1 and nitrates at the station K. Computed values of temperature, oxygen and salinity were decreased during modeling but remaining variables increased, extremely – nitrates. The physical parameters were simulated the most effectively. Among nutrients phosphorus compounds were modeled twice better than nitrogen ones. Much effort is needed to be done for modeling of ammonia. The correlation coefficients were referred to vertical and horizontal structure of the aquatoriums. The best correlation coefficients were received for variables at the intermediate layer but at the surface one appeared good effectiveness (Tab. 3.2). Nitrogen compounds were the most increased parameters at all layers. Taking into account simulations localized at divide areas, the excellent correlation coefficients have been got at the second area (area II) – waters at the open boundary the Gulf of Gdansk. The highest effectiveness of simulations was obtained at this area too (Tab. 3.3). The

23

simulations were mostly increased at the near shore area (area I) in front of the mouth of the Vistula river.

Table 3.1 Coefficients of correlation, bias and effectiveness for state variables at the stations of the Gulf of Gdansk in 1994 – 2002

Station NH4 NO3 NTOT O2 PO4 PTOT S SiO4 T correlation coefficient

P1 0.68 0.51 0.62 0.91 0.84 0.83 0.92 0.87 0.94 ZN2 0.45 0.59 0.44 0.72 0.36 0.44 0.46 0.22 0.95

K 0.39 0.64 0.66 0.90 0.81 0.81 0.87 0.59 0.96 All ZG 0.40 0.63 0.64 0.88 0.74 0.70 0.90 0.59 0.96

bias P1 1.28 0.65 1.04 1.03 1.02 1.01 0.91 0.79 0.99

ZN2 1.54 1.73 1.47 0.98 1.52 1.25 0.9 0.51 0.98 K 1.01 1.65 1.17 1.01 1.16 1.07 0.91 0.74 0.99

All ZG 1.05 1.46 1.06 0.99 1.09 0.97 0.92 0.73 0.98 effectiveness

P1 0.13 0.34 0.37 0.75 0.71 0.69 0.60 0.64 0.89 ZN2 -0.14 0.02 -0.28 0.49 -0.34 -0.01 0.06 -0.10 0.96

K 0.04 0.08 0.15 0.75 0.64 0.65 0.58 0.26 0.92 All ZG 0.04 0.16 0.20 0.76 0.55 0.49 0.70 0.24 0.91

Table 3.2 Coefficients of correlation, biases and effectiveness for state variables at the layers of the Gulf of Gdansk and southern Baltic in 1994 – 2002

Layer NH4 NO3 NTOT O2 PO4 PTOT S SiO4 T

correlation coefficient 1 0.51 0.63 0.64 0.80 0.54 0.65 0.58 0.32 0.97 2 -0.08 0.64 0.54 0.76 0.43 0.38 0.85 0.32 0.81 3 0.37 0.18 0.58 0.72 0.56 0.52 0.93 0.59 0.55

bias 1 1.3 1.59 1.07 0.97 1.56 1.27 0.94 0.76 0.76 2 1.21 1.43 1.05 0.96 1.22 1.13 0.95 0.84 1.02 3 0.62 1.08 1.03 1.28 0.80 0.73 0.86 0.64 1.05

effectiveness 1 -0.06 0.15 0.16 0.61 -0.09 0.24 0.03 0.05 0.94 2 -0.52 0.19 0.26 0.52 0.05 0.08 0.64 -0.04 0.65 3 0.05 -0.17 0.33 0.41 0.16 0.05 0.46 -0.23 0.05

Table 3.3 Coefficients of correlation, biases and effectiveness for state variables at the areas of the Gulf of Gdansk (area 1 and 2) and the southern Baltic (area 3) in 1994 – 2002

Area NH4 NO3 NTOT O2 PO4 PTOT S SiO4 T correlation coefficient

1 0.47 0.58 0.44 0.74 0.43 0.42 0.50 0.28 0.97 2 0.49 0.67 0.60 0.91 0.85 0.83 0.92 0.88 0.94 3 0.28 0.75 0.49 0.89 0.68 0.70 0.95 0.74 0.95

bias 1 1.37 1.66 1.35 0.97 1.53 1.21 0.93 0.62 0.98 2 0.67 1.25 1.04 1.03 1.04 1.03 0.92 0.80 0.99 3 1.25 1.19 0.92 0.97 0.94 0.85 0.94 0.74 0.97

effectiveness 1 -0.12 0.07 -0.21 0.53 -0.18 -0.03 0.03 -0.02 0.93 2 0.14 0.34 0.34 0.76 0.71 0.69 0.61 0.65 0.89 3 -0.12 0.52 0.17 0.78 0.36 0.28 0.78 0.25 0.90

24

4. Statistic characteristics of the model quality

Defined correlations demonstrated the strength of relationships between the modelled and the measured values, irrespective of whether the modelled simulations were overstated or underrated in relation to the measured ones. Absolute bias testifies to the relationship of the modelled values and observations (Fig. 5.1). The modelled simulations were overstated for nitrogen compounds at most stations, while underrated for phosphorus compounds. Contents of silicate silicon were definitely underrated at all station. Dissolved oxygen simulations were slightly overstated in the Gdańsk Deep (station P1) and little underrated than observed ones at the others (station: K, ZN2, NP). Modelled temperature values diverged the least from the observed ones, while salinity simulations were relatively little underrated in relation to the measured ones. In comparison with simulations nitrate nitrogen only at the shallow station K was underestimated and at the others overstated. Ammonium and total nitrogen concentration measurements were underrated at the stations P1 and K (like at the all ones together), while at the others located near the mouth of the Vistula River (ZN2 and NP) were overstated (Fig. 4.1).

decr

ease

d

va

lues

i

ncre

ased

-0.5

0.0

0.5

1.0

1.5

2.0


P1

decr

ease

d

va

lues

i

ncre

ased

-0.5

0.0

0.5

1.0

1.5

2.0


P101

decr

ease

d

va

lues

i

ncre

ased

-0.5

0.0

0.5

1.0

1.5

2.0


NP

decr

ease

d

va

lues

i

ncre

ased

-0.5

0.0

0.5

1.0

1.5

2.0


ZN2

decr

ease

d

va

lues

i

ncre

ased

-0.5

0.0

0.5

1.0

1.5

2.0


K

decr

ease

d

va

lues

i

ncre

ased

-0.5

0.0

0.5

1.0

1.5

2.0


all stationsat the Gulf of Gdansk

Fig. 4.1 Absolute bias of the model calculated for state variables of ProDeMo model at stations P1 P101 NP ZN2 K and all stations for 1994–2002

The smallest range of divergence between modeled and measured variables of state appeared at the intermediary layer. Simulation of the temperature, salinity and dissolved oxygen were

25

very close to observations there nearly in the every layer and areas. Modelled silicates silicon were underestimated all over the places but phosphates only in the bottom layer whereas nitrogen and phosphorus compounds were overestimated, particularly phosphates were overstated more than 50 % at the surface layer as well as at the area in front of the mouth of the Vistula river (Fig. 4.2).

decr

ease

d

va

lues

i

ncre

ased

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00


layer I

a)

decr

ease

d

va

lues

i

ncre

ased

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00


area I

b)

decr

ease

d

va

lues

i

ncre

ased

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00


layer II

c)

decr

ease

d

va

lues

i

ncre

ased

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00


area II

d)

decr

ease

d

va

lues

i

ncre

ased

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00


layer III

e)

decr

ease

d

va

lues

i

ncre

ased

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00


area III

f)

Fig. 4.2 Absolute bias of the model calculated for state variables of ProDeMo model at the surface intermediate and bottom layers as well as areas placed at the Gulf of Gdansk in 1994–2002

Correlation coefficients combined with such supplementary criteria as conditional and unconditional bias and gave an idea of correlation effectiveness (Fig. 4.3). It means effective improvement of simulation with respect to observations. The correlation effectiveness expressed by determination coefficient which equals R2

is often an overstated value, as it reveals the strength of relationship when there is no model bias. By reducing effectiveness Nash-Sutcliff coefficient takes into account the bias and expresses real correlation of compared values. In the case of heavy bias, this effectiveness declines to zero or even reaches negative values indicating no effectiveness at all (Fig. 4.3a-f).

Effectiveness of the simulations were referred to layers and areas. There have been assigned surface, intermediate and bottom layers as well as three areas: near mouth of the Vistula river, open boundary of the Gulf of Gdansk and southern Baltic. The variables at the open part of Gulf

26

of Gdansk were simulated the most effectively. Physical parameters like temperature, salinity and oxygen dissolved have reached effectiveness coefficients in range 0.62 – 0.9. Silicon and phosphorus compounds were demonstrated with effectiveness of 0.68 – 0.71 but nitrogen ones of 0.05 – 0.47. Simulations of variable states at the southern Baltic waters have got even high (0.78 – 0.9) positive coefficients, for physical parameters. At the area close to mouth of the Vistula river obtained estimation of effectiveness for the temperature and oxygen dissolved was pretty good but for remaining parameters rather weak even for phosphates and silicon negative.

The modeled vertically structure of the state variables were differentiated. The highest values of effectiveness were gained for the temperature and oxygen but opposite for phosphates and silicates at the surface layer (Fig. 4.3a,c,e). At the intermediate layer only effectiveness for nitrogen ammonia was negative, the other values were satisfying. At the bottom layer obtained coefficients were beneath 50% of effectiveness.

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


layer I

a)

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


area I

b)

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


layer II

c)

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


area II

d)

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


layer III

e)

effe

ctiv

enes

s (E

=R2 -C

2 -B2 )

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


area III

f)

Fig. 4.3 Coefficients of effectiveness for state variables at layers: a) surface, c) intermediate, e) bottom and areas: b) near the mouth of the Vistula river, d) open boundary Gulf of Gdansk, f) Baltic southern in 1994 – 2002

With all observation stations considered, the best effectiveness was achieved for temperature, salinity and oxygen dissolved in water, which confirms good quality of the hydrodynamic model. The best simulated phosphorus and silicate compounds reached even over 65% and nitrates more than 50% effectively. The estimation of effectiveness largely declined for silicate silicon, total

27

nitrogen and nitrate nitrogen, while they were even negative for silicate silicon and ammonium nitrogen (Fig. 4.3).

Comparing simulations with observations by means of a special correlation coefficient in the function of total quadratic error a statistical analysis was also made (Fig. 5.4, 5.5). Physical parameters were excellently correlated with regard to surface layer (Fig. 5.4a). Well simulated were phosphorus, silicon and nitrogen compounds except ammonium nitrogen. Complete profiles of two stations extreme located at the Gulf of Gdansk P1 and ZN2 showed very good correlation for temperature, salinity, oxygen dissolved also nitrate and silicon at P1, good for phosphorus and nitrogen compounds at station P1, phosphorus at ZN2 as well as satisfied for silicate and nitrogen at ZN2. These results appeared as evident influence of the Vistula river plume (Fig. 5.4b).

All measurements from all stations and times were used for particular variables. The best correlated was salinity and total nitrogen, the weakest – ammonium and nitrate nitrogen (Fig. 4.4c). The parameters best simulated by the model were: salinity, water temperature and oxygen, well simulated were total phosphorus and nitrogen and phosphate phosphorus. Silicate silicon, nitrate nitrogen and ammonium nitrogen simulations clearly fall behind the others.

integral square error [Ise]

coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4Ptot

SiO4

O2TS

NO3

Ntot

NH4

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1

0.4

0.5

0.6

0.7

0.8

0.9

1.0 PO4PtotSiO4O2TSNO3NtotNH4

excellent

good

exce

llent

good

station P1

satis

fied

satisfied

a) integral square error [Ise]

coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4

Ptot

SiO4

O2 T S

NO3

Ntot

NH4

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

goodex

celle

nt

good

station ZN2

satis

fied

satisfied

b)


coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4

Ptot

SiO4

O2 TS

NO3

Ntot

NH4

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

station K

satis

fied

satisfied

c) integral square error [Ise]

coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4Ptot

SiO4

O2 TS

NO3

Ntot

NH4

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good all stations

at the Gulf of Gdansksatis

fied

satisfied

d)

Fig. 4.4 Special coefficients of correlation in the function of total quadratic error for whole profiles state variables at a) the station P1 b) station ZN2 b) station K c) all stations and terms from the period 1994-2002

Taking into account all measurements from all stations and times used for particular variables the correlation was considered for vertical (layers) and horizontal (areas) their structure. The surface layer parameters are located somewhat lower on the graph (Fig. 4.5e) than intermediary and bottom layer ones (Fig. 4.5a) thus indicating that the simulations departed more from the measured values. In this layer the best correlation between simulations and measurements was obtained by temperature, salinity and oxygen dissolved, good – total phosphorus and nitrogen but remaining parameters only satisfying.

Considering the variables spatially according to areas evaluated at waters in front of the Vistula river showed, temperature, salinity, oxygen dissolved were simulated excellently, total phosphorus quite well, remaining as satisfied (Fig. 4.5b). At the area of open part the Gulf of Gdansk most modeled variables reached the best correlation with the observations. The similar situation appeared at the intermediary layer. At the waters of the southern Baltic the simulations

28

correlated with measurements getting coefficients decreasing along the diagonal line, from the best value for salinity to the least adequately for ammonium nitrogen (Fig. 4.5d, f).


coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4

Ptot

SiO4

O2 TS

NO3

Ntot

NH4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

the surface layer for 1994-2002satis

fied

satisfied

a) integral square error [Ise]

coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4

Ptot

SiO4

O2TS

NO3

Ntot

NH4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

the area I for 1994-2002satis

fied

satisfied

b)


coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4

Ptot

SiO4

O2 TS

NO3

Ntot

NH4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

the inermediary layer for 1994-2002satis

fied

satisfied

c) integral square error [Ise]

coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4Ptot

SiO4

O2TS

NO3

Ntot

NH4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

the area II for 1994-2002satis

fied

satisfied

d)


coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4

Ptot

SiO4 O2

TS

NO3

Ntot

NH4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

the bottom layer for 1994-2002satis

fied

satisfied

e) integral square error [Ise]

coef

ficie

nt o

f cor

rela

tion

[Rs]

PO4Ptot

SiO4

O2TS

NO3

Ntot

NH4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9


excellent

good

exce

llent

good

the area III for 1994-2002satis

fied

satisfied

f)

Fig. 4.5 Special coefficients of correlation in the function of total quadratic error for state variables for all measurements at (left panel): a) surface layer c) intermediate layer e) bottom layer and (right panel) b) area in front of the Vistula river d) open boundary Gulf of Gdansk f) southern Baltic from the period 1994-2002

The statistical measures describing the quality of the model and based on mean quadratic error (correlation and bias coefficients) and total quadratic error (special correlation coefficient), confirm a very good quality of the simulations modelled for physical parameters, good for phosphate phosphorus and silicate silicon and poorer for nitrogen compounds.

5. Definition of scenarios

Three basic scenarios have been considered in the assessment. In defining of each scenario the rate of economic growth, population projections, agriculture policy as well as transport development have been taken into account. Here are the main assumptions of these scenarios: 1. Policy targets - high scenario

This scenario assumes 5-6% increase in the GDP rate in 2004-2020. In that scenario the high rate of economic growth enables realization of the National Program of Municipal Wastewater Treatment (according to Directive 91/271/EEC). There is 75% reduction of the discharged nutrient loads in Polish agglomerations above 2 000 p.e. There is expected 1% growth of the population in years 2000-2015. There will be also 20% rise in migrations balance from the cities.

29

In agriculture policy applying the Code of the Good Agriculture Practise limits uncontrolled pollution of the environment by natural fertilizers, but the use of mineral fertilizers is increasing. 2. Policy targets – low scenario

This scenario assumes lower economic growth between 2 and 4% in 2004-2020. In that scenario lower rate of economic growth does not make possible all assumptions of the National Program of Municipal Wastewater Treatment (according to Directive 91/271/EEC). Wastewater treatments which were planned to be built by 2010 will have been built by the end of 2015. The investments in 410 agglomerations for the years 2011-2015 will not be done. In agriculture policy, besides the storage of manure is not improving, but at the same time the use of mineral fertilizers is not increasing either. 3. Deep green scenario

In Deep Green scenario are accomplished all aims of the scenario Policy Targets concerning building of wastewater treatment plants. Except for this, ecological awareness of the society and the campaign against usage of the laundry detergents with phosphates causes their removal from the market. As a result of this the share of the laundry detergents without phosphates is 90%. Furthermore, it results in lower discharge of phosphates in sewage, thus the load of phosphates from wastewater treatment plants declines by 20% in comparison to Policy Targets scenario. Good Agricultural Practise is introduced and the use of mineral fertilizers is decreasing.

The detailed description of the scenarios is given in the report: Viscat, Report on the redefiniton of scenarios by Bartczak et al., 2003. These scenarios have been investigated within the Vistula River catchment area by using the MONERIS – river catchment nutrient emission model (reference…). The results of the application of the MONERIS model: the discharge of total nitrogen and total phosphorus from the Vistula River to the Gulf of Gdańsk determines the input data for the calculations of the N and P loads from the Vistula River to the Gulf of Gdańsk. The projections of loads are given in Tab. 5.1

Table 5.1 Loads of total nitrogen and total phosphorus to the Vistula River in three scenarios

Load from the Vistula River [103 tons/year] N-Tot P-Tot Scenarios

2002 2005 2010 2015 2002 2005 2010 2015 Policy targets low 114.6 111.7 104.9 104.5 5.86 4.38 3.61 3.46 Policy targets high 114.6 104.8 104.2 104.6 5.86 3.61 3.46 3.47

Deep green 114.6 104.0 104.3 103.5 5.86 3.30 3.32 3.19

The total nitrogen discharged by the Vistula River is reduced in each scenario comparing the forecasts for the year 2015 and the year 2002. Depending on the scenario the reduction of total nitrogen is equal from 8.8 % for Policy target low scenario to 9.7 % for Deep Green scenario. One can assume that there are two important conclusions: firstly, the reduction of total nitrogen in all scenarios is rather small (do not exceed 10 %) and secondly the difference in projections of discharge of total nitrogen in each scenarios are very small and can be neglected.

The reduction of total phosphorus discharge (comparison of 2015 is much larger and is equal from 40.9 % for the Policy target low scenario to 45.5 % for Deep green scenario. The difference between low and high policy targets scenarios in 2015 are very small. However; in Policy target high scenario the significant redaction of total nitrogen and total phosphorus is observed even in 2005 year, whereas in low scenario is rather gradual in 2002-2015 period.

5.1. Method of analysis In order to assess the influence of the different economic development scenarios on the

ecological state of the Gulf of Gdańsk the calibrated, verified and validated ProDeMo model has been applied. The environmental state of the Gulf of Gdańsk has been evaluated for the 2003-2015 projections. The simulations have been carried out as the continuation of the ProDeMo model calculations for the years 1994-2002. Year 2002 has been chosen as a reference year.

30

From this year three scenarios have been calculated for the 13 years each with different loads values from the Vistula River for total nitrogen and total phosphorus. Loads of total N and total P have been calculated by the Monaris model for the 2005, 2010 and 2015 years (Tab. 5.1) and they have determined the input data for the ProDeMo application in the Gulf of Gdańsk. A linear distribution has been apply in order to calculate the load values between the years with given data. For the estimation of partition of total nitrogen and total phosphorus into organic and inorganic forms the 2002 distribution pattern has been used.

All the remaining input data for the ProDeMo: meteorological conditions, atmospheric deposition, discharges and loads from the other rivers have been defined as in the 2002 year.

The forecast of the Gulf of Gdańsk has been investigated by analyses of the following parameters and processes:

• Total nitrogen and total phosphorus budget calculations • Spatial distributions of: • Total nitrogen and total phosphorus • Deposition of nitrogen and phosphorus in the sediment • N/P ratio • Phytoplankton biomass • Primary production. The results from the last year of model simulations 2010 for each scenario has been

compared with the reference year 2002. Moreover, the results of the simulations have been compared between each other.

5.2. Results

5.2.1. Budget calculations of the total nitrogen and total phosphorus for the Gulf of Gdańsk

The budget calculations for total nitrogen and total phosphorus have been done in order to study the reaction of the Gulf of Gdańsk on different loading scenario from the Vistula River (Fig. 5.1 and Fig. 5.2). The budget calculations includes: • river input (all rivers outflowing to the Gulf of Gdańsk including the Vistula Lagoon), • exchange with the open sea by the open boundary, • exchange with atmosphere (in case of nitrogen the denitrification process is included) • and exchange with sediment phase (sedimentation and release processes).

In the reference year 2002, the total river input of nitrogen and phosphorus was equal to 130.9 ·103 and 7.39 ·103 tons/year respectively. These figures also includes the discharge from the rivers outflowing to the Vistula Lagoon that creates the ecosystem itself with very limited water and mass exchange with the Gulf of Gdańsk. However, the Vistula River plays the most important role in creation of ecosystem behaviours in the Gulf of Gdańsk. The contribution from the Vistula River (Tab. 5.1) to total river input is dominant (87.5 % for nitreogen and 79.3 % for phosphorus). In the scenario calculations only reductions of loads from the Vistula River are considered in the budget calculations. All loads from other rivers are the same as in 2002 year.

The reduction of river input for the total nitrogen in three evaluated scenarios is rather small, in range of 7.4-7.8 % (Fig. 5.1). However, the reductions of phosphorus loads from rivers are much larger (from 30.5 % for Policy target low scenario to 34.7 % for Deep green scenario), thus this influence on the limiting conditions for growth of phytoplankton (Fig. 5.3). One can observe that during the reference year 2002 the nitrogen is the limiting factor, N/P ratio < 16 (Fig 5.4), whereas in the 2010 year in all scenarios the phosphorus became a limiting one (N/P ratio < 16). This means that there is more inorganic nitrogen present in the water column and the rate of exchange between open see for the 2010 (all scenario) is about 25 % higher than in 2002 reference year. However, the net exchange is almost the same for the 2002 and for 2010 year of all scenario. There is always more nitrogen being transported thought the Gulf of Gdansk toward

31

open sea than being transported to the Gulf. Comparing to the total river input, the net flux of total nitrogen towards the open sea is equal to 86.5 % for the 2002 year and 90.6 % for all scenarios.

River input

Atmosphere

Baltic Sea

Gulf of Gdańsk

Sediment

113.2

29.1

1 764

1 651

0.1 4.

5 4.6

130.9

2002 2010 LOW

River input

Atmosphere

Baltic Sea

Gulf of Gdańsk

Sediment

110

29.1

2 081

2 191

1.2 5.

7 4.6

121,4

2010 HIGH

River input

Atmosphere

Baltic Sea

Gulf of Gdańsk

Sediment

109.3

28.9

2 082

2 191

1.1 5.

8 4.6

120.7

2010 DEEP GREEN

River input

Atmosphere

Baltic Sea

Gulf of Gdańsk

Sediment

109.2

28.7

2 083

2 192

1.2 5.

8 4.6

120.7

Fig. 5.1 Total nitrogen budget calculations for the Gulf of Gdansk for the reference year 2002 and three scenarios [103 tons/year]

32

2002 Atmosphere

River input

Baltic Sea

Gulf of Gdańsk

Sediment

6.09

1.91

217.90

211.81

0.25

7.39

Atmosphere2010 LOW

River input

Baltic Sea

Gulf of Gdańsk

Sediment

6.02

1.68

218.55

212.53

0.25

5.14

Atmosphere2010 HIGH

River input

Baltic Sea

Gulf of Gdańsk

Sediment

5.88

1.65

217.62

211.74

0.25

5.00

2010 DEEP GREEN Atmosphere

River input

Baltic Sea

Gulf of Gdańsk

Sediment

5.68

1.67

216.89

211.21

0.25

4.86

Fig. 5.2 Total phosphorus budget calculations for the Gulf of Gdansk for the reference year 2002 and three scenarios [103 tons/year]

33

a)

2002 2010 LOW

2010 HIGH0

5

10

16

20

40

60

80

100

120

140

160

180

200

N:P

2010 DEEP GREEN

b)

2002 2010 LOW

2010 HIGH0

10

20

60

100

140

180

N:P

2010 DEEP GREEN

Fig. 5.3. N/P ration for the winter - mean value for February a) and summer - mean values for July b) for the standard year 2002 and three scenario (2010).

The distribution of the N/P ratio has been calculated in order to analyse the potential limiting conditions (winter conditions) and the real limiting condition under the intensive growth of phytoplankton (summer time) (Fig. 3). It has been observed that in the reference year 2002,

34

which represent recent biogeochemical conditions, the nitrogen is limiting nutrient in the large part of the Gulf of Gdańsk (N/P < 16), whereas in all scenarios in 2010 year phosphorus limits the growth of phytoplankton in whole Gulf (N/P > 16). Therefore, there is much less inorganic nitrogen during summer in reference year 2002 than in the same time of the year during the scenarios projections. The distributions of phosphorus are opposite: there is more inorganic phosphorus in 2002 than in the scenarios, when if any free phosphorus appears in the water it is immediately taken up by phytoplankton.

The content of the nitrogen and phosphorus are much larger in the Vistula Lagoon (Fig. 5.4. – 5.11) High contents of nitrogen and phosphorus are caused by rather high loads from the rivers and the fact that the Vistula River is very shallow and almost closed water body with very limited water exchange with the open sea (only narrow Pilawa Stright).

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

DIN [g m-3]

-0.2 -0.1 0 0.1 0.2 0 0.005 0.01 0.015 0.02 0.025

2010 DEEP GREEN

Fig. 5.4 Surface winter distributions (mean values for February) of inorganic nitrogen [g m-3] DIN for the for the standard year 2002 and three scenario (2010)

35

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

N-Tot [g m-3]

-0.2 -0.1 0 0.1 0.2 0 0.01 0.02 0.03

2010 DEEP GREEN

Fig. 5.5 Surface winter distributions (mean values for February) of total nitrogen [g m-3] for the for the standard year 2002 and three scenario (2010)

36

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

PO4[g m-3]

0 0.01 0.02 0.03 0 0.0005 0.001 0.0015

2010 DEEP GREEN

Fig. 5.6 Surface winter distributions (mean values for February) of phosphates phosphorus [g m-3] for the for the standard year 2002 and three scenario (2010)

37

2002 2010 LOW

2010 HIGH

2010 LOW - DG2002 - 2010 HIGH

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

PTOT [g m-3]

0.00 0.01 0.02 0.03 0.04 0.05 0 0.001 0.002 0.003

2010 DEEP GREEN

Fig. 5.7 Surface winter distributions (mean values for February) of total phosphorus [g m-3] for the for the standard year 2002 and three scenario (2010)

38

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.025

0.05

0.1

0.15

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DIN [g m-3]

-0.06 -0.03 0 0.03 0.06 -0.002 -0.001 0 0.001 0.002

2010 DEEP GREEN

Fig. 5.8 Surface summer distributions (mean values for July) of inorganic nitrogen [gm-3] for the for the standard year 2002 and three scenario (2010)

39

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

N-Tot [g m-3]

-0.06 -0.03 0 0.03 0.06 0 0.001 0.002 0.003 0.004

2010 DEEP GREEN

Fig. 5.9 Surface summer distributions (mean values for July) of total nitrogen [gm-3] for the for the standard year 2002 and three scenario (2010)

40

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

PO4[g m-3]

0 0.002 0.004 0.006 0 0.0002 0.0004 0.0006

2010 DEEP GREEN

Fig. 5.10 Surface summer distributions (mean values for July) of phosphate phosphorus [gm-3] for the for the standard year 2002 and three scenario (2010)

41

2002 2010 LOW

2010 HIGH

2010 LOW - DG2002 - 2010 HIGH

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

PTOT [g m-3]

0 0.005 0.01 0.015 0 0.001 0.002

2010 DEEP GREEN

Fig. 5.11 Surface summer distributions (mean values for July) of total phosphorus [gm-3] for the for the standard year 2002 and three scenario (2010)

5.2.2. Primary productions, phytoplankton biomass and the fluxes to the sediment

The main consequence of the high loads of nitrogen and the phosphorus discharge to the sea environment is the increase of the biological productivity. The model calculations has allowed to study the spatial distribution of the primary production, its effects on the phytoplankton biomass and to analyse total productivity rates for the defined scenarios.

The primary production depends on three basic factors: nutrient availability, solar radiation and the water temperature. As it was shown in the Fig 5.4 – 5.11 the highest concentrations of inorganic nitrogen and phosphorus are located nearby the Vistula River. The Vistula River waters mainly flows along the coast, therefore the costal waters are the most biologically productive areas of the Gulf of Gdansk (Fig. 5.12). There is a general tendency: the further from the land towards the open sea, the rate of the primary production is lower. The values for the central part of the Gulf of Gdańsk are almost half the values in the Eastern part of the Gulf. The rate of primary production in the open waters of the Gulf of Gdańsk does not varies significantly between the scenarios, so this part of the Gulf is less sensitive to the nutrients loads changes. The areas with most visible evidence in difference between the reference year 2002 and the Policy targets high scenario are located in the North direction from the Vistula River outlet and the along the Hel Peninsula. The loads of the nitrogen and phosphorus by the Vistula River have its

42

strong direct impact on the rates of the primary production. The primary production is the lowest for the Deep green scenario where the phosphorus loads from the Vistula is also the lowest one.

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

40

80

120

160

200

Primary production[gC m-2/ year ]

-15 -10 -5 0 5 10 15 0 0.5 1 1.5 2 2.5

2010 DEEP GREEN

Fig. 5.12 Distribution of the annual rate of primary production in the Gulf of Gdańsk for the reference year 2002 and the scenarios (2010) and comparisons

The N:P ratio in river waters and consequently in the sea water determines effects on the productivity of the water environment. If nitrogen is the limiting nutrient than the reduction of phosphorus loads may not cause any reduction in primary production unless the reduction reached certain level (N:P=16). Below this value phosphorus limits the growth of phytoplankton. This situation has been observed in evaluating the three scenario: in reference year 2002 nitrogen is limiting nutrient, whereas in all considered scenarios the phosphorus is.

The primary production per annual has been calculated for the whole considered area (Tab. 5.2). The lowest value represents the Deep green scenario: the primary production is 7.1 % less than in the reference year 2002. This has been also evidenced in the spatial annual distribution of primary production (Fig. 5.12). The reduction in biological productivity for Policy targets low and high scenarios are 5.9 % and % 6.6 respectively. These reductions are not very significant comparing to the reductions of phosphorus and loads: depending on the scenario from 30.5 % for Policy target low scenario to 34.7 % for the Deep green scenario. However, one should remember that the Gulf of Gdańsk water is still reach in nutrients and there is a exchange of matter with the Baltic Sea. In order to observe further reduction in the biological productivity more time and the reductions in other sources of nutrients in the Baltic is necessary.

43

Table 5.2. Biological productivity of the Gulf of Gdańsk for the reference year and the scenarios.

Scenario Primary production [106 kg/year]

Reference year 2002 953.6 Policy targets low 897.1 Policy targets high 890.6

Deep green 885.9 Following the primary production process the distribution of the phytoplankton biomass can

be observed (Fig. 5.13). In general the shape of distributions of primary productions and phytoplankton biomass are somewhat similar, besides the shallow waters: internal Puck Bay and the Vistula Lagoon. Due to the low water depth, in these regions the low primary production is observed, whereas the concentration of the phytoplankton biomass is very high.

2002 2010 LOW

2010 HIGH

2010 LOW-DG2002 - 2010 HIGH

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Phytoplanktonbiomass[gC m-3]

-0.01 -0.005 0 0.005 0.01-0.001 -0.0005 0 0.0005 0.001

2010 DEEP GREEN

Fig. 5.13 Distribution of the phytoplankton biomass in the summer (mean values for July) in the Gulf of Gdańsk for the reference year 2002 and the scenarios (2010) and comparisons.

Consequently the fluxes of nitrogen and phosphorus to the sediment are highest where the primary production and the phytoplankton biomass are highest (Fig. 5.14). In this regions the sedimentation of detritus is responsible for the high values of the flux rate. In case of phosphorus the flux to the sediment is also very high in the deep part of the Gulf of Gdańsk due to the high flux of phosphorus adsorbed on the suspended matter.

44

HIGH LOW

LOW -DGDEEP GEEN

N-SED [g m-2/ year ]0 1 2 3 4 5 6 7 8 9 10

LOW HIGH

LOW - DGDEEP GREEN

P-SED [g m-2/ year ]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Fig. 5.14. Distribution of the annual nitrogen and phosphorus fluxes to the in the Gulf of Gdańsk for the reference year 2002 and the scenarios (2010) and comparisons.

45

6. Conclusions

Influence of the Vistula river on the ecosystem of the Gulf of Gdansk and the southern Baltic has been solved by mathematical modelling approach. The ecohydrodynamic model was developed, calibrated and implemented for investigated area. Obtained results of modelling were referred to observations from coastal monitoring. The model subjected to statistical measures demonstrated as a high quality one. The essential biogeochemical processes at the ecosystem were described correctly. It provided results for hindcast in 1994 – 2002 and became as a reliable tool for forecast based on assumed three scenarios for 2002-2015.

Depending on the scenarios the reduction of total nitrogen load to the Gulf of Gdańsk is equal from 8.8 % for Policy target low scenario to 9.7 % for Deep Green scenario. The reduction of total phosphorus load is much larger: from 40.9 % for the Policy target low scenario to 45.5 % for Deep green scenario.

The considered scenarios, even if they varies in the assumptions, they are not varies significantly between each other in respect to the total nitrogen and total phosphorus discharged to the Gulf of Gdańsk. The differences in nitrogen loads can be neglected, while the differences in phosphorus loads are rather small (less than 5%).

These above conclusions have important impact of the analyses of the influence of the Gulf of Gdańsk on three considered scenarios:

• The lowest biological productivity has been obtained for Deep green scenario: the primary production is 7.1 % less than in the reference year 2002. The reduction in biological productivity for Policy targets low and high scenarios are 5.9 % and % 6.6 respectively less than in the reference year 2002.

• These reduction of biological productivity is not very significant comparing to the reductions of phosphorus loads: depending on the scenario from 40.9 % for the Policy target low scenario to 45.5 % for Deep green scenario.

• The costal waters are the most biologically productive areas of the Gulf of Gdańsk including the recreational area along the beaches in Gdańsk and along the Vistula Lagoon. In analysed scenarios, the reduction of primary production rate in these areas is rather low.

• Due to the fact that in the analysed scenarios the reduction of phosphorus loads is much higher (more than 40 %) than nitrogen loads (less than 10 %) the phosphorus became a limiting nutrient in the Gulf of Gdańsk. Further reduction of phosphorus load should lead to the reduction of biological productivity in the Gulf of Gdańsk.

• In order to observe further reduction in the biological productivity longer forecast time is necessary.

• Furthermore, the policy targeting on the reduction of nutrients should not limit to the single gulfs or bays but has to cover the whole Baltic Sea.

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49

Appendix I Table I-1. State variable of the ProDeMo Model

State variable Description Unit

[CDIAT] Carbon in diatoms [gC m-3]

[CDINOFL] Carbon in dinoflagellate [gC m-3]

[CGREEN] Carbon in green algae [gC m-3]

[CBLUE-GR] Carbon in blue-green algae [gC m-3]

[CautDIAT] Carbon in autumn diatoms [gC m-3]

[CZOOP] Carbon in zooplankton biomass [gC m-3]

[CDETR] Carbon in detritus [gC m-3]

[N-NO3] Nitrate nitrogen [g m-3]

[N-NH4] Ammonium nitrogen [g m-3]

[NDETR] Nitrogen in detritus [g m-3]

[P-PO4] Phosphate phosphorus [g m-3]

[PDETR] Phosphorus in detritus [g m-3]

[Si-SiO4] Silicate silicon [g m-3]

[SiDETR] Silicon in detritus [g m-3]

[DO] Dissolved oxygen [g m-3]

[NSED] Nitrogen in sediment (active layer) [g m-2]

[PSED] Phosphorus in sediment (active layer) [g m-2]

[SiSED] Silicon in sediment (active layer) [g m-2]

50

Appendix II Table II-1. Calibration coefficients for phytoplankton

Value Coefficient DIAT DINOFL GREEN BLUEGR autDIAT

Unit Description

Gmax 2.9 2.5 2.7 2.8 2.7 2.9 Maximum growth rate for phytoplankton

Topt -1 2 5 10 10 -1 Optimum temperature for phytoplankton growth

Tmin 3 7 11 15 15 3 Minimum temperature for phytoplankton growth

Tmax 6 12 22 30 17 6 Maximum temperature for phytoplankton growth

Is 60 90 200 650 30 60 Optimum light intensity for phytoplankton growth

KMN 0.01 0.005 0.005 0.0005 0.01 0.01 Michelis’ constant for nitrogen

KMP 0.004 0.003 0.003 0.001 0.003 0.004 Michelis’ constant for phosphorus

KMsi 0.03 0 0 0 0.03 0.03 Michelis’ constant for silicon

KRakt 0 0 0 0 0 0 Parameter for active respiration

KRstr 0 0 0 0 0 0 Parameter for stress respiration

DRbie 0.1 0.1 0.1 0.1 0.1 0.1 Parameter for non-active respiration

QRbie 1.09 1.09 1.09 1.09 1.09 1.09 Temperature constant for non-active respiration

L 0.07 0.05 0.05 0.05 0.05 0.07 Phytoplankton mortality rate

Paval 0.9 0.7 1 0.3 0.6 0.9 Parameter of food availability

Vs 0.3 0.2 0.1 0.01 0.1 0.3 Sedimentation rate

aNC 0.22 0.22 0.22 0.22 0.22 0.22 Nitrogen to carbon ratio in phytoplankton biomass

aPC 0.025 0.025 0.025 0.025 0.025 0.025 Phosphorus to carbon ratio in phytoplankton biomass

aSiC 0.2 0 0 0 0.2 0.2 Silicon to carbon ratio in phytoplankton biomass

Table II-2. Calibration coefficients for zooplankton

Coefficient Value Unit Description FrZmax 5.00 [m3 gC-1 d-1] Maximum filtration rate for phytoplankton QZ 1.05 [-] Temperature constant for zooplankton afr 3.00 [-] Filtration constant for zooplankton bfr 50.00 [m3 g-1] Parameter for filtration by zooplankton Zas 0.80 [-] Parameter for assimilation by zooplankton KZakt 0.02 [-] Parameter for active respiration DRbieZ 0.02 [-] Parameter for non-active respiration QRbieZ 1.07 [-] Temperature constant for non-active respiration LZ 0.04 [d-1] Zooplankton mortality rate

51

Table II-3. Calibration coefficients for carbon

Coefficient Value Unit Description KmC 0.001 [d-1] Carbon mineralization rate QmC 1.047 [-] Temperature constant for carbon mineralization rate MDOC 0.0 [-] Oxygen parameter for carbon mineralization rate VsDE 0.16 [m d-1] Detritus sedimentation rate KmCS 0.003 [-] Carbon mineralization rate in sediment

QmCS 1.0 [-] Temperature constant for carbon mineralization rate in sediment

CS 30 [g m-2] Carbon content in sediment active layer

Table II-4 Calibration coefficients for nitrogen

Coefficient Value Unit Description KnN 0.1 [d-1] Nitrification coefficient QnN 1.1 [-] Temperature constant for nitrification TKrnN 2.0 [ºC] Critical temperature for nitrification

DOKrnN 3.0 [gO2 m-3] Critical oxygen content for nitrification

KdnN 0.09 [d-1] Denitrification coefficient QdnN 1.12 [-] Temperature constant for denitrification TKrdnN 2.0 [ºC] Critical temperature for denitrification

DOMaxdnN 2.0 [gO2 m-3] Critical oxygen (maximum) content for denitrification

DOKrdnN 0.5 [gO2 m-3] Critical oxygen content for denitrification

KrdnN 4.0 [-] Multiplication factor for denitrification below critical value of oxygen content

KmN 0.005 [d-1] Nitrogen mineralization rate QmN 1.1 [-] Temperature constant for nitrogen mineralization MDON 1.0 [-] Oxygen parameter for nitrogen mineralization aNCZ 0.07 [-] Carbon to nitrogen ratio for zooplankton KmNS 0.0022 [-] Nitrogen mineralization rate in sediment (active layer) QmNS 1.0 [-] Temperature constant for nitrogen mineralization in sediment

FSnitr 0.0 [-] Fraction of ammonium nitrogen undergoing immediate nitrification in sediment

FSden 0.7 [-] Fraction of nitrate nitrogen undergoing immediate denitrification in sediment

NBG 0 [gm-3] Critical concentration of the inorganic nitrogen in the surface layer for blue-green algae

52

Table II-5. Calibration coefficients for phosphorus

Coefficient Value Unit Description KmP 0.005 [d-1] Phosphorus mineralization rate

QmP 1.047 [-] Temperature constant for phosphorus mineralization

MDOP 0.1 [-] Oxygen parameter for phosphorus mineralization

aPCD 0.002 [-] Carbon to phosphorus ratio for zooplankton

Fpip 0.35 [-] Fraction of phosphorus adsorbed on inorganic particles

VsSP 0.25 [m d-1] Sedimentation rate of inorganic particles

KmPS 0.013 [-] Phosphorus mineralization rate in sediment (active layer)

QmPS 1.0 [-] Temperature constant for phosphorus mineralization in sediment

Table II-6. Calibration coefficients for silicon

Coefficient Value Unit Description

KmSi 0.0007 [d-1] Silicon mineralization rate

QmSi 1.047 [-] Temperature constant for silicon mineralization

MDOSi 1.0 [-] Oxygen parameter for silicon mineralization

aSiCD 0.2 [-] Carbon to silicon ratio for diatoms

aSiCD 0.0 [-] Carbon to silicon ratio for zooplankton

KmSiS 0.015 [-] Silicon mineralization rate in sediment (active layer)

QmSiS 1.0 [-] Temperature constant for silicon mineralization in sediment

Table II-7. Calibration coefficients for oxygen

Coefficient Value Unit Description

BDO 0.5 [m4 g-1 d-1] Parameter for oxygen flux to atmosphere in case of over saturation conditions

RDOW 0.1 [m2 g-1 s2 d-1] Reaeretion coefficient

aOC 7 [-] Oxygen to carbon ratio during photosynthesis

aOnn 5.71 [-] Oxygen to nitrogen ratio during nitrification

aOnden 3.43 [-] Oxygen to nitrogen ratio during denitrification

aOMm 2.06 [-] Oxygen to nitrogen ratio during mineralization

aOPm 2.06 [-] Oxygen to phosphorus ratio during mineralization

aOsim 2.29 [-] Oxygen to silicon ratio during mineralization

Table II-8. Parameters for light penetration

Parameter Value Unit Description

Kd0 0.17 [m-1] Light extinction coefficient (steady value)

KdChla 25.0 [m2g-1] Light extinction coefficient depending on chlorophyll concentration

KdOC 0.0 [m2g-1] Light extinction coefficient depending on organic carbon concentration

53

Appendix III. Equations of the model

Phytoplankton

6.1.1. Change of phytoplankton mass

[ ] ( ) [ ] [ ]z

CCt

C isiiii

ii ∂

∂+⋅−−−=

∂∂ VLDRG iZ

where: Gi – phytoplankton growth; Ri – phytoplankton respiration; DZi – grazing of phytoplankton; Li – decay of phytoplankton; i – phytoplankton group (DIAT or nDIAT);

Phytoplankton growth (Gi):

iiii BITi GGGGG ⋅⋅⋅= max

Phytoplankton growth as the function of water temperature:

⟩

−

−

≤

−

−

=

iii

i

iii

i

i

optopt

opt

optopt

opt

T

TTTT

TT

TTTT

TT

G 2

max

2

min

3.2

3.2

exp

Phytoplankton growth in relation to intensity of active radiation– IPAR [W/m2]:

−=

iii

s

PAR

s

PARI I

II

IG 1exp

Value IPAR on given depth is determined by solving the equation:

[ ]

⋅+⋅⋅+⋅=

∂∂ ∑ ]C[KdCKdKd DETROCiChla0 iChl

iPAR

PAR CIz

I

Phytoplankton growth in relation to concentration of nutrients compounds:

( )iiii SiPNB GGGG ,,min=

Phytoplankton growth depending on the concentration of inorganic nitrogen:

[ ] [ ][ ] [( )]34

34NONNHN

NONNHN−+−+

−+−=

iMNiN K

G

Phytoplankton growth depending on the concentration of inorganic phosphorus:

[ ][ ]4

4POP

POP−+

−=

iMPiP K

G

Phytoplankton growth depending on the concentration of inorganic silicon:

[ ][ ]4

4SiOSi

SiOSi−+

−=

iMSiiSi K

G

54

Blue-green algae growth with nitrogen limitation conditions for surface layer (fixation process):

( )

≤−+−>−+−

=BGP

BGPNB NG

NGGG

i

iii ]NHN[]NON[

]NHN[]NON[,min

43

43

Respiration of phytoplankton (Ri):

2011 −⋅+

−+= T

RbieRbieB

iRstriRakti iii

iiQD

GGKGKR

Grazing of phytoplankton by zooplankton (DZi):

[ ]ZOOPavalZi Ci

⋅⋅= FrPD

Filtration by zooplankton :

[ ]

⋅−+

⋅=

∑

−

iavalfrfr

TZZ

iPba

QFrFr

i

20max

Cexp1

Zooplankton

6.1.2. Change of zooplankton biomass:

[ ] ( ) [ ]ZOOPZZZZOOP C

tC

⋅−−=∂

∂ LRA

where: AZ – assimilation of phytoplankton by zooplankton; RZ – zooplankton respiration; LZ – decay of zooplankton

Assimilation of phytoplankton by zooplankton

[ ]iCiaval

iAsZ PFrZA ∑⋅⋅=

Zooplankton respiration (RZ): 20−⋅+= T

RbieZRbieZZZaktZ QDAKRi

Excretion by zooplankton [d-1]

[ ] Zi

avalZ APFrLi

−= ∑ iC

Mineralization of carbon, nitrogen, phosphorus and silicon

Coefficient of mineralization of carbon, nitrogen, phosphorus and silicon depending on the temperature and concentration of oxygen (MC, MN, MP, MSi,, MCS, MNS, MPS, MSiS):

2

220

]DO[]DO[

+⋅⋅= −

XDO

TmXmXX

MQKM

where:

55

X –carbon (C), carbon in sediment (CS), nitrogen (N), nitrogen in sediment (NSED), phosphorus (P), phosphorus in sediment (PSED), silicon (Si) or silicon in sediment (SiSED); MDOx – oxygen coefficient of mineralization .

Carbon

6.1.3. Fluxes from sediment

SCC CMSSED

⋅=

Flax from active to non-active layer [d-1]:

[ ] [ ] SCi

DEiout CSVsVsC

−+= ∑ DETRi CC

Carbon in detritus

[ ] [ ] [ ] [ ] [ ]z

VMWLLt sDETRCZZ

ii ∂

∂+⋅−++=

∂∂ ∑ DETR

DETRZOOPiDETR CCC)(CC

Nitrogen

6.1.4. Fluxes from sediment

Total flux of inorganic nitrogen [gm-2 d-1] (as a result of mineralization) from sediment into water:

]N[ SED⋅=SEDNN MS

Fluxes of ammonium nitrogen, nitrate nitrogen from sediment into water [gm-2d-1]:

NSNitrNH SFS ⋅−= )1(4

NSDenSNitrNO SFFS ⋅−⋅= )1(3

6.1.5. nitrogen in sediment:

[ ] [ ] [ ] SEDoutNDEi

NCi NSVsaVst i

−−+=∂

∂ ∑ DETRiSED NCN

[ ] outSEDout CN ⋅= SEDN

NSEDout – flux of nitrogen from active to non-active layer [gm-2d-1]

6.1.6.

6.1.7. nitrate nitrogen :

[ ] [ ] [

[ ] ( )[ ]

]*

i

320

4203

31C

NO-NNH-NNO-N

∆+−⋅⋅⋅−

+⋅⋅−⋅⋅=∂

∂

∑

−−

HNO

iNNCi

TdnNdnN

TnNnN

zS

PaG

QKQKt

ii

56

where: ()*– the last term of the equation is applied only for bottom layer ; ∆zH – thickness of bottom layer and phytoplankton group ( takes values DIAT, nDIAT).

Preference of ammonium nitrogen take-up over nitrate nitrogen take-up for particular phytoplankton groups:

[ ] [ ][ ]( ) [ ]( )

[ ][ ] [ ]( ) [ ]( )334

4

34

34

NO-NNO-NNH-NNH-N

NO-NNH-NNO-NNH-N

+⋅+

⋅+

+⋅+⋅

=i

i

ii MN

MN

MNMNiN K

KKK

P

6.1.8. ammonium nitrogen :

[ ] [ ] ( ) [ ] [ ]

[ ]*

20

OOPiDETR4

44NH-N

CCNNH-N

∆+⋅⋅−

+⋅⋅+⋅⋅⋅−+⋅=∂

∂

−

∑

HNHT

nNnN

NCZZi

NCNiiN

zS

QK

aRaPGRMt Zii

6.1.9. nitrogen in detritus:

[ ] [ ] ( ) [ ] [ ] [ ]z

VsMWaLaLt DENNNCZ

iNCi Zi ∂

∂+−⋅++⋅=

∂∂ ∑ DETR

DETRZOOPiDETR NNCCN

Excretion of nitrogen by zooplankton [d-1]:

[ ]Zii NCZ

iNCavalN aAaPFrW −= ∑ iC

Phosphorus Fluxes from sediment:

]P[ SED⋅=SEDPP MS

6.1.10. phosphorus in sediment:

[ ] [ ] [ ] SEDoutPDE

iPCi PSVsaVs

t i−−+=

∂∂ ∑ DETRi

SED PCP

[ ] outSEDout CP ⋅= SEDP

PSEDout– flux of phosphorus from active to non-active layer [gm-2d-1]

6.1.11. phosphate phosphorus:

[ ] [ ] ( ) [ ] [ ]

[ ] *4

PIPSP

OOPiDETR4

PO-PfVs

CCPPO-P

∆+∂

∂⋅⋅+

+⋅⋅+⋅⋅−+=∂

∂ ∑

HP

iPCZZNCiiP

zS

z

aRaGRMt Zi

57

6.1.12. phosphorus in detritus :

[ ] [ ] ( ) [ ] [ ] [ ]z

VsMWaLaLt DEPPPCZ

iPCi Zi ∂

∂+−⋅++⋅=

∂∂ ∑ DETR

DETRZOOPiDETR PPCCP

Excretion of phosphorus by zooplankton [d-1]:

[ ]Zii PCZ

iPCavalP aAaPFrW −= ∑ iC

Silicon Fluxes from sediment:

]Si[ SED⋅=SEDSiSi MS

6.1.13. silicon in sediment:

[ ] [ ] [ ] SEDoutSiDEi

PSii SiSVsaVst i

−−+=∂

∂ ∑ DETRiSED SiCSi

[ ] outSEDout CiSi ⋅= SEDS

SiSEDout– flux of silicon from active to non-active layer [gm-2d-1]

6.1.14.

6.1.15. silicate silicon:

[ ] [ ] ( ) [ ] [ ]*

OOPiDETR4 CCSiSiO-Si

∆+⋅⋅+⋅⋅−+=∂

∂ ∑ HSi

iSiCZZSiCiiSi z

SaRaGRMt Zi

6.1.16. silicon in detritus:

[ ] [ ] ( ) [ ] [ ] [ ]z

iVsiMWaLaLt DESiPSiCZ

iSiCi Zi ∂

∂+−⋅++⋅=

∂∂ ∑ DETR

DETRZOOPiDETR SSCCSi

Rate of excretion of silicon by zooplankton [d-1]:

[ ]Zii SiCZ

iSiCavalSi aAaPFrW −= ∑ iC

58

Dissolved oxygen

[ ] ( )[ ] [ ] [ ]

[ ] [ ] [ ]

[ ] [ ] [ ]

[ ] [ ]ndn

Zi

Zi

ONNOT

nNnNONTdnNdnN

OSiSiSiSiCZSiCi

i

OPPPPCZPCi

i

OCCCZi

iiDO

azS

QKaQK

azSiMaRaR

azSMaRaR

azSMRRG

zR

t

⋅

∆+⋅⋅−⋅⋅⋅+

+⋅

∆−⋅−−−+

+⋅

∆−⋅−−−+

+⋅

∆−⋅−−−+∆

=∂

∂

−−

∑

∑

∑

*

420

320

*DETRZOOPi

*DETRZOOPi

*DETRZOOPi

3NH-NNO-N

SCC

PCC

CCCDO

Oxygenation as a result of reaeration or removal of extra oxygen in case of oversaturation :

( )( )( )

>−⋅≤−⋅⋅=

STSTDO

STSTWDODOCCBCCURR

]DO[gdy]DO[]DO[gdy]DO[

**210

()** - only for surface layer

Degree of saturation of water with oxygen at given salinity and temperature:

)]000077774.00000374.0007991.0(41022.000256.0[0841.0652.14

⋅−⋅−⋅+−⋅⋅+⋅−=

TSTSTSCST

59

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