Modelling the Effects of Inflow Parameters on Lake ... - Springer Link

Environmental Modeling and Assessment 8: 63–70, 2003.  2003 Kluwer Academic Publishers. Printed in the Netherlands.

Modelling the effects of inflow parameters on lake water quality Monzur Alam Imteaz a , Takashi Asaeda b and David A. Lockington c a Parramatta City Council, Sydney, NSW 2124, Australia

E-mail: [email protected] b Department of Environmental Science & Human Engineering Saitama University, 255 Shimo Okubo, Urawa, Saitama, 338, Japan c Department of Civil Engineering The University of Queensland, Brisbane, QLD 4072, Australia

A one-dimensional lake water quality model which includes water temperature, phytoplankton, phosphorus as phosphate, nitrogen as ammonia, nitrogen as nitrate and dissolved oxygen concentrations, previously calibrated for Lake Calhoun (USA) is applied to Uokiri Lake (Japan) for the year 1994. The model simulated phytoplankton and nutrient concentrations in the lake from July to November. Most of the water quality parameters are found to be the same as for Lake Calhoun. To predict probable lake water quality deterioration from algal blooming due to increased nutrient influx from river inflow, the model was run for several inflow water conditions. Effects of inflow nutrient concentration, inflow volume, inflow water temperatures are presented separately. The effect of each factor is considered in isolation although in reality more than one factor can change simultaneously. From the results it is clear that inflow nutrient concentration, inflow volume and inflow water temperature show very regular and reasonable impacts on lake water quality. Keywords: water quality, phytoplankton, phosphate, ammonia, river inflow

1. Introduction Eutrophication of lakes is a serious problem for water supply as well as for aquatic ecosystems [7]. A common indicator of lake eutrophication is phytoplankton population density and speciation [2] which results in green, turbid and smelly water. Eutrophication also causes the generation of toxic algae as well as deoxygenation of water, which are harmful for other organisms and destroys ecological balance [10]. In the winter, usually solar radiation, water temperature and vertical mixing are the limiting factors causing the low growth rate of phytoplankton and the abundance of nutrients. In summer, the increase in solar radiation, water temperature and decrease of vertical mixing rate cause blooms of phytoplankton provided the amounts of nutrients are sufficient. As the summer bloom occurs, nutrients become depleted and a decline in the concentration of phytoplankton occurs. The effects of these factors are well known and several authors have developed mathematical models including them (e.g., [3,11]). Imteaz and Asaeda [8] have developed a one dimensional lake water quality model based on DYRESM [6] which incorporates a “double plume concept” [1] of artificial mixing. The model was calibrated and assessed for Lake Calhoun (USA). However, for this kind of complex model having numerous water quality parameters, calibration and application for a single lake is not sufficient to establish the applicability of the model. It is necessary to use the model for other lakes as well and check the consistency of the parameter values used for the calibration. The present paper describes the simulation results of the model for Uokiri Lake (Hiroshima, Japan) in this context. The concentration of nutrients has a significant role in the formation of algal blooms and inflow water is often the most significant source of nutrient supply. With the increase

of industrialization and human activities, inflow water can carry high concentrations of nutrients that mainly come from waste disposal to the river (e.g., [12]). To predict the possible water quality deterioration due to an increase of inflow nutrient concentration and to determine the maximum possible degree of amelioration, which can be achieved through controlling nutrients supply, it is necessary to study the generalized effects of inflow nutrients’ on reservoir water quality. 2. Overview of the model and comparison The analysis consists mainly of two steps. In the first step the vertical distributions of physical quantities were evaluated under given meteorological conditions, in the second step vertical distributions of chemical and biological quantities were evaluated under the generated physical and meteorological conditions. A time step of one day was used for the conservation of physical and biological parameters. A process based one dimensional reservoir simulation model, DYRESM [6], which can simulate water temperature and salinity, was modified [8] to produce daily variations of biological and chemical quantities. Although a 3D model would produce accurate results, but for small/medium size deep lakes having small inflows compared to total storage, a one-dimensional model would be good enough to produce accurate results. Imberger and Patterson [4] described in detail a number of criteria required for a lake to be one-dimensional in nature. DYRESM 1D model presently being used in 51 countries around the world with good accuracy (http://www.cwr.uwa.edu.au/users/ttfadmin/model/ dyresm1d/). The lakes considered in this paper are small sized having high depth, for which 1D model should be good enough to produce accurate results.

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M.A. Imteaz et al. / Modelling the effects of inflow parameters on lake water quality

2.1. Basic physical model (DYRESM) This model is based on the assumption of one dimensionality, that is, the variations in the lateral directions are small compared with the variations in the vertical. It considers several horizontal layers in a lake or reservoir and the thickness of these layers is variable and set by the model. As inflow and outflow enter or leave the lake, the affected layers expand or contract and those above move up or down to accommodate the volume change. To model also parameterizes mixed layer deepening due to convective overturn, wind stirring, seiche-induced shear and billowing. Each process contributes to a turbulence kinetic energy (TKE) budget. The model determines the potential energy required to lift each layer and if there is sufficient TKE it mixes the layer. Thus, layer thickness increases as underlying layers are mixed. If layers exceed a maximum limit, they are split. The vertical movement of layers is accompanied by a thickness change as the area changes with vertical position. Mixing is modelled by the amalgamation of adjacent layers. A detailed description of DYRESM is given by Imberger and Patterson [5] and Imberger et al. [6]. 2.2. Biological model Eight state variables – phytoplankton (as chlorophyll-a), phosphorus as phosphate, nitrogen as ammonia, nitrogen as nitrate, dissolved oxygen, BOD, internal phosphorus and internal nitrogen were considered for the biological model. Vertical diffusion of biological state variables in the hypolimnion is estimated using the turbulent diffusion algorithm described by Imberger and Patterson [5]. Conservation equations for these variables were solved after each day. The phytoplankton biomass can be represented in the model as the concentration of chlorophyll-a, either for the entire phytoplankton population, or as the individual contributions by different groups. In the present case however only the total phytoplankton population is considered. Conservation equations are very similar to DYRESM WQ presented by Hamilton & Schladow [3] and MINLAKE by Riley & Stefan [11] with some modifications (equations are given in appendix A).

(a rising plume) was used, whereas in the modified model a “double plume concept” (a simultaneous rising plume and a downward plume) was used. In the “single plume model” entrainment of ambient water to the plume water is considered only during the rising of plume, i.e., no entrainment was considered during the downward plunge. But in the “double plume model” entrainment of ambient water is considered for both the rising plume and downward plume, which is more realistic. The significance of the “double plume model” was discussed in detail by Imteaz & Asaeda [8]. The model was calibrated for Uokiri lake (Hiroshima, Japan) for the year 1994, where the bubbler was used intermittently from 20 July to 7 August, 22 August to 5 September and from 20 September to 4 October. Most of the biological parameters were found to be same as for Lake Calhoun. This is usual for these values of those parameters to be different for different lakes. In general the parameters related to algae (i.e., growth rate, saturation light intensity, internal nutrients in algae cell, respiration rate and nutrients uptake rate by algae) were different. This might be due to their being different types of algae in the two different lakes. Figure 1 shows the comparison of model results for phosphorus as phosphate (PO4 -P) at different depths with field data. It is found that model predictions near the surface are within an acceptable range for the observed data. At 5 and 10 m depths the model results show some discrepancy with the observed data during the initial period of simulation but at later periods, the model result is closer to the observed data. The reason for this initial discrepancy is that the sample was taken in the vicinity of the bubble port where nutrient concentration reduces rapidly due to mixing with epilimniotic water of lower nutrient concentration, on the other hand the model represents an average concentration for the whole lake which usually requires a longer time to be mixed. There are significant fluctuations in the model results, which are due to the intermittent operation of the bubbler; with the operation of the bubbler, nutrient concentrations near the surface increase and with the cessation of operation they de-

2.3. Comparison and validation of the model A model coupling both parts discussed above is used to simulate the lake phytoplankton concentration and nutrient concentration. As bubble plumes are widely used for the artificial mixing of lake water to improve the water quality, a bubble model which was developed by Asaeda and Imberger [1] was incorporated with the above coupled model to simulate the effect of a bubble plume. Details of the incorporation of the bubble plume model and simulation results after calibration for Lake Calhoun (USA) were given by Imteaz & Asaeda [8,9] and Imteaz [7]. The major difference between DYRESM WQ [3] and the present model is the destratification part. In DYRESM WQ a “single plume concept”

Figure 1. Comparison of model results for PO4 -P with field data (arrows show the destratification periods).


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Table 1 Calibrated values of parameters for Uokiri Lake Gmax = 1.10 IPmin = 0.1 kON = 0.03 KZ = 40.0 Z = 1.0 KDO = 0.4 θO = 1.02

IS = 101.0 kB = 0.02 kOP = 0.03 SN = 60.0 YNBOD = 0.041 ηB = 0.5 θS = 1.02

IN max = 15.0 km = 0.02 kz = 0.38 SP = 55.0 YPBOD = 0.004 Pf = 0.1 θNO = 1.02.

Figure 2. Comparison of model results for NH3 -N with field data (arrows show destratification periods).

IN min = 1.7 IPmax = 11.0 kr = 0.05 kNO = 0.05 KN = 200.0 KP = 70.2 UN max = 2.2 UPmax = 0.5 KON = 22.0 KBOD = 40.0 θ = 1.02 θZ = 1.02

acceptable range with respect to the observed data. Figure 3 shows the comparison of model results at different depths for algal concentration, represented by the concentration of chlorophyll-a (Chl-a), with observed data. It is found that model results are close to the observed data. With the operation of the bubbler the Chl-a concentration decreased rapidly but again with the end of operation the Chl-a concentration increases during mid August. Again it decreased due to further application of the bubbler in late August. After the final cessation of the bubbler operation on 4 October the Chl-a concentration remained low for the rest of the period until November. This is due to winter mixing by vertical convection. It is clear that the model can simulate all the stated conditions and lake phytoplankton as well as nutrient concentrations with or without artificial mixing. This calibrated model was used to predict and generalize the effects of river inflow on phytoplankton concentration in the lake. Calibrated values for the parameters are given in table 1. 3. Generalized effects

Figure 3. Comparison of model results for Chl-a with field data (arrows show destratification periods).

crease. For this particular lake, algal growth was limited by the phosphorus concentration. With the increase of the algal population, phosphorus concentration decreases as it is continuously consumed by algae until at some stage the concentration becomes limiting causing the reduction of algal concentration. With the reduction of algal concentration again the phosphorus concentration increases with the continuous supply from inflow and bottom sediment. Figure 2 shows the comparison of model results at different depths for nitrogen as ammonia (NH3 -N) with observed data. It is found that model results for different depths are within an

To obtain generalized effects of inflow conditions on algal blooming in a reservoir, an imaginary lake of surface area 2.80 × 105 m2 , maximum depth 24 m and maximum storage volume of 5.1 × 106 m3 was considered. A sinusoidal variation was considered for the meteorological data, i.e., solar radiation, air temperature and inflow water temperature. The simulation period was from April to November. The sinusoidal variation was assumed in such a way that the lowest value occurs at the beginning (February) and end (November) of the simulation period with the maximum value at the middle (mid July) of the simulation period. Figure 4 shows the assumed distribution of solar radiation, air temperature and inflow water temperature. Inflow and outflow volume was assumed constant (10,000 m3 /day) throughout the simulation period. Stratified DO, BOD, nutrients and algal concentrations were assumed as the initial condition over the depth of the lake. The model was run for several conditions by changing inflow parameters. Although the generalized effects were determined for a particular lake with precise volume, the qualitative nature of the effects discussed in this paper should be similar for all lakes. Inflow from the river contains significant amounts of nutrients and these have considerable effects on nutrient concentration in the lake, especially in the summer period when the lake becomes thermally stratified and strong temperature gradients inhibit vertical mixing. In that case, nutri-

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Figure 4. Assumed input data for solar radiation, air temperature and inflow water temperature.

Figure 5. Effect of inflow nutrients concentrations on total Chl-a in lake.

ents released from the sediment are not available for the algae, which remains in the epilimnion. As a result nutrients carried by the inflow water become the dominant source for algal growth. As phytoplankton requires nutrients for its metabolism, the phytoplankton population will increase if the nutrient concentration is increased. Figure 5 shows the effect of inflow nutrient concentration on phytoplankton population. For the base simulation (100% as shown in figure), the concentrations of inflow nutrients were assumed as: phosphorus as phosphate 25 mg/l, nitrogen as ammonia 250 mg/l and nitrogen as nitrate 300 mg/l. It is found that inflow nutrient concentration had no effect at the first stage of the simulation period (i.e., before summer), significant effects at mid stage of the simulation period (i.e., at summer) and very little effect at the end of simulation period (i.e., beginning of winter). This is because during winter the lake phytoplankton concentration reduces significantly and before spring the phytoplankton concentration is very low. Consequently the concentration of nutrients is very high as the smaller population of phytoplankton has consumed a correspondingly smaller amount of nutrients. Also, nutrients released from sediments mix throughout the depth due to convection, adding to the total concentration. For these reasons the lake has a high amount of nutrients, which is much higher than the required nutrient level for the phytoplankton. Therefore a change in inflow nutrient concentrations does not create any significant difference in phytoplankton biomass before summer and phytoplankton growth is limited by solar radiation only. However, during summer when the concentration of phytoplankton biomass is very high, the

Figure 6. Effect of inflow nutrients concentration on seasonal total Chl-a.

amount of available nutrients becomes insufficient for further growth of algal biomass. That means although available solar radiation is sufficient for more algal growth, nutrients become the limiting factor. So any change in nutrients affects the algal biomass in the lake. From figure 5 it is found that as inflow nutrient concentration decreases, the peak of total Chl-a shifts earlier towards spring or early summer. This is because with the decrease of inflow nutrients concentration epilimniotic nutrients also decrease, which causes the nutrient to become limiting earlier than before when inflow nutrients were higher. As nutrients become limiting it causes a reduction in Chl-a forming an earlier peak. Also it is found that as inflow nutrient concentration continues increasing, algal growth for the whole simulation period ceases to be limited by nutrient and there is no change of algal biomass with the increase of inflow concentration. To obtain the generalized effect of inflow nutrients concentration, the model was applied for many different cases. Results are given in figure 6. In this figure the total amount of Chl-a for the total computation period (sum of the mass of algae in all days throughout the period) was plotted against inflow nutrients concentration. It reveals that as the inflow nutrients concentration increases, the total amount of phytoplankton also increases linearly until a level where again the nutrient becomes excess and the total amount of Chl-a remains the same (even if the inflow nutrients concentration increases). The rate of increase of Chl-a biomass reduces as this limit is approached. This is because with the increase of inflow nutrients, as nutrients become abundant for some additional days, the total nutrient limiting period reduces causing a slower rate of increase of total Chl-a. The rate of increase of total phytoplankton with the increase of inflow nutrients depends on the inflow volume. If inflow volume is high, the rate of increase will also be high. With very high inflow volume, this trend changes. In this case mixing occurs in the epilimnion, which reduces the concentration of Chl-a. Figure 7 shows the effect of inflow volume, expressing total seasonal Chl-a against inflow volume for various inflow nutrient concentrations. From the figure it is found that for higher inflow nutrients concentration, the effect of inflow volume is significant. At the beginning with the increase of inflow volume seasonal total phytoplankton also increases due to increased concentration of nutrients. For higher inflow volume, the total seasonal Chl-a decreased due to mixing effects in the epilimnion. This de-


Figure 7. Effect of inflow volume on seasonal total Chl-a.

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Figure 9. Effect of fluctuating inflow water temperature on total Chl-a.

Figure 8. Effect of inflow water temperature on total Chl-a in lake.

Figure 10. Effect of fluctuating inflow volume on total Chl-a.

creasing trend was not the same for the case with low inflow nutrient concentrations. In this case the total Chl-a biomass increased with the increase of inflow volume but later remained constant with further increase of inflow volume. For low inflow nutrient concentrations, the effect of mixing and the effect of higher nutrient supply compensate each other. In the case of high inflow nutrient concentrations, as total algal biomass becomes very high, even with the lower inflow volumes, the effect of mixing dominates, reducing the total algal biomass. The supply of additional nutrients was not enough to maintain that high level of algal biomass and outweigh the effect of mixing in the epilimnion. For high inflow nutrients concentrations, total Chl-a biomass approaches to the same value as inflow volume increases. Inflow water temperature also has a significant effect on phytoplankton concentration in the lake as it determines the intrusion level (i.e., the depth affected by the inflow). If the intrusion level is within the epilimnion it can change the epilimnion nutrients considerably causing a change in phytoplankton concentration. Figure 8 shows the effects of different inflow water temperature. A significant difference was found during the blooming period, i.e., in summer. For lower inflow temperature the intrusion goes down lower than the epilimnion earlier than for the case with higher inflow temperature. As inflow goes below the epilimnion, the contribution to the epilimnion ceases, subsequently supply of nutrients at the epilimnion ceases. Thus nutrient concentration becomes limiting earlier causing an earlier peak with lower magnitude. For this case, although nutrients increase below the epilimnion since the solar radiation is limiting at this lower level, there is no increase in the phytoplankton.

For higher inflow temperature, the magnitude of total Chl-a was higher. Since inflow temperature was higher, the contribution of inflow nutrients to the epilimnion lasts for a longer period causing an increase of nutrients in the epilimnion and a peak of higher magnitude. In all the above cases, the inflow temperature was considered to vary sinusoidally with a smooth variation as shown in figure 4. In reality, inflow water temperature may fluctuate on alternate days; the effect of fluctuating inflow temperature is shown in figure 9. The assumed fluctuating inflow temperature has the same seasonal minimum and maximum values but with higher and lower than the average smooth inflow temperature in alternate days. It is found that the effect of the fluctuating inflow temperature is insignificant for almost all the period except in summer. In summer the fluctuating inflow temperature produces higher algal concentrations than the original smooth variation of inflow temperature. Usually in summer inflow water temperature is lower than lake surface temperature, so inflow intrudes to a distance below the surface. For the fluctuating inflow temperature on alternate days, the higher inflow temperature results in the inflow going to or near the surface. Due to this supply of nutrient on alternate days, the concentration of nutrients is higher in the epilimnion causing a larger bloom. In all the above cases inflow volume was considered constant (10,000 m3 /day) throughout the year. To check the effect of variable inflow volume, the model was simulated for fluctuating inflow volume. The fluctuation was such that a higher and a lower than the constant inflow volume was assumed on alternate days. Figure 10 shows the effect of fluctuating inflow volume. From the figure it is found that there

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is no significant difference in total chl-a between this fluctuating inflow volume and the constant inflow volume. There is only a small difference in summer. 4. Conclusion It is found that the modified DYRESM model can successfully simulate lake chlorophyll-a as well as nutrient concentrations with or without artificial mixing. Although model simulations are not very close to the observed field data, this level of discrepancy is acceptable for this kind of complex water quality problem. The model was first calibrated for Lake Calhoun, USA. Although it is likely that biological parameters will be different for different lakes, for the calibration of Uokiri lake, our target was to keep the values of the parameters the same as for Lake Calhoun as much as possible. In general parameters related to algae (i.e., growth rate, saturation light intensity, internal nutrients in algae cell, respiration rate and nutrients uptake rate by algae) were different. This might be due to there being different types of algae in the two different lakes. Unfortunately there was not enough field data to verify the model for a period of a whole year. However, the available data covers the peak algal blooming period (i.e., summer), which is the period of concern. The model can be used to predict probable water quality deterioration due to a change in any meteorological and/or inflow factors. It is found that inflow nutrient concentration and flux has a significant role in the formation of an algal bloom. With the increase of inflow nutrients total algal biomass increases significantly. At the beginning, the rate of increase of the algal biomass with nutrient concentration is high and linear. However, if the nutrient concentration continues increasing the rate of increase of algal biomass is reduced and eventually becomes zero (i.e., with the further increase of nutrients there is additional increase of algal biomass). Using the model it is possible to assess the maximum possible deterioration of water quality by the inflowing nutrients. The reduction of inflow nutrients results in algal biomass decreasing significantly with a shift of peak towards spring. Thus it is possible to improve water quality significantly by reducing the supply of nutrients from inflow with the model predicting the probable improvement of water quality. Inflow volume has two opposite effects on the algal biomass; with the increase of inflow volume algal biomass also increases due to supply of additional nutrients, but for high inflow volume algal biomass decreases due to mixing in the epilimnion. The effect of inflow water temperature is significant if inflow nutrient concentration is not suffciently high. Obviously if inflow temperature is much lower than surface water temperature, especially in summer, it will not cause the water quality to deteriorate. It is found that if average inflow temperature is low then a fluctuating inflow temperature produces worse water quality conditions than for an average smooth inflow temperature. But if the average inflow temperature is high then there is no significant difference. Also it

is found that there is no significant difference in water quality between fluctuating inflow volume and smooth average inflow volume. Our aim was to establish a generalized relationship, i.e., to quantify the effects of inflow parameters on lake water quality and to establish some numerical relationship. Although we could not come up with any concrete relationship, our work might be the basis of such future efforts.

Appendix A Equations for phytoplankton production, nutrients cycling and dissolved oxygen budget are given here. Definitions of the parameters are given in section below. Equation for phytoplankton (chlorophyll-a), ∂Chlai = Gmax θ T −20 Chlai min f (Ii ), f (IPi ), f (IN i ) ∂t − kr θ T −20 Chlai − km θ T −20 Chlai Chlai − kz ZθzT −20 Pf , Kz + Chlai where expressions of light and nutrients limitation functions are given by Ii Ii IPi − IPmin f (Ii ) = exp 1 − , , f (IPi ) = Is Is IPi IN i − IN min I [1 − exp(−ηh)] . f (IN i ) = , Ii = IN i ηh The equation for soluble reactive phosphorus (P) is given by ∂Pi = kr θ T −20 IPi + km θ T −20 (IPi − IPmin ) ∂t T −20 + kOP θO BOD · YPBOD Chlai + kz ZθzT −20 Pf (IPi − IPmin ) Kz + Chlai ASi KDO + SP θST −20 Vi KDO + DOi IPmax − IPi Pi − Chlai UPmax θ T −20 . IPmax − IPmin KP + Pi The equation for ammonia nitrogen (NH) is given by ∂NH i = kr θ T −20 IN i + km θ T −20 (IN i − IN min ) ∂t Chlai (IN i − IN min ) + kz ZθzT −20 Pf Kz + Chlai T −20 BOD · YNBOD + kON θO ASi KDO DOi T −20 + SN θST −20 − kNO θNO NH i Vi KDO + DOi KON + DOi IN max − IN i − Chlai UN max θ T −20 IN max − IN min NH i + NOi × PNH . KN + NH i + NOi


The equation for nitrate nitrogen (NO) is given by IN max − IN i ∂NOi = −Chlai UN max θ T −20 ∂t IN max − IN min NH i + NOi × (1 − PNH ) KN + NH i + NOi DOi T −20 + kNO θNO NH i . KON + DOi The term for preferential ammonium uptake, PNH , is given by PNH = 1 −

NO . NO + NH

The equation for internal phosphorus (IP) is given by ∂IP IPmax − IPi Pi = Chlai UPmax θ T −20 ∂t IPmax − IPmin KP + Pi − kr θ T −20 IPi − km θ T −20 IPi Chlai T −20 − kz Zθz Pf IPi Chlai . Kz + Chlai The equation for internal nitrogen (IN) is given by IN max − IN i NH i + NOi ∂IN = Chlai UN max θ T −20 ∂t IN max − IN min KN + NH i + NOi − kr θ T −20 IN i − km θ T −20 IN i Chlai T −20 − kz Zθz Pf IN i Chlai . Kz + Chlai Equation for dissolved oxygen is given by Wg (C ∗ − DOS ) ∂DO = ∂t h + Gmax θ T −20 Chlai min f (Ii ), f (IPi ), f (IN i ) YOC IN max − IN i NH i + NOi + Chlai UN max θ T −20 IN max − IN min KN + NH i + NOi × (1 − PNH )YNP − kr θ T −20 Chlai YOC + km θ T −20 Chlai YOC DOi − kB θ0T −20 BODi KBOD + DOi DOi T −20 − kNO θNO NH i YON NH i , KON + DOi where C ∗ = 14.652 − 0.41022 · TS + 7.99E − 3 · TS2 − 7.7774E − 5 · TS3 . Equation for biochemical oxygen demand is given by ∂BOD = −km θ T −20 Chlai YOC ∂t DOi + kB θ0T −20 BODi . KBOD + DOi

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Definition of parameters Asi BOD C∗ DO DOS f(I) f(IN) f(IP) Gmax h Ii Is IN IN max IN min IP IPmax IPmin kB km kNO kON kOP kr kz KDO KBOD KN KP KZ KON NH NO P Pf

Area of sediment in contact with a layer (m2 ), Biochemical oxygen demand (mg/l), Saturated oxygen concentration at the surface temperature (mg/l), Dissolve oxygen concentration (mg/l), Oxygen concentration at the surface (mg/l), Light limiting function for growth, Internal nitrogen limiting function for growth, Internal phosphorus limiting function for growth, Maximum growth rate of phytoplankton (day−1 ), Depth of surface layer (m), Mean photosynthetically active radiation in layer (µE m−2 s−1 ), Saturation light intensity of phytoplankton (µ E m−2 s−1 ), Internal nitrogen concentration (mg N/mg Chl-a), Maximum internal nitrogen concentration (mg N/mg Chl-a), Minimum internal nitrogen concentration (mg N/mg Chl-a), Internal phosphorus concentration (mg P/mg Chl-a), Maximum internal phosphorus conc. (mg P/mg Chl-a), Minimum internal phosphorus conc. (mg P/mg Chl-a), Rate coeff. for detrital breakdown (day−1 ), Rate coeff. for mortality of phytoplankton (day−1), Rate coeff. for nitrification (day−1 ), Rate coeff. for mineralization of nitrogen in organic form (day−1), Rate coeff. for mineralization of phosphorus in organic form (day−1), Rate coeff. for respiration of phytoplankton (day−1), Rate coeff. for zooplankton grazing on phytoplankton (day−1), Adjustment for the effect of oxygen on sediment nutrient release (mg/l), Half saturation constant for dependence of detrital decay on DO (mg/l), Half saturation constant for external nitrogen uptake for phytoplankton (mg/m3 ), Half saturation const. for external phosphorus uptake for phytoplankton (mg/m3 ), Half saturation const. for zooplankton grazing (mg/m3), Half saturation constant for effect of oxygen on nitrification (mg/l), Concentration of ammonium (mg/m3), Concentration of nitrate (mg/m3 ), Concentration of phosphate (mg/m3), Preference factor for grazing of zooplankton on phytoplankton,

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SN SP T TS UN max UPmax V Wg YOC YON YNP YNBOD YPBOD Z θ θo θz θNO θS ηB h Chlai


Release rate of ammonia from the sediment (mg m−2 day−1), Release rate of phosphorus from the sediment (mg m−2 day−1), Water temperature (◦ C) Water temperature at surface (◦ C) Maximum rate of nitrogen uptake for phytoplankton (mg N/mg Chl-a/day), Maximum rate of phosphorus uptake for phytoplankton (mg P/mg Chl-a/day), Volume of a layer (m3 ), Transfer velocity of oxygen at surface (m/s), Ratio of mass of oxygen produce or respired to mass of Chl-a, Stoichiometric ratio of oxygen to nitrogen for nitrification, Stoichiometric ratio of oxygen to nitrogen for nitrate reduction, Yield ratio of N due to organic nitrogen decay, Yield ratio of P due to organic phosphorus decay, Zooplankton biomass (mg/m3), Temperature multiplier for growth of phytoplankton, Temperature multiplier for organic decay, Temperature multiplier for zooplankton grazing on phytoplankton, Temperature multiplier for nitrification, Temperature multiplier for sediment nutrient release, Light extinction coefficient for phytoplankton, Thickness of a layer (m), Concentration of chlorophyll-a at layer i.

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