Examples of Ecological Lake Models and Their Application

In this section we give a brief overview of model structures, calibration strategies, and applications of five selected ecological lake models. This overview is far

Table 1 Structure of typical formulations of process rates

Process Structure of rate formulation

Growth of phytoplankton Pgro,ALG = kgro,ALG,max,To ? fT(T) • f/(/) • fN(CN) • Calg

Growth of Zooplankton Pgro,Zoo = kgro,zoo,max,To • fT(T) • fo2 (Co2 ) • fg(CALG) • Czoo

Respiration of phytoplankton or Zooplankton Presp,/ = kresp,i,To • fT(T) • fo2 (Co2 ) • C;,i = ALG, Zoo

Death of phytoplankton or Zooplankton pdeath,i = kdeativjo • fT(T) • C;,i = ALG, Zoo

Oxic mineralization Pminer = kminer,To • fT(T) • fo2 (Co2 ) • CPoM

T, temperature; I, light intensity; CN, nutrient concentration; COz, dissolved oxygen concentration; CALG, concentration of phytoplankton; CZOo, concentration of zooplankton; CPOm, concentration of dead particulate organic material; k, specific transformation rates at reference conditions.

Table 2 Typical formulations of the functions used for describing the dependence of process rates on important influence factors

Formulations

fg(CALG)

VK2 +12

CALG

Rrrefr

KALG + CALG

Name/comment

0 else

Monod Hill

Exponential Blackman

Monod Steele Walker Smith

Monod

Linear Arrhenius

Monod

Exponential for CALG > C0 with threshold from being complete. Nevertheless, it provides insight into the variety of approaches used in science and management. We will briefly present an aggregated trophic-level lake model (biogeochemical - ecological lake model, BELAMO), two functional group lake models (simulation by means of analytical lake model, SALMO and computational aquatic ecosystem dynamics model, CAEDYM), a dominant-species algal community model (phytoplankton response to environmental change model, PROTECH), and an adaptive property model (structural dynamics model).

BELAMO

The BELAMO represents a relatively simple, aggregated trophic-level lake model with emphasis on biogeochemical cycles rather than ecology. A particular feature is the consideration of closure of element cycles by explicit consideration of mineralization processes in the sediment.

Model overview

BELAMO describes the concentrations of phytoplankton, zooplankton, dissolved oxygen, ammonium, nitrate, phosphate, and degradable and inert dead organic particles in the water column and in the sediment. The model considers growth, respiration, and death of phytoplankton and zooplankton, mineralization, nitrification, and phosphate uptake on sinking particles. The model is 1D and resolves the depth of the lake. The physical processes vertical mixing, advection, sedimentation, mobility of zooplankton, and molecular diffusion in the sediment and across the water sediment interface are considered. Phytoplankton can grow with a variable stoichiometry with respect to phosphorous depending on the phosphate concentration in the water column to describe the low phosphorus content of phytoplankton growing during phosphate-limited periods in summer.

Calibration strategy

BELAMO applications estimate kinetic parameters of transformation processes with the attempt of finding 'universal' values across lakes of different trophic state. As all phytoplankton species are aggregated to a single state variable, it is hard to use kinetic parameters measured for selected cultured species in this model. To avoid nonidentifiability problems during the parameter estimation, sensitivity, and identifiability analysis techniques are used.

Model applications

BELAMO so far has been applied to three lakes of different trophic state. It is a research model to summarize knowledge and test hypothesis with a focus on biogeo-chemical cycles.

Figure 3 shows measured and calculated profiles of phytoplankton, dissolved oxygen, phosphate, and nitrate in Greifensee.

The profiles clearly demonstrate the yearly cycle of mixing and stratification and its effect on the nutrient cycle. Phytoplankton shows a first maximum in spring, followed by a second in summer. Dissolved oxygen concentrations are nearly uniform in spring; during summer stratification, there is a strong oxygen depletion in the hypolimnion. Phosphate is not limiting phytoplankton growth in spring, but is during the summer and fall months. There is a significant increase in phosphate concentrations in the hypolimnion during the summer and fall months due to mineralization of organic particles in the sediment. Nitrate shows a severe depletion in the deep hypolimnion during the stratification period primarily due to anoxic mineralization in the sediment.

SALMO

SALMO represents a functional group lake model. The emphasis is on a very detailed description of the plankton growth dynamics. Recently SALMO was extended to

SALMO-HR (high resolution). In this version the ecological model is coupled to a hydrothermodynamic model of the water column.

Model overview

SALMO describes orthophosphate, dissolved inorganic nitrogen, dissolved oxygen, organic particles, three functional groups of phytoplankton, and zooplankton concentrations in a lake. The processes growth and mortality of phytoplankton and zooplankton and mineralization are considered. Sedimentation of phytoplankton and migration of zooplankton is also modeled.

SALMO was designed to mechanistically describe physical, chemical, and biological processes according to a maximum of generality. The model uses only a small number of state variables but more complex process formulations than other models in order to achieve this goal. Each functional group of phytoplankton is characterized by an indicator species, the properties of which were measured or compiled from the literature. Fish are considered implicitly by their predation rate on zooplankton. The nutrient release from the sediment is modeled as an empirical function of oxygen depletion and denitrification.

SALMO describes the water body as two mixed reactors representing the epilimnion and the hypolim-nion. The depth of the epilimnion has to be specified as a boundary condition. SALMO-HR uses a very detailed hydrothermodynamic model of the water column.

April April June June

O2(mgl

10 15 20 25 30 35

PO4 (mg P l-1) 0.5

10 15 20 25 30 35

r 15 f20

o 25

30 35

r 15 f20

o 25

30 35

Figure 3 Lake data (markers) compared with simulation results (lines) of the model BELAMO. Profiles of phytoplankton, dissolved oxygen, phosphate, and nitrate in Greifensee are shown for the year 1989. From Mieleitner J and Reichert P (2006) Analysis of the transferability of a biogeochemical lake model to lakes of different trophic state. Ecological Modelling 194: 49-61.

Calibration strategy

In contrast to most other ecological lake models, the parameters of SALMO are not fitted. Measured values are used for all parameters. The parameter values for phytoplankton growth are determined in the laboratory for key species of each functional group.

This strategy not to calibrate the model has the advantage that the parameters are not adapted to a specific lake at a specific time and the parameters are universal for that reason. This improves the prediction quality and the generality of the model.

Model applications

SALMO is used as a tool to improve the understanding of the ecosystem and to support management decisions. It has been successfully applied to more than 20 lakes and reservoirs of different trophic states and has been used to calculate scenarios for different discharge regimes, climate change scenarios, changing nutrient input, and biomanipulations.

Figure 4 shows an example of an application of SALMO to the Bautzen Reservoir, Germany. The agreement between calculated and measured concentrations achieved without modifying model parameters is remarkably high. This example shows the interactions between phytoplankton and zooplankton and the depletion of phosphate during the summer.

CAEDYM

The CAEDYM is an ecological model that can be linked to different hydrodynamic models. In our list of example models, CAEDYM represents a functional group lake model of very high degree of resolution of ecosystem variables and processes. This is a chance for a detailed representation of many processes and mass fluxes, but also a challenge with respect to the number of model parameters and to calibration.

40 30 20 10

200 150 100 50

JFMAMJJASOND TS BAUTZEN - 1978

Figure 4 Application of SALMO to the Bautzen Reservoir. Simulated and measured concentration time series of total phytoplankton biomass (top), dissolved phosphate (middle), and zooplankton (bottom) for the mixed layer of the hypereutrophic Bautzen Reservoir. From Benndorf J and Recknagel F (1982) Problems of application of the ecological model SALMO to lakes and reservoirs having various trophic states. Ecological Modelling 17: 129-145.

JFMAMJJASOND TS BAUTZEN - 1978

Figure 4 Application of SALMO to the Bautzen Reservoir. Simulated and measured concentration time series of total phytoplankton biomass (top), dissolved phosphate (middle), and zooplankton (bottom) for the mixed layer of the hypereutrophic Bautzen Reservoir. From Benndorf J and Recknagel F (1982) Problems of application of the ecological model SALMO to lakes and reservoirs having various trophic states. Ecological Modelling 17: 129-145.

Model overview

The ecosystem model implemented in CAEDYM is based on a detailed description of the ecosystem. The user can choose between different ecological configuration options and use a different model for each specific application. CAEDYM can be used for freshwater, estuaries, or coastal waters. The model gives the user a large flexibility in the choice of state variables, processes, and process formulations.

The state variables that can be used include concentrations of dissolved oxygen, ammonium, nitrate, phosphate, silica, dissolved inorganic carbon, quickly and slowly degradable dissolved and particulate organic matter, up to two groups of inorganic suspended solids, bacteria, up to seven groups of phytoplankton, up to five groups of zooplankton, up to five groups of fish, and pathogens in the water column, up to four groups of benthic macroalgae, seagrass, up to three groups of benthic invertebrates, and up to seven groups of benthic algae and others. The nonliving components in the water column are also modeled in the sediment. Process descriptions for primary production, secondary production, nutrient and metal cycling, and oxygen dynamics and exchange with the sediment are included in the model. CAEDYM can be coupled to 0D, 1D, 2D, and 3D lake hydrodynamics programs. It can be coupled to DYRESM (a 1D hydrodynamic model for lakes and reservoirs) or ELCOM (a 3D hydrodynamic model).

Calibration strategy

CAEDYM studies follow the reductionist approach with a detailed, general lake ecosystem model. Model parameters are fitted, but the attempt is made to find 'universal'

values that do not depend on the particular application. In typical applications, most parameters are held constant, some are fitted jointly for several systems, and some may need site-specific calibration.

Model applications

CAEDYM has been applied to many lakes and reservoirs. It is used by many research groups and can be downloaded as freeware.

CAEDYM has been used to evaluate different management strategies, to quantify nutrient cycles, and other processes.

Figure 5 shows an application of the model to the Prospect Reservoir in Sydney, Australia. The simulations qualitatively and quantitatively reproduce the measurements with some problems in the concentrations of phytoplankton.

PROTECH

The PROTECH describes the phytoplankton growth in lakes at the species level. The emphasis of this model is on describing the dynamics of phytoplankton composition in a wide range of different ecosystems.

Model overview

PROTECH is designed to make simulations of the dynamic changes in the populations of different species of phytoplankton within a reservoir or lake environment which may be subject to thermal stratification, periodic destratification, and hydraulic exchange.

Chlorophyll a, phosphorous, nitrogen, and silica are modeled. The phytoplankton model is very detailed; up to eight species can be selected from a library of 18 phytoplankton species. The effect of zooplankton is described by the death rate of phytoplankton. The maximum growth rate of the different phytoplankton species is calculated using correlations with surface area and volume of the species. Adjustments for temperature dependence, light limitation, and nutrient limitation are made.

The physical model is 1D. It divides the water body into mixed layers.

Calibration strategy

The parameters for the growth of the phytoplankton species are not fitted in PROTECH. However, the choice of considered species is site specific.

1988

Year

1989

1988

Year

1989

1988

Year

1989

1988

Year

1989

Figure 5 Simulation results of the model CAEDYM. Comparison of measured time series with 1D simulations of the Prospect Reservoir at 2 m (black symbols, thin line) and 17 m depth (white symbols, thick line). From Romero JR, Antenucci JP, and Imberger J (2004) One- and three-dimensional biogeochemical simulations of two differing reservoirs. Ecological Modelling 174: 143-160. The panels show temperature (a), dissolved oxygen (b), filterable reactive phosphorus (c), total phosphorus (d), nitrate (e), ammonium (f), total nitrogen (g), and chlorophyll a (h).

Model applications

PROTECH has been applied to different lakes across the world. It has been used to explore ecological theory, to assess the reactions of phytoplankton to changes in temperature and nutrient concentrations, and to support management decisions. It was also coupled to a climate model and to predict the changes in phyto-plankton communities due to climate change. Figure 6 shows a comparison of measured functional groups of phytoplankton with PROTECH simulations. The changes of chlorophyll a concentrations of two functional groups are shown. In the spring there is a bloom of R species, followed by a period with low phytoplankton concentrations and a bloom of CS species during the summer. The correspondence of the model results with the data is remarkable. In general, the correspondence is better at the functional group level than at the species level.

Structural Dynamic Model

Structural dynamic modeling is an approach that represents an adaptive property model in our list of example models. See more details under Structural Dynamic Models.

Model Overview

Structural dynamics modeling is one of the approaches to consider adaptive processes in ecosystem models. The approach is based on the hypothesis that an ecosystem tends to move away from thermodynamic equilibrium.

This is quantified by exergy, defined as the amount of work that a system can perform when it is brought into thermodynamic equilibrium with its environment.

Modeling Approach

During the calibration period, some model parameters are adapted dynamically to maximize exergy while reducing the residuals. This leads to time-dependent parameters.

Example Application

Figure 7 shows a comparison of a conventional modeling approach, a structurally dynamic modeling approach, and a further improved simulation with data. It is evident, that the structurally dynamic model fits the data much better than the conventional calibration.

0.03

1: observations a: usual calibration b: structurally dynamic c: further caibration 1

1: observations a: usual calibration b: structurally dynamic c: further caibration 1

180.00

360.00

Figure 7 Time series of phytoplankton. Comparison of data with simulations from Zhang J, Jorgensen SE, Tan CO, and Beklioglu M (2003) A structurally dynamic modelling - Lake Mogan, Turkey as a case study. Ecological Modelling 164(2): 103-120.

0.00

90.00

180.00

270.00 Time (days)

360.00

450.00

Figure 7 Time series of phytoplankton. Comparison of data with simulations from Zhang J, Jorgensen SE, Tan CO, and Beklioglu M (2003) A structurally dynamic modelling - Lake Mogan, Turkey as a case study. Ecological Modelling 164(2): 103-120.

Z 30

20 10 0

CS (real data) R (real data) CS (PROTECH) R (PROTECH)

0 50 100 150 200 250 Days from 1/1/74

Figure 6 Time series of data and PROTECH model results for two functional groups of phytoplankton. Phytoplankton is divided into R-strategists (ruderals) and a CS-group (intermediate group of competitive C-strategists, stress-tolerant S-strategists). From Elliott JA, Irish AE, Reynolds CS, and Tett P (2000) Modelling freshwater phytoplankton communities: An exercise in validation. Ecological Modelling 128(1): 19-26.

See also: Death; Decomposition and Mineralization; Respiration; The Significance of O2 for Biology.

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