Lake Ecosystem Model Research Articles

A new general dynamic model to predict biomass and production of bacterioplankton in lakes

The main aim of this work is to present a new dynamic model to predict bacterioplankton production and biomass. This model has been developed as a submodel within the framework of a more comprehensive lake ecosystem model, LakeWeb, which is based on nine key functional groups of organisms. Beside bacterioplankton, LakeWeb accounts for phytoplankton, two types of zooplankton (herbivorous and predatory), two types of fish (prey and predatory), as well as zoobenthos, macrophytes and benthic algae. The model uses ordinary differential equations and gives seasonal (weekly) variations and accounts in a general way for all major abiotic/biotic interactions and feedbacks for entire lakes (the ecosystem approach). The new dynamic model has not been calibrated and tested in the traditional way using data from one or a few well-investigated lakes. Instead, it has been calibrated using empirical regressions based on data from many lakes. We have presented empirical reference models utilising data from a new database, which includes many lakes situated in the former Soviet Union. They were investigated during the Soviet period and those results have been largely unknown in the West. The basic aim of the dynamic model is that it should capture typical functional and structural patterns in many lakes. We have given algorithms for (1) bacterioplankton production, (2) elimination (related to the turnover time of bacterioplankton), (3) bacterioplankton consumption by herbivorous zooplankton, and the factors influencing these processes/rates. We have demonstrated that the new dynamic model gives predictions that agree well with the values given by the empirical reference models, and also expected and requested divergences from these regressions when they do not provide sufficient resolution. The new dynamic model is driven by data easily accessed from standard monitoring programs or maps and meant to be of practical use in lake management.

The influence of biomanipulations (fish removal) on the structure of lake foodwebs, case studies using the LakeWeb-model

This paper presents results on how intensive fishing (fish removal) islikely to influence the structure of lake foodwebs. The work is based on acomprehensive dynamic lake ecosystem model, LakeWeb, which accounts forproduction, biomasses, predation and abiotic/biotic interactions of nine keyfunctional groups of organisms: phytoplankton, bacterioplankton, two types ofzooplankton (herbivorous and predatory), two types of fish (prey and predatory),zoobenthos, macrophytes and benthic algae. The model uses ordinary differentialequations, the ecosystem scale and gives seasonal variations (the calculationtime is 1 week). It is designed to account for all fundamental abiotic/bioticinteractions and feedbacks for lakes in general for the nine target groups. TheLakeWeb-model has been calibrated and critically tested using empirical data andregressions based on data from many lakes. It has been shown that the model canclosely capture typical functional and structural patterns in lakes, whichshould give credibility to the results presented in this work. Obtaining suchresults using traditional methods, i.e., extensive field studies in one or a fewlakes, would be very demanding (in terms of money, persons involved and time).In this paper, results are presented for two lakes, one Swedish and oneBelarussian. The intensive fishing operations carried out in LakeBlacksastjarn, Sweden, to reduce Hg-concentrations in fish did notsucceed. A typical cost of an intensive fishing is about 10,000–30,000 USDper lake of this size (≤ 0.25 km2). The costs toremove fish would be about 40–120 USD per kg ww fish removed! Intensivefishing simulated for Lake Batorino, Belarus, to reduce the fish biomass willlikely increase the prey fish biomass as long as the predation pressure on preyfish is lower than during the prefishing stage. The biomass of predatory fishwill recover only slowly. However, this operation is not likely to succeed inlowering the algal volume in lakes with a high biomass of predatory zooplankton.This is easy to state qualitatively and the LakeWeb-model offers a practicallyuseful tool to quantify such changes and identify lakes where biomanipulationsare likely to fail or succeed.

Modelling production and biomasses of zoobenthos in lakes

This work presents a dynamic model to predict zoobenthos in lakes. The model has been developed within the framework of a more comprehensive lake ecosystem model, LakeWeb, which also accounts for the following functional groups of organisms, phytoplankton, bacterioplankton, two types of zooplankton (herbivorous and predatory), macrophytes, prey fish and predatory fish. This work also presents a new data-base for zoobenthos in lakes. Many of the lakes included in this study are situated in the former Soviet Union. They were investigated during the Soviet period and those results have been largely unknown in the West. Using this data-base, this work also presents new empirical models for zoobenthos. The new dynamic model gives seasonal variations (the calculation time, dt, is 1 week using Euler's method and enough iterations to get stable solutions). The basic aim of the dynamic model is that it should capture general functional and structural patterns in lakes. We have demonstrated by several model tests along limnological gradients (total phosphorus concentrations, pH, lake colour, latitude and lake size) that the dynamic model gives predictions that agree well with the values given by the empirical regressions, and also expected and requested divergences from these regressions when they do not provide sufficient resolution. It would have been very difficult indeed to carry out such tests regarding ecosystem responses using traditional methods with extensive field studies in a few lakes. We have given algorithms for (1) production of zoobenthos from eating macrophytes, benthic algae and sediments, (2) elimination (related to the turnover time of zooplankton), and (3) zoobenthos consumption by prey fish, and the factors influencing these processes/rates. The model is driven by data easily accessed from standard monitoring programs or maps a prerequisite for practical utility in contexts of lake management.

Lumbering operations, lake humification and consequences for the structure of the lake foodweb: A case study using the LakeWeb-model for lake Stora Kröntjärn, Sweden

This work presents a scenario to demonstrate how a given lake (Lake Stora Krontjarn, Sweden) would respond to changes in colour related to lumbering operations in its watershed. The questions posed are: How would lake colour values increase, for how long would such increases last and how would this influence the production and biomasses of key functional organisms in the lake? The work is based on a comprehensive lake ecosystem model, LakeWeb, which accounts for production, biomasses, predation, abiotic/biotic interactions of nine key functional groups of organisms, phytoplankton, bacterioplankton, two types of zooplankton (herbivorous and predatory), two types of fish (prey and predatory), as well as zoobenthos, macrophytes and benthic algae. The LakeWeb-model has been calibrated and critically tested using empirical data and regressions for many lakes and it can capture typical functional and structural patterns in lakes. To obtain results like these by traditional field-work in one or more lakes would be very demanding (in terms of money, persons and time). It has been shown that single tributary peaks in colour concentrations are often "drowned" in weekly mean lake values. The lumbering operations must be extensive and continue for a long time to cause significant increases in tributary colour values in order to significantly influence fundamental lake foodweb structures. This means that it is often realistic to assume that lumbering activities do not strongly influence lake foodweb structures. The LakeWeb-model with the given mass-balance model for lake colour can be a useful tool to assess situations when this might not be valid.

ECOBAS — modelling and documentation

Until now modelling and model documentation were two different processes. As a consequence, model documentation was prone to error. It was rarely possible to run larger models from their documentation. Model exchange was limited to simple models due to different languages in which they were created. To facilitate more efficient model creation, documentation and exchange we are introducing ECOBAS system. The system consists of three parts: A standard Model Interchange Format (ECOBAS_MIF), Modelling Assistant (ECOBAS_MA) and a WWW site for exchange of ecological models (ECOBAS_WWW). MIF is an intuitively clear model specification language to create and document models. Apart from specification of mathematical constructs and variables, it contains specification of units, dimensions, environment for which the model was created and validated, methods that were used in measuring variables, addresses of model creators and references. MA ensures that modelling and documentation is done in one step. It guides the user to write a complete and concise syntax, checks units and dimensions, enables handling submodels and exports the source code into different text editors and viewers in the form of ASCII, TEX, PDF, HTML files, languages (FORTRAN) and software packages (SIMPLEX, EXTEND and SciLab, while conversion into other software is planned). WWW site ( http://eco.wiz.uni-kassel.de) is used as a market place to exchange model documents. To demonstrate how MA works we reimplement Rostherne model into MIF (Krivtsov, V., Bellinger, E., Sigee, D., Corliss, J., 1998. Application of sem xrma data to lake ecosystem modelling, Ecol. Model. 113: 95–124).

Numerical study on biological water purification functions of lakes and attached sublakes using a lake ecosystem model

Numerical study on biological water purification functions of lakes and attached sublakes using a lake ecosystem model

Indirect regulation rule for consecutive stages of ecological succession

The lake ecosystem model ‘Rostherne’ allowed a theoretical insight into delayed causal relationships in aquatic ecosystems. Model simulations were used to demonstrate the possibility of influencing a species dominant at a later stage of ecological succession, by alleviating growth limitation of a different species, dominant at an earlier stage. Such delayed relationships are characteristic of various types of systems (including ecological), and can be illustrated by using a simple Stella model presented here. The stated indirect regulation rule for consecutive stages of ecological succession provides an important theoretical basis both for certain ecological manipulations and for the better understanding of various environmental relationships. It should, therefore, prove useful for theoretical analysis of system dynamics, studies of terrestrial and aquatic ecosystems, management of natural resources, Environmental Assessment and Auditing.

Application of SEM XRMA data to lake ecosystem modelling

The model Rostherne represents the first attempt to apply SEM XRMA (scanning electron microscopy X-ray microanalysis) data to lake ecosystem modelling. It considers subsystems proved to be most important for Rostherne mere (Cheshire, UK) with incorporation of uptake dependency of one nutrient upon internal deficiency in another. The model showed a reasonable fit ( R 2=0.87, P<0.001) between measured data and simulation curves for most of the considered variables (i.e. P, Si, chlorophyll- a and algal concentrations in the lake water, nutrient mass fractions of algal cells, etc.) and could, therefore, have been used to estimate some parameters and variables which were not measured otherwise (e.g. sedimentation and growth rates, etc.). The possibility of incorporating alternative expressions for the processes considered is discussed and tasks for future research in relation to coupling of various submodels with the proposed submodel of nutrient uptake are envisaged.

Testing different sub-models for the partition coefficient and the retention rate for radiocesium in lake ecosystem modelling

The partition coefficient ( K d) and the retention rate (RR) are fundamental components of dynamic, mass-balance models, not just for radionuclides in fresh waters but for most contaminants in most ecosystems. K d may be regarded as an ‘entry gate’ and RR and ‘exist gate’. Uncertainties in K d and RR cause uncertainties in model predictions. It also means that uncertainties in important rates for within-ecosystem processes, like sedimentation, diffusion, advection, biouptake and excretion, cannot be adequately evaluated when great uncertainties exist for K d and RR. Empirical data show that Kd may vary two orders of magnitude with environmental factors, like pH. This is important since K d regulates the amount of substances in dissolved and particulate phases and hence also pelagic and benthic transports. The pelagic transport is directly linked to the outflow and retention of substances in the water mass, and thus also to concentrations and ecological effects. There are many approaches for sub-models for K d and RR. Which provide the best predictive power? The aim of this work is to test different approaches for K d and RR, and to discuss benefits and drawbacks of these alternatives within the framework of a lake model for radiocesium (the VAMP model).

A new, simple, general technique to predict seasonal variability of river discharge and lake temperature for lake ecosystem models

The aim of this work is to present a new technique to predict seasonal variability in tributary water discharge, lake water retention rate and lake temperature (surface and deep water temperature and stratification) when empirical data are missing, and the basic objective is to model ecosystem rather than hydrological processes. The main features of the technique are the curves (called the norms) describing the maximum (monthly) variability and the smoothing functions (the moderators) to change the maximum variability of the norms. The smoothing functions are calculated from readily available “map parameters” (latitude, longitude, altitude, mean annual precipitation, catchment area and lake volume). The norms apply to all lakes of a given type. The aims of this work are to present: (1) the new technique to predict seasonal variability in tributary water discharge ( Q); the basic aim is to give an account of the construction of a norm and a seasonal variability moderator; (2) a model based on the same technique to predict seasonal variabilities in surface and bottom water temperature; (3) a model for the retention rate of lake water; (4) sensitivity tests illustrating how these models work, (5) examples how to use these models within the framework of a larger lake ecosystem model; and (6) examples showing that by accounting for the seasonal variability in this way, one can improve the behaviour and predictive accuracy of dynamic lake models. The seasonal moderator technique gives dimensionless expressions that may be used in dynamic models wherever one would like to account for seasonal variability in rates and coefficients. This paper is a technical account of the method. It has, however, been outside the scope to provide thorough empirical calibrations.

The lake ecosystem simulation program

The computer program LAKE simulates a shallow lake ecosystem. The program is based on a mathematical model. In the model the most important aspects of several models for water resources management are integrated (Collins and Wlosinski, 1988; Jørgensen, 1976; Jørgensen et al., 1978; Scheffer, 1988). Furthermore, the model describes several ecological processes that have not yet been described by lake-ecosystem models so far. In the computer program, the mathematical model and an advanced, object oriented, user interface are combined. Following this approach the use of the original research models was extended to a use for the purpose of teaching lake ecology. We suggest that the same approach may be followed to open research models to other groups concerned with water resources management, such as management authorities, industry, agricultural extension, nature conservation and recreation.

Fitting the dynamic model PCLake to a multi-lake survey through Bayesian Statistics

A method is presented for the regression of dynamic lake ecosystem models on multi-lake data. The method draws upon Bayesian Statistics as the main inference engine, as outlined by Box and Draper (1965), M.J. Box (1971) and Box and Tiao (1973/1992). The Bayesian approach allows the calculation of the uncertainty of parameters and predictions both before and after the model is confronted with data. There are several modelling objectives that can be dealt with through this technique in a unifying way: calibration of parameters, on the basis of prior knowledge and the available data; estimation of parameter uncertainty and correlation structure; estimation of predictive uncertainty for the assessment of trends and scenario analyses; validation of model structure in relation to residual errors. Moreover the method allows an iterative approach between hypothesis generation and data analysis. The method is applied to perform a regression and uncertainty analysis of the model PCLake on data from an 18-lake Dutch survey. PCLake is a dynamic nutrient-ecosystem model with a closed nutrient budget, comprising one water and one sediment layer. The model was run until steady state was reached and results were compared to summer-averaged field data from the survey. The output variables selected are chlorophyll- a and total phosphorus concentrations. The analysis was done for three selected parameters, considered uniformly distributed within predefined ranges. Posterior distributions were calculated for each lake on the basis of 125 three-parameter combinations. The residual error of the prediction of chlorophyll- a was reduced from a factor of 3.8 on the basis of the prior uncertainty analysis down to a factor of 2.3 after regression on both variables. For total P concentrations these factors were 1.4 before regression and 1.5 afterwards, hence a small trade-off to match chlorophyll levels. The prior uncertainty factor of mean chlorophyll predictions was reduced from 1.9 before regression to 1.1 after regression on both outputs, while for mean total P predictions these factors were 1.1 and 1.05, respectively. The conclusion can be drawn that chlorophyll- a is particularly sensitive to the three parameters, while total P is determined to a large extent by the lake-specific input parameters. The posterior parameter distributions reflected these differences in sensitivity. Pairwise correlations between parameters were low. Analysis of systematic and case-specific deviations between model regression and data helps to identify other critical parameters and possible structural modifications. It is concluded that through Bayesian Statistics empirical and dynamical water quality modelling can be integrated.

The lake ecosystem simulation program

The computer program LAKE simulates a shallow lake ecosystem. The program is based on a mathematical model. In the model the most important aspects of several models for water resources management are integrated (Collins and Wlosinski, 1988, Jørgensen, 1976; Jørgensen et al., 1978; Scheffer, 1988). Furthermore, the model describes several ecological processes that have not yet been described by lake-ecosystem models so far. In the computer program, the mathematical model and an advanced, object oriented, user interface are combined. Following this approach the use of the original research models was extended to a use for the purpose of teaching lake ecology. We suggest that the same approach may be followed to open research models to other groups concerned with water resources management, such as management authorities, industry, agricultural extension, nature conservation and recreation.

Investigations of the lake ecosystem model emsy by means of the simulation system sonches

A simplified model (EMSY) for shallow eutrophic lakes including phytoplankton, detritus, zooplankton, dissolved inorganic N and P and organic matter in the sediment has been developed and tested on data for three lakes. Comparisons of model results with the measurements of 10 years, as well as with simulation results of a more extended model, were made. They demonstrated the suitability of this simplified model. A further step in modelling will be the coupling of the model EMSY with the river model ERNA to a model of the whole river system. The simulation system SONCHES has been proved as a tool to facilitate the programming and handling of the model.

A Systems Engineering Methodology for Structuring and Calibrating Lake Ecosystem Models

A methodology is presented which makes use of both theory-based and data-based information to structure and calibrate low-order dynamic models for lake ecosystem analysis. A brief historical review explores the inductive and deductive aspects of past modeling efforts and describes the motivation for this research. A methodology, summarized in a flowchart, is discussed in terms of data analysis, conceptualization, development of a mathematical model, calibration, and three feedback stages for validity checks. This approach has been applied to the study of nutrient cycling in the south basin of Lake George, NY. The results of several iterations of the methodology are given and discussed in terms of statistical validity and agreement with biological theory. The final model is a set of difference equations containing two state variables and three external variables, and shows a good fit to the existing data. This is one of the first lake ecosystem studies to make extensive use of data in order to develop model relationships and estimate parameters.

A study of parameter estimation procedures of a model for lake phosphorus dynamics

Theoretical lake ecosystem models are often constructed by synthesis of proven and hypothesized mechanisms. These include parameters that are determined through visual (graphic) or algorithmic procedures of comparing model output with data, and the models are then considered “calibrated”. These models generally include terms nonlinear in system variables and parameters, which leads to nonuniqueness of the parameter determination. We investigate this problem by examination of our procedures applied to a simplified sub-model of phosphorus dynamics in Greifensee. An attempt is made to reduce the ambiguities by a procedure which assigns a weight to parameter self-consistency using additional simulated data. This approach is still open to criticism and additional approaches are proposed for investigation.

A generalized model for simulating lake ecosystems

CLEAN, a generalized lake-ecosystem model with strong ecological realism, has been developed in response to one aspect of the growing need for models suitable for helping man to manage his environment. The model currently consists of twenty-eight ordinary differ ential equations which represent approximately six teen compartments, including attached aquatic plants, phytoplankton, zooplankton, bottom-dwelling aquatic insects, fish, suspended organic matter, decomposers, sediments, and nutrients. These equations can be linked in any meaningful combination to simulate a given point in a lake (a separate model for lake cir culation is available to represent spatial variations and to couple simulations of different regions of the lake). Subprogram functions exist for each principal physiological and ecological process, and a submodel for lake water balance is presently being implemented. The program is written in FORTRAN for UNIVAC and IBM time-sharing systems. The model has provided intuitionally realistic simu lations and has given us insight into the effects of nutrient enrichment on the functioning of the lake ecosystem as a whole. Sensitivity analysis has in dicated priorities for further studies to obtain more precise estimates of parameters. Also, evalua tion of the logic and organization of the model by experimenting with it are providing information to use in planning new experimental approaches. CLEAN is presently being tested using data from Lake George, New York, and Lake Wingra. Wisconsin.