Qualitative assessment - Current research topics within “eutrophication-based ecological modelling”

A modelling software usually aids the development of an ecological model, but the level of dependence on the modelling software depends on the modeller's comfort (Jackson et al.

2000). There is a broad spectrum of modelling software available to the modeller. On one end of the spectrum, there are general programming languages such as C, Basic, FORTRAN, Pascal, etc., which give the user complete freedom over the model construction but at the same time total responsibility of handling all the tedious details. At the other end of the spectrum, user- friendly modelling software with attractive graphical interfaces such as STELLA, Simulink, ModelMaker, etc., give the user freedom from handling the underlying implementation details that have limitations over model construction. Between these two extremities lies several programming packages such as MATLAB and spreadsheets, which provide different functions to ease the user from handling programming details while at the same time allowing some control to the modeller.

Different ecological models can be broadly categorised into the white box and black box models (Jørgensen & Bendoricchio 2001). The white box model is one in which the causality of the input-output relation is known. On the other hand, a black-box model does not explain why a particular behaves in a specific manner for a given input. In practice, most models can be described as grey models as they combine white and black box models. Jørgensen and Bendoricchio (2001) further made another classification of the ecological models based on their application given in the following list.

▪ Biogeochemical and bioenergetics dynamic models

The biogeochemical and bioenergetics dynamic models are mostly white-box models, which apply the principles of mass and energy conservation to develop the differential equation.

These models are easy to understand, interpret and develop, but a relatively good database is required and becomes challenging to calibrate when many parameters are involved in the model. Eutrophication models are a type of biogeochemical models.

▪ Steady-state biogeochemical models

The steady-state biogeochemical models are used when the database for model construction is small, but these models fail to give any information about the ecosystem's behaviour with the change in time.

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▪ Population dynamic models

The population dynamic models are one of the most popular ecological models that can pre- dict the development of a population with time, incorporating the age structure and impact factors. However, there is a requirement for a relatively good and homogenous database.

▪ Structurally dynamic models

The structurally dynamic models allow modellers to incorporate dynamic parameters, con- sidering the adaptation factor of different species and shift in the species composition. How- ever, there is a need for goal function or artificial intelligence for this model to work correctly, making this model time-consuming.

▪ Fuzzy models

As the name suggests, the fuzzy models apply to a fuzzy dataset and semi-quantitative infor- mation (linguistic formulation). These models are not suitable for complex model formula- tion.

▪ Artificial Neural Networks

Artificial neural networks can be described as black-box models, which requires a sizeable heterogeneous dataset from different ecosystems or a homogenous dataset from a specific ecosystem to represent the relationship between the state variables and forcing functions of the model.

▪ Spatial models

The spatial models are those models that show the spatial distribution of different processes, forcing functions and state variables. GIS can be used to describe those models.

▪ Individual-based models

The individual-based models consider the uniqueness of the different individuals within a species, which, though disregarded in biogeochemical models, may be vital for the survival of that species. These models can be very complex.

▪ Ecotoxicological models

Ecotoxicological models are, basically, biogeochemical or population dynamic models that are being applied to ecotoxicology. These models earn a particular place in classification due to limited knowledge of ecotoxicological parameters and the use of safety factors.

▪ Stochastic models

Stochastic models incorporate randomness either in forcing functions or model parameters.

A stochastic model can be any of the previously described models with randomness factored in it.

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▪ Hybrid models

Hybrid models are a combination of any two previously described models. Such models bring the dual advantage of coupling the advantages and minimising the disadvantages of the par- ent models. One example of the hybrid model is the outcome of combining a biogeochemical dynamic model and an ANN model.

In the following part of this section, some of the developments in ecological modelling, especially in eutrophication modelling since the 1980s, are discussed.

Scavia (1980) developed an ecological model consisting of epilimnion, hypolimnion and sediments of Lake Ontario that simulates various state variables such as phytoplankton, zoo- plankton, different forms of nitrogen, phosphorus, silicon, carbon, dissolved oxygen, particu- late sediment and pore water dynamics. This ecological model illustrated the significance of detritus and herbivorous zooplankton in the lake, thereby serving as an analytical tool for the large ecosystem.

Matsuoka et al. (1986) developed a mathematical model to predict the fate of nutrients among four levels, with fourteen state variables in each segment, for Japan’s largest shallow lake, Kasumigaura that was suffering from the problem of artificial eutrophication caused by urbanization, agricultural growth and fishing culture. These state variables included phyto- plankton, zooplankton, fish, crustacean, external nutrients and fresh sediments. One of the highlights of this eutrophication model is that most of the parameter values were based on the in-situ measurements and batch-culture experiments using strains from the lake while calibrating the model. This model was applied as a predictive device to get the nature of water quality in the future.

Dejak et al. (1987) integrated a two-dimensional diffusion model with a two-dimensional advection model for the lagoon of Venice to develop a three-dimensional model which is ca- pable of simulating the dispersion of eight state variables: phytoplankton, zooplankton, am- monia, nitrites and nitrates, degradable organic compounds and temperature. The three-di- mensional eutrophication model can estimate the eddy diffusion constant that incorporates the tide's dispersion action.

Lake Taihu is among the five largest freshwater lakes in China that have been severely affected by eutrophication since the 1980s. Different models have been developed to study this lake, such as Hydrodynamic models, Mass transportation and cycling models and ecolog- ical models. The first ecological model was developed by Dou et al. (1995) to link the hydro- dynamic aspects of the lake to chemical and biological processes occurring in the lake. The entire lake was divided into thirty sub-zones, and various sub-models were developed for

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each sub-zone. In 1999, Hu created another model for eutrophication in Lake Taihu. It was one of the earliest versions of the EcoTaihu model (Hu 2016). This three-dimensional model was developed by combining another three-dimensional hydrodynamic model (Hu et al.

1998a; Hu et al. 1998b), a model describing the impacts of water hyacinth on the water qual- ity of Lake Taihu (Hu et al. 1998c) and a model based on a physio-biological engineering ex- periment for water purification using Trapa natans var. bispinosa (Hu et al. 1998b). This model was further developed by incorporating the carbon cycle, which allowed the depiction of pH in the lake and revealed that the lake acted either as a sink or as a source at different times (Zhang et al. 2008; Weiping et al. 2011). In 2010, another improvement was incorpo- rated into the EcoTaihu model by redefining the sub-model for fish. This improved model re- vealed that by introducing the fish into the lake, the production of the released fish could in- crease and change the population structure in the lake. This model also revealed that by re- leasing certain species of fish, the nature of the lake could also be changed. For example, if the Ctenopharygodon idellus was released, it could temporarily curb the fast-growing macro- phytes population. On the other hand, if the grass carp was released into the lake, it bolstered the phytoplankton and algae population. Zhang et al. (2013) further improved the EcoTaihu model by incorporating an additional layer of algae to explain the movement and disappear- ance of the mat-like algal bloom on the surface of water under weak and strong wind respec- tively.

Karul et al. (2000) developed a three-layered Levenberg-Marquardt feed-forward learning algorithm to develop eutrophication models for three water bodies of Turkey ― Keban Dam, Mogan and Eymir Lakes. To develop neural networks, the eutrophication phenomenon was converted into an input-output problem and data for the input layer was collected through an extensive six-year-long field-monitoring program. The input parameters for the Keban Dam were phosphate, nitrate, alkalinity, suspended solids, pH and water temperature, electrical conductivity, dissolved oxygen and Secchi depth. For the Mogan and Eymir Lakes, the authors' input parameters were total phosphorus, nitrate and ammonia, the temperature in water, electrical conductivity, pH, turbidity, Secchi depth, and suspended solids. Suspended solids, turbidity and Secchi depths were considered in the neural network to simulate the role of light in the euphotic zones. Chlorophyll-a was selected as the primary target output for the network. Additionally, three typical eutrophication indicators, Cyanophyceae species, Aphani- zomenon sp., Microcystis sp. and Oscillatoria sp., were used as target outputs. The so developed eutrophication models' results revealed a relatively good correlation between calculated and measured values for Keban Dam and a high correlation between the same for the much smaller and more homogenous Mogan and Eymir Lakes.

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Drago et al. (2001) used a three-dimensional model, TROPHY3D, to analyse the advection and diffusion of suspended solids and conservative pollutants in the ambient water and their effect on trophic behaviour. The TROPHY3D model used a finite difference method for spatial integration and a Runge-Kutta-IV or Euler method for temporal integration of the differential equations used in the model. The model was also able to predict the biochemical interactions between detritus, phytoplankton, nutrients, zooplankton and dissolved oxygen.

Rukhovets et al. (2003) developed a new three-dimensional mathematical model for Lake Ladoga, the largest freshwater European lake located in north-western Russia, to simulate phytoplankton growth. In this model, the authors selected fourteen state variables that in- cluded different phytoplankton complexes, zooplankton, dissolved organic matter, detritus, dissolved mineral phosphorus and dissolved oxygen. It is based on the ideas of phytoplankton succession in the lake given by Petrova in the 1980s (Rukhovets et al. 2003). Prior to this model, Menshutkin and Vorob’eva (1989) successfully created a one-box model for eight dif- ferent groups of phytoplankton communities in the Volkhov Bay. This model incorporated the temperature conditions of the lake as well as the nutrient supply, but it failed to consider the fact that the zooplankton and fish eat phytoplankton. Moreover, the modellers assumed in- stantaneous mixing of the nutrients in the lake. The new three-dimensional model was an improvement of the works done by Menshutkin et al. (1998) with a more detailed description of the phytoplankton community. Zhang et al. (2003) also developed a structurally dynamic eutrophication model for Lake Mogan, Ankara, Turkey, which was able to describe the com- petition between phytoplankton and submerged plants in the lake. In this model, the energy was used as a goal function to develop the dynamic adaptation and seasonality of plankton species.

Malmaeus and Håkanson (2004) developed an extensive dynamic model to predict the phosphorus concentration and the consequences of eutrophication on the lake ecosystem.

The model is called Lake Eutrophication, Effect, Dose, Sensitivity model (LEEDS). It was de- veloped with easily accessible lake variables. The LEEDS model was novel in many ways. It incorporated two levels for colloidal phosphorus, a seasonal factor for lake outflow, higher settling velocity for re-suspended material, a new algorithm to model the mixing between deep water and surface water, and phosphorus diffusion from sediment areas accumulation.

Trolle et al. (2008) used the one-dimensional lake ecosystem model, DYRESM-CAED, to know the effect of total phosphorus loading reduction on moderately deep lake Ravn's eco- system dynamics in Denmark. The model was calibrated with the observed data for oxygen and temperature for seven years and then validated for another period of five years. When

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put to use, the DYRESM-CAED was able to predict that a significant reduction in total phos- phorus is needed to meet the phytoplankton biomass concentration as per the European Un- ion Water Framework Directive (WFD).

Mukherjee et al. (2008) developed a model representing the carbon dynamics in a simu- lated pond in Ranchi, India, for cultural eutrophication assessment. The model mainly in- cluded processes such as respiration, decomposition and photosynthesis that play an essen- tial role in the nutrient dynamics of the system. In eutrophication models, it is usually chal- lenging to model the carbon cycle in detail, but this model successfully shows that the de- pendence of nutrients processes on an accurate and detailed description of the carbon cycle.

Taguchi and Nakata (2009) developed a numerical model that highlighted the role of mac- rophytes colonies in the shore zone in water purification. The model was applied to Lake Suwa, Lake Kasumi, Lake Biwa and some small lakes attached to Lake Biwa. The model in- cluded interactions between the compartments of pelagic and benthic regions. Meteorologi- cal and hydrodynamic conditions were considered among the forcing functions. The out- comes of the model were reported to have good agreement with the observed values obtained from the water quality monitoring campaign.

He et al. (2011) developed a numerical model based on the environmental fluid dynamics code (EFDC) for Beijing Gaunting Reservoir. Three state variables for phytoplankton species, cyanobacteria, green algae and diatom, were considered for the model and vertical tempera- ture profiles, chlorophyll-a and nutrient concentrations in the water column were used during model calibration. The model so developed was put to use as an investigative tool, which re- vealed that the peak chlorophyll-a could be reduced by reducing external loadings of nutrients with constructed wetlands, bio-manipulation or diverting water from the Cetian Reservoir.

However, one of the significant shortcomings of this model is that it was calibrated with only one year of data, and therefore, it was capable of reflecting only the short-term effects of ap- plying management scenarios.

Xu et al. (2013) developed a structurally dynamic model based on the software Pamolare- II for the Baiyangdian Lake in North China. Pamolare (Planning and Management of Lakes and Reservoirs) is a modelling software developed by the International Environmental Technol- ogy Centre of UNEP (IETC-UNEP) and International Lake Environment Committee (ILEC), which offers four eutrophication models with different complexity levels. The first model is the Vollenweider plot with one state variable of phosphorus or nitrogen loading in g/m²/year.

The second model contains four state variables. The state variables are nitrogen and phos- phorus in water and sediments. Several correlations were also provided to calculate other state variables. The third model is more complicated than the previous two models, providing

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a two-layer model with 21 state variables. The fourth model is an improvement of the third model with the application of the structurally dynamic approach. Pamolare-II is the next ver- sion of the Pamolare software, which provides structurally dynamic models focusing on shal- low lakes for eutrophication lake management. The Baiyangdian Lake model was developed by Xu et al. (2013) to predict the ecological health condition of the lake under different sce- narios of submerged plant removal from the lake. The ecological health conditions were indi- cated by phytoplankton biomass, the ratio of zooplankton to phytoplankton biomass, eco-ex- ergy and structural eco-exergy. The conceptual diagram of the Baiyangdian Lake model in- cluded 12 state variables correlated by 45 processes.

Magnea et al. (2013) developed a simplified mathematical model to describe the phospho- rus, phytoplankton, zooplankton and fish dynamics in the alpine lake ecosystems. The model was developed to study the scenario when brook trout (Salvelinus frontinalis) were intro- duced artificially in the lake ecosystems. The model so developed was used to study twelve alpine lakes in Gran Paradiso National Park, Italy.

Zouiten et al. (2013) developed a mathematical eutrophication model called Environmen- tal Hydraulics Institute Eutrophication Model (EnvHydrEM), especially for coastal regions, which considered 19 state variables including phytoplankton, different forms of carbon, ni- trogen, phosphorus and silica, carbonaceous organic matter, zooplankton, bacterioplankton, detritus, iron and manganese. The EnvHydrEM described all the possible interactions be- tween the defined state variables by considering all the biological and chemical processes in- volved in the ecosystem. It was further applied in the Victoria lagoon in Northern Spain to gauge its efficiency.

Prokopkin et al. (2014) developed an investigative mathematical model to confirm the presence of a phytoflagellate population in the stratified Lake Shira, Khakasia in Russia by considering the microbial dynamics and phytoflagellate relationship with the trophic levels of the lake. The outcome of such a model was that it confirmed the abundant presence of cryptographic algae in the water column, above the chemocline, in the summer season. This 1-dimensional model is a perfect example of how modelling can corroborate certain species in the ecosystem, which otherwise has indirect evidence of presence.

Xu et al. (2014) developed a simple yet effective eutrophication model, using parameters based on both literature survey and experimental investigation, that incorporated the knowledge on bioaccumulation and algal growth for eutrophication in Xikeng Reservoir, Shenzhen City, China. The authors combined the cumulative effects of meteorological factors, water quality factors and biological factors on eutrophication to develop such a cumulative

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eutrophication risk evaluation model. The highlight of this model is that a large set of param- eters and experiments to simulate the eutrophication process is not a prerequisite for its func- tioning.

Li-kun et al. (2017) developed a two-dimensional eutrophication model for an urban lake in the Tianjin region to describe the spatiotemporal variation of water quality and establish relationships between phytoplankton, zooplankton and nutrients. Navier-Stokes equations and finite volume method were used to define the hydraulic model, and the Bayesian method was employed for model calibration and parameter posterior distribution acquisition. The model simulated five state variables that included phosphate, nitrate, ammonia, chlorophyll- a and dissolved oxygen. The calculations from the two-dimensional model revealed higher values for the state variables in the regions closer to the lake periphery than at the centre, indicating the significant role of nutrient loading of rainfall-runoff on algal growth and water quality. Thus, the 2-dimensional model was able to provide crucial information that can result in an effective management strategy to counter severe eutrophication in urban lakes.

Das et al. (2018) developed a mathematical model to simulate the phytoplankton distribu- tion and nutrient cycle along the River Jagaddal, which is an easterly branch of the Saptamu- khi East Gulley of the Saptamukhi River in Sundarbans Estuarine System, India. The authors designed their model based on the compartmental ecosystem model developed by Fasham et al. (1990). Their model considered phytoplankton and nitrate in the water column as two state variables. The differential equations for these state variables were based on Haney and Jackson (1996). The authors further carried out a sensitivity analysis of their model based on a variance-based sensitivity analysis method. Through sensitivity analysis, they understood the crucial parameter of the model and, in turn, predicting the underlying ecological process involved for such an influence. The model equations were integrated using the fourth-order Runge-Kutta algorithm, implemented by the C++ programming language. The sensitivity anal- ysis was carried out in MATLAB.

McCullough et al. (2018) developed a relatively simple, dynamic, mass balanced model, incorporating five state variables of different forms of organic carbon and dissolved oxygen to investigate the dominance of allochthonous organic carbon in the organic carbon dynamics of a lake in the long run. The model so developed was validated in five different lakes in the U.S.A and Canada. McCullough et al. (2018) also used the model to predict the seasonal varia- tion in organic carbon budgets.

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