Lake Eutrophication Model Research Articles

A generically parameterized model of Lake eutrophication: The impact of Stoichiometric ratios and constraints on the abundance of natural phytoplankton communities (GPLake-S)

Water quality improvement to avoid excessive phytoplankton blooms often requires eutrophication management where both phosphorus (P) and nitrogen (N) play a role. While empirical eutrophication studies and ecological resource competition theory both provide insight into phytoplankton abundance in response to nutrient loading, they are not seamlessly linked in the current state of eutrophication research. We argue that understanding species competition for multiple nutrients and light in natural phytoplankton communities is key to assessing phytoplankton abundance under changing nutrient supply. Here we present GPLake-S, a mechanistic model rooted in ecological resource competition theory, which has only eight parameters and can predict chlorophyll-a to nutrient relationships for phytoplankton communities under N, P, N+P colimitation and light limitation. GPLake-S offers a simple mechanistic tool to make first estimates of chlorophyll-a levels and nutrient thresholds for generic lake properties, accounting for variation in N:P ratio preferences of phytoplankton species. This makes the model supportive of water management and policy.

Critical load of phosphorus in reservoirs of a tropical semi‐arid region

The over-enrichment of water bodies by nutrients and the increase in primary production is a natural process that happens slowly, however, this process has been occurring in recent decades rapidly, due to the increase in the external load of anthropogenic nutrients, mainly phosphorus. Lake and reservoir eutrophication models seeking to calculate the critical load of phosphorus often do not consider the temporal variation in water volume. In this study, a dynamic model was used to estimate critical loads of phosphorus from six reservoirs in Brazil's semi-arid region, all of which experience great water volume variation, to describe the variation in water balance together with the variation in phosphorus mass balance. The critical load of phosphorus was defined as the load that guaranteed total phosphorus concentrations of up to 30 mg/m3 throughout 90% of the simulation period. A total of 40 scenarios were simulated and combined two vertical flows of phosphorus, five concentrations of phosphorus in the affluent volumes, and four water demands. Results revealed that the critical load of phosphorus was strongly affected by water demand, what pose a strong dilemma toward the operation of reservoirs in the semi-arid region of Brazil between rationing stored water for use in long periods of drought or stimulating water use to increase water turnover rates. The critical load of phosphorus was also affected by phosphorus concentration in affluent volumes, and the vertical flow of phosphorus between the sediment and water columns. The findings of this study can help for better understanding of the impact of temporal variations in lake and reservoir water volumes to define critical loads of phosphorus more accurately and control eutrophication more effectively in these environments.

Dynamics of a lake-eutrophication model with nontransient/transient impulsive dredging and pulse inputting

In this work, we present a lake-eutrophication model with nontransient/transient impulsive dredging and pulse inputting. We obtain globally asymptotically stable conditions for the phytoplankton-extinction periodic solution of system (2.1). Furthermore, we gain the permanent conditions for system (2.1). Finally, we employ computer simulations to illustrate the results. Our results indicate the effective controlling strategy for water resource management.

Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication

Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.

A combination method for multicriteria uncertainty analysis and parameter estimation: a case study of Chaohu Lake in Eastern China.

Eutrophication models are of great importance and are valuable tools for the development of policy and legislation. However, the parameter uncertainty and substantial computational cost lead to difficulties in decision-making, especially for complex models with multiple indicators. A multicriteria uncertainty analysis and parameter estimation (MUAPE) method, which selected behavioral parameters combined with Pareto domination and simultaneously obtained acceptable values for modeling by the maximum likelihood concept and kernel density estimation, was shown. This method, which did not assign thresholds and weights, was applied to analyze the uncertainty of the Chaohu Lake eutrophication model and estimate parameters. The results of the behavioral parameters were compared using different criterion sets, the relative error (RE) and the root mean square error (RMSE), and the results showed little discrepancy in terms of the effects on parameter uncertainty represented by the marginal probability density. The uncertainties of the parameters related to algal kinetics (i.e., BMR, PM, and KESS) were smaller than those of nutrient- and temperature-related parameters (i.e., KDN, Nitm, KTB, and KTHDR) for both sets of criteria. However, the reduction in the joint uncertainty of the two parameters was greater when RE was used than when RMSE was used. The acceptable values for the key parameters of the Chaohu Lake eutrophication model were also obtained by the RE criterion. The results strongly agreed with the observed values, and parameters could be applied for model prediction. This result indicated that the combination method was not only practical for reducing parameter uncertainty but also useful for determining parameter values. This method provides a basis for multicriteria uncertainty analysis and parameter estimation in eutrophication modeling.

Time scale of resilience loss: Implications for managing critical transitions in water quality.

Regime shifts involving critical transitions are a type of rapid ecological change that are difficult to predict, but may be preceded by decreases in resilience. Time series statistics like lag-1 autocorrelation may be useful for anticipating resilience declines; however, more study is needed to determine whether the dynamics of autocorrelation depend on the resolution of the time series being analyzed, i.e., whether they are time-scale dependent. Here, we examined timeseries simulated from a lake eutrophication model and gathered from field measurements. The field study involved collecting high frequency chlorophyll fluorescence data from an unmanipulated reference lake and a second lake undergoing experimental fertilization to induce a critical transition in the form of an algal bloom. As part of the experiment, the fertilization was halted in response to detected early warnings of the algal bloom identified by increased autocorrelation. We tested these datasets for time-scale dependence in the dynamics of lag-1 autocorrelation and found that in both the simulation and field experiment, the dynamics of autocorrelation were similar across time scales. In the simulated time series, autocorrelation increased exponentially approaching algal bloom development, and in the field experiment, the difference in autocorrelation between the manipulated and reference lakes increased sharply. These results suggest that, as an early warning indicator, autocorrelation may be robust to the time scale of the analysis. Given that a time scale can be shortened by increasing sampling frequency, or lengthened by aggregating data during analysis, these results have important implications for management as they demonstrate the potential for detecting early warning signals over a wide range of monitoring frequencies and without requiring analysts to make situation-specific decisions regarding aggregation. Such an outcome provides promise that data collection procedures, especially by automated sensors, may be used to monitor and manage ecosystem resilience without the need for strict attention to time scale.

A Generically Parameterized model of Lake eutrophication (GPLake) that links field-, lab- and model-based knowledge

Worldwide, eutrophication is threatening lake ecosystems. To support lake management numerous eutrophication models have been developed. Diverse research questions in a wide range of lake ecosystems are addressed by these models. The established models are based on three key approaches: the empirical approach that employs field surveys, the theoretical approach in which models based on first principles are tested against lab experiments, and the process-based approach that uses parameters and functions representing detailed biogeochemical processes. These approaches have led to an accumulation of field-, lab- and model-based knowledge, respectively. Linking these sources of knowledge would benefit lake management by exploiting complementary information; however, the development of a simple tool that links these approaches was hampered by their large differences in scale and complexity. Here we propose a Generically Parameterized Lake eutrophication model (GPLake) that links field-, lab- and model-based knowledge and can be used to make a first diagnosis of lake water quality. We derived GPLake from consumer-resource theory by the principle that lacustrine phytoplankton is typically limited by two resources: nutrients and light. These limitations are captured in two generic parameters that shape the nutrient to chlorophyll-a relations. Next, we parameterized GPLake, using knowledge from empirical, theoretical, and process-based approaches. GPLake generic parameters were found to scale in a comparable manner across data sources. Finally, we show that GPLake can be applied as a simple tool that provides lake managers with a first diagnosis of the limiting factor and lake water quality, using only the parameters for lake depth, residence time and current nutrient loading. With this first-order assessment, lake managers can easily assess measures such as reducing nutrient load, decreasing residence time or changing depth before spending money on field-, lab- or model- experiments to support lake management.

Detecting and Predicting Tipping Points

Tipping points are sudden, and sometimes irreversible and catastrophic, changes in a system’s dynamical regime. Complex networks are now widely used in the analysis of time series from a complex system. In this paper, we investigate the scope of network methods to indicate tipping points. In particular, we verify that the permutation entropy of transition networks constructed from time series observations of the logistic map can distinguish periodic and chaotic regimes and indicate bifurcations. The permutation entropy of transition networks, the mean edge betweenness of visibility graphs and the number of code words in compression networks, are each shown to indicate the onset of transition of a pitchfork bifurcation system. Our study shows that network methods are effective in detecting transitions. Network-based forecasts can be applied to models of real systems, as we illustrate by considering a lake eutrophication model.

Enhanced lake-eutrophication model combined with a fish sub-model using a microcosm experiment.

Eutrophication models are effective tools for assessing aquatic environments. The lake ecosystem consists of at least three trophic levels: phytoplankton, zooplankton, and fish. However, only a few studies have included fish sub-models in existing eutrophication models. In addition, no specific value or range is available for certain parameters of the fish sub-model. In the present study, a lake microcosm experimental system was established to determine the range of fish sub-model parameters. A three-trophic-level eutrophication model was established by combining the fish sub-model and eutrophication model. The Bayesian Markov Chain Monte Carlo and genetic algorithm method was used to calibrate the parameters of the eutrophication model. The results show that the maximum relative errors were due to phosphate (5.31%), the minimum relative error was due to nitrate (1.94%), and the relative error of dissolved oxygen, ammonia N, zooplankton, and chlorophyll ranged from 3 to 4%. Compared with the two-trophic-level eutrophication model, the relative errors of ammonia nitrogen (4.17%), phosphate (- 5.31%), and nitrate (1.94%) in the three-trophic-level eutrophication model were lower than those in the two-trophic-level eutrophication model, indicating that the three-trophic-level eutrophication model can obtain highly accurate simulation results and provide a better understanding of eutrophication models for future use.

Detecting early-warning signals in periodically forced systems with noise.

Early-warning signals for imminent regime shifts in multi-stable systems are highly desirable because it is often difficult to revert a system to the previous state once a transition has occurred. In this paper, two indicators, the phase lag and amplitude difference of the system's response, are extended to detect early-warning signals of a periodically driven, bistable complex system with noise. Our results show that both indicators can announce a regime shift of a complex system with small noise, namely, the critical point of the regime shift near a bifurcation point of the corresponding deterministic system. However, they fail to early indicate the regime shift in the case of large noise where the shift is far from the original bifurcation point. Based on the moment-expanding scheme, we reduce a large noise to a small one, and then both indicators work well again. We illustrate this approach via a parameterized lake eutrophication model verified by data. The regime shift to eutrophication could be detected in advance by studying the phase lag and amplitude difference of phosphorus concentrations. A basic statistical test is performed for the robustness of the proposed indicators. This approach provides a theoretical basis to prevent ecological environment deteriorations.

Sensitivity analysis of the Chaohu Lake eutrophication model with a new index based on the Morris method

Abstract Chaohu Lake is a large shallow lake in eastern China, and few eutrophication model studies have been conducted there. We present practical sensitivity indices based on the Morris method to compare the sensitivity of a parameter group on one model output with that of one parameter on multiple model outputs. The new sensitivity indices were employed to measure the parameter sensitivity of the Chaohu Lake eutrophication model. The results of the sensitivity analysis demonstrate that the most sensitive parameters on cyanobacteria biomass, NH4, NO3, and PO4 were BMR, KDN, Nitm, and KRP, and the most sensitive parameter groups were algae-related, nitrogen-related, and phosphorus-related, which all directly participate in their cycles. Furthermore, Nitm, KRP, KDN, KHP, BMR, KTB, KTHDR, and KTCOD were the most important for the Chaohu Lake eutrophication model. The water environment characteristics, such as the cyanobacteria life stage in the simulated period, significantly affected parameter sensitivity. The power-law relationship between the new sensitivity index and the standard deviation of model variables in the Chaohu Lake model were also determined. This finding allows us to estimate the interactions between parameters using their sensitivity index. The results provide a basis for further improvement of the Chaohu Lake eutrophication model.

Ensemble Kalman filter based data assimilation in the Delft3D-BLOOM lake eutrophication model

Ensemble Kalman filter based data assimilation in the Delft3D-BLOOM lake eutrophication model

Vulnerability: From the conceptual to the operational using a dynamical system perspective

This work proposes to address a lack of conceptual consensus surrounding the concept of vulnerability, by fostering a minimal definition as a measure of potential future harm, and by basing it on a stochastic controlled dynamical system framework. Harm is defined as a normative judgment on a trajectory. Considering all the possible trajectories from an initial state leads to the definition of vulnerability indicators as statistics derived from the probability distribution of harm values. This framework 1) promotes a dynamic view of vulnerability by eliciting its temporal dimension and 2) clarifies the descriptive and normative aspects of a system's representation. As illustrated by a simple model of lake eutrophication, this work makes vulnerability a precise yet flexible concept which fosters discussion on trade-offs between vulnerability sources, and also on adaptation. Links with economics, with control theory, and with algorithmic methods such as dynamic programming are highlighted.

A Comprehensive Modeling Approach for Reservoir Water Quality Assessment and Management Due to Point and Nonpoint Source Pollution

A comprehensive modeling approach has been developed for use in formulating a watershed management plan to improve the water quality of Cedar Creek reservoir, one of five large water supply reservoirs in north central Texas operated by Tarrant Regional Water District. Eutrophication, or specifically the increase in concentrations of chlorophyll-a (chl'a') over the last 18 years, is a major concern for the water managers. To develop a watershed management plan, the watershed model SWAT was linked with the lake eutrophication model WASP. Several intensive field campaigns and surveys were conducted to collect extensive water quality and land management data for model setup and calibration. In addition to the streamflow, the SWAT model was well calibrated for sediment (including channel erosion) and nutrients. Further, a simple modification to the SWAT in-stream routine allowed simulation of the nutrient load due to channel erosion. The in-stream water quality parameters for SWAT were based on an independent QUAL-2E model calibration. The calibrated SWAT model showed that more than 85% of the total N and total P loading to the lake are from watershed nonpoint sources. Although cropland occupies only 6% of the watershed area, it contributed more than 43% of the sediment, 23% of total N, and 42% of total P loading from the watershed. The channel erosion contributed about 35% of the total sediment load. The watershed model identified subbasins that contribute considerable amounts of sediment and nutrients. Based on these loads, the calibrated WASP model showed that the watershed nonpoint-source nutrient load (total N and total P) should be reduced by at least 35% to see a significant reduction in chl'a' concentrations when compared to the WASP calibration levels.

Burrowing mayfly (Ephemeroptera: Ephemeridae: Hexagenia spp.) bioturbation and bioirrigation: A source of internal phosphorus loading in Lake Erie

Traditional lake eutrophication models predict lower phosphorus concentrations with decreased external loads. However, in lakes where decreased external phosphorus loads are accompanied by increasing phosphorus concentrations, a seeming “trophic paradox” exists. Western Lake Erie is an example of such a paradox. Internal phosphorus loads may help explain this paradox. We examined bioturbation and bioirrigation created from burrowing mayfly, Hexagenia spp., as a possible source of internal phosphorus loading. Phosphorus concentrations of experimental microcosms containing lake sediments , filtered lake water, and nymphs (417/m 2 ) collected from western Lake Erie were compared to control microcosms containing sediments and lake water over a 7-day period. Phosphorus concentrations in microcosms containing Hexagenia were significantly greater than microcosms without nymphs. Further, we estimate the soluble reactive phosphorus flux from the sediments due to Hexagenia is 1.03 mg/m 2 /day. Thus, Hexagenia are a source of internal phosphorus loading. High densities of Hexagenia nymphs in western Lake Erie may help explain the “trophic paradox.” Furthermore, Hexagenia may be a neglected source of internal phosphorus loading in any lake in which they are abundant. Future studies of phosphorus dynamics in lakes with Hexagenia must account for the ability of these organisms to increase lake internal phosphorus loading.

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.

Indicators of regime shifts in ecological systems: What do we need to know and when do we need to know it

Because novel ecological conditions can cause severe and long-lasting environmental damage with large economic costs, ecologists must identify possible environmental regime shifts and pro-actively guide ecosystem management. As an illustrative example, we applied six potential indicators of impending regime shifts to S. R. Carpenter and W. A. Brock's model of lake eutrophication and analyzed whether or not they afforded adequate advance warning to enable preventative interventions. Our initial analyses suggest that an indicator based on the high-frequency signal in the spectral density of the time-series provides the best advance warning of a regime shift, even when only incomplete information about underlying system drivers and processes is available. In light of this result, we explored two key factors associated with using indicators to prevent regime shifts. The first key factor is the amount of inertia in the system; i.e., how fast the system will react to a change in management, given that a manager can actually control relevant system drivers. If rapid, intensive management is possible, our analyses suggest that an indicator must provide at least 20 years advance warning to reduce the probability of a regime shift to < 5%. As time to intervention is increased or intensity of intervention is decreased, the necessary amount of advance warning required to avoid a regime shift increases exponentially. The second key factor concerns the amount and type of variability intrinsic to the system, and the impact of this variability on the power of an indicator. Indicators are considered powerful if they detect an impending regime shift with adequate lead time for effective management intervention, but not so far in advance that interventions are too costly or unnecessary. Intrinsic "noise" in the system obscures the "signal" provided by all indicators, and therefore, the power of the indicators declines rapidly with increasing within- and between-year variability in measurable variables or parameters. Our results highlight the key role of human decisions in managing ecosystems and the importance of pro-active application of the precautionary principle to avoid regime shifts.

Lake eutrophication management modeling using dynamic programming

Lake eutrophication problems have received considerable attention in Taiwan, especially because they relate to the quality of drinking water. In this study, steady-state river water quality and lake eutrophication models are solved using dynamic programming algorithms to find the nutrient removal rates for eutrophication control during dry season. The kinetic cycle of chlorophyll-a, phosphorus and nitrogen for a complete-mixed lake is considered in the optimization framework. The Newton-iterative technique is adopted to solve the nonlinear equations for the steady-state lake eutrophication model. The optimization framework is applied to Cheng-Ching Lake in southern Taiwan. Several nutrient loading scenarios for eutrophication control are studied. Optimization results for nutrient removal rates and corresponding wastewater treatment capacities of each reach of the Kao-Ping River define the least cost approach to lake eutrophication control. A natural purification method, structural free water surface wetland, is also suggested to save more investment and improve river water quality at the same time.

Evaluating lake eutrophication with enhanced thematic mapper data in Wuhan

By analyzing the enhanced thematic mapper (ETM) images of September 1999, and quality observation data for many consecutive years in several parts of the Donghu Lake in Wuhan, China, the authors discovered a good linear relation between grey scale (GS) abstracted from ETM b5, b7 images and eutrophication level of the lakes, and extended the study to eight other major lakes in the area of Wu- han by using lake eutrophication models. Based on the in situ monitoring data, we also evaluated the eu- trophication level of the lakes with modified trophic index method brought by M. Aizaki et al. The results of the two methods showed that the most of the lakes were eutrophicated, and even hyper-eutrophicated in some areas. Six of the 8 lakes had very similar trophic state index (TSI) values. Although two of them differed in TSI value, but within an order, while it was different largely from the one by traditional method. The difference of the results between the two methods might have been due to three causative reasons. First, remote sensing technology reflects the overall status of a certain area corresponding to the ETM images in a certain period, but the modified TSI reflects the annual average values of the monitoring spots. Second, the time the ETM images taken is later than that of in situ data. Third, ETM images are affected by clouds, water depth, and suspended matter. In short, remote sensing result agreed greatly with the in situ monitoring data, indicating that remote sensing technology is feasible and effective for moni- toring and evaluating the lake eutrophication in the Wuhan area and it also can be used to evaluate large-scope lake eutrophication.

Rising variance: a leading indicator of ecological transition

Regime shifts are substantial, long-lasting reorganizations of complex systems, such as ecosystems. Large ecosystem changes such as eutrophication, shifts among vegetation types, degradation of coral reefs and regional climate change often come as surprises because we lack leading indicators for regime shifts. Increases in variability of ecosystems have been suggested to foreshadow ecological regime shifts. However, it may be difficult to discern variability due to impending regime shift from that of exogenous drivers that affect the ecosystem. We addressed this problem using a model of lake eutrophication. Lakes are subject to fluctuations in recycling associated with regime shifts, as well as fluctuating nutrient inputs. Despite the complications of noisy inputs, increasing variability of lake-water phosphorus was discernible prior to the shift to eutrophic conditions. Simulations show that rising standard deviation (SD) could signal impending shifts about a decade in advance. The rising SD was detected by studying variability around predictions of a simple time-series model, and did not depend on detailed knowledge of the actual ecosystem dynamics.