Ecological Modelling of Lake Erie: Sensitivity Analysis and Simulation of Nutrient, Phytoplankton and Zooplankton Dynamics

Abstract

Lake Erie has undergone a substantial amount of ecosystem changes over the past century; including cultural eutrophication and several invasions by industrious exotic species. Simple mass balance models for phosphorus have been useful in guiding policy decisions that led to reduced eutrophication, but new, confounding threats to the ecological health of Lake Erie continue to appear and lake managers continue to need useful tools to better understand the lake. As more complex ecological questions are asked to guide future management decisions, more complex ecological models are developed in an effort to provide some clues. The walleye fishery in Lake Erie is economically very important. Walleye recruitment has been highly variable from year to year since the 1990s. Modelling zooplankton is desired as a diagnostic tool for elucidating the quality of habitat – spatially and temporally – that is available to walleye in their vulnerable larval state. ELCOM-CAEDYM (or ELCD) is a 3-dimensional, coupled hydrodynamic and ecological model, which has been successfully applied to Lake Erie to model the nutrients and phytoplankton. The objectives of this study were to better understand the ELCOM-CAEDYM model of Lake Erie through a sensitivity analysis (SA), which has not been done before, and to explicitly simulate zooplankton in this model. An SA is important for determining which of the uncertain parameters have the greatest impact on the output variables. Due to the complexity of the CAEDYM model and the highly interdependent functions and variables modelled, a local SA (comparing changes in output by perturbing parameters one-at-a-time from some baseline configuration) was not desirable. Local SA’s ignore the possibility of a parameter’s effects being correlated to the status of other parameters. However, quantitative global methods are enormously computationally expensive for a complex model. The Lake Erie ELCD model simulates temperature, mixing, nutrient cycles, and phytoplankton dynamics. Phytoplankton are represented by 5 functional groups. With the explicit inclusion of 2 functional groups of zooplankton (copepods and cladocerans), the model uses over 300 function parameters in addition to requiring meteorological data and river inflow characteristics throughout the simulation. The model is set up with a 2-km grid over 40 layers with a 5-minute timestep from April 11 to September 1. This full simulation takes 6 days to complete. A quantitative global method to evaluate all parameters potentially significant to zooplankton would be impossible. The Morris method was selected for its streamlined global sampling procedure combined with the manageable computational demands of a one-at-a-time analysis. This method provides the relative sensitivity of diagnostic outputs to perturbed parameters. Ninety-one parameters were selected to be evaluated in 3680 simulations for the Morris SA. The selection of which parameters to evaluate and their assigned ranges are critical components in any SA. The ranges for parameters that represent a measurable quantity were assessed based on observed values in Lake Erie and other relevant studies. For some parameters, a measured realistic range was unknown. In these cases, values from relevant published models or judgements based on experience with the ELCD-Erie model were used to choose a suitable range. To assess the sensitivity of CAEDYM variables to parameters, DYRESM was substituted for ELCOM to vastly decrease the computation time of a single run. DYRESM is not suitable to model the entire lake due to the large size and irregular shape of the entire lake. Therefore, only the West Basin was modelled and analysed using DYCD. The West Basin was of special interest for a sensitivity analysis of CAEDYM parameters with respect to zooplankton because it is an important area for walleye larval development. DYCD output profiles for temperature, total chlorophyll a (TChla as a surrogate for total phytoplankton concentration) were similar in magnitudes and seasonal dynamics compared to ELCD outputs in deep West Basin stations. The sensitivity of zooplankton, TChla and TP to each parameter was assessed using two single value diagnostics: the simulated seasonal maximum and the simulated day on which peak maximum was reached. Zooplankton were sensitive to almost all of the zooplankton parameters perturbed in the analysis. This may indicate that modelling zooplankton is extremely complex, relying on many dynamic processes, or that evaluated ranges were not constrained well enough. An example of sensitivity to a poorly known parameter is the messy feeding coefficient. Reducing the uncertainty of this parameter would improve the confidence in the zooplankton assimilation submodel. Other parameters that stood out for being especially significant to zooplankton were: the respiration rate, mortality rate, internal phosphorus to carbon ratio, the temperature multiplier and standard temperature for feeding dynamics, and the half saturation constant. Most of these are easily explained as they directly aid or impede growth or they directly affect zooplankton losses. The most significant phytoplankton parameters on TChla and zooplankton outputs were, not surprisingly, the maximum growth rate and the mortality and respiration coefficient. Some particulate matter parameters proved to be important to outputs as well. More than 2500 of the 3680 parameter configurations resulted in unrealistic zooplankton simulations: peak values that did not much exceed initial conditions on the first day of the simulation. The SA exercise pinpointed a few configurations that resulted in reasonable peak zooplankton values and timing; these runs were used as a starting point for calibrating the ELCD model. Parameters were further manually adjusted by quickly checking their impacts on DYCD before applying them to ELCD. Post SA and minor calibration, the modelled zooplankton results were dramatically better than initial modelling attempts prior to the SA. Zooplankton concentrations throughout the lake were close to measured ranges and in some parts of the lake seasonal patterns were also similar to measured patterns. Modelled zooplankton results were least consistent with observations in the south west area of the lake: zooplankton were overestimated in late June-early July and they subsequently crashed and were underestimated in late July-August. It is supposed that this is due to higher grazing pressure from fish larvae in that area of the lake, which is not explicitly modelled. Although it is not anticipated that the south west seasonal zooplankton patterns will improve through parameter calibration (since predator effects are uniformly characterized throughout the lake by the same mortality factor) , further calibration is needed to improve results in the rest of the lake since copepods are generally overestimated and cladocerans generally underestimated. Phytoplankton groups must also be calibrated simultaneously to ensure that they are still operating within reasonable concentrations given more successful zooplankton simulations.