Elsevier

Ecological Modelling

Volume 187, Issues 2–3, 25 September 2005, Pages 179-200
Ecological Modelling

Eutrophication model for Lake Washington (USA): Part II—model calibration and system dynamics analysis

https://doi.org/10.1016/j.ecolmodel.2005.01.039Get rights and content

Abstract

We developed a complex eutrophication model to simulate the current chemical and biological properties of Lake Washington (USA). The model reproduces the key epilimnetic and hypolimnetic temporal patterns of the system and results in a good fit between simulated and observed monthly values. The relative error of model estimates was below 20% for most of the water quality parameters (phytoplankton, phosphate, total phosphorus, total nitrogen, dissolved oxygen). Discrepancies between simulated and observed ammonium levels were mainly due to the explicitly modeled egestion of excess nitrogen during zooplankton feeding. This indicates that the relation between secondary production and nutrient recycling has significant effects on the fractionation of the major elements (C, N and P) and regulates their distribution between the particulate/dissolved and inorganic/organic pools. The model was forced by 1962 nutrient loadings, when the lake received large quantities of treated wastewater treatment effluent, and accurately predicted the phytoplankton community responses (phytoplankton biomass and cyanobacteria dominance) and the nitrogen and phosphorus annual cycles for these conditions. We used Monte Carlo simulations to reproduce the meteorological forcing (air temperature, solar radiation, precipitation and subsequent river inflows) that in large part regulates phytoplankton interannual variability for the last 25 years in the lake. We found three seasonal components (modes of variability). The first component (January, May, November, December) is associated with the conditions that determine the abundance of the herbivorous cladocerans; the second component (June–September) coincides with the summer-stratified period, and the third component (February–April) is associated with the initiation and peak of the spring bloom. Finally, an illustrative application of two scenarios of nutrient loading increase at 25% of the 1962 levels indicated that both phytoplankton and cyanobacteria growth are likely to be stimulated. The three seasonal components still characterize phytoplankton dynamics, but changes in the relationships between summer phytoplankton/cyanobacteria biomass and total phosphorus/phosphate concentrations indicate the likelihood of structural shifts towards relaxation of the present phosphorus-limiting conditions and promotion of cyanobacteria dominance. Integration of the present eutrophication model with a hydrodynamic model with enhanced vertical resolution will allow more realistic predictions.

Introduction

The concept of model validation has been extensively debated during the last three decades, and the ecological literature is replete with contradictory viewpoints about the feasibility or even the definition of model validation (Van Horn, 1971, Caswell, 1976, Holling, 1978, Oreskes et al., 1994, Rykiel, 1996). For example, Oreskes et al. (1994) claimed models which attempt to reproduce open natural systems can never be validated. This paper also questioned the adequacy of environmental models for public policy decision-making and claimed earth science models have only heuristic value. At the other end of the spectrum, some authors consider model validation to be a mere technical process that aims to determining the level of agreement between the model and an independent data-set obtained from a real system (Goodall, 1972, Mayer and Butler, 1993, Power, 1993). Rykiel (1996) argued that there are “semantic and philosophical considerations” that cause this confusion, but also emphasized the lack of universal validation tests and standards as another source of ambiguity for the whole modeling procedure. Most importantly, he emphasized the need for modelers to clearly specify the model objectives, explicitly state what they consider to be acceptable model behavior and to define the model operational domain. Undoubtedly, there are both subjective and objective aspects of the validation process that confuse its meaning, while this confusion is accentuated by the often times dual nature of environmental models in scientific hypothesis testing and engineering practice (Caswell, 1988).

In aquatic science, there are simulation models that have been developed for theoretical purposes in order to explore aspects of system dynamics that are technologically or economically unattainable by other means (Franks, 1995). These theoretical models also provide a foundation from which one can analyze chemical or trophic dynamics (Norberg and DeAngelis, 1997), test new ecological theories for aquatic systems (Jorgensen, 1995), couple physical processes with biological dynamics (Kamykowski et al., 1994) or study their transition towards chaotic behavior (Rinaldi and Muratori, 1993, Scheffer et al., 2000). The second category, which is not always mutually exclusive with the previous theoretical class, includes models that have been constructed for management and forecasting purposes. The performance of these models is constrained by available data, and they are used as heuristic tools to identify the underlying dynamics of the system behavior or as predictive tools to explore hypothetical conditions that are not described by current observations. As Franks (1995) pointed out the former class of models interpolate within the data, while the later extrapolate beyond the data. In the aquatic ecosystems literature, there are numerous references to models that have been used for understanding oceanic ecosystems (e.g., bloom dynamics, the global carbon cycle) and predicting biotic responses to climate change (Fasham et al., 1993, Frost and Kishi, 1999, Boyd and Doney, 2002, Kawamiya, 2002), but this class of models has also been used as management tools for predicting eutrophication or integrating environmental with socioeconomic concerns (Ambrose et al., 1991, Cerco and Cole, 1994, Hamilton and Schladow, 1997, Turner, 2000, Arhonditsis et al., 2000, Arhonditsis et al., 2002).

Based on the previous classification, the eutrophication model that we presented in Part I can serve both theoretical and practical engineering/management purposes. For example, we introduced a dynamic parameterization for modeling the effects of both food quality and quantity on zooplankton gross growth efficiency, and also used a multi-elemental approach that makes it possible to examine recent conceptual advances in stoichiometric nutrient recycling theory. In this sense, our model was used for addressing questions of the type “What would happen if …?”, which in turn identified components of the system that require further research (Franks, 1995). At the same time, the basic goal for the development of this biogeochemical model is to support management-planners and decision-makers as a methodological tool for testing Lake Washington's resilience under various management scenarios. Therefore, our model evaluation was based on the calibration and validation processes, as they were defined in a “limited technical sense” by Rykiel (1996). During calibration, we attempted to obtain a “sufficient” description of the lake's mean annual patterns by adjustment and estimation of model parameters and constants. Inevitably, given the lack of conventional and widely accepted standards of model performance, the characterization “sufficient” entails some subjectivity. However, goodness-of-fit assessments were based on commonly applied diagnostic measures in modeling practice (Mayer and Butler, 1993, Power, 1993), and thus the performance of our model can be compared with similar studies. We also considered two components of the validation process, the conceptual and operational validation. The former aims to provide justification for the formulations used and the rationale for the simplifications adopted and was extensively discussed in Part I. The later examines the engineering value of the model and demonstrates whether the model outputs meet the performance standards required for the model's ultimate management purpose. [Note that here we distinguish between model calibration and operational validation.] As a part of the operational validation of the model, we explored the simulated internal structure of the system (i.e., “structural validation” sensu Ziegler, 1976), and assessed its correspondence with the actual processes or cause-effect relationships reported in the Lake Washington literature. In addition, since the model's intended application is for predictive purposes, we included a series of perturbations (nutrient loading, meteorological forcing) that reproduced past, current and future hypothesized states for this system. The model showed a satisfactory behavior and produced realistic patterns. Ironically the present model structure is not directly comparable with past conditions in Lake Washington, because during that period Daphnia was not a prominent member of the zooplankton community. This supports the notion that simulation models cannot replicate the enormous complexity of natural systems (Reckhow, 1999), and thus the modeling procedure should be considered an iterative process where model formulation and validation criteria always evolve in a parallel manner with the real system (Rykiel, 1996). Finally, this paper emphasizes the need for integrating the present eutrophication model with a hydrodynamic model having a fine vertical resolution, and suggests aspects of Lake Washington dynamics that should be incorporated into future monitoring programs.

Section snippets

Model application and calibration results

The data-set used for model calibration was collected on a bi-weekly (during the summer) or monthly (the rest of the year) basis from 12 inshore and offshore sampling stations from January 1995 to December 2001 (Arhonditsis et al., 2003, Fig. 1). The environmental variables monitored included chlorophyll a, phosphate, total phosphorus, nitrate, ammonium, total nitrogen, dissolved oxygen and total organic carbon. The data were binned by month based on time-weighted averages — bi-weekly or

Nitrogen and phosphorus budgets

The simulated annual nitrogen and phosphorus cycles for the epilimnion and hypolimnion are presented in Fig. 4, Fig. 5. As mentioned in Part I, external loading was based on mean annual nutrient cycles over the past 10 years for all important Lake Washington tributaries (Brett et al., in press). The model considers an annual hydrologic loading of 1152 × 106 m3 year−1 from fluvial and aerial sources. After a correction for evaporative losses at the lake surface, these inputs correspond to a

Model performance under increased nutrient loading

One of the most desirable properties of an eutrophication model is its capability to predict how the system will respond to changes in external forces such as nutrient loading. Power (1993) described this procedure as the predictive validation of the model, which basically assesses the model-fit with independent data sets or data acquired from the real system after model calibration. A common modeling practice is to split the available data into two subsets, and use the first for calibrating

Future modifications and conclusions

Our eutrophication model provided a good representation of the key epilimnetic and hypolimnetic patterns in Lake Washington (USA). A satisfactory fit was obtained between simulated and observed monthly values and the relative error was below 20% for the major water quality parameters (phytoplankton, phosphate, total phosphorus, total nitrogen, dissolved oxygen). Furthermore, the model was forced by the 1962 nutrient loadings (when the lake received the maximum input of secondary sewage

Acknowledgments

This study was supported by a grant from the King County, Department of Natural Resources and Parks, Wastewater Treatment Division. We thank Jonathan Frodge, Curtis L. DeCasperi, Kevin Shock (King County, Department of Natural Resources and Parks), David A. Beauchamp, and Michael M. Mazur (School of Aquatic and Fisheries Sciences, University of Washington) for helpful comments to earlier drafts of the two manuscripts. We are indebted to Wang Dan (Department of Environmental Engineering,

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