Maryam Ramin

Eutrophication Risk Assessment in Hamilton Harbour: System Analysis and Evaluation of Nutrient Loading Scenarios

ABSTRACT Environmental modeling has been an indispensable tool of the Hamilton Harbour restoration efforts, where a variety of data-oriented and process-based models have been used for linking management actions with potential ecosystem responses. In this study, our objective is to develop a biogeochemical model that can effectively describe the interplay among the different ecological mechanisms modulating the eutrophication problems in Hamilton Harbour, Ontario, Canada. First, we provide the rationale for the model structure adopted, the simplifications included, and the formulations used during the development phase of the model. We then present the results of a calibration exercise and examine the ability of the model to sufficiently reproduce the average observed patterns along with the major cause—effect relationships underlying the Harbour water quality conditions. The present modeling study also undertakes an estimation of the critical nutrient loads in the Harbour based on acceptable probabilities of compliance with different water quality criteria (e.g., chlorophyll a, total phosphorus). Our model suggests that the water quality goals for TP (17 µg L-1) and chlorophyll a concentrations (5–10µg L-1) will likely be met, if the Hamilton Harbour RAP phosphorus loading target at the level of 142 kg day-1 is achieved. We also provide evidence that the anticipated structural shifts of the Zooplankton community will determine the restoration rate as well as the stability of the new trophic state in the Harbour.

Bayesian calibration of mathematical models: Optimization of model structure and examination of the role of process error covariance

Abstract The integration of Bayesian inference techniques with mathematical modeling offers a promising means to improve ecological forecasts and management actions over space and time, while accounting for the uncertainty underlying model predictions. In this study, we address two important questions related to the ramifications of the statistical assumptions typically made about the model structural error and the prospect of Bayesian calibration to guide the optimization of model complexity. Regarding the former issue, we examine statistical formulations that whether postulate conditional independence or explicitly accommodate the covariance among the error terms for various model endpoints. Our analysis evaluates the differences in the posterior parameter patterns and predictive performance of a limiting nutrient (phosphate)–phytoplankton–zooplankton–detritus (particulate phosphorus) model calibrated with three alternative statistical configurations. The lessons learned from this exercise are combined with those from a second comparative analysis that aims to optimize model structure. In particular, we selected three formulas of the zooplankton mortality term (linear, hyperbolic, sigmoidal) and examine their capacity to determine the posterior parameterization as well as the reproduction of the observed ecosystem patterns. Our analysis suggests that the statistical characterization of the model error as well as the mathematical representation of specific ecological processes can be influential to the inference drawn by a modeling exercise. Our findings could be useful when selecting the most suitable statistical framework for model calibration and/or making informative decisions about model structure optimization. In the absence of adequate prior knowledge, we also advocate the use of Bayesian model averaging for obtaining weighted averages of the forecasts from different model structures and/or statistical descriptions of the process error terms.

9.10 – Integration of Bayesian Inference Techniques with Mathematical Modeling

The credibility of the scientific methodology of numerical models and their adequacy to form the basis of public policy decisions have been frequently challenged. The first part of this chapter aims to address the issue of model reliability by evaluating the current state of aquatic biogeochemical modeling. We provide evidence that there is still considerable controversy among modelers and the resource managers about how to develop, evaluate, and interpret mathematical models. Our arguments are that (1) models are not always developed in a consistent manner, clearly stated purpose, and predetermined acceptable model performance level, and (2) the potential users select models without properly assessing their technical value. The second part of this presentation argues that the development of novel methods for rigorously assessing the uncertainty underlying model predictions should be a top priority of the modeling community. Striving for novel uncertainty analysis tools, we introduce Bayesian calibration of process-based models as a methodological advancement that warrants consideration in aquatic ecosystem research. This modeling framework combines the advantageous features of both process-based and statistical approaches, that is, mechanistic understanding that remains within the bounds of data-based parameter estimation. The incorporation of mechanism improves the confidence in predictions made for a variety of conditions, whereas the statistical methods provide an empirical basis for parameter value selection and allow for realistic estimates of predictive uncertainty. Other advantages of the Bayesian approach include the ability to sequentially update beliefs as new knowledge is available, and the consistency with the scientific process of progressive learning and the policy practice of adaptive management. Finally, we illustrate some of the anticipated benefits from the Bayesian calibration framework, well suited for stakeholders and policy makers when making environmental management decisions, using the Hamilton Harbour – a eutrophic system in Ontario, Canada – as a case study.