Eutrophication risk assessment using Bayesian calibration of process-based models: Application to a mesotrophic lake

We introduce the Bayesian calibration of process-based models to address the urgent need for robust modeling tools that can effectively support environmental management. The proposed framework aims to combine the advantageous features of both mechanistic and statistical approaches. Models that are based on mechanistic understanding yet remain within the bounds of data-based parameter estimation can accommodate rigorous and complete error analysis. The incorporation of mechanism improves the confidence in predictions made for a variety of conditions, while the statistical methods provide an empirical basis for parameter estimation and allow for estimates of predictive uncertainty. Our illustration focuses on eutrophication modeling but the proposed methodological framework can be easily transferred to a wide variety of disciplines (e.g., hydrology, ecotoxicology, air pollution). We examine the advantages of the Bayesian calibration using a four state variable (phosphate-detritus-phytoplankton-zooplankton) model and the mesotrophic Lake Washington (Washington State, USA) as a case study. Prior parameter distributions were formed on the basis of literature information, while Markov chain Monte Carlo simulations provided a convenient means for approximating the posterior parameter distributions. The model reproduces the key epilimnetic temporal patterns of the system and provides realistic estimates of predictive uncertainty for water quality variables of environmental interest. Finally, we highlight the benefits of Bayesian parameter estimation, such as the quantification of uncertainty in model predictions, optimization of the sampling design of monitoring programs using value of information concepts from decision theory, alignment with the policy practice of adaptive management, and expression of model outputs as probability distributions, that are perfectly suited for stakeholders and policy makers when making decisions for sustainable environmental management.