Accommodating environmental thresholds and extreme events in hydrological models: A Bayesian approach

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Extreme events appear to play an important role in pollutant export and the overall functioning of watershed systems. Because they are expected to increase in frequency as urbanization and recent climate change trends continue, the development of techniques that can effectively accommodate the behavior of watersheds during extreme events is one of the challenges of the contemporary modeling practice. In this regard, we present a Bayesian framework which postulates that the watershed response to precipitation occurs in distinct states. Precipitation depth above a certain threshold triggers an extreme state, which is characterized by a qualitatively different response of the watershed to precipitation. Our calibration framework allows us to identify these extreme states and to characterize the different watershed behavior by allowing parameter values to vary between states. We applied this framework to SWAT model implementations in two creeks in the Hamilton Harbour watershed of Redhill Creek, an urban catchment, and Grindstone Creek, an agricultural one. We found that our framework is able to coherently identify watershed states and state-specific parameters, with extreme states being characterized by a higher propensity for runoff generation. Our framework resulted in better model fit above the precipitation threshold, although there were not consistent improvements of model fit overall. We demonstrate that accommodating threshold-type of behavior may improve the use of models in locating critical source areas of non-point source pollution.