Hydrological model selection: A Bayesian alternative

Abstract

The evaluation and comparison of hydrological models has long been a challenge to the practicing hydrological community. No single model can be identified as ideal over the range of possible hydrological situations. With the variety of models available, hydrologic modelers are faced with the problem of determining which model is best applied to a catchment for a particular modeling exercise. The model selection problem is well documented in hydrologic studies, but a broadly applicable as well as theoretically and practically sound method for comparing model performance does not exist in the literature. Bayesian statistical inference, with computations carried out via Markov chain Monte Carlo (MCMC) methods, offers an attractive alternative to conventional model selection methods allowing for the combination of any preexisting knowledge about individual models and their respective parameters with the available catchment data to assess both parameter and model uncertainty. The aim of this study is to present a method by which hydrological models may be compared in a Bayesian framework. The study builds on previous work (Marshall et al., 2004) in which a Bayesian approach implemented using MCMC algorithms was presented as a simple and efficient basis for assessing parameter uncertainty in hydrological models. In this study, a model selection framework is developed in which an adaptive Metropolis algorithm is used to calculate the model's posterior odds. The model used to illustrate our approach is a version of the Australian Water Balance Model (Boughton, 1993) reformulated such that it can have a flexible number of soil moisture storages. To assess the model selection method in a controlled setting, artificial runoff data were created corresponding to a known model configuration. These data were used to evaluate the accuracy of the model selection method and its sensitivity to the size of the sample being used. An application of the Bayesian model identification methodology to 11 years of daily streamflow data from the Murrumbidgee River at Mittagang Crossing in southeastern Australia concludes our study.