Efficient Bayesian Model Selection in Hydrological Modelling

With the wide range of models available, hydrologic modellers are faced with the choice of which model is best applied to a catchment for a particular modelling exercise. Assessing the relative performance of competing models can be difficult given the limited data that is available and further complicated by difficulties in obtaining a unique set of values for the model parameters. Traditional techniques such as those involving split-sample validation are useful, but suffer from increased uncertainty due to the reduction of the sample used. Bayesian statistical inference, with computations carried out via Markov Chain Monte Carlo (MCMC) methods, offer an efficient alternative allowing for the combination of any pre-existing knowledge about individual models and their respective parameters with the available catchment data to assess the parameter uncertainty. Bayesian inference can also provide a framework to evaluate the evidence in favour of a model, given a group of competing models. The traditional approach requires calculation of the Bayes factor, which is the posterior probability ratio of the models (assuming equal prior probabilities). 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 in which the parameters of the Australian Water Balance Model (AWBM) were estimated using computations carried out via MCMC methods. The study considers the variability of soil moisture within the Bass River catchment, by formulating the AWBM to include a different number of soil moisture stores. A model selection framework is developed by calculating Bayes factors using a method based on direct estimation of a models’ marginal likelihood. The framework uses an adaptive Metropolis algorithm to calculate the model’s posterior odds. To assess the model selection method in a controlled setting, artificial runoff data were created corresponding to the two storage model. These data were used to check if the method would select the 2 store model convincingly. The method was then applied to real catchment data to determine which model configuration best represents the catchment.