Bayesian analysis of rainfall-runoff models: insights to parameter estimation, model comparison and hierarchical model development

Abstract

One challenge that faces hydrologists in water resources planning is to predict the catchment's response to a given rainfall. Estimation of parameter uncertainty (and model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference, with computations carried out via Markov Chain Monte Carlo (MCMC) methods, offers an attractive approach to model specification, allowing for the combination of any pre-existing knowledge about individual models and their respective parameters with the available catchment data to assess both parameter and model uncertainty. This thesis develops and applies Bayesian statistical tools for parameter estimation, comparison of model performance and hierarchical model aggregation. The work presented has three main sections. The first area of research compares four MCMC algorithms for simplicity, ease of use, efficiency and speed of implementation in the context of conceptual rainfall-runoff modelling. Included is an adaptive Metropolis algorithm that has characteristics that are well suited to hydrological applications. The utility of the proposed adaptive algorithm is further expanded by the second area of research in which a probabilistic regime for comparing selected models is developed and applied. The final area of research introduces a methodology for hydrologic model aggregation that is flexible and dynamic. Rigidity in the model structure limits representation of the variability in the flow generation mechanism, which becomes a limitation when the flow processes are not clearly understood. The proposed Hierarchical Mixtures of Experts (HME) model architecture is designed to do away with this limitation by selecting individual models probabilistically based on predefined catchment indicators. In addition, the approach allows a more flexible specification of the model error to better assess the risk of likely outcomes based on the model simulations. Application of the approach to lumped and distributed rainfall runoff models for a variety of catchments shows that by assessing different catchment predictors the method can be a useful tool for prediction of catchment response.