Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm

Abstract

Two Monte Carlo-based approaches for assessing parameter uncertainty in complex hydrologic models are considered. The first, known as importance sampling, has been implemented in the generalised likelihood uncertainty estimation (GLUE) framework of Beven and Binley. The second, known as the Metropolis algorithm, differs from importance sampling in that it uses a random walk that adapts to the true probability distribution describing parameter uncertainty. Three case studies are used to investigate and illustrate these Monte Carlo approaches. The first considers a simple water balance model for which exact results are known. It is shown that importance sampling is inferior to Metropolis sampling. Unless a large number of random samples are drawn, importance sampling can produce seriously misleading results. The second and third case studies consider more complex catchment models to illustrate the insights the Metropolis algorithm can offer. They demonstrate assessment of parameter uncertainty in the presence of bimodality, evaluation of the significance of split-sample tests, use of prior information and the assessment of confidence limits on hydrologic responses not used in calibration. When compared with the capabilities of traditional inference based on first-order approximation, the Metropolis algorithm provides a quantum advance in our capability to deal with parameter uncertainty in hydrologic models.