Combining site and regional flood information using a Bayesian Monte Carlo approach

Regression-based methods are widely used in flood regionalization. Since the generalized least squares (GLS) regression model properly accounts for both model and sampling errors, realistic estimates of uncertainty can be obtained. This study presents a general Bayesian approach for inferring the GLS regional regression model and for combining with any available site information to obtain the most accurate flood quantiles. A robust block Metropolis scheme is developed to sample the posterior distribution of the GLS regression model parameters. A particular feature of the sampler is the use of a uniform proposal for the regional model error variance to avoid convergence difficulties. A simple but general procedure, based on importance sampling, is developed to combine any kind of site information with regional information. The benefit of this approach is that all available information is fully exploited, and uncertainty is rigorously quantified as well as being minimized. Two case studies are presented. A synthetic case study illustrates the complex nature of the posterior distribution for the regional model error variance with its shape dependent on how much sampling error dominates the total error in the regional GLS model. A second case study involving 24 sites from the east coast of Australia is presented for the log Pearson III model. It demonstrates the significant benefit of combining site and regional information and the quantification of uncertainty.