A general and practical Bayesian procedure for regional and at-site flood frequency analysis

Regression-based methods are widely used in flood regionalisation. The generalised least squares (GLS) regression model properly distinguishes between model and sampling errors and, thus, provides the most realistic estimates of uncertainty. This study presents a general Bayesian approach for inferring the GLS regional regression model and for pooling 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 to avoid convergence difficulties for the regional model error variance. A simple but general procedure, based on importance sampling, is developed to pool 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 minimised. Moreover, the algorithms are simple to program and, as a result, offer a practical tool for comprehensive flood frequency analysis. A case study involving 26 sites from north-eastern NSW is presented for the log-Pearson 3 model. The results demonstrate the significant benefit of pooling site and regional information and the quantification of uncertainty