Analysis of runoff extremes using spatial hierarchical Bayesian modeling

A spatial hierarchical Bayesian method is developed to model the extreme runoffs over two spatial domains in Columbia River Basin, USA. This method combines the limited number of data from different locations. The two spatial domains contain 31 and 20 gage stations, respectively, with daily streamflow records ranging from 30 to over 130 years. The generalized Pareto distribution (GPD) is employed for the analysis of extremes. Temporally independent data are generated using declustering procedure, where runoff extremes are first grouped into clusters and then the maximum of each cluster is retained. The GPD scale parameter is modeled based on a Gaussian geostatistical process and additional variables including the latitude, longitude, elevation, and drainage area are incorporated by means of a hierarchy. Metropolis-Hasting within Gibbs Sampler is used to infer the parameters of the GPD and the geostatistical process to estimate the return levels across the basins. The performance of the hierarchical Bayesian model is evaluated by comparing the estimates of 100 year return level floods with the maximum likelihood estimates at sites that are not used during the parameter inference process. Various prior distributions are used to assess the sensitivity of the posterior distributions. The selected model is then employed to estimate floods with different return levels in time slices of 15 years in order to detect possible trends in runoff extremes. The results show cyclic variations in the spatial average of the 100 year return level floods across the basins with consistent increasing trends distinguishable in some areas.