An extreme comparison of two downscaling approaches using Bayes factors

Extreme rainfall events are the long-standing hydrological interest of flood defence and water resources management. Although traditional extreme value theory allows stationary extreme assessment, recent development of rainfall downscaling approaches driven by projections of Global Climate models (GCMs) facilitates non-stationary extreme assessments. Additionally, using stochastic downscaling, the downscaled rainfall series can be probabilistic so that the inherent uncertainty of the used approaches can be explicitly presented. However, there is little work on performance benchmarking of extremes simulated by alternative downscaling approaches. In the United Kingdom (UK), two independently developed downscaling methodologies are (1) the UK climate projections (UKCP09) weather generators and (2) the Generalised linear model (GLM) approach. Both downscaling approaches can provide daily rainfall series at catchment scale. As a quantitative benchmark, Bayes factors are proposed as a tool for comparing ensemble extremes generated from the two UK models. Using Monte Carlo Integration and Laplace's approximation, Bayes factors for the 30th largest annual event within a 30 year period of the two methods are approximated for six catchments in the UK. Despite their similar average monthly statistics (i.e. mean, variance, autocorrelation and skewness), results show that the preferred approach for extreme results is catchment specific. The implications and possible interpretations of diverse extreme results from different downscaling approaches are discussed.