Filling the matrix: an ANOVA-based method to emulate regional climate model simulations for equally-weighted properties of ensembles of opportunity

Abstract

Collections of large ensembles of regional climate model (RCM) downscaled climate data for particular regions and scenarios can be organized in a usually incomplete matrix consisting of GCM (global climate model) x RCM combinations. When simple ensemble averages are calculated, each GCM will effectively be weighted by the number of times it has been downscaled. In order to facilitate more equal and less arbitrary weighting among downscaled GCM results, we present a method to emulate the missing combinations in such a matrix, enabling equal weighting among participating GCMs and hence among regional consequences of large-scale climate change simulated by each GCM. This method is based on a traditional Analysis of Variance (ANOVA) approach. The method is applied and studied for fields of seasonal average temperature, precipitation and surface wind and for the 10-year return value of daily precipitation and of 10-m wind speed for a completely filled matrix consisting of 5 GCMs and 4 RCMs. We quantify the skill of the two averaging methods for different numbers of missing simulations and show that ensembles where lacking members have been emulated by the ANOVA technique are better at representing the full ensemble than corresponding simple ensemble averages, particularly in cases where only a few model combinations are absent. The technique breaks down when the number of missing simulations reaches the sum of the numbers of GCMs and RCMs. Also, the method is only useful when inter-simulation variability is limited. This is the case for the average fields that have been studied, but not for the extremes. We have developed analytical expressions for the degree of improvement obtained with the present method, which quantify this conclusion.