Bayesian Model Averaging’s Problematic Treatment of Extreme Weather and a Paradigm Shift That Fixes It

Abstract

Methods of ensemble postprocessing in which continuous probability density functions are constructed from ensemble forecasts by centering functions around each of the ensemble members have come to be called Bayesian model averaging (BMA) or ?dressing? methods. Here idealized ensemble forecasting experiments are used to show that these methods are liable to produce systematically unreliable probability forecasts of climatologically extreme weather. It is argued that the failure of these methods is linked to an assumption that the distribution of truth given the forecast can be sampled by adding stochastic perturbations to state estimates, even when these state estimates have a realistic climate. It is shown that this assumption is incorrect, and it is argued that such dressing techniques better describe the likelihood distribution of historical ensemble-mean forecasts given the truth for certain values of the truth. This paradigm shift leads to an approach that incorporates prior climatological information into BMA ensemble postprocessing through Bayes?s theorem. This new approach is shown to cure BMA?s ill treatment of extreme weather by providing a posterior BMA distribution whose probabilistic forecasts are reliable for both extreme and nonextreme weather forecasts.