Bayesian post-processing of multi-model ensemble forecasts

Ensemble weather forecasts often under-represent uncertainty, leading to over-confidence in their predictions. Multi-model ensemble (MME) forecasts combining several individual ensembles have been shown to display greater skill than single-ensemble forecasts in predicting temperatures, but tend to retain some bias in their joint predictions. Established postprocessing techniques may be able to correct bias and calibration issues in univariate forecasts, but are generally not designed to handle multivariate forecasts (of several variables or at several locations, say). This thesis proposes a flexible multivariate Bayesian postprocessing framework, based on a directed acyclic graph representing the relationships between the ensembles and the weather quantity of interest. The posterior forecast is inferred from available ensemble forecasts and an estimate of the shared model error, obtained from a collection of past forecast-observation pairs. Further contributions of the thesis address the problem of improving the estimate of this shared discrepancy, in order to obtain a more accurate and better calibrated posterior forecast. The first of these focuses on the selection of appropriate training cases from which to estimate the required correction, using analogues selected on the basis of a low-dimensional representation of the prevailing weather regime predicted by each ensemble. The second is motivated by reducing the uncertainty about the discrepancy, by combining two sources of information through Bayes linear updateing. The second-order exchangeability representation underpinning Bayes linear statistics is extended and used to derive a fully multivariate linear adjustment that is able to approximate probabilistic Bayesian inference and is flexible enough to accommodate a judgement of non-zero excess marginal kurtosis. The new methods are evaluated on their performance in postprocessing operational forecasts winter surface air temperatures over selected regions of the UK.