Advanced statistical post-processing of ensemble weather forecasts

Abstract

Today, weather forecasts are generated by evolving the current state of the atmosphere through time subject to established mathematical and physical laws. The resulting forecasts are considerably more accurate than those produced using any other approach that humans have devised to predict the weather. Nonetheless, these forecasts are imperfect. In particular, errors arise in the forecast due to limitations in both our theoretical understanding of the atmosphere and our practical ability to reproduce it. This, combined with the atmosphere's chaotic nature, means obtaining a perfect forecast of the future weather is, for practical purposes, impossible. It is therefore imperative that a forecast is issued alongside its associated uncertainty. This is often achieved by generating an ensemble of weather forecasts that differ in their initial conditions, and possibly also the formulation of the dynamical weather model which with they are produced. However, due to errors in their construction, operational ensemble forecasts themselves possess systematic deficiencies. For this reason, it is necessary to apply an a posteriori adjustment to the ensemble forecast, so that it provides a more realistic representation of the weather that will occur. Several statistical methods have been proposed for this purpose that can not only correct for systematic errors present in the dynamical models, but can issue forecasts that are probabilistic, thus accounting for the uncertainty inherent in the forecast scenario. Such statistical post-processing methods have become an integral component of operational forecasting suites over the last decade. Recently, however, studies have demonstrated that conventional post-processing methods can be ameliorated by leveraging additional sources of information within the statistical models. With this in mind, this thesis seeks to recognise circumstances under which the performance of dynamical weather models is expected to change, thereby indicating what information should be incorporated within statistical post-processing methods. In particular, previous studies have indicated that the errors in dynamical weather models may depend on the occurrence of certain patterns in the synoptic-scale behaviour of the atmosphere, and we therefore postulate that these atmospheric regimes can be utilised when post-processing. A general framework for incorporating this regime information into established post-processing methods is proposed, and its merits are demonstrated in a variety of circumstances. A novel approach to evaluate the performance of forecasts is also introduced that can help to identify situations where incorporating information into post-processing methods is expected to be beneficial.