A coherent set of theoretically-based techniques is being developed for probabilistic forecasting of weather variates. The basic technique, called Bayesian Processor of Output (BPO), processes single values of multiple predictors, extracted from the output of a numerical weather prediction (NWP) model, into a posterior distribution function of a predictand. The extended technique, called Bayesian Processor of Ensemble (BPE), processes an ensemble of estimates of a predictand generated by multiple integrations of a NWP model, and optimally fuses the ensemble with climatic data in order to quantify uncertainty about the predictand. As is well known, Bayes theorem provides the optimal theoretical framework for fusing information from different sources and for obtaining the posterior distribution function of a predictand. Using a family of such distribution functions, a given raw ensemble can be mapped into a posterior ensemble, which is well calibrated at every point in space and time, has maximum informativeness, and preserves the spatio-temporal and inter-variate dependence structure of the NWP output fields. The challenge is to develop and test the BPE suitable for operational forecasting.

The BPE will be developed and tested in two versions, for (i) binary predictands (e.g., indicator of precipitation occurrence), and (ii) continuous predictands (e.g., precipitation amount conditional on precipitation occurrence, temperature, visibility, ceiling height, wind speed). The first test will involve the production and verification of probabilistic temperature forecasts for up to 16 days ahead. The primary benchmark for evaluation of the BPE will be the frequentist technique used currently in operational forecasting by the National Centers for Environmental Prediction.

This talk will give a tutorial introduction to the principles and procedures behind the BPE, using the temperature ensemble data as a demonstration vehicle. It will also set the stage for a report of empirical results from the search for the sufficient statistics of the ensemble — the subject of a companion talk at this conference.