The Bayesian Processor of Ensemble (BPE) is a theoretically-based technique for probabilistic forecasting of weather variates. It processes an ensemble of forecasts output from a numerical weather prediction (NWP) model, combines forecasts (ensemble or single value) from several models, and optimally fuses them with climatic data in order to quantify uncertainty about a predictand in the form of a posterior distribution function. Using a family of such distribution functions, a given raw ensemble can be mapped into a posterior ensemble, which is well calibrated (against the climatic distribution of the predictand) 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 BPE comes furnished with (i) the meta-Gaussian model for multivariate distributions, which fits meteorological data well as it allows all forms (non-Gaussian) of marginal distribution functions, as well as non-linear and heteroscedastic dependence structures between predictors and predictand, (ii) a method for identifying sufficient statistics of an ensemble (to reduce the dimensionality without losing predictive information), (iii) a procedure for estimating parameters from asymmetric samples (typically, a long climatic sample of the predictand and a short joint sample of the forecast-predictand vector), and (iv) a method for handling non-stationarities in the predictand and the forecast due to the annual cycle and the lead time.

This talk will provide an overview of the principles and procedures behind the BPE, and will illustrate them with various data, including 20-member ensemble forecasts and high-resolution forecasts of surface temperature produced at the National Centers for Environmental Prediction.