The meta-Gaussian Bayesian Processor of Forecast and its preliminary experiments

One of the trend of the public weather service is to provide users with probabilistic weather forecasts. The continuous improvement of probabilistic forecasting techniques realizes the constant optimization of probabilistic forecast information. Among numerous techniques and methods for probabilistic forecasting, the Bayesian Processor of Forecast (BPF) is a new statistical probabilistic forecasting technique based on the Bayesian statistical theory. The BPF can, based on the Bayesian statisical theory, transform a deterministic forecast from a deterministic forecasting system into a probabilistic forecast according to the statistical relationship between historical observations and forecasts from that system that is able to denote the forecasting performance of that deterministic system to quantify the forecasting uncertainty of that deterministic forecast. The meta-Gaussian likelihood model is suitable for several kinds of stochastic dependence structures with monotone likelihood ratio, so the metaGaussian BPF adopting this kind of likelihood model can be flexibly applied in many fields, such as meteorology, and hydrology. After the Bayes theorem with two continuous random variables and the normallinear BPF are briefly introduced, this paper discusses the metaGaussian BPF for a continuous predictand using one single predictor. In order to test its performance, a preliminary experiment of the metaGaussian BPF is carried out, using daily control forecasts (with a leadtime of 96 hours) from the NMC, ECMWF and NCEP ensemble predictions of surface temperature ( T2m ) at 00:00 UTC at Changsha station and Wuhan station during January 2008 as the deterministic forecasting data. The analysis of experiment results shows that the metaGaussian BPF can transform a control forecast of T2m from any one of the three ensemble predictions into a probabilistic forecast of T2m, which quantifies the forecasting uncertainty of that control forecast; the performances of the T2m probabilistic forecasts obtained from different control forecasts are different from each other.