Extended-Range Probability Forecasts Based on Dynamical Model Output

A probability forecast has advantages over a deterministic forecast as the former offers information about the probabilities of various possible future states of the atmosphere. As physics-based numerical models find their success in modern weather forecasting, an important task is to convert a model forecast, usually deterministic, into a probability forecast. This study explores methods to do such a conversion for NCEP’s operational 500-mb-height forecast and the discussion is extended to ensemble forecasting. Compared with traditional model-based statistical forecast methods such as Model Output Statistics, in which a probability forecast is made from statistical relationships derived from single model-predicted fields and observations, probability forecasts discussed in this study are focused on probability information directly provided by multiple runs of a dynamical model—eleven 0000 UTC runs at T62 resolution. To convert a single model forecast into a strawman probability forecast (single forecast probability or SFP), a contingency table is derived from historical forecast–verification data. Given a forecast for one of three classes (below, normal, and above the climatological mean), the SFP probabilities are simply the conditional (or relative) frequencies at which each of three categories are observed over a period of time. These probabilities have good reliability (perfect for dependent data) as long as the model is not changed and maintains the same performance level as before. SFP, however, does not discriminate individual cases and cannot make use of information particular to individual cases. For ensemble forecasts, ensemble probabilities (EP) are calculated as the percentages of the number of members in each category based on the given ensemble samples. This probability specification method fully uses probability information provided by the ensemble. Because of the limited ensemble size, model deficiencies, and because the samples may be unrepresentative, EP probabilities are not reliable and appear to be too confident, particularly at forecast leads beyond day 6. The authors have attempted to combine EP with SFP to improve the EP probability (referred to as modified forecast probability). Results show that a simple combination (plain average) can considerably improve upon both the EP and SFP.