An evolving seasonal forecasting system using Bayes' theorem

Probabilistic seasonal forecasts are produced based on ensembles of two-tier seasonal forecasts made with two different atmospheric models, the results of which are combined. The approach rigorously avoids including information from the future at any time, either forecast or observed, and the system evolves as more forecasts are made and analyses produced. Categorical probability forecasts are produced by application of Bayes' theorem and consist of the probability of observing a particular category given the category in which the ensemble mean forecast falls. These probabilities are estimated from the past operation of the forecast system. The approach differs, therefore, from those that appeal to the intrinsic scatter of the ensemble members or other information to generate the probability estimates.. The method is applied to a sequence of retrospective forecasts covering the period from 1969 to 1994. Skill is measured using the Brier skill score which also evolves with time. Scores for the globe for 500-hPa heights increase with time as the system incorporates additional information but skill is marginal in other than the below normal category. Skill in the tropical area is somewhat higher, and in the Canadian region somewhat lower, than for the globe. Skill broadly compares with other assessments using these data. There is some indication, based on the evolution with time, that skill may continue to increase slowly as more information enters the forecast system.