Categorical Climate Forecasts through Regularization and Optimal Combination of Multiple GCM Ensembles*

A Bayesian methodology is used to assess the information content of categorical, probabilistic forecasts of specific variables derived from a general circulation model (GCM) forecast ensemble, and to combine a ''prior'' forecast (climatological probabilities of each category) with a categorical probabilistic forecast derived from a GCM ensemble to develop posterior, or ''regularized'' categorical probabilities. The combination algorithm assigns a weight to a particular model forecast and to climatology. The ratio of the sample likelihood of the model based on the posterior categorical probabilities, to that based on climatological probabilities, computed over the period of record of historical forecasts, provides a measure of the skill or information content of a candidate model. The weight given to a GCM forecast serves as a secondary indicator of its information content. Model weights are determined by maximizing the likelihood ratio. Results using the so-called ranked probability skill score as an objective function are also obtained, and are found to be very similar to the likelihood-based results.