Combination of Multi-Model Probabilistic Forecasts Using Objectively Determined Weights

In this study, we develop an objective weighting method to combine multiple seasonal probabilistic forecasts in the North American Multi-Model Ensemble (NMME). The method is applied to predict precipitation (P) and temperature (T) over the North American continent, and the analysis is conducted using the 1982-2010 hindcasts from eight NMME models, including the CFSv2, CanCM3, CanCM4, CM2.1, FLOR, GEOS5, CCSM4, and CESM models, with weights determined by minimizing Brier Score using ridge regression. Calculation of weights for models in a multi-model ensemble framework has been attempted before, but nearly always for forecasts in terms of physical units — in contrast we work here with forecasts expressed as probabilities. Strategies to improve the performance of ridge regression are explored, such as excluding more years for cross validation, eliminating a-priori models with negative skill, and increasing the effective sample size by pooling information from neighboring grids. A set of constraints is placed to confine the weights within a reasonable range or restrict the weights departing wildly from equal weights, which is the fall-back. So when the predictor-predictand (model forecast-verifying observation) relationships are weak, the multi-model ensemble forecasts return to equal-weight combination. We will present our evaluation for Season-1 probabilistic P and T forecasts in tercile category initialized in January, April, July, and October. Assessments based on various performance metrics (e.g., Brier Score, Probability Anomaly Correlation, and Ranked Probability Skill Score) and reliability (or attributes) will be provided. Challenges arising from category forecasts and how to optimally combine and distribute probabilities into three classes (i.e., above, near, and below normal) will also be discussed.