Combination of Multimodel Probabilistic Forecasts Using an Optimal Weighting System

Abstract

Abstract In this study, an optimal weighting system is developed that combines multiple seasonal probabilistic forecasts in the North American Multimodel Ensemble (NMME). The system is applied to predict temperature and precipitation over the North American continent, and the analysis is conducted using the 1982–2010 hindcasts from eight NMME models, including the CFSv2, CanCM3, CanCM4, GFDL CM2.1, Forecast-Oriented Low Ocean Resolution (FLOR), GEOS5, CCSM4, and CESM models, with weights determined by minimizing the Brier score using ridge regression. Strategies to improve the performance of ridge regression are explored, such as eliminating a priori models with negative skill and increasing the effective sample size by pooling information from neighboring grids. A set of constraints is put in place to confine the weights within a reasonable range or restrict the weights from departing wildly from equal weights. So when the predictor–predictand relationship is weak, the multimodel ensemble forecast returns to an equal-weight combination. The new weighting system improves the predictive skill from the baseline, equally weighted forecasts. All models contribute to the weighted forecasts differently based upon location and forecast start and lead times. The amount of improvement varies across space and corresponds to the average model elimination percentage. The areas with higher elimination rates tend to show larger improvement in cross-validated verification scores. Some local improvements can be as large as 0.6 in temporal probability anomaly correlation (TPAC). On average, the results are about 0.02–0.05 in TPAC for temperature probabilistic forecasts and 0.03–0.05 for precipitation probabilistic forecasts over North America. The skill improvement is generally greater for precipitation probabilistic forecasts than for temperature probabilistic forecasts.