Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation
WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
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Ensemble prediction systems typically show positive spread-error correlation, but are subject to forecast bias and underdispersion. This work proposes the use of ensemble model output statistics EMOS, an easy to implement post-processing technique that addresses both forecast bias and underdispersion. The technique is based on multiple linear regression. The EMOS technique yields probabilistic forecasts that take the form of Gaussian predictive probability density functions PDFs for continuous weather variables, and can be applied to gridded model output. The EMOS predictive mean is an optimal, bias-corrected weighted average of the ensemble member forecasts, with coefficients that are constrained to be nonnegative and associated with the member model skill. The EMOS predictive mean provides a highly accurate deterministic-style forecast. The EMOS predictive variance is a linear function of the ensemble spread. Formatting the EMOS coefficients, the method of minimum CRPS estimation is introduced. The minimum CRPS estimator finds the coefficient values that optimize the continuous ranked probability score CRPS for the training data. The EMOS technique was applied to 48-hour forecasts of sea level pressure and surface temperature over the North American Pacific Northwest. When compared to the bias-corrected ensemble, deterministic-style EMOS forecasts of sea level pressure had root-mean-square error 9 less and mean absolute error 8 less. The EMOS predictive PDFs were much better calibrated than the raw ensemble or the bias-corrected ensemble, and they were sharp in that prediction intervals were considerably shorter on average than those obtained from climatological forecasts. Perhaps surprisingly, the EMOS ensemble was frequently sharper than the raw ensemble. When compared to the bias-corrected ensemble, EMOS improved the continuous ranked probability score by 16. It also improved the ignorance score by 3.7.
- Statistics and Probability