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Laurence J. Wilson
Stephane Beauregard
Adrian E. Raftery
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Richard Verret


Bayesian model averaging (BMA) has recently been proposed as a way of correcting underdispersion in ensemble forecasts. BMA is a standard statistical procedure for combining predictive distributions from different sources. The output of BMA is a probability density function (pdf), which is a weighted average of pdfs centered on the bias-corrected forecasts. The BMA weights reflect the relative contributions of the component models to the predictive skill over a training sample. The variance of the BMA pdf is made up of two components, the between-model variance, and the within-model error variance, both estimated from the training sample. This paper describes the results of experiments with BMA to calibrate surface temperature forecasts from the 16-member Canadian ensemble system. Using one year of ensemble forecasts, BMA was applied for different training periods ranging from 25 to 80 days. The method was trained on the most recent forecast period, then applied to the next day’s forecasts as an independent sample. This process was repeated through the year, and forecast quality was evaluated using rank histograms, the continuous rank probability score, and the continuous rank probability skill score. An examination of the BMA weights provided a useful comparative evaluation of the component models, both for the ensemble itself and for the ensemble augmented with the unperturbed control forecast and the higher-resolution deterministic forecast. Training periods around 40 days provided a good calibration of the ensemble dispersion. Both full regression and simple bias-correction methods worked well to correct the bias, except that the full regression failed to completely remove seasonal trend biases in spring and fall. Simple correction of the bias was sufficient to produce positive forecast skill out to 10 days with respect to climatology, which was improved by the BMA. The addition of the control forecast and the full-resolution model forecast to the ensemble produced modest improvement in the forecasts for ranges out to about 7 days. Finally, BMA produced significantly narrower 90% prediction intervals compared to a simple Gaussian bias correction, while achieving similar overall accuracy.

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