Heteroscedastic Ensemble Postprocessing

Abstract

Ensemble variances provide a prediction of the flow-dependent error variance of the ensemble mean or, possibly, a high-resolution forecast. However, small ensemble size, unaccounted for model error, and imperfections in ensemble generation schemes cause the predictions of error variance to be imperfect. In previous work, the authors developed an analytic approximation to the posterior distribution of true error variances, given an imperfect ensemble prediction, based on parameters recovered from long archives of innovation and ensemble variance pairs. This paper shows how heteroscedastic postprocessing enables climatological information to be blended with ensemble forecast information when information about the distribution of true error variances given an ensemble sample variance is available. A hierarchy of postprocessing methods are described, each graded on the amount of information about the posterior distribution of error variances used in the postprocessing. These homoscedastic methods are used to assess the value of knowledge of the mean and variance of the posterior distribution of error variances to ensemble postprocessing and explore sensitivity to various parameter regimes. Testing was performed using both synthetic data and operational ensemble forecasts of a Gaussian-distributed variable, to provide a proof-of-concept demonstration in a semi-idealized framework. Rank frequency histograms, weather roulette, continuous ranked probability score, and spread-skill diagrams are used to quantify the value of information about the posterior distribution of error variances. It is found that ensemble postprocessing schemes that utilize the full distribution of error variances given the ensemble sample variance outperform those that do not.