Smoothing forecast ensembles with fitted probability distributions

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Abstract
Forecast ensembles from the European Centre for Medium‐Range Weather Forecasts Ensemble Prediction System for surface‐weather variables are smoothed by fitting Gaussian distributions. The possibility of bifurcation or other non‐Gaussian behaviours in an ensemble is allowed for by including probability mixtures of two Gaussian distributions when justified by the data. Variables that are clearly non‐Gaussian (wind speed and cloud cover) are transformed before fitting, and multivariate data with dimensions as high as four are considered. The smoothed ensembles provide more‐accurate quantile and probability estimates in a perfect‐model setting, particularly for small ensemble sizes and more‐extreme events. This advantage increases in the presence of random errors in the ensemble means, but diminishes for underdispersed ensembles. Allowing representation of ensembles as Gaussian mixtures also leads to a sharper ‘spread–skill’ relationship in the data considered. Copyright © 2002 Royal Meteorological Society.

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