A Framework for Statistical Postprocessing of Ensemble Forecasts Using Cluster-Weighted Modeling

A framework for statistical postprocessing of ensemble forecasts is introduced based on modeling jointly the probability density of the raw ensemble and the calibrated predictive distribution of a quantity of interest. The probability density of the raw ensemble is modeled as a sum over clusters; each cluster is associated with a simple, e.g., linear probabilistic model into the space of the calibrated forecast. The total predictive distribution is given as a sum over the ensemble members. The clusters may be conditioned on additional variables such as large-scale flow regimes or different forecast models used for different ensemble members. The standard choice for the basic cluster distributions is Gaussian; for nonnegative or strongly skewed variables such as wind speed or precipitation other distributions may be more appropriate. Model parameters are estimated from historical data according to maximum likelihood using a suitable expectation-maximization algorithm. The new methodology contains known methods such as Bayesian model averaging, nonhomogeneous Gaussian regression and ensemble dressing as special cases. The technique is tested with reforecast data for 2m temperature in the UK. Substantial gains in forecast skill over more traditional postprocessing methods are demonstrated.