A Practical Model Blending Technique Based on Bayesian Model Averaging

We have developed a technique called Decaying Average Bayesian Model Averaging (DABMA) to blend multiple numerical weather prediction (NWP) forecasts into a single probabilistic consensus. DABMA is based on the Bayesian Model Averaging (BMA) technique proposed by Raftery et al. (2005), but is easier to implement because the algorithm has a closed-form solution and requires less data storage. To create a consensus forecast from an ensemble of NWP models, DABMA assigns weights to each model and creates a probability density function (PDF) by dressing each model with a Gaussian kernel. The DABMA-weighted mean provides an accurate deterministic forecast while the accompanying PDF describes the forecast uncertainty. The DABMA weights and kernel parameters are updated daily with a simple decaying average technique that tracks recent performance. The DABMA storage requirements are small because older model forecasts may be discarded as soon as they are used in the update.

We have conducted several experiments to evaluate DABMA. We applied both DABMA and the original BMA technique to output from a stochastic ensemble and found the methods were comparable in terms of mean absolute error and statistical reliability. The DABMA weights and kernel widths, however, were more stable from day-to-day suggesting DABMA may be less prone to overfitting. To experiment with real data, we used DABMA to blend temperature forecasts from several deterministic MOS products. The DABMA-weighted mean was more accurate than the equally-weighted mean and the DABMA probabilistic forecasts were well-calibrated. We also applied DABMA to output from the Short Range Ensemble Forecast (SREF) System. Specifically, we created calibrated probabilistic forecasts of partial thicknesses and upper air temperatures to facilitate precipitation type forecasting. Based on these experiments, we believe the DABMA technique can be used to generate probabilistic forecast guidance by combining forecasts from a diverse set of numerical weather prediction systems (so called "model blending”).