Combining spatial and ensemble information for probabilistic weather forecasting

Forecast ensembles typically show a spread-skill relationship, but they are also often underdispersive, and therefore uncalibrated. Bayesian Model Averaging (BMA) is a statistical post-processing method that generates calibrated ensemble of forecasts for single weather quantities.

This paper presents a simple statistical method, called Spatial Bayesian Model Averaging (Spatial BMA), that extends BMA to forecasts of weather fields by combining it with the Geostatistical Output Perturbation (GOP) Method and that reduces to BMA for each location individually.

Spatial BMA produces a statistical ensemble of forecasts of weather fields, that accounts for the spatial structure of the metereological field and honors the ensemble information contained in the dynamical ensemble. Members of the Spatial BMA ensemble are generated according to BMA weights and are obtained by "dressing" members of the underlying nsemble with a forecast error field simulated using a geostatistical model, as in the GOP method.

We applied Spatial BMA to 48-hour mesoscale forecasts of temperature over the North-American Pacific Northwest for the one-year period January-December 2004, using the University of Washington MM5 eight-member ensemble. Marginal verification showed that the Spatial BMA ensemble is better calibrated than the raw ensemble. Joint verification indicated that the Spatial BMA ensemble reproduces the spatial structure of the observations more accurately than the raw ensemble or the Independent BMA ensemble, that is an ensemble obtained by applying the BMA technique independently at each observing station. Verification for average forecasts over National Weather Service Forecast Zones and for minimum forecast temperature along a freeway showed that accounting for spatial correlation is of essential importance for such composite quantities that are important for forecasts for the public and for decision makers. In both situations, the Spatial BMA ensemble was much better calibrated than the raw ensemble or the Independent BMA ensemble, both of which were severely underdispersive.