Calibrated Probabilistic Mesoscale Weather Field Forecasting: The Geostatistical Output Perturbation

Probabilistic weather forecasting consists of finding a joint probability distribution for future weather quantities or events. It is typically done by using a numerical weather prediction model, perturbing the inputs to the model in various ways, often depending on data assimilation, and running the model for each perturbed set of inputs. The result is then viewed as an ensemble of forecasts, taken to be a sample from the joint probability distribution of the future weather quantities of interest. This is typically not feasible for mesoscale weather prediction carried out locally by organizations without the vast data and computing resources of national weather centers. Instead, we propose a simpler method which breaks with much previous practice by perturbing the outputs, or deterministic forecasts, from the model. Forecast errors are modeled using a geostatistical model, and ensemble members are generated by simulating realizations of the geostatistical model. The method is applied to 48-hour mesoscale forecasts of temperature in the US Pacific Northwest in 2000 and 2002. The resulting forecast intervals turn out to be well calibrated for individual meteorological quantities, to be sharper than those obtained from approximate climatology, and to be consistent with aspects of the spatial correlation structure of the observations.