University of Washington - Department of Statistics & CSSS
Probabilistic weather forecasting consists of finding a joint probability distribution for future weather quantities or events. Information about the uncertainty of weather forecasts can be important for decision-makers (e.g. public transportation authorities, airlines, shipping, military, event planning), as well as the public, but currently is routinely provided only for the probability of precipitation, and not for other weather quantities such as temperature, wind, or amount of precipitation. It is typically done by using a numerical weather prediction model, perturbing the inputs to the model (initial conditions, lateral boundary conditions, physics parameters) in various ways, 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 often uncalibrated, however, and is typically underdispersed.
We first consider probabilistic forecasting of a single weather quantity, such as the temperature at a given place in 48 hours time. We propose a principled statistical method for postprocessing ensembles based on Bayesian Model Averaging (BMA), which is a standard method for combining predictive distributions from different sources. We next consider probabilistic forecasting of an entire weather field. We propose a simple method, the Geostatistical Output Perturbation (GOP) method, which breaks with much previous practice by perturbing the outputs, or deterministic forecasts, and not the inputs, from the numerical weather prediction model. Forecast errors are modeled using a geostatistical model, and the members of the new statistical ensemble are generated by simulating realizations of the geostatistical model using the circulant embedding method.
We applied both methods to probabilistic forecasting of temperature in the Pacific Northwest, and they turned out to be empirically well calibrated for individual meteorological quantities, to be sharper than those obtained from approximate climatology, and to be consistent with the spatial correlation structure of the observations. We also consider the issue of displaying complex information about uncertainty in a way that is useful to users who are under severe time pressure and constraints, and demonstrate the UW BMA Ensemble website, which is a first effort to do this.
This is joint work with Tilmann Gneiting (UW), Yulia Gel (Waterloo), Fadoua Balabdaoui (Gottingen), Michael Polakowski (Oregon State), and Patrick Tewson (UW-APL).