Bayesian approach to decision making using ensemble weather forecasts

The economic value of ensemble-based weather or climate forecasts is generally assessed by taking the ensembles at "face value." That is, the forecast probability is estimated as the relative frequency of occurrence of an event among a limited number of ensemble members. Despite the economic value of probability forecasts being based on the concept of decision making under uncertainty, in effect, the decision maker is assumed to ignore the uncertainty in estimating this probability. Nevertheless, many users are certainly aware of the uncertainty inherent in a limited ensemble size. Bayesian prediction is used instead in this paper, incorporating such additional forecast uncertainty into the decision process. The face-value forecast probability estimator would correspond to a Bayesian analysis, with a prior distribution on the actual forecast probability only being appropriate if it were believed that the ensemble prediction system produces perfect forecasts. For the cost-loss decision-making model, the economic value of the face-value estimator can be negative for small ensemble sizes from a prediction system with a level of skill that is not sufficiently high. Further, this economic value has the counterintuitive property of sometimes decreasing as the ensemble size increases. For a more plausible form of prior distribution on the actual forecast probability, which could be viewed as a "recalibration" of face-value forecasts, the Bayesian estimator does not exhibit this unexpected behavior. Moreover, it is established that the effects of ensemble size on the reliability, skill, and economic value have been exaggerated by using the face-value, instead of the Bayesian, estimator.