Use of Probability Forecasts to Maximize Various Skill Scores

Whereas categorical forecasts designate a specific category of weather as the predicted future condition, probability forecasts express the uncertainty attending a forecast by giving estimates of the probability of occurrence of each possible weather category at a given time in the future. To compare the accuracy of the two types of forecast, a probability forecast can be converted into a categorical forecast by a procedure of optimization with reference to any prescribed criterion, for example, a loss function. In this paper optimization procedures are derived for converting probability forecasts to categorical forecasts when the precribed criterion is any one of three commonly used skill scores: Heidke, Vernon and Appleman. Probability forecasts of ceiling and visibility are used as examples.