A Measure of Skill in Forecasting a Continuous Variable

Abstract

To test the skill of a forecaster the rule for the score S, for the quantitative forecast of Temperature or a similar variable, becomes S = ?ln(1 ? P1P2 ? 1 where P1 is the cumulative climatic frequency of the forecast value TF, or the cumulative climatic frequency of the subsequently verified value Tv, whichever is smaller. The value P2 is the greater of these two frequencies. Such frequencies must be made conditional to the initial state of the weather in order to properly reward forecasters for recognizing future changes in the weather. For the quantitative forecast of precipitation, or similar variables, there are several alternate formulas for skill scores, each formula depending upon whether or not any precipitation is forecast or observed, or both forecast and observed. This system of scoring assures that unskilled strategies, such as the forecasting of the mart frequent values, or persistence forecasting, will net the forecaster an expected average of zero. For individual accurate forecasts the rewards are greatest but still depend on the frequency or infrequency of the verified events. For inaccurate forecasts the rewards can be positive or negative, depending upon the sign and amount of change that is predicted, as well as the subsequent verification.