Chance Behavior of Skin Scores

Abstract

The skill score S=(R ? E)/(T ? E) (representing R actual and E expected successful categorical forecasts in a total of T forecasts) remains a valid tool for assessing the overall quality of current probabilistic long-range forecasts, which start from categorical subdivisions of the forecast area. The skill score definition is modified to become a chi variate with one degree of freedom. Two sets of skill scores computed from forecasts of U.S. monthly precipitation and mean temperature are shown to have frequency distributions of similar shape with nonzero means and standard deviations generally corresponding to smaller independent numbers of verification points than those actually used. The largest skill scores of those examined were obtained for recent precipitation forecasts during a period when forecasts using only climatology were similarly skillful. This suggests that co-operation on part of the climate system remains an essential success ingredient in extended forecasting. A sequential procedure for monitoring the changing level of operational forecasting skill is described.