Submitted to Monthly Weather Review

One widely accepted measure of the utility of ensemble prediction systems is the rela-tionship between ensemble spread and deterministic forecast accuracy. Unfortunately, this relationship is often characterized by spread-error linear correlations, which oversimplies the true spread-error relationship and ignores the possibility that some end users have categorical sensitivities to forecast error. In the present paper, a simulation study is undertaken to es-timate the idealized spread and error statistics for stochastic ensemble prediction systems of nite size. Under a variety of spread and error metrics, the stochastic ensemble spread-error joint distributions are characterized by increasing scatter as the ensemble spread grows larger. A new method is introduced that recognizes the inherent nonlinearity of spread-error joint distributions and capitalizes on the fact that the probability of large forecast errors increases with ensemble spread. The ensemble spread-error relationship is measured by the skill of probability forecasts that are constructed from a history of ensemble-mean forecast errors using only cases with similar ensemble spread. Thus, the value of ensemble spread information is quantied by the ultimate benet that is realized by end users of the probability forecast