Ensemble simulations and forecasts provide probabilistic information about the inherently uncertain climate system. Counting the number of ensemble members in a category is a simple nonparametric method of using an ensemble to assign categorical probabilities. Parametric methods of assigning quantile-based categorical probabilities include distribution fitting and generalized linear regression. Here the accuracy of counting and parametric estimates of tercile category probabilities is compared. The methods are first compared in an idealized setting where analytical results show how ensemble size and level of predictability control the accuracy of both methods. The authors also show how categorical probability estimate errors degrade the rank probability skill score. The analytical results provide a good description of the behavior of the methods applied to seasonal precipitation from a 53- yr, 79-member ensemble of general circulation model simulations. Parametric estimates of seasonal precipitation tercile category probabilities are generally more accurate than the counting estimate. In addition to determining the relative accuracies of the different methods, the analysis quantifies the relative importance of the ensemble mean and variance in determining tercile probabilities. Ensemble variance is shown to be a weak factor in determining seasonal precipitation probabilities, meaning that differences between the tercile probabilities and the equal-odds probabilities are due mainly to shifts of the forecast mean away from its climatological value.
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