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8.1A
Forecast verification of extremes: Use of extreme value theory

Making use of the calibration-refinement factorization, the focus is on modeling the extreme tails of the conditional distribution of the weather observation given a forecast. In this way, only the univariate (not the more complex bivariate) statistical extreme value theory need be considered. Extremes have two basic features, their rate of occurrence and their intensity. The exceedance of a high (or falling below a low) threshold by the weather variable is modeled by a conditional Poisson distribution, whose rate parameter is expanded as a function of the forecast. Likewise, the excess over a high (or deficit below a low) threshold of the weather variable is modeled by a conditional generalized Pareto distribution, whose scale parameter depends on the forecast. In this way, whether or not there is any skill (or how much skill exists) in forecasting weather extremes corresponds to determining whether or not (or to what extent) using the forecast as a covariate improves the fit (e.g., via a likelihood ratio test).

As a check, the proposed method is applied to Monte Carlo simulations for the hypothetical situation in which the joint distribution of forecasts and observations is a bivariate normal. It is further applied to a set of specialized NWS minimum temperature forecasts and observations at Yakima, WA. Because of the risk of damage to fruit buds from freezing during their development, these forecasts were made available to orchardists each spring.