Probabilities for ensemble forecasts reflecting climate information

A simple but general probability adjustment procedure is proposed for creating climate-series/probability sets that reflect historical frequencies adjusted for climate forecast information. Often forecast information is given as the conditional probability of below-normal, normal, and above-normal temperature or rainfall depths, though forecast information also can be described by the conditional mean and standard deviation of key variables such as seasonal runoff. Probability adjustment methods developed by Croley and by Wilks assign the same probability to all climate series in selected categories. This results in a discontinuity at the interval boundaries, and can seriously misrepresent the mean and variance of the conditional distribution of key variables. The proposed adjustment is based on a frequency model of the unconditional and conditional distributions of key variables. This framework allows derivation of a consistent and smooth set of probabilities for climate series across the entire range of a key variable reflecting the change in the likelihood of each individual climate series. Examples show the improvements obtained in the approximation of the moments and the cumulative distribution function. The paper also considers multivariate adjustments to reflect several forecasts considering different time periods, different regions, or different variables. Examples for normal and non-normal cases illustrate the care needed to ensure that the cross-correlations among climate variables are correctly represented, otherwise the joint dependence is easily distorted.