A new model for quantifying climate episodes

When long records of climate (precipitation, temperature, stream runoff, etc.) are available, either from instrumental observations or from proxy records, the objective evaluation and comparison of climatic episodes becomes necessary. Such episodes can be quantified in terms of duration (the number of time intervals, e.g. years, the process remains continuously above or below a reference level) and magnitude (the sum of all series values for a given duration). The joint distribution of duration and magnitude is represented here by a stochastic model called BEG, for 'bivariate distribution with exponential and geometric marginals'. The model is based on the theory of random sums, and its mathematical derivation confirms and extends previous empirical findings. Probability statements that can be obtained from the model are illustrated by applying it to a 2300-year dendroclimatic reconstruction of water-year precipitation for the eastern Sierra Nevada-western Great Basin. Using the Dust Bowl drought period as an example, the chance of a longer or greater drought is 8%. Conditional probabilities are much higher, i.e. a drought of that magnitude has a 62% chance of lasting for 11 years or longer, and a drought that lasts 11 years has a 46% chance of having an equal or greater magnitude. In addition, because of the bivariate model, we can estimate a 6% chance of witnessing a drought that is both longer and greater. Additional examples of model application are also provided. This type of information provides a way to place any climatic episode in a temporal perspective, and such numerical statements help with reaching science-based management and policy decisions. Copyright (C) 2005 Royal Meteorological Society.