The Poisson Distribution for the Frequency of Rare Levels of Persistent Meteorological Elements.

摘要

Statistical models for meteorological phenomena typically break down at the extremes. For example, the day-to-day rainfall at a location in a given month may be modeled as a Markov process with effective determination of model parameters for a broad range of rainfall categories up to but excluding that of unusually high precipitation. Current techniques of modeling and estimation are somewhat inadequate for determination of quantities such as the probability that a specified extreme level of precipitation will occur at least three times in a given month, and the probability that the extreme level will not occur two days in succession during a given month. This paper delineates the role of the Poisson distribution in approximating such probabilities. The Poisson approximation is shown to be applicable under considerable relaxation of the classical independence assumption, which is inappropriate in meteorology due to the tendency of weather elements such as temperature, atmospheric pressure, and rainfall to 'persist'. Exact bounds on the error of approximation are derived under general conditions, and special attention is given to the case of Markov dependence. Some numerical illustration is provided.