A Simple Stochastic Model of the Precipitation Process

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  • 1 Department of Meteorology, University of Uppsala, Uppsala, Sweden
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Abstract

A simple and rather general model of the precipitation process is reviewed and some applications and comparisons are made using data from Sweden. This model has been used by several authors so the article is partly a survey of earlier works but also adds some new aspects, comparisons and practical techniques. The model used is a compound Poisson–exponential (Cpe) process. This is a continuous stochastic process, which is compounded from a Poisson process with a number parameter (the mean number of independent precipitation events) and an exponential distribution with an amount parameter (the mean amount at each event). The meaning and the limitations of these physical interpretations are discussed briefly. The basic process can be applied on, e.g., integrated precipitation amounts, the Cpe distribution, and on maximum amounts, the max Cpe distribution. The first application has been discussed in many works, the latter was developed recently and independently by Revfeim (1983a) and Alexandersson (1983). One advantage of this model is that it does not need to be extended or modified to handle periods with zero precipitation. Another advantage is that the parameters can be estimated from the series of monthly precipitation totals. It is important that these techniques do not involve too lengthy calculations which would considerably hamper the practical use. Thus a very fast way of deriving percentiles from a single table for a Cpe distribution is developed here.

Abstract

A simple and rather general model of the precipitation process is reviewed and some applications and comparisons are made using data from Sweden. This model has been used by several authors so the article is partly a survey of earlier works but also adds some new aspects, comparisons and practical techniques. The model used is a compound Poisson–exponential (Cpe) process. This is a continuous stochastic process, which is compounded from a Poisson process with a number parameter (the mean number of independent precipitation events) and an exponential distribution with an amount parameter (the mean amount at each event). The meaning and the limitations of these physical interpretations are discussed briefly. The basic process can be applied on, e.g., integrated precipitation amounts, the Cpe distribution, and on maximum amounts, the max Cpe distribution. The first application has been discussed in many works, the latter was developed recently and independently by Revfeim (1983a) and Alexandersson (1983). One advantage of this model is that it does not need to be extended or modified to handle periods with zero precipitation. Another advantage is that the parameters can be estimated from the series of monthly precipitation totals. It is important that these techniques do not involve too lengthy calculations which would considerably hamper the practical use. Thus a very fast way of deriving percentiles from a single table for a Cpe distribution is developed here.

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