A point process model of summer season rainfall occurrences

A point process model of summer season rainfall occurrences is developed. The model, which is termed an RCM process, is a member of the family of Cox processes (Poisson processes for which the rate of occurrence of events varies randomly over time). Model development is based on counts and interarrival time statistics estimated from Potomac River basin rainfall data. The counting parameters used are the conditional intensity function, index of dispersion, and counts spectrum; the interarrival time parameters are the coefficient of variation and the autocorrelation function. Explicit results are presented for the counts and interarrival time parameters of RCM processes. Of particular importance in this paper is the interpretation of clustering suggested by the form of the RCM process. For the RCM process the rate of occurrence alternates between two states, one of which is 0, the other positive. During periods when the intensity is 0, no events can occur. The form of the intensity process suggests that clustering of summer season rainfall occurrences in the Potomac River basin results from the alternation of wet and dry periods. Computational results are presented for two extensions of the RCM process model of rainfall occurrences: a marked RCM process model of rainfall occurrences and associated storm depths and a bivariate RCM process model of rainfall occurrences at two sites.