A Markov Renewal Model for rainfall occurrences

A probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented. By defining an event as a day with measurable precipitation the model is cast into the discrete‐time point process framework. In the proposed model the sequence of times between events is formed by sampling from two geometric distributions, according to transition probabilities specified by a Markov chain. The model belongs to the class of Markov renewal processes and exhibits clustering relative to the independent Bernoulli process. As a special case, it reduces to a renewal model with a mixture distribution for the interarrival times. The rainfall occurrence model coupled with a mixed exponential distribution for the nonzero daily rainfall amounts was applied to the daily rainfall series for Snoqualmie Falls, Washington, and was successful in preserving the short‐term structure of the occurrence process, as well as the distributional properties of the seasonal rainfall amounts.