A stochastic model for the time distribution of hourly rainfall depth

Abstract

A probabilistic characterization of temporal storm patterns is presented wherein a storm is defined as an uninterrupted sequence of consecutive hourly rainfalls. A stochastic model is proposed to determine the probability distributions of rainfall accumulated at the end of each time unit within a total storm duration. An illustrative application of the model was made by using a 32‐year hourly rainfall record at Dorval Airport on Montreal Island. The hourly rainfall depth was assumed to be an exponentially distributed random variable. The probability of any given number of consecutive rainy hours was determined by first‐ and second‐order Markov chains. Statistical tests were performed to test the fit of the Markov model to the sequence of wet hours. The agreement between the observations and the proposed model is discussed. It is concluded that the methodology in this study is more flexible and more general than those that have been used in previous investigations. By using the stochastic model developed, a storm profile can be characterized in terms of the time of occurrence of a storm, the total storm depth, and the probability estimates of accumulated rainfalls at the end of each time unit within the total storm duration.