A Stochastic Model of Dimensionless Thunderstorm Rainfall

Abstract

A concise stochastic model for the nondimensional thunderstorm rainfall process at a point is proposed. The accumulated precipitation process for individual thunderstorms is nondimensionalized by dividing the precipitation at any time by the total precipitation and the elapsed time by the total duration. The dimensionless process is divided into 100 equal time increments, and the depth increments are rescaled to range between 0 and 1. The sequence of rescaled increments Z1, Z2,…, Z9 are assumed to represent a nonhomogeneous Markov process in discrete time with continuous state space. The expected value of the kth rescaled increment, given the k‐1st increment, is assumed to be a linear function of that increment, and the marginal distribution of the first increment and the conditional distributions are assumed to be described by the beta distribution. An analyses of data for 275 thunderstorms observed at the Walnut Gulch Experimental Watershed in southeastern Arizona showed that the proposed model structure is a good approximation for this region. The number of model parameters can be reduced from 26 to a minimum of 10 by approximating the 2 parameters in the conditional expectation function and the conditional beta parameter as polynomial functions of the dimensionless time. Likelihood ratio tests and the Akaike information criterion suggest that the dependence parameters are independent of storm amount and duration, but the conditional beta parameter αk is larger for short‐duration storms than for long‐duration storms. A 13‐parameter model is recommended for disaggregating thunderstorm rainfall in southeastern Arizona.