Simulation Models of Sequences of Dry and Wet Days

Abstract

A new statistical model has been developed for the simulation of sequences of dry and wet days. The model is based on the discrete autoregressivemoving average (DARMA) family of stochastic processes, which includes the Markov chain as a particular case. The model building is based on a three‐step procedure consisting of identification, estimation, and model selection. The model identification and parameter estimation are based on the best fit of the autocorrelation function, while the selection of the optimum model is based on the best reproduction of the probability distribution function of the lengths of the runs of dry days and wet days. The model has thus the property of reproducing the persistence of dry spells and wet spells which are important in the evaluation and forecast of droughts and floods. Excellent results were obtained with rainfall data from Indiana, which indicate that the models are useful for scheduling irrigation of crops in the Central United States and possibly elsewhere.