A simple method for generating daily rainfall data

Abstract

In recent years, agricultural scientists have developed considerable interest in modeling and simulation of rainfall as new ways of analyzing rainfall data and assessing its impact on agriculture. Among the proposed methods, a combination of Markov chain and gamma distribution function is recognized as a simple approach and is demonstrated to be effective in generating daily rainfall data for many environments. Unfortunately, this method requires that many years of daily weather records be available for estimating the model parameters. Thus the availability of the weather data limits the applicability of the simulation method. When these model parameters are evaluated over time and at different places, however, certain general characteristics are revealed. First, the transitional probability of a wet day followed by a wet day tends to be greater but parallel to the transitional probability of a dry day followed by a wet day. This phenomenon leads to a linear relationship of the transitional probabilities to the fraction of wet days per month. Second, the beta parameter in a gamma distribution function, which is used to describe the amount of rainfall, is closely related to the amount of rain per wet day owing to the positive skewness of the rainfall distribution. Based on these relationships, a simple method is introduced, by which model parameters can be estimated from monthly summaries instead of from daily values. The suggested method, therefore, provides a convenient vehicle for applying weather simulation models to areas in which its use had been impossible because of the unavailability of long series of daily weather data.