A study on the characteristics of rainfall data and its parameter estimates

Abstract

The modeling of the rainfall process has been of interest in simulation studies to assess its impact in the fields of agriculture, water management and others. The rainfall data series used has been obtained from the Malaysian Drainage and Irrigation Department for a 33 year period from 1975 to 2007. The purpose of this study is to investigate the Tweedie family of distributions and determine the appropriate distribution to model the rainfall data using the parameter estimated. Based on the estimated parameter, it was suggested that the Gamma distribution which is a special case of the Tweedie family of distributions is suitable to model the rainfall data instead of the Poisson-gamma distribution. Consequently, a combination of a first order Markov chain and gamma distribution function is identified to model the rainfall process of occurrence and amount separately on a monthly timescale for the ten selected rain gauge stations across Peninsular Malaysia. These model parameter estimates were obtained using the method of maximum likelihood. Conversely, during the estimation of these model parameters certain general characteristics were revealed. Firstly, the transitional probability of a wet day to a wet day was higher but parallel to the transition from a dry day to a wet day. This characteristic revealed the linear relationship between the transitional probabilities and the monthly fraction of wet days. Secondly, the parameter in the gamma distribution functions used to describe the amount of rainfall, is related to the monthly amount of rain per wet day. Therefore, a short method is proposed using the regression technique to estimate the model parameters from these monthly summaries. The relative error analysis revealed that there was no significant difference between the long and short method parameter estimates. Hence, this short method would be very useful in cases where there is a lack of detailed daily rainfall data available.