Stochastic Modeling of Rainfall in Peninsular Malaysia Using Bartlett Lewis Rectangular Pulses Models

Abstract

Three versions of Bartlett Lewis rectangular pulse rainfall models, namely, the Original Bartlett Lewis (OBL), Modified Bartlett Lewis (MBL), and 2N-cell-type Bartlett Lewis model (BL2n), are considered. These models are fitted to the hourly rainfall data from 1970 to 2008 obtained from Petaling Jaya rain gauge station, located in Peninsular Malaysia. The generalized method of moments is used to estimate the model parameters. Under this method, minimization of two different objective functions which involve different weight functions, one weight is inversely proportional to the variance and another one is inversely proportional to the mean squared, is carried out using Nelder-Mead optimization technique. For the purpose of comparison of the performance of the three different models, the results found for the months of July and November are used for illustration. This performance is assessed based on the goodness of fit of the models. In addition, the sensitivity of the parameter estimates to the choice of the objective function is also investigated. It is found that BL2n slightly outperforms OBL. However, the best model is the Modified Bartlett Lewis MBL, particularly when the objective function considered involves weight which is inversely proportional to the variance.