Comparing rainfall patterns between regions in Peninsular Malaysia via a functional data analysis technique

Normally, rainfall data is collected on a daily, monthly or annual basis in the form of discrete observations. The aim of this study is to convert these rainfall values into a smooth curve or function which could be used to represent the continuous rainfall process at each region via a technique known as functional data analysis. Since rainfall data shows a periodic pattern in each region, the Fourier basis is introduced to capture these variations. Eleven basis functions with five harmonics are used to describe the unimodal rainfall pattern for stations in the East while five basis functions which represent two harmonics are needed to describe the rainfall pattern in the West. Based on the fitted smooth curve, the wet and dry periods as well as the maximum and minimum rainfall values could be determined. Different rainfall patterns are observed among the studied regions based on the smooth curve. Using the functional analysis of variance, the test results indicated that there exist significant differences in the functional means between each region. The largest differences in the functional means are found between the East and Northwest regions and these differences may probably be due to the effect of topography and, geographical location and are mostly influenced by the monsoons. Therefore, the same inputs or approaches might not be useful in modeling the hydrological process for different regions.