Spatial and temporal variabilities of rainfall data using functional data analysis

Abstract

The main concern of this study is to build a functional data object from discrete rainfall observations by looking at how rainfall fluctuates, both spatially and temporally, in the form of smoothing curves. The functional data methods employed in this study are able to extract additional information contained in the function and its derivatives which may not be normally available from traditional statistical methods. Functional concepts such as functional descriptive statistics and functional analysis of variance were applied to describe the spatial and temporal rainfall variations at the stations and at any time throughout the year. This study involves 32 rainfall stations in Peninsular Malaysia and rainfall records for 32 years. Eleven basis functions were used to describe the unimodal rainfall pattern for stations in the East Peninsula, while five and seven bases were required to describe the rainfall pattern for stations in the northwest, west, southwest, and central regions of the peninsula. Based on the location and scale curves, the highest mean and the highest variability of rainfall were observed during the northeast monsoon flow. On the other hand, the concept of functional analysis of variance allows the detailed information in determining when, in a time series, differences may exist in rainfall profiles between two or more regions. In general, the findings suggested that the rainfall profiles of the regions are very dependent on their geographical and spatial locations, as well as the monsoon effect, which reflects the time of year.