Statistical analysis of wind and rainfall with functional data analysis technique

Abstract

The speed of wind and rainfall throughout Peninsular Malaysia varies from one region to another, depending on the direction of winds and rainfall that occur because of strong wind and the monsoons. Our data consist of daily mean wind and rainfall data from ten stations and covering 25 years period from 1985 to 2009. The purpose of this study is to convert the wind and rainfall data into a smooth curve by using Functional Data Analysis (FDA) method. The Fourier basis is used in this study in which the wind and rainfall data indicate periodic pattern for ten stations. In this method, to avoid such overfitting data, roughness penalty is added to the least square when constructing functional data object from the observed data. By using small basis functions, the difference is very small between with and without roughness penalty, showing that it is safer to smooth only when required. Meanwhile, with large basis functions and the difference of sum of square is very large, roughness penalty should be added in order to obtain optimal fit data. The graphs with contour plot show the relationship between wind and rainfall data, which illustrate the correlation and cross-correlations functions. Functional linear model also presents the relationship that may exist between wind (functional data) and rainfall (scalar response). Square multiple correlations give strong positive linear correlation, which concludes that the rainfall is influenced by the wind speed.