Statistical analysis on mean rainfall and mean temperature via functional data analysis technique

Abstract

Generally, the climate variable such as rainfall and temperature data are collected on daily, monthly and annual basis which is in the form of discrete observations. The purpose of this study is to build up a functional data object from these observations which could be used to represent the continuous rainfall-temperature process at each station. This study is interested in looking on how daily means for both temperature and rainfall fluctuate at each station over time. Smoothing technique such as Fourier series is used to capture the variations. Based on the fitted smoothing curve, a summary statistics on a typical weather patterns and variability in these rainfall and temperature patterns could be examined. Using the concept of functional analysis, the test results indicated that there exist significance differences in the functional means of rainfall and temperature between studied stations. Besides, a functional relationship between rainfall and temperature could also be established based on functional linear models.