Analysing maximum monthly temperatures in South Africa for 45 years using functional data analysis

Abstract

The paper uses Functional Data Analysis (FDA) to explore space and time variation of monthly maximum temperature data of 16 locations in South Africa for the period 1965 - 2010 at intervals of 5 years. We explore monthly maximum temperature variation by first representing data using the B-spline basis functions. Thereafter registration of the smooth temperature curves was performed. This data was then subjected to analysis using phase-plane plots which revealed the constant shifting of energy over the years analysed. We next applied functional Principal Component Analysis (fPCA) to reduce the dimension of maximum temperature curves by identifying the maximum variation without loss of relevant information, which revealed that the first functional PCA explains mostly summer variation while the second functional PCA explains winter variation. We next explored the functional data using functional clustering using K-means to reveal the spatial location of maximum temperature clusters across the country, which revealed that maximum temperature clusters were not consistent over the 45 years of data analysed, and that the cluster points within a cluster were not necessarily always spatially adjacent. The overall analysis has displayed that maximum temperature clusters have not been static across the country over time. To the best of our knowledge, this the first instance of performing in-depth analysis of maximum temperature data for 16 locations in South Africa using various FDA methods.