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.
