Abstract

Relative humidity (RH) is an important component of the environment, and exhibits complex temporal patterns that may be difficult to characterise adequately using conventional statistical summaries of high-frequency meteorological observations. Functional Data Analysis (FDA) provides a framework for representing these observations as continuous functions, enabling the investigation of temporal variation, rates of change and dominant patterns of variability. This study applies FDA to high-frequency meteorological data from the South African Weather Service to investigate the temporal dynamics of RH and its relationships with temperature and wind speed. Hourly observations collected in Cape Town over the period 1995–2024 are represented as smooth functions over time. Functional descriptive analysis is used to examine the mean structure and variability of RH, while functional principal component analysis is employed to identify dominant modes of variation. Functional derivatives are also considered to investigate changes in RH over time and to provide further insight into its temporal dynamics. The relationships between RH and the other meteorological variables are investigated within a functional regression framework. The findings from the study are intended to contribute to the development of functional statistical approaches for environmental data analysis and to inform further research into the modelling and prediction of RH.