Functional data analysis and characterisation of temperature and rainfall patterns in Peninsular Malaysia

Effective flood management and climate change adaptation in Malaysia require an in-depth analysis of key climate variables, particularly average annual temperature and rainfall. However, the complexity and high dimensionality of climate datasets present significant analytical challenges for conventional statistical methods. This study employed Functional Data Analysis (FDA) to address these challenges, as FDA offers a more effective means of handling continuous variability in time series data compared to traditional methods. By transforming discrete climate observations into continuous functional representations, FDA captures intricate patterns in the data, offering insights beyond the capabilities of conventional statistical approaches. The study aimed to investigate climate patterns in Peninsular Malaysia by smoothing, aligning, and examining the temporal evolution of climate patterns using FDA methods. Curve smoothing was applied using the roughness penalty approach to ensure accurate functional modelling, and beta-spline functions were adopted to optimise the smoothing process. Landmark registration was then used to align climate curves based on consistent features such as seasonal maxima and minima, enabling clearer temporal analysis. The functional representation of climate curves allowed for the extraction of key statistical features such as mean, variance, and derivative, providing deeper insight into climatic patterns over time. The results showed that transforming discrete climate data into continuous functional forms enabled the analysis to capture seasonal patterns and extreme weather variations more effectively. The registered curves produced stable and interpretable mean curves, while the functional descriptive analysis yielded valuable insights into the pattern of climatic variables. In conclusion, the functional methods prove more effective than conventional techniques in representing and analysing climate variables.