Scalar-on-Function Regression for Modeling Climate Variable Associations

Abstract

This study aims to investigate the scalar-on-functional relationship through functional regression, focusing on scalar responses, total annual rainfall, and functional predictors represented by daily temperature curves within the context of Malaysia's climate patterns. The distinctiveness of Malaysia's tropical climate, marked by high humidity and consistent temperatures throughout the year, underscores the importance of understanding this relationship for accurate climate modeling and forecasting. A key component of this study is the application of a roughness penalty in constructing Fourier basis functions for temperature regression coefficients, which ensures a smooth and flexible representation of the temperature curves. The study will compare models with a limited number of basis functions against those with a larger number of basis functions supplemented by an additional roughness penalty. The analysis utilises climate data from twelve stations across Peninsular Malaysia, spanning 2010 to 2017. The findings indicate that models incorporating a roughness penalty demonstrate superior performance, as the penalty helps mitigate overfitting by controlling excessive complexity in the estimated functions. Moreover, the results underscore the significant interactions between rainfall and temperature over time, offering critical insights into the dynamics of the Malaysian climate. These insights potentially enhance the region's water resource management, agricultural planning, and climate adaptation strategies.