Modelling Spatial and Non-Linear Trends in Climate Data Using Gaussian Process Regression and Generalized Additive Model

Abstract

Accurate modeling of climate variability is critical for understanding the impacts of climate change and supporting data-driven adaptation strategies. Traditional parametric models, while widely used, often struggle to capture the complex non-linear relationships and spatial dependencies that characterize climate systems, especially in regions with diverse geography such as Kenya. This study aimed to apply two non-parametric statistical approaches—Generalized Additive Models (GAM) and Gaussian Process Regression (GPR)—to model spatial and non-linear trends in climate data over Kenya. Daily climate variables, including temperature and precipitation, were obtained from the ERA5-Land dataset using Google Earth Engine, spanning the period from 2015 to 2024. GAM was used to model the smooth effects of covariates such as time, elevation, and precipitation, while GPR was implemented using a Mat´ern covariance kernel to capture residual spatial autocorrelation. The models were evaluated using RMSE, MAE, and 2 , and parameter estimation was conducted via penalized likelihood and L-BFGS optimization techniques. The results demonstrated that GAM effectively captured structured non-linear effects and provided interpretable smooth functions, while GPR performed better in modeling spatial variability and uncertainty. Both models outperformed traditional linear approaches, with GPR offering superior accuracy in areas with high spatial heterogeneity. The findings affirm that GAM and GPR are powerful and complementary tools for climate modeling in complex environmental contexts. In conclusion, this study confirms the suitability of non-parametric approaches for climate modeling in data-rich, spatially heterogeneous settings. Further research is recommended to explore integrated hybrid GAM–GPR models, extend the methodology to multivariate climate indicators, and evaluate its performance in other regions or under future climate scenarios.