A functional mixed effect model approach to explore regional climate patterns in Bangladesh

As global warming intensifies, localized climate studies have become essential to understanding the nuanced impacts of climate change, particularly in vulnerable countries like Bangladesh. While global climate models highlight general trends, the detailed temporal and regional variations within countries remain underexplored. Bangladesh, with its susceptibility to climate extremes, requires precise methodologies to analyze short-term climate projections and inform adaptive strategies. This study utilizes the Functional Linear Mixed-effects Model (FLMM), a sophisticated statistical framework for analyzing functional data with repeated observations, to investigate the effects of temporal and regional variations of the effect of daily temperature on annual precipitation across Bangladesh from 2008 to 2022. The population slope function $$\beta _{t}$$ was represented using 35 Fourier basis functions, while individual-level variability $$b_i{(t)}$$ was captured using 25 basis functions. A Residual Maximum Likelihood with Expected Maximisation algorithm (REML-based EM algorithm) estimated fixed effects and random effect variance parameters. The findings reveal significant district-wise variations in rainfall estimates, influenced by daily temperature patterns over time. Additionally, a functional autoregressive model (FAR(1)) highlights the influence of one-year rainfall differences on precipitation projections for the subsequent year. By capturing localized variability and addressing uncertainties, the model provides valuable insights for short-term climate forecasting, resource prioritization, and adaptive planning. Such insights can inform targeted interventions, including flood mitigation measures, drought-resistant agriculture, and dynamic resource allocation for climate adaptation strategies in Bangladesh.