A Reduced-Order Physics-Based Heat Transport Model for Spatiotemporal Heatwave Dynamics in Arid Environments: A UAE Case Study

Heatwaves are a major climate hazard in arid environments, affecting public health, infrastructure, energy demand, and environmental sustainability. This study develops a reduced-order, physics-based spatiotemporal framework for regional temperature reconstruction and heatwave analysis, using the United Arab Emirates as a case study. The framework is derived from an advection–diffusion heat-transport equation, while the implemented model adopts a reduced diffusion–forcing formulation driven by ERA5-derived surface solar radiation, sensible heat flux, and near-surface specific humidity. The model is solved on a structured grid using finite-difference discretisation and evaluated primarily through one-step reconstruction over a chronologically held-out test period. Heat-waves are identified using location-specific 90th-percentile thresholds estimated exclusively from training-period temperatures, together with a minimum dura-tion of three consecutive days. The one-step reconstruction achieves an R 2 of 0.956, RMSE of 1.18◦C, and MAE of 0.83◦C; duration-based heatwave detection yields an F1-score of 0.843 and accuracy of 94.2%. A supplementary recursive experiment under prescribed ERA5 forcing and reference-based boundary condi-tions shows increasing error with integration horizon, with R 2 decreasing from 0.875 at 3 days to 0.761 at 30 days and RMSE increasing to 2.76◦C. These results demonstrate that a parsimonious diffusion–forcing PDE can reproduce dominant regional temperature patterns and sustained heatwave behaviour while exposing the accumulation of structural error under recursive integration. The framework provides a reproducible baseline for future extensions involving explicit advection, irregular-domain discretisation, prognostic forcing, and hybrid physics–learning models.