Machine learning additive corrections in a gray-box model for air temperature in the Southwest Amazon rainforest: Dry and wet season analysis

This study develops an integrative modeling approach combining gray-box modeling and machine learning (ML) to predict micrometeorological dynamics in the Amazon rainforest, specifically at the Jaru Biological Reserve in Rondônia, Brazil. A physics-based “dry model,” describing temperature dynamics primarily through radiative forcing and cooling processes, provides a baseline subsequently corrected by ML-derived additive terms. A fully connected neural network with 641 parameters successfully learned nonlinear corrections, significantly reducing prediction errors by over 60% in the dry season and by approximately 55.5% in the wet season. To ensure model reliability, we employed bootstrap ensemble modeling with 100 trained networks to quantify prediction uncertainty, revealing well-calibrated confidence intervals for the dry season (94.2% empirical coverage for nominal 90% intervals) but systematic biases during the wet season (mean bias: 2.08 K), highlighting fundamental limitations when key moisture-related processes are omitted from the physics-based framework. Systematic comparison with Gaussian process regression and polynomial approximations validated our uncertainty quantification approach while demonstrating that the neural network bootstrap ensemble provides superior robustness across diverse seasonal conditions. To enhance interpretability, neural corrections were approximated using symbolic (polynomial) regression, revealing dominant nonlinear temperature–radiation interactions in both dry and wet conditions. Our findings demonstrate marked seasonal contrasts in radiative forcing, atmospheric clarity, and cooling efficiency, underscoring the need for seasonally tailored modeling strategies. This combined physics-informed and data-driven methodology offers reliable and interpretable models essential for managing environmental impacts amid increasing anthropogenic and climatic pressures on the Amazon.