Physics-Guided Probabilistic Land Surface Temperature Forecasting with Uncertainty-Weighted Surface Energy Balance Regularization

Land surface temperature (LST) is closely linked to land–atmosphere energy exchange, while conventional point forecasting cannot quantify forecast uncertainty or explicitly enforce physical consistency over long horizons. We propose Physics-former-Rn-SG to address two limitations: fixed physical penalties cannot adapt to state-dependent forecast reliability, while directly coupling uncertainty to physics weighting can encourage variance inflation. The model integrates a variable-wise iTransformer, NIG evidential prediction, supervised future -forcing heads, and a reduced Rn-SEB residual. A stop-gradient, normalized, and clipped weighting scheme enables uncertainty-adaptive physical regularization while preventing the physics loss from directly driving variance inflation. Evaluated on MPI-Saale and DE-Gri data from 2024 to 2025, the model achieved the lowest mean MAE in all 16 site horizon combinations across 96–384 h forecasts. Its average absolute MAE advantage was 0.157 °C over NIG-iTransformer and 0.046 °C over fixed Rn-SEB, with the latter improvement smaller and more variable across sites, horizons, and validation protocols. Multi-level coverage error, CRPS, WIS, NLL, and ECE were also lowest. The variance inflation ratio decreased from 1.323 to 1.019 with stop-gradient. In the matched DE-Gri full-flux benchmark, reduced Rn-SEB maintained prediction accuracy while reducing training and inference time by about 11.0% and 6.5%, respectively. Overall, Physics-former-Rn-SG balances forecast accuracy, calibration, and physical consistency, with potential as a station-scale forecasting or post-processing tool for uncertainty-aware environmental applications.