A physics-guided uncertainty calibration framework for reliable probabilistic rainfall forecasting under heavy and extreme rainfall conditions

Reliable rainfall forecasting requires not only accurate point predictions but also well-calibrated estimates of predictive uncertainty, particularly during heavy and extreme events where forecast errors carry the greatest operational consequence. Deterministic machine learning models provide point forecasts without quantifying uncertainty, while existing probabilistic methods generally derive uncertainty from statistical relationships in the available data without explicitly conditioning it on the physical state of the atmosphere. This study presents a physics-guided uncertainty calibration framework for probabilistic rainfall forecasting. A two-stage architecture employs gradient-boosted regression to estimate the conditional mean and a separate heteroscedastic model trained on out-of-fold residuals to estimate the predictive variance. An interpretable Atmospheric Instability Score, constructed from moisture, thermodynamic, synoptic, and dynamic indicators weighted by variance-model feature importance, then scales the predictive variance on a per-sample basis. The framework is evaluated on the WeatherAUS dataset (145,460 daily observations, 49 stations) for next-day rainfall using rolling-origin validation across five expanding windows. Physics-guided calibration is found not to improve average probabilistic skill, as the Continuous Ranked Probability Score (CRPS) achieves its best overall value without calibration. It does, however, yield statistically significant improvements in the regimes of greatest operational importance, reducing CRPS by 0.76% for heavy rainfall (20–50 mm, n = 1,632; p < 10 –18 ) and by up to 4.25% for extreme rainfall (>50 mm, n = 362, p < 10 –11 ), improving 70.5% and 76.2% of days respectively. The optimal calibration strength increases monotonically with rainfall intensity. The framework therefore trades average sharpness for tail reliability, at a computational cost an order of magnitude below comparable probabilistic baselines.