Physics-Informed Deep Learning for Precipitation Estimation and Forecasting: Methods, Applications, and Challenges

Deep learning has improved precipitation estimation and forecasting, but high predictive skill does not by itself ensure physically credible behavior, robustness under distribution shift, or reliable uncertainty. This critical narrative review examines physics-informed deep learning across quantitative precipitation estimation, radar and satellite nowcasting, short-range forecasting, numerical weather prediction post-processing, and selected Earth-system applications. We use a two-dimensional analytical framework—form of physical knowledge and point of model integration—to compare mechanisms that are often grouped under the same label but provide different levels of physical guarantee. Across the literature, useful physical information is strongly task- and scale-dependent. Physically meaningful inputs and transport-aware structures are most convincing when they represent processes that are both observable and dominant over the forecast horizon. Soft equation or consistency losses can reduce violations, but their effect depends on constraint validity, weighting, data quality, and precipitation regime. Hard parameterizations and output projections provide stronger guarantees for specified relations, although this does not necessarily translate into better precipitation forecasts when those relations are incomplete or scale-mismatched. Evidence for cross-region robustness, extreme-event reliability, and operational maturity remains comparatively limited. A key evidence gap is whether these benefits persist under matched ablations and transfer across regions, sensors, and precipitation regimes.