Physics-aware machine learning revolutionizes scientific paradigm for process-based modeling in hydrology

Accurate hydrological understanding and water cycle prediction are crucial for addressing scientific and societal challenges associated with the management of water resources. Existing reviews predominantly concentrate on the development of machine learning (ML) in this field, yet there is a clear distinction between hydrology and ML as separate paradigms. Here, we introduce physics-aware ML as a transformative approach to overcome the perceived barrier and revolutionize both fields. Specifically, we present a comprehensive review of the physics-aware ML methods, building a structured community (PaML) of existing methodologies that integrate prior physical knowledge or physics-based modeling into ML. We systematically analyze these PaML methodologies with respect to four aspects: physical data-guided ML, physics-informed ML, physics-embedded ML, and physics-aware hybrid learning. These four approaches integrate ML with physics in diverse manners, offering models that balance interpretability, generalization, computational cost, representation, and operability. PaML facilitates ML-aided hypotheses, accelerating insights from big data and fostering scientific discoveries. We initiate a systematic exploration of hydrology in PaML, including rainfall-runoff and hydrodynamic processes. Our study highlights the most promising and challenging directions for different objectives in process-based hydrology, such as advancing PaML-based solutions and enhancing parameterization, calibration, data generation, spatio-temporal representation, and uncertainty quantification through PaML methods. Finally, a new PaML-based hydrology community, termed HydroPML, is released as a foundation for hydrological applications. HydroPML enhances the explainability and causality of ML and lays the groundwork for the digital water cycle's realization.