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Abstract The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. A well-calibrated model can reasonably propagate information from observations to unobserved variables via model physics, but traditional calibration is highly inefficient and results in non-unique solutions. Here we propose a novel differentiable parameter learning (dPL) framework that efficiently learns a global mapping between inputs (and optionally responses) and parameters. Crucially, dPL exhibits beneficial scaling curves not previously demonstrated to geoscientists: as training data increases, dPL achieves better performance, more physical coherence, and better generalizability (across space and uncalibrated variables), all with orders-of-magnitude lower computational cost. We demonstrate examples that learned from soil moisture and streamflow, where dPL drastically outperformed existing evolutionary and regionalization methods, or required only ~12.5% of the training data to achieve similar performance. The generic scheme promotes the integration of deep learning and process-based models, without mandating reimplementation. 

Abstract. Recently, deep learning (DL) has emerged as a revolutionary andversatile tool transforming industry applications and generating new andimproved capabilities for scientific discovery and model building. Theadoption of DL in hydrology has so far been gradual, but the field is nowripe for breakthroughs. This paper suggests that DL-based methods can open up acomplementary avenue toward knowledge discovery in hydrologic sciences. Inthe new avenue, machine-learning algorithms present competing hypotheses thatare consistent with data. Interrogative methods are then invoked to interpretDL models for scientists to further evaluate. However, hydrology presentsmany challenges for DL methods, such as data limitations, heterogeneityand co-evolution, and the general inexperience of the hydrologic field withDL. The roadmap toward DL-powered scientific advances will require thecoordinated effort from a large community involving scientists and citizens.Integrating process-based models with DL models will help alleviate datalimitations. The sharing of data and baseline models will improve theefficiency of the community as a whole. Open competitions could serve as theorganizing events to greatly propel growth and nurture data science educationin hydrology, which demands a grassroots collaboration. The area ofhydrologic DL presents numerous research opportunities that could, in turn,stimulate advances in machine learning as well.