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.

Recently, deep learning (DL) has emerged as a revolutionary and versatile tool transforming industry applications and generating new and improved capabilities for scientific discovery and model building. The adoption of DL in hydrology has so far been gradual, but the field is now ripe for breakthroughs. This paper suggests that DL-based methods can open up a complementary avenue toward knowledge discovery in hydrologic sciences. In the new avenue, machine-learning algorithms present competing hypotheses that are consistent with data. Interrogative methods are then invoked to interpret DL models for scientists to further evaluate. However, hydrology presents many challenges for DL methods, such as data limitations, heterogeneity and co-evolution, and the general inexperience of the hydrologic field with DL. The roadmap toward DL-powered scientific advances will require the coordinated effort from a large community involving scientists and citizens. Integrating process-based models with DL models will help alleviate data limitations. The sharing of data and baseline models will improve the efficiency of the community as a whole. Open competitions could serve as the organizing events to greatly propel growth and nurture data science education in hydrology, which demands a grassroots collaboration. The area of hydrologic DL presents numerous research opportunities that could, in turn, stimulate advances in machine learning as well.

There is a drastic geographic imbalance in available global streamflow gauge and catchment property data, with additional large variations in data characteristics. As a result, models calibrated in one region cannot normally be migrated to another without significant modifications. Currently in these regions, non‐transferable machine learning models are habitually trained over small local data sets. Here we show that transfer learning (TL), in the senses of weight initialization and weight freezing, allows long short‐term memory (LSTM) streamflow models that were pretrained over the conterminous United States (CONUS, the source data set) to be transferred to catchments on other continents (the target regions), without the need for extensive catchment attributes available at the target location. We demonstrate this possibility for regions where data are dense (664 basins in Great Britain), moderately dense (49 basins in central Chile), and scarce with only remotely sensed attributes available (5 basins in China). In both China and Chile, the TL models showed significantly elevated performance compared to locally trained models using all basins. The benefits of TL increased with the amount of available data in the source data set, and seemed to be more pronounced with greater physiographic diversity. The benefits from TL were greater than from pretraining LSTM using the outputs from an uncalibrated hydrologic model. These results suggest hydrologic data around the world have commonalities which could be leveraged by deep learning, and synergies can be had with a simple modification of the current workflows, greatly expanding the reach of existing big data. Finally, this work diversified existing global streamflow benchmarks.

Recently, rainfall‐runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics‐NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method ( δ MC‐Juniata‐hydroDL2) that mimics the classical Muskingum‐Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness ( n ) and channel geometries from raw reach‐scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real‐world data, the trained differentiable routing model produced more accurate long‐term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km ² ) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national‐scale hydrologic flood simulations.