It has been proposed that conservation laws might not be beneficial for accurate hydrological modeling due to errors in input (precipitation) and target (streamflow) data (particularly at the event time scale), and this might explain why deep learning models (which are not based on enforcing closure) can out-perform catchment-scale conceptual and process-based models at predicting streamflow. We test this hypothesis at the event and multi-year time scale using physics-informed (mass conserving) machine learning and find that: (1) enforcing closure in the rainfall-runoff mass balance does appear to harm the overall skill of hydrological models, (2) deep learning models learn to account for spatiotemporally variable biases in data (3) however this “closure” effect accounts for only a small fraction of the difference in predictive skill between deep learning and conceptual models.

The hydrology community is engaged in an intense debate regarding the merits of machine learning (ML) models over traditional models. These traditional models include both conceptual and process-based hydrological models (PBHMs). Many in the hydrologic community remain skeptical about the use of ML models, because they consider these models “black-box” constructs that do not allow for a direct mapping between model internals and hydrologic states. In addition, they argue that it is unclear how to encode a priori hydrological expertise into ML models. Yet at the same time, ML models now routinely outperform traditional hydrological models for tasks such as streamflow simulation and short-range forecasting. Not only that, they are demonstrably better at generalizing runoff behavior across sites and therefore better at making predictions in ungauged basins, a long-standing problem in hydrology. In recent model experiments, we have shown that ML turbulent heat flux parameterizations embedded in a PBHM outperform the process-based parameterization in that PBHM. In this case, the PBHM enforced energy and mass constraints, while the ML parameterization calculated the heat fluxes. While this approach provides an interesting proof-of-concept and perhaps acts as a bridge between traditional models and ML models, we argue that it is time to take a bigger leap than incrementally improving the existing generation of models. We need to construct a new generation of hydrologic and land surface models (LSMs) that takes advantage of ML technologies in which we directly encode the physical concepts and constraints that we know are important, while being able to flexibly ingest a wide variety of data sources directly. To be employed as LSMs in coupled earth system models, they will need to conserve mass and energy. These new models will take time to develop, but the time to start is now, since the basic building blocks exist and we know how to get started. If nothing else, it will advance the debate and undoubtedly lead to better understanding within the hydrology and land surface communities regarding the merits and demerits of the competing approaches. In this presentation, we will discuss some of these early studies, illustrate how ML models can offer hydrologic insight, and argue the case for the development of ML-based LSMs.