Towards hybrid modeling of the global hydrological cycle

Abstract. State-of-the-art global hydrological models (GHMs) exhibit large uncertainties in hydrological simulations due to the complexity, diversity, and heterogeneity of the land surface and subsurface processes, as well as the scale dependency of these processes and associated parameters. Recent progress in machine learning, fueled by relevant Earth observation data streams, may help overcome these challenges. But machine learning methods are not bound by physical laws, and their interpretability is limited by design. In this study, we exemplify a hybrid approach to global hydrological modeling that exploits the data adaptivity of neural networks for representing uncertain processes within a model structure based on physical principles (e.g., mass conservation) that form the basis of GHMs. This combination of machine learning and physical knowledge can potentially lead to data-driven, yet physically consistent and partially interpretable hybrid models. The hybrid hydrological model (H2M), extended from Kraft et al. (2020), simulates the dynamics of snow, soil moisture, and groundwater storage globally at 1∘ spatial resolution and daily time step. Water fluxes are simulated by an embedded recurrent neural network. We trained the model simultaneously against observational products of terrestrial water storage variations (TWS), grid cell runoff (Q), evapotranspiration (ET), and snow water equivalent (SWE) with a multi-task learning approach. We find that the H2M is capable of reproducing key patterns of global water cycle components, with model performances being at least on par with four state-of-the-art GHMs which provide a necessary benchmark for H2M. The neural-network-learned hydrological responses of evapotranspiration and grid cell runoff to antecedent soil moisture states are qualitatively consistent with our understanding and theory. The simulated contributions of groundwater, soil moisture, and snowpack variability to TWS variations are plausible and within the ranges of traditional GHMs. H2M identifies a somewhat stronger role of soil moisture for TWS variations in transitional and tropical regions compared to GHMs. With the findings and analysis, we conclude that H2M provides a new data-driven perspective on modeling the global hydrological cycle and physical responses with machine-learned parameters that is consistent with and complementary to existing global modeling frameworks. The hybrid modeling approaches have a large potential to better leverage ever-increasing Earth observation data streams to advance our understandings of the Earth system and capabilities to monitor and model it.