Deep Learned Process Parameterizations Provide Better Representations of Turbulent Heat Fluxes in Hydrologic Models

Deep learning (DL) methods have shown great promise for accurately predicting hydrologic processes but have not yet reached the complexity of traditional process‐based hydrologic models (PBHM) in terms of representing the entire hydrologic cycle. The ability of PBHMs to simulate the hydrologic cycle makes them useful for a wide range of modeling and simulation tasks, for which DL methods have not yet been adapted. We argue that we can take advantage of each of these approaches by embedding DL methods into PBHMs to represent individual processes. We demonstrate that this is viable by developing DL‐based representations of turbulent heat fluxes and coupling them into the Structure for Unifying Multiple Modeling Alternatives (SUMMA), a modular PBHM modeling framework. We developed two DL parameterizations and integrated them into SUMMA, resulting in a one‐way coupled implementation which relies only on model inputs and a two‐way coupled implementation, which also incorporates SUMMA‐derived model states. Our results demonstrate that the DL parameterizations are able to outperform calibrated standalone SUMMA benchmark simulations. Further we demonstrate that the two‐way coupling can simulate the long‐term latent heat flux better than the standalone benchmark and one‐way coupled configuration. This shows that DL methods can benefit from PBHM information, and the synergy between these modeling approaches is superior to either approach individually. Plain Language Summary Machine learning (ML) and process‐based methods are two approaches to hydrologic modeling. Process‐based hydrologic models (PBHMs) represent the hydrologic cycle by solving equations which have been developed from physical theory or experimentation, while ML models make predictions based on patterns learned from large amounts of data. A particular sub‐field of ML called deep learning (DL) has been shown to often outperform process‐based models. However, current DL models do not represent all aspects of the hydrologic cycle (such as streamflow, evaporation, groundwater storage, and snowpack) at once, as is often done in PBHMs. As a result, DL models in hydrology are often single purpose, while PBHMs can be used for many different scientific and/or engineering purposes. We show how individual DL models that simulate evaporation and convective heat transport at the land surface can be incorporated into a PBHM. We show that DL simulated evaporation and convective heat transport better than the PBHM.