Knowledge-Informed Deep Learning for Hydrological Model Calibration: An Application to Coal Creek Watershed in Colorado

Abstract. Deep learning (DL)-assisted inverse mapping has shown promise in hydrological model calibration by directly estimating parameters from observations. However, the increasing computational demand for running the state-of-the-art hydrological model limits sufficient ensemble runs for its calibration. In this work, we present a novel knowledge-informed deep learning method that can efficiently conduct the calibration using a few hundred realizations. The method involves two steps. First, we determine decisive model parameters from a complete parameter set based on the mutual information (MI) between model responses and each parameter computed by a limited number of realizations (~50). Second, we perform more ensemble runs (e.g., several hundred) to generate the training sets for the inverse mapping, which selects informative model responses for estimating each parameter using MI-based parameter sensitivity. We applied this new DL-based method to calibrate a process-based integrated hydrological model, the Advanced Terrestrial Simulator (ATS), at Coal Creek Watershed, CO. The calibration is performed against observed stream discharge (Q) and remotely sensed evapotranspiration (ET) from the water year 2016 to 2018. Preliminary MI analysis on 50 realizations resulted in a down-selection of seven out of fourteen ATS model parameters. Then, we performed a complete MI analysis on 396 realizations and constructed the inverse mapping from informative responses to each of the selected parameters using a deep neural network. Compared with calibration using all observations, the new inverse mapping improves parameter estimations, thus enhancing the performance of ATS forward model runs. The Nash-Sutcliffe efficiency (NSE) of streamflow predictions increases from 0.65 to 0.80 when calibrating against Q alone. Using ET observation, on the other hand, does not show much improvement on the performance of ATS modeling mainly due to both the uncertainty of the remotely sensed product and the insufficient coverage of the model ET ensemble in capturing the observation. By using observed Q only, we further performed a multi-year analysis and show that Q is best simulated (NSE: 0.85) by including in calibration the dry year flow dynamics that shows more sensitivity to subsurface characteristics than the other wet years. Our success highlights the importance of leveraging data-driven knowledge in DL-assisted hydrological model calibration.