Knowledge-informed deep learning for hydrological model calibration: an application to Coal Creek Watershed in Colorado

Abstract

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 2017 to 2019. Preliminary MI analysis on 50 realizations resulted in a down-selection of 7 out of 14 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 observations covering all time steps, 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 0.53 to 0.8 when calibrating against Q alone. Using ET observations, 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 multiyear analysis and show that Q is best simulated (NSE > 0.8) by including in the calibration the dry-year flow dynamics that show more sensitivity to subsurface characteristics than the other wet years. Moreover, when continuing the forward runs till the end of 2021, the calibrated models show similar simulation performances during this evaluation period as the calibration period, demonstrating the ability of the estimated parameters in capturing climate sensitivity. Our success highlights the importance of leveraging data-driven knowledge in DL-assisted hydrological model calibration.

Using Mutual Information for Global Sensitivity Analysis on Watershed Modeling

“…To accurately compute MI based on the 1,000 realizations, we divided each dimension into 10 evenly bins, leading to 100 bins in a two‐dimensional space p ( x , y ) in Equation . The 100 uniformly distributed bins allow reliable calculation of MI using a few hundred realizations (<1,000), which can be afforded by using modern supercomputing resources for computationally expensive hydrological models such as the Advanced Terrestrial Simulator (Coon et al., 2019; Jiang et al., 2022a).…”

Expanding the Spatial Reach and Human Impacts of Critical Zone Science

“…Machine‐learning methods have been shown to outperform traditional calibration approaches in estimating subsurface parameters because they can directly infer parameters from observations and better capture the highly nonlinear relationships with fewer realizations (Cromwell et al., 2021; Jiang et al., 2021). Another deep neural network model used widely available time series of streamflow data to estimate subsurface permeability, which can be further used to estimate flow paths and weathering fronts (Jiang et al., 2022; Tartakovsky et al., 2020). By incorporating the governing equations of Darcy's Law and Richards equation into its loss function, the model enhanced accuracy with limited data availability.…”

Enhancing Streamflow Prediction Physically Consistently Using Process-Based Modeling and Domain Knowledge: A Review

“…Utilizing machine learning algorithms to update hydrological model parameters has demonstrated comparable effectiveness in enhancing model accuracy compared to established techniques based on residual error and simulated flow-related adjustments [87,[128][129][130]. For instance, Yu et al [131] investigated three integration approaches combining the HBV model and LSTM.…”

“…All three approaches outperformed the individual models, with the third approach exhibiting superior performance. Jiang et al [129] proposed a knowledge-informed inverse mapping technique that estimates each parameter using only responses that share significant mutual information with the parameter. This approach demonstrates the potential for incorporating domain knowledge into machine learning algorithms for hydrological parameterization.…”

“…Using process-based models merely as data-generating tools limits their ability to provide feedback within the modeling framework [122,129,161]. Consequently, the integrated modeling framework remains less interpretable.…”