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Abstract. High-resolution, spatially distributed process-based (PB) simulators are widely employed in the study of complex catchment processes and their responses to a changing climate. However, calibrating these PB simulators using observed data remains a significant challenge due to several persistent issues, including the following: (1) intractability stemming from the computational demands and complex responses of simulators, which renders infeasible calculation of the conditional probability of parameters and data, and (2) uncertainty stemming from the choice of simplified representations of complex natural hydrologic processes. Here, we demonstrate how simulation-based inference (SBI) can help address both of these challenges with respect to parameter estimation. SBI uses a learned mapping between the parameter space and observed data to estimate parameters for the generation of calibrated simulations. To demonstrate the potential of SBI in hydrologic modeling, we conduct a set of synthetic experiments to infer two common physical parameters – Manning's coefficient and hydraulic conductivity – using a representation of a snowmelt-dominated catchment in Colorado, USA. We introduce novel deep-learning (DL) components to the SBI approach, including an “emulator” as a surrogate for the PB simulator to rapidly explore parameter responses. We also employ a density-based neural network to represent the joint probability of parameters and data without strong assumptions about its functional form. While addressing intractability, we also show that, if the simulator does not represent the system under study well enough, SBI can yield unreliable parameter estimates. Approaches to adopting the SBI framework for cases in which multiple simulator(s) may be adequate are introduced using a performance-weighting approach. The synthetic experiments presented here test the performance of SBI, using the relationship between the surrogate and PB simulators as a proxy for the real case. 

Abstract Water table depth (WTD) has a substantial impact on the connection between groundwater dynamics and land surface processes. Due to the scarcity of WTD observations, physically‐based groundwater models are growing in their ability to map WTD at large scales; however, they are still challenged to represent simulated WTD compared to well observations. In this study, we develop a purely data‐driven approach to estimating WTD at continental scale. We apply a random forest (RF) model to estimate WTD over most of the contiguous United States (CONUS) based on available WTD observations. The estimated WTD are in good agreement with well observations, with a Pearson correlation coefficient (r) of 0.96 (0.81 during testing), a Nash‐Sutcliffe efficiency (NSE) of 0.93 (0.65 during testing), and a root mean square error (RMSE) of 6.87 m (15.31 m during testing). The location of each grid cell is rated as the most important feature in estimating WTD over most of the CONUS, which might be a surrogate for spatial information. In addition, the uncertainty of the RF model is quantified using quantile regression forests. High uncertainties are generally associated with locations having a shallow WTD. Our study demonstrates that the RF model can produce reasonable WTD estimates over most of the CONUS, providing an alternative to physics‐based modeling for modeling large‐scale freshwater resources. Since the CONUS covers many different hydrologic regimes, the RF model trained for the CONUS may be transferrable to other regions with a similar hydrologic regime and limited observations. 

The water content in the soil regulates exchanges between soil and atmosphere, impacts plant livelihood, and determines the antecedent condition for several natural hazards. Accurate soil moisture estimates are key to applications such as natural hazard prediction, agriculture, and water management. We explore how to best predict soil moisture at a high resolution in the context of a changing climate. Physics-based hydrological models are promising as they provide distributed soil moisture estimates and allow prediction outside the range of prior observations. This is particularly important considering that the climate is changing, and the available historical records are often too short to capture extreme events. Unfortunately, these models are extremely computationally expensive, which makes their use challenging, especially when dealing with strong uncertainties. These characteristics make them complementary to machine learning approaches, which rely on training data quality/quantity but are typically computationally efficient. We first demonstrate the ability of Convolutional Neural Networks (CNNs) to reproduce soil moisture fields simulated by the hydrological model ParFlow-CLM. Then, we show how these two approaches can be successfully combined to predict future droughts not seen in the historical timeseries. We do this by generating additional ParFlow-CLM simulations with altered forcing mimicking future drought scenarios. Comparing the performance of CNN models trained on historical forcing and CNN models trained also on simulations with altered forcing reveals the potential of combining these two approaches. The CNN can not only reproduce the moisture response to a given forcing but also learn and predict the impact of altered forcing. Given the uncertainties in projected climate change, we can create a limited number of representative ParFlow-CLM simulations (ca. 25 min/water year on 9 CPUs for our case study), train our CNNs, and use them to efficiently (seconds/water-year on 1 CPU) predict additional water years/scenarios and improve our understanding of future drought potential. This framework allows users to explore scenarios beyond past observation and tailor the training data to their application of interest (e.g., wet conditions for flooding, dry conditions for drought, etc…). With the trained ML model they can rely on high resolution soil moisture estimates and explore the impact of uncertainties. 

Integrated hydrologic models solve coupled mathematical equations that represent natural processes, including groundwater, unsaturated, and overland flow. However, these models are computationally expensive. It has been recently shown that machine leaning (ML) and deep learning (DL) in particular could be used to emulate complex physical processes in the earth system. In this study, we demonstrate how a DL model can emulate transient, three-dimensional integrated hydrologic model simulations at a fraction of the computational expense. This emulator is based on a DL model previously used for modeling video dynamics, PredRNN. The emulator is trained based on physical parameters used in the original model, inputs such as hydraulic conductivity and topography, and produces spatially distributed outputs (e.g., pressure head) from which quantities such as streamflow and water table depth can be calculated. Simulation results from the emulator and ParFlow agree well with average relative biases of 0.070, 0.092, and 0.032 for streamflow, water table depth, and total water storage, respectively. Moreover, the emulator is up to 42 times faster than ParFlow. Given this promising proof of concept, our results open the door to future applications of full hydrologic model emulation, particularly at larger scales.