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Abstract Finding similarities between model parameters across different catchments has proved to be challenging. Existing approaches struggle due to catchment heterogeneity and non‐linear dynamics. In particular, attempts to correlate catchment attributes with hydrological responses have failed due to interdependencies among variables and consequent equifinality. Machine Learning (ML), particularly the Long Short‐Term Memory (LSTM) approach, has demonstrated strong predictive and spatial regionalization performance. However, understanding the nature of the regionalization relationships remains difficult. This study proposes a novel approach to partially decouple learning the representation of (a) catchment dynamics by using theHydroLSTMarchitecture and (b) spatial regionalization relationships by using aRandom Forest(RF) clustering approach to learn the relationships between the catchment attributes and dynamics. This coupled approach, calledRegional HydroLSTM, learns a representation of “potential streamflow” using a single cell‐state, while the output gate corrects it to correspond to the temporal context of the current hydrologic regime. RF clusters mediate the relationship between catchment attributes and dynamics, allowing identification of spatially consistent hydrological regions, thereby providing insight into the factors driving spatial and temporal hydrological variability. Results suggest that by combining complementary architectures, we can enhance the interpretability of regional machine learning models in hydrology, offering a new perspective on the “catchment classification” problem. We conclude that an improved understanding of the underlying nature of hydrologic systems can be achieved by careful design of ML architectures to target the specific things we are seeking to learn from the data. 

Abstract Integrated hydrologic models can simulate coupled surface and subsurface processes but are computationally expensive to run at high resolutions over large domains. Here we develop a novel deep learning model to emulate subsurface flows simulated by the integrated ParFlow‐CLM model across the contiguous US. We compare convolutional neural networks like ResNet and UNet run autoregressively against our novel architecture called the Forced SpatioTemporal RNN (FSTR). The FSTR model incorporates separate encoding of initial conditions, static parameters, and meteorological forcings, which are fused in a recurrent loop to produce spatiotemporal predictions of groundwater. We evaluate the model architectures on their ability to reproduce 4D pressure heads, water table depths, and surface soil moisture over the contiguous US at 1 km resolution and daily time steps over the course of a full water year. The FSTR model shows superior performance to the baseline models, producing stable simulations that capture both seasonal and event‐scale dynamics across a wide array of hydroclimatic regimes. The emulators provide over 1,000× speedup compared to the original physical model, which will enable new capabilities like uncertainty quantification and data assimilation for integrated hydrologic modeling that were not previously possible. Our results demonstrate the promise of using specialized deep learning architectures like FSTR for emulating complex process‐based models without sacrificing fidelity. 

Increases in evapotranspiration (ET) from global warming are decreasing streamflow in headwater basins worldwide. However, these streamflow losses do not occur uniformly due to complex topography. To better understand the heterogeneity of streamflow loss, we use the Budyko shape parameter (ω) as a diagnostic tool. We fit ω to 37-year of hydrologic simulation output in the Upper Colorado River Basin (UCRB), an important headwater basin in the US. We split the UCRB into two categories: peak watersheds with high elevation and steep slopes, and valley watersheds with lower elevation and gradual slopes. Our results demonstrate a relationship between streamflow loss and ω. The valley watersheds with greater streamflow loss have ω higher than 3.1, while the peak watersheds with less streamflow loss have an average ω of 1.3. This work highlights the use of ω as an indicator of streamflow loss and could be generalized to other headwater basin systems. 

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. 

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 Hydrogeologic models generally require gridded subsurface properties, however these inputs are often difficult to obtain and highly uncertain. Parametrizing computationally expensive models where extensive calibration is computationally infeasible is a long standing challenge in hydrogeology. Here we present a machine learning framework to address this challenge. We train an inversion model to learn the relationship between water table depth and hydraulic conductivity using a small number of physical simulations. For a 31M grid cell model of the US we demonstrate that the inversion model can produce a reliable K field using only 30 simulations for training. Furthermore, we show that the inversion model captures physically realistic relationships between variables, even for relationships that were not directly trained on. While there are still limitations for out of sample parameters, the general framework presented here provides a promising approach for parametrizing expensive models.