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Several studies have demonstrated the ability of long short-term memory (LSTM) machine-learning-based modeling to outperform traditional spatially lumped process-based modeling approaches for streamflow prediction. However, due mainly to the structural complexity of the LSTM network (which includes gating operations and sequential processing of the data), difficulties can arise when interpreting the internal processes and weights in the model. Here, we propose and test a modification of LSTM architecture that is calibrated in a manner that is analogous to a hydrological system. Our architecture, called “HydroLSTM”, simulates the sequential updating of the Markovian storage while the gating operation has access to historical information. Specifically, we modify how data are fed to the new representation to facilitate simultaneous access to past lagged inputs and consolidated information, which explicitly acknowledges the importance of trends and patterns in the data. We compare the performance of the HydroLSTM and LSTM architectures using data from 10 hydro-climatically varied catchments. We further examine how the new architecture exploits the information in lagged inputs, for 588 catchments across the USA. The HydroLSTM-based models require fewer cell states to obtain similar performance to their LSTM-based counterparts. Further, the weight patterns associated with lagged input variables are interpretable and consistent with regional hydroclimatic characteristics (snowmelt-dominated, recent rainfall-dominated, and historical rainfall-dominated). These findings illustrate how the hydrological interpretability of LSTM-based models can be enhanced by appropriate architectural modifications that are physically and conceptually consistent with our understanding of the system. 

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.