Accurate simulation of terrestrial water storage (TWS), the integrated volume of water in soil, groundwater, snow, surface water and vegetation per unit area, is challenging. TWS is a critical but often overlooked model diagnostic that can  improve understanding of hydrological processes, water resource management, and  climate change impacts assessment. Observations of TWS anomalies from the Gravity Recovery and Climate Experiment (GRACE) satellite and its follow-on (GRACE-FO) missions provide observational constraints on model-simulated TWS. The similarity between large spatial scales of GRACE TWS retrievals and global land models like the Community Land Model (CLM) facilitates  comparison of model-simulated and observed TWS anomalies as a function of input parameter values.  We demonstrate an approach to optimize CLM parameters for improved TWS simulation, using history matching with Evidential Deep Neural Networks (EDNN). History matching is a constraining technique that identifies plausible parameter sets by comparing model outputs to observations. To reduce the  computational expense of generating large perturbed parameter ensembles (PPEs) we use an emulator  EDNN that provides a probabilistic framework for representing uncertainty in the relationship between input parameters and TWS.  A key advantage of the EDNN approach is estimation of both epistemic and aleatoric uncertainty with the use of a single model, reducing the need to sample or train multiple ensembles. We applied the proposed methodology that utilizes history matching with EDNN to a real-world case study in which we  compared CLM simulations to observed TWS data (e.g., from the GRACE satellite mission) over the Contiguous United States (CONUS). The optimization process focuses on key parameters (e.g., dry surface layer, decay factor for fractional saturated area, and medlyn slope of conductance-photosynthesis relationship) within the CLM that govern water storage dynamics. The resulting  parameter sets  yield model simulations of TWS that agree with observations. Moreover, uncertainty estimates could improve TWS simulations, enabling more robust assessments of global water availability and hydrological changes.

Accurate estimates of snow water equivalent (SWE) are essential for understanding hydrological processes and managing effective management of water resources, particularly in snow-dominated regions. Many methods for estimating SWE rely on in-situ measurements and/or numerical models. In-situ measurements, such as those provided by the USDA Snotel network, have the advantage of being direct observations of SWE but are only sparsely available and suffer from challenges of representativity. At the same time, numerical models embed knowledge of the physical processes underlying the snowpack accumulation and ablation but can be computationally expensive to run over large areas. In this study, we investigate applying deep learning techniques to predict the spatiotemporal distribution of SWE from a combination of atmospheric forcings derived from the Weather Research and Forecasting (WRF) model, geographic parameters related to topography and land cover that influence snow persistence, and historical observations of snow presence/absence from remote sensing data. By leveraging static variables and dynamic atmospheric forcings from WRF  as input features, we train a convolutional long short-term memory (ConvLSTM) network to predict SWE. Our proposed deep learning model aims to accelerate the prediction of spatially distributed SWE compared to traditional methods and can complement process-based land surface models often used to predict SWE. The computational savings associated with training and forward integration of machine learning based models open the door to high-resolution ensemble forecasting of SWE and assimilation of observations for real-time SWE estimation.