  Process-based hydrologic models are invaluable tools for understanding the
terrestrial water cycle and addressing modern water resources problems.
However, many hydrologic models are computationally expensive and, depending on
the resolution and scale, simulations can take on the order of hours to days to
complete. While techniques such as uncertainty quantification and optimization
have become valuable tools for supporting management decisions, these analyses
typically require hundreds of model simulations, which are too computationally
expensive to perform with a process-based hydrologic model. To address this
gap, we propose a hybrid modeling workflow in which a process-based model is
used to generate an initial set of simulations and a machine learning (ML)
surrogate model is then trained to perform the remaining simulations required
for downstream analysis. As a case study, we apply this workflow to simulations
of variably saturated groundwater flow at a prospective managed aquifer
recharge (MAR) site. We compare the accuracy and computational efficiency of
several ML architectures, including deep convolutional networks, recurrent
neural networks, vision transformers, and networks with Fourier transforms. Our
results demonstrate that ML surrogate models can achieve under 10% mean
absolute percentage error and yield order-of-magnitude runtime savings over
processed-based models. We also offer practical recommendations for training
hydrologic surrogate models, including implementing data normalization to
improve accuracy, using a normalized loss function to improve training
stability and downsampling input features to decrease memory requirements.
