  Fine-resolution spatial patterns of water table depth (WTD) play a crucial
role in shaping ecological resilience, hydrological connectivity, and
anthropocentric objectives. Generally, a large-scale (e.g., continental or
global) spatial map of static WTD can be simulated using either
physically-based (PB) or machine learning-based (ML) models. We construct three
fine-resolution (500 m) ML simulations of WTD, using the XGBoost algorithm and
more than 20 million real and proxy observations of WTD, across the United
States and Canada. The three ML models were constrained using known physical
relations between WTD's drivers and WTD and were trained by sequentially adding
real and proxy observations of WTD. We interpret the black box of our
physically constrained ML models and compare it against available literature in
groundwater hydrology. Through an extensive (pixel-by-pixel) evaluation, we
demonstrate that our models can more accurately predict unseen real and proxy
observations of WTD across most of North America's ecoregions compared to three
available PB simulations of WTD. However, we still argue that large-scale WTD
estimation is far from being a solved problem. We reason that due to biased
observational data mainly collected from low-elevation floodplains, the
misspecification of equations within physically-based models, and the
over-flexibility of machine learning models, verifiably accurate simulations of
WTD do not yet exist. Ultimately, we thoroughly discuss future directions that
may help hydrogeologists decide how to proceed with WTD estimations, with a
particular focus on the application of machine learning and the use of proxy
satellite data.
