Joseph Janssen , Ardalan Tootchi, Ali A Ameli

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.