Comparing Physics‐Based, Conceptual and Machine‐Learning Models to Predict Groundwater Levels by <scp>BMA</scp>

Groundwater level observations are used as decision variables for aquifer management, often in conjunction with models to provide predictions for operational forecasting. In this study, we compare different model classes for this task: a spatially explicit 3D groundwater flow model (MODFLOW), an eigenmodel, a transfer-function model, and three machine learning models, namely, multi-layer perceptron models, long short-term memory models, and random forest models. The models differ widely in their complexity, input requirements, calibration effort, and run-times. They are tested on four groundwater level time series from the Wairau Aquifer in New Zealand to investigate the potential of the data-driven approaches to outperform the MODFLOW model in predicting individual target wells. Further, we wish to reveal whether the MODFLOW model has advantages in predicting all four wells simultaneously because it can use the available information in a physics-based, integrated manner, or whether structural limitations spoil this effect. Our results demonstrate that data-driven models with low input requirements and short run-times are competitive candidates for local groundwater level predictions even for system states that lie outside the calibration data range. There is no "single best" model that performs best in all cases, which motivates ensemble forecasting with different model classes using Bayesian model averaging. The obtained Bayesian model weights clearly favor MODFLOW when targeting all wells simultaneously, even though the competing approaches had the chance to fine-tune for each tested well individually. This is a remarkable result that strengthens the argument for physics-based approaches even for seemingly "simple" groundwater level prediction tasks.