Where and What to Sample Next? Bayesian Data-Worth Analysis for Regional Groundwater Models Using Multilevel GLUE

Highly parameterized numerical models of groundwater flow and contaminant transport play a central role in water resources management. Quantifying and analysing uncertainties associated with such models is a key challenge for decision-making, especially under the impacts of climate change. Furthermore, an important question often being overlooked in groundwater model applications is where the next observation point should be located and which state variable should be observed in order to reduce (predictive) uncertainty. We utilize the recently introduced Multilevel Generalized Likelihood Uncertainty Estimation methodology (MLGLUE; DOI: 10.1029/2024WR037735) to perform Bayesian inversion, accelerated by exploiting different spatial model resolutions. For a given model we consider two scenarios; in one scenario we utilize all available state observations while we remove environmental tracer observations from the dataset in a second scenario. We analyse the intrinsic data-worth of environmental tracer observations with respect to simulation uncertainty, especially regarding the estimates of quantities of interest derived from model outputs. Besides simulated observation equivalents we let the computational model also return potential future observations during inversion. We then use measures from information theory to select potential future observations which will result in the most substantial reduction of uncertainty regarding quantities of interest in both scenarios. We apply the combined methodology to a synthetic example as well as a previously developed steady-state regional groundwater flow and transport model. Our results demonstrate that the worth of environmental tracer observations is substantial to reduce model output uncertainty and to increase model accuracy. We show that future environmental tracer observations are especially relevant to better constrain estimates of quantities of interest when sampled at informative locations. The approach promises to improve the capabilities of groundwater models used for decision support and water resources management.