Surface-water divides can be delineated by analyzing digital elevation models. They might, however, significantly differ from groundwater divides because the groundwater surface does not necessarily follow the surface topography. Thus, in order to delineate a groundwater divide, hydraulic-head measurements are needed. Because installing piezometers is cost- and labor-intensive, it is vital to optimize their placement. In this work, we introduce an optimal design analysis that can identify the best spatial configuration of piezometers. The method is based on formal minimization of the expected posterior uncertainty in localizing the groundwater divide. It is based on the preposterior data impact assessor, a Bayesian framework that uses a random sample of models (here: steady-state groundwater flow models) in a fully non-linear analysis. For each realization, we compute virtual hydraulic-head measurements at all potential well installation points and delineate the groundwater divide by particle tracking. Then, for each set of virtual measurements and their possible measurement values, we assess the uncertainty of the groundwater-divide location after Bayesian updating, and finally marginalize over all possible measurement values. We test the method mimicking an aquifer in South-West Germany. Previous works in this aquifer indicated a groundwater divide that substantially differs from the surface-water divide. Our analysis shows that the uncertainty in the localization of the groundwater divide can be reduced with each additional monitoring well. In our case study, the optimal configuration of three monitoring points involves the first well being close to the topographic surface water divide, the second one on the hillslope toward the valley, and the third one in between.
Uncertainty in training image‐based inversion of hydraulic head data constrained to ERT data: Workflow and case study
