A Stochastic Framework to Optimize the Monitoring Strategy for the Delineation of a Groundwater Divide

The boundaries of surface-water catchments can be delineated by analyzing digital elevation models using geographic information systems. Surface-water divides and groundwater divides, however, might significantly differ from each other because the groundwater surface does not necessarily follow the surface topography. Hydraulic-head measurements are needed to properly delineate a groundwater divide and thereby the subsurface boundary of a catchment, but piezometers are expensive. It is therefore vital to optimize the placement of the necessary piezometers. In this work, we introduce an optimal design analysis, which can identify the best configuration of potential piezometer placements within a given set. The method is based on the formal minimization of the expected posterior uncertainty within a sampling-based Bayesian framework. It makes use of a random ensemble of behavioral steady-state groundwater flow models. For each behavioral realization we compute virtual hydraulic-head measurements at all potential well points and delineate the groundwater divide by particle tracking. We minimize the uncertainty of the groundwater-divide location by marginalizing over the virtual measurements. We test the method mimicking a real aquifer in South-West Germany. Previous works in this aquifer indicated a groundwater divide that is shifted compared to the surface-water divide. The analysis shows that the uncertainty in the localization of the groundwater divide can be reduced with each new well. A comparison of the maximum uncertainty reduction at different numbers of wells quantifies the added value of information for each new well. In our case study, the uncertainty reduction obtained by three monitoring points is maximized when the first well is close to the topographic surface water divide, the second one in the valley, and the third one in between.