Sequential optimization of temperature measurements to estimate groundwater-surface water interactions

The groundwater-surface water (GW-SW) exchange fluxes are driven by a complex interplay of subsurface processes and their interactions with surface hydrology, which have a significant impact on the water and contaminant exchanges. Due to the complexity of these systems, the accurate estimation of GW-SW fluxes is important for quantitative hydrological studies and should be based on relevant data and careful experimental design. Therefore, the effective design of monitoring networks that can identify relevant subsurface information are essential for the optimal protection of our water resources. In this study, we present novel deep learning (DL)-driven approaches for sequential and static Bayesian optimal experimental design (BOED) in the subsurface, with the goal of estimating the GW-SW exchange fluxes from a set of temperature measurements. We apply probabilistic Bayesian neural networks (PBNN) to conditional density estimation (CDE) within a BOED framework, and the predictive performance of the PBNN-based CDE model is evaluated by a custom objective function based on the Kullback-Leibler divergence to determine optimal temperature sensor locations utilizing the information gain provided by the measurements. This evaluation is used to determine the optimal sequential sampling strategy for estimating GW-SW exchange fluxes in the 1D case, and the results are compared to the static optimal sampling strategy for a 3D conceptual riverbed-aquifer model based on a real case study. Our results indicate that probabilistic DL is an effective method for estimating GW-SW fluxes from temperature data and designing efficient monitoring networks. Our proposed framework can be applied to other cases involving surface or subsurface monitoring and experimental design.