Estimation of hydraulic conductivity in a watershed using sparse multi-source data via Gaussian process regression and Bayesian experimental design

Enhanced water management systems depend on accurate estimation of subsurface hydraulic properties. However, geologic formations can vary significantly, so information from a single source (e.g., widely spaced boreholes) is insufficient in characterizing subsurface aquifer properties. Therefore, multiple sources of information are needed to complement the hydrogeology understanding of a region. This study presents a numerical framework in which information from different measurement sources is combined to characterize the 3D random field in a multi-fidelity prediction model. Coupled with the model, a Bayesian experimental design was used to determine the best future sampling locations. The Upper Sangamon watershed in east-central Illinois was selected as the case study site, where the multi-fidelity Gaussian process model was used to estimate the hydraulic conductivity in the region of interest. Multi-source observation data were obtained from electrical resistivity and borehole pumping tests. The accuracy of the model prediction is dependent on the locations and the distribution of both high- and low-fidelity data. Furthermore, the multi-fidelity model was compared with the single-fidelity model. The uncertainties and confidence in the measurements and parameter estimates were quantified and used to design future cycles of data collection to further improve the confidence intervals.