Sangamon watershed is recognized as one of the most worth noting regions for water and environmental supply planning and management purposes according to its intensively management for soybean and corn production. It is also a representative area with limited geological and hydraulic measurement data, in which sustainable ground water and environmental management is essential. To better understand the hydraulic properties of the entire watershed, a multi-fidelity Gaussian Processes (Kriging) model was applied to predict the hydraulic conductivity of the upper Sangamon watershed, using previous multi-sources of field observation data (Electrical Earth Resistivity and pumping test data). The model also provided a quantification of uncertainty of the predicted values, which helps us to make reliable suggestions for the future design of hydraulic observations. The data fidelity effect to the model was discussed by comparing multi-fidelity and single-high-fidelity Kriging results. The model predicted values suggest that the accuracy of multi-fidelity Kriging depends on the locations and the distribution of both the high- and low-fidelity data. When high-fidelity data points are sparse and far away from the low-fidelity data points, the information provided from the low-fidelity data becomes extremely important, which can greatly enhance the model performance and accuracy. This study has paved the way to a more efficient parameter estimation in under-sampled sites by effectively estimating large-scale parameter maps using small-scale measurements and by applying uncertainty quantification method to a real watershed observation case. It will also draw upon and contribute to advances in Bayesian experimental design, and will optimally result in financial savings.

Enhanced water management systems depend on accurate estimation of hydraulic properties of subsurface formations. This is while hydraulic conductivity of geologic formations could vary significantly. Therefore, using information only from widely spaced boreholes will be insufficient in characterizing subsurface aquifer properties. Hence, there is a need for other sources of information to complement our hydro-geophysics understanding of a region of interest. This study presents a numerical framework where information from different measurement sources is combined to characterize the 3-dimensional random field representing the hydraulic conductivity of a watershed in a Multi-Fidelity estimation model. Coupled with this model, a Bayesian experimental design will also be presented that is used to select the best future sampling locations. This work draws upon unique capabilities of electrical resistivity tests as well as statistical inversion. It presents a Multi-Fidelity Gaussian Processes (Kriging) model to estimate the geological properties in Upper Sangamon Watershed in east central Illinois, using multi-source observation data, obtained from electrical resistivity and pumping tests. We demonstrate the accuracy of Co-Kriging that is dependent on the locations and the distribution of both the high- and low-fidelity data, and also discuss its comparison with Single-High-Fidelity Kriging results. The uncertainties and confidence in the measurements and parameter estimates are then quantified and are in turn used to design future cycles of data collection to further improve the confidence intervals.

Enhanced water management systems depend on accurate estimation of hydraulic properties of subsurface formations. This is while hydraulic conductivity of geologic formations could vary significantly. Herein, we studied an intensively managed area located in the Upper Sangamon Watershed in Central Illinois, U.S.A., and generated 2D maps of hydraulic conductivity over a large-scale region with quantified uncertainties in different depth layers. In doing so, we made use of low cost, small-scale measurements obtained from the Electrical Earth Resistivity together with more accurate, more expensive pumping tests in a calibration framework based on Kriging. We offered a cost-effective approach to reliably characterize the hydraulic conductivity properties in under-sampled sites and can be particularly used in obtaining large-scale parameter maps for a region using small-scale measurements in an efficient way. This work also includes optimal sensor placement, where the best locations for future data collection are selected by considering the current confidence levels estimated by the Kriging model, which is related to the expected value of information from future sensor data. Our approach is based on the Bayesian experimental design, which selects the best locations, out of a set of candidate locations, based on the value of information that each location is expected to offer.