Quantitative methods to direct exploration based on hydrogeologic information

Andrew J. Graettinger (corresponding author) Department of Civil and Environmental Engineering, University of Alabama, Tuscaloosa, AL 35487, USA E-mail: andrewg@coe.eng.ua.edu Jejung Lee Department of Geosciences, University of Missouri – Kansas City, Kansas City MO 64110, USA E-mail: leej@umkc.edu Howard W. Reeves US Geological Survey, USGS Michigan Water Science Center, 6520 Mercantile Way, Suite 5, Lansing , MI 48911, USA E-mail: hwreeves@usgs.gov Deepu Dethan Environmental Resources Management, 1110 Montlimar Drive, Suite 150, Mobile, AL 36609, USA E-mail: Deepu.Dethan@erm.com Quantitatively Directed Exploration (QDE) approaches based on information such as model sensitivity, input data covariance and model output covariance are presented. Seven approaches for directing exploration are developed, applied, and evaluated on a synthetic hydrogeologic site. The QDE approaches evaluate input information uncertainty, subsurface model sensitivity and, most importantly, output covariance to identify the next location to sample. Spatial input parameter values and covariances are calculated with the multivariate conditional probability calculation from a limited number of samples. A variogram structure is used during data extrapolation to describe the spatial continuity, or correlation, of subsurface information. Model sensitivity can be determined by perturbing input data and evaluating output response or, as in this work, sensitivities can be programmed directly into an analysis model. Output covariance is calculated by the First-Order Second Moment (FOSM) method, which combines the covariance of input information with model sensitivity. A groundwater flow example, modeled in MODFLOW2000, is chosen to demonstrate the seven QDE approaches. MODFLOW-2000 is used to obtain the piezometric head and the model sensitivity simultaneously. The seven QDE approaches are evaluated based on the accuracy of the modeled piezometric head after information from a QDE sample is added. For the synthetic site used in this study, the QDE approach that identifies the location of hydraulic conductivity that contributes the most to the overall piezometric head variance proved to be the best method to quantitatively direct exploration.