Quantitative methods to direct exploration based on hydrogeologic information

Abstract

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 MODFLOW-2000, 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.

Directed site exploration for permeable reactive barrier design

“…All QDE approaches in Graettinger et al [23] are based on three matrices: (1) covariance of input parameters, (2) sensitivity of model outputs, and (3) covariance of model outputs. Each of the data elements in these matrices is related to a specific location within a site.…”

“…Among seven approaches presented in Graettinger et al [23], two approaches, the largest variance (LV) and most contributing input (MCI) to output covariance were applied in this PRB example. The LV identifies the location of the largest output uncertainty produced from input parameters.…”

“…The difference is that instead of using the PRB performance, we identify which input data have the greatest effect on model results given a specific design by rearranging matrix calculation in FOSM and find the data location that contributes the most to output variances across a site for a given PRB design. The original concept for QDE was to direct exploration to the location of greatest variance in model outputs, which is where model results are most uncertain [22][23][24]. This QDE approach has been successfully applied to groundwater remediation to find a next sampling location that is most likely to increase remedial design reliability [22].…”

“…This QDE approach has been successfully applied to groundwater remediation to find a next sampling location that is most likely to increase remedial design reliability [22]. Further development of the QDE approach by Graettinger et al [23] investigated and evaluated seven different techniques to direct exploration through re-analysis and comparison of the input variance matrix, output variance matrix, and model sensitivity matrix using MOD-FLOW 2000 [16]. This work determined that the piezometric head model was most improved by obtaining additional samples at locations where input information contributed the most to overall output variance.…”

Screening‐Level Sensitivity Analysis for the Design of Pump‐and‐Treat Systems

“…Other related work has examined the use of sensitivity analysis in developing predictive models for source water protection (Bakr and Butler 2005; Esling et al 2008) and permeable reactive barriers (Painter and Milke 2007; Lee et al 2009). Additional research has explored the use of sensitivity analysis to guide hydrogeologic data collection (James et al 1996; Graettinger et al 2006).…”