Data‐Worth Assessment for a Three‐Dimensional Optimal Design in Nonlinear Groundwater Systems

Abstract

Groundwater model predictions are often uncertain due to inherent uncertainties in model input data. Monitored field data are commonly used to assess the performance of a model and reduce its prediction uncertainty. Given the high cost of data collection, it is imperative to identify the minimum number of required observation wells and to define the optimal locations of sampling points in space and depth. This study proposes a design methodology to optimize the number and location of additional observation wells that will effectively measure multiple hydrogeological parameters at different depths. For this purpose, we incorporated Bayesian model averaging and genetic algorithms into a linear data‐worth analysis in order to conduct a three‐dimensional location search for new sampling locations. We evaluated the methodology by applying it along a heterogeneous coastal aquifer with limited hydrogeological data that is experiencing salt water intrusion (SWI). The aim of the model was to identify the best locations for sampling head and salinity data, while reducing uncertainty when predicting multiple variables of SWI. The resulting optimal locations for new observation wells varied with the defined design constraints. The optimal design (OD) depended on the ratio of the start‐up cost of the monitoring program and the installation cost of the first observation well. The proposed methodology can contribute toward reducing the uncertainties associated with predicting multiple variables in a groundwater system.

Monitoring Brine Leakage From Deep Geologic Formations Storing Carbon Dioxide: Design Framework Validation Using Intermediate‐Scale Experiment

“…GA was selected for this analysis because it has been successfully applied in similar OD frameworks developed by Wöhling et al (2016) and Safi et al (2019) to design monitoring systems for shallow groundwater systems.…”

“…(2016) and Safi et al. (2019) to design monitoring systems for shallow groundwater systems. In addition, the GA can search the global minimum of a discontinuous, non‐convex solution space with multi‐attribute variables (Wöhling et al., 2016), as is the case in the leakage problem.…”

“…(2016), Vilhelmsen and Ferré (2018), and Safi et al. (2019), 40% of the current population was retained as elite candidates in the next population ($${P}_{2}$$), top two ranked designs were treated as parents for producing 15% of the offspring using Laplace crossover function, and remaining individuals were resampled randomly outside the admissible range from vector X using a Power mutation function (Deep et al., 2009). A relatively high percentage of the mutated individuals was considered in this work to intensively explore the solution space, particularly after assigning an initial guess of the best locations.…”

“…Despite the above approaches, non‐linear methods still pose different degrees of numerical challenges in determining model prediction uncertainties compared to linear techniques. Moreover, the uncertainty analysis computational cost tends to be directly proportional to model non‐linearity and complexity (Safi et al., 2019). Thus, the applicability of such methods to complex groundwater transport models is tied to how much computational capacity is available to the user.…”

Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

“…Bayesian statistics is gaining popularity in hydrological modeling (e.g., [1][2][3][4][5][6]). It is an appealing choice for ranking candidate conceptual models [7][8][9][10], modeling propositions [2,[11][12][13][14][15] and scenarios [16,17].…”