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The presence of well‐connected paths is commonly observed in spatially heterogeneous porous formations. Channels consisting of high hydraulic conductivity (K) values strongly affect fate and transport of dissolved species in the subsurface environment. Several studies have established a correlation between connectivity properties of the spatially variableK‐field and solute first arrival times. However, due to limited knowledge of the spatial structure of theK‐field, connectivity metrics are subject to uncertainty. In this work, we utilize the concept of the minimum hydraulic resistance and least resistance path to evaluate the connectivity of aK‐field in a stochastic framework. We employ a fast graph theory‐based algorithm to alleviate the computational burden associated with stochastic computations in order to investigate both the impact of the hydrogeological structural conceptualization and domain dimensionality (2‐D vs. 3‐D) on the uncertainty of the minimum hydraulic resistance. Finally, we propose an iterative data acquisition strategy that can be utilized to identify the least resistance path (which is linked to preferential flow channels) in real sites. A synthetic benchmark test is presented, showing the advantages of the proposed sampling strategy when compared to a regular sampling strategy. By using the iterative data sampling strategy, we were able to reduce first arrival time uncertainty by 47% (when compared to the regular sampling strategy), while maintaining site characterization efforts constant.

An inadequate characterization of hydrogeological properties can significantly decrease the trustworthiness of subsurface flow and transport model predictions. A variety of data assimilation methods have been proposed in order to estimate hydrogeological parameters from spatially scarce data by incorporating them into the governing physical models. In order to quantify the accuracy of the estimations, several metrics have been used such as Rank Histograms, root‐mean‐square error (RMSE), and Ensemble Spread. However, these commonly used metrics do not regard the spatial correlation of the aquifer's properties. This can cause permeability fields with very different spatial structures to have similar histograms or RMSE. In this paper, we propose an approach based on color coherence vectors (CCV) for evaluating the performance of these estimation methods. CCV is a histogram‐based technique for comparing images that incorporate spatial information. We represent estimated fields as digital three‐channel images and use CCV to compare and quantify the accuracy of estimations. The appealing feature of this technique is that it considers the spatial structure embedded in the estimated fields. The sensitivity of CCV to spatial information makes it a suitable metric for assessing the performance of data assimilation techniques. Under various factors, such as numbers of measurements and structural parameters of the log conductivity field, we compare the performance of CCV with the RMSE.