摘要
SummaryA critical issue facing groundwater flow models is the estimation of representative hydraulic conductivity assigned to the model units. In this study, an experiment-based, high-resolution hydraulic conductivity map offers a test case to evaluate this parameter. Various hydrogeological units are distinguished, each is of irregular shape with distinct heterogeneity pattern created by physical sedimentation. Extending a previous study which used numerical upscaling to compute equivalent conductivities for these units (at two upscaling scales) [Zhang, Y., Gable, C.W., Person, M., 2006. Equivalent hydraulic conductivity of an experimental stratigraphy – implications for basin-scale flow simulations. Water Resources Research 42, W05404. doi:10.1029/2005WR004720], this study compares them with local statistics and effective conductivities predicted by a stochastic theory. Results suggest that for a system with moderate lnK variance (4.07) and low topographic slope (1°), the arithmetic mean (KA) provides a good estimate for the maximum principal component (Kmax) of the equivalent conductivity. The minimum principal component (Kmin) lies between the harmonic and geometric means: its closeness to the geometric mean is affected by heterogeneity pattern and upscaling scale. Using Kmax (alternatively, the arithmetic mean), geometric mean, and ln(K) variance, the stochastic theory predicts a Kmin that is consistent with the up-scaled value. Similarly, knowing Kmin, Kmax predicted by theory is also consistent with the up-scaled value. For most deposits (some with variance greater than 1), a low-variance version of the theory is more accurate than a high-variance version. However, the increase of topographic slope (to 4°) and total lnK variance (to 16) result in increased deviation of Kmax from KA. High variance also results in significantly larger anisotropy ratio, possibly due to the dominance of preferential flow. Finally, for select units, equivalent conductivity exhibits scale effect. Field scale representative elementary volume thus does not exist and upscaling the full unit is necessary to obtain the representative conductivity.