THE TRANSVERSE HURST COEFFICIENT AS A MEASURE OF “CONNECTIVITY” AND CONTROL OF TRANSPORT EXTREMES IN ALLUVIAL AQUIFERS

Recent studies have proposed ad-hoc methods to induce enhanced connectivity in numerical representations of aquifers. In most, the effect on solute transport is reasonably small. Here we adopt a simple method to characterize connectivity that is supported by some data sets: anisotropic fractal scaling of the 2-point correlation function of hydraulic conductivity (K). The transverse index of that scaling (the Hurst coefficient H) need not be the same as the longitudinal---here treated as orthogonal and parallel to the mean hydraulic gradient, respectively. We find that changes in the transverse H in synthetic aquifers represent different degrees of layering and strongly segregate a plume into fast and slow components. While some of the moments and their growth rates appear similar for homogeneous versus layered systems, the bimodal nature of transport in the highly layered or connected material is systematic and drastic, especially when one considers that risk is dominated by early---and cleanup costs are dominated by late---arrivals of contaminant plumes. The effect of conditioning is not the same for the more connected systems. Conditioning (on a regular grid) with some known K data has less benefit in the more connected systems, indicating that strategic sampling is needed.