  Numerical transport models based on the advection-dispersion equation (ADE)
are built on the assumption that sub-grid cell transport is Fickian such that
dispersive spreading around the average velocity is symmetric and without
significant tailing on the front edge of a solute plume. However, anomalous
diffusion in the form of super-diffusion due to preferential pathways in an
aquifer has been observed in field data, challenging the assumption of Fickian
dispersion at the local scale. This study develops a fully Lagrangian method to
simulate sub-grid super-diffusion in a multi-dimensional regional-scale
transport. The underlying concept is based on previous observations that
solutions to space-fractional ADEs, which can describe super-diffusive
dispersion, can be obtained by transforming solutions of classical ADEs. The
transformations are equivalent to randomizing particle travel time or relative
velocity for each model time step. Here, the time randomizing procedure known
as subordination is applied to flow field output from MODFLOW simulations.
Numerical tests check the applicability of the novel method in mapping
regional-scale super-diffusive transport conditioned on local properties of
multi-dimensional heterogeneous media.
