Macrodispersivity and large-scale hydrogeologic variability

Although groundwater velocities vary over a wide range of spatial scales it is generally only feasible to model the largest variations explicitly. Smaller-scale velocity variability must be accounted for indirectly, usually by increasing the magnitude of the dispersivity tensor (i.e. by introducing a so-called macrodispersivity). Most macrodispersion theories tacitly assume that a macrodispersivity tensor which works well when there is only small-scale velocity variability will also work well when there is larger-scale variability. We analyze this assumption in a high resolution numerical experiment which simulates solute transport through a two-scale velocity field. Our results confirm that a transport model which uses an appropriately adjusted macrodispersivity can reproduce the large-scale features of a solute plume when the velocity varies only over small scales. However, if the velocity field includes both small and large-scale components, the macrodispersivity term does not appear to be able to capture all of the effects of small-scale variability. In this case the predicted plume is more well mixed and consistently underestimates peak solute concentrations at all times. We believe that this result can be best explained by scale interactions resulting from the nonlinear transformation from velocity to concentration. However, additional analysis will be required to test this hypothesis.