Uncertainty in deterministic groundwater transport models due to the assumption of macrodispersive mixing: evidence from the Cape Cod (Massachusetts, U.S.A.) and Borden (Ontario, Canada) tracer tests

Deterministic transport models based on the advection-dispersion equation are widely used to simulate groundwater contaminant transport. Only the largest heterogeneities and velocity field variations are explicitly modeled by the advection part of such models because subsurface explorations allow limited understanding of the distribution of heterogeneity and velocities. Smaller heterogeneities and associated velocity field variations are not incorporated in the modeled velocity field, but their overall mixing effect is represented implicitly as macrodispersion. As a result, such models do not replicate the complex small-scale variation of actual concentration distributions, but instead simulate a smoother concentration distribution. This discrepancy causes significant uncertainty in modeled concentrations. In this paper, such uncertainty is quantified for the detailed concentration distribution data sets of the Cape Cod and Borden natural-gradient tracer tests. Models of these tests could be made with relatively little uncertainty about the source distribution, large-scale flow field, and apparent macrodispersitivities. As earlier moment analyses reveal, the ensemble-average bromide migration in both tests was approximately consistent with classical advection-dispersion theory. Therefore, the reported uncertainties are primarily due to the use of macrodispersivity to represent mixing caused by small-scale velocity field variations. Analytic three-dimensional transport models were used to simulate the migration of bromide, a non-reactive tracer. The distribution of log(ca/cm), where ca is actual concentration and cm is modeled concentration at the same point, had a standard deviation of 0.70 for both tests. The distribution of vertically-averaged concentration predictions, log(Σca/Σcm), where the summation is over each multi-level sampler, had a standard deviation of 0.45 for both tests. Comparing the peak actual concentration to the peak modeled concentration at any given time results in a standard deviation of 0.12 in the statistic log(ca(max)/cm(max)) for both tests. Although the uncertainties listed above pertain to the scales of un-modeled velocity variation in these models at these sites, the reported uncertainties could serve as lower bound estimates for most deterministic model applications. Uncertainty due to the assumption of macrodispersive mixing tends to increase as the plume scale decreases or as the scale of un-modeled velocity field variations increases.