Comparison of transfer function and deterministic modeling of area‐averaged solute transport in a heterogeneous field

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Abstract
The predictions of two one‐dimensional solute transport models describing area‐averaged mean field concentrations under steady state water flow conditions were tested through numerical experiments. The two models are based on different solute dispersion process hypotheses, namely, the stochastic‐convective process of the convective lognormal transfer function model and the advective‐dispersive process of the advection‐dispersion equation model. Two hypothetical random fields having different correlation structures for their hydraulic and retention properties were generated through a random scaling factor δ. The numerical experiments were conducted by running solute transport simulations in these hypothetical fields, and the simulation results were used to calibrate the two process models. The simulation results demonstrated that even under steady state, one‐dimensional water flow in the medium having a short correlation length scale, considerable local variations in solute concentration were still present in the simulation results. The observed dispersion in the mean field data was intermediate between the representations in the two extreme process hypotheses of the two models tested, and neither model was accurate over the entire range of testing. Predictions of the asymptotic dispersivity based on the analysis used in saturated flow were not valid under unsaturated conditions. Complete knowledge of the velocity field was required in the latter case to predict the asymptotic dispersivity.