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Solute transport in a heterogeneous soil for boundary and initial conditions: Evaluation of first-order approximations

Abstract:

We compared four different approaches to derive the statistics of the solute travel time γ and horizontal displacement η from spatial covariance functions of the pore water velocity u in an unsaturated heterogeneous soil profile using a Lagrangian framework. The effects of four simplifications that are generally used to derive γ and η statistics were evaluated: (1) first-order approximation of the stochastic flow equation, (2) first-order expansion of the inverse vertical pore water velocity 1/u2, (3) identical distributions of u and of solute particle velocity w, and (4) vertical solute trajectories. Alternatives that comprehend numerical solutions of the stochastic flow equation to derive distributions of u and 1/u2, using a flux-weighted distribution of u to represent the distribution of w and using two dimensional covariance functions to represent the effect of horizontal deviations of the particle trajectories, were discussed. The statistics of γ and η derived in a Lagrangian framework were compared with the statistics derived from two types of transport simulations in generated, two-dimensional heterogeneous soil profiles: simulations (1) for uniform solute flux at the soil surface (uniform boundary value problem, UBVP) and (2) for a uniform initial concentration profile (uniform initial value problem, UIVP). The considered heterogeneity of the saturated hydraulic conductivity, K(sat), was relatively large, σ2 ln K(sat) = 2.55, but it was based on conductivity measurements in a loam soil and found to be realistic for pbkp_redicting solute transport in this soil. For the UBVP simulations the best pbkp_redictions of the solute travel time and horizontal displacement statistics were obtained using the flux-weighted distribution of simulated u. For the UIVP Simulations the distribution of w was not stationary but changed from the nonweighted distribution of u for small travel depths to the flux-weighted distribution of u for larger travel depths.