Analytical solutions to evaluate the stream tube approach for field-scale modeling of evaporation

Quantifying upward flow across larger areas of the landscape is important for water resources management and research involving global exchange processes. The stream tube or parallel column model may be used for this purpose. Columns should be narrow enough to account for variability of local parameters and wide enough to minimize the effect of lateral flow. To provide guidance with the selection of minimum column width, an approximate analytical solution was obtained for steady flow in a medium composed of two vertical soil columns. The normalized matric flux potential, Phi, was used as a dependent variable. The two-dimensional solution consisted of a one-dimensional term and a perturbation term to ensure continuity in water flux and soil pressure head, h. Comparison of two-dimensional and one-dimensional stream tube results showed little difference in hand Phi, except near the interface. The greatest effect was found for finer textured soils. An analytical expression for the lateral flux was obtained from the solution for Phi. For "wet" conditions involving a shallow water table and high surface water contents, the lateral flux was found to be no more than 5% of the evaporative flux. For "dry" conditions with miniscule fluxes, the evaporative and lateral fluxes may be of the same order of magnitude; application of the stream tube model could involve considerable error. The analytical solutions are convenient to evaluate the impact of stream tube width for different evaporation scenarios and also to verify more elaborate numerical schemes.