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Unsaturated flow in spatially variable fields: 3. Solute transport models and their application to two fields
Author(s) -
Bresler Eshel,
Dagan Gedeon
Publication year - 1983
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr019i002p00429
Subject(s) - infiltration (hvac) , mathematics , mechanics , soil water , flow (mathematics) , horizontal plane , dispersion (optics) , soil science , water flow , hydrology (agriculture) , geotechnical engineering , environmental science , geometry , geology , meteorology , physics , optics
An approximate model of salt transport in a spatially variable field during infiltration and redistribution is presented. The water flow is assumed to be vertical, and both pore water velocity and depth of wetting front change in the horizontal plane due to the variability of soil hydraulic properties. These variables are computed with the aid of the model developed in part 1 (Dagan and Bresler, this issue) and part 2 (Bresler and Dagan, this issue) of the present study. The salt transport in the vertical profile is computed by using an approximate, closed form solution of the convection‐dispersion equation, with the value of the dispersivity increasing from zero to its maximum (3 cm) as the front propagates downward. The concentration profiles vary in the horizontal plane because of the aforementioned variation of water flow variables. The expectation value and the variance of the concentration are computed as function of depth and time for the two variable soils considered in part 2 (Panoche, with large variability, and Bet Dagan, with lesser variability). The results are compared with those based on a numerical simulation of the water flow and salt transport, as well as with those pertaining to an equivalent, deterministic, uniform soil (for the expected value). It is shown that the approximate model yields quite accurate results when compared with the numerical simulations for the field of large variability, while some differences are present for the more uniform one. In any case, the results for the expected value, based on the traditional approach of replacing the variable field by an equivalent uniform one, include a much larger error. It is suggested that the approximate, simplified model presented here may serve as a basis for simulation of additional effects not considered here, e.g., adsorption, root extraction, and change of soil properties due to salt content. The main conclusion is that in spite of the apparent complexity, the statistical moments of salt concentration in a spatially variable field can be determined by using simple flow models. Therefore further refinement of models of transport in homogeneous columns does not seem to be warranted, and the research effort should be concentrated on the study of field variability.