C soil

In the case of upward movement of solute into the root-zone from a shallow water table,

C soil increases continually with time, unless downward diffusion of solute equal or exceeds the upward solute flux. This formulation can be used for assessing the effect of irrigation on soil salinity because of its ability to interpret first of all the non-steady conditions and secondly, leaching flux value.

3.1.2 The Solute Movement in Soil in Presence of Plant Water Uptake in a Shallow Water Table Environment

This situation is preponderant for the oasis in the region. The following analysis and equations can be very helpful for agricultural and water management inside. The salts can move (Wagenet (1984)) in the soil by both the convective transport and the diffusion process. The importance of each of these process varies as the magnitude of water flux varies. When the water flux becomes smaller, the diffusion becomes relatively important. The convective and the diffusion fluxes can be combined to give a total flux (Brutsaert, 1982). To predict the solute movement in soil in presence of plant water uptake in a shallow water table environment, we can use the advection-dispersion equation. To solve the equation, the root zone can be divided into a series of layers. Then, for each layer we introduce a constant coefficient form with layer-averaged values for each property. In this case, the solute transport in the soil can be described as(Connel and Haverkamp (1996)):

C is the solute concentration, ro is the unsaturated volumetric moisture content a is the dispersivity, z is positive downwards q is the soil moisture flux

Ar (z, t)is the root water uptake at position z and time t

If we assume that the solute and water uptake relationship can be approximated as vertical one-dimensional process we can write (Connel and Haverkamp (1996)):

This equation can be easily solved if we use a transformation that permits to write it as follows:

Q is a space transformation replacing the moisture flux, q(x, t) with the surface moisture flux q0(t) and using the equality f(Q,t) = C(z,t) (Connel and Haverkamp (1996)).

Also we must signal that the solute movement in an isotropic soil during one-dimensional dispersion can be modelled analytically by assuming that both the velocity and the dispersion coefficient are constant with respect to time and space.

3.1.3 Solute Transport in a Tile-Drained Soil-Aquifer System

The governing equation for two-dimensional solute transport in unsaturated-saturated zones during steady state water flow that includes the effects of convective transport, dispersion, and linear equilibrium reactions between the solute and the porous medium on solute transport in a tile-drained soil aquifer system (Kamara et al., (1991)) is as follows:

C is the dissolved solute concentration, Rf is the retardation factor, ro is the volumetric water content (equal to the porosity in the saturated zone) oxx, Oxy, oyx and oyy are components of the dispersion coefficient tensor qx and qy are the Darcian specific discharge components 0(x,y,t) is a source or a sink term

The retardation factor in the equation accounts for linear equilibrium interactions between the solute and porous medium and is given by

pKd f a p is the bulk density of the medium Kd a solute distribution coefficient

The dispersion coefficients for a two-dimensional isotropic porous medium can be calculated as follow:

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