aL and aT are the longitudinal and transverse dispersivities,
Those equations predicted reasonably well the two-dimensional solute transport in groundwater. They are very useful when modelling the rising water table for every season, kind of soil and sort of plant. So we can choose the efficient hydro-agricultural technique to apply and the tolerant plant to install.
3.2 Equations to Estimate Water Flow Distribution and Solute Transport in Soils under Irrigation Systems
When to propose ideas of management inside an agriculture field like the oasis, an important question to ask which irrigation technique to apply and if we can apply many techniques in the same field? To give a convincing respond we must formulate the water flow distribution and uptake.
3.2.1 Equation to use when Analysing Water Flux under any Irrigation System in Regions with Irregular Boundaries for Soil Properties
For a vast region (North Africa), a more generalised case must be studied: unsaturated, partially saturated and saturated porous media, regions with irregular boundaries for physical properties of soil, vegetation and climate, non-uniform soils having arbitrary degree of local anisotropy.To analyse the water flow under any agricultural system for those general cases in vertical, horizontal and three-dimensional plan, we can use the following equation (Feddes at al. 1978; Vogel and Hopmans 1992; Hamdy, A. and Choukr-allah, R. 2002):
c #=¿ (Kxx ih+Kxz dh+KxZ)+# (KZx dh+k. dh+*»)- A dt dx dx dz dz dx dz h(x,z,t) is the soil water pressure head;
C(h) is the specific water capacity;
Ar is the sink term that represents the root uptake;
x and z (positive upwards) are spatial co-ordinates;
t is the time
0 is the volumetric water content
Kij is the hydraulic conductivity in the directions i and j
1 and j are the spatial co-ordinates x and z respectively
To describe the water flow, solute transport and water uptake by the roots we can as many authors consider a volume of soil on which the mass balance is applied and for which the concentration of solute is considered per a unit volume. We can then simulate seasonal variations of soil water distribution and salinity in irrigated soil subject to water extraction by the developing plant roots. The governing equation describing soil water flow in two dimensional saturated-unsaturated soil system is based on the assumptions that the air flow is negligible and water is the only fluid in the porous media and that the Darcy's law is applicable. Also we assume that the soil-water pressure and the hydraulic conductivity are continuous functions of the soil water content.
3.2.2 Distribution of Water for Several Type of Soil under Trickle Irrigation
In the case when to install new oasis in large zone with several type of soil and for which we think to apply the trickle irrigation, the equations that govern the flow of water and non-interacting solutes in unsaturated soil system are given as follows (Bresler, 1973, 1975):
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