Izt 0z 0 ot z 0t

the solution of Equation (8.31) can be expressed as &(z,t) = &i(z,t) + &2(z,t) (8.37)

The second class of solutions is obtained from Equation (8.31) subject to the following boundary and initial conditions:

Moreover it is important to add that since ft(z, t) and the conductive flux (-D ■ (Sft/Sz)) both satisfy the Equation (8.31), then the total flux (-D ■ (SV/Sz) + V ■ V) also satisfies (8.31). This is important because the flux at the surface is often the known boundary condition.


The soil water content vertical profiles obtained from this example have an inflection point or not depending on the time and on the value of a parameter p defined below. Furthermore, the soil moisture at the surface increases gradually with time.

The following boundary conditions are assumed.

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