# Calculation of Vertical Moisture Flow in a Soil Body during Evaporation, Infiltration and Redistribution

• F. Kastanek
Part of the Ecological Studies book series (ECOLSTUD, volume 4)

## Abstract

In order to supply a mathematical solution for non-steady moisture movement in the unsaturated stage, it is necessary to define unequivocally initial and boundary conditions. Moreover, knowledge about the relations between θ, h and k (or D or C) is necessary. If the functional relationships cannot be presented in a simple form or if the initial and boundary conditions are not simple, it may become necessary to apply numerical methods. Freeze (1969) gives a s.urvey of the known numerical methods for calculating both vertical and horizontal flow problems in unsaturated soils. In the same paper, Freeze also gives a numerical solution for the computation of vertical non-steady moisture movement when taking the groundwater into account. In his considerations he took as a basis the differential equation:
$$C\frac{{\partial h}}{{\partial t}} = \frac{{\partial h}}{{\partial z}}\left( {k\frac{{\partial h}}{{\partial z}}} \right) + \frac{{\partial k}}{{\partial z}}$$
(1)
Hanks, Klute and Bresler (1969) and Bresler, Kemper and Hanks (1969) treat the same subject. Their starting point, however, leads to another differential equation
$$\frac{{\partial \theta }}{{\partial t}} = \frac{{\partial h}}{{\partial z}}\left( {D\frac{{\partial \theta }}{{\partial z}}} \right) + \frac{{\partial k}}{{\partial z}}$$
(2)
Moreover, they consider hysteresis effects.

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### References

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