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

Chapter

## 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 Hanks, Klute and Bresler (1969) and Bresler, Kemper and Hanks (1969) treat the same subject. Their starting point, however, leads to another differential equation Moreover, they consider hysteresis effects.

*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)

$$ \frac{{\partial \theta }}{{\partial t}} = \frac{{\partial h}}{{\partial z}}\left( {D\frac{{\partial \theta }}{{\partial z}}} \right) + \frac{{\partial k}}{{\partial z}} $$

(2)

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### References

- Bresler, E., Kemper, W. D., Hanks, R. J.: Infiltration, redistribution and subsequent evaporation of water from soil as affected by wetting rate and hysteresis. Soil Sci. Amer. Proc.
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## Copyright information

© Springer-Verlag Berlin · Heidelberg 1973