Extension of the Fujita Solution to air and water movement in soils

Abstract

For specific soil properties the fundamental solution of Fujita (1952b) is extended to include the effect of air movement on horizontal absorption. This exact solution is then used to determine the accuracy and range of applicability of two approximations to the sorptivity with air effects previously presented by Parlange et al. (1982) and Sander and Parlange (1984). The optimal sorptivity of Parlange et al. has very good accuracy while the surface water content θ s is near saturation but decreases in accuracy as θ s decreases. The approximate sorptivity of Sander and Parlange, however, proves to be extremely accurate for all θ s with a maximum error of only 0.5%. Sander and Parlange additionally give an approximation to the water profile which is also shown by comparison with the exact solution to have a maximum error of only 0.5%. The aim of this paper is primarily of a theoretical nature in that we use the exact solution to check the accuracy of the approximate solutions as stated above. Alternatively, the solution may be used for checking the accuracy of numerical models.