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Flux-Gradient Relationships and Soil-Water Diffusivity from Curves of Water Content versus Time¹

ABSTRACT

Direct analysis of a family of curves of soil-water content versus time at different fixed positions enables assessment of the flux-gradient relationship prior to the calculation of soilwater diffusivity. The method is evaluated on both smooth and random-error data generated from the solution of the horizontal soil-water intake problem with a known diffusivity function. Interpolation, differentiation, and integration are carried out by least-squares curve fitting based on the two recently developed techniques of parabolic splines and sliding parabolas, with all computations performed by computer. Results are excellent for both smooth and random-error input data, whether in terms of recovering the original known diffusivity function, assessing the nature of the flux-gradient relationship, or in making the numerous checks and validations at various intermediate stages of computation. The method applies for any horizontal soil-wetting process independently of the specific boundary conditions, including water entry through a nonzero inlet resistance. It should be adaptable to horizontal dewatering, and extendable to vertical flow.

¹ Journal Paper No. 5174, Purdue University Agr. Exp. Sta. West Lafayette, Ind. 47907. Contribution from the Department of Agronomy. Partial support was from funds provided by the US Department of the Interior, Office of Water Resources Research, as authorized under the Water Resources Research Act of 1964.

² Graduate Research Assistant, Postdoctoral Research Associate, and Professor of Soils, respectively. First author is now Lecturer on the Faculty of Agriculture, Ahmadu Bello Univ., Zaria, Nigeria; the second is Assistant Soil Scientist, Univ. of Hawaii, Honolulu.

Received for publication July 2, 1973. Accepted for publication September 7, 1973.