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Estimating the Variability of Unsaturated Soil Hydraulic Conductivity Using Simple Equations¹

ABSTRACT

Description of transient water flow requires knowledge, or estimation, of the relationship between the unsaturated soil hydraulic conductivity, K, and volumetric water content. A variety of studies have related K() to the saturated conductivity K_o by equations involving the volumetric water content, , and its value at saturation, _o. The relationship is expressed here in terms of either the difference between and _o or the ratio of to _o, so that K() is obtained by multiplying K_o by exp[ß( – _o)] or by [/_o]^{2b + 3} respectively, with ß and b being constants for any one sampling point. The quantity ß in the equation involving ( – _o) can be obtained from field data by four different mathematical methods. When this equation was used to compute distributions of lnK() from measured distributions of lnK_o and lnß, the first four moments of the resulting distributions of lnK() all differed considerably according to the mathematical method used, although K_o and ß were derived in each case from the same set of field data. When both equations were used to estimate lnK(), using the same distributions of lnK_o and appropriate distributions of lnß or lnb, there were large differences between them in the moments of the resulting distributions. The estimate of lnK() from the equation using /_o had much the larger variance, mainly because the variance of lnb was about three times that of lnß.

¹ Joint contribution from Rothamsted Exp. Stn., Harpenden, Herts, UK, and New York Agric. Exp. Stn., Cornell Univ., Ithaca, NY.

² Professor, Dep. of Agronomy, Cornell Univ. and Soil Scientist, Soils and Plant Nutrition Dep., Rothamsted.

Received for publication December 23, 1985.