On the variability and use of the hydraulic conductivity alpha parameter in stochastic treatments of unsaturated flow

The quasi‐linear parameterization for unsaturated hydraulic conductivity K(Ψ) = K_s exp (αΨ), where K is hydraulic conductivity, Ψ is soil water matric potential, K_s is saturated hydraulic conductivity, and α is a porous material parameter, has been used in both stochastic and deterministic models of unsaturated water flow in porous materials. In the stochastic approach, K_s is assumed lognormally distributed, but α and the volumetric soil water capacity C = dθ/dΨ, with θ volumetric soil water content, are assumed normally distributed. We point out here that α and K_s are related to the same internal pore geometry of the soil. This interrelationship ensures that if K_s is lognormal, then α, and possibly C, will also be lognormal. Additionally, we present preliminary field results which indicate that α is better described by a lognormal than a normal distribution. The quasi‐linear parameterization can be expected to be correct only in some integral sense. Predictions of increases in the variability of hydraulic conductivity with decreasing Ψ may therefore be prejudiced by the use of the exponential form for K(Ψ). Tests of the sensitivity of stochastic model predictions to both the parameterizations adopted for K(Ψ) and the assumed distribution functions of parameters seem warranted. Reliable experimental evidence on field variability of K(Ψ) and Ψ(θ) at substantial negative values of Ψ are also needed. Published in 1992 by the American Geophysical Union.