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 = d θ/ d Ψ, 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.