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(PSI) = K(s) exp (alpha-PSI), where K is hydraulic conductivity, PSI is soil water matric potential, K(s) is saturated hydraulic conductivity, and alpha 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 alpha and the volumetric soil water capacity C = d-theta/d-PSI, with theta-volumetric soil water content, are assumed normally distributed. We point out here that alpha and K(s) are related to the same internal pore geometry of the soil. This interrelationship ensures that if K(s) is lognormal, then alpha, and possibly C, will also be lognormal. Additionally, we present preliminary field results which indicate that alpha 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 PSI may therefore be prejudiced by the use of the exponential form for K(PSI). Tests of the sensitivity of stochastic model predictions to both the parameterizations adopted for K(PSI) and the assumed distribution functions of parameters seem warranted. Reliable experimental evidence on field variability of K(PSI) and PSI(theta) at substantial negative values of PSI are also needed.