A Note on the Apparent Conductivity of Stratified Porous Media in Unsaturated Steady Flow Above a Water Table

We aim at deriving the apparent unsaturated conductivity (AUC) K(ap), defined as the ratio between the mean flux and the mean head gradient in a stratified vadose zone above the water table. This is achieved for steady flow generated by a constant infiltrating flux applied at the soil surface. By adopting the first-order approximation in the two parameters of the conductivity curve, and under a few additional simplifying assumptions, we were able to analytically compute K(ap). It is shown that this latter varies between K(ap) ≡ KH (the harmonic mean) at the water table, and K(ap) ≡ Kef (the effective conductivity in gravitational flow) far above the water table. Profiles of the AUC are illustrated, and the impact of parameters values is discussed.