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The unsaturated hydraulic conductivity function for soil can be calculated directly from a moisture retention function and a single measurement of hydraulic conductivity at some water content. If the moisture retention function can be represented by ψ = ψc (θ/θa)−b, where ψc is the air entry water potential, θ, is the saturated water content, and b is an emperically determined constant, then the hydraulic conductivity is given by k = ks (θ/θs)2b+3, where ks is the saturated hydraulic conductivity. Agreement of k calculated using this procedure with experimentally determined conductivities for five soil samples was found to be at least as good as with other calculation procedures.
Gaylon S. Campbell (Sat,) studied this question.