We sometimes have measurements of soil hydraulic conductivity at saturation and perhaps at one or two water contents below saturation, but we often need a mathematical function to allow calculation of hydraulic conductivity for all other values of water content. For this reason, soil hydraulic conductivity functions have been developed corresponding to each of the soil water retention functions presented in Chapter 3. The hydraulic conductivity function of Brooks and Corey , is defined by:
where K(θ) is the hydraulic conductivity as a function of volumetric water content, Ks is the saturated hydraulic conductivity, and λ is the same pore-size distribution index used in the Brooks and Corey water retention curve. Larger values of λ indicate more uniformly-sized pores, while small values indicate a wide distribution of pore sizes are present.
The hydraulic conductivity function corresponding to the water retention model of Campbell  is defined by:
where again b is a parameter related to the pore size distribution. The most commonly-used hydraulic conductivity function corresponding to the water retention model of van Genuchten  is defined by:
where n is a pore-size distribution index similar to λ, and m is a parameter defined in this case by m = 1 – 1/n.