Unified Solution for Infiltration and Drainage with Hysteresis Theory and Field Test

Hysteresis has been found in both the hydraulic conductivity, K, vs. pressure head, ψ, relationship, and the soil water content, θ, vs. ψ relationship. This limits the application of a unified solution for infiltration and drainage. A Haines' Jump model of hysteresis is proposed and combined with the Broadbridge and White form of K(θ) and the diffusivity, D, relationship, D(θ). This allows a unified analytical solution for infiltration and drainage. This solution accounts for hysteresis by allowing the inverse macroscopic capillary length scale, α, to be hysteretic. A method of a priori estimating the hysteretic nature of α is proposed and tested. The hysteretic change in α can be estimated from other θ(ψ) hysteresis models and then used in combination with the Broadbridge and White hydraulic functions. The predicted hysteresis in a was similar to that obtained from inverse procedures. The unified solution was applied to field-measured soil water storage during infiltration and drainage. Neglecting hysteresis resulted in poor prediction of water storage during drainage based on hydraulic parameters estimated from infiltration. This was especially true for drainage with high initial water content. Incorporating the proposed hysteresis model resulted in prediction error less than measurement error. In addition, a single unified inverse procedure for estimating hydraulic parameters from combined infiltration and drainage measurements can now be developed.