Constant flux infiltration and drainage in unsaturated heterogeneous soils

Infiltration and drainage are important natural processes in ecology, agriculture and water-resources management. The goal of this study was to further our understanding of the movement of water during infiltration and drainage through heterogeneous field soils. Specific objectives included developing a new analytical solution of Richards' equation for soil water flow, new field measurement techniques, and inverse procedures for estimating soil hydraulic parameters. A series of constant flux infiltration and subsequent drainage experiments were conducted on a heterogeneous sandy soil. Two hundred Multipurpose Time Domain Reflectometry probes were installed along a 7.5 m transect at 4 depths. The probes measured soil water storage, W(t), as a function of time and pressure head during both transient and steady state conditions. The local water flux at each location was determined using the measured water storage during constant infiltration. Measurements at steady state were used to obtain the effective hydraulic conductivity and retention curves for the site. The uniqueness and stability of the inverse problem for estimating the local hydraulic properties from measured water storage during transient infiltration were analyzed. With two pressure head measurements, one at initial condition and the other at steady-state, a single transient W(t) provided unique and stable estimates of saturated hydraulic conductivity, Ks, inverse capillary length scale, alpha, another shape parameter and saturated water content, qs. The estimated parameters and a proposed Haines Jump model of hysteresis accurately predicted the soil water storage during drainage for different initial conditions. A method of a priori estimation of the Haines Jump was proposed and tested. To account for the spatial variability of hydraulic parameters in the horizontal direction, a unified stochastic analytical solution for infiltration and drainage was developed using a small perturbation method. The solution had very good agreement with Monte Carlo simulation for two extremes of spatial correlation between alpha and Ks fields. The average soil water storage to a fixed depth, W, in the heterogeneous soil was essentially identical to that of a homogeneous soil with soil hydraulic properties equal to the mean hydraulic properties of the heterogeneous soil. The variance of soil water storage to a fixed depth, however, depended on W, the variances of soil hydraulic properties, water flux density, and cross-correlation of the soil hydraulic properties. The new unified stochastic solution can also be used for inverse determination of the mean, variance, and correlation length scale of hydraulic parameters.