Generallized Coupled Source-Sink Model for Evaluating Transient Water Uptake in Trickle Irrigation: I. Model Formulation for Soils with Vertical Heterogeneity

We recently derived analytical solutions of the linearized infiltration equation for steady flows from point sources into a cylindrically confined homogeneous soil domain. The same basic concepts were used in this study to obtain the solution for unsteady flows from a surface point source toward a subsurface point sink in a cylindrically confined soil with saturated hydraulic conductivity that varies exponentially with depth. As in the previous study, the infinite and finite Hankel transformations, now coupled with the Laplace transform, were used to obtain general solutions for point sources in a cylindrical domain. The solutions were incorporated into a coupled source sink model to illustrate the influence of soil vertical heterogeneity on steady, maximum water uptake rates and on the rate of attainment of apparently steady conditions in the root zone. Illustrative simulations include: (i) steady flow patterns that develop in coupled source sink systems in various soil textures with vertical heterogeneity; and (ii) effects of soil vertical heterogeneity on temporal variations in water uptake. Applications of a steady coupled source-sink model that assumes only a time-dependent sink resistance, and of an unsteady model that also takes account of a time-dependent water source, for studying the effects of the frequency and the duration of cyclic water applications on water uptake are considered in detail in the companion article.