Relative Water Uptake Rate as a Criterion for Trickle Irrigation System Design: I. Coupled Source–Sink Steady Water Flow Model

We have developed a new modeling approach for designing the geometry of trickle irrigation systems: root water uptake rate is treated as the unknown, i.e., sought after, quantity. It is determined from solutions to the linearized, steady‐water‐flow problem that describes the interaction between surface point (or line) sources and subsurface point (or line) sinks. We postulate that a sink that creates a maximum allowable suction defines an upper bound to the relative water uptake, and propose to use this upper bound as a design criterion. In the basic scenarios of a coupled source and sink, as few as three system parameters—the soil sorptive number (inverse of the sorptive length) and the depth and radius of the conceived rooting zone—can be sufficient to characterize the competition between root water uptake and deep percolation processes. In its dimensionless form, the proposed water uptake model is general for all soil types and all source–sink geometries. Evaporation is taken into account in the basic solutions for a source–sink couple with matric‐flux‐potential‐dependent evaporative water flux at the soil surface. Local resistance can be incorporated into the model by adding a skin resistance at the soil–sink interface. In addition to evaluating the relative water uptake rate, we also plotted contours of constant matric flux potential (pressure head and saturation degree) and streamlines, including the dividing streamlines that delineate the water capture zone and separate it from the deep percolation zone and the evaporation zone. Using computations, we elucidated the effects of the above system parameters on the relative water uptake rate and water flow patterns for three‐ and two‐dimensional systems; these computations describe single drippers, drip tapes, and drip lines with closely spaced drippers.