Relative Water Uptake Rate as a Criterion for the Design of Trickle Irrigation Systems.

In this lecture we are going to describe a new modeling approach and demonstrate its applicability for designing the geometry of trickle irrigation systems, namely the spacing between the emitters and drip lines. The major difference between our and previous modeling approaches is that we refer to the root water uptake as to the unknown solution of the problem and not as to a known input. We postulate that the solution to the steady water flow problem with a root sink that is acting under constant, maximum suction defines un upper bound to the relative water uptake in actual transient situations and propose to use it as a design criterion. We assume that the soil hydraulic conductivity increases exponentially with its matric head, which allows the linearization of the Richards equation, formulated in terms of the Kirchhoff matric flux potential. Since the transformed problem is linear, the relative water uptake for any given configuration of sources and sinks can be calculated by superposition of the Green's functions of all relevant water sources and sinks. In addition to evaluating the relative water uptake, we also derived analytical expressions for the steam functions. The stream lines separating the water uptake zone from the percolating water provide insight to the dependence of the shape and extent of the actual rooting zone on the source-sink geometry and soil properties. A minimal number of just 2 system parameters: Gardner's (1958) α as a soil type quantifier and the depth of the pre-assumed active root zone are sufficient to characterize the interplay between capillary and gravitational effects on water flow and the competition between the processes of root water uptake and percolation. To account also for evaporation from the soil surface, when significant, another parameter is required, adopting the solution of Lomen and Warrick (1978).