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

Abstract

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.

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

“…To evaluate how the soil vertical heterogeneity (ß) can affect plant water uptake rates at various ratios between the cylinder radius (R^) and the rooting zone radius RQ (= ar^/l, where rî s the physical radius of the conceived rooting zone), we use the coupled source-sink model (Communar and Friedman, 2010a), According to this model, the MFP generated by a surface point source í^^ at {R,Z) = (0, 0) and a subsurface point sink $j¡ located at depth Z. (= azjl, in which z, is the physical depth) is [27] where $j,^ and $jj are the MFPs normalized with the source strength {q^^, and qj= qjq^^ is the a priori unknown relative water uptake rate (RWUR), The sink is simulated by using the solution for a steady subsurface point source, i,e., the value of $ .…”

“…The nature ofthe conceived rooting zone (Communar and Friedman, 2010a) of soil dryness at its boundary and streamlines that meet the boundary and physically end there, where water is given up to the interior plant roots, was chosen for the sake of mathematical tractability. The choice of a single interior point sink rather than arrays of interior point or line sinks already provides a good workable model.…”

Determination of Soil Hydraulic Parameters with CyclicIrrigation Tests

“…Analytical solutions for steady infiltration from shallow circular ponds at the soil surface (Wooding, 1968; Warrick, 1985) and from subsurface and surface point sources (Raats, 1971; Philip, 1971) were found useful for designing the geometry of drip irrigation systems (Bresler, 1978; Amoozegar‐Fard et al, 1984; Revol et al (1997a, 1997b); Communar and Friedman, 2010a, 2010b, 2010c, 2010d, 2011). Different methods, such as the dripper (pond radius) method (Shani et al, 1987; Or, 1996; Revol et al, 1997a, 1997b; Yitayew et al, 1998) and a multiple‐disk approach (Smettem and Clothier, 1989; Lazarovitch et al, 2007) have been used for evaluating the two parameters α and K s of Gardner's relationship from in situ measurements.…”

Generalized Coupled Source–Sink Model for Evaluating Transient Water Uptake in Trickle Irrigation: II. Irrigation Scheduling Scenarios

“…In the present study, we refer to the general case where the water uptake rate is smaller than the evaluated maximum due to, e.g., limiting evaporative conditions (and stomata closure) or a strong decrease in the local water conductance between the bulk soil and the root surface (Communar and Friedman, 2010a), To account for this circumstance, a dimensionless film resistance C, can be added to the sink interface. Such a "skin effect" causes a drop of A<3?…”

“…An additional assumption, that plant roots extract water from the soil under conditions of maximum suction, was made in deriving the coupled source-sink model used for evaluating the temporal patterns of water uptake rates (WUR) under various intermittent irrigation scenarios. The steady version of this model provides useful results that describe the influence of the density and geometry of plants and water sources (Communar and Friedman, 2010a, 2010b, 2010cMeiri et al, 2011) and of soil vertical heterogeneity (Communar and Friedman, 2012) on the relative water uptake rate (RWUR, the ratio between water uptake and water application rates). In this study, we developed a modified water-uptake model.…”