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

Abstract

The previously derived coupled source-sink modeling approach for vertically heterogeneous cylindrical domains was extended to conditions prevailing when water uptake is controlled by diurnally time-varying, transpirationdriven plant resistance and by cyclic water applications, both leading to unsteady flow regimes in the rooting zone. Examples include simulations of diurnal variations in water uptake rates by plant roots (sinks) in homogeneous and vertically heterogeneous soils of various texture, under conditions of steady, continuous and unsteady water application, representative of various irrigation scheduling practices: pulsed, daily, and every few days. In coarsetextured, fast-responding soil, it is possible to meet the diurnal transpiration demand, but water losses through deep percolation are high. In soils of finer texture, daily short applications in the morning result in uptake patterns skewed toward morning, whereas all-day-long irrigation pushes the temporal uptake pattern toward the afternoon. In fine-textured soils irrigated every few days, similar water uptake volumes result from either prolonged, all-day, or short, morning applications, but the through-cycle uptake rates are more even with all-day applications.Abbreviations: MFP, matric flux potential; RWUR, relative water uptake rate; RWUV, relative water uptake volume; WUR, water uptake rate; WUV, water uptake volume. W e derived both exact and approximate solutions for steady and timedependent How from point sources in vertically heterogeneous cylindrical domains (Communar and Friedman, 2012)-solutions that reproduce flow patterns similar to those generated by a square array of water sources. The analytical solutions are based on the assumption that the hydraulic conductivity is an exponential function of both pressure head and depth (Philip, 1972;Philip and Forrester, 1975) and a linear function of water content (Warrick, 1974). 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. The modification includes a time-dependent sink (plant-atmosphere) resistance that accounts for hourly changes in water uptake that follow the transpiration demand

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

“…In Communar and Friedman (2012), we analyze the effects of the duration and frequency of cyclic irrigation under conditions determined by various combinations of soil profile (texture and vertical heterogeneity) and density of plants and emitters. Temporal patterns of RWURs under cyclic irrigation is simulated either with a quasi-steady coupled source-sink model that assumes that only sink resistance is time-dependent, corresponding to hourly transpiration patterns, or with an unsteady model that also takes account of a time-dependent water source.…”

“…Temporal patterns of RWURs under cyclic irrigation is simulated either with a quasi-steady coupled source-sink model that assumes that only sink resistance is time-dependent, corresponding to hourly transpiration patterns, or with an unsteady model that also takes account of a time-dependent water source. The www.soils.org/publications/sssaj analytical solutions derived previously and in this study are used also in Communar and Friedman (2012 with an expression of the same type for LOJ_…”

“…(1978), in expedmenes wieh an undiseurbed fine sandy loam, found ehae ehe SHC increased exponendally wich depeh, wieh a coefficiene of 0.184 cm"^ Therefore, a heeerogeneous soil model ehae eakes ineo accoune ehe variaeion in hydraulic conduceiviey wieh depeh can provide more insighe ineo processes associaeed wich wacer infilcracion and upeake ehan a homogeneous soil model. This areicle, eogeeher wieh Communar and Friedman (2012), coneinues our seudy of che design of erickle irrigaeion syseems. To exeend ehe coupled source-sink modeling approach for managemene purposes, a eime-dependene poine-source solueion and a eime-dependene sink resiscance chac cakes accoune of hourly changes in eranspiraeion demands were incorporaeed ineo che model.…”

“…The influence of soil heeerogeneiey on flow paeeerns is illuscraced ehrough ploes of sereamlines and coneours of waeer coneenes. Applicaeions of a seeady coupled source-sink model chac assumes only a cimedependenc sink resiscance, and of an unsceady model chac also accotincs for a cime-dependenc wacer source, for scudying che effecc of che frequency of ineermieeene waeer applicaeion on waeer upeake is considered in deeail in Communar and Friedman (2012).…”

Steady Infiltration from a Surface Point Source into a Two-Layered Cylindrically Confined and Unconfined Soil Region with Root Water Extraction

“…Modeling of water flow from irrigation sources into a soil domain with plant roots is of interest for irrigation design and scheduling (Dasberg and Or, 1999; Communar and Friedman, 2010a,b,c, 2012a,b). In this context, steady‐state solutions to the quasilinear flow equation for a homogeneous soil with a spatially distributed extraction sink term (Raats, 1974; Warrick, 1974; Philip, 1997) appeared useful for the interpretation of laboratory and field results.…”