Effect of root water extraction on wetted regions from continuous irrigation sources

Analytical studies of flow from irrigation sources into regions of root water uptake typically require the root distribution and the local water extraction rate as data of the problem. In reality, these are strongly influenced by local soil water content and, hence, position relative to the source. This work introduces a model with moisture-dependent root water extraction rate, so that the spatial distribution of uptake is no longer a datum, but emerges as part of the solution. For a diversity of conditions we obtain simple steady solutions describing the interactions between continuous sources and regions of wetting and water extraction. It is shown that as the uptake rate increases, the region decreases markedly in size and becomes more symmetrical in the vertical; for sources at depths that are small relative to the sorptive length, interaction with the surface becomes important; surface evaporation losses significantly reduce the region and increase asymmetry; with non-evaporating surfaces, the region is larger and more symmetrical. The dimensionless coefficient beta, proportional to the ratio of the local extraction rate to the Kirchhoff potential, determines behaviour. Estimating beta under controlled and field conditions is discussed.