Soilwater distribution in a nonuniformly irrigated field with root extraction

A steady-state solution is developed for two-dimensional distributions of irrigation water flux at the soil surface and water extraction by plant roots. The solution of the linear equation is based on the small perturbations method, in which a small parameter is introduced into the governing differential equation. For the sprinkler irrigation method, this parameter is determined by scaling the soil characteristic length, α, by the distance between the sprinklers. Linearization is attained by assuming that the unsaturated hydraulic conductivity is exponentially related to the pressure head. Vertical distribution of the two-dimensional plant-root uptake is based on the one-dimensional model, which meets the approximation that the extraction pattern of plant roots is 40, 30, 20, and 10% of the total transpiration requirements in each successively deeper quarter of the root zone. Water extraction by plant roots increases lateral unsaturated flow beyond that which occurs as a result of irrigation nonuniformity. However, for a homogeneous soil profile, this lateral flow component increases water availability to those parts of the field where water shortages occur because of irrigation nonuniformity. Indeed, actual irrigation uniformity increases as measured by the decrease in the amplitude of the vertical flux around the mean. Younger plants suffer more from spatial fluctuations of irrigation water than do older plants, which have deeper roots. Actual irrigation uniformity, as measured by water availability to roots, is also affected by the distance between sprinklers and by soil type.