An Explicit Equation for the Maximum Water Application Depth in Center Pivot Irrigation

A simple explicit formula was derived to determine the maximum irrigation depth ($D_{\max }$) that can be applied per irrigation without any runoff under a center pivot and/or linear move irrigation system. The analysis is built on the assumption that $D_{\max }$ is achieved when the water application rate is tangential to the Green-Ampt infiltration rate function. The surface storage was not considered here but tillage effects can be inherently incorporated if parameters of the Green-Ampt equation are properly measured. A power form formula was proposed to simulate the infiltration rate, while the application rate pattern had a parabolic shape. The proposed equation for $D_{\max }$ is a function of soil saturated hydraulic conductivity, sorptivity, and the peak application rate. Numerical examples covering different combinations of soil properties and peak application rates indicated the high accuracy of the proposed formula with maximum and average absolute errors of 1 and 0.4 mm from the numerical stepwise solution, respectively. The quick calculation of $D_{\max }$ here allows us to easily estimate a minimum lateral speed that will not trigger runoff under center pivots.