A New Analytical Model for Predicting the Three-Dimensional Wetted Volume Under a Vertical Line Source Irrigation System

Vertical line source irrigation is a localized water-saving technique suitable for deep-rooted crops, but the geometric structure of the wetted bulb lacks a systematic analytical modeling method. This study established a simplified three-dimensional (3D) analytical model to predict the wetted volume under vertical line source irrigation conditions. First, the model determined boundary points based on an empirical wetting-front equation and fitted the wetting profile with ellipse–parabola functions to derive analytical expressions for area and volume. Then, using aeolian sandy soil as the research object, the model predicted that during 0–250 min of irrigation, the wetted pattern area increased from 80.0 cm2 to 5050.6 cm2, and the wetted volume increased from 251.3 cm3 to 208,014.4 cm3. At 250 min, the lower, middle, and upper volume components accounted for 67.3%, 24.2%, and 8.4%, respectively. Finally, the model was validated using loam soil, and the results showed good agreement between the calculated and measured values. The model requires only simple input and enables fast computation. It effectively characterizes the three-dimensional spatiotemporal variation of the wetted bulb and provides a theoretical reference for the design of pipe spacing and irrigation quota.