Mathematical Zero‐Inertia Modeling of Surface Irrigation: Advance in Borders

Abstract

A basis for comprehensive analytical models, equations, and their solutions for border or furrow irrigation advance is derived. This basis consists of an analytical solution of the zero‐inertia (ZI) differential equations, which assumes a moving momentum representative cross section in the water body. It takes into account the time‐varying character of infiltration and does not contain any restrictions on the infiltration formula used. Subsequently, this solution is specifically developed for a zero‐inertia model of border irrigation advance (ZIMBA). It proved efficient in three types of application: (1) Simulation of irrigation advance in sloping borders; (2) replacing within a numerical model of the cumbersome, but widely used mass‐balance techniques for calculating the flow in the tip region of the wave; and (3) generating initial values for starting a numerical simulation of border irrigation. The results of ZIMBA are compared to observed values and to results of a full hydrodynamic model. For the data analyzed here, the prediction error always remains below 4%.