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

Abstract

A zero‐inertia (ZI) model for irrigation advance in furrows (ZIFA) is developed. It is based on an analytical solution of the ZI differential equations and accounts for three principally different approaches to describe adequately the various types of furrow shapes. ZIFA takes into account the varying character of infiltration and does not contain any restriction for modeling the infiltration phenomenon. Besides simulation of advance flow in level or sloping borders with variable inflow, ZIFA provides also the possibility to remove two weak points in rigorous numerical modeling, namely to replace both the approximate Witham solution for generating initial values as well as cumbersome mass‐balance techniques used to describe the flow in the tip region of the advancing wave. ZIFA compared very favorably to a full hydrodynamic model as well as to field data and the outcome of a numerical ZI model.