Modeling and error analysis of kinematic-wave equations of furrow irrigation

Abstract

A moving control volume approach was used to model the advance phase of a furrow irrigation system whereas a fixed control volume was used to model the nearly stationary phase and the runoff rate. The resulting finite-difference equations of the kinematic-wave model were linearized and explicit algebraic expressions were obtained for computation of advance and runoff rate. The solutions for the advance increment and the runoff rate were compared with the nonlinear scheme, the zero-inertia model, and a set of field data. A close agreement was found between the models and the field data. Assuming a constant infiltration rate, a differential equation was derived to estimate the error between the kinematic-wave model and the zero-inertia model in predicting the flow cross-sectional area along the field length. The differential equation and two dimensionless terms were used to define the limits for use of the kinematic-wave model in furrow irrigation.