Simple mathematical model for water advance determination

Abstract.

The explicit volume balance model was modified and combined with the motion equation of the zero inertia to predict water advance in border irrigation. A system of dimensionless notation was used to obtain implicit and explicit solutions of the model. This model is simpler than previously used models, yet maintains a high degree of accuracy. The proposed model requires no programming and can easily be performed using a hand calculator. The outcomes of the proposed model were comparable to those of the more sophisticated zero inertia model. Using well-documented field examples, the proposed model provided acceptable results, implying that it could be used in practice to determine the advance distance with insignificant errors. In addition, the model is applicable to conditions under which the traditional volume balance model fails.