Comparison of Methods Predicting Advance Time in Furrow Irrigation

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In the design of furrow irrigation, and in general in surface irrigation, the reliable estimation of the advance time at the furrow end (tL) is a key issue for improving the efficiency and uniformity of irrigation. In this study, three methods are used for estimating the tL, and their results are compared with the experimental data of fifteen different furrows from the international literature. These methods are as follows: (a) the Valiantzas equation, (b) the method presented by Walker and Skogerboe, based on solving the volume balance equation by the Newton–Raphson iterative procedure and (c) the method of Philip and Farrell. The first two methods assume that the infiltration is described by the Lewis–Kostiakov equation and the extended Lewis–Kostiakov equation, respectively, while in the case of the Philip and Farrell method, the infiltration is described by the Philip equation and the Lewis-Kostiakov equation. The results showed that in most cases of the first two methods, the absolute relative error value of the predicted time tL was less than 10%. The Philip and Farrell method using the Lewis–Kostiakov infiltration equation underestimates the time tL and fails especially in the case where the volume of the surface water is not negligible compared to the total volume of water entering the system. The Valiantzas method is recommended because it was simpler and easier to use and showed greater prediction accuracy of tL, resulting in better planning of irrigation systems and contributing to water saving, which is currently a big issue.