Advance and recession curves are of great importance for assessing the performance of border irrigation. In recent years, scaling techniques have helped to reduce the required measurements and to provide formulation of soil–water relations. The purpose of this study was to develop an invariant equation for calculating advance and recession curves in border irrigation using scaling techniques. The kinematic wave model and the Philip infiltration equation were used to simulate border irrigation. Scale factors were defined such that the kinematic wave equation remained independent of the initial and boundary conditions of the soil. Scaled advance and recession curves showed certain patterns, which led us to introduce a power and a binomial equation for advance and recession phases, respectively. The scaled equations were applied on 25 vegetated and non-vegetated borders. Four performance indices were calculated for each border, including application efficiency -Ea-, deep percolation ratio -DPR-, tail water ratio -TWR- and water requirement efficiency -Er-. Results showed that the maximum differences between measured and estimated values were 4% for E a, 9% for DPR and 4% for Er. Considering the simplicity and soil-condition independence of the proposed method, it can be concluded that scaled advance and recession curves could provide a reasonable estimate of border irrigation performance. © 2019 John Wiley & Sons, Ltd

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