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ORIGINAL PAPER

A new analytical method for derivation of infiltration parameters Amin Seyedzadeh1 · Amir Panahi1 · Eisa Maroufpoor2 Received: 8 February 2020 / Accepted: 25 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract With the assumption that the water advance and the infiltration opportunity have an exponential relationship, a new equation was derived to estimate the time of water advance along a surface-irrigated field. Using the derived advance equation, a new method was developed for estimating the Kostiakov–Lewis infiltration parameters. The proposed advance equation and Elliot and Walker’s advance equation (two-point method) were evaluated using field advance data from seven locations. The evaluation results were based on the dRMS and NSE indices, which showed the superiority of the proposed equation. The advance equations were compared based on their infiltration depth differences and a comparison showed the superiority of the proposed equation. Also, the average values of infiltration depth in the average actual and computed infiltration opportunity time of the advance phase, and the average infiltration opportunity of the total irrigation time, were compared to the average values of actual infiltration depth using the relative error index. Results showed that the proposed method more accurately estimated the average infiltration depth with an average relative error 5.27% for total irrigation time, 1.90% for average computed infiltration opportunity, 1.80% for average actual infiltration opportunity, and 3.86% for infiltrated depth difference in more than 75% of the cases. The proposed equation and the new method for calculating infiltration coefficients can be recommended for practical use. List of symbols i Cumulative infiltration iavg Average infiltration depth of water in the field t The time of water infiltration in soil tL The time for water advance to L t L The time for water advance to L/2 2

tx The time for water advance to x tx′ The time for reverse advance to x′ x The length of the water advance in the field based on the beginning of the field ′ x The length of the water advance in the field based on the field end L The total length of advance * Eisa Maroufpoor [email protected] Amin Seyedzadeh [email protected] Amir Panahi [email protected] 1



Department of Irrigation and Reclamation Engineering, University of Tehran, Tehran, Iran



Department of Water Engineering, Faculty of Agriculture, University of Kurdistan, Sanandaj, Iran

2

a The exponent coefficient of Kostiakov– Lewis cumulative infiltration equation k The coefficient of Kostiakov–Lewis cumulative infiltration equation fo The final infiltration rate of water in the soil Ao Water flow cross-section at the beginning of the field p The coefficient of Elliot and Walker’s advance equation tu Advance time at any point between zero and x (integral variable) u Advance location (integral variable) n Counter H Average depth ratio at times tL and t L 2

resulting from th