Document Type : Research Paper


1 PhD student, Water Engineering Department, Isfahan University of Technology.

2 Professor, Water Engineering Department, Isfahan University of Technology.

3 Associate Professor, Water Engineering Department, Isfahan University of Technology.

4 Professor, Department of Soil Science, Isfahan University of Technology.


In order to design or evaluate an irrigation system, the infiltration phenomenon and its variations should be determined accurately. In saline and sodic soil and water conditions, the importance of this issue will become greater. The main objective of this study was to estimate the coefficients of different infiltration equations (Kostiakov, Kostiakov-Lewis, Horton, Philip, and U. S. Soil Conservation) and to evaluate the performance of these equations under different qualities of irrigation water, initial soil moistures, and constant water head. Using a laboratory method, infiltrations were measured in soil columns for constant water head. Then, by applying the cumulative infiltration and drainage outflow data to HYDRUS-1D model, soil hydraulic parameters were determined by the inverse solution. To determine the coefficients of infiltration equations, the outputs of the HYDRUS-1D model including cumulative infiltration verses time were corrolated. The values of root mean square error (RMSE), standard deviation root mean square error (SDRMSE), normalized root mean square error (NRMSE), percent relative absolute error (AE) and percent relative error (RE), were used to evaluate the performance of each infiltration equation and to rank the equations. The equation that had the highest rank was considered as the best and more stable equation. The Horton equation with RMSE, SDRMSE, NRMSE and AE of 0.043, 0.018, 0.006 and 1 and the Kostiakov equation with the values of 0.234, 0.175, 0.025 and 4, were the most and the least suitable eqations, respectively. The evaluation of the performance of infiltration equations using statistical indicators showed that the Kostiakov-Lewis and the Kostiakov infiltration equations were the best and the worst equations, respectively. Comparison of NRMSE values showed that in most cases, under deficit irrigation, infiltration equations estimate infiltration more accurately. For a given treatment, the errors of Kostiakov-Lewis and Philip infiltration equations increased as the amount of irrigation water increased, and as the end of the season approached. The rest of the equations did not show any especial trends. To measure infiltration, it is necessary to consider the effects of irrigation water quality, initial soil moisture, and water heads, because these parameters influence the coefficients of infiltration equations and, consequently, the irrigation efficiency.


  1. امداد، م. ر؛ و س. ح، طباطبایی. 1392. تاثیر کیفیت آبیاری (شوری-سدیمی) بر تغییرات نفوذ و راندمان کاربرد آب در آبیاری جویچه­ای. مجله پژوهش آب ایران، سال هفتم، شماره دوازدهم، بهار و تابستان، صفحات 157-151.
  2. پرچمی عراقی، ف.، س. م، میرلطیفی، ش، قربانی دشتکی. و م، مهدیان. 1389. ارزیابی برخی مدل­های نفوذ آب به خاک در برخی کلاس­های بافتی و کاربری­های اراضی. نشریه آبیاری و زهکشی ایران، شماره 2، جلد 4، صفحات 203-193.
  3. ثامنی، ع.، م، پاکجو.، س. ع. ا، موسوی. و ع. ا، کامکارحقیقی. 1393. ارزیابی چند رابطه نفوذ آب به خاک با کاربرد آب­های شور و سدیمی. نشریه پژوهش آب در کشاورزی، جلد 28، شماره 2، صفحات 408-395.
  4. جوادی، ع.، م، مشعل. و ح، ابراهیمیان. 1393. تحلیل حساسیت معادلات نفوذ آب به خاک و ضرایب آنها نسبت به رطوبت اولیه و بار آبی. نشریه آب و خاک مشهد (علوم و صنایع کشاورزی)، جلد 28، شماره 5، صفحات 907-899.
  5. علیزاده، ح. ع.، ع، لیاقت. و م، نوری محمدیه. 1388. ارزیابی توابع کاهش جذب آب توسط گوجه­فرنگی در شرایط تنش همزمان شوری و خشکی. نشریه آب و خاک (علوم و صنایع کشاورزی)، جلد 23، شماره 3، صفحات 97-88.
  6. محمودیان شوشتری، م. 1376. پارامترهای معادله نفوذ کوستیاکوف-لوییز معادل با پارامترهای معادل نفوذ SCS، مجله خاک و آب، جلد 11، شماره 1.
  7. Duan, R., C.B.  Fedler., and J. Borrelli. 2011. Field evaluation of infiltration models in lawn Soil. Irrigation Science, 29: 379–389.
  8. Ebrahimian, H., A. Liaghat, M. Parsinejad, F. Abbasi., and M. Navabian. 2012. Comparison of one- and two-dimensional models to simulate alternate and conventional furrow fertigation. Journal of Irrigation and Drainage Engineering, 138(10): 929–938.
  9. Ho, R. 2006. Handbook of univariate and multivariate data analysis and interpretation with SPSS. Chapman and Hall/CRC. 403pp.
  10. Horton, R.E. 1940. An approach towards a physical interpretation of infiltration capacity. Soil Science Society of America Proceedings, 5: 399–417.
  11. Kostiakov, A.N. 1932. On the dynamics of the coefficient of water-percolation in soils and on the necessity for studying it from a dynamic point of view for purposes of amelioration. Transactions Congress International Society for Soil Science, 6th, Moscow, Part A: 17–21.
  12. Mashayekhi, P., Sh. Ghorbani-Dashtaki, M.R. Mosaddeghi., and H. Shirani. 2016. Different scenarios for inverse estimation of soil hydraulic parameters from double-ring infiltrometer data using HYDRUS-2D/3D. International Agrophysics. Volume 30, Issue 2, 203–210
  13. Mezencev, V.J. 1948. Theory of formation of the surface runoff. Meteorologiae Hidrologia, 3: 33–40.
  14. Philip, J.R. 1957. The theory of infiltration: 1. The infiltration equation and its solution. Soil Science, 83: 345–357.
  15. Sy, N.L. 2006. Modeling the infiltration process with a multi-layer perceptron artificial neural network. Hydrological Science Journal, 51:3–20.
  16. US Department of Agriculture, Natural Resources and Conservation Service. (1974). National Engineering Handbook. Section 15. Border Irrigation. National Technical Information Service, Washington, DC, Chapter 4.
  17. Yongyong, Z., W. Pute, Z. Xining., and L. Ping. 2012. Evaluation and modeling of furrow infiltration for uncropped ridge–furrow tillage in Loess Plateau soils. Soil Research, 50: 360–370.
  18. Zolfaghari, A., S. Mirzaee., and M. Gorji. 2012. Comparison of different models for estimating cumulative infiltration. International Soil Science, 7:108–115.