Explicit Solution of Horton’s Equation for Infiltration Capacity
Publication: Journal of Irrigation and Drainage Engineering
Volume 150, Issue 6
Abstract
Horton’s infiltration capacity is often used to separate rainfall excess from a rainfall hyetograph in watershed modeling. Nevertheless, this infiltration capacity is an implicit function of cumulative infiltration in soil, which is inconvenient in practical applications. This study found an explicit expression of infiltration capacity that is the sum of a steady-state term and a transitional term. The steady-state term is the critical infiltration rate or minimum infiltration capacity, and the transitional term is represented by a Lambert W function that tends to zero as time (or cumulative infiltration in soil) tends to infinity. The proposed method can be easily used, together with a unit hydrograph model, for direct runoff in watershed modeling.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The author thanks Prof. David A. Chin at the University of Miami, who suggested this research in a personal communication. The author is also grateful to the two reviewers, AE, and the Editor for their constructive comments that made the manuscript more presentable.
References
Akan, A. O. 1992. “Horton infiltration equation revisited.” J. Irrig. Drain. Eng. 118 (5): 828–830. https://doi.org/10.1061/(ASCE)0733-9437(1992)118:5(828).
Bauer, S. W. 1974. “A modified Horton equation for infiltration during intermittent rainfall.” Hydrol. Sci. Bull. 19 (2): 219–225. https://doi.org/10.1080/02626667409493900.
Chin, D. A. 2021. Water-resources engineering. 4th ed. Hoboken, NJ: Pearson.
Chow, V. T., D. Maidment, and L. W. Mays. 1988. Applied hydrology. New York: McGraw-Hill.
Gebul, M. A. 2022. “Simplified approach for determination of parameters for Kostiakov’s infiltration equation.” Water Pract. Tech. 17 (11): 2435–2446. https://doi.org/10.2166/wpt.2022.142.
Green, I. R. A. 1986. “An explicit solution of the modified Horton equation.” J. Hydrol. 83 (1–2): 23–27. https://doi.org/10.1016/0022-1694(86)90180-0.
Green, W. H., and C. A. Ampt. 1911. “Studies on soil physics-1. The flow of air and water through soils.” J. Agric. Sci. 4 (1): 1–24. https://doi.org/10.1017/S0021859600001441.
Guo, J. 2022. “Application of general unit hydrograph model for baseflow separation from rainfall and streamflow data.” J. Hydrol. Eng. 27 (11): 04022027. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002217.
Guo, J. C. Y., W. Wang, and J. Li. 2023. Urban drainage and storage practices. Boca Raton, FL: CRC Press.
Horton, R. E. 1933. “The role of infiltration in the hydrologic cycle.” Trans. Am. Geophys. Uni. 14 (1): 446–460. https://doi.org/10.1029/TR014i001p00446.
Horton, R. E. 1939. “Analysis of runoff-plat experiments with varying infiltration-capacity.” EOS 20 (4): 693–711. https://doi.org/10.1029/TR020i004p00693.
Horton, R. E. 1940. “The infiltration-theory of surface-runoff.” EOS 21 (2): 541. https://doi.org/10.1029/TR021i002p00541-1.
Keita, A., M. Zorom, M. D. Faye, D. D. Damba, Y. Konate, L. G. Hayde, and B. Lidon. 2023. “Achieving real-world saturated hydraulic conductivity: Practical and theoretical findings from using an exponential one-phase decay model.” Hydrology 10 (12): 235. https://doi.org/10.3390/hydrology10120235.
Mishra, S. K., J. V. Tyagi, and V. P. Singh. 2003. “Comparison of infiltration models.” Hydrol. Process. 17 (13): 2629–2652. https://doi.org/10.1002/hyp.1257.
Ponce, V. M. 1989. Engineering hydrology: Principles and practices. Hoboken, NJ: Prentice Hall.
Terstriep, M. L., and J. B. Stall. 1974. The Illinois urban drainage area simulator, ILLUDAS. Bulletin 58. Urbana, IL: Illinois State Water Survey.
Wang, N., and X. Chu. 2020. “Revised Horton model for event and continuous simulations of infiltration.” J. Hydrol. 589 (Oct): 125215. https://doi.org/10.1016/j.jhydrol.2020.125215.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 150 • Issue 6 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Apr 3, 2024
Accepted: Jul 17, 2024
Published online: Oct 12, 2024
Published in print: Dec 1, 2024
Discussion open until: Mar 12, 2025
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.