Relative Roles of Time–Area Curve and Storage Coefficient on the Shape of Clark’s Instantaneous Unit Hydrograph: Analytical Approach
Publication: Journal of Hydrologic Engineering
Volume 26, Issue 3
Abstract
The Clark’s instantaneous unit hydrograph (IUH) has been developed to transform excess precipitation into a runoff hydrograph, dependent on basin characteristics with flow velocity in a basin. In this study, the relative effects of the time–area curve and storage coefficient on the shape of the Clark IUH are analytically evaluated under hypothetical conditions of an elliptical-shaped basin and a straight flow direction of raindrops throughout total travel lengths. The time–area curve of an ellipse is derived by considering constant flow velocity in the basin, which is then used as input to the linear reservoir with a given storage coefficient to derive the Clark IUH by solving the continuity equation. The derived Clark IUH is evaluated with various shapes of elliptical basins and different storage coefficients. The time–area curve of a basin is found to be the dominant factor influencing the shape of the Clark IUH. The storage coefficient controls the steepness of the curve, while maintaining the overall shape of the Clark IUH unchanged.
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
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2020R1A2C200871411).
References
Abramowitz, M., and I. A. Stegun. 1970. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover.
Asano, Y., T. Uchida, and M. Tomomura. 2020. “A novel method of quantifying catchment-wide average peak propagation speed in hillslopes: Fast hillslope responses are detected during annual floods in a steep humid catchment.” Water Resour. Res. 56 (1): e2019WR025070. https://doi.org/10.1029/2019WR025070.
Beven, K. J. 2020. “A history of the concept of time of concentration.” Hydrol. Earth Syst. Sci. 24 (5): 2655–2670. https://doi.org/10.5194/hess-24-2655-2020.
Clark, C. O. 1945. “Storage and the unit hydrograph.” Trans. Am. Soc. Civ. Eng. 110 (1): 1419–1446.
Czyzyk, K., D. Mirossi, A. Abdoulhak, S. Hassani, J. D. Niemann, and J. Gironas. 2020. “Impacts of channel network type on the unit hydrograph.” Water 12 (3): 669–692. https://doi.org/10.3390/w12030669.
Diskin, M. H. 1964. “A basic study of the linearity of the rainfall-runoff process in watersheds.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Illinois.
Gupta, V. K., E. C. Waymire, and C. T. Wang. 1980. “A representation of an instantaneous unit hydrograph from geomorphology.” Water Resour. Res. 16 (5): 855–862. https://doi.org/10.1029/WR016i005p00855.
Hosseini, S. M., N. Mahjouri, and S. Riahi. 2016. “Development of a direct geomorphologic IUH model for daily runoff estimation in ungauged watersheds.” J. Hydrol. Eng. 21 (6): 05016008. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001333.
McCuen, R. H. 2005. Hydrologic analysis and design. 3rd ed. Upper Saddle River, NJ: Prentice Hall.
Moussa, R. 2003. “On morphometric properties of basins, scale effects and hydrological response.” Hydrol. Process. 17: 33–58. https://doi.org/10.1002/hyp.1114.
Nash, J. E. 1957. “The form of the instantaneous unit hydrograph.” Int. Assoc. Hydrol. Sci. Publication 45 (3): 114–121.
Petroselli, A., S. Asgharinia, T. Sabzevari, and B. Saghafian. 2020. “Comparison of design peak flow estimation methods for ungauged basins in Iran.” Hydrol. Sci. J. 65 (1): 127–137. https://doi.org/10.1080/02626667.2019.1686506.
Rodriguez-Iturbe, I., and J. B. Valdes. 1979. “The geomorphologic structure of hydrologic response.” Water Resour. Res. 15 (5): 1409–1420. https://doi.org/10.1029/WR015i006p01409.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 26 • Issue 3 • March 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 27, 2020
Accepted: Oct 28, 2020
Published online: Jan 5, 2021
Published in print: Mar 1, 2021
Discussion open until: Jun 5, 2021
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.