General Unit Hydrograph from Chow’s Linear Theory of Hydrologic Systems and Its Applications
Publication: Journal of Hydrologic Engineering
Volume 27, Issue 10
Abstract
This research solves Chow’s linear hydrologic systems equations thoroughly to result in a theoretical instantaneous unit hydrograph (UH), which is a superposition of many () negative exponential functions. This implies that the instantaneous UH can be imagined as a superposition of many linear reservoirs in parallel. Mathematically, at , the theoretical UH (in terms of Taylor series) converges to the writer’s general UH that is a simple analytic expression derived inductively from empiricism. Therefore, this research turns the recent conceptual general UH to a theoretical law that approximates real-world watershed processes as a time-invariant linear hydrologic system. Specifically, we first review Chow’s linear hydrologic systems model and apply it to a conceptual watershed with an instantaneous storm, which results in a theoretical instantaneous UH and an S-hydrograph in the superposition of many negative exponential functions. The resulting S-hydrograph then is shown mathematically to be identical to the writer’s general UH at . Finally, the general theoretical UH is applied to 10 real-world watersheds for 19 rainfall-runoff simulations. It is noteworthy that the proposed method has two advantages: (1) it is general for storms with different rainfall durations, and (2) it does not require to define excess rainfall and direct runoff in advance because rainfall losses and baseflow can be a part of the solution process. It is expected that this research provides a deeper understanding of the general UH and thus helps promote its applications in practice.
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Data Availability Statement
MATLAB codes for Figs. 3–9, which support the findings of this study, are available from the author upon request.
Acknowledgments
The author appreciates the constructive comments offered by the four anonymous reviewers, the associate editor, and the editor, who have helped improve this paper significantly during its preparation.
References
Chaudhary, F. H., M. A. Simoes, and W. M. F. Filho. 1976. “Chow’s general hydrologic system model.” J. Hydraul. Eng. 102 (9): 1387–1390. https://doi.org/10.1061/JYCEAJ.0004619.
Chow, V. T. 1964. Handbook of applied hydrology. New York: McGraw-Hill.
Chow, V. T., and V. C. Kulandaiswamy. 1971. “General hydrologic system model.” J. Hydraul. Div. 97 (6): 791–804. https://doi.org/10.1061/JYCEAJ.0002994.
Chow, V. T., and V. C. Kulandaiswamy. 1982. “The IUH of general hydrologic system model.” J. Hydraul. Eng. 108 (7): 830–844. https://doi.org/10.1061/JYCEAJ.0005884.
Chow, V. T., D. R. Maidment, and L. W. Mays. 1988. Applied hydrology. New York: McGraw-Hill.
Diskin, M. H., and A. Boneh. 1975. “Determination of an optimal IUH for linear, time invariant systems from multi-storm records.” J. Hydrol. 24 (1): 57–76. https://doi.org/10.1016/0022-1694(75)90142-0.
Dooge, J. C. I. 1973. Linear theory of hydrologic systems. Washington, DC: Agricultural Research Service.
Edson, C. G. 1951. “Parameters for relating unit hydrographs to watershed characteristics.” EOS Trans. Am. Geophys. Union 32 (4): 591–596. https://doi.org/10.1029/TR032i004p00591.
Gray, D. M. 1962. “Derivation of hydrographs for small watersheds from measurable physical characteristics.” Accessed July 16, 2022. http://lib.dr.iastate.edu/researchbulletin/vol34/iss506/1.
Guo, J. 2022. “General and analytic unit hydrograph and its applications.” J. Hydrol. Eng. 27 (2): 04021046. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002149.
Huang, W. L. 1937. “The analysis of the rainfall-runoff correlation.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Illinois Urbana-Champaign.
Jeng, R. I., and G. C. Coon. 2003. “True form of instantaneous unit hydrograph of linear reservoirs.” J. Irrig. Drain. Eng. 129 (1): 11–17. https://doi.org/10.1061/(ASCE)0733-9437(2003)129:1(11).
Kulandaiswamy, V. C. 1964. “A basic study of the rainfall excess-surface runoff relationship in a basin system.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Illinois Urbana-Champaign.
Liu, C. C. K. 1976. “Numerical evaluation of response functions of a nonlinear rainfall-runoff model: Flood hydrograph analysis in the Chemung River basin.” Ph.D. thesis, Dept. of Civil Engineering, Cornell Univ.
Long, J. L. 1962. “The effect of flood magnitude on unit hydrograph characteristics.” M.S. thesis, Dept. Civil Engineering, Univ. of Iowa.
Mays, L. W., and L. R. Coles. 1980. “Optimization of unit hydrograph determination.” J. Hydraul. Eng. 106 (1): 85–97. https://doi.org/10.1061/JYCEAJ.0005361.
Mays, L. W., and C.-K. Taur. 1982. “Unit hydrographs via nonlinear programming.” Water Resour. Res. 18 (4): 744–752. https://doi.org/10.1029/WR018i004p00744.
McCann, R. C., and V. P. Singh. 1981. “The general hydrologic system model.” J. Hydraul. Div. 107 (12): 1581–1592. https://doi.org/10.1061/JYCEAJ.0005779.
Nash, J. E. 1957. “The form of instantaneous unit hydrograph.” [In Chinese.] Int. Assoc. Sci. Hydrol. Publ. 45 (3): 114–121.
Rui, X. F., N. N. Liu, Z. Ling, and X. Liang. 2012. “Development and inspiration of unit hydrograph.” [In Chinese.] Adv. Sci. Tech. Water Resour. 32 (2): 1–5.
Shen, H., Z. Xu, L. Li, and X. Hao. 2021. “Study on unit hydrograph model for rainfall-runoff simulation of urban roofs.” [In Chinese.] J. Hydraul. Eng. 52 (3): 333–340.
Shen, H., Z. Xu, Q. Li, and S. Zhang. 2016. “Simulation of rainfall runoff on permeable slope based on Nash instantaneous unit hydrograph.” [In Chinese.] J. Hydraul. Eng. 47 (5): 708–713. https://doi.org/10.13243/j.cnki.slxb.20150885.
Sherman, L. K. 1932. “Stream flow from rainfall by unit-graph method.” Eng. News-Rec. 108 (Apr): 501–505.
Singh, V. P., and R. C. McCann. 1980. “Use of cumulants to estimate coefficients in Chow-Kulandaiswamy’s GHS model.” Hydrol. Res. 11 (2): 83–92. https://doi.org/10.2166/nh.1980.0007.
Singh, V. P., and S. Vimal. 2022. “A unified framework for governing equations of hydrologic flows.” J. Hydrol. Eng. 27 (1): 04021044. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002150.
Xu, Z., and T. Cheng. 2019. “Basic theory for urban water management and sponge city—Review on urban hydrology.” [In Chinese.] J. Hydraul. Eng. 50 (1): 53–61. https://doi.org/10.13243/j.cnki.slxb.20181056.
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© 2022 American Society of Civil Engineers.
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Received: Oct 25, 2021
Accepted: Mar 25, 2022
Published online: Aug 1, 2022
Published in print: Oct 1, 2022
Discussion open until: Jan 1, 2023
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