Technical Papers
Jul 30, 2019

Review of Time-of-Concentration Equations and a New Proposal in Italy

Publication: Journal of Hydrologic Engineering
Volume 24, Issue 10

Abstract

The time of concentration is a fundamental parameter used for hydrological analysis in professional and scientific communities. The availability of equations for its estimation leads to significant variability and uncertainty. In this work, the most commonly used 24 equations were selected among the empirically based models to compare their estimates and to quantify the accuracy in predicting the time of concentration observed from 46 river basins in northern Italy. The practical definition for direct time of concentration estimation used in this work computes it as the time from the end of effective rainfall to the end of direct runoff on the recession limb of the total hydrograph. The results show a large discrepancy between the observed values and those estimated with the selected equations: the best performances are achieved by Bransby-Williams, Giandotti, Soil Conservation Service, Témez, and Ferro equations. The catchment classification into classes of basins with homogeneous climatological and physiographic characteristics shows that none of the analyzed equations significantly improves the predictions. Finally, a new equation is proposed for the area of the Upper Po River Basin that can significantly decrease the time-of-concentration estimation error.

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Acknowledgments

The authors are grateful to ARPA Regione Piemonte (Italy) for providing meteorological and hydrological observations.

References

Arnold, J. G., and P. M. Allen. 1999. “Automated methods for estimating baseflow and ground water recharge from streamflow records.” J. Am. Water Resour. Assoc. 35 (2): 411–424. https://doi.org/10.1111/j.1752-1688.1999.tb03599.x.
Bell, F. C., and S. O. Kar. 1969. “Characteristic response times in design flood estimation.” J. Hydrol. 8 (2): 173–196. https://doi.org/10.1016/0022-1694(69)90120-6.
Bocchiola, D., C. De Michele, S. Pecora, and R. Rosso. 2003. “On the response time of Italian watersheds.” L’Acqua 7: 45–55.
Boscarello, L. A., G. Ravazzani, A. Cislaghi, and M. Mancini. 2016. “Regionalization of flow-duration curves through catchment classification with streamflow signatures and physiographic–climate Indices.” J. Hydrol. Eng. 21 (3): 05015027. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001307.
California Highways and Public Works. 1955. California culvert practice: Reprint of a series of technical abstracts [appearing in each issue from Aug. 1942 to Sept.-Oct. 1943]. Sacramento, CA: State of California, Dept. of Public Works, Division of Highways.
Calkins, D., and T. Dunne. 1970. “A salt tracing method for measuring channel velocities in small mountain streams.” J. Hydrol. 11 (4): 379–392. https://doi.org/10.1016/0022-1694(70)90003-X.
Cavazza, S. 1969. Contributo allo studio degli eventi di piena nei piccoli bacini imbriferi, 1–30. Rome: Atti del Convegno Nazionale “L’idrologia e la sistemazione dei piccoli bacini.
Chapman, T. 1999. “A comparison of algorithms for stream flow recession and baseflow separation.” Hydrol. Processes 13 (5): 701–714. https://doi.org/10.1002/(SICI)1099-1085(19990415)13:5%3C701::AID-HYP774%3E3.0.CO;2-2.
Chow, V. T., D. R. Maidment, and L. W. Mays. 1988. Applied hydrology. Singapore: McGraw-Hill.
de Almeida, I. K., A. K. Almeida, J. A. A. Anache, J. L. Steffen, and T. A. Alves Sobrinho. 2014. “Estimation on time of concentration of overland flow in watersheds: A review.” Geociências 33 (4): 661–671.
Dooge, J. C. I. 1973. Linear theory of hydrologic systems. Washington, DC: Agricultural Research Service, USDA.
Eaton, T. D. 1954. “The derivation and synthesis of the unit hydrograph when rainfall records are inadequate.” J. Inst. Eng. Aust. 26: 239–243.
Eckhardt, K. 2005. “How to construct recursive digital filters for baseflow separation.” Hydrol. Processes 19 (2): 507–515. https://doi.org/10.1002/hyp.5675.
Ermini, R., and M. Fiorentino. 1988. I tempi di ritardo caratteristici dei corsi d’acqua pugliesi, 371–390. Rome: Gruppo nazionale per la difesa dalle catastrofi idrogeologiche, Linea 1.
Espey, W. H. J., C. W. Morgan, and F. D. Masch. 1966. Study of some effects of urbanization on storm runoff from a small watershed. Austin, TX: Center for Research in Water Resources, Univ. of Texas.
FAA (Federal Aviation Administration). 1970. Advisory circular on airport drainage. Washington, DC: USDOT.
Fang, X., D. B. Thompson, T. G. Cleveland, and P. Pradhan. 2007. “Variations of time of concentration estimates using NRCS velocity method.” J. Irrig. Drain. Eng. 133 (4): 314–322. https://doi.org/10.1061/(ASCE)0733-9437(2007)133:4(314).
Fang, X., D. B. Thompson, T. G. Cleveland, P. Pradhan, and R. Malla. 2008. “Time of concentration estimated using watershed parameters determined by automated and manual methods.” J. Irrig. Drain. Eng. 134 (2): 202–211. https://doi.org/10.1061/(ASCE)0733-9437(2008)134:2(202).
Fattorelli, S., and L. Marchi. 1988. Metodi deterministici per la valutazione dei deflussi di piena. Rome: Gruppo nazionale per la difesa dalle catastrofi idrogeologiche, Linea 1.
Ferro, V. 2006. “Riqualificazione ambientale dei corsi d’acqua.” In Quaderni di Idronomia Montana. Giardini Naxos, Italy: Nuova Editoriale Bios.
Flavell, D. J. 1983. “The rational method applied to small rural catchments in the south west of Western Australia.” J. Civ. Eng. Trans. 25 (2): 121–127.
Gentile, F., and G. Trisorio Liuzzi. 1992. “Sul tempo di ritardo in alcuni bacini del subappenino dauno.” Quaderni di Idronomia Mont. 11–12: 183–194.
Gericke, O. J., and J. C. Smithers. 2014. “Review of methods used to estimate catchment response time for the purpose of peak discharge estimation.” Hydrol. Sci. J. 59 (11): 1935–1971. https://doi.org/10.1080/02626667.2013.866712.
Gericke, O. J., and J. C. Smithers. 2016. “Are estimates of catchment response time inconsistent as used in current flood hydrology practice in South Africa?” J. S. Afr. Inst. Civ. Eng. 58 (1): 02–15. https://doi.org/10.17159/2309-8775/2016/v58n1a1.
Giandotti, M. 1934. Previsione delle piene e delle magre dei corsi d’acqua, 107. Rome: Memorie e studi idrografici, Servizio Idrografico Italiano.
Grimaldi, S., A. Petroselli, F. Tauro, and M. Porfiri. 2012. “Time of concentration: A paradox in modern hydrology.” Hydrol. Sci. J. 57 (2): 217–228. https://doi.org/10.1080/02626667.2011.644244.
Haktanir, T., and N. Sezen. 1990. “Suitability of two-parameter gamma and three-parameter beta distributions as synthetic unit hydrographs in Anatolia.” Hydrol. Sci. J. 35 (2): 167–184. https://doi.org/10.1080/02626669009492416.
Hannah, D. M., S. R. Kansakar, A. J. Gerrard, and G. Rees. 2005. “Flow regimes of Himalayan rivers of Nepal: Nature and spatial patterns.” J. Hydrol. 308 (1–4): 18–32. https://doi.org/10.1016/j.jhydrol.2004.10.018.
Henderson, F. M., and R. A. Wooding. 1964. “Overland flow and groundwater flow from a steady rainfall of finite duration.” J. Geophys. Res. 69 (8): 1531–1540. https://doi.org/10.1029/JZ069i008p01531.
Herbst, M., and M. C. Casper. 2008. “Towards model evaluation and identification using self-organizing maps.” Hydrol. Earth Syst. Sci. Discuss. 12 (2): 657–667. https://doi.org/10.5194/hess-12-657-2008.
Holecek, J., and J. Vocel. 1965. “Measurement of time of travel in the Volynka experimental basin.” In Representative and Experimental Areas Symp. of Budapest IAHS, 299–310. Budapest, Hungary: IAHS Press.
Indelicato, S. 1988. Verifica di modelli di valutazione del rischio idraulico-geologico ed efficacia degli interventi. Rome: Gruppo nazionale per la difesa dalle catastrofi idrogeologiche, Linea 3.
Johnstone, D., and W. P. Cross. 1949. Elements of applied hydrology. New York: Ronald Press Company.
Kirpich, Z. P. 1940. “Time of concentration of small agricultural watersheds.” Civ. Eng. 10 (6): 362–368.
Köplin, N., B. Schädler, D. Viviroli, and R. Weingartner. 2012. “Relating climate change signals and physiographic catchment properties to clustered hydrological response types.” Hydrol. Earth Syst. Sci. 16 (7): 2267–2283. https://doi.org/10.5194/hess-16-2267-2012.
Lim, K. J., B. A. Engel, Z. Tang, J. Choi, K.-S. Kim, S. Muthukrishnan, and D. Tripathy. 2005. “Automated web gis based hydrograph analysis tool, WHAT.” J. Am. Water Resour. Assoc. 41 (6): 1407–1416. https://doi.org/10.1111/j.1752-1688.2005.tb03808.x.
Loukas, A., and M. C. Quick. 1996. “Physically-based estimation of lag time for forested mountainous watersheds.” Hydrol. Sci. J. 41 (1): 1–19. https://doi.org/10.1080/02626669609491475.
Marek, M. 2011. Hydraulic design manual. Austin, TX: Design Division, Texas Dept. of Transportation.
McCuen, R. H. 2005. Hydrologic analysis and design. Upper Saddle River, NJ: Prentice Hall.
McCuen, R. H., S. L. Wong, and W. J. Rawls. 1984. “Estimating urban time of concentration.” J. Hydraul. Eng. 110 (7): 887–904. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:7(887).
Merlo, C. 1973. “Determinazione mediante il “metodo razionale” delle portate massime di piena di data frequenza nei” piccoli bacini”.” In Annali della Facoltà di Scienze Agrarie. Turin, Italy: Tipografia Vincenzo Bona.
Mockus, V. 1972. “Design hydrographs.” Chap. 21 in Hydrology, national engineering handbook. Edited by V. McKeever, W. Owen, and R. Rallison, 127. Washington, DC: USDA.
Natural Resources Conservation Service. 1986. Urban hydrology for small watersheds. Washington, DC: USDA.
O’Kelly, J. J. 1955. “The employment of unit hydrographs to determine the flows of Irish arterial drainage channels.” In Proc. Inst. Civ. Eng. 4 (4): 365–412. https://doi.org/10.1680/ipeds.1955.11869.
Pasini, P. 1910. “Coefficienti udometrici desunti dal lavoro delle macchine nelle bonifiche meccaniche.” Giornale del Genio Civile 48 (2): 385–413.
Pavlovic, S. B., and G. E. Moglen. 2008. “Discretization issues in travel time calculation.” J. Hydrol. Eng. 13 (2): 71–79. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:2(71).
Pegram, G., and M. Parak. 2004. “A review of the regional maximum flood and rational formula using geomorphological information and observed floods.” Water SA 30 (3): 377–384. https://doi.org/10.4314/wsa.v30i3.5087.
Perdikaris, J., B. Gharabaghi, and R. Rudra. 2018. “Evaluation of the simplified dynamic wave, diffusion wave and the full dynamic wave flood routing models.” Earth Sci. Res. 7 (2): 14. https://doi.org/10.5539/esr.v7n2p14.
Pilgrim, D. H. 1976. “Travel times and nonlinearity of flood runoff from tracer measurements on a small watershed.” Water Resour. Res. 12 (3): 487–496. https://doi.org/10.1029/WR012i003p00487.
Pilgrim, D. H. 1989. “Regional methods for estimation of design floods for small to medium sized drainage basins in Australia.” In Proc., Baltimore Symp., IAHS Publ. 181, 247–260. Wallingford, UK: IAHS Press.
Pilgrim, D. H., and G. E. McDermott. 1981. “Design floods for small rural catchments in eastern New South Wales.” In Proc., 1st National Local Government Engineering Conf. 1981: Reprints of Papers, 226–234. Canberra, Australia: Institution of Engineers of Australia.
Priestley, C. H. B., and R. J. Taylor. 1972. “On the assessment of surface heat flux and evaporation using large-scale parameters.” Mon. Weather Rev. 100 (2): 81–92. https://doi.org/10.1175/1520-0493(1972)100%3C0081:OTAOSH%3E2.3.CO;2.
Puglisi, S., and P. Zanframundo. 1978. “Osservazioni idrologiche in piccolo bacini del subappenino Dauno.” Giornale del Genio Civile 10–12: 439–453.
Ramser, C. E. 1927. “Run-off from small agricultural areas.” J. Agric. Res. 34 (9): 797–823.
Salimi, E. T., A. Nohegar, A. Malekian, M. Hoseini, and A. Holisaz. 2017. “Estimating time of concentration in large watersheds.” Paddy Water Environ. 15 (1): 123–132. https://doi.org/10.1007/s10333-016-0534-2.
Sharifi, S., and S. M. Hosseini. 2011. “Methodology for identifying the best equations for estimating the time of concentration of watersheds in a particular region.” J. Irrig. Drain. Eng. 137 (11): 712–719. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000373.
Sheridan, J. M. 1994. “Hydrograph time parameters for flatland watersheds.” Trans. ASAE 37 (1): 103–113. https://doi.org/10.13031/2013.28059.
Supino, G. 1964. Le reti idrauliche. Bologna, Italy: Patron Ed.
Témez, J. R. 1978. Calculo hidrometeoorologico de caudales maximos en pequenas cuencas naturales. Madrid, Spain: Direccion General de Carreteras, Ministério de Obras Publicas y Urbanismo.
Turazza, D. 1867. Trattato di idrometria o di idraulica pratica. Padova, Italy: Tipografia editrice F. Sacchetto.
Ventura, G. 1905. “Bonificazione della bassa pianura bolognese: Studio sui coefficienti udometrici.” Giornale del Genio Civile 43 (3): 3–36.
Vesanto, J., and E. Alhoniemi. 2000. “Clustering of the self-organizing map.” IEEE Trans. Neural Networks 11 (3): 586–600. https://doi.org/10.1109/72.846731.
Villani, P. 1988. Alcune considerazioni sul fattore di riduzione areale e sulla sua influenza nella derivazione della piena media. Rome: Gruppo nazionale per la difesa dalle catastrofi idrogeologiche, Linea 1.
Williams, G. B. 1922. “Flood discharges and the dimensions of spillways in India.” Engineering (London) 134 (9): 321–322.
Wong, T. S. 2009. “Evolution of kinematic wave time of concentration formulas for overland flow.” J. Hydrol. Eng. 14 (7): 739–744. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000043.
Wong, T. S. W., and C.-N. Chen. 1997. “Time of concentration formula for sheet flow of varying flow regime.” J. Hydrol. Eng. 2 (3): 136–139. https://doi.org/10.1061/(ASCE)1084-0699(1997)2:3(136).
Woodward, D. E. 2010. “Time of concentration.” Chap. 15 in Hydrology, national engineering handbook. Edited by C. C. Hoeft, A. Humpal, and G. Cerrelli, 29. Washington, DC: USDA.
Woolhiser, D. A., and J. A. Liggett. 1967. “Unsteady, one-dimensional flow over a plane—The rising hydrograph.” Water Resour. Res. 3 (3): 753–771. https://doi.org/10.1029/WR003i003p00753.

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Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 24Issue 10October 2019

History

Received: Nov 12, 2018
Accepted: Mar 20, 2019
Published online: Jul 30, 2019
Published in print: Oct 1, 2019
Discussion open until: Dec 30, 2019

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Assistant Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Milan 20133, Italy (corresponding author). ORCID: https://orcid.org/0000-0002-6850-0883. Email: [email protected]
Laura Boscarello [email protected]
Postdoctoral Researcher, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Milan 20133, Italy. Email: [email protected]
Alessio Cislaghi [email protected]
Postdoctoral Researcher, Dept. of Agricultural and Environmental Sciences, Univ. of Milan, Milan 20133, Italy. Email: [email protected]
Marco Mancini [email protected]
Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Milan 20133, Italy. Email: [email protected]

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