Research Article
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Numerical approximation of the hydrological time of concentration

Year 2021, Volume: 5 Issue: 2, 121 - 136, 30.06.2021
https://doi.org/10.30521/jes.823017

Abstract

The time of concentration, that is the time it takes for a single "drop of water" to move superficially from the most distant point of the watershed to the exit point, is a fundamental parameter of the hydrological analysis. Many studies have been conducted to propose empirical formulas to calculate the time of concentration. One of the best known is the Temez formula based on time series data collected in accounts in Spain with areas of less than 3,000 km2. This expression uses the main channel length as a parameter as in many works, for small slopes is approximated by the distance between the geographic coordinates between the starting and ending points, leading for larger catchments and slopes to approaches with a high error. In this work, using a proper discretization of the curve, by using polynomial interpolation methods, we improve the calculation of the length of the main channel and therefore, we provide a more reliable method for calculating the time of concentration using the Temez expression. We illustrate the proposed scheme with different numerical examples comparing the results with those provided by other methods.

Supporting Institution

Junta de Extremadura through Research Group Grants

Thanks

Ministerio de Economía y Competitividad [MTM2017-83583-P] of Spain

References

  • [1] Gracia-Sánchez J, Maza-Álvarez JA. Morfología de Ríos [Rivers morphology]. In: Engineering Institute of the UNAM eds. Manual de Ingeniería de Ríos. Mexico City, United Mexican States: Series of the Institute of Engineering Publishing, 1997, pp. 1-46.
  • [2] Hoeft CC, Humpal A, Cerrelli G. Time of concentration. In: Garrison C, Osenkowsky T, Layer D, Pizzi S, Hayes W, editors. Hydrology, National Engineering Handbook. Washington DC, United States: U.S. Department of Agriculture Publishing, 2010, pp: 1-29.
  • [3] Chow VT, Maidement DR, Mays LW. Applied Hydrology. Singapore, Republic of Singapore: McGraw-Hill, 1988.
  • [4] Johnstone D, Cross WP. Elements of applied hydrology. New York: Ronald Press Company, 1949.
  • [5] Perdikaris J, Gharabaghi B, Rudra R. Evaluation of the simplified dynamic wave, diffusion wave and the full dynamic wave flood routing models. Earth Sciences Research Journal 2018, 7 (2), 14-27, DOI: 10.5539/esr.v7n2p14
  • [6] Temez JR. Cálculo Hidrometeorológico de Caudales Máximos en Pequeñas Cuencas Naturales [Hydrometeorological Calculation of Maximum Flows in Small Natural Basins]. Madrid, Spain: Ministry of Public Works and Urbanism Publising,1978.
  • [7] Williams GB. Flood discharges and the dimensions of spillways in India. The Engineer 1922, 134 (9), 321 -322.
  • [8] Zhao Q, Zhu Y, Wan D, Yu Y, Cheng X. Research on the Data-Driven Quality Control Method of Hydrological Time Series Data. Water 2018, 10 (12), 1712, DOI: 10.3390/w10121712
  • [9] Taraglio S, Chiesa S, La Porta, L, Pollino M, Verdecchia M, Tomassetti B, Colaiuda,V, Lombardi A. Decision support system for smart urban management: resilience against natural phenomena and aerial environmental assessment, Int. J. Sust. Energy Planning and Management 2009, 24, 135-146, DOI: https://doi.org/10.5278/ijsepm.3338
  • [10] Giandotti M. Previsione dell epiene e dell emagre dei corsid’acqua [Prediction of full and thin water runs]. Roma, Italy: Servizio Idrografico Italiano Publishing, 1934.
  • [11] Kirpich, ZP. Time of concentration of small agricultural watersheds. Civil Engineering Journal 1940, 10 (6) 362-368.
  • [12] Burden RL, Faires, JD. Análisis Numérico [Numerical analysis]. Mexico City, United Mexican States: Grupo Editorial Iberoamérica, 1985.
  • [13] Martínez G, Díaz JJ. Morfometría en la Cuenca hidrológica de San José del Cabo, Baja California Sur, México [Morphometry in the hydrological basin of San José del Cabo, Baja California Sur, Mexico]. Revista Geológica de América Central, 2010, 44, 83-100, DOI: 10.15517/rgac.v0i44.3447
  • [14] Nagy ED., Torma P, Bene K. Comparing Methods for Computing the Time of Concentration in a Medium-Sized Hungarian Catchment. JSlovak Journal of Civil Engineering 2017, 24 (4), 8-14, DOI: 10.1515/sjce-2016-0017
  • [15] Ravazzani G, Boscarello L, Cislaghi A, Mancini M. Review of Time-of-Concentration Equations and a New Proposal in Italy. Journal of Hydrologic Engineering, 2019, 24 (10), 04019039, DOI: 10.1061/(ASCE)HE.1943-5584.0001818
  • [16] Viessman W, Lewis GL. Introduction to Hydrology. Massachusetts, United States of America: Addison-Wesley Publishing, 1995.
  • [17] Pusineri G, Pedraza R, Lozeco C. Uso de modelos digitales de elevación y de sistemas de información geográfica en la modelación hidrológica [Use of digital elevation models and geographic information systems in hydrological modeling]. Geográfica digital 2005, 2 (3), 1-16, DOI: http://dx.doi.org/10.30972/geo.232664
  • [18] Grimaldi S, Petroselli A, Tauro F, Porfiri M. Time of concentration: A paradox in modern hydrology. Hydrological Sciences Journal, 2012, 57 (2) 217-228, https://doi.org/10.1080/02626667.2011.644244
  • [19] Benavente, MC. Análisis numérico de los perfiles hidrográficos [Numerical analysis of hydrographic profiles]. Geographical Research Letters 1985, 11, 103-113. DOI: 10.18172/cig.947
  • [20] Castillo O, Contreras A, Mejías A, Roldán, J, Ruiz, V. Caudal de Referencia, Método Racional Modificado de Témez. [Reference Flow, Temez's Modified Rational Method]. University of Cádiz, Cádiz, Spain,1991.
Year 2021, Volume: 5 Issue: 2, 121 - 136, 30.06.2021
https://doi.org/10.30521/jes.823017

Abstract

References

  • [1] Gracia-Sánchez J, Maza-Álvarez JA. Morfología de Ríos [Rivers morphology]. In: Engineering Institute of the UNAM eds. Manual de Ingeniería de Ríos. Mexico City, United Mexican States: Series of the Institute of Engineering Publishing, 1997, pp. 1-46.
  • [2] Hoeft CC, Humpal A, Cerrelli G. Time of concentration. In: Garrison C, Osenkowsky T, Layer D, Pizzi S, Hayes W, editors. Hydrology, National Engineering Handbook. Washington DC, United States: U.S. Department of Agriculture Publishing, 2010, pp: 1-29.
  • [3] Chow VT, Maidement DR, Mays LW. Applied Hydrology. Singapore, Republic of Singapore: McGraw-Hill, 1988.
  • [4] Johnstone D, Cross WP. Elements of applied hydrology. New York: Ronald Press Company, 1949.
  • [5] Perdikaris J, Gharabaghi B, Rudra R. Evaluation of the simplified dynamic wave, diffusion wave and the full dynamic wave flood routing models. Earth Sciences Research Journal 2018, 7 (2), 14-27, DOI: 10.5539/esr.v7n2p14
  • [6] Temez JR. Cálculo Hidrometeorológico de Caudales Máximos en Pequeñas Cuencas Naturales [Hydrometeorological Calculation of Maximum Flows in Small Natural Basins]. Madrid, Spain: Ministry of Public Works and Urbanism Publising,1978.
  • [7] Williams GB. Flood discharges and the dimensions of spillways in India. The Engineer 1922, 134 (9), 321 -322.
  • [8] Zhao Q, Zhu Y, Wan D, Yu Y, Cheng X. Research on the Data-Driven Quality Control Method of Hydrological Time Series Data. Water 2018, 10 (12), 1712, DOI: 10.3390/w10121712
  • [9] Taraglio S, Chiesa S, La Porta, L, Pollino M, Verdecchia M, Tomassetti B, Colaiuda,V, Lombardi A. Decision support system for smart urban management: resilience against natural phenomena and aerial environmental assessment, Int. J. Sust. Energy Planning and Management 2009, 24, 135-146, DOI: https://doi.org/10.5278/ijsepm.3338
  • [10] Giandotti M. Previsione dell epiene e dell emagre dei corsid’acqua [Prediction of full and thin water runs]. Roma, Italy: Servizio Idrografico Italiano Publishing, 1934.
  • [11] Kirpich, ZP. Time of concentration of small agricultural watersheds. Civil Engineering Journal 1940, 10 (6) 362-368.
  • [12] Burden RL, Faires, JD. Análisis Numérico [Numerical analysis]. Mexico City, United Mexican States: Grupo Editorial Iberoamérica, 1985.
  • [13] Martínez G, Díaz JJ. Morfometría en la Cuenca hidrológica de San José del Cabo, Baja California Sur, México [Morphometry in the hydrological basin of San José del Cabo, Baja California Sur, Mexico]. Revista Geológica de América Central, 2010, 44, 83-100, DOI: 10.15517/rgac.v0i44.3447
  • [14] Nagy ED., Torma P, Bene K. Comparing Methods for Computing the Time of Concentration in a Medium-Sized Hungarian Catchment. JSlovak Journal of Civil Engineering 2017, 24 (4), 8-14, DOI: 10.1515/sjce-2016-0017
  • [15] Ravazzani G, Boscarello L, Cislaghi A, Mancini M. Review of Time-of-Concentration Equations and a New Proposal in Italy. Journal of Hydrologic Engineering, 2019, 24 (10), 04019039, DOI: 10.1061/(ASCE)HE.1943-5584.0001818
  • [16] Viessman W, Lewis GL. Introduction to Hydrology. Massachusetts, United States of America: Addison-Wesley Publishing, 1995.
  • [17] Pusineri G, Pedraza R, Lozeco C. Uso de modelos digitales de elevación y de sistemas de información geográfica en la modelación hidrológica [Use of digital elevation models and geographic information systems in hydrological modeling]. Geográfica digital 2005, 2 (3), 1-16, DOI: http://dx.doi.org/10.30972/geo.232664
  • [18] Grimaldi S, Petroselli A, Tauro F, Porfiri M. Time of concentration: A paradox in modern hydrology. Hydrological Sciences Journal, 2012, 57 (2) 217-228, https://doi.org/10.1080/02626667.2011.644244
  • [19] Benavente, MC. Análisis numérico de los perfiles hidrográficos [Numerical analysis of hydrographic profiles]. Geographical Research Letters 1985, 11, 103-113. DOI: 10.18172/cig.947
  • [20] Castillo O, Contreras A, Mejías A, Roldán, J, Ruiz, V. Caudal de Referencia, Método Racional Modificado de Témez. [Reference Flow, Temez's Modified Rational Method]. University of Cádiz, Cádiz, Spain,1991.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Juan Ramón BARRÓN FERNÁNDEZ 0000-0001-8374-2330

Carmen CALVO-JURADO 0000-0001-9842-081X

Project Number GR18023
Publication Date June 30, 2021
Acceptance Date May 2, 2021
Published in Issue Year 2021 Volume: 5 Issue: 2

Cite

Vancouver BARRÓN FERNÁNDEZ JR, CALVO-JURADO C. Numerical approximation of the hydrological time of concentration. JES. 2021;5(2):121-36.

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