Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds

The time of concentration is the time it takes a drop of water in a basin to travel from the most distant point to the outlet, and is one of the most important parameters, along with the morphometric characteristics, for determining the design flow rate in rainfall-runoff models. This study aims to...

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Autores:
Echeverri-Díaz, Jamilton
Coronado-Hernández, Oscar E.
Gustavo, Gatica
Linfati, Rodrigo
Méndez-Anillo, Rafael D.
Coronado-Hernandez, Jairo R.
Tipo de recurso:
Article of investigation
Fecha de publicación:
2022
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
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Acceso en línea:
https://hdl.handle.net/11323/10788
https://repositorio.cuc.edu.co/
Palabra clave:
Urbanized watersheds
Time of concentration
USDA NRCS
Linear regression analysis
Sensitivity analysis
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openAccess
License
Atribución 4.0 Internacional (CC BY 4.0)
id RCUC2_fe49cab5b73313818c01970091f10800
oai_identifier_str oai:repositorio.cuc.edu.co:11323/10788
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.eng.fl_str_mv Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
title Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
spellingShingle Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
Urbanized watersheds
Time of concentration
USDA NRCS
Linear regression analysis
Sensitivity analysis
title_short Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
title_full Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
title_fullStr Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
title_full_unstemmed Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
title_sort Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watersheds
dc.creator.fl_str_mv Echeverri-Díaz, Jamilton
Coronado-Hernández, Oscar E.
Gustavo, Gatica
Linfati, Rodrigo
Méndez-Anillo, Rafael D.
Coronado-Hernandez, Jairo R.
dc.contributor.author.none.fl_str_mv Echeverri-Díaz, Jamilton
Coronado-Hernández, Oscar E.
Gustavo, Gatica
Linfati, Rodrigo
Méndez-Anillo, Rafael D.
Coronado-Hernandez, Jairo R.
dc.subject.proposal.eng.fl_str_mv Urbanized watersheds
Time of concentration
USDA NRCS
Linear regression analysis
Sensitivity analysis
topic Urbanized watersheds
Time of concentration
USDA NRCS
Linear regression analysis
Sensitivity analysis
description The time of concentration is the time it takes a drop of water in a basin to travel from the most distant point to the outlet, and is one of the most important parameters, along with the morphometric characteristics, for determining the design flow rate in rainfall-runoff models. This study aims to determine the sensitivity of the parameters included in different equations for the calculation of the time of concentration. A case study was conducted on small, urbanized watersheds in the city of Montería, Colombia. The study uses information obtained through field work using GPS equipment and electronic total station, supplemented by geographic information contained in the city drawings of the local sewage company, which includes data on elevations above sea level with sub-metric precision. The time of concentration determined by the 12 empirical equations was compared to the results obtained from the equation proposed by the Natural Resources Conservation Service (NRCS), which was considered as a baseline formulation for the intricacy of calculation. Based on this comparison, it was found that the Carter equation is the one that best fits the results obtained from the NRCS equation because it displayed highly significant goodness of fit values. Even though the equations by Kirpich, Ventura, California Culvert Practice, Simas-Hawkins and TxDOT provide a relatively good fit compared to other empirical equations, they tend to over-estimate time of concentration values, which could lead to the under-estimation of the design flow rates. For this reason, sensitivity analysis of the parameters of these equations represents an alternative for improving the calculation of the time of concentration. The current research analyses deepen the influence of some parameters in the estimation of time of concentration. The research can also be used by designers and engineers in the city of Montería, Colombia, as an important reference to compute time of concentrations in urbanized watersheds.
publishDate 2022
dc.date.issued.none.fl_str_mv 2022-09-13
dc.date.accessioned.none.fl_str_mv 2024-02-23T17:54:10Z
dc.date.available.none.fl_str_mv 2024-02-23T17:54:10Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.spa.fl_str_mv Text
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dc.type.version.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.citation.spa.fl_str_mv Echeverri-Díaz, J.; Coronado-Hernández, Ó.E.; Gatica, G.; Linfati, R.; Méndez-Anillo, R.D.; Coronado-Hernández, J.R. Sensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds. Water 2022, 14, 2847. https://doi.org/10.3390/w14182847
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/11323/10788
dc.identifier.doi.none.fl_str_mv 10.3390/w14182847
dc.identifier.eissn.spa.fl_str_mv 2073-4441
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC – Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv Echeverri-Díaz, J.; Coronado-Hernández, Ó.E.; Gatica, G.; Linfati, R.; Méndez-Anillo, R.D.; Coronado-Hernández, J.R. Sensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds. Water 2022, 14, 2847. https://doi.org/10.3390/w14182847
10.3390/w14182847
2073-4441
Corporación Universidad de la Costa
REDICUC – Repositorio CUC
url https://hdl.handle.net/11323/10788
https://repositorio.cuc.edu.co/
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournal.spa.fl_str_mv Water
dc.relation.references.spa.fl_str_mv 1. González-Álvarez, Á.; Viloria-Marimón, O.M.; Coronado-Hernández, Ó.E.; Vélez-Pereira, A.M.; Tesfagiorgis, K.; CoronadoHernández, J.R. Isohyetal maps of daily maximum rainfall for different return periods for the Colombian Caribbean Region. Water 2019, 11, 358. [CrossRef]
2. Vahabzadeh, G.; Saleh, I.; Safari, A.; Khosravi, K.; Vahabzadeh, G.; Saleh, I.; Safari, A.; Khosravi, K. Determination of the best method of estimating the time of concentration in pasture watersheds (case study: Banadak Sadat and Siazakh Watersheds, Iran). J. Biodivers. Environ. Sci. 2013, 3, 150–159.
3. Vélez, J.J.; Gutierrez, B.A. Estimación del tiempo de concentración y tiempo de rezago en la cuenca experimental urbana de la quebrada San Luis, Manizales. Dyna 2011, 78, 58–71.
4. Avila, L.; Ávila, H. Hazard Analysis in Urban Streets Due to Flash Floods: Case Study of Barranquilla, Colombia. In World Environmental and Water Resources Congress; American Society of Civil Engineers: Reston, VA, USA, 2016; pp. 144–154. Available online: ascelibrary.org (accessed on 9 September 2021).
5. Salimi, E.T.; Nohegar, A.; Malekian, A.; Hoseini, M.; Holisaz, A. Estimating time of concentration in large watersheds. Paddy Water Environ. 2017, 15, 123–132. [CrossRef]
6. McCuen, R.H.; Wong, S.L.; Rawls, W.J. Estimating urban time of concentration. J. Hydraul. Eng. 1984, 110, 887–904. [CrossRef]
7. Amatya, D.; Cupak, A.; Walega, A. Influence of tIme of concentratIon on variation of runoff from a small urbanized watershed. Geomat. Landmanagement Landsc. 2015, 2, 7–19.
8. Ibáñez, S.A.; Moreno, H.R.; Gisbert, J.M.B. Métodos Para la Determinación del Tiempo de Concentración (tc) de una Cuenca Hidrográfica; Universidad Politecnica de Valencia: Valencia, Spain, 2011.
9. Grimaldi, S.; Petroselli, A.; Tauro, F.; Porfiri, M. Time of concentration: A paradox in modern hydrology. Hydrol. Sci. J. 2012, 57, 217–228. [CrossRef]
10. Fang, X.; Thompson, D.B.; Cleveland, T.G.; Pradhan, P. Variations of Time of Concentration Estimates Using NRCS Velocity Method. J. Irrig. Drain. Eng. 2007, 133, 314–322. [CrossRef]
11. De Almeida, I.K.; Almeida, A.K.; Anache, J.A.A.; Steffen, J.L.; Alves, T. Estimation on time of concentration of overland flow in watersheds: A review. Geociências 2014, 33, 661–671.
12. Gericke, O.J.; Smithers, J.C. Review of methods used to estimate catchment response time for the purpose of peak discharge estimation. Hydrol. Sci. J. 2014, 59, 1935–1971. [CrossRef]
13. Sharifi, S.; Hosseini, S.M. Methodology for Identifying the Best Equations for Estimating the Time of Concentration of Watersheds in a Particular Region. J. Irrig. Drain. Eng. 2011, 137, 712–719. [CrossRef]
14. U.S. Department of Agriculture Natural Resources Conservation Service (USDA-NRSC); C.E.D. Urban Hydrology for Small Watersheds, Technical Release 55 (TR-55); U.S. Department of Agriculture Natural Resources Conservation Service (USDA-NRSC), C.E.D.: Washington, DC, USA, 1986.
15. Kirpich, Z.P. Time of concentration of small agricultural watersheds. Civ. Eng. 1940, 10, 362.
16. Gericke, O.J.; Smithers, J.C. Are estimates of catchment response time inconsistent as used in current flood hydrology practice in South Africa? J. S. Afr. Inst. Civ. Eng. 2016, 58, 2–15. [CrossRef]
17. Miller, W. Evolving a shortcut for design of storm sewers. Munic 1951, 89, 42–59.
18. Highways, C.D.O. California Culvert Practice; Department of Public Works, Division of Highways: Sacramento, CA, USA, 1960.
19. Ravazzani, G.; Boscarello, L.; Cislaghi, A.; Mancini, M. Review of Time-of-Concentration Equations and a New Proposal in Italy. J. Hydrol. Eng. 2019, 24, 04019039. [CrossRef]
20. Carter, R.W. Magnitude and Frequency of Floods in Suburban Areas; U.S. Geological Survey: Reston, VA, USA, 1961.
21. Federal Aviation Agency (FAA). Airport Drainage; Department of Transport Advisory Circular: Washington, DC, USA, 1970.
22. Welle, P.I.; Woodward, D. Engineering Hydrology—Time of Concentration; Bloomsbury Publishing: London, UK, 1986.
23. Texas Department of Transportation. Hydraulic Design Manual (Revised); Texas Department of Transportation: Austin, TX, USA, 1994.
24. Li, M.-H.; Chibber, P. Overland Flow Time of Concentration on Very Flat Terrains. Transp. Res. Rec. J. Transp. Res. Board 2008, 2060, 133–140. [CrossRef]
25. Li, M.-H.; Chibber, P.; Cahill, A.T. Estimating time of concentration of overland flow on very flat terrains. In 2005 ASAE Annual Meeting; American Society of Agricultural and Biological Engineers: St. Joseph, MI, USA, 2005; p. 1.
26. Chow, T.; Maidment, D.; Mays, L. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1988.
27. Williams, G. Flood discharges and the dimensions of spillways in India. Engineering 1922, 134, 321–322.
28. Fang, X.; Thompson, D.B.; Cleveland, T.G.; Pradhan, P.; Malla, R. Time of concentration estimated using watershed parameters determined by automated and manual methods. J. Irrig. Drain. Eng. 2008, 134, 202–211. [CrossRef]
29. Kerby, W.S. Time of concentration for overland flow. Civ. Eng. 1959, 29, 60.
30. González, Á.; Molina, J.; Meza, B.; Viloria, O.; Tesfagiorgis, K.; Mouthón, J. Assessing the Performance of Different Time of Concentration Equations in Urban Ungauged Watersheds: Case Study of Cartagena de Indias, Colombia. Hydrology 2020, 7, 47. [CrossRef]
31. Coronado-Hernández, Ó.E.; Merlano-Sabalza, E.; Díaz-Vergara, Z.; Coronado-Hernández, J.R. Selection of Hydrological Probability Distributions for Extreme Rainfall Events in the Regions of Colombia. Water 2020, 12, 1397. [CrossRef]
32. Kobiyama, M.; Grison, F.; Lino, J.F.L.; Silva, R.V. Time of concentration in the UFSC campus catchment, Florianópolis-SC (Brazil), calculated with morfometric and hydrological methods. In Proceedings of the Regional Conference on Geomorphology, UFG-IUG, Goiania, Brazil, 6–10 September 2006; Volume 110.
33. Krisnayanti, D.; Bunganaen, W.; Frans, J.H.; Serán, Y.; Legono, D. Curve Number Estimation for Ungauged Watershed in Semi-Arid Region. Civ. Eng. J. 2021, 7, 1070–1083. [CrossRef]
34. Michailidi, E.M.; Antoniadi, S.; Koukouvinos, A.; Bacchi, B.; Efstratiadis, A. Timing the time of concentration: Shedding light on a paradox. Hydrol. Sci. J. 2018, 63, 721–740. [CrossRef]
35. Lopes, A.L. Performance of time of concentration formulas for urban and rural basins. Rev. Bras. Recur. Hídricos 2005, 10, 5–23.
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spelling Atribución 4.0 Internacional (CC BY 4.0)© 2022 by the authors. Licensee MDPI, Basel, Switzerland.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Echeverri-Díaz, JamiltonCoronado-Hernández, Oscar E.Gustavo, GaticaLinfati, RodrigoMéndez-Anillo, Rafael D.Coronado-Hernandez, Jairo R.2024-02-23T17:54:10Z2024-02-23T17:54:10Z2022-09-13Echeverri-Díaz, J.; Coronado-Hernández, Ó.E.; Gatica, G.; Linfati, R.; Méndez-Anillo, R.D.; Coronado-Hernández, J.R. Sensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds. Water 2022, 14, 2847. https://doi.org/10.3390/w14182847https://hdl.handle.net/11323/1078810.3390/w141828472073-4441Corporación Universidad de la CostaREDICUC – Repositorio CUChttps://repositorio.cuc.edu.co/The time of concentration is the time it takes a drop of water in a basin to travel from the most distant point to the outlet, and is one of the most important parameters, along with the morphometric characteristics, for determining the design flow rate in rainfall-runoff models. This study aims to determine the sensitivity of the parameters included in different equations for the calculation of the time of concentration. A case study was conducted on small, urbanized watersheds in the city of Montería, Colombia. The study uses information obtained through field work using GPS equipment and electronic total station, supplemented by geographic information contained in the city drawings of the local sewage company, which includes data on elevations above sea level with sub-metric precision. The time of concentration determined by the 12 empirical equations was compared to the results obtained from the equation proposed by the Natural Resources Conservation Service (NRCS), which was considered as a baseline formulation for the intricacy of calculation. Based on this comparison, it was found that the Carter equation is the one that best fits the results obtained from the NRCS equation because it displayed highly significant goodness of fit values. Even though the equations by Kirpich, Ventura, California Culvert Practice, Simas-Hawkins and TxDOT provide a relatively good fit compared to other empirical equations, they tend to over-estimate time of concentration values, which could lead to the under-estimation of the design flow rates. For this reason, sensitivity analysis of the parameters of these equations represents an alternative for improving the calculation of the time of concentration. The current research analyses deepen the influence of some parameters in the estimation of time of concentration. The research can also be used by designers and engineers in the city of Montería, Colombia, as an important reference to compute time of concentrations in urbanized watersheds.20 páginasapplication/pdfengMultidisciplinary Digital Publishing Institute (MDPI)Switzerlandhttps://www.mdpi.com/2073-4441/14/18/2847Sensitivity of empirical equation parameters for the calculation of time of concentration in urbanized watershedsArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Water1. González-Álvarez, Á.; Viloria-Marimón, O.M.; Coronado-Hernández, Ó.E.; Vélez-Pereira, A.M.; Tesfagiorgis, K.; CoronadoHernández, J.R. Isohyetal maps of daily maximum rainfall for different return periods for the Colombian Caribbean Region. Water 2019, 11, 358. [CrossRef]2. Vahabzadeh, G.; Saleh, I.; Safari, A.; Khosravi, K.; Vahabzadeh, G.; Saleh, I.; Safari, A.; Khosravi, K. Determination of the best method of estimating the time of concentration in pasture watersheds (case study: Banadak Sadat and Siazakh Watersheds, Iran). J. Biodivers. Environ. Sci. 2013, 3, 150–159.3. Vélez, J.J.; Gutierrez, B.A. Estimación del tiempo de concentración y tiempo de rezago en la cuenca experimental urbana de la quebrada San Luis, Manizales. Dyna 2011, 78, 58–71.4. Avila, L.; Ávila, H. Hazard Analysis in Urban Streets Due to Flash Floods: Case Study of Barranquilla, Colombia. In World Environmental and Water Resources Congress; American Society of Civil Engineers: Reston, VA, USA, 2016; pp. 144–154. Available online: ascelibrary.org (accessed on 9 September 2021).5. Salimi, E.T.; Nohegar, A.; Malekian, A.; Hoseini, M.; Holisaz, A. Estimating time of concentration in large watersheds. Paddy Water Environ. 2017, 15, 123–132. [CrossRef]6. McCuen, R.H.; Wong, S.L.; Rawls, W.J. Estimating urban time of concentration. J. Hydraul. Eng. 1984, 110, 887–904. [CrossRef]7. Amatya, D.; Cupak, A.; Walega, A. Influence of tIme of concentratIon on variation of runoff from a small urbanized watershed. Geomat. Landmanagement Landsc. 2015, 2, 7–19.8. Ibáñez, S.A.; Moreno, H.R.; Gisbert, J.M.B. Métodos Para la Determinación del Tiempo de Concentración (tc) de una Cuenca Hidrográfica; Universidad Politecnica de Valencia: Valencia, Spain, 2011.9. Grimaldi, S.; Petroselli, A.; Tauro, F.; Porfiri, M. Time of concentration: A paradox in modern hydrology. Hydrol. Sci. J. 2012, 57, 217–228. [CrossRef]10. Fang, X.; Thompson, D.B.; Cleveland, T.G.; Pradhan, P. Variations of Time of Concentration Estimates Using NRCS Velocity Method. J. Irrig. Drain. Eng. 2007, 133, 314–322. [CrossRef]11. De Almeida, I.K.; Almeida, A.K.; Anache, J.A.A.; Steffen, J.L.; Alves, T. Estimation on time of concentration of overland flow in watersheds: A review. Geociências 2014, 33, 661–671.12. Gericke, O.J.; Smithers, J.C. Review of methods used to estimate catchment response time for the purpose of peak discharge estimation. Hydrol. Sci. J. 2014, 59, 1935–1971. [CrossRef]13. Sharifi, S.; Hosseini, S.M. Methodology for Identifying the Best Equations for Estimating the Time of Concentration of Watersheds in a Particular Region. J. Irrig. Drain. Eng. 2011, 137, 712–719. [CrossRef]14. U.S. Department of Agriculture Natural Resources Conservation Service (USDA-NRSC); C.E.D. Urban Hydrology for Small Watersheds, Technical Release 55 (TR-55); U.S. Department of Agriculture Natural Resources Conservation Service (USDA-NRSC), C.E.D.: Washington, DC, USA, 1986.15. Kirpich, Z.P. Time of concentration of small agricultural watersheds. Civ. Eng. 1940, 10, 362.16. Gericke, O.J.; Smithers, J.C. Are estimates of catchment response time inconsistent as used in current flood hydrology practice in South Africa? J. S. Afr. Inst. Civ. Eng. 2016, 58, 2–15. [CrossRef]17. Miller, W. Evolving a shortcut for design of storm sewers. Munic 1951, 89, 42–59.18. Highways, C.D.O. California Culvert Practice; Department of Public Works, Division of Highways: Sacramento, CA, USA, 1960.19. Ravazzani, G.; Boscarello, L.; Cislaghi, A.; Mancini, M. Review of Time-of-Concentration Equations and a New Proposal in Italy. J. Hydrol. Eng. 2019, 24, 04019039. [CrossRef]20. Carter, R.W. Magnitude and Frequency of Floods in Suburban Areas; U.S. Geological Survey: Reston, VA, USA, 1961.21. Federal Aviation Agency (FAA). Airport Drainage; Department of Transport Advisory Circular: Washington, DC, USA, 1970.22. Welle, P.I.; Woodward, D. Engineering Hydrology—Time of Concentration; Bloomsbury Publishing: London, UK, 1986.23. Texas Department of Transportation. Hydraulic Design Manual (Revised); Texas Department of Transportation: Austin, TX, USA, 1994.24. Li, M.-H.; Chibber, P. Overland Flow Time of Concentration on Very Flat Terrains. Transp. Res. Rec. J. Transp. Res. Board 2008, 2060, 133–140. [CrossRef]25. Li, M.-H.; Chibber, P.; Cahill, A.T. Estimating time of concentration of overland flow on very flat terrains. In 2005 ASAE Annual Meeting; American Society of Agricultural and Biological Engineers: St. Joseph, MI, USA, 2005; p. 1.26. Chow, T.; Maidment, D.; Mays, L. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1988.27. Williams, G. Flood discharges and the dimensions of spillways in India. Engineering 1922, 134, 321–322.28. Fang, X.; Thompson, D.B.; Cleveland, T.G.; Pradhan, P.; Malla, R. Time of concentration estimated using watershed parameters determined by automated and manual methods. J. Irrig. Drain. Eng. 2008, 134, 202–211. [CrossRef]29. Kerby, W.S. Time of concentration for overland flow. Civ. Eng. 1959, 29, 60.30. González, Á.; Molina, J.; Meza, B.; Viloria, O.; Tesfagiorgis, K.; Mouthón, J. Assessing the Performance of Different Time of Concentration Equations in Urban Ungauged Watersheds: Case Study of Cartagena de Indias, Colombia. Hydrology 2020, 7, 47. [CrossRef]31. Coronado-Hernández, Ó.E.; Merlano-Sabalza, E.; Díaz-Vergara, Z.; Coronado-Hernández, J.R. Selection of Hydrological Probability Distributions for Extreme Rainfall Events in the Regions of Colombia. Water 2020, 12, 1397. [CrossRef]32. Kobiyama, M.; Grison, F.; Lino, J.F.L.; Silva, R.V. Time of concentration in the UFSC campus catchment, Florianópolis-SC (Brazil), calculated with morfometric and hydrological methods. In Proceedings of the Regional Conference on Geomorphology, UFG-IUG, Goiania, Brazil, 6–10 September 2006; Volume 110.33. Krisnayanti, D.; Bunganaen, W.; Frans, J.H.; Serán, Y.; Legono, D. Curve Number Estimation for Ungauged Watershed in Semi-Arid Region. Civ. Eng. J. 2021, 7, 1070–1083. [CrossRef]34. Michailidi, E.M.; Antoniadi, S.; Koukouvinos, A.; Bacchi, B.; Efstratiadis, A. Timing the time of concentration: Shedding light on a paradox. Hydrol. Sci. J. 2018, 63, 721–740. [CrossRef]35. Lopes, A.L. Performance of time of concentration formulas for urban and rural basins. Rev. Bras. Recur. Hídricos 2005, 10, 5–23.2011814Urbanized watershedsTime of concentrationUSDA NRCSLinear regression analysisSensitivity analysisPublicationORIGINALSensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds.pdfSensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds.pdfArtículoapplication/pdf5006265https://repositorio.cuc.edu.co/bitstreams/6b5f6204-8a27-44ba-9a7b-6d68c80d8c42/download3998cd3db00d80e7f12622c72f8ad3c7MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-814828https://repositorio.cuc.edu.co/bitstreams/8c8de18e-c792-455e-b811-6682fbb4ea9a/download2f9959eaf5b71fae44bbf9ec84150c7aMD52TEXTSensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds.pdf.txtSensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds.pdf.txtExtracted texttext/plain59963https://repositorio.cuc.edu.co/bitstreams/cee16033-79a7-4ffa-a0d1-ed3d41effcba/download460ac973a9d9437d09ab47c7d72b2501MD53THUMBNAILSensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds.pdf.jpgSensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds.pdf.jpgGenerated Thumbnailimage/jpeg16097https://repositorio.cuc.edu.co/bitstreams/48129a17-58be-47d2-85c3-8276fd2bd7d7/download8887ad7d366e240cd96c981bb51da0a6MD5411323/10788oai:repositorio.cuc.edu.co:11323/107882024-09-17 11:02:26.356https://creativecommons.org/licenses/by/4.0/© 2022 by the authors. 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ada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.


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