Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia

Frequency analysis of extreme events is used to estimate the maximum rainfall associated with different return periods and is used in planning hydraulic structures. When carrying out this type of analysis in engineering projects, the hydrological distributions that best fit the trend of maximum 24 h...

Full description

Autores:
Coronado-Hernández, Oscar E.
Merlano-Sabalza, Ernesto
Díaz-Vergara, Zaid
Coronado-Hernandez, Jairo R.
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/6921
Acceso en línea:
https://hdl.handle.net/11323/6921
https://doi.org/10.3390/w12051397
https://repositorio.cuc.edu.co/
Palabra clave:
Maximum rainfall
Colombia
Regionalization
Probability distribution
Precipitación máxima
Colombia
Regionalización
Distribución de probabilidad
Rights
openAccess
License
CC0 1.0 Universal
id RCUC2_df90077d6cc0e1cb5e73df6c9c41bb15
oai_identifier_str oai:repositorio.cuc.edu.co:11323/6921
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.spa.fl_str_mv Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
dc.title.translated.spa.fl_str_mv Selección de distribuciones de probabilidad hidrológica para eventos de lluvia extrema en las regiones de Colombia
title Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
spellingShingle Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
Maximum rainfall
Colombia
Regionalization
Probability distribution
Precipitación máxima
Colombia
Regionalización
Distribución de probabilidad
title_short Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
title_full Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
title_fullStr Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
title_full_unstemmed Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
title_sort Selection of hydrological probability distributions for extreme rainfall events in the regions of Colombia
dc.creator.fl_str_mv Coronado-Hernández, Oscar E.
Merlano-Sabalza, Ernesto
Díaz-Vergara, Zaid
Coronado-Hernandez, Jairo R.
dc.contributor.author.spa.fl_str_mv Coronado-Hernández, Oscar E.
Merlano-Sabalza, Ernesto
Díaz-Vergara, Zaid
Coronado-Hernandez, Jairo R.
dc.subject.spa.fl_str_mv Maximum rainfall
Colombia
Regionalization
Probability distribution
Precipitación máxima
Colombia
Regionalización
Distribución de probabilidad
topic Maximum rainfall
Colombia
Regionalization
Probability distribution
Precipitación máxima
Colombia
Regionalización
Distribución de probabilidad
description Frequency analysis of extreme events is used to estimate the maximum rainfall associated with different return periods and is used in planning hydraulic structures. When carrying out this type of analysis in engineering projects, the hydrological distributions that best fit the trend of maximum 24 h rainfall data are unknown. This study collected maximum 24 h rainfall records from 362 stations distributed throughout Colombia, with the goal of guiding hydraulic planners by suggesting the probability distributions they should use before beginning their analysis. The generalized extreme value (GEV) probability distribution, using the weighted moments method, presented the best fits of frequency analysis of maximum daily precipitation for various return periods for selected rainfall stations in Colombia.
publishDate 2020
dc.date.accessioned.none.fl_str_mv 2020-08-13T16:56:55Z
dc.date.available.none.fl_str_mv 2020-08-13T16:56:55Z
dc.date.issued.none.fl_str_mv 2020-05-10
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
format http://purl.org/coar/resource_type/c_6501
status_str acceptedVersion
dc.identifier.issn.spa.fl_str_mv 20734441
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/6921
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.3390/w12051397
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 20734441
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/6921
https://doi.org/10.3390/w12051397
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv 1. Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw-Hill: Bogotá, Colombia, 1994.
2. Frechet, M. Sur la loi de probabilité de l’ecart máximum (On the probability law of máximum values). Ann. de la Soc. Pol. de Math. 1927, 6, 93–116.
3. Maidment, D. Handbook of Hydrology; Mc Graw-Hill: New York, NY, USA, 1992.
4. Clarke, R.T.; Dias de Paiva, R.; Bertacchi, C. Comparison of methods for analysis of extremes when records are fragmented: A case study using Amazon basin rainfall data. J. Hydrol. 2009, 368, 26–29. [CrossRef]
5. Bedient, P.B.; Huber, W.C. Hydrology and Floodplain Analysis. Prentice-Hall: Upper Saddle River, NJ, USA, 2002; pp. 168–224.
6. Arnaez, J.; Lasanta, T.; Ruiz-Flaño, P.; Ortigosa, L. Factors affecting runoff and erosion under simulated rainfall in Mediterranean vineyards. Soil Tillage Res. 2007, 93, 324–334. [CrossRef]
7. Gonzalez-Alvarez, A.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Ramos, H.M. Effect of the Non-Stationarity of Rainfall Events on the Design of Hydraulic Structures for Runoff Management and Its Applications to a Case Study at Gordo Creek Watershed in Cartagena de Indias. Colomb. Fluids 2018, 3, 27. [CrossRef]
8. Obeysekera, J.; Salas, J.D. Quantifying the uncertainty of design floods under nonstationary conditions. J. Hydrol. Eng. 2014, 19, 1438–1446. [CrossRef]
9. Obeysekera, J.; Salas, J.D. Frequency of recurrent extremes under nonstationarity. J. Hydrol. Eng. 2016, 21, 04016005. [CrossRef]
10. Yang, T.; Shao, Q.; Hao, Z.-C.; Chen, X.; Zhang, Z.; Xu, C.-Y.; Sun, L. Regional frequency analysis and spatio-temporal pattern characterization of rainfall extremes in the Pearl River Basin, China. J. Hydrol. 2009, 380, 386–405. [CrossRef]
11. Nunn, Dwight. Ingetec, S.A-Empresa de Acueducto y Alcantarillado de Bogotá. In Estimating of Maximum Daily Precipitation of Tributaries of Bogotá River; Ingetec: Bogotá, Colombia, 1968.
12. Pathak, C.S. Frequency analysis of rainfall maximums for Central and South Florida, Technical Publication EMA # 390. 2001. Available online: http://my.sfwmd.gov/portal/page/portal/pg_grp_tech_pubs/portlet_ tech_pubs/ema-390.pdf (accessed on 12 March 2018).
13. Gumbel, E.J. The return period of flood flows. Ann. Math. Stat. 1941, 2, 163–190. [CrossRef]
14. Weibull, W. A statistical theory of the strength of materials. In Proceedings of the Ingeniors Vetenskaps Akademien (The Royal Swedish Institute for Engineering Research) No. 51, Stockholm, Sweden, 1 Januray 1939; 1939; pp. 5–45.
15. Grego, J.M.; Yates, P.A. Point and standard error estimation for quantiles of mixed flood distribution. J. Hydrol. 2010, 391, 289–301. [CrossRef]
16. Koutrouvelisa, I.A.; Canavos, G.C. A comparison of moment-based methods of estimation for thelogPearson type 3 distribution. J. Hydrol. 2000, 234, 71–81. [CrossRef]
17. Xuewu, J.; Jing, D.; Shen, H.W.; Salas, J.D. Plotting positions for Pearson type-III distribution. J. Hydrol. 2003, 74, 1–29. [CrossRef]
18. Makkonen, L. Problems in the extreme value analysis. Struct. Saf. 2006, 30, 405–419. [CrossRef]
19. Kolmogorov, A.N. Sulla determinazione empirica di una legge di distribuzione. G. dell’Instituto Ital. degli Attuari 1933, 4, 83–91.
20. Smirnov, N.V. Estimate of deviation between empirical distribution functions in two independent samples. Bull. Mosc. Univ. 1939, 2, 3–16.
21. Smirnov, N.V. Table for estimating the goodness of fit of empirical distributions. Ann. Math. Stat. 1948, 19, 279–281. [CrossRef]
22. Mahdi, S.; Cenac, M. Estimating Parameters of Gumbel Distribution using the Methods of Moments, Probability Weighted Moments and Maximum Likelihood. Rev. de Matemáticas Teoría y Apl. 2005, 12, 151–156. [CrossRef]
23. Seckin, N.; Yurtal, R.; Haktanir, T.; Dogan, A. Comparison of Probability Weighted Moments and Maximum Likelihood Methods Used in Flood Frequency Analysis for Ceyhan River Basin. Arab. J. Sci. Eng. 2009, 35, 49–69.
24. Ministerio de Vivienda, Ciudad y Territorio. República de Colombia. Resolution 0330 of 8 June 2017. Available online: http://www.minvivienda.gov.co/ResolucionesAgua/0330%20-%202017.pdf (accessed on 20 March 2020).
25. Ministerio de Transporte, Instituto Nacional de Vías. República de Colombia. Manual on Drainage Design for Highways. 2009. Available online: https://www.invias.gov.co/index.php/archivo-y-documentos/ documentos-tecnicos/especificaciones-tecnicas/984-manual-de-drenaje-para-carreteras/file (accessed on 20 March 2020).
26. Gonzalez-Alvarez, A.; Viloria-Marimón, O.; Coronado-Hernández, O.E.; Vélez-Pereira, A.; Tesfagiorgis, K.; Coronado-Hernández, J. Isohyetal Maps of Daily Maximum Rainfall for Different Return Periods for the Colombian Caribbean Region. Water 2019, 11, 358. [CrossRef]
27. Krishnamoorthy, K.; Peng, J. Some properties of the exact and score methods for binomial proportion and sample size calculation. Commun. Stat. Simul. Comput. 2007, 36, 1171–1186. [CrossRef]
28. El Adlouni, S.; Bobée, B. Hydrological Frequency Analysis Using HYFRAN-PLUS Software. User’s Guide available with the software DEMO 2015. Available online: http://www.wrpllc.com/books/HyfranPlus/ indexhyfranplus3.html (accessed on 20 March 2020).
dc.rights.spa.fl_str_mv CC0 1.0 Universal
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/publicdomain/zero/1.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv CC0 1.0 Universal
http://creativecommons.org/publicdomain/zero/1.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.spa.fl_str_mv Corporación Universidad de la Costa
dc.source.spa.fl_str_mv Water
institution Corporación Universidad de la Costa
dc.source.url.spa.fl_str_mv https://www.mdpi.com/2073-4441/12/5/1397/htm
bitstream.url.fl_str_mv https://repositorio.cuc.edu.co/bitstreams/3c0a8d97-cd6c-4d1f-89f4-6c1d81e674aa/download
https://repositorio.cuc.edu.co/bitstreams/07a64e74-a2a9-4226-aa01-3821336a27d6/download
https://repositorio.cuc.edu.co/bitstreams/c39d6a09-2c6e-4848-96ab-7f540d1da2f7/download
https://repositorio.cuc.edu.co/bitstreams/9c64d53a-7326-4254-b497-7e0f7e3c4ecf/download
https://repositorio.cuc.edu.co/bitstreams/9f961bc0-8079-4782-94ed-f62ea088b193/download
bitstream.checksum.fl_str_mv 093944c54d9c8d250642ec84d9b06ed5
42fd4ad1e89814f5e4a476b409eb708c
e30e9215131d99561d40d6b0abbe9bad
bd7fca89b5c4446730bb4903ef08fe5b
2d638a7c0ef12da338389ca3aa4b740c
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio de la Universidad de la Costa CUC
repository.mail.fl_str_mv repdigital@cuc.edu.co
_version_ 1811760805849333760
spelling Coronado-Hernández, Oscar E.Merlano-Sabalza, ErnestoDíaz-Vergara, ZaidCoronado-Hernandez, Jairo R.2020-08-13T16:56:55Z2020-08-13T16:56:55Z2020-05-1020734441https://hdl.handle.net/11323/6921https://doi.org/10.3390/w12051397Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Frequency analysis of extreme events is used to estimate the maximum rainfall associated with different return periods and is used in planning hydraulic structures. When carrying out this type of analysis in engineering projects, the hydrological distributions that best fit the trend of maximum 24 h rainfall data are unknown. This study collected maximum 24 h rainfall records from 362 stations distributed throughout Colombia, with the goal of guiding hydraulic planners by suggesting the probability distributions they should use before beginning their analysis. The generalized extreme value (GEV) probability distribution, using the weighted moments method, presented the best fits of frequency analysis of maximum daily precipitation for various return periods for selected rainfall stations in Colombia.El análisis de frecuencia de eventos extremos se utiliza para estimar la precipitación máxima asociada con diferentes períodos de retorno y se utiliza en la planificación de estructuras hidráulicas. Al realizar este tipo de análisis en proyectos de ingeniería, las distribuciones hidrológicas que mejor se ajustan a la tendencia de máxima Se desconocen los datos de precipitación de 24 h. Este estudio recopiló registros de precipitación máxima de 24 h de 362 estaciones distribuidos por toda Colombia, con el objetivo de orientar a los planificadores hidráulicos sugiriendo distribuciones de probabilidad que deben usar antes de comenzar su análisis. El extremo generalizado La distribución de probabilidad del valor (GEV), utilizando el método de momentos ponderados, presentó los mejores ajustes de análisis de frecuencia de la precipitación máxima diaria para varios períodos de retorno para lluvias seleccionadas estaciones en Colombia.Coronado-Hernández, Oscar E.-will be generated-orcid-0000-0002-6574-0857-600Merlano-Sabalza, ErnestoDíaz-Vergara, ZaidCoronado-Hernandez, Jairo R.-will be generated-orcid-0000-0003-4360-6128-600engCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Waterhttps://www.mdpi.com/2073-4441/12/5/1397/htmMaximum rainfallColombiaRegionalizationProbability distributionPrecipitación máximaColombiaRegionalizaciónDistribución de probabilidadSelection of hydrological probability distributions for extreme rainfall events in the regions of ColombiaSelección de distribuciones de probabilidad hidrológica para eventos de lluvia extrema en las regiones de ColombiaArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersion1. Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw-Hill: Bogotá, Colombia, 1994.2. Frechet, M. Sur la loi de probabilité de l’ecart máximum (On the probability law of máximum values). Ann. de la Soc. Pol. de Math. 1927, 6, 93–116.3. Maidment, D. Handbook of Hydrology; Mc Graw-Hill: New York, NY, USA, 1992.4. Clarke, R.T.; Dias de Paiva, R.; Bertacchi, C. Comparison of methods for analysis of extremes when records are fragmented: A case study using Amazon basin rainfall data. J. Hydrol. 2009, 368, 26–29. [CrossRef]5. Bedient, P.B.; Huber, W.C. Hydrology and Floodplain Analysis. Prentice-Hall: Upper Saddle River, NJ, USA, 2002; pp. 168–224.6. Arnaez, J.; Lasanta, T.; Ruiz-Flaño, P.; Ortigosa, L. Factors affecting runoff and erosion under simulated rainfall in Mediterranean vineyards. Soil Tillage Res. 2007, 93, 324–334. [CrossRef]7. Gonzalez-Alvarez, A.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Ramos, H.M. Effect of the Non-Stationarity of Rainfall Events on the Design of Hydraulic Structures for Runoff Management and Its Applications to a Case Study at Gordo Creek Watershed in Cartagena de Indias. Colomb. Fluids 2018, 3, 27. [CrossRef]8. Obeysekera, J.; Salas, J.D. Quantifying the uncertainty of design floods under nonstationary conditions. J. Hydrol. Eng. 2014, 19, 1438–1446. [CrossRef]9. Obeysekera, J.; Salas, J.D. Frequency of recurrent extremes under nonstationarity. J. Hydrol. Eng. 2016, 21, 04016005. [CrossRef]10. Yang, T.; Shao, Q.; Hao, Z.-C.; Chen, X.; Zhang, Z.; Xu, C.-Y.; Sun, L. Regional frequency analysis and spatio-temporal pattern characterization of rainfall extremes in the Pearl River Basin, China. J. Hydrol. 2009, 380, 386–405. [CrossRef]11. Nunn, Dwight. Ingetec, S.A-Empresa de Acueducto y Alcantarillado de Bogotá. In Estimating of Maximum Daily Precipitation of Tributaries of Bogotá River; Ingetec: Bogotá, Colombia, 1968.12. Pathak, C.S. Frequency analysis of rainfall maximums for Central and South Florida, Technical Publication EMA # 390. 2001. Available online: http://my.sfwmd.gov/portal/page/portal/pg_grp_tech_pubs/portlet_ tech_pubs/ema-390.pdf (accessed on 12 March 2018).13. Gumbel, E.J. The return period of flood flows. Ann. Math. Stat. 1941, 2, 163–190. [CrossRef]14. Weibull, W. A statistical theory of the strength of materials. In Proceedings of the Ingeniors Vetenskaps Akademien (The Royal Swedish Institute for Engineering Research) No. 51, Stockholm, Sweden, 1 Januray 1939; 1939; pp. 5–45.15. Grego, J.M.; Yates, P.A. Point and standard error estimation for quantiles of mixed flood distribution. J. Hydrol. 2010, 391, 289–301. [CrossRef]16. Koutrouvelisa, I.A.; Canavos, G.C. A comparison of moment-based methods of estimation for thelogPearson type 3 distribution. J. Hydrol. 2000, 234, 71–81. [CrossRef]17. Xuewu, J.; Jing, D.; Shen, H.W.; Salas, J.D. Plotting positions for Pearson type-III distribution. J. Hydrol. 2003, 74, 1–29. [CrossRef]18. Makkonen, L. Problems in the extreme value analysis. Struct. Saf. 2006, 30, 405–419. [CrossRef]19. Kolmogorov, A.N. Sulla determinazione empirica di una legge di distribuzione. G. dell’Instituto Ital. degli Attuari 1933, 4, 83–91.20. Smirnov, N.V. Estimate of deviation between empirical distribution functions in two independent samples. Bull. Mosc. Univ. 1939, 2, 3–16.21. Smirnov, N.V. Table for estimating the goodness of fit of empirical distributions. Ann. Math. Stat. 1948, 19, 279–281. [CrossRef]22. Mahdi, S.; Cenac, M. Estimating Parameters of Gumbel Distribution using the Methods of Moments, Probability Weighted Moments and Maximum Likelihood. Rev. de Matemáticas Teoría y Apl. 2005, 12, 151–156. [CrossRef]23. Seckin, N.; Yurtal, R.; Haktanir, T.; Dogan, A. Comparison of Probability Weighted Moments and Maximum Likelihood Methods Used in Flood Frequency Analysis for Ceyhan River Basin. Arab. J. Sci. Eng. 2009, 35, 49–69.24. Ministerio de Vivienda, Ciudad y Territorio. República de Colombia. Resolution 0330 of 8 June 2017. Available online: http://www.minvivienda.gov.co/ResolucionesAgua/0330%20-%202017.pdf (accessed on 20 March 2020).25. Ministerio de Transporte, Instituto Nacional de Vías. República de Colombia. Manual on Drainage Design for Highways. 2009. Available online: https://www.invias.gov.co/index.php/archivo-y-documentos/ documentos-tecnicos/especificaciones-tecnicas/984-manual-de-drenaje-para-carreteras/file (accessed on 20 March 2020).26. Gonzalez-Alvarez, A.; Viloria-Marimón, O.; Coronado-Hernández, O.E.; Vélez-Pereira, A.; Tesfagiorgis, K.; Coronado-Hernández, J. Isohyetal Maps of Daily Maximum Rainfall for Different Return Periods for the Colombian Caribbean Region. Water 2019, 11, 358. [CrossRef]27. Krishnamoorthy, K.; Peng, J. Some properties of the exact and score methods for binomial proportion and sample size calculation. Commun. Stat. Simul. Comput. 2007, 36, 1171–1186. [CrossRef]28. El Adlouni, S.; Bobée, B. Hydrological Frequency Analysis Using HYFRAN-PLUS Software. User’s Guide available with the software DEMO 2015. Available online: http://www.wrpllc.com/books/HyfranPlus/ indexhyfranplus3.html (accessed on 20 March 2020).PublicationORIGINALwater-12-01397-v3.pdfwater-12-01397-v3.pdfapplication/pdf1339362https://repositorio.cuc.edu.co/bitstreams/3c0a8d97-cd6c-4d1f-89f4-6c1d81e674aa/download093944c54d9c8d250642ec84d9b06ed5MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/07a64e74-a2a9-4226-aa01-3821336a27d6/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/c39d6a09-2c6e-4848-96ab-7f540d1da2f7/downloade30e9215131d99561d40d6b0abbe9badMD53THUMBNAILwater-12-01397-v3.pdf.jpgwater-12-01397-v3.pdf.jpgimage/jpeg66008https://repositorio.cuc.edu.co/bitstreams/9c64d53a-7326-4254-b497-7e0f7e3c4ecf/downloadbd7fca89b5c4446730bb4903ef08fe5bMD54TEXTwater-12-01397-v3.pdf.txtwater-12-01397-v3.pdf.txttext/plain32008https://repositorio.cuc.edu.co/bitstreams/9f961bc0-8079-4782-94ed-f62ea088b193/download2d638a7c0ef12da338389ca3aa4b740cMD5511323/6921oai:repositorio.cuc.edu.co:11323/69212024-09-17 12:47:04.511http://creativecommons.org/publicdomain/zero/1.0/CC0 1.0 Universalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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

Publicaciones similares