Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia

Previous soil moisture conditions play an important role in the design of hydraulic structures because they are directly related to the runoff threshold associated with a return period. These represent one of the main determinants of the runoff response of a drainage basin. One of the main difficult...

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Autores:
Salgado-Cassiani, Julio Jose
Coronado-Hernández, Oscar E.
Gustavo, Gatica
Linfati, Rodrigo
Coronado-Hernandez, Jairo R.
Coronado Hernández, Oscar E.
Tipo de recurso:
Article of journal
Fecha de publicación:
2022
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/9219
Acceso en línea:
https://hdl.handle.net/11323/9219
https://doi.org/ 10.3390/w14081217
https://repositorio.cuc.edu.co/
Palabra clave:
Precipitation
Frequency analysis
Return period
Antecedent moisture condition
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openAccess
License
Atribución 4.0 Internacional (CC BY 4.0)
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oai_identifier_str oai:repositorio.cuc.edu.co:11323/9219
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repository_id_str
dc.title.eng.fl_str_mv Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
title Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
spellingShingle Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
Precipitation
Frequency analysis
Return period
Antecedent moisture condition
title_short Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
title_full Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
title_fullStr Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
title_full_unstemmed Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
title_sort Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, Colombia
dc.creator.fl_str_mv Salgado-Cassiani, Julio Jose
Coronado-Hernández, Oscar E.
Gustavo, Gatica
Linfati, Rodrigo
Coronado-Hernandez, Jairo R.
Coronado Hernández, Oscar E.
dc.contributor.author.spa.fl_str_mv Salgado-Cassiani, Julio Jose
Coronado-Hernández, Oscar E.
Gustavo, Gatica
Linfati, Rodrigo
Coronado-Hernandez, Jairo R.
dc.contributor.author.none.fl_str_mv Coronado Hernández, Oscar E.
dc.subject.proposal.eng.fl_str_mv Precipitation
Frequency analysis
Return period
Antecedent moisture condition
topic Precipitation
Frequency analysis
Return period
Antecedent moisture condition
description Previous soil moisture conditions play an important role in the design of hydraulic structures because they are directly related to the runoff threshold associated with a return period. These represent one of the main determinants of the runoff response of a drainage basin. One of the main difficulties facing hydrologists in Colombia lies in the time spent gathering and analyzing information related to the selection of antecedent moisture conditions. In this study, complete records from 19 rainfall stations located in the Atlántico region, Colombia, were used to analyze the cumulative precipitation during the 5 days prior to the annual maximum daily precipitation associated with different return periods using the Gev, Gumbel, Pearson Type III and Log Pearson Type III probability distributions. Different interpolation methods (IDW, kriging and spline) were applied to evaluate the spatial distribution of the antecedent moisture conditions. The main contribution of this research is establishing, using a probabilistic approach, the behavior of antecedent moisture conditions in a particular region, which can be used by engineers and designers to plan water infrastructure. This probabilistic approach was applied to a case study of the Atlántico region, Colombia, where the spatial distribution of antecedent moisture conditions was calculated for several return periods. The results indicate that the better results were obtained with the IDW interpolation method, and the Pearson Type III and Gumbel distributions also showed the best fits based on the Akaike criterion.
publishDate 2022
dc.date.accessioned.none.fl_str_mv 2022-06-08T12:21:59Z
dc.date.available.none.fl_str_mv 2022-06-08T12:21:59Z
dc.date.issued.none.fl_str_mv 2022-04-10
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/acceptedVersion
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dc.identifier.citation.spa.fl_str_mv Salgado-Cassiani, J.J.; Coronado-Hernández, O.E.; Gatica, G.; Linfati, R.; Coronado-Hernández, J.R. Probabilistic Approach to Determine the Spatial Distribution of the Antecedent Moisture Conditions for Different Return Periods in the Atlántico Region, Colombia. Water 2022, 14, 1217. https://doi.org/ 10.3390/w14081217
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/9219
dc.identifier.url.spa.fl_str_mv https://doi.org/ 10.3390/w14081217
dc.identifier.doi.spa.fl_str_mv 10.3390/w14081217
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 Salgado-Cassiani, J.J.; Coronado-Hernández, O.E.; Gatica, G.; Linfati, R.; Coronado-Hernández, J.R. Probabilistic Approach to Determine the Spatial Distribution of the Antecedent Moisture Conditions for Different Return Periods in the Atlántico Region, Colombia. Water 2022, 14, 1217. https://doi.org/ 10.3390/w14081217
10.3390/w14081217
2073-4441
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/9219
https://doi.org/ 10.3390/w14081217
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartofjournal.spa.fl_str_mv Water
dc.relation.references.spa.fl_str_mv 1. Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology, 1st ed.; McGraw-Hill: New York, NY, USA, 1988; pp. 350–376.
2. Ceballos, A.; Schnabel, S. Hydrological behaviour of a small catchment in the dehesa landuse system (Extremadura, SW Spain). J. Hydrol. 1998, 210, 146–160. [CrossRef]
3. Dusek, J.; Vogel, T. Hillslope-storage and rainfall-amount thresholds as controls of preferential stormflow. J. Hydrol. 2016, 534, 590–605. [CrossRef]
4. Berne, A.; Delrieu, G.; Creutin, J.D.; Obled, C. Temporal and spatial resolution of rainfall measurements required for urban hydrology. J. Hydrol. 2004, 299, 166–179. [CrossRef]
5. Manfreda, S.; Fiorentino, M.; Iacobellis, V. DREAM A distributed model for runoff, evapotranspiration, and antecedent soil moisture simulation. Adv. Geosci. 2005, 2, 31–39. [CrossRef]
6. Lazzari, M.; Piccarreta, M.; Ray, L.R.; Manfreda, S. Modeling Antecedent Soil Moisture to Constrain Rainfall Thresholds for Shallow Landslides Occurrence. In Landslides: Investigation and Monitoring; Ram, L.R., Lazzari, M., Eds.; IntechOpen: London, UK, 2020. Available online: https://www.intechopen.com/chapters/72592 (accessed on 1 February 2022).
7. Lazzari, M.; Piccarreta, M.; Manfreda, S. The role of antecedent soil moisture conditions on rainfall-triggered shallow landslides. Nat. Hazards Earth Syst. Sci. 2018, 1–11. Available online: https://nhess.copernicus.org/preprints/nhess-2018-371/ (accessed on 20 February 2022). [CrossRef]
8. Poveda, G.; Jaramillo, A.; Gil, M.M.; Quinceno, N.; Mantilla, R.I. Seasonality in ENSO-related precipitation, river discharges, soil moisture, and vegetation index in Colombia. Water Resour. Res. 2001, 37, 2169–2178. [CrossRef]
9. Kim, G.-S.; Lee, S.-g.; Lee, J.; Park, E.; Song, C.; Hong, M.; Ko, Y.-J.; Lee, W.-K. Effects of Forest and Agriculture Land Covers on Organic Carbon Flux Mediated through Precipitation. Water 2022, 14, 623. [CrossRef]
10. Darouich, H.; Ramos, T.B.; Pereira, L.S.; Rabino, D.; Bagagiolo, G.; Capello, G.; Simionesei, L.; Cavallo, E.; Biddoccu, M. Water Use and Soil Water Balance of Mediterranean Vineyards under Rainfed and Drip Irrigation Management: Evapotranspiration Partition and Soil Management Modelling for Resource Conservation. Water 2022, 14, 554. [CrossRef]
11. Waylen, P.; Poveda, G. El Niño-Southern Oscillation and aspects of western South American hydro-climatology. Hydrol. Process 2002, 16, 1247–1260. [CrossRef]
12. de Alcântara, L.R.P.; Coutinho, A.P.; dos Santos Neto, S.M.; Carvalho de Gusmão da Cunha Rabelo, A.E.; Antonino, A.C.D. Modeling of the Hydrological Processes in Caatinga and Pasture Areas in the Brazilian Semi-Arid. Water 2021, 13, 1877. [CrossRef]
13. U.S. Water Resources Council. A Uniform Technique for Determining Flood Flow Frequencies; Bulletin 15; U.S. Water Resources Council: Washington, DC, USA, 1967.
14. Cunnane, C. Methods and merits of regional flood frequency analysis. J. Hydrol. 1988, 100, 269–290. [CrossRef]
15. Webster, V.L.; Stedinger, J. Log-Pearson Type III Distribution and Its Application in Flood Frequency Analysis. I: Distribution Characteristics. J. Hydrol. Eng. 2007, 12, 482–491.
16. Burgess, C.P.; Taylor, M.A.; Stephenson, T.; Mandal, A. Frequency analysis, infilling and trends for extreme precipitation for Jamaica (1895–2100). J. Hydrol. 2015, 3, 424–443. [CrossRef]
17. González-Álvarez, Á.; Viloria-Marimón, O.; Coronado-Hernández, Ó.E.; Vélez-Pereira, A.; Tesfagiorgis, K.; Coronado-Hernández, J.R. Isohyetal Maps of Daily Maximum Rainfall for Different Return Periods for the Colombian Caribbean Region. Water 2019, 11, 358. [CrossRef]
18. Pizarro, R.; Ingram, B.; Gonzalez-Leiva, F.; Valdés-Pineda, R.; Sangüesa, C.; Delgado, N.; García-Chevesich, P.; Valdés, J.B. WEBSEIDF: A Web-Based System for the Estimation of IDF Curves in Central Chile. Hydrology 2018, 5, 40. [CrossRef]
19. Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control 1974, 19, 716–723. [CrossRef]
20. Akaike, H. Information theory and an extension of the maximum likelihood principle. In Selected Papers of Hirotugu Akaike; Springer: Berlin/Heidelberg, Germany, 1998; pp. 199–213.
21. Salas, J.D.; Obeysekera, J.; Vogel, R.M. Techniques for assessing water infrastructure for nonstationary extreme events: A review. Hydrol. Sci. J. 2018, 63, 325–352. [CrossRef]
22. Ikechukwu, M.N.; Ebinne, E.; Idorenyin, U.; Raphael, N.I. Accuracy Assessment and Comparative Analysis of IDW, Spline and Kriging in Spatial Interpolation of Landform (Topography): An Experimental Study. Earth Environ. Sci. 2017, 9, 354–371. [CrossRef]
23. Ngongondo, C.; Li, L.; Gong, L.; Xu, C.-Y.; Alemaw, B.F. Flood frequency under changing climate in the upper kafue river basin, southern africa: A large scale hydrological model application. Stoch. Environ. Res. Risk Assess. 2013, 27, 1883–1898. [CrossRef]
24. López, J.; Goñi, M.; Martín, I.S.; Erro, J. Regional frequency analysis of annual maximum daily rainfall in Navarra. Quantiles mapping. Ing. Del Agua 2019, 23, 33–51. [CrossRef]
25. Bhunia, G.S.; Shit, P.K.; Maiti, R. Comparison of GIS-based interpolation methods for spatial distribution of soil organic carbon (SOC). J. Saudi Soc. Agric. Sci. 2018, 17, 114–126. [CrossRef]
26. Vargas, A.; Santos, A.; Cárdenas, E.; Obregón, N. Distribution and spatial interpolation of rainfall in Bogotá, Colombia. Dyna 2011, 167, 151–159.
27. Simpson, G.; Wu, Y.H. Accuracy and Effort of Interpolation and Sampling: Can GIS Help Lower Field Costs? Int. J. Geo-Inf. 2014, 3, 1317–1333. [CrossRef]
28. Mohamed, M.; Attia, K.; Azab, S. ssessment of Coastal Vulnerability to Climate Change Impacts using GIS and Remote Sensing: A Case Study of Al-Alamein New City. J. Clean. Prod. 2021, 290, 125723.
29. Malam Issa, O.; Valentin, C.; Rajot, J.L.; Cerdan, O.; Desprats, J.F.; Bouchet, T. Runoff generation fostered by physical and biological crusts in semi-arid sandy soils. Geoderma 2011, 167–168, 22–29. [CrossRef]
30. Dunne, T. Relation of field studies and modeling in the prediction of storm runoff. J. Hydrol. 1983, 65, 25–48. [CrossRef]
31. Barling, R.D.; Moore, I.D.; Grayson, R.B. A quasi-dynamic wetness index for characterizing the spatial distribution of zones of surface saturation and soil water content. Water Resour. Res. 1994, 30, 1029–1044. [CrossRef]
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spelling Salgado-Cassiani, Julio JoseCoronado-Hernández, Oscar E.Gustavo, GaticaLinfati, RodrigoCoronado-Hernandez, Jairo R.Coronado Hernández, Oscar E.2022-06-08T12:21:59Z2022-06-08T12:21:59Z2022-04-10Salgado-Cassiani, J.J.; Coronado-Hernández, O.E.; Gatica, G.; Linfati, R.; Coronado-Hernández, J.R. Probabilistic Approach to Determine the Spatial Distribution of the Antecedent Moisture Conditions for Different Return Periods in the Atlántico Region, Colombia. Water 2022, 14, 1217. https://doi.org/ 10.3390/w14081217https://hdl.handle.net/11323/9219https://doi.org/ 10.3390/w1408121710.3390/w140812172073-4441Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Previous soil moisture conditions play an important role in the design of hydraulic structures because they are directly related to the runoff threshold associated with a return period. These represent one of the main determinants of the runoff response of a drainage basin. One of the main difficulties facing hydrologists in Colombia lies in the time spent gathering and analyzing information related to the selection of antecedent moisture conditions. In this study, complete records from 19 rainfall stations located in the Atlántico region, Colombia, were used to analyze the cumulative precipitation during the 5 days prior to the annual maximum daily precipitation associated with different return periods using the Gev, Gumbel, Pearson Type III and Log Pearson Type III probability distributions. Different interpolation methods (IDW, kriging and spline) were applied to evaluate the spatial distribution of the antecedent moisture conditions. The main contribution of this research is establishing, using a probabilistic approach, the behavior of antecedent moisture conditions in a particular region, which can be used by engineers and designers to plan water infrastructure. This probabilistic approach was applied to a case study of the Atlántico region, Colombia, where the spatial distribution of antecedent moisture conditions was calculated for several return periods. The results indicate that the better results were obtained with the IDW interpolation method, and the Pearson Type III and Gumbel distributions also showed the best fits based on the Akaike criterion.24 páginasapplication/pdfengMultidisciplinary Digital Publishing Institute (MDPI)SwitzerlandAtribución 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_abf2Probabilistic approach to determine the spatial distribution of the antecedent moisture conditions for different return periods in the Atlántico region, 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/acceptedVersionhttps://www.mdpi.com/2073-4441/14/8/1217/htmColombiaAtlánticoWater1. Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology, 1st ed.; McGraw-Hill: New York, NY, USA, 1988; pp. 350–376.2. Ceballos, A.; Schnabel, S. Hydrological behaviour of a small catchment in the dehesa landuse system (Extremadura, SW Spain). J. Hydrol. 1998, 210, 146–160. [CrossRef]3. Dusek, J.; Vogel, T. Hillslope-storage and rainfall-amount thresholds as controls of preferential stormflow. J. Hydrol. 2016, 534, 590–605. [CrossRef]4. Berne, A.; Delrieu, G.; Creutin, J.D.; Obled, C. Temporal and spatial resolution of rainfall measurements required for urban hydrology. J. Hydrol. 2004, 299, 166–179. [CrossRef]5. Manfreda, S.; Fiorentino, M.; Iacobellis, V. DREAM A distributed model for runoff, evapotranspiration, and antecedent soil moisture simulation. Adv. Geosci. 2005, 2, 31–39. [CrossRef]6. Lazzari, M.; Piccarreta, M.; Ray, L.R.; Manfreda, S. Modeling Antecedent Soil Moisture to Constrain Rainfall Thresholds for Shallow Landslides Occurrence. In Landslides: Investigation and Monitoring; Ram, L.R., Lazzari, M., Eds.; IntechOpen: London, UK, 2020. Available online: https://www.intechopen.com/chapters/72592 (accessed on 1 February 2022).7. Lazzari, M.; Piccarreta, M.; Manfreda, S. The role of antecedent soil moisture conditions on rainfall-triggered shallow landslides. Nat. Hazards Earth Syst. Sci. 2018, 1–11. Available online: https://nhess.copernicus.org/preprints/nhess-2018-371/ (accessed on 20 February 2022). [CrossRef]8. Poveda, G.; Jaramillo, A.; Gil, M.M.; Quinceno, N.; Mantilla, R.I. Seasonality in ENSO-related precipitation, river discharges, soil moisture, and vegetation index in Colombia. Water Resour. Res. 2001, 37, 2169–2178. [CrossRef]9. Kim, G.-S.; Lee, S.-g.; Lee, J.; Park, E.; Song, C.; Hong, M.; Ko, Y.-J.; Lee, W.-K. Effects of Forest and Agriculture Land Covers on Organic Carbon Flux Mediated through Precipitation. Water 2022, 14, 623. [CrossRef]10. Darouich, H.; Ramos, T.B.; Pereira, L.S.; Rabino, D.; Bagagiolo, G.; Capello, G.; Simionesei, L.; Cavallo, E.; Biddoccu, M. Water Use and Soil Water Balance of Mediterranean Vineyards under Rainfed and Drip Irrigation Management: Evapotranspiration Partition and Soil Management Modelling for Resource Conservation. Water 2022, 14, 554. [CrossRef]11. Waylen, P.; Poveda, G. El Niño-Southern Oscillation and aspects of western South American hydro-climatology. Hydrol. Process 2002, 16, 1247–1260. [CrossRef]12. de Alcântara, L.R.P.; Coutinho, A.P.; dos Santos Neto, S.M.; Carvalho de Gusmão da Cunha Rabelo, A.E.; Antonino, A.C.D. Modeling of the Hydrological Processes in Caatinga and Pasture Areas in the Brazilian Semi-Arid. Water 2021, 13, 1877. [CrossRef]13. U.S. Water Resources Council. A Uniform Technique for Determining Flood Flow Frequencies; Bulletin 15; U.S. Water Resources Council: Washington, DC, USA, 1967.14. Cunnane, C. Methods and merits of regional flood frequency analysis. J. Hydrol. 1988, 100, 269–290. [CrossRef]15. Webster, V.L.; Stedinger, J. Log-Pearson Type III Distribution and Its Application in Flood Frequency Analysis. I: Distribution Characteristics. J. Hydrol. Eng. 2007, 12, 482–491.16. Burgess, C.P.; Taylor, M.A.; Stephenson, T.; Mandal, A. Frequency analysis, infilling and trends for extreme precipitation for Jamaica (1895–2100). J. Hydrol. 2015, 3, 424–443. [CrossRef]17. González-Álvarez, Á.; Viloria-Marimón, O.; Coronado-Hernández, Ó.E.; Vélez-Pereira, A.; Tesfagiorgis, K.; Coronado-Hernández, J.R. Isohyetal Maps of Daily Maximum Rainfall for Different Return Periods for the Colombian Caribbean Region. Water 2019, 11, 358. [CrossRef]18. Pizarro, R.; Ingram, B.; Gonzalez-Leiva, F.; Valdés-Pineda, R.; Sangüesa, C.; Delgado, N.; García-Chevesich, P.; Valdés, J.B. WEBSEIDF: A Web-Based System for the Estimation of IDF Curves in Central Chile. Hydrology 2018, 5, 40. [CrossRef]19. Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control 1974, 19, 716–723. [CrossRef]20. Akaike, H. Information theory and an extension of the maximum likelihood principle. In Selected Papers of Hirotugu Akaike; Springer: Berlin/Heidelberg, Germany, 1998; pp. 199–213.21. Salas, J.D.; Obeysekera, J.; Vogel, R.M. Techniques for assessing water infrastructure for nonstationary extreme events: A review. Hydrol. Sci. J. 2018, 63, 325–352. [CrossRef]22. Ikechukwu, M.N.; Ebinne, E.; Idorenyin, U.; Raphael, N.I. Accuracy Assessment and Comparative Analysis of IDW, Spline and Kriging in Spatial Interpolation of Landform (Topography): An Experimental Study. Earth Environ. Sci. 2017, 9, 354–371. [CrossRef]23. Ngongondo, C.; Li, L.; Gong, L.; Xu, C.-Y.; Alemaw, B.F. Flood frequency under changing climate in the upper kafue river basin, southern africa: A large scale hydrological model application. Stoch. Environ. Res. Risk Assess. 2013, 27, 1883–1898. [CrossRef]24. López, J.; Goñi, M.; Martín, I.S.; Erro, J. Regional frequency analysis of annual maximum daily rainfall in Navarra. Quantiles mapping. Ing. Del Agua 2019, 23, 33–51. [CrossRef]25. Bhunia, G.S.; Shit, P.K.; Maiti, R. Comparison of GIS-based interpolation methods for spatial distribution of soil organic carbon (SOC). J. Saudi Soc. Agric. Sci. 2018, 17, 114–126. [CrossRef]26. Vargas, A.; Santos, A.; Cárdenas, E.; Obregón, N. Distribution and spatial interpolation of rainfall in Bogotá, Colombia. Dyna 2011, 167, 151–159.27. Simpson, G.; Wu, Y.H. Accuracy and Effort of Interpolation and Sampling: Can GIS Help Lower Field Costs? Int. J. Geo-Inf. 2014, 3, 1317–1333. [CrossRef]28. Mohamed, M.; Attia, K.; Azab, S. ssessment of Coastal Vulnerability to Climate Change Impacts using GIS and Remote Sensing: A Case Study of Al-Alamein New City. J. Clean. Prod. 2021, 290, 125723.29. Malam Issa, O.; Valentin, C.; Rajot, J.L.; Cerdan, O.; Desprats, J.F.; Bouchet, T. Runoff generation fostered by physical and biological crusts in semi-arid sandy soils. Geoderma 2011, 167–168, 22–29. [CrossRef]30. Dunne, T. Relation of field studies and modeling in the prediction of storm runoff. J. Hydrol. 1983, 65, 25–48. [CrossRef]31. Barling, R.D.; Moore, I.D.; Grayson, R.B. A quasi-dynamic wetness index for characterizing the spatial distribution of zones of surface saturation and soil water content. Water Resour. Res. 1994, 30, 1029–1044. 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