{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T00:37:20Z","timestamp":1760575040986,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:00:00Z","timestamp":1760486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005283","name":"Funda\u00e7\u00e3o Cearense de Apoio ao Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["UNI-0210-00316.01.00\/23"],"award-info":[{"award-number":["UNI-0210-00316.01.00\/23"]}],"id":[{"id":"10.13039\/501100005283","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Water"],"abstract":"<jats:p>In semi-arid regions, flood events are often characterized by rapid runoff and high hydrological variability, posing significant challenges for infrastructure safety and flood risk assessment. Traditional flood frequency analysis methods, typically based on univariate models using annual flood peak, may fail to capture the full complexity of such events. This study investigates the limitations of the univariate approach through the analysis of the 2004 flood event in the Jaguaribe River basin (Brazil), which caused the Castanh\u00e3o Reservoir to receive a discharge of more than 5 hm3 and fill from 4.5% to over 70% of its capacity in just 55 days. Although the peak discharge in 2004 was not an exceptional record, the combination of high flood volume and short duration revealed a much rarer event than suggested by peak flow alone. To improve compound flood risk assessment, a bivariate frequency analysis based on copula functions was applied to jointly model flood peak and average flood intensity. The latter is a variable newly proposed in this study to better capture the short-duration but high-volume flood until peak that can strongly influence dam safety. Specifically, for the 2004 event, the univariate return period of flood peak was only 35 years, whereas the joint return period incorporating both peak flow and average flood intensity reached 995 years\u2014underscoring a potential underestimation of flood hazard when relying solely on peak flow metrics. Our bivariate return periods and the average flood intensity metric provide actionable information for climate adaptation, supporting adaptive rule curves and risk screening during initial impoundment and high-inflow events in semi-arid reservoirs. Collectively, the proposed methodology offers a more robust framework for assessing extreme floods in intermittent river systems and offers practical insights for dam safety planning in climatically variable regions such as the Brazilian Semi-Arid.<\/jats:p>","DOI":"10.3390\/w17202963","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:12:29Z","timestamp":1760523149000},"page":"2963","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bivariate Return Period Copula Application of Flood Peaks and Volumes for Climate Adaptation in Semi-Arid Regions"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9317-3645","authenticated-orcid":false,"given":"T. M. C.","family":"Studart","sequence":"first","affiliation":[{"name":"Hydraulic and Environmental Engineering Department (DEHA), Federal University of Cear\u00e1, Fortaleza 60440-900, CE, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1756-0429","authenticated-orcid":false,"given":"J. D.","family":"Pontes Filho","sequence":"additional","affiliation":[{"name":"Research Institute for Meteorology and Water Resources (FUNCEME), Fortaleza 60115-221, CE, Brazil"}]},{"given":"G. R.","family":"Gomez","sequence":"additional","affiliation":[{"name":"Hydraulic and Environmental Engineering Department (DEHA), Federal University of Cear\u00e1, Fortaleza 60440-900, CE, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5221-1139","authenticated-orcid":false,"given":"M. M.","family":"Portela","sequence":"additional","affiliation":[{"name":"Civil Engineering Research and Innovation for Sustainability (CERIS), Instituto Superior Tecnico (IST), University of Lisbon (UL), 1649-004 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5989-1731","authenticated-orcid":false,"given":"F. A.","family":"Sousa Filho","sequence":"additional","affiliation":[{"name":"Hydraulic and Environmental Engineering Department (DEHA), Federal University of Cear\u00e1, Fortaleza 60440-900, CE, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1038\/d41586-023-00626-9","article-title":"Flash Floods: Why Are More of Them Devastating the World\u2019s Driest Regions? Setting the Agenda in Research","volume":"615","author":"Yin","year":"2023","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nabinejad, S., and Sch\u00fcttrumpf, H. (2023). Flood Risk Management in Arid and Semi-Arid Areas: A Comprehensive Review of Challenges, Needs, and Opportunities. Water, 15.","DOI":"10.3390\/w15173113"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Villarini, G., and Smith, J.A. (2010). Flood Peak Distributions for the Eastern United States. Water Resour. Res., 46.","DOI":"10.1029\/2009WR008395"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.advwatres.2004.09.010","article-title":"Distribution of the Extreme Peak Floods of the Tiber River from the XV Century","volume":"28","author":"Calenda","year":"2005","journal-title":"Adv. Water Resour."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1111\/j.1753-318X.2008.00022.x","article-title":"Bivariate Flood Frequency Analysis: Part 1. Determination of Marginals by Parametric and Nonparametric Techniques","volume":"1","author":"Karmakar","year":"2008","journal-title":"J. Flood Risk Manag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1007\/s11269-005-9008-9","article-title":"Fitting Drought Duration and Severity with Two-Dimensional Copulas","volume":"20","author":"Shiau","year":"2006","journal-title":"Water Resour. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"100227","DOI":"10.1016\/j.wace.2019.100227","article-title":"Evaluating the Effects of Climate Extremes on Crop Yield, Production and Price Using Multivariate Distributions: A New Copula Application","volume":"26","author":"Alidoost","year":"2019","journal-title":"Weather Clim. Extrem."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Filho, J.P., Portela, M., Studart, T., and Souza Filho, F. (2020). A Continuous Drought Risk Monitoring System, CDRMS, Based on Copulas. Water: Ecology and Management, Vide Leaf.","DOI":"10.37247\/WEM.1.2020.7"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1016\/j.jhydrol.2015.05.030","article-title":"Copula Based Drought Frequency Analysis Considering the Spatio-Temporal Variability in Southwest China","volume":"527","author":"Xu","year":"2015","journal-title":"J. Hydrol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1061\/(ASCE)1084-0699(2007)12:4(347)","article-title":"Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask","volume":"12","author":"Genest","year":"2007","journal-title":"J. Hydrol. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jhydrol.2006.06.033","article-title":"Bivariate Rainfall Frequency Distributions Using Archimedean Copulas","volume":"332","author":"Zhang","year":"2007","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Favre, A.C., Adlouni, S.E., Perreault, L., Thi\u00e9monge, N., and Bob\u00e9e, B. (2004). Multivariate Hydrological Frequency Analysis Using Copulas. Water Resour. Res., 40.","DOI":"10.1029\/2003WR002456"},{"key":"ref_13","first-page":"968","article-title":"Relation Entre Pics et Volumes de Crues: \u00c9tude Des D\u00e9terminants Climatiques et Hydrologiques","volume":"60","author":"Szolgay","year":"2015","journal-title":"Hydrol. Sci. J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pontes Filho, J.D., Souza Filho, F.d.A., Martins, E.S.P.R., and Studart, T.M.d.C. (2020). Copula-Based Multivariate Frequency Analysis of the 2012\u20132018 Drought in Northeast Brazil. Water, 12.","DOI":"10.3390\/w12030834"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s00704-011-0524-7","article-title":"Bivariate Drought Frequency Analysis Using the Copula Method","volume":"108","author":"Mirabbasi","year":"2012","journal-title":"Theor. Appl. Climatol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1061\/(ASCE)1084-0699(2005)10:1(50)","article-title":"Bivariate Statistical Approach to Check Adequacy of Dam Spillway","volume":"10","author":"Salvadori","year":"2005","journal-title":"J. Hydrol. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.geodrs.2015.11.001","article-title":"Classification and Development of Shallow Soils (<50cm) in the USA","volume":"6","author":"Bockheim","year":"2015","journal-title":"Geoderma Reg."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1007\/s00267-015-0444-x","article-title":"Paradigms and Public Policies on Drought in Northeast Brazil: A Historical Perspective","volume":"55","author":"Campos","year":"2015","journal-title":"Environ. Manag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1007\/s00704-019-02930-9","article-title":"Rainfall-Related Natural Disasters in the Northeast of Brazil as a Response to Ocean-Atmosphere Interaction","volume":"138","author":"Silva","year":"2019","journal-title":"Theor. Appl. Climatol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5041","DOI":"10.5194\/hess-22-5041-2018","article-title":"Seasonal Drought Prediction for Semiarid Northeastern Brazil: Verification of Six Hydro-Meteorological Forecast Products","volume":"22","author":"Delgado","year":"2018","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1002\/qj.49710343505","article-title":"Dynamics of Climatic Hazards in Northeast Brazil","volume":"103","author":"Heller","year":"1977","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s10584-011-0227-1","article-title":"Exploring the Climate Problems of Brazil\u2019s Nordeste: A Review","volume":"112","author":"Hastenrath","year":"2012","journal-title":"Clim. Chang."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1175\/1520-0442(1998)011<0551:TRBTPA>2.0.CO;2","article-title":"The Relationships between Tropical Pacific and Atlantic SST AndNortheast Brazil Monthly Precipitation","volume":"11","author":"Uvo","year":"1998","journal-title":"J. Clim."},{"key":"ref_24","unstructured":"U.S. Department of the Interior Bureau of Reclamation (2014). Design Standards No. 13 Dams."},{"key":"ref_25","unstructured":"International Commission on Large Dams-Commission Internationale Des Grands Barrages (2017). Dam Surveillance Lessons Learnt from Case Histories, International Commission on Large Dams-Commission Internationale Des Grands Barrages."},{"key":"ref_26","unstructured":"Du, \u00c9., Dans, R., De, L.G., S\u00e9curit\u00e9, L.A., and Barrage, D.U. (2005). Risk Assessment in Dam Safety Management A Reconnaissance of Benefits, Methods and Current Applications, Association of State Dam Safety Officials."},{"key":"ref_27","unstructured":"(2013). Dam Safety Guidelines 2007, Canadian Dam Association."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.aqpro.2015.02.057","article-title":"Flood Frequency Analysis of Tel Basin of Mahanadi River System, India Using Annual Maximum and POT Flood Data","volume":"4","author":"Guru","year":"2015","journal-title":"Aquat. Procedia"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1515\/johh-2016-0049","article-title":"Joint Modelling of Flood Peaks and Volumes: A Copula Application for the Danube River","volume":"64","author":"Papaioannou","year":"2016","journal-title":"J. Hydrol. Hydromech."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Joe, H. (1997). Multivariate Models and Dependence Concepts, Chapman & Hall.","DOI":"10.1201\/9780367803896"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v052.i03","article-title":"Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine","volume":"52","author":"Brechmann","year":"2013","journal-title":"J. Stat. Softw."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zehe, E., and Bl\u00f6schl, G. (2004). Predictability of Hydrologic Response at the Plot and Catchment Scales: Role of Initial Conditions. Water Resour. Res., 40.","DOI":"10.1029\/2003WR002869"},{"key":"ref_33","first-page":"56","article-title":"Mecanismos Atmosf\u00e9ricos Associados \u00e0 Ocorr\u00eancia de Precipita\u00e7\u00e3o Intensa Sobre o Nordeste do Brasil Durante Janeiro\/2004","volume":"21","author":"Ferreira","year":"2006","journal-title":"Rev. Bras. De Meteorol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1016\/j.envsci.2011.05.017","article-title":"Flash Flood Forecasting, Warning and Risk Management: The HYDRATE Project","volume":"14","author":"Borga","year":"2011","journal-title":"Environ. Sci. Policy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/qj.29","article-title":"Flash Flood Forecasting: What Are the Limits of Predictability?","volume":"133","author":"Collier","year":"2007","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.jhydrol.2016.04.007","article-title":"A Method for Probabilistic Flash Flood Forecasting","volume":"541","author":"Hardy","year":"2016","journal-title":"J. Hydrol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.5194\/hess-16-1543-2012","article-title":"Extreme Flood Response to Short-Duration Convective Rainfall in South-West Germany","volume":"16","author":"Borga","year":"2012","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1016\/j.advwatres.2005.09.005","article-title":"Asymmetric Copula in Multivariate Flood Frequency Analysis","volume":"29","author":"Grimaldi","year":"2006","journal-title":"Adv. Water Resour."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.jhydrol.2014.03.044","article-title":"Variability and Trend in the Hydrology of the Yangtze River, China: Annual Precipitation and Runoff","volume":"513","author":"Chen","year":"2014","journal-title":"J. Hydrol."}],"container-title":["Water"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4441\/17\/20\/2963\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:26:14Z","timestamp":1760523974000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4441\/17\/20\/2963"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,15]]},"references-count":39,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["w17202963"],"URL":"https:\/\/doi.org\/10.3390\/w17202963","relation":{},"ISSN":["2073-4441"],"issn-type":[{"value":"2073-4441","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,15]]}}}