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References on Copula Function topic

This page is managed by Jing Li, University of Adelaide,

I update January 15th, 2009...thanks to Francesco Serinaldi, Sander Vandenberghe and Emna Gargouri.
II update Fabruary 23th, 2009...thanks to Francesco Serinaldi, Emna Gargouri, Taha Ouarda, Shenglian Guo

III update March 15th, 2009.....thanks to Sander Vandenberghe
IV update April 22nd, 2009.....thanks to Salvatore Grimaldi

V update May 20th, 2009....thanks to Taha Ouarda
VI update June 16, 2009....thanks to
Sander Vandenberghe
VII update July 27, 2009....thanks to Arturo Erdely, Sander Vandenberghe, Salvatore Grimaldi
VIII update September 21, 2009......thanks to Fateh Chebana, Salvatore Grimaldi

IX update October 15, 2009......thanks to Sander Vandenberghe, Salvatore Grimaldi
X update November 16, 2009.....thanks to
Sander Vandenberghe, Salvatore Grimaldi  (we have 141 references!!!!)
XI update December 15, 2009...thanks to Salvatore Grimaldi (Merry Christmas!!!)
XII update January 15, 2010......thanks to Salvatore Grimaldi (Happy New Year!!!)
XIII update February 15, 2010....thanks to Caroline Keef, Fateh Chebana, Emna Gargouri
XIV update March 15, 2010.......thanks to
Sander Vandenberghe
XV update April 15, 2010...........
thanks to Sander Vandenberghe, Ebru Eris and Salvatore Grimaldi
XVI update May 15, 2010...........thanks to Salvatore Grimaldi
XVII update June 16, 2010...........thanks to Sander Vandenberghe and Salvatore Grimaldi
XVIII update July 15, 2010........thanks to Salvatore Grimaldi and Sander Vandenberghe
XIX update September 15, 2010.......Thanks to Hemant Chowdhary, Salvatore Grimaldi and Sander Vandenberghe
XX update October 15, 2010......Thanks to Salvatore Grimaldi and Sander Vandenberghe
XXI update November 16, 2010......Thanks to Arturo Erdely, Hemant Chowdhary and Salvatore Grimaldi
XXII update December 20, 2010......Thanks to Salvatore Grimaldi and Sander Vandenberghe
XXIII update January 17, 2011 ....Thanks to Sander Vandenberghe

XXIV update February 15, 2011.....Thanks to Salvatore Grimaldi and Sander Vandenberghe
XXV update March 28, 2011......Thanks to Salvatore Grimaldi
XXVI update April 15, 2011......Thanks to Salvatore Grimaldi and Sander Vandenberghe

XXVII update May 16, 2011........Thanks to Salvatore Grimaldi and Ebru Eris
XXVIII update June 15, 2011........Thanks to Sander Vandenberghe
XXIX update July 15, 2011...........Thanks to Fateh Chebana and Jing Li
XXX update August 16, 2011........Thanks to Sander Vandenberghe
XXXI update September 20, 2011........Thanks to Uwe Haberlandt and Salvatore Grimaldi
XXXII update October 11, 2011........Thanks to Salvatore Grimaldi
XXXIII update December 5, 2011........Thanks to Salvatore Grimaldi and Jing Li
XXXIV update December 22, 2011........Thanks to Salvatore Grimaldi
XXXV update December 24, 2011......Thanks to Salvatore Grimaldi and Jing Li(Merry Christmas!!!)
XXXVI update January 1 , 2012......Thanks to Salvatore Grimaldi and Jing Li

XXXVII update Feburary 23 , 2012......Thanks to Salvatore Grimaldi and Jing Li
XXXVIII update March 16, 2012......Thanks to Amir AghaKouchak and Salvatore Grimaldi
XXXIX update April 25, 2012......Thanks to Jing Li
XXXX update May 14, 2012......Thanks to Jing Li
XXXXI update June 25, 2012......Thanks to Jing Li
XXXXII update August 22, 2012......Thanks to Jing Li
XXXXIII update October 15, 2012......Thanks to Jing Li
XXXXIV update November 26, 2012......Thanks to Guangtao Fu and Jing Li
XXXXV update December 21, 2012......Thanks to Fateh Chebana and Amir AghaKouchak
XXXXVI update January 22, 2012...... Thanks to Jing Li
XXXXVII update Feburary 28, 2013...... Thanks to Phil Howlett and Jing Li (Notice that we have updates in 2012 and 2007)
XXXXVIII update April 16, 2013....thanks to Salvatore Grimaldi, Fateh Chebana, Jing Li, and
Amir AghaKouchak
XXXXIX update October 24, 2013...thanks to Thomas Wahl
XXXXX update November 8, 2013....thanks to Salvatore Grimaldi and Xing Zheng Wu
XXXXXI update May 19, 2014...thanks to Amir AghaKouchak and Thomas Wahl
XXXXXII update December 1, 2014 thanks to Jing Li, Fateh Chabana, and  Nejc Bezak
XXXXXIII update January 12, 2015 thanks to
Amir AghaKouchak
XXXXXIV update February 23, 2015 thanks to Niko Verhoest
XXXXXV update December, 2015 thanks to Niko Verhoest
XXXXXVI update March, 2016 thanks to Ana Requena

References with *star are the last update

This page will list papers that decribe Copula applications or paper published in "applicative" Journals . For theoretical paper related to Copula please refer to Copula Wiki (

Before 2003

Deheuvels, P. (1979), Empirical dependence function and properties - nonparametric test of independence, Bulletin De La Classe, Des Sciences Academie Royale De Belgique, 65 (6), 274–292.

Genest, C., and L. P. Rivest (1993), Statistical inference procedures for bivariate Archimedean copulas, Journal of the American Statistical Association, 88 (423), 1034–1043.

Genest, C., K. Ghoudi, and L. P. Rivest (1995), A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82 (3), 543–552.

Shih, J. H., and T. A. Louis (1995), Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51 (4), 1384–1399.

Ghoudi, K., A., Khoudraji et L.P., Rivest (1998) Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles. Rev Can  Stat. 26 (1), 187-197.

Durrleman, V., A. Nikeghbali, and T.Roncalli (2000), Which copula is the right one?, Tech. rep., Groupe de Recherche Opérationnelle, Crédit Lyonnais.

Belguise, O. (2001) Tempêtes: étude des dépendances entre les branches auto et incendie avec la théorie des copulas. Mémoire DUAS 3ème année : Actuariat : Strasbourg 1,   Université Louis Pasteur, Strasbourg, France.

Genest, C., and L. P. Rivest (2001), On the multivariate probability integral transformation, Statistics & Probability Letters, 53 (4), 391–399.

Nagaraja H.N., Choudhary P.K., Matalas N. (2002) “Number of Records in a Bivariate Sample with Application to Missouri River Flood Data” Methodology And Computing In Applied Probability, Volume 4, Number 4, December 2002 , pp. 377-391(15)

Roncalli, T. (2002) Théorie des valeurs extrêmes. DESS, Université Paris IX Dauphine, France.


De Michele C, Salvadori G (2003) A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. Journal of Geophysical Research, 108(D2), 4067, doi:10.1029/2002JD002534.

Genest, C., and J. C. Boies (2003), Detecting dependence with Kendall plots, American Statistician, 57 (4), 275–284.


Beersma JJ, Buishand TA (2004) Joint probability of precipitation and discharge deficits in the Netherlands. Water Resources Research 40:W12508, doi:10.1029/2004WR003265.

Favre A-C, El Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40:W01101, doi:10.1029/2003WR002456.

Hall P.; Tajvidi N. (2004) “Prediction Regions for Bivariate Extreme Events” Australian & New Zealand Journal of Statistics, Volume 46, Number 1, March 2004 , pp. 99-112(14)

Hürlimann, W. (2004) Fitting bivariate cumulative returns with copulas Comp. Statis. Data Anal. 45, 355–372.

Salvadori G, De Michele C (2004) Analytical calculation of storm volume statistics involving Pareto-like intensity-duration marginals. Geophysical Research Letters, 31, L04502, doi:10.1029/2003GL018767.

Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resources Research, 40:W12511, doi:10.1029/2004wr003133.

Salvadori, G. (2004), Bivariate return periods via 2-copulas, Statistical Methodology, 1, 129–144.

Sancetta, A., Satchell, S. (2004) The Bernstein copula and its applications to modeling and approximations of multivariate distributions. Econometric Theory 20, 535-562.

Wist, H. T., D. Myrhaug, and H. Rue (2004), Statistical properties of successive wave heights and successive wave periods, Applied Ocean Research, 26 (3-4), 114–136.


De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydrologic Engineering, 10(1), 50–57.

de Waal DJ, van Gelder PHAJM (2005),  Modelling of extreme wave heights and periods through copulas.  Extremes, 8, 345–356.

Fermanian, J. D. (2005), Goodness-of-fit tests for copulas, Journal of Multivariate Analysis, 95 (1), 119–152.

Frahm, G., M. Junker, and R. Schmidt (2005), Estimating the tail-dependence coefficient: properties and pitfalls, Insurance Mathematics & Economics, 37 (1), 80–100.

Genest, C., and B. Rémillard (2005), Validity of the parametric bootstrap for goodness-of-fit testing in semiparametrica1 models, Tech. rep., Groupe d’études et de Recherche en Analyse des Décisions.

Trivedi, P.K., Zimmer, D.M. (2005) Copula Modeling: An Introduction for Practitioners. Foundations and Trends in Econometrics 1, 1-111.

Vrac, M., A. Chedin, and E. Diday (2005), Clustering a global field of atmospheric profiles by mixture decomposition of copulas, Journal of Atmospheric and Oceanic Technology, 22 (10), 1445–1459.


Bárdossy A (2006) Copula-based geostatistical models for groundwater quality parameters. Water Resources Research, 42, W11416, doi:10.1029/2005WR004754.

Genest, C., J. F. Quessy, and B. Remillard (2006), Goodness-of-fit procedures for copula models based on the probability integral transformation, Scandinavian Journal of Statistics, 33 (2), 337–366.

Grimaldi S, Serinaldi F (2006) Design hyetographs analysis with 3-copula function. Hydrological Sciences Journal, 51(2), 223−238.

Grimaldi S, Serinaldi F (2006) Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources, 29(8), 1115–1167.

Huard, D., G. Evin, and A. C. Favre (2006), Bayesian copula selection, Computational Statistics and Data Analysis, 51 (2), 809–822.

Kolev, N., U. dos Anjos, and B. V. D. Mendes (2006), Copulas: A review and recent developments, Stochastic Models, 22 (4), 617–660.

Renard B, Lang M (2006) Use of a Gaussian copula for multivariate extreme value analysis. Advances in Water Resources, doi:10.1016/j.advwatres.2006.08.001.

Salvadori G, De Michele C (2006) Statistical characterization of temporal structure of storms. Advances in Water Resources, 29(6), 827–842.

Shiau JT (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resources Management, 20, 795–815, 2006.

Shiau, J. T., H. Y. Wang, and C. T. Tsai (2006), Bivariate frequency analysis of floods using copulas, Journal of American Water Resources Association, 42 (6), 1549–1564.

Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. Journal of Hydrologic Engineering 11(2), 150–164.


Chebana, F., and T.B.M.J., Ouarda (2007). “Multivariate L-moment homogeneity test”, Water Resources Research. 43, W08406, doi:10.1029/2006WR005639, 1-14.

de Waal DJ, van Gelder PHAJM, Nel A (2007) Estimating joint tail probabilities of river discharges through the logistic copula, Environmetrics, 18, 621–631.

De Michele, C., G. Salvadori, G. Passoni, and R. Vezzoli (2007), A multivariate model of sea storms using copulas, Coastal Engineering, 54 (10), 734–751.

Dupuis DJ (2007) Using copulas in hydrology: Benefits, cautions, and issues. Journal of Hydrologic Engineering, 12(4): 381–393.

Gao, H., E. Wood, M. Drusch, and M. McCabe (2007), Copula-derived observation operators for assimilating TMI and AMSR-E retrieved soil moisture into land surface models, Journal of Hydrometeorology, 8 (3), 413–429.

Gebremichael M, Krajewski WF (2007) An application of copulas to modeling temporal sampling errors in satellite-derived rainfall estimates.  Journal of Hydrologic Engineering, 12(4), 404-408.

Genest C, Favre A-C. (2007) Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12(4), 347 - 368.

Genest C, Favre A-C, Béliveau J, Jacques C (2007) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resources Research, 43: W09401, doi:10.1029/2006WR005275.

Kao S-C, Govindaraju RS (2007) A bivariate frequency analysis of extreme rainfall with implications for design. Journal of Geophysical Research, 112, D13119, doi:10.1029/2007JD008522.

Kao S-C, Govindaraju RS (2007) Probabilistic structure of storm surface runoff considering the dependence between average intensity and storm duration of rainfall events. Water Resources Research, 43, W06410, doi:10.1029/2006WR005564.

Kim, G., M. J. Silvapulle, and P. Silvapulle (2007), Comparison of semiparametric and parametric methods for estimating copulas, Computational Statistics & Data Analysis, 51 (6), 2836–2850.

Kuhn G, Khan S, Ganguly AR, Branstetter ML (2007) Geospatial–temporal dependence among weekly precipitation extremes with applications to observations and climate model simulations in South America. Advances in Water Resources, 30, 2401–2423.

Matús, R. (2007), The modelling of hydrological joint events using aggregation operators, Ph.D. thesis, Slovak University of Technology Bratislava, Faculty of Civil Engineering, Bratislava, Slovakia.

Qin Z, Sun G, Yan T, Song H, Zhang J (2007), Application of multivariate probability analysis using copulas to ocean engineering. Marine Forecasts (in Chinese), 24(2), 83-90.

Piantadosi, J., P. G. Howlett and J. Boland (2007), Matching the grade correlation coefficient using a copula with maximum disorder, Journal of Industrial and Management Optimization, 3(2), P. 305-312.

Poulin A, Huard D, Favre A-C, Pugin S (2007) Importance of tail dependence in bivariate frequency analysis. Journal of Hydrologic Engineering, 12(4), 394–403.

E. Porcu, J. Mateu (2007) “Mixture-based modeling for space-time data Environmetrics” Volume 18, Issue 3, May 2007,  285-302

Renard, B., and M. Lang (2007), Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology, Advances In Water Resources, 30 (4), 897–912.

Salvadori G, De Michele C (2007) On the Use of Copulas in Hydrology: Theory and Practice. Journal of Hydrologic Engineering, 12(4), 369–380.

Salvadori G., C. De Michele, N.T. Kottegoda, and R. Rosso. Extremes in Nature. An approach using Copulas, volume 56 of Water Science and Technology Library Series. Springer, Dordrecht, 2007. ISBN: 978-1-4020-4415-1.

Shiau JT, Feng S, Nadarajah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrological Processes, 21(16), 2157–2163.

Serinaldi, F. (2007), Analysis of inter-gauge dependence by Kendall’s tau, upper tail dependence coefficient, and 2-copulas with application to rainfall fields, Stochastic Environmental Research and Risk Assessment, doi:10.2007/s00477-007-0176-4.2

Serinaldi, F., and S. Grimaldi (2007), Fully nested 3-copula: procedure and application on hydrological data, Journal of Hydrologic Engineering, 12 (4), 420–430.

Singh VP, Zhang L (2007) IDF curves using the Frank Archimedean copula. Journal of Hydrologic Engineering, doi: 10.1061/(ASCE)1084-0699(2007)12:6(651).

Yan, J. (2007), Enjoy the joy of copulas: with a package copula, Journal of Statistical Software, 21 (4).

Yan B, Guo S, Xiao Y (2007). Synchronous-asynchronous encounter probability of rich-poor precipitation between water source area and water receiving areas in the Middle Route of South-to-North Water Transfer Project. Journal of China Hydraulic Engineering (in Chinese), 38(10), 1178-1185.

Yan B, Guo S, Xiao Y, Fang B (2007), Analysis on Drought Characteristics Based on Bivariate Joint Distribution. Arid Zone Research (in Chinese), 24(4), 537-542.

Xiao Y, Guo S, Xiong L, Liu P, Fang B (2007), A new random simulation method for constructing synthetic flood hydrographs. Journal of Sichuan University: Engineering Science Edition (in Chinese), 39(2), 55-60.

Xiao Y, Guo S, Liu P, Fang B (2007), Derivation of design flood hydrograph based on Copula function. Journal of Wuhan University (in Chinese), 40(4), 13-17

Zhang L, Singh VP (2007) Gumbel-Hougaard copula for trivariate rainfall frequency analysis. Journal of Hydrologic Engineering, 12(4), 409-419.

Zhang L, Singh VP (2007) Trivariate flood frequency analysis using the Gumbel-Hougaard copula. Journal of Hydrologic Engineering, 12(4), 431-439.   

Zhang L, Singh VP (2007) Bivariate rainfall frequency distributions using Archimedean copulas. Journal of Hydrology, 332, 93-109 doi:10.1016/j.jhydrol.2006.06.033.


El Adlouni, S. and T. B.M.J. Ouarda (2008). Étude de la loi conjointe Débit-Niveau par les copules: Cas de la rivière Châteauguay. Canadian Journal of Civil Engineering, 35: 1128-1137, DOI : 10.1139/L08-054.

Bárdossy A, Li J (2008) Geostatistical interpolation using copulas.  Water Resources Research 2008; doi:10.1029/2007WR006115.

L. Bel, J. N. Bacro, Ch. Lantuéjoul (2008) “Assessing extremal dependence of environmental spatial fields Environmetrics” Volume 19, Issue 2, Date: March 2008, Pages: 163-182

*De Michele C., G. Salvadori, and R. Rosso. Discussion of ”Bivariate flood frequency analysis using the copula method” by L. Zhang and V. P. Singh. J. Hydrol. Eng., 13(4):286–287, 2008. doi: 10.1061/(ASCE)1084-0699(2008)13:4(286).

Evin G, Favre A-C (2008) A new rainfall model based on the Neyman-Scott process using cubic copulas. Water Resources Research, 44: W03433, doi:10.1029/2007WR006054.

Fang B, Guo S, Xiao Y, Liu P, Wu J (2008), Annual maximum flood occurrence dates and magnitudes frequency analysis based on bivariate joint distribution. Advances in Water Science (in Chinese), 19(4), 505-511.

Feng P, Wang Z, Tian W (2008), Hydrological risk assessment of long-distance water transfer system based on the two-dimensional Gumbel distribution. Journal of Catastrophology (in Chinese), 23(1), 23-26.

Gargouri-Ellouze, E. & Chebchoub, A. (2008) Modélisation de la structure de dépendance hauteur–durée d’événements pluvieux par la copule de Gumbel. Hydrol. Sci. J. 53(4) 802-817. 

Guillotte, S.  and Perron, F., (2008) “A Bayesian estimator for the dependence function of a bivariate extreme-value distribution Un estimateur bayésien de la function de dépendance d'une loi des valeurs extrêemes bivariée” The Canadian Journal of Statistics/La revue canadienne de statistique, Volume 36, Number 3, September, pp. 383-396(14), Statistical Society of Canada/Societe statistique du Canada

Guo S, Yan B, Xiao Y, Fang B, Zhang N (2008). Application of Copula functions in multivariate hydrological analysis and estimation. Journal of Chinese Hydrology, 28(3), 1-7.

U. Haberlandt, A.-D. Ebner von Eschenbach, and I. Buchwald (2008) “A space-time hybrid hourly rainfall model for derived flood frequency analysis” Hydrol. Earth Syst. Sci., 12, 1353-1367, 2008

Kallenberg, W. C.M. (2008)  Modelling dependence. Insurance: Mathematics and Economics 42, 127–146.

Kao S-C, Govindaraju RS (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resources Research, 44, W02415, doi:10.1029/2007WR006261.

Klein, B., Schumann, A., Pahlow, M. (2008) Application of multivariate statistical methods in flood protection planning for river basins: The river unstrut case study [Hochwasserschutzplanung in Flussgebieten unter Verwendung der Multivariaten Statistik am Beispiel der Unstrut] Wasser Wirtschaft, 98 (11), pp. 29-34.

Lennartsson, J., A. Baxevani, and D. Chen (2008), Modelling precipitation in Sweden using multiple step markov chains and a composite model, Journal of Hydrology, 363 (1-4), 42–59, doi:10.1016/j.jhydrol.2008.10.003

Leonard M., Metcalfe A., Lambert M. (2008) “Frequency analysis of rainfall and streamflow extremes accounting for seasonal and climatic partitions” Journal of Hydrology, Volume 348, Issues 1-2, 1 January 2008, Pages 135-147

Li, Y.-H., Shi, B.-P., Zhang, J. (2008) Copula joint function and its application in probability seismic hazard analysis (2008) Acta Seismologica Sinica English Edition, 21 (3), pp. 296-305.

Maity R, Kumar DN (2008) Probabilistic prediction of hydroclimatic variables with nonparametric quantification of uncertainty. Journal of Geophysical Research, 113, D14105, doi:10.1029/2008JD009856.

Mercier, G., Moser, G., Serpico, S.B. (2008)  Conditional copulas for change detection in heterogeneous remote sensing images IEEE Transactions on Geoscience and Remote Sensing, 46 (5), pp. 1428-1441.

Miina, J., Heinonen, J. (2008) Stochastic simulation of forest regeneration establishment using a multilevel multivariate model Forest Science, 54 (2), pp. 206-219.

G. Moser, and S. B. Serpico (2008), Conditional copulas for change detection in heterogeneous remote sensing images, IEEE Transactions on Geoscience and Remote Sensing, 46 (5), 1428–1441, doi:10.1109/TGRS.2008.916476.

Nikoloulopoulos AK, Karlis D (2008) Fitting copulas to bivariate earthquake data: The seismic gap hypothesis revisited.  Environmetrics, 19, 251–269.

Norris, P. M., L. Oreopoulos, A. Y. Hou, W.-K. Tao, and X. Zeng, (2008) “Representation of 3D heterogeneous cloud fields using copulas: Theory for water clouds” QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 134: 1843–1864 (2008)

Pan, M., E. F. Wood, R. Wojcik, and M. F. McCabe (2008), Estimation of regional terrestrial water cycle using multi-sensor remote sensing observations and data assimilation, Remote Sensing of Environment, 112 (4), 1282–1294, doi: 10.1016/j.rse.2007.02.039

Serinaldi F (2008a) Analysis of inter-gauge dependence by Kendall’s τK, upper tail dependence coefficient, and 2-copulas with application to rainfall fields.  Stochastic Environmental Research and Risk Assessment, doi:10.1007/s00477-007-0176-4.

Serinaldi F (2008b).  Copula-based mixed models for bivariate rainfall data: An empirical study in regression perspective. Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-008-0249-z.

Sun, T. (2008), Modeling of multivariate rainfall data with autocorrelated discrete-continuous mixture margins using copulas, Ph.D. thesis, York University, Toronto, Toronto, Ontario.

Villarini G, Serinaldi F, Krajewski WF (2008) Modeling radar-rainfall estimation uncertainties using parametric and non-parametric approaches. Advances in Water Resources, 31(12), 1674–1686.

Xiao Y, Guo S, Liu P, Xiong L, Fang B (2008). Seasonal flood frequency analysis and flood prevention standard. Advances in Water Science (in Chinese), 19(1), 54-60.

Xiao, Y., Guo, S., Liu, P., Fang, B. (2008)  A new design flood hydrograph method based on bivariate joint distribution IAHS-AISH Publication, (319), pp. 75-82.

Xie, H., Huang, J.-S. Review of bivariate hydrological frequency distribution (2008) Shuikexue Jinzhan/Advances in Water Science, 19 (3), pp. 443-452.

Xu Y, Li J, Cao F, Ran Q (2008), Applications of Copula in hydrological extreme analysis. Journal of Zhejiang University (Engineering Science) (in Chinese), 42(7), 1119-1122.

Wang, M.; Rennolls, K.; Tang, S. (2008) “Bivariate Distribution Modeling of Tree Diameters and Heights: Dependency Modeling Using Copulas” Forest Science, Volume 54, Number 3, June 2008 , pp. 284-293(10)

Zhang N, Guo S, Yan B, Liu P (2008), Seasonal Design Flood Based on Copula Function. Journal of China Hydrology (in Chinese), 28(5), 28-32.

Zhang N, Guo S, Liu P, Yan B, Wan M (2008), Seasonal design floods and flood fontrol water levels based on Copula. Journal of Wuhan University (in Chinese), 41(6), 33-36.

Zhang T, Zhao C, Luo W (2008), Random simulation of flood hydrographs based on Copula function. Journal of Wuhan University (in Chinese), 41(4), 1-4.


Bárdossy, A., Pegram, G.G.S. Copula based multisite model for daily precipitation simulation  (2009) Hydrology and Earth System Sciences 13 (12), pp. 2299-2314

F.Chebana, T. B. M. J. Ouarda, P. Bruneau, M. Barbet, S. El Adlouni, M. Latraverse (2009) “Multivariate homogeneity testing in a northern case study in the province of Quebec, Canada” Hydrological Processes 23 (12),(p 1690-1700) DOI: 10.1002/hyp.7304

Chebana, F., and T. B. M. J. Ouarda (2009), Index flood-based multivariate regional frequency analysis, Water Resources Research, 45, doi:10.1029/2008WR007490.

Chen, J., Zhang, X.-C., Liu, W.-Z., Li, Z. (2009) Evaluating and extending cligen precipitation generation for the Loess Plateau of China Journal of the American Water Resources Association, 45 (2), pp. 378-396.

Cheng Wang, Ni-Bin Chang, Gour-Tsyh Yeh (2009) “Copula-based flood frequency (COFF) analysis at the confluences of river systems” Hydrological Processes, E23 (10), 1471-1486, doi:{10.1002/hyp.7273}

Chowdhary, H. (2009) Discussion of "IDF curves using the Frank Archimedean copula" by Vijay P. Singh and Lan Zhang Journal of Hydrologic Engineering, 14 (1), pp. 107-108.

Chowdhary, H., Singh, V.P. (2009) Copula approach for reducing uncertainty in design flood estimates in insufficient data situations Proceedings of World Environmental and Water Resources Congress 2009 - World Environmental and Water Resources Congress 2009: Great Rivers 342, pp. 4758-4771

Denault, M., Dupuis, D., Couture-Cardinal, S. Complementarity of hydro and wind power: Improving the risk profile of energy inflows  (2009) Energy Policy 37 (12), pp. 5376-5384

Gargouri-Ellouze, E., and Z. Bargaoui (2009), Investigation with Kendall plots of infiltration index-maximum rainfall intensity relationship for regionalization, Physics and Chemistry of the Earth, 34 (10-12), 642–653, doi:10.1016/j.pce.2009.02.001,

Gartsman, B., R. van Nooyen, and A. Kolechkina (2009), Implementation issues for total risk calculation for groups of sites, Physics and Chemistry of the Earth, 34 (10-12), 619–625, doi:10.1016/j.pce.2008.12.001,

Kao, S.-C., Govindaraju, R.S., Niyogi, D. (2009) A spatio-temporal drought analysis for the midwestern US  Proceedings of World Environmental and Water Resources Congress 2009 - World Environmental and Water Resources Congress 2009: Great Rivers 342, pp. 4654-4663

Karamouz, M., A. Ahmadi, and A. Moridi (2009), Probabilistic reservoir operation using bayesian stochastic model and support vector machine, Advances in Water Resources, 32 (11), 1588 – 1600, doi:10.1016/j.advwatres.2009.08.003.

Karmakar, S., Simonovic, S.P. (2009) “Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions” Journal of Flood Risk Management, Volume 2, Number 1, March 2009 , pp. 32-44(13)

Keef C., Svensson C.,  Tawn J. A. (2009) “Spatial dependence in extreme river flows and precipitation for Great Britain” Journal of Hydrology, vol. 378, Pages 240-252

He, X.  and P. Gong,  (2009) “Measuring the coupled risks: A copula-based CVaR model”.  Journal of Computational and Applied Mathematics 223, 1066–1080.

Li, S.-P., Feng, J.-F., Wang, H.-L. (2009) “Regime shifts of the marine ecosystem with copula”  Tianjin Daxue Xuebao (Ziran Kexue yu Gongcheng Jishu Ban)/Journal of Tianjin University Science and Technology 42 (6), pp. 533-538

Liu, Z.-M., Chen, Z.-S. (2009) Risk study of the bivariate encounter of interzone rainstorm and flood level of the outer river Shuikexue Jinzhan/Advances in Water Science 20 (5), pp. 619-625

Omar S. Muhaisen;  Francisco Osorio; Pedro A. García (2009) Two-copula based simulation for detention basin design Civil Engineering and Environmental Systems, 1029-0249, Volume 26, Issue 4, First published 2009, Pages 355 – 366

Osorio F. Muhaisen O.,and García P.A. (2009) Copula-Based Simulation for the Estimation of Optimal Volume for a Detention Basin J. Hydrologic Engrg. Volume 14, Issue 12, pp. 1378-1382

Mesfioui M., J.-F. Quessy, M.-H. Toupin (2009) "On a new goodness-of-fit process for families of copulas" Canadian Journal of Statistics,
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Naveau, P., A. Guillou, D. Cooley, and J. Diebolt (2009), Modelling pairwise dependence of maxima in space, Biometrika, 96 (1), 1-17, doi:{10.1093/biomet/asp001}.

Nijssen, D., A. Schumann, M. Pahlow, and B. Klein (2009), Planning of technical flood retention measures in large river basins under consideration of imprecise probabilities of multivariate hydrological loads, Natural Hazards and Earth System Sciences, 9 (4), 1349–1363.

Yan B, Guo S, Guo J, Zhang N (2009), Comparative study of multivariate hydrological frequency analysis methods. Journal of Wuhan University (in Chinese), 42(1).

P. Laux, S. Wagner, A. Wagner, J. Jacobeit, A. Bárdossy, H. Kunstmann (2009) “Modelling daily precipitation features in the Volta Basin of West Africa” International Journal of Climatology” 29 (7, Sp.Iss. SI), 937-954, doi:{10.1002/joc.1852}

Piantadosi, J., J. Boland, and P. Howlett (2009), Generating Synthetic Rainfall on Various Timescales-Daily, Monthly and Yearly, Environmental Modeling & Assessment, 14 (4), 431–438, doi:10.1007/s10666-008-9157-3, 17th

Pinya, M.A.S., Madsen, H., Rosbjerg, D. (2009) Assessment of the risk of inland flooding in a tidal sluice regulated catchment using multi-variate statistical techniques Physics and Chemistry of the Earth, 34 (10-12), pp. 662-669 doi: 10.1016/j.pce.2009.03.001

Serinaldi, F. (2009), A multisite daily rainfall generator driven by bivariate copula-based mixed distributions, Journal of Geophysical Research - Atmospheres, 114, doi:{10.1029/2008JD011258}.

Serinaldi, F. (2009), Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective, Stochastic Environmental Research and Risk Assessment, 23 (5), 677–693, doi:10.1007/s00477-008-0249-z.

Serinaldi, F., B. Bonaccorso, A. Cancelliere, and S. Grimaldi (2009), Probabilistic characterization of drought properties through copulas, Physics and Chemistry of the Earth, 34 (10-12), 596–605, doi:10.1016/j.pce.2008.09.004,

Singh, V.P., Zhang, L. (2009) Closure to "IDF curves using the Frank Archimedean copula" by Vijay P. Singh and Lan Zhang Journal of Hydrologic Engineering, 14 (1), p. 108.

Shiau J.T. and Modarres R. (2009) Copula-based drought severity-duration-frequency analysis in Iran Meteorological Applications  16: 481–489

Xu, Y.-P., Tong, Y.-B., Fu, Q., Zhu, R.(2009) “Impact analysis for rainfall depthsimulation of different durations through several Copulas”  Zhejiang Daxue Xuebao (Gongxue Ban)/Journal of Zhejiang University (Engineering Science) 43 (6), pp. 1107-1111



AghaKouchak, A., A. Bárdossy, and E. Habib (2010), Conditional simulation of remotely sensed rainfall data using a non-gaussian v- transformed copula, Advances in Water Resources, 33 (6), 624 – 634, doi:DOI:10.1016/j.advwatres.2010.02.010.

AghaKouchak, A., A. Bárdossy, and E. Habib (2010), Copula-based uncertainty modelling: application to multisensor precipitation estimates, Hydrological Processes, 24, 2111–2124, doi:10.1002/hyp.7632.

Aghakouchak, A., G. Ciach, and E. Habib (2010), Estimation of tail dependence coefficient in rainfall accumulation fields, Advances in Water Resources, 33(9), 1142-1149, doi:10.1016/j.advwatres.2010.07.003.

Aghakouchak, A., E. Habib, and A. Bardossy (2010b), A comparison of three remotely sensed rainfall ensemble generators, Atmospheric Research, 98 (2-4), 387-399, doi:10.1016/j.atmosres.2010.07.016.

Chen, L., Guo, S. L., Yan, B. W., Liu, P. and Fang, B. (2010), A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence, Hydrological Sciences Journal, 55(8), 1264-1280.

Chowdhary, H. (2010), Discussion of ’Gumbel-Hougaard copula for trivariate rainfall frequency analysis’ by L. Zhang and Vijay P. Singh., Journal of Hydrologic Engineering, 13 (10), 992–994.

Chowdhary, H., and V. P. Singh (2010), Reducing uncertainty in estimates of frequency distribution parameters using composite likelihood approach and copula-based bivariate distributions, Water Resour. Res.,  46, W11516, doi:10.1029/2009WR008490.

Durante, F., and G. Salvadori (2010), On the construction of multivariate extreme value models via copulas, Environmetrics, 21 (2), 143–161, doi:10.1002/env.988.

Erdely, A., J.M. Gonzalez-Barrios (2010), A nonparametric symmetry test for absolutely continuous bivariate copulas. Statistical Methods and Applications, 19 (4), 541-565.

Ghizzoni, T., G. Roth, and R. Rudari (2010), Multivariate skew-t approach to the design of accumulation risk scenarios for the flooding hazard, Advances in Water Resources, 33 (10), 1187-1290, doi:10.1016/j.advwatres.2010.08.003.

Goda, K. (2010), Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands, Structural Safety, 32 (2), 112–113.

Ghosh, S. (2010), Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula, Hydrological Processes, 24(24), 3558-3567,  doi:10.1002/hyp.7785.

Kao, S.-C., and R. S. Govindaraju (2010), A copula-based joint deficit index for droughts, JOURNAL OF HYDROLOGY, 380 (1-2), 121-134, doi:10.1016/j.jhydrol.2009.10.029.

Kazianka, H., and J. Pilz (2010), Copula-based geostatistical modeling of continuous and discrete data including covariates, Stochastic Environmental Research and Risk Assessment, 24 (5), 661–673, doi:10.1007/s00477-009-0353-8.

Kershaw Jr., J. A., E. W. Richards, J. B. McCarter, and S. Oborn (2010), Spatially correlated forest stand structures: A simulation approach using copulas, Computers and Electronics in Agriculture, 74(1), 120-128,  doi:10.1016/j.compag.2010.07.005.

Klein B., M. Pahlow, Y. Hundecha, and A. Schumann (2010), Probability Analysis of Hydrological Loads for the Design of Flood Control Systems Using Copulas, J. Hydrologic Engineering, Volume 15, Issue 5, pp. 360-369

Liu, D.-F., B.-T. Xie, and H.-J. Li (2010), Design flood volume of the three gorges dam project, Journal of Hydrologic Engineering, 16 (1), 71-80.

Mirakbari M., Ganji A., and Fallah S.R. (2010), Regional Bivariate Frequency Analysis of Meteorological Droughts, Journal of Hydrologic Engineering, 15(12), 985-1000.

Muhaisen, O.S.H., Elramlawee, N.J.E., Garcia, P.A. (2010), Copula-EVT-based simulation for optimal rubble-mound breakwater design, Civil Engineering and Environmental Systems, 27(4), 315-328. 

Salvadori, G., and C. De Michele (2010), Multivariate multiparameter Extreme Value models and Return Periods: a copula approach, Water Resour. Res., 46, W10501, doi:10.1029/2009WR009040.

Samaniego, L., A. Bárdossy, and R. Kumar (2010), Streamflow prediction in ungauged catchments using copula-based dissimilarity measures, Water Resour. Res., 46, W02506, doi:10.1029/2008WR007695.

Sang, H., and A. E. Gelfand (2010), Continuous spatial process models for spatial extreme values, Journal of Agricultural Biological and Environmental Statistics, 15 (1), 49–65, doi:10.1007/s13253-009-0010-1.

Shiau, J.-T., H.-Y. Wang, and C.-T. Tsai (2010), Copula-based depth-duration-frequency analysis of typhoons in Taiwan, Hydrology Research, 41, 414–423, doi:10.2166/nh.2010.048.

Song, S., and V. P. Singh (2010), Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data, STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, 24 (3), 425-444, doi:10.1007/s00477-009-0331-1.

Song, S., and V. P. Singh (2010), Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm, Stochastic Environmental Research and Risk Assessment, 24 (5), 783–805, doi:10.1007/s00477-010-0364-5.

Vandenberghe, S., N. E. C. Verhoest, and B. De Baets (2010), Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall, WATER RESOURCES RESEARCH, 46, W01512, doi:10.1029/2009WR007857.

Vandenberghe, S., N. E. C. Verhoest, E. Buyse, and B. De Baets (2010), A stochastic design rainfall generator based on copulas and mass curves, Hydrol. Earth Syst. Sci., 14, 2429-2442, doi:10.5194/hess-14-2429-2010. 

Wang, X., M. Gebremichael, and J. Yan (2010), Weighted likelihood copula modeling of extreme rainfall events in Connecticut, Journal of Hydrology, 390(1-2),108-115.

Wong, G., M. F. Lambert, M. Leonard, and A. V. Metcalfe (2010), Drought Analysis Using Trivariate Copulas Conditional on Climatic States, JOURNAL OF HYDROLOGIC ENGINEERING, 15 (2), 129-141, doi:10.1061/(ASCE)HE.1943-5584.0000169.

Wu, Z.-K., L. Zhao, and Y.-J. Ge (2010), Statistical analysis of wind velocity and rainfall intensity joint probability distribution of Shanghai area in typhoon condition, Kongqi Donglixue Xuebao/Acta Aerodynamica Sinica, 28 (4), 393–399.

Xu, Y.-P., M. J. Booij, and Y.-B. Tong (2010), Uncertainty analysis in statistical modeling of extreme hydrological events, Stochastic Environmental Research and Risk Assessment, 24 (5), 567–578, doi:10.1007/s00477-009-0337-8.

Zegpi, M. & Fernández, B. (2010), Hydrological model for urban catchments - analytical development using copulas and numerical solution, Hydrological Sciences Journal, 55(7), 1123-1136.



Ashkar, F. and F. Aucoin (2011), A broader look at bivariate distributions applicable in hydrology, J. of Hydrology, 405(3-4), pp. 451-461, doi:10.1002/hyp.8117.

Balistrocchi, M. and B. Bacchi (2011), Modelling the statistical dependence of rainfall event variables through copula functions,  Hydrol. Earth Syst. Sci., 15(6), 1959-1977.

Bárdossy, A. (2011), Interpolation of groundwater quality parameters with some values below the detection limit, Hydrol. Earth Syst. Sci., 15(9), 2763-2775. 

Barry, A. P. and Y.-P. Guo (2011), A probabilistic description of rain storms incorporatingI peak intensities, Journal of Hydrology, ISSN 002-1694, 10.1016/j.jhydrol.2011.07.040. 

Chebana, F., and T.B.M.J. Ouarda (2011), Depth-based multivariate descriptive statistics with hydrological applications, Journal of Geophysical Research D: Atmospheres, 116 (10), D10120.

Chebana, F., and T.B.M.J. Ouarda (2011), Multivariate extreme value identification using depth functions, Environmetrics, 22 (3), 441-455.

Chebana F., and T.B.M.J. Ouarda (2011), Multivariate quantiles in hydrological frequency analysis, Environmetrics, 22 (1), 63-78.

Chen Z., Z. Liu and J. Lu (2011), Flood joint probability distribution of the Xijiang River and Beijiang River in Guangdong provence, Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni, 50(2), pp. 110-115.

Chowdhary, H., L. Escobar, and V. P. Singh (2011), Identification of suitable copulas for bivariate frequency analysis of flood peaks and flood volumes, Hydrology Research, 42 (2-3), 193-216.

Fontanazza, C. M. and G. Freni, F. La Loggia and V. Notaro (2011), Uncertainty evaluation of design rainfall for urban flood risk analysis, Water Science and Technology, 63(11), pp. 2641-2650, doi: 10.2166/wst.2011.169.

Gargouri-Ellouze, E. Akbarand, N.S. and Nadeem, S. (2011), Modelling nonlinear bivariate dependence using the Boubaker polynomical copula: Application to infiltration rainfall patterns in Saddine-1 (Makthar, Northern Tunisia). Studies in Nonlinear Sciences, 2(1): 13-18.

Golian, S.,  B. Saghafian, M. Elmi, and R. Maknoon (2011), Probabilistic rainfall thresholds for flood forecasting: evaluating different methodologies for modelling rainfall spatial correlation (or dependence), Hydrological Processes,  25 (13), 2046-2055.

Gyasi-Agyei, Y. (2011), Copula-based daily rainfall disaggregation model, Water Resources Research, 47, W07535.

Karamouz, N., N. Noori, A. Moridi, A. Ahmadi (2011), Evaluation of floodplain variability considering impacts of climate change, Hydrological Processes, 25, 90-103.

Kazianka, H. and J. Pilz (2011), Bayesian spatial modeling and interpolation using copulas, Computers and Geosciences, 37, 310-319.

Lee, T., and J. D. Salas (2011), Copula-based stochastic simulation of hydrological data applied to Nile river flows, Hydrology Research, 42 (4), 318-330.

Li, J., A. Bárdossy, L. Guenni, and M. Liu (2011), A copula based observation network design approach, Environmental Modelling & Software, Volume 26, Issue 11, pp. 1349-1357, doi:10.1016/j.envsoft.2011.05.001

Liu, C.-L., Q. Zhang, V. P. Singh and Y. Cui (2011), Copula-based evaluations of drought variations in Guangdong, South China, Natural Hazards, 59 (3), 1533-1546.

Marchant, B.P., N.P.A. Saby,  C.C. Jolivet, D. Arrouays, R.M. Lark (2011), Spatial prediction of soil properties with copulas, Geoderma, 162 (3-4), 327-334.

Neppel, L., N. Pujol and R. Sabatier (2011), A multivariate regional test for detection of trends in extreme rainfall: The case of extreme daily rainfall in the French Mediterranean area, Advances in Geosciences, 26, pp. 145-148, doi: 10.5194/adgeo-26-145-2011.

Palynchuk, B. A. and Y. Guo (2011), A probabilistic description of rain storms incorporating peak intensities, J. of Hydrology, 409(1-2), pp 71-80, doi: 10.1016/j.jhydrol.2011.07.040.

Renard, B. (2011), A Bayesian hierarchical approach to regional frequency analysis, Water Resources Research, 47(11), doi: 10.1029/2010WR010089. 

Sadri, S., and D.H. Burn (2011), A Fuzzy C-Means approach for regionalization using a bivariate homogeneity and discordancy approach, Journal of Hydrology, 401 (3-4), 231-239.

Salvadori, G., and C. De Michele (2011), Estimating strategies for multiparameter multivariate extreme value copulas,  Hydrol. Earth Syst. Sci., 15, 141-150, doi:10.5194/hess-15-141-2011.

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Solari, S. and M. A. Losada (2011), Non-stationary wave height climate modeling and simulation, Journal of Geophysical Research, 116, C09032, 18 pp., 2011 doi:10.1029/2011JC0070101.

van den Berg, M.J., Vandenberghe S., De Baets B., and Verhoest N.E.C. (2011), Copula-based downscaling of spatial rainfall: a proof of concept, Hydrol. Earth Syst. Sci., 15, 1445-1457, doi:10.5194/hess-15-1445-2011.

Vandenberghe, S., N. Verhoest, C. Onof, and B. De Baets (2011), A comparative copula-based bivariate frequency analysis of observed and simulated storm events: a case study on Bartlett-Lewis modeled rainfall, Water Resources Research, 47, W07529.

Zhang, Q., Y.D. Chen, X.H. Chen, and J.F. Li (2011), Copula-based analysis of hydrological extremes and implications of hydrological behaviors in the Pearl river basin, China, Journal of Hydrologic Engineering, 16 (7), 598-607.


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Hagspiel, S., Papaemannouil, A., Schmid, M. and Andersson, G. (2011), Copula-based modeling of statistic wind power in Europe and implications for the Swiss power grid, Applied Energy. doi: 10.1016/j.apenergy.2011.10.039.

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Hao Z. and V.-P. Singh (2012), Entropy-copula method for single-site monthly streamflow simulation, Water Resources Research, 48, W06604, DOI:10.1029/2011WR011419.

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Reddy M. J. and P. Ganguli (2012), Bivariate flood frequency analysis of upper Godavari River flows using Archimedean Copulas, Water Resources Management, Vol. 26, Iss. 14, P. 3995-4018

Serinaldi F., S. Grimaldi, M. Abdohosseini, P.  Corona and D. Cimini (2012) Testing copula regression against benchmark models for point and interval estimation of tree wood volume in beech stands, European Journal of Forest Research, DOI: 10.1007/s10342-012-0600-2.

Wahl T., Mudersbach and J. Jensen (2012), Assessing the hydrodynamic boundary conditions for risk analyses in coastal areas: a multivariate statistical apprach based on copula functions, Natual Hazards Earth System Sciences, 12, 495-510.

Wang Y., H. Ma, D. Sheng and D. Wang (2012) Assessing the interactions between Cholorophyll and environmental variables using copula method, Journal of Hydrologic Engineering, Vol. 17, Iss. 4, P. 495-506.

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Ministero dell'Ambiente e della Tutela del Territorio e del Mare

Institute for Environmental Protection and Research

 Honors Center of Italian Universities - H2CU 
Sapienza University of Rome

University of Tuscia,
Viterbo, Italy


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