Comparison between classical univariate frequency analysis and bivariate analysis with copula
- Authors: Mojca Šraj, Nejc Bezak, Mitja Brilly
- Citation: Acta hydrotechnica, vol. 26, no. 44, pp. 37-48, 2013.
- Abstract: Frequency analyses are a basis for designing discharge estimations. Univariate flood frequency analyses are usually applied in hydrological practice. Hydrological processes are multivariate, however multivariate analyses are needed. Copula function can be used for multivariate modelling. Classical univariate flood frequency analyses are a precondition for the copula analyses. Flood frequency analyses were made on the annual maximum series data from gauging station Litija on the Sava River. Three copulas from the Archimedean family were used; parameters were estimated with method of moments (based on the Kendall correlation coefficient). Some joint return periods were calculated and compared with the univarite return periods. Differences between return periods were not negligible. In the case of a flood event in 1990, which was the largest in the observed period, TAND was 92 years and TOR was 17 years. Univariate return periods lay between these two values. Statistical and graphical performance measures were used to choose the best fit copula function. Gumbel-Hougaard copula gave better results than Clayton and Frank copulas.
- Keywords: copula function, bivariate analyses, Kendall’s correlation coefficient, Archimedean copula family, joint return period OR, joint return period AND
- Full text: a44ms.pdf
- References:
- Agencija RS za okolje (2013). Atlas okolja. http://gis.arso.gov.si/atlasokolja/profile.aspx?id=Atlas_Okolja_AXL@Arso (Pridobljeno 6. 2. 2013).
- Ane, T., Kharoubi, C. (2003). Dependence structure and risk measure, Journal of Business, 76(3), 411–438.
- Balistrocchi, M., Bacchi, B. (2011). Modelling the statistical dependence of rainfall event variables through copula functions, Hydrology and Earth System Sciences, 15(6), 1959–1977.
- Bezak, N. (2012). Verjetnostna analiza visokovodnih konic z metodo vrednosti nad izbranim pragom in z metodo letnih maksimumov = Flood frequency analysis with peaks over threshold method and annual maximum series method. Thesis, Univerza v Ljubljani, FGG, 106 p. (in Slovenian).
- Bezak, N., Brilly, M., Šraj, M. (2013). Comparison between the peaks over threshold method and the annual maximum method for flood frequency analyses, Hydrological Sciences Journal. DOI:10.1080/02626667.2013.831174
- Brilly, M., Polič, M. (2005). Public perception of flood risks, flood forecasting and mitigation, Natural Hazards and Earth System Sciences, 5(3), 345–355.
- Brilly, M., Šraj, M. (2005). Osnove hidrologije. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo, 309 p. (in Slovenian).
- Chen, L., Singh, V. P., Shenglian, G., Hao, Z., Li, T. (2012). Flood Coincidence Risk Analysis Using Multivariate Copula Functions, Journal of Hydrologic Engineering, 17(6), 742–755.
- 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.
- Dupuis, D. J. (2007). Using copulas in hydrology: Benefits, cautions, and issues, Journal of Hydrologic Engineering, 12(4), 381–393.
- Đurović, B., Mikoš, M. (2004). Preventive management of risks due to natural hazards – Procedures in the alpime countries and in Slovenia, Acta hydrotechnica, 22(36), 17–35.
- Favre, A.C., El Adlouni, S., Perreault, L., Thiemonge, N., Bobee, B. (2004). Multivariate hydrological frequency analysis using copulas, Water Resources Research, 40(1), 1–12.
- Fisher, N. I., Switzer, P. (2001). Graphical assessment of dependence: Is a picture worth 100 tests?, American Statistician, 55(3), 233–239.
- Ganguli, P., Reddy, M. J. (2013). Probabilistic assessment of flood risks using trivariate copulas, Theoretical and Applied Climatology, 111(1-2), 341–360.
- Genest, C., Boies, J. C. (2003). Detecting dependence with Kendall plots, American Statistician, 57(4), 275–284.
- 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., Remillard, B., Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study, Insurance: Mathematics and Economics, 44(2), 199–213.
- Grimaldi, S., Serinaldi, F. (2006). Design hyetograph analysis with 3-copula function, Hydrological Sciences-Journal-des Sciences Hydrologiques, 51(2), 223–238.
- Karmakar, S., Simonovic, S. P. (2008). Bivariate flood frequency analysis: Part 1. Determination of marginals by parametric and nonparametric techniques, Journal of Flood Risk Management, 1(4), 190–200.
- 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, 2(1), 32–44.
- Kobold, M. (2011). Primerljivost poplave septembra 2010 z zabeleženimi zgodovinskimi poplavnimi dogodki = Comparison of Floods in September 2010 with Registered Historic Flood Events, Ujma, 25, 48–56 (In Slovenian).
- Kobold, M., Zgonc, A., Sušnik, M. (2005). Uncertainty of precipitation measurements and predictions in flash flood modelling, Acta hydrotechnica, 23(39), 79–98 (in Slovenian).
- Ma, M., Song, S., Ren, L., Jiang, S., Song, J. (2011). Multivariate drought characteristics using trivariate Gaussian and Student-t copulas, Hydrological Processes, 27(8), 1175–1190.
- Mikoš, M., Brilly, M., Ribičič, M. (2004). Floods and landslides in Slovenia, Acta hydrotechnica, 22(37), 113–133 (in Slovenian).
- Nelsen, R. B. (1999). An introduction to copulas. Springer, New York, 269 p.
- 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.
- Renard, B., Lang, M. (2007). Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology, Advances in Water Resources, 30, 897–912.
- Salvadori, G., De Michele, C., Kottegoda, N. T., Rosso, R. (2007). Extremes in nature an approach using Copulas. Springer, Dordrecht, 292 p.
- Salvadori, G., De Michele, C. (2007). On the use of copulas in hydrology: Theory and practice. Journal of Hydrologic Engineering, 12(4), 369–380.
- Šraj, M., Bezak, N. (2013). Analiza visokovodnih valov Save v Litiji = The analysis of flood waves on the Sava River in Litija, Ujma, 27, 228–235. (In Slovenian).
- Šraj, M., Bezak, N., Brilly, M. (2012). The influence of the choice of method on the results of frequency analysis of peaks, volumes and durations of flood waves of the Sava River in Litija, Acta hydrotechnica, 25(42), 41–58. (In Slovenian).
- Turk, G. (2012). Verjetnostni račun in statistika = Probability and Statistics. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo, 264 p. (in Slovenian).
- Ulaga, F. (2011). Hidrološka postaja Litija na Savi = Hydrological station Litija on the Sava River, Naše okolje, 18(8), 81–85 (in Slovenian).
- Wong, G., Lambert, M. F., Leonard, M., Metcalfe, A. V. (2010). Drought Analysis Using Trivariate Copulas Conditional on Climatic States, Journal of Hydrologic Engineering, 15(2), 129–141.
- Zhang, L., Singh, V. P. (2006). Bivariate Flood Frequency Analysis Using the Copula Method, Journal of Hydrologic Engineering, 11(2), 150–164.
- Zhang, L., Singh, V. P. (2007). Trivariate Flood Frequency Analysis Using the Gumbel-Hougaard Copula, Journal of Hydrologic Engineering, 12(4), 431–439.