Browse > Article
http://dx.doi.org/10.7465/jkdi.2017.28.4.797

Analysis of extreme wind speed and precipitation using copula  

Kwon, Taeyong (Department of Statistics, Daegu University)
Yoon, Sanghoo (Department of Statistics and Computer Science, Daegu University & Institute of Basic Science, Deagu University)
Publication Information
Journal of the Korean Data and Information Science Society / v.28, no.4, 2017 , pp. 797-810 More about this Journal
Abstract
The Korean peninsula is exposed to typhoons every year. Typhoons cause huge socioeconomic damage because tropical cyclones tend to occur with strong winds and heavy precipitation. In order to understand the complex dependence structure between strong winds and heavy precipitation, the copula links a set of univariate distributions to a multivariate distribution and has been actively studied in the field of hydrology. In this study, we carried out analysis using data of wind speed and precipitation collected from the weather stations in Busan and Jeju. Log-Normal, Gamma, and Weibull distributions were considered to explain marginal distributions of the copula. Kolmogorov-Smirnov, Cramer-von-Mises, and Anderson-Darling test statistics were employed for testing the goodness-of-fit of marginal distribution. Observed pseudo data were calculated through inverse transformation method for establishing the copula. Elliptical, archimedean, and extreme copula were considered to explain the dependence structure between strong winds and heavy precipitation. In selecting the best copula, we employed the Cramer-von-Mises test and cross-validation. In Busan, precipitation according to average wind speed followed t copula and precipitation just as maximum wind speed adopted Clayton copula. In Jeju, precipitation according to maximum wind speed complied Normal copula and average wind speed as stated in precipitation followed Frank copula and maximum wind speed according to precipitation observed Husler-Reiss copula.
Keywords
Copula; extreme value; k-fold cross validation;
Citations & Related Records
Times Cited By KSCI : 7  (Citation Analysis)
연도 인용수 순위
1 Kim, S.D., Ryu, J. S., Oh, K. R. and Jeong, S. M. (2012). An application of copulas-based joint drought index for determining comprehensive drought conditions. Journal of Korean Society of Hazard Mitigation, 12, 223-230.
2 Kwak, J. W., Kim, D. G., Lee, J. S. and Kim, H. S. (2012). Hydrological drought analysis using copula theory. Journal of the Korea Society of Civil Engineers, 32, 161-168.
3 Kwak, M. J. (2016). Estimation of the joint conditional distribution for repeatedly measured bivariate cholesterol data using nonparametric copula. Journal of the Korean Data & Information Science Society, 27, 689-700.   DOI
4 Nelsen, R. B. (2006). An introduction to copulas, Springer, New York.
5 Park, J. B., Kal, B. S. and Heo, J. R. (2015). The study to estimate the fitness of bivariate rainfall frequency analysis considering the interdependence between rainfall and wind speed. Journal of Korean Society of Hazard Mitigation, 15, 103-110.
6 Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain "Goodness of Fit" criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193-212.   DOI
7 Schoelzel, C. and Friederichs, P. (2008). Multivariate non-normally distributed random variables in climateresearch introduction to the copula approach. Nonlinear processes in Geophysics, 15, 761-772.   DOI
8 Renard, B. and Lang, M. (2007). Use of gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Advances in Water Resources, 30, 897-912.   DOI
9 Requena, A. L., Mediero, L. and Garrote, L. (2013). A bivariate return period based on copula for hydrologic dam design: accounting for reservoir routing in risk estimation. Hydrologic Earth System Sciences, 17, 3023-3038.   DOI
10 Salvadori, G. and Friederichs, P. (2010). Multivariate multiparameter extreme value models and return peiods: a copula approach. Water Resources Research, 46, W10501, doi:10.1029/2009WR009040.   DOI
11 Smirnov, N. V. (1939). On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bulletin of Mathematical University of Moscow, 2, 3-16.
12 Choi, C. H., Lee, H. S. and Ju, H. C. (2013). Analyzing rainfall patterns and pricing rainfall insurance using copula Journal of the Korean Data & Information Science Society, 24, 603-623.   DOI
13 Durante, F. and Salvadori, G. (2010). On the construction of multivariate extreme value models via copulas. Environmetrics, 21, 143-161.
14 Shih, J. H. and Louis, T. A. (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51, 1384-1399.   DOI
15 Shin, H. J., Sung, L. M. and Heo, J. H. (2010). Derivation of modified anderson-darling test statistics and power test for the gumbel distribution. Journal of Korea Water Resources Association, 43, 813-822.   DOI
16 Sklar, A. (1959). Fonctions de reparation rma n dimensions et leurs marges. Publication de l'institute de statistique de l'universite de Paris, 8, 229-231.
17 So, J. M., Sohn, K. H. and Bae, D. H. (2014). Estimation and assessment of bivariate joint drought index based on copula functions. Journal of Korea Water Resources Association, 47, 171-182.   DOI
18 Genest, C., Ghoudi, K. and Rivest, L. P. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Printed in Great Britain, 82, 543-552.
19 Favre, A. C., Adlouni, S. E., Perreault, L., Thiemonge, N. and Bobee, B. (2004). Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40, W01101, doi:10.1029/2003WR002456.   DOI
20 Genest, C. and Favre, A. C. (2007). Everything you always wanted to know about copula but afraid to ask. Journal of Hydrology, 12, 347-368.
21 Hofert, M., Kojadinovic, I., Maechler, M. and Yan, J. (2015). Copula: multivariate dependence with copulas, R package version 0.999-14, http:CRAN.R-project.org/package=copula.
22 Joe, H. and Xu, J. J. (1996). The estimation method of inference functions for margins for multivariate models, Department of Statistics, University of British Columbia.
23 Joo, K. W., Shin, J. Y. and Heo, J. H. (2012). Bivariate frequency analysis of rainfall using copula model. Journal of Korea Water Resources Association, 45, 827-837.   DOI
24 Kao, S. C. and Govindaraju, R. S. (2007). A bivariate frequency analysis of extreme rainfall with implications for design. Journal of Geophysical Research, 112, D13119, doi:10.1029/2007JD008522.   DOI
25 Cherubini, U., Luciano, E. and Vecchiato, W. (2004). Copula methods in finance, John Wiley & Sons.
26 Zhang, L. and Singh, W. P. (2006). Bivariate flood frequency analysis using the copula method. Journal of Hydrologic Engineering, 11, 150-164.   DOI
27 Thompson, R. (1966). Bias of the one-sample cramer-von mises test. Journal of the American Statistical Association, 61, 246-247.
28 Yoo, J. Y., Shin, J. Y., Kim, D. K. and Kim, T. W. (2013). Drought risk analysis using stochastic rainfall generation model and copula functions. Journal of Korea Water Resources Association, 46, 425-437.   DOI