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http://dx.doi.org/10.3741/JKWRA.2017.50.11.745

A development of Bayesian Copula model for a bivariate drought frequency analysis  

Kim, Jin-Young (ISAN Corporation)
Kim, Jin-Guk (Department of Civil Engineering, Chonbuk National University)
Cho, Young-Hyun (Korea Water Resources Corporation (K-water))
Kwon, Hyun-Han (Department of Civil Engineering, Chonbuk National University)
Publication Information
Journal of Korea Water Resources Association / v.50, no.11, 2017 , pp. 745-758 More about this Journal
Abstract
The copula-based models have been successfully applied to hydrological modeling including drought frequency analysis and time series modeling. However, uncertainty estimation associated with the parameters of these model is not often properly addressed. In these context, the main purposes of this study are to develop the Bayesian inference scheme for bivariate copula functions. The main applications considered are two-fold: First, this study developed and tested an approach to copula model parameter estimation within a Bayesian framework for drought frequency analysis. The proposed modeling scheme was shown to correctly estimate model parameters and detect the underlying dependence structure of the assumed copula functions in the synthetic dataset. The model was then used to estimate the joint return period of the recent 2013~2015 drought events in the Han River watershed. The joint return period of the drought duration and drought severity was above 100 years for many of stations. The results obtained in the validation process showed that the proposed model could effectively reproduce the underlying distribution of observed extreme rainfalls as well as explicitly account for parameter uncertainty in the bivariate drought frequency analysis.
Keywords
Copula; Bayesian; Bivariate drought frequency analysis; Uncertainty analysis;
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Times Cited By KSCI : 9  (Citation Analysis)
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1 Kuo, J.-T., Hsu, Y.-C., Tung, Y.-K., Yeh, K.-C., and Wu, J.-D. (2008). "Dam overtopping risk assessment considering inspection program." Stochastic Environmental Research and Risk Assessment, Vol. 22, pp. 303-313.   DOI
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, Vol. 32, No. 3B, pp. 161-168.   DOI
3 Kwon, H.-H, Casey, B., and Lall, U. (2008). "Climate informed flood frequency analysis and prediction in montana using hierarchical Bayesian modeling." Geophysical Research Letters, Vol. 35, L05404.
4 Kwon, H.-H., and Lall, U. (2016). "A copula-based nonstationary frequency analysis for the 2012-2015 drought in California." Water Resources Research, Vol. 52, No. 7, pp. 5662-5675.   DOI
5 Lee, J.-J., and Kwon, H.-H. (2011). "Analysis on spatio-temporal pattern and regionalization of extreme rainfall data." Journal of Korean Society of Civil Engineers, Vol. 31, No. 1B, pp. 13-20.
6 Lee, T. S., and Son, C. Y. (2016). "Analyzing the drought event in 2015 through statistical drought frequency analysis." Journal of Korea Water Resource Associate, Vol. 49, No. 3, pp. 177-186.   DOI
7 Melching, C. S., Wenzel, H., and Yen, B. C. (1987). "Application of system reliability analysis to flood forecasting." Application of Frequency and Risk in Water Resources, Edited by V. P. Singh, Reidel Publishing Company.
8 Na, B.-K., Kim, J.-Y., Kwon, H.-H., and Lim, J.-Y. (2014). "Improvement of hydrologic dam risk analysis model considering uncertaintyof hydrologic analysis process." Journal of Korea Water Resource Associate, Vol. 47, No. 10, pp. 853-865.   DOI
9 Nelssen, R. B. (2006). "An introduction to Copula." Springer, New York, pp. 109-115.
10 Shiau, J. T., and Modarres, R. (2009). "Copula-based drought severityduration-frequency analysis in Iran." Meteorological Applacations, Vol. 16, No. 4, pp. 481-489.   DOI
11 Shiau, J.-T., and Shen, H. W. (2001). "Recurrence analysis of hydrologic droughts of differing severity." Journal of Water Resources Planning and Management, Vol. 127, No. 1, pp. 30-40.   DOI
12 Sklar, M. (1959). Fonctions de repartition a n dimensions et leurs marges. Universite Paris 8.
13 Yoo, J. Y., Lee, J. H., and Kim, T. W. (2016). "Estimation of drought risk through the bivariate drought frequency analysis using copula functions." Journal of Korea Water Resource Associate, Vol. 49, No. 3, pp. 217-225.   DOI
14 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 Resource Associate, Vol. 46, No. 1, pp. 425-437.   DOI
15 Yu, J. S., Yoo, J. Y., Lee, J.-H., and Kim, T.-W. (2016). "Estimation of drought risk through the bivariate drought frequency analysis using copula functions." Journal of Korea Water Resource Associate, Vol. 49, No. 3, pp. 217-225.   DOI
16 Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2003). Bayesian data analysis. CRC press, United States of America.
17 Yevjevich, V. (1967). "An objective approach to definitions and investigations of continental hydrologic droughts." Hydrology Paper, No. 23, Colorado State University, Fort Collins, pp. 4-18.
18 Chun, S.-Y., Kim, Y.-T., and Kwon, H.-H. (2015). "Drought frequency analysis using hidden markov chain model and bivariate copula function." Journal of Korea Water Resource Associate, Vol. 48, No. 12, pp. 969-979.   DOI
19 Akaike, H. (1974). "A new look at the statistical model identification." IEEE Transactions on Automatic Control, Vol. 19, No. 6, pp. 716-723.   DOI
20 Bonaccorse, B., Cancelliere, A., and Rossi, G. (2003). "An analytical formulation of return period of drought severity." Vol. 17, No. 3, pp. 157-174.   DOI
21 Fernandez, B., and Salas, J. D. (1999). "Return period and risk of hydrologic events. I: Mathematical formulation." Journal of Hydrologic Engineering, Vol. 4, No. 4, pp. 297-307.   DOI
22 Findley, D. F. (1991). "Counter examples to Parsimony and BIC." Annals of the Institute of Statistical Mathematics, Vol. 43, No. 3, pp. 505-514.   DOI
23 Geman, S., and Geman, D. (1984). "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images." IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, pp. 721-741.
24 Gelfand, A. E., and Smith, A. F. (1990). "Sampling-based approaches to calculating marginal densities." Journal of the American Statistical Association, Vol. 85, No. 410, pp. 398-409.   DOI
25 Gelman, A., and Hill, J. (2006). Data analysis using regression and multilevel/hierarchical model. Cambridge University Press.
26 Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). Boca Raton: Chapman and Hall/CRC.
27 Joe, H. (1997). Multivariate models and dependence concept. Chapman & Hall, London.
28 Kim, J. S., Jain, S., and Yoon, S. K. (2012). "Warm season streamflow variability in the Korean Han river basin: links with atmospheric teleconnections." International Journal of Climatology, doi: 10.1002/joc.2290.   DOI
29 Kim, J.-Y., So, B.-J., Kim, T.-W., and Kwon, H.-H. (2016). "A development of trivariate drought frequency analysis approach using copula function." Journal of Korea Water Resource Associate, Vol. 49, No. 10, pp. 823-833.
30 Kim, T.-W., Valdes, J. B., and Yoo, C. S. (2003). "Nonparametric approach for estimating return periods of droughts in arid regions." Journal of Hydrologic Engineering, Vol. 8, No. 5, pp. 237-246.   DOI
31 Kim, T.-W., Valdes, J. B., and Yoo, C. S. (2006). "Nonparametric approach for bivariate drought characterization using palmer drought index." Journal of Hydrologic Engineering, Vol. 11, No. 2, pp. 134-143.   DOI