All Issue

2019 Vol.52, Issue 12 Preview Page

Research Article

A development of bivariate regional drought frequency analysis model using copula function

Copula 함수를 이용한 이변량 가뭄 지역빈도해석 모형 개발

Jin-Guk Kima
,
Jin-Young Kimb
,
Woo-Sik Banc
,
Hyun-Han Kwond*
김 진국a
,
김 진영b
,
반 우식c
,
권 현한d*
aPh.D Course, Department of Civil and Environmental Engineering, Sejong University
bManager, Water Management Division, ISAN Corporation
cGeneral Manager, Hangang Regional Head Office Regional Water Resources Management Department, K-water
dProfessor, Department of Civil & Environmental Engineering, Sejong University
a세종대학교 건설환경공학과 박사과정
b㈜이산 수자원부 과장
cK-water 한강권역부문 한강물관리처 물관리센터장
d세종대학교 건설환경공학과 교수
* Corresponding Author
31 December 2019. pp. 985-999
PDF XML Citation
Abstract

Over the last decade, droughts have become more severe and frequent in many regions, and several studies have been conducted to explore the recent drought. Copula-based bivariate drought frequency analysis has been widely used to evaluate drought risk in the context of point frequency analysis. However, the relatively significant uncertainties in the parameters are problematic when available data are limited. For this reason, the primary purpose of this study is to develop a regional drought frequency model based on the Copula function. All parameters, including marginal and copula functions in the regional frequency model, were estimated simultaneously. Here, we present a case study of recent drought 2013-2015 over the Han-River watershed where severe drought risk is consistently found to increase. The proposed model provided a reliable way to significantly reduce the uncertainty of parameters with a Bayesian modeling framework. The uncertainty of the joint return period in the regional frequency analysis is nearly three times lower than that of the point frequency analysis. Accordingly, DIC values in the regional frequency analysis model are significantly decreased by 15. The results confirm that the proposed model is not only reliably representing characteristics of historical droughts and dependencies between drought variables, but also providing the efficacy of understanding regional drought characteristics.

Keywords
Copula
Bayesian
Bivariate drought regional frequency analysis
Uncertainty

전 세계적으로 극심한 가뭄현상이 반복적으로 발생하고 있으며, 이러한 가뭄을 분석하기 위한 연구가 다수 진행되고 있다. 최근 코플라 함수를 활용한 이변량 가뭄빈도해석에 대한 연구가 다수 진행된 바 있으나, 대부분 지점빈도해석에 국한되어 진행되었으며, 통계적으로 부족한 자료의 기간을 보완하기 위한 대안으로 지역빈도해석 개념을 도입한 연구는 미진한 실정이다. 이러한 점에서 본 연구에서는 기존의 베이지안 기법과 코플라 함수를 연계한 이변량 지역빈도해석 모형을 개발하였다. 최종적으로 이변량 코플라 가뭄 지역빈도해석 모형을 한강유역에 적용하여 2013-2015년에 발생한 가뭄 사상을 평가하였으며, 기존에 개발된 이변량 지점빈도해석 결과와 비교를 통해 모형의 해석결과에 대한 신뢰성을 확보하였다. 결과적으로 이변량 지점빈도해석에 비해 가뭄사상에 대한 결합재현기간의 불확실성 구간이 약 3배 가까이 감소하였으며, DIC 통계량 산정결과 약 15이상 개선된 것을 확인하였다. 본 연구를 통해 제안된 베이지안 코플라 기반 이변량 가뭄 지역빈도해석 모형은 가뭄자료의 분포특성 및 자료간의 상관성을 효과적으로 재현하는데 유리할 뿐만 아니라, 지역적인 가뭄특성을 효과적으로 평가할 수 있는 장점을 확인할 수 있었다.

키워드
코플라
베이지안
이변량 가뭄 지역빈도해석
불확실성
References
1
Akalke, H. (1974). "A new look at the statistical model identification." IEEE Transactions on Automatic Control, Vol. 19, No. 6, pp. 716-723.
10.1109/TAC.1974.1100705
2
Bonaccorse, B., Cancelliere, A., and Rossi, G. (2003). "An analytical formulation of return period of drought severity." Stochastic Environmental Research and Risk Assessment, Vol. 17, No. 3, pp. 157-174.
10.1007/s00477-003-0127-7
3
Cancelliere, A., and Salas, J.D. (2010). "Drought probabilities and return period for annual streamflows series." Journal of Hydrology, Vol. 391, No. 1-2, pp. 77-89.
10.1016/j.jhydrol.2010.07.008
4
Fernández, 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.
10.1061/(ASCE)1084-0699(1999)4:4(297)
5
Findley, D.F. (1991). "Counterexamples to parsimony and BIC." Annals of the Institute of Statistical Mathematics, Vol. 43, No. 3, pp. 505-514.
10.1007/BF00053369
6
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.
10.1080/01621459.1990.10476213
7
Gelman, A., and Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, New York.
10.1017/CBO9780511790942
8
Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2003). Bayesian data analysis. CRC press, United States of America.
9
Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004). Bayesian data analysis (2nd ed.). Boca Raton: Chapman and Hall/CRC, CRC press, USA.
10
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.
10.1109/TPAMI.1984.476759622499653
11
Guttman, N.B. (1999). "Accepting the standardized precipitation index: a calculation algorithm 1." Journal of the American Water Resources Association, Vol. 35, No. 2, pp. 311-322.
10.1111/j.1752-1688.1999.tb03592.x
12
Hong, C.S., and Lee, J.H. (2011). "VaR estimation of multivariate distribution using copula functions." Korean Journal of Applied Statistics, Vol. 24, No. 3, pp. 523-533.
10.5351/KJAS.2011.24.3.523
13
Hosking, J.R.M., and Wallis, J.R. (2005). Regional frequency analysis: an approach based on L-moments. Cambridge University Press, New York.
14
Joe, H. (1997). Multivariate models and dependence concept. CRC Press, USA.
10.1201/b13150
15
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, Vol. 32, No. 4, pp. 635-640.
10.1002/joc.2290
16
Kim, J.Y., Kim, J.G., Cho, Y.H., and Kwon, H.H. (2017). "A development of Bayesian copula model for a bivariate drought frequency analysis." Journal of Korea Water Resource Association, KWRA, Vol. 50, No. 11, pp. 745-758.
17
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 Association, KWRA, Vol. 49, No. 10, pp. 823-833.
10.3741/JKWRA.2016.49.10.823
18
Kim, J., Lim, J., and Kwon, H. (2014). "Development of hierarchical Bayesian spatial regional frequency analysis model considering geographical characteristics." Journal of Korea Water Resource Association, KWRA, Vol. 47, No. 5, pp. 469-482.
10.3741/JKWRA.2014.47.5.469
19
Kwak, J.W., Kim, D.G., Lee, J.S., and Kim, H.S. (2012). "Hydrological drought analysis using copula theory." Journal of The Korean Society of Civil Engineers, KSCE, Vol. 32, No. 3B, pp. 161-168.
20
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.
10.1002/2016WR018959
21
Kwon, H.H., Brown, C., and Lall, U. (2008). "Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling." Geophysical Research Letters, Vol. 35, No. 5.
10.1029/2007GL032220
22
Kwon, H.H., Kim, J.Y., Kim, O.K., and Lee, J.J. (2013). "A development of regional frequency model based on hierarchical Bayesian model." Journal of Korea Water Resource Association, KWRA, Vol. 46, No. 1, pp. 13-24.
10.3741/JKWRA.2013.46.1.13
23
Lee, J.J., and Kwon, H.H. (2011). "Analysis on spatio-temporal pattern and regionalization of extreme rainfall data." Journal of The Korean Society of Civil Engineers, KSCE, Vol. 31, No. 1B, pp. 13-20.
24
Lee, J.J., Kwon, H.H., and Kim, T.W. (2010). "Concept of trend analysis of hydrologic extreme variables and nonstationary frequency analysis." Journal of The Korean Society of Civil Engineers, KSCE, Vol. 30, No. 4B, pp. 389-397.
25
Lee, T., and Son, C. (2016). "Analyzing the drought event in 2015 through statistical drought frequency analysis." Journal of Korea Water Resource Association, KWRA, Vol. 49, No. 3, pp. 177-186.
10.3741/JKWRA.2016.49.3.177
26
Mathier, L., Perreault, L., Bobée, B., and Ashkar, F. (1992). "The use of geometric and gamma-related distributions for frequency analysis of water deficit." Stochastic Hydrology and Hydraulics, Vol. 6, No. 4, pp. 239-254.
10.1007/BF01581619
27
Nam, W.S., Kim, T.S., Shin, J.Y., and Heo, J.H. (2008). "Regional rainfall frequency analysis by multivariate techniques." Journal of Korea Water Resource Association, KWRA, Vol. 41, No. 5, pp. 517-525.
10.3741/JKWRA.2008.41.5.517
28
Nelsen, R.B. (2007). An introduction to copulas. Springer Science & Business Media, USA.
29
Oh, T.S., Kim, J.S., Moon, Y.I., and Yoo, S.Y. (2006). "The study on application of regional frequency analysis using kernel density function." Journal of Korea Water Resource Association, KWRA, Vol. 39, No. 10, pp. 891-904.
10.3741/JKWRA.2006.39.10.891
30
Oh, T.S., Moon Y.I., and Oh, K.T. (2008). "Estimation of probability precipitation by regional frequency analysis using cluster analysis and variable kernel density function." Journal of The Korean Society of Civil Engineers, KSCE, Vol. 28, No. 2B, pp. 225-236.
31
Park, S.J., and Lee, C.W. (2018). "Monitoring of the drought in the upstream area of Soyang river, Inje-Gun, Kangwon-do using KOMPSAT-2/3 satellite." Korean Journal of Remote Sensing, Vol. 34, No. 6-3, pp. 1319-1327.
32
Potter, K.W. (1987). "Research on flood frequency analysis: 1983-1986." Reviews of Geophysics, Vol. 25, No. 2, pp. 113-118.
10.1029/RG025i002p00113
33
Radice, R., Marra, G., and Wojtyś, M. (2016). "Copula regression spline models for binary outcomes." Statistics and Computing, Vol. 26, No. 5, pp. 981-995.
10.1007/s11222-015-9581-6
34
Shiau, J.T. (2006). "Fitting drought duration and severity with two- dimensional copulas." Water resources management, Vol. 20, No. 5, pp. 795-815.
10.1007/s11269-005-9008-9
35
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.
10.1061/(ASCE)0733-9496(2001)127:1(30)
36
Sklar, A. (1959). "Fonctions de répartition àn dimensions et leurs marges." Publications de l'Institut Statistique de l'Université de Paris, Vol. 8, pp. 229-231.
37
Vaziri, H., Karami, H., Mousavi, S.F., and Hadiani, M. (2018). "Analysis of hydrological drought characteristics using copula function approach." Paddy and Water Environment, Vol. 16, No. 1, pp. 153-161.
10.1007/s10333-017-0626-7
38
Yevjevich, V.M. (1967). An objective approach to definitions and investigations of continental hydrologic droughts. Hydrology papers (Colorado State University), No. 23, Fort Collins, Colorado.
39
Zelenhasić, E., and Salvai, A. (1987). "A method of streamflow drought analysis." Water resources research, Vol. 23, No. 1, pp. 156-168.
10.1029/WR023i001p00156
Information
  • Publisher :KOREA WATER RESOURECES ASSOCIATION
  • Publisher(Ko) :한국수자원학회
  • Journal Title :Journal of Korea Water Resources Association
  • Journal Title(Ko) :한국수자원학회 논문집
  • Volume : 52
  • No :12
  • Pages :985-999
  • Received Date : 2019-10-06
  • Revised Date : 2019-11-20
  • Accepted Date : 2019-11-20
  • DOI :https://doi.org/10.3741/JKWRA.2019.52.12.985
Journal Informaiton Journal of Korea Water Resources Association Journal of Korea Water Resources Association
Online Submission
Archives
  • scopus
  • KCI-수자원
  • NRF
  • KOFST
  • KISTI Current Status
  • KISTI Cited-by
  • crosscheck
  • orcid
  • open access
  • ccl
Journal Informaiton Journal Informaiton - close