A development of nonstationary rainfall frequency analysis model based on mixture distribution

Hong-Geun Choi; Hyun-Han Kwon; Moon-Hyung Park

doi:10.3741/JKWRA.2019.52.11.895

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2019 Vol.52, Issue 11 Preview Page Next Page

Research Article

A development of nonstationary rainfall frequency analysis model based on mixture distribution 혼합분포 기반 비정상성 강우 빈도해석 기법 개발

30 November 2019. pp. 895-904

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Abstract

It has been well recognized that extreme rainfall process often features a nonstationary behavior, which may not be effectively modeled within a stationary frequency modeling framework. Moreover, extreme rainfall events are often described by a two (or more)-component mixture distribution which can be attributed to the distinct rainfall patterns associated with summer monsoons and tropical cyclones. In this perspective, this study explores a Mixture Distribution based Nonstationary Frequency (MDNF) model in a changing rainfall patterns within a Bayesian framework. Subsequently, the MDNF model can effectively account for the time-varying moments (e.g. location parameter) of the Gumbel distribution in a two (or more)-component mixture distribution. The performance of the MDNF model was evaluated by various statistical measures, compared with frequency model based on both stationary and nonstationary mixture distributions. A comparison of the results highlighted that the MDNF model substantially improved the overall performance, confirming the assumption that the extreme rainfall patterns might have a distinct nonstationarity.

Keywords

Two (or more)-component mixture distribution

Bayesian framework

Time-varying moments

극치 강우 자료는 정상성 빈도모델에서 효과적으로 구현되지 않는 비정상성 거동을 종종 보인다. 또한, 극치 사상의 확률밀도함수는 여름 장마와 태풍 등의 서로 다른 강우 패턴에 의해 2개 이상의 첨두를 가지는 혼합분포형태이다. 이러한 강우 패턴의 변화에 대해 Bayesian 이론을 활용한 비정상성 혼합분포(mixture distribution based nonstationary frequency, MDNF)모델을 제안하였다. 2개의 Gumbel 분포형이 혼합된 MDNF 모델은 Gumbel 분포형 매개변수 중 하나인 위치매개변수의 시변성을 효과적으로 설명한다. 제안한 모델의 성능평가를 위해 정상성 혼합분포모델과의 다양한 통계치 결과를 비교하였다. 정상성 혼합분포모델보다 전반적으로 향상된 성능을 보여주는 MDNF 모델을 통해 극치 강우 패턴이 비정상성을 보인다는 가정을 확인할 수 있다.

키워드

2요소 혼합분포형

베이지안 이론

시변성

References

Choi, H. G., Uranchimeg, S., Kim, Y. T., and Kwon, H. H. (2018). "A Bayesian approach to Gumbel mixture distribution for the estimation of parameter and its use to the rainfall frequency analysis." Journal of the Korean Society of Civil Engineers, KSCE, Vol. 38, No. 2, pp. 249-259.

El Adlouni, S., Bobée, B., and Ouarda, T. B. M. J. (2008). "On the tails of extreme event distributions in hydrology." Journal of Hydrology, Vol. 355, No. 1-4, pp. 16-33.

10.1016/j.jhydrol.2008.02.011

Gelman, A., Chew, G. L., and Shnaidman, M. (2004). "Bayesian analysis of serial dilution assays." Biometrics, Vol. 60, No. 2, pp. 407-417.

10.1111/j.0006-341X.2004.00185.x15180666

Heo, J. H., Kim, G. D., and Han, J. H. (1999). "Derivation of rainfall Intensity-Duration-Frequency equation based on the approproate probability distribution." Journal of Korea Water Resources Association, KWRA, Vol. 32, No. 3, pp. 247-254.

Ho, C. H., Lee, J. Y., Ahn, M. H., and Lee, H. S. (2003). "A sudden change in summer rainfall characteristics in Korea during the late 1970s." International Journal of Climatology: A Journal of the Royal Meteorological Society, Vol. 23, No. 1, pp. 117-128.

10.1002/joc.864

Kwon, H. H., and Moon, Y. I. (2006). "Improvement of overtopping risk evaluations using probabilistic concepts for existing dams." Stochastic Environmental Research and Risk Assessment, Vol. 20, No. 4, p. 223-237.

10.1007/s00477-005-0017-2

Kwon, H. H., Brown, C., and Lall, U. (2008a). "Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling." Geophysical Research Letters, Vol. 35, No. 5.

10.1029/2007GL032220

Kwon, H. H., Khalil, A. F., and Siegfried, T. (2008b). "Analysis of Extreme Summer Rainfall Using Climate Teleconnections and Typhoon Characteristics in South Korea 1." JAWRA Journal of the American Water Resources Association, Vol. 44, No. 2, pp. 436-448.

10.1111/j.1752-1688.2008.00173.x

Kwon, H. H., Kim, J. G., Lee, J. S., and Na, B. K. (2012). "Uncertainty assessment of single event rainfall-runoff model using bayesian model." Journal of Korea Water Resources Association, KWRA, Vol. 45, No. 5, pp. 505-516.

10.3741/JKWRA.2012.45.5.505

Kwon, H. H., Moon, Y. I., and Khalil, A. F. (2007). "Nonparametric monte carlo simulation for flood frequency curve derivation: an application to a Korean watershed 1." JAWRA Journal of the American Water Resources Association, Vol. 43, No. 5, pp. 1316-1328.

10.1111/j.1752-1688.2007.00115.x

Lee, J. J., Lee, J. S., Kim, B. I., and Park, J. Y. (2000). "Derivation of probable rainfall intensity formula of individual zone based on the representative probability distribution." Journal of Korea Water Resources Association, KWRA, Vol. 33, No. S1, pp. 124-129.

Lee, S. H., and Kwon, W. T. (2004). "A variation of summer rainfall in Korea." Journal of the Korean Geographical Society, Vol. 39, No. 6, pp. 819-832.

10.4055/jkoa.2004.39.2.142

Ministry of Construction & Transportation (2000). Korea probabilistic rainfalls map : development of water resources management techniques, - research report, pp. 2-3.

Park, C. Y., Moon, J. Y., Cha, E. J., Yun, W. T., and Choi, Y. E. (2008). "Recent changes in summer precipitation characteristics over South Korea." Journal of the Korean Geographical Society, Vol. 43, No. 3, pp. 324-336.

Shin, J. Y., and Lee, T. (2014). "Parameter estimation of the mixture normal distribution for hydro-meteorological variables using meta-heuristic maximum likelihood." Journal of the Korean Society of Hazard Mitigation, Vol. 14, No. 4, pp. 93-100.

10.9798/KOSHAM.2014.14.4.93

Smith, J. A. (1987). "Estimating the upper tail of flood frequency distributions." Water Resources Research, Vol. 23, No. 8, pp. 1657-1666.

10.1029/WR023i008p01657

Yoon, P. Y., Kim, T. W., Yang, J. S., and Lee, S. O. (2012). "Estimating quantiles of extreme rainfall using a mixed Gumbel distribution model." Journal of Korea Water Resources Association, KWRA, Vol. 45, No. 3, pp. 263-274.

10.3741/JKWRA.2012.45.3.263

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 :11
Pages :895-904
Received Date : 2019-08-07
Revised Date : 2019-10-07
Accepted Date : 2019-10-07
DOI :https://doi.org/10.3741/JKWRA.2019.52.11.895

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

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