All Issue

2016 Vol.49, Issue 6 Preview Page
Comparison of probability distributions to analyze the number of occurrence of torrential rainfall events

집중호우사상의 발생횟수 분석을 위한 확률분포의 비교

Sang Ug Kima*
,
Hyeung Bae Kima
김 상욱a*
,
김 형배a
aDept. of Civil Engineering, Kangwon National University
a강원대학교 공과대학 토목공학과
*교신저자. *Corresponding Author. 
30 June 2016. pp. 481-493
PDF XML Citation
Abstract

LISFLOOD-FP model in which channel flows are resolved separately from the floodplain flows using either a kinematic or diffusive wave approximation has been used to analyze flooding behavior on the lower Mankyung River influenced by backwater. A calibration and validation process was applied using the previous flood events to assess the model performance. Sensitivity analysis was conducted for main calibrated parameters, such as Manning roughness coefficient and downstream boundary condition. Also, we examined the effect of warm-up for the initial conditions. The results show that the computed hydrograph is in good agreement with measured data on the study reach, even though it was a hydrologic kinematic wave model. The sensitive analysis show that the difference between the computed results may be greater depending on the used calibrated parameters and that the sufficient calibration/validation process against various flood events is necessary. If the flood inundation simulation is performed using the validated model, it is expected to be able to contribute about river planning and policy decision-making for flood damage reduction.

Keywords
torrential rainfall
Poisson distribution
zero-inflated
Bayesian
informative prior distribution

본 연구에서는 최근 기후변화로 인한 집중호우의 발생횟수의 경향을 확률적으로 분석함에 있어 1개월 동안 80 mm/day 이상의 강우사상을 집중호우로 정의하여, 대구 및 부산 강우관측소로부터 수집된 384개월 동안의 집중호우를 분석하였다. 집중호우 월별 발생횟수와 같은 형식의 자료의 확률적 분석은 대개 Poisson 분포 (POI)가 사용되나 자료에 포함된 0자료의 과잉은 확률분포를 왜곡시키는 문제를 발생시킨다. 본 연구에서는 이 문제를 개선하기 위하여 개발된 일반화 Poisson 확률분포 (GPD), 0-과잉 Poisson 확률분포 (ZIP), 0-과잉 일반화 Poisson 확률분포 (ZIGP), Bayesian 0-과잉 일반화 Poisson 확률분포 (Bayesian ZIGP)를 집중호우 자료에 적용하고, 5개 모형의 특성을 비교분석하였으며, Bayesian ZIGP 모형의 구축에 있어서는 정보적 사전분포를 사용함으로써 모형의 정확도를 개선하였다. 분석결과 분석하고자 하는 자료에 0이 과다하게 포함되어 있는 경우 POI 및 GPD 분포는 관측결과와는 다른 결과를 제시하여 적절한 모형으로 고려되지 못함을 알 수 있었다. 5가지 모형 중 정보적 사전분포를 탑재한 Bayesian ZIGP 모형이 가장 관측 자료와 유사한 결과를 도출하였으나 모형의 구축에 수반되는 실용적인 측면을 고려하면 ZIP 모형도 충분히 사용될 수 있는 모형으로 추천되었다.

키워드
집중호우
Poisson 분포
0-과잉
베이지안
정보적 사전분포
References
1
Abdul, R.U. and Zeephongsekul, P. (2014) "Copula based analysis of rainfall severity and duration: a case study" Theoretical and Applied Climatology Vol. 115, No. 12, pp. 153-166.
2
Angers, J.F., and Biswas, A. (2003) "A Bayesian analysis of zero-inflated generalized Poisson model." Computational Statistics & Data Analysis Vol. 42, No. 1-2, pp. 37-46.
3
Bates, B.C., and Campbell, E.P. (2001) "A Markov Chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling." Water Resources Research Vol. 37, No. 4, pp. 937-947.
4
Berger, J.O. (1985) Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York.
5
Bertucio, R.C., and Julius, J.A. (1990) "Analysis of CDF:Surry, Unit 1 internal events." US Nuclear Regulatory Commission NUREG/CR-4550, Vol. 5, pp. 2-8.
6
Bohning, D., Dietz, E., Schlattmann, P., Mendonca, L., and Kirchner, U. (1999) "The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology." Journal of the Royal Statistical Society Series A (Statistics in Society) Vol. 162, No. 2, pp. 195-209.
7
Carlin, B.P., and Louis, T.A. (1996) Bayes and empirical Bayes methods for data analysis. Chapman and Hall, New York.
8
Chapman, T. (1998) "Stochastic modelling of daily rainfall: the impacts of adjoining wet days on the distribution of rainfall amounts." Environmental Modelling and Software Vol. 13, No. 3-4, pp. 317-324.
9
Chib, S., and Greenberg, E. (1995) "Understanding the Metropolis-Hastings algorithm." Journal of the American Statistical Association Vol. 49, No. 4, pp. 327-335.
10
Chung, E.S., and Kim, S.U. (2013) "Bayesian rainfall frequency analysis with extreme value using the informative prior distribution." KSCE Journal of Civil Engineering Vol. 17, No. 6, pp. 1502-1514.
11
Cohen, Jr. A.C. (1960) "Estimating the parameters of a modified Poisson distribution." Journal of American Statistical Association Vol. 55, No. 289, pp. 139-143.
12
Consul, P.C., Jain, G.C. (1973) "A Generalization of the Poisson distribution." Technometrics Vol. 15, No. 4, pp. 791-799.
13
Gamerman, D. (1997) Markov Chain Monte Carlo-Stochastic simulation for Bayesian inference. Chapman&Hall, London UK.
14
Gelman, A., and Rubin, D.B. (1992) "Inference from iterative simulation using multiple sequences." Statistical Science Vol. 7, No. 4, pp. 457- 511.
15
Geweke, J. (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian statistics 4, eds. Bernardo, J.M., Berger, J., Dawid, A.P., and Smith, A.F.M. Oxford, UK, Oxford University Press.
16
Goyal, M.K. (2014) "Statistical analysis of long term trends of rainfall during 1901-2002 at Assam, India." Water Resources Management Vol. 28, No. 6, pp. 1501-1515.
17
HSBC (2011) Climate investment update. HSBC Global Research, 13 October.
18
Jimoh, O.D., and Webster, P. (1996) "Optimum order of Markov chain for daily rainfall in Nigeria." Journal of Hydrology Vol. 185, No. 1-4, pp. 45-69.
19
Kaplan, S. (1985) "Two-stage Poisson-type problem in probabilistic risk analysis." Risk Analysis Vol. 5, No. 3, pp. 227-230.
20
Katz, R.W., and Parlange, M.B. (1995) "Generalizations of chain-dependent processes: applications to hourly precipitation." Water Resources Research Vol. 31, pp. 1331-1341.
21
Kavetski, D., Kuczera, G., and Franks, S.W. (2006) "Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory." Water Resources Research 42: W03407
22
Kim, S.U., and Lee, K.S. (2010) "Regional low flow frequency analysis using Bayesian regression and prediction at ungauged catchment in Korea." KSCE Journal of Civil Engineering Vol. 14, No. 1, pp. 87-98.
23
Lambert, D. (1992) "Zero inflated Poisson regression with an application to defects in manufacturing." Technometrics Vol. 34, No. 1, pp. 1-14.
24
Lee, K.S., and Kim, S.U. (2008) "Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method." Hydrological Processes Vol. 22, No. 12, pp. 1949-1964.
25
Lee, C.E., Kim, S.U., and Lee, S. (2014) "Time-dependent reliability analysis using Bayesian MCMC on the reduction of reservoir storage by sedimentation." Stochastic Environmental Research Risk Assessment Vol. 28, No. 3, pp. 639-654.
26
Malakoff, D. (1999) "Bayes offers a ‘New way to make sense of numbers’." Science Vol. 286, No. 5444, pp. 1460-1464.
27
Maritz, J.S., and Lwin, T. (1989) "Empirical Bayes Approach to Multiparameter Estimation: With Special Regerence to Multinomial Distribution" Ann. Inst. Statis. Math. Vol. 41, No. 1, pp. 81-99.
28
Marshall, L., Nott, D., and Sharma, A. (2004) "A comparative study of Markov Chain Monte Carlo methods for conceptual rainfall-runoff modeling." Water Resources Research 40: W02501
29
Mullahy, J. (1986) "Specification and testing of some modified count data models." Journal of Econometrics Vol. 33, No. 3, pp. 341-365.
30
Raftery, A.E., and Lewis, S. (1992) How many iterations in the Gibbs sampler? In: Bernardo, J.M., Berger, J., Dawid, A.P., and Smith, A.F.M. (ed) Bayesian statistics 4, Oxford University Press, Oxford, UK, pp. 763-773.
31
Roberts, G.O., Gelman, A., and Gilks, W.R. (1994) Weak convergence and optimal scaling of random walk Metropolis-Hastings algorithms. Technical Report, University of Cambridge.
32
Saidi, H., Ciampittiello, M., Dresti, C., and Ghiglieri, G. (2015) "Assessment of trends in extreme precipitation event: A case study in Piedmont (North-West Italy)." Water Resources Management Vol. 29, No. 1, pp. 63-80.
33
Seidou, O., Ouarda, T.B.M.J., Barbet, M., Bruneau, P., and Bobee, B. (2006) "A parametric Bayesian combination of local and regional information in flood frequency analysis." Water Resources Research Vol. 42: W11408
34
Singh, S.N. (1963) "A note on inflated Poisson distribution." Journal of Indian Statistical Association Vol. 1, pp. 140-144.
35
Todorovic, P., and Yevjevich, V. (1969) Stochastic process of precipitation. Hydrology papers 35, Colorado State University, Fort Collins, Colorado
36
Wheeler, T.A. (1993) "Analysis of the LaSalle Unit 2 nuclear power plant: risk methods integration and evaluation program (RMIEP): parameter estimation analysis and screening human reliability analysis." US Nuclear Regulatory Commission NUREG/CR-4832:Vol. 5.
Information
  • Publisher :KOREA WATER RESOURECES ASSOCIATION
  • Publisher(Ko) :한국수자원학회
  • Journal Title :Journal of Korea Water Resources Association
  • Journal Title(Ko) :한국수자원학회 논문집
  • Volume : 49
  • No :6
  • Pages :481-493
  • Received Date : 2016-02-12
  • Revised Date : 2016-03-22
  • Accepted Date : 2016-03-22
  • DOI :https://doi.org/10.3741/JKWRA.2016.49.6.481
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