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http://dx.doi.org/10.3741/JKWRA.2008.41.3.325

Regional Low Flow Frequency Analysis Using Bayesian Multiple Regression  

Kim, Sang-Ug (Seoul National University BK21 SIR Group, Seoul National University)
Lee, Kil-Seong (Dept. of Civil and Environmental Engineering, Seoul National University)
Publication Information
Journal of Korea Water Resources Association / v.41, no.3, 2008 , pp. 325-340 More about this Journal
Abstract
This study employs Bayesian multiple regression analysis using the ordinary least squares method for regional low flow frequency analysis. The parameter estimates using the Bayesian multiple regression analysis were compared to conventional analysis using the t-distribution. In these comparisons, the mean values from the t-distribution and the Bayesian analysis at each return period are not significantly different. However, the difference between upper and lower limits is remarkably reduced using the Bayesian multiple regression. Therefore, from the point of view of uncertainty analysis, Bayesian multiple regression analysis is more attractive than the conventional method based on a t-distribution because the low flow sample size at the site of interest is typically insufficient to perform low flow frequency analysis. Also, we performed low flow prediction, including confidence interval, at two ungauged catchments in the Nakdong River basin using the developed Bayesian multiple regression model. The Bayesian prediction proves effective to infer the low flow characteristic at the ungauged catchment.
Keywords
Regional low flow frequency analysis; Uncertainty; Bayesian multiple regression; t-distribution; Ungauged catchment;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Stedinger, J.R. (1983). "Confidence intervals for design events." Journal of Hydraulic Engineering, Vol. 109, No. 1, pp. 13-27   DOI
2 Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E. (1993). "Frequency Analysis of Extreme Events." in Handbook of Hydrology, Maidment, D.(eds). McGraw-Hill, New York, Chapter 18
3 Vicens, G.J., Rodriguez-Iturbe, I., and Schaake Jr, J.C. (1975). "A Bayesian framework for the use of regional information in hydrology." Water Resources Research, Vol. 11, No. 3, pp. 405-414   DOI
4 Vrugt, J.A., Gupta, H.V., Bouten, W., and Sorooshian, S. (2003). "Shuffled complex evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters." Water Resources Research, Vol. 39, No. 8, SWC 1-16
5 Wang, Q.J. (2001). "A Bayesian joint probability approach for flood record augmentation." Water Resources Research, Vol. 37, No. 6, pp. 1707-1712   DOI   ScienceOn
6 Wood, E.F., and Rodriguez-Iturbe, I. (1975a). "Bayesian inference and decision making for extreme hydrologic events." Water Resources Research, Vol. 11, No. 4, pp. 533-542   DOI
7 Wood, E.F., and Rodriguez-Iturbe, I. (1975b). A Bayesian approach to analyze uncertainty among flood frequency models. Water Resources Research, Vol. 11, No. 6, pp. 839-843   DOI
8 Zhang, B., and Govindaraju, R.S. (2000). "Prediction of watershed runoff using Bayesian concepts and modular neural networks." Water Resources Research, Vol. 3, pp. 753-762   DOI   ScienceOn
9 Lee, K.S., and Kim, S.U. (2007). "Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method." Hydrological Processes, In press(on-line published)   DOI   ScienceOn
10 Martz, H.F. and Waller, R.A. (1982). Bayesian Reliability Analysis. John Wiley & Sons, N.Y
11 O'Connell, D.R.H., Ostenaa, D.A., Levish, D.R., Klinger, and R.E. (2002). "Bayesian flood frequency analysis with paleohydrologic bound data." Water Resources Research, Vol. 38, No. 5, pp. 1-14
12 Reis Jr., D.S., and Stedinger, J.R. (2005). "Bayesian MCMC flood frequency analysis with historical information." Journal of Hydrology, Vol. 313, pp. 97-116   DOI   ScienceOn
13 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   DOI   ScienceOn
14 Sorensen, D. and Gianola, D. (2002). Likelihood, Bayesian, and MCMC methods in Quantitative Genetics. Springer-Verlag, New York
15 Kuczera, G., and Parent E. (1998). "Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm." Journal of Hydrology, Vol. 211, pp. 69-85   DOI   ScienceOn
16 Madsen, H., and Rosbjerg, H.D. (1997). "Generalized least squares and empirical Bayes estimation in regional partial duration series index flood modeling." Water Resources Research, Vol. 33, No. 4, pp. 771-781   DOI   ScienceOn
17 Kingston, G.B., Lambert, M.F., and Maier, H.R. (2005). "Bayesian training of artificial neural networks used for water resources modeling." Water Resources Research, Vol. 41, W12409   DOI   ScienceOn
18 Krzysztofowicz, R. (1983a). "Why should forecaster and a decision maker use Bayes theorem." Water Resources Research, Vol. 19, No. 2, pp. 327-336   DOI
19 Krzysztofowicz, R. (1983b). "A Bayesian Markov model of the flood forecast process." Water Resources Research, Vol. 19, No. 6, pp. 1455-1465   DOI
20 Kuczera, G. (1999). "Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference." Water Resources Research, Vol. 35, No. 5, pp. 1551-1557   DOI   ScienceOn
21 Durrans, S.R. and Tomic, S. (1996). "Regionalization of low-flow frequency estimates: An Alabama case study." Water Resources Bulletin, Vol. 32, No. 1, pp. 23-37
22 Kavetski, D., Kuczera, G., and Fanks, S.W. (2006). "Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory." Water Resources Research, Vol. 42, W03407   DOI   ScienceOn
23 Reis Jr., D.S., Stedinger, J.R., and Martins, E.S. (2005). "Bayesian generalized least squares regression with application to log Pearson type III regional skew estimation." Water Resources Research, Vol. 41, W10419   DOI   ScienceOn
24 Thiemann, M., Trosset, M., Gupta, H.V., and Sorooshian, S. (2001). "Bayesian recursive parameter estimation for hydrologic models." Water Resources Research, Vol. 37, No. 10, pp. 2521-2535   DOI   ScienceOn
25 Whitley, R.J. and Hromadka II, T.V. (1999). "Approximate confidence intervals for design floods for a single site using a neural network." Journal of Hydrology, Vol. 153, pp. 265-290   DOI   ScienceOn
26 Gringorten, I.I. (1963). "A plotting rule for extreme probability paper." Journal of Geophysics Research, Vol. 68, No. 3, pp. 813-814   DOI
27 Kaufman L., and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis, John Wiley & Sons, N.Y
28 건교부, 한국수자원공사 (2006). 유역조사 보고서(낙동강유역)
29 Hosking, J.R.M, and Wallis, J.R. (1997). Regional Frequency Analysis. Cambridge University Press, New York
30 Kelly, K.S. and Krizysztofowicz, R. (1994). "Probability distributions for flood warning systems." Water Resources Research, Vol. 30, No. 4, pp. 1145-1152   DOI   ScienceOn
31 김상욱 (2007). Low flow frequency analysis using Bayesian approach. 박사학위논문, 서울대학교
32 김상욱 (2008). "Bayesian MCMC를 이용한 저수량 점빈도분석: II. 적용과 비교분석." 한국수자원학회논문집, 한국수자원학회, 제41권, 제1호, pp. 49-63   DOI
33 Ashkar, F. and Quarda, T.B.M.J. (1998). "Approximate confidence intervals for quantiles of gamma and generalized gamma distributions." Journal of Hydrologic Engineering, Vol. 3, No. 1, pp. 43-51   DOI   ScienceOn
34 Chatterjee, S. and Price, B. (1977). Regression Analysis by Example. John Wiley & Sons, N.Y
35 Chowdhury, J.U., and Stedinger, J.R. (1991). "Confidence interval for design flood with estimated skew coefficient." Journal of Hydraulic Engineering, Vol. 117, No. 7, pp. 811-931   DOI
36 Cohn, T.A., Lane, W.L., and Stedinger, J.R. (2001). "Confidence intervals for expected moments algorithm flood quantile estimates." Water Resources Research, Vol. 37, No. 6, pp. 1695-1706   DOI   ScienceOn
37 Coles, S.G., and Powell, E.A. (1996). "Bayesian methods in extreme value modeling: A review and new developments." International Statistical Review, Vol. 64, No. 1, pp. 119-136   DOI   ScienceOn