Browse > Article
http://dx.doi.org/10.3741/JKWRA.2016.49.5.411

Assessment of uncertainty associated with parameter of gumbel probability density function in rainfall frequency analysis  

Moon, Jang-Won (Dept. of Civil Engineering, Seoul University)
Moon, Young-Il (Dept. of Civil Engineering, Seoul University)
Kwon, Hyun-Han (Dept. of Civil Engineering, Chonbuk National University)
Publication Information
Journal of Korea Water Resources Association / v.49, no.5, 2016 , pp. 411-422 More about this Journal
Abstract
Rainfall-runoff modeling in conjunction with rainfall frequency analysis has been widely used for estimating design floods in South Korea. However, uncertainties associated with underlying distribution and sampling error have not been properly addressed. This study applied a Bayesian method to quantify the uncertainties in the rainfall frequency analysis along with Gumbel distribution. For a purpose of comparison, a probability weighted moment (PWM) was employed to estimate confidence interval. The uncertainties associated with design rainfalls were quantitatively assessed using both Bayesian and PWM methods. The results showed that the uncertainty ranges with PWM are larger than those with Bayesian approach. In addition, the Bayesian approach was able to effectively represent asymmetric feature of underlying distribution; whereas the PWM resulted in symmetric confidence interval due to the normal approximation. The use of long period data provided better results leading to the reduction of uncertainty in both methods, and the Bayesian approach showed better performance in terms of the reduction of the uncertainty.
Keywords
Uncertainty; Bayesian Analysis; Parameter Uncertainty; Frequency Analysis; Gumbel Distribution;
Citations & Related Records
Times Cited By KSCI : 11  (Citation Analysis)
연도 인용수 순위
1 Congdon, P. (2007). "Bayesian statistical modelling", John Wiley & Sons.
2 Coles, S., Pericchi, L. R. and Sisson, S. (2003). "A fully probabilistic approach to extreme rainfall modeling.", Journal of Hydrology, Vol. 273, No. 1, pp. 35-50.   DOI
3 Coles, S. and Pericchi, L. (2003). "Anticipating catastrophes through extreme value modelling. Journal of the Royal Statistical Society: Series C (Applied Statistics)", Vol. 52, No. 4, pp. 405-416.
4 Hamed, K. and Rao, A.R. (1999). "Flood Frequency Analysis", CRC Press,
5 Greenwood, J. A., Landwehr, J. M., Matalas, N. C., and Wallis, J. R. (1979). "Probability weighted moments: Definition and relation to parameters of several distributions expressible in inverse form." Water Resources Research, Vol. 15, No. 5, pp. 1049-1054.   DOI
6 Han, J. W., Kwon, H.-H. and Kim T.-W. (2009). "Reliability Evaluation of Parameter Estimation Methods of Probability Density Function for Estimating Probability Rainfalls", Journal of KOSHAM, Vol. 9, No. 6, pp. 143-151.
7 Hong, C. S., Wone, S. Y., Ahn, J. H., Ahn, W. S. (2001). "Reliability analysis for the estimation of frequency-based rainfall", Journal of KOSHAM, Vol. 9, No. 6, pp. 143-151.
8 Hosking, J.R.M., and Wallis, J.R. (1986a). "Paleoflood hydrology and flood frequency analysis." Water Resources Research, Vol. 22, pp, 543-550.   DOI
9 Jung, J. H. and Yoon, Y. N. (2007). "Planning of water resource system", Goomibook, Seoul, Korea (in Korean).
10 Kuczera, G. (1996). "Correlated rating curve error in flood frequency inference.", Water Resources Research, Vol. 32, No. 7, pp. 2119-2127.   DOI
11 Kim, S. U., Lee, K. S. (2008a). "At-site low flow frequency analysis using Bayesian MCMC: I. Theoretical background and construction of prior distribution", Journal of Korean Water Resources Association, Vol. 1, No. 3, pp. 111-122.
12 Kim, S. U., Lee, K. S. (2008b). "At-site low flow frequency analysis using Bayesian MCMC: II. Application and Comparative Studies", Journal of Korean Water Resources Association, Vol. 41, No. 1, pp. 49-63.   DOI
13 Kim, Y. S., Heo, J. H. and Ryu, H. J., (1995). "Study on Applicability of Probability Weighted Moment Method to Rainfall Frequency Analysis", Journal of Korean Society of Civil Engineers, Vol. 15, No. 6, pp. 1647-1658.
14 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 Korean Society of Civil Engineers, Vol. 30, No. 4B, pp. 389-397.
15 Kwon, H. H., Moon, Y. I., Kim, B. S. and Yoon, S. Y. (2008). "Parameter Optimization and Uncertainty Analysis of the NWS-PC Rainfall-Runoff Model Coupled with Bayesian Markov Chain Monte Carlo Inference Scheme", Journal of Korean Society of Civil Engineers, Vol. 28, No. 4B, pp. 383-392.
16 Kwon, Y. M., Park, J. W. and Kim, T.-W. (2009). "Estimation of Design Rainfalls Considering an Increasing Trend in Rainfall Data", Journal of Korea Water Resources Association, Vol. 29, No. 2B, pp. 131-139.
17 Lee, C.J., Ahn, J.H. and Kim, T.W. (2010). "Evaluation of probability rainfalls estimated from non-stationary rainfall frequency analysis", Journal of Korean Water Resources Association, Vol. 43, No. 2, pp. 187-199.   DOI
18 Lee, J.S. (2006). Hydrology, Goomibook, Seoul, Korea (in Korean).
19 Lee, S. B. (2004). "A Comparative Study on Parametric and Nonparametric Methods of Rainfall Frequency Analyses", M.S. dissertation, Yonsei University.
20 Ministry of Land, Transport and Maritime Affairs (2012). "Guideline of estimating design flood (in Korean)."
21 O'Connell, D. R., Ostenaa, D. A., Levish, D. R. and Klinger, R. E. (2002). "Bayesian flood frequency analysis with paleohydrologic bound data.", Water Resources Research, Vol. 38, No. 5, pp. 16-1.
22 Park, Y.J., Kwon H.-H., Chung, E.S., Kim, T.-W. (2014). "Comparison of design rainfalls from the annual maximum and the non-annual exceedance series", Journal of the Korean Society of Civil Engineers, Vol. 34, No. 2, pp. 469-478.   DOI
23 Shin, J. Y., Park, Y. J. and Kim T.-W. (2013). "Estimation of Future Design Rainfalls in Administrative Districts Using Nonstationary GEV Model", Journal of KOSHAM, Vol. 13, No. 3, pp. 147-156.
24 Reis, D. S. and Stedinger, J. R. (2005). "Bayesian MCMC flood frequency analysis with historical information. Journal of Hydrology", Vol. 313, No. 1, pp. 97-116.   DOI
25 Seo, Y. M. and Park, K. B. (2011). "Uncertainty Analysis for Parameter Estimation of Probability Distribution in Rainfall Frequency Analysis Using Bootstrap", Journal of the Environmental Sciences, Vol. 20, No. 3, pp. 321-327.   DOI
26 Seo, Y.M. and Park, K.B. (2011). "Uncertainty analysis for parameters of probability distribution in rainfall frequency analysis by Bayesian MCMC and Metropolis Hastings Algorithm", Journal of the Environmental Sciences, vol. 20, No. 3, pp.329-340.   DOI
27 Tasker, G.D. (1987). "Comparison of methods for estimating low flow characteristic of streams", Water Resources Bull., Vol. 23, No. 6, pp. 1077-1083.   DOI