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http://dx.doi.org/10.12652/Ksce.2017.37.1.0029

A Bayesian GLM Model Based Regional Frequency Analysis Using Scaling Properties of Extreme Rainfalls  

Kim, Jin-Young (Chonbuk National University)
Kwon, Hyun-Han (Chonbuk National University)
Lee, Byung-Suk (Chonbuk National University)
Publication Information
KSCE Journal of Civil and Environmental Engineering Research / v.37, no.1, 2017 , pp. 29-41 More about this Journal
Abstract
Design rainfalls are one of the most important hydrologic data for river management, hydraulic structure design and risk analysis. The design rainfalls are first estimated by a point frequency analysis and the IDF (intensity-duration-frequency) curve is then constructed by a nonlinear regression to either interpolate or extrapolate the design rainfalls for other durations which are not used in the frequency analysis. It has been widely recognised that the more reliable approaches are required to better account for uncertainties associated with the model parameters under circumstances where limited hydrologic data are available for the watershed of interest. For these reasons, this study developed a hierarchical Bayesian based GLM (generalized linear model) for a regional frequency analysis in conjunction with a scaling function of the parameters in probability distribution. The proposed model provided a reliable estimation of a set of parameters for each individual station, as well as offered a regional estimate of the parameters, which allow us to have a regional IDF curve. Overall, we expected the proposed model can be used for different aspects of water resources planning at various stages and in addition for the ungaged basin.
Keywords
IDF curve; Bayesian GLM; Scaling property; Uncertainty;
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Times Cited By KSCI : 8  (Citation Analysis)
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1 Lee, J. J., Kwon, H. H. and Hwang, K. N. (2010). "Concept of seasonality analysis of hydrologic extreme variables and design rainfall estimation using nonstrationary frequency analysis." Journal of Korea Water Resources Association, KWRA, Vol. 43, No. 8, pp. 733-745 (in Korean).   DOI
2 Menabde, M. and Sivapalan, M. (2000). "Modeling of rainfall time series and extremes using bounded random cascades and levy-stable distributions." Water Resources Research, Vol. 36, pp. 3293-3300.   DOI
3 Menabde, M., Seed, A. and Pegram, G. (1999). "A simple scaling model for extreme rainfall." Water Resources Research, Vol. 35, No. 1, pp. 335-339.   DOI
4 Sherman, C. W. (1931). "Frequency and intensity of excessive rainfall at Boston." Trans. Am. Soc. Civ. Eng., Vol. 95, pp. 951-960.
5 Shin, J. Y., Kim, T. S., Kim, S. Y. and Heo, J. H. (2007). "Parameter estimation of intensity-duration-frequency formula using genetic algorithm (II): Separation of Short and Long Durations." Journal of Korea Water Resources Association, KWRA, Vol. 40, No. 10, pp. 823-832.   DOI
6 Singh, V. P. and Zhang, L. (2007). "IDF curves using the frank archimedean copula." Journal of hydrologic engineering, Vol. 12, No. 6, pp. 651-662.   DOI
7 Veneziano, D. and Langousis, A. (2005). "The areal reduction factor: A mutifractal analysis." Water Resource Research, Vol. 41, W07008, doi:10.1029/2004WR003765.   DOI
8 Willems, P. (2000). "Compound intensity-duration-frequency relationships of extreme precipitation for two seasons and two storm types." Journal of Hydrology, Vol. 233, pp. 189-205.   DOI
9 Yoo, C. S., Kim, N. W. and Jung, K. S. (2001). "A point rainfall model and rainfall intensity-duration-frequency analysis." Journal of Korea Water Resources Association, KWRA, Vol. 34, No. 6, pp. 577-586 (in Korean).
10 Yu, P. S., Yang, T. C. and Lin, C. S. (2004). "Regional rainfall intensity formulas based on scaling property of rainfall." Journal of Hydrology, Vol. 295, pp. 108-123.   DOI
11 Daniel, C., Douglas, N. and Philippe, N. (2007). "Bayesian spatial modeling of extreme precipitation return levels." Journal of the American Statistical Association, Vol. 102, No. 479, pp. 824-840.   DOI
12 Ariff, N. M., Jemain, A. A., Ibrahim, K. and Wan Zin, W. Z. (2012). "IDF relationships using bivariate copula for storm events in Peninsular Malaysia." Journal of Hydrology, Vol. 470-471, pp. 158-171.   DOI
13 Bernard, M. M. (1932). "Formulas for rainfall intensities of long durations." Trans. Am. Soc. Civ. Eng., Vol. 96, pp. 592-624.
14 Bougadis, J. and Adamowsi, K. (2006). "Scaling model of a rainfall intensity-duration-frequency relationship." Hydrological Processes, Vol. 20, pp. 3747-3757.   DOI
15 Deidda, R. (2000). "Rainfall downscaling in a space-time multifractal framework." Water Resource Research, Vol. 36, pp. 1779-1794.   DOI
16 Garcia-Marin, A. P., Ayuso-Munoz, J. L., Jimenez-Hornero, F. J. and Estevez, J. (2013). "Selecting the best IDF model by using the multifractal approach." Hydrological processes, Vol. 27, pp. 433-443.   DOI
17 Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian Data Analysis. CHAPMAN&HALL/CRC.
18 Gupta, V. K. and Waymire, E. C. (1993). "A statistical analysis of mesoscale rainfall as a random cascade." J. Appl. Meteoro., Vol. 32, pp. 251-267.   DOI
19 Heo, J. H., Kim, K. D. and Han, J. H. (1999). "Derication 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 (in Korean).
20 Harris, D. M., Menabde, A. S. and Austin, G. (1998). "Breakdown coefficients and scaling properties of rain fields." Nonlinear Processes in Geophysics, Vol. 5, pp. 93-104.   DOI
21 Katz, R. W., Parlange, M. B. and Naveau, P. (2002). "Statistics of extremes in hydrology." Water Resources Research, Vol. 25, pp. 1287-1304.   DOI
22 Hosking, J. R. M., Wallis, J. R. and Wood, E. F. (1985). "An appraisal of the regional flood frequency procedure in the UK Flood Studier Report." Hydrological Sciences Journal, Vol. 30, No. 1, pp. 85-109.   DOI
23 James, B. E. and Thomas, H. J. (2004). "A hierarchical bayesian approach to seasonal hurricane modeling." Journal of Climate, doi:http://dx.doi.org/10.1175/1520-0442(2004)017<2813:AHBATS> 2.0.CO;2.   DOI
24 Jung, Y. H., Kim, S. Y., Kim, T. S. and Heo, J. H. (2008). "Rainfall quantile estimation using scaling property in Korea." Journal of Korea Water Resources Association, KWRA, Vol. 41, No. 9, pp. 873-884 (in Korean).   DOI
25 Kim, J. Y., Kim, J. G., Lee, J. C. and Kwon, H. H. (2016). "A development of rating-curve usign Bayesian Multi-Segmented model." Journal of Korea Water Resources Association, KWRA, Vol. 49, No. 3, pp. 253-262 (in Korean).   DOI
26 Kim, J. Y., Kwon, H. H. and Lim, J. Y. (2014). "Development of hierarchical bayesian spatial regional frequency analysis model considering geographical characteristics." Journal of Korea Water Resources Association, KWRA, Vol. 47, No. 5, pp. 469-482 (in Korean).   DOI
27 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 (in Korean).   DOI
28 Kim, K. T., Kim, T. S., Kim, S. Y. and Heo, J. H. (2008). "Application of intensity-duration-frequency curve to korea derived by cumulative distribution function." Journal of Korean Society of Civil Engineer, KSCE, Vol. 28, No. 4B, pp. 363-374.
29 Kuo, C. C., Gan, T. Y. and Chan, S. (2013). "Regional intensityduration-frequency curves derived from ensemble empirical mode decomposition and scaling property." Journal of Hydrologic Engineering, Vol. 18, No. 1, pp. 66-74.   DOI
30 Kwon, H. H. and Myeong, S. J. (2011). "Development of a future disaster risk assessment model for climate change using bayesian GLM and statistical downscaling model." Korean Society of Hazard Mitigation, Vol. 11, No. 6, pp. 207-216 (in Korean).
31 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 Resources Association, KWRA, Vol. 46, No. 1, pp. 13-24 (in Korean).   DOI
32 Kwon, H. H., Upmanu, L. and Jayantha, O. (2009). "Simulation of daily rainfall scenarios with interannual and mutidecadal climate cycles for South Florida." Stochastic Environmental Research and Risk Assessment, Vol. 23, pp. 879-896. doi:10.1007/s00477-008-0270-2.   DOI