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An Hourly Extreme Data Estimation Method Developed Using Nonstationary Bayesian Beta Distribution

비정상성 Bayesian Beta 분포를 이용한 시 단위 극치자료 추정기법 개발

  • Kim, Yong-Tak (Chonbuk National University-Department of Civil Engineering) ;
  • Kim, Jin-Young (Chonbuk National University-Department of Civil Engineering) ;
  • Lee, Jae Chul (Chungnam State University-Department of Civil Engineering and Informatics) ;
  • Kwon, Hyun-Han (Chonbuk National University-Department of Civil Engineering)
  • Received : 2017.01.25
  • Accepted : 2017.04.12
  • Published : 2017.05.30

Abstract

Extreme rainfall has become more frequent over the Korean peninsula in recent years, causing serious damages. In a changing climate, traditional approaches based on historical records of rainfall and on the stationary assumption can be inadequate and lead to overestimate (or underestimate) the design rainfalls. A main objective of this study is to develop a stochastic disaggregation method of seasonal rainfall to hourly extreme rainfall, and offer a way to derive the nonstationary IDF curves. In this study, we propose a novel approach based on a Four-Parameter Beta (4P-beta) distribution to estimate the nonstationary IDF curves conditioned on the observed (or simulated) seasonal rainfall, which becomes the time-varying upper bound of the 4P beta distribution. Moreover, this study employed a Bayesian framework that provides a better way to take into account the uncertainty in the model parameters. The proposed model showed a comparable design rainfall to that of GEV distribution under the stationary assumption. As a nonstationary rainfall frequency model, the proposed model can effectively translate the seasonal variation into the sub-daily extreme rainfall.

Keywords

References

  1. Bae, D. H., Jung, I. W., Lee, B. J., and Lee, M. H. (2011). Future Korean Water Resources Projection Considering Uncertainty of GCMs and Hydrological Models, Korea Water Resources Association, 44(5), 389-406. [Korean Literature] https://doi.org/10.3741/JKWRA.2011.44.5.389
  2. Burton, A., Kilsby, C. G., Fowler, H. J., Cowpertwait, P. S. P., and O'Connell, P. E. (2008). RainSim: A Spatialtemporal Stochastic Rainfall Modelling System, Environmental Modelling & Software, 23(12), 1356-1369. https://doi.org/10.1016/j.envsoft.2008.04.003
  3. Choi, Y. J. and Moon, J. Y. (2000). Observed Trends in The Daily Precipitation Intensity of Korea Summer Season, Korean Meteorological Society, 339-341. [Korean Literature]
  4. Coles, S., Pericchi, L. R., and Sisson, S. (2003). A Fully Probabilistic Approach to Extreme Rainfall Modeling, Journal of Hydrology, 273, 35-50. https://doi.org/10.1016/S0022-1694(02)00353-0
  5. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis, 3rd Edition, CRC Press.
  6. Jang, S. S., Ahn, S. R., Joh, H. K., and Kim, S. J. (2015). Assessment of Climate Change Impact on Imha-Dam Watershed Hydrologic Cycle under RCP Scenarios, Journal of the Korean Association of Geographic Information Studies, 18(1), 156-169. [Korean Literature] https://doi.org/10.11108/kagis.2015.18.1.156
  7. Jeong, H. G., Kim, S. J., and Ha, R. (2013). Assessment of Climate Change Impact on Storage Behavior of Chungju and the Regulation Dams Using SWAT Model, Korea Water Resources Association, 46(12), 1235-1247. [Korean Literature] https://doi.org/10.3741/JKWRA.2013.46.12.1235
  8. Joh, H. K., Kim, S. B., Cheong, H., Shin, H. J., and Kim, S. J. (2011). Projection of Future Snowfall by Using Climate Change Scenarios, Journal of the Korean Association of Geographic Information Studies, 14(3), 188-202. [Korean Literature] https://doi.org/10.11108/kagis.2011.14.3.188
  9. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995). Continuous Univariate Distributions, 2, Wiley.
  10. Jun, C. H. and Yoo, C. (2013). Analysis on the Characteristics about Representative Temporal-distribution of Rainfall in the Annual Maximum Independent Rainfall Events at Seoul using Beta Distribution, Korea Water Resources Association, 46(4), 361-372. [Korean Literature] https://doi.org/10.3741/JKWRA.2013.46.4.361
  11. Katz, R. W., Parlange, M. B., and Naveau, P. (2002). Statistics of Extremes in Hydrology, Advances in Water Resources, 25, 1287-1304. https://doi.org/10.1016/S0309-1708(02)00056-8
  12. Kim, D. K., Kwon, H. H., Hwang, S., and Kim, T. W. (2014). Evaluation of the Applicability of the Poisson Cluster Rainfall Generation Model for Modeling Extreme Hydrological Events, Journal of the Korean Society of Civil Engineers, 34(3), 773-784. https://doi.org/10.12652/Ksce.2014.34.3.0773
  13. Kim, D. K., Shin, J. Y., Lee, S. O., and Kim, T. W. (2013). The Application of the Poisson Cluster Rainfall Generation Model to the Flood Analysis, Journal of Korea Water Resources Association, 46(5), 439-447. https://doi.org/10.3741/JKWRA.2013.46.5.439
  14. Kim, J. Y., Park, C. Y., and Kwon, H. H., (2016). A Development of Downscaling Scheme for Sub-daily Extreme Precipitation using Conditional Copula Model, Korea Water Resources Association, 49(10), 863-876. [Korean Literature]
  15. Kim, S. U. and Lee, K. S. (2008). At-site Low Flow Frequency Analysis Using Bayesian MCMC: I. Theoretical Background and Construction of Prior Distribution, Journal of Korea Water Resources Association, 41(1), 35-47. https://doi.org/10.3741/JKWRA.2008.41.1.035
  16. Kwon, H. H., Brown, C., and Lall, U. (2008). Climate Informed Flood Frequency Analysis and Prediction in Montana Using Herarhical Bayesian Modeling, Geophysical Research Letters, 35.
  17. Kwon, H. H., Kim, J. G., Lee, J. S., and Na, B. K. (2012). Uncertainty Assessment of Single Event Rainfallrunoff Model Using Bayesian Model, Journal of Korea Water Resources Association, 45(5), 505-516. https://doi.org/10.3741/JKWRA.2012.45.5.505
  18. Kwon, H. H., Lall, U., and Obeysekera, J. (2009). Simulation of Daily Rainfall Scenarios with Interannual and Multidecadal Climate Cycles for South Florida, Stochastic Environmental Research and Risk Assessment, 23(7), 879-896. https://doi.org/10.1007/s00477-008-0270-2
  19. 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, Journal of the Korean Society of Hazard Mitigation, 11(6), 207-216. [Korean Literature] https://doi.org/10.9798/KOSHAM.2011.11.6.207
  20. Kwon, J. W. and Kang, B. S. (2008). Downscaling Climate Simulation Using Spatio-temporal Random Cascade Model in Korea Region, Korea Water Resources Association, 120-124. [Korean Literature]
  21. Kwon, Y. M. and Kim, T. W. (2009). Derived I-D-F Curve in Seoul Using Bivariate Precipitation Frequency Analysis, Korean Society of Civil Engineers, 29(2b), 155-162. [Korean Literature]
  22. Kyoung, M. S., Sivakumar, B., Kim, H. S., and Kim, B. S. (2008). Chaotic Disaggregation of Daily Rainfall Time Series, Korea Water Resources Association, 41(9), 959-967. [Korean Literature] https://doi.org/10.3741/JKWRA.2008.41.9.959
  23. Lee, J. J., Kwon, H. H., and Hwang, K. N. (2010). Concept of Seasonality Analysis of Hydrologic Extreme Variables and Design Rainfall Estimation Using Nonstationary Frequency Analysis, Journal of Korea Water Resources Association, 43(8), 733-745. [Korean Literature] https://doi.org/10.3741/JKWRA.2010.43.8.733
  24. Lee, M. H., Jung, I. W., and Bae, D. H. (2011). Korean Flood Vulnerability Assessment on Climate Change, Korea Water Resources Association, 44(8), 653-666. [Korean Literature] https://doi.org/10.3741/JKWRA.2011.44.8.653
  25. Lima, C. H. R. and Lall, U. (2010a). Climate Informed Long Term Seasonal Forecasts of Hydroenergy Inflow for the Brazilian Hydropower system, Journal of Hydrology, 381, 65-75. https://doi.org/10.1016/j.jhydrol.2009.11.026
  26. Lima, C. H. R. and Lall, U. (2010b). Climate Informed Monthly Streamflow Forecasts for the Brazilian Hydropower Network Using a Periodic Ridge Regression Model, Journal of Hydrology, 380, 438-449. https://doi.org/10.1016/j.jhydrol.2009.11.016
  27. Lima, C. H. R. and Lall, U. (2010c), Spatial Scaling in a Changing Climate: A Hierarchical Bayesian Model for Non-stationary Multi-site Annual Maximum and Monthly Streamflow, Journal of Hydrology, 383, 307-318. https://doi.org/10.1016/j.jhydrol.2009.12.045
  28. McGuffie, K., Henderson-Sellers, A., Holbrook, N., Kothavala, Z., Balachova, O., and Hoekstra, J. (1999). Assessing Simulations of Ddaily Temperature and Precipitation Variability with Global Climate Models for Present and Enhanced Greenhouse Climates, International Journal of Climatology, 19, 1-26 https://doi.org/10.1002/(SICI)1097-0088(199901)19:1<1::AID-JOC348>3.0.CO;2-T
  29. Osborn, T. J., Hulme, M., and Basnett, T. A. (2000). Observed Trends in the Daily Intensity of United Kongdom Precipitation, International Journal of Climatology, 20(4), 347-364. https://doi.org/10.1002/(SICI)1097-0088(20000330)20:4<347::AID-JOC475>3.0.CO;2-C
  30. Renard, B., (2011). A Bayesian Hierarchical Approach to Regional Frequency Analysis, Water Resources Research, 47(11), http://doi.wiley.com/10.1029/2010WR010089.
  31. Seo, Y. M. and Park, K. B. (2011). Uncertainty Analysis for Parameter Estimation of Probability Distribution in Rainfall Frequency Analysis Using Bootstrap, Journal of Environmental Science International, 20(3), 321-327. [Korean Literature] https://doi.org/10.5322/JES.2011.20.3.321
  32. Shin, J. Y., Kim, T. W., and Kim, D. K. (2012). Application of GEV Model to Nonstationary Rainfall Frequency Analysis for the Administrative District, Korea Society of Hazard Mitigation, 22. [Korean Literature]
  33. So, B. J., Kwon, H. H., and An, J. H., (2012). Trend Analysis of Extreme Precipitation Using Quantile Regression, Korea Water Resources Association, 45(8), 815-826. [Korean Literature] https://doi.org/10.3741/JKWRA.2012.45.8.815
  34. Sohn, K. H., Bae, D. H., and Ahn, J. H. (2014). Projection and Analysis of Drought according to Future Climate and Hydrological Information in Korea, Korea Water Resources Association, 47(1), 71-82. [Korean Literature] https://doi.org/10.3741/JKWRA.2014.47.1.71
  35. Viglione, A., Merz, R., Salinas, J. L., and Bloschl, G. (2013). Flood frequency hydrology: 3. A Bayesian analysis, Water Resources Research, 49(2), 675-692, http://doi.wiley.com/10.1029/2011WR010782.