Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
권호 표지
DOI QR코드

DOI QR Code

Drought Risk Analysis Using Stochastic Rainfall Generation Model and Copula Functions

추계학적 강우발생모형과 Copula 함수를 이용한 가뭄위험분석

  • Yoo, Ji Young (Department of Civil and Environmental Engineering, Hanyang University) ;
  • Shin, Ji Yae (Department of Civil and Environmental Engineering, Hanyang University) ;
  • Kim, Dongkyun (Department of Civil and Urban Engineering, Hongik University) ;
  • Kim, Tae-Woong (Department of Civil and Environmental Engineering, Hanyang University)
  • 유지영 (한양대학교 대학원 건설환경공학과) ;
  • 신지예 (한양대학교 대학원 건설환경공학과) ;
  • 김동균 (홍익대학교 건설도시공학부) ;
  • 김태웅 (한양대학교 공학대학 건설환경플랜트공학과)
  • Received : 2012.12.14
  • Accepted : 2013.01.21
  • Published : 2013.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

This study performed the bivariate drought frequency analysis for duration and severity of drought, using copula functions which allow considering the correlation structure of joint features of drought. We suggested the confidence intervals of duration-severity-frequency (DSF) curves for the given drought duration using stochastic scheme of monthly rainfall generation for 57 sites in Korea. This study also investigated drought risk via illustrating the largest drought events on record over 50 and 100 consecutive years. It appears that drought risks are much higher in some parts of the Nakdong River basin, southern and east coastal areas. However, such analyses are not always reliable, especially when the frequency analysis is performed based on the data observed over relatively short period of time. To quantify the uncertainty of drought frequency curves, the droughts were filtered by different durations. The 5%, 25%, 50%, 75%, and 95% confidence intervals of the drought severity for a given duration were estimated based on the simulated rainfall time series. Finally, it is shown that the growing uncertainties is revealed in the estimation of the joint probability using the two marginal distributions since the correlation coefficient of two variables is relatively low.

본 연구에서는 가뭄빈도해석을 위해 이변량 확률분포함수를 적용하였으며, 가뭄 특성(가뭄 지속기간과 심도)의 상호관계를 고려하여 지역적 가뭄특성을 종합적으로 판단하였다. 또한 단변량 가뭄해석의 한계점을 극복하기 위한 방안으로 이변량 가뭄해석을 수행하였으며, 이를 위해 코플라 함수를 적용하였다. 가뭄 발생의 확률 및 경향성을 종합적으로 나타내어 줄 수 있는 결합 확률밀도함수를 추정한 후, 지점별 가뭄빈도해석 및 과거 최대가뭄사상에 대한 단변량 및 이변량 재현기간을 산정하여 비교 분석하였다. 또한, 우리나라의 과거 최대가뭄사상에 대한 가뭄위험도분석을 위해, 연속되는 50년과 100년동안 최소 한번 발생하는 확률(과거 최대가뭄사상 크기의 가뭄)을 강우관측지점별로 계산하여 가뭄위험지역을 예상하였다. 그러나 우리나라와 같이 강수자료의 기록연한이 짧은 경우에는 이변량 가뭄빈도해석을 수행하는 데 큰 불확실성을 야기할 가능성이 있다. 그러므로 가뭄해석 결과의 불확실성을 정량화시키기 위한 방안으로 강수모의기법을 활용하였으며, 그 결과 관측된 가뭄사상으로 추정된 이변량 가뭄빈도곡선에 대한 5%, 25%, 50%, 75%, 그리고 95%의 신뢰구간을 제시할 수 있었다. 또한 가뭄 지속기간과 심도의 95% 신뢰수준에 대한 이변량 가뭄재현기간의 경계값(상한값 및 하한값)을 추정하였다. 그 결과 불확실성의 원인은 가뭄빈도해석 시 고려되었던 두 변량에 대한 낮은 상관성으로 인해, 확률적인 방법으로 결합분포모형을 추정하는 데 있어 발생한 불확실성인 것으로 확인되었다.

Keywords

References

  1. Adamowski, K. (1985). "Nonparametric kernel estimation of flood frequencies."Water Resources Research, Vol. 21, No. 11, pp. 1585-1590. https://doi.org/10.1029/WR021i011p01585
  2. Adamowski, K. (1996). "Nonparametric estimation of lowflow frequencies." Journal of Hydraulic Engineering, Vol. 122, pp. 46-49. https://doi.org/10.1061/(ASCE)0733-9429(1996)122:1(46)
  3. Bonaccorso, B., Cancelliere, A., and Rossi, G. (2003). "An analytical formulation of return period of drought severity." Stochastic Environmental Research and Risk Assessment, Vol. 17, No. 3, pp. 157-174. https://doi.org/10.1007/s00477-003-0127-7
  4. Cancelliere, A., and Salas, J.D. (2004). "Drought length properties for periodic-stochastic hydrologic data." Water Resources Research, Vol. 40 No. W02503, doi: 10.1029/2002WR001750.
  5. Chow, V.T., Maidment, D.R., and Mays, L.W. (1988). Applied Hydrology. McGraw-Hill Book Company.
  6. Chung, C., and Salas, J.D. (2000). "Drought occurrence probabilities and risks of dependent hydrologic processes." Journal of Hydrologic Engineering, Vol. 5, No. 3, pp. 259-268. https://doi.org/10.1061/(ASCE)1084-0699(2000)5:3(259)
  7. Delleur, J.W., and Kavvas, M.L. (1978). "Stochastic models for monthly rainfall forecasting and synthetic generation." Journal of Applied Meteorology, Vol. 17, No. 10, pp. 1528-1536. https://doi.org/10.1175/1520-0450(1978)017<1528:SMFMRF>2.0.CO;2
  8. Dracup, J.A., Lee, K.S., and Paulson, E.G. Jr. (1980). "On the definition of droughts."Water Resources Research, Vol. 16, No. 2, pp. 297-302. https://doi.org/10.1029/WR016i002p00297
  9. Entekhabi, D., Rodriguez-Iturbe, I., and Eagleson, P.S. (1989). "Probabilistic representation of the temporal rainfall process by a modified Neyman-Scott Rectangular Pulses Model: Parameter estimation and validation." Water Resources Research, Vol. 95, No. 95, pp. 295-302.
  10. Fernandez, B., and Salas, J.D. (1999). "Return period and risk of hydrologic events. I: mathematical formulation." Journal of Hydrologic Engineering, Vol. 4, No. 4, pp. 297-307. https://doi.org/10.1061/(ASCE)1084-0699(1999)4:4(297)
  11. Gonzalez, J., and Valdes, J.B. (2003). "Bivariate drought recurrence analysis using tree ring reconstructions." Journal of Hydrologic Engineering, Vol. 8, No. 5, pp. 247-258. https://doi.org/10.1061/(ASCE)1084-0699(2003)8:5(247)
  12. Haan, C.T. (2002). Statistical Method in Hydrology. The Iowa State University Press, Ames, IO, pp. 496.
  13. Kao, S.C., and Govindaraju, R.S. (2007). "A bivariate frequency analysis of extreme rainfall with implications for design." Journal of Geophysical Research, Vol. 112, No. D13119, doi:10.1029/2007JD008522.
  14. Kao, S.C., and Govindaraju, R.S. (2010). "A copula-based joint deficit index for droughts." Journal of Hydrology, Vol. 380, No. 1-2, pp. 121-134. https://doi.org/10.1016/j.jhydrol.2009.10.029
  15. Kim, S.D., Ryu, J.S., Oh, K.R., and Jeong, S.M. (2012). "An application of copulas-based joint drought index for determining comprehensive drought conditions" Journal of Korean Society of Hazard Mitigation, Vol. 12, No. 1, pp. 223-230. https://doi.org/10.9798/KOSHAM.2012.12.1.223
  16. Kim, T.W., and Valdes, J.B. (2005). "Synthetic generation of hydrologic time series based on nonparametric random generation." Journal of Hydrologic Engineering, Vol. 10, No. 5, pp. 395-404. https://doi.org/10.1061/(ASCE)1084-0699(2005)10:5(395)
  17. Kim, T.W., Valdés, J.B., and Yoo, C. (2003). "Nonparametric approach for estimating return periods of droughts in arid regions." Journal of Hydrologic Engineering, Vol. 8, No. 5, pp. 237-246. https://doi.org/10.1061/(ASCE)1084-0699(2003)8:5(237)
  18. Kim, T.W., Valdes, J.B., and Yoo, C. (2006). "Nonparametric approach for bivariate drought characterization using Palmer drought index." Journal of Hydrologic Engineering, Vol. 11, No. 2, pp. 134-143. https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(134)
  19. Kwak, J.W., Kim, D.G., Lee, J.S., and Kim, H.S. (2012). "Hydrological drought analysis using copula theory" Journal of the Korea Society of Civil Engineers, Vol. 32, No. 3B, pp. 161-168.
  20. Lall, U. (1995). "Recent advance in nonparametric function estimation: Hydrologic application." Reviews of Geophysics, Vol. 33, No. S2, pp. 1093-1102. https://doi.org/10.1029/95RG00343
  21. Loaiciga, H., and Leipnik, R. (1996). "Stochastic renewal model of low-flow streamflow sequences." Stochastic Hydrology and Hydraulics, Vol. 10, No. 1, pp. 65-85. https://doi.org/10.1007/BF01581794
  22. McKee, T.B., Doesken, N.J., and Kleist, J. (1993). "The relationship of drought frequency and duration to time scales." Eighth Conference on Applied Climatology, American Meteorological Society, Anaheim, California, pp. 179-184.
  23. Mirakbari, M., Ganji, A., and Fallah, S. (2010). "Regional bivariate frequency analysis of meteorological droughts." Journal of Hydrologic Engineering, Vol. 15, No. 12, pp. 985-1000. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000271
  24. Mishra, A.K., and Desai, V.R. (2005). "Drought forecasting using stochastic models" Stochastic Environmental Research and Risk Assessment, Vol. 19, No. 5, pp. 326-339. https://doi.org/10.1007/s00477-005-0238-4
  25. Moon, Y.I., and Lall, U. (1994). "Kernel quantile function estimator for flood frequency analysis." Water Resources Research, Vol. 30, No. 11, pp. 3095-3103. https://doi.org/10.1029/94WR01217
  26. Narayana, I.R. (1982). "Stochastic modeling of monthly rainfall." Journal of Hydrology, Vol. 57, No. 3-4, pp. 375-387. https://doi.org/10.1016/0022-1694(82)90156-1
  27. Nelsen, R.B. (2006). An Introduction to Copulas. Springer, New York, pp. 109-155.
  28. Oliveria, J.D.T. (1975). "Bivariate extremes: extensions." Bulletin of the International Statistical Institute, Vol. 46, No. 3-4, pp. 241-251.
  29. Rosenberg, K.J. (2004). Stochastic Modeling of Rainfall and Generation of Synthetic Rainfall Data at Mawson Lakes. Ph.D. Thesis, University of South Australia, Adelaide, Australia.
  30. Salas, J.D., Fu, C., Cancelliere, A., Dustin, D., Bode, D., Pineda, A., and Vincent, E. (2005). "Characterizing the severity and risk of drought in the Poudre River, Colorado." Journal of Water Resources Planning and Management, Vol. 131, No. 5, pp. 383-393. https://doi.org/10.1061/(ASCE)0733-9496(2005)131:5(383)
  31. Scott, D.W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization. Wiley, New York.
  32. Sen, Z. (1980). "Statistical analysis of hydrologic critical droughts" Journal of the Hydraulics Division, Vol. 106, No. 1, pp. 99-115.
  33. Sharma, A., and O'Neill, R. (2002). "A nonparametric approach for representing interannual dependence in monthly streamflow sequences." Water Resources Research, Vol. 38, No. 7, pp. 5-1:5-10.
  34. Shiau, J.T., and Shen, H.W. (2001). "Recurrence analysis of hydrologic droughts of differing severity." Journal ofWater Resources Planning and Management, Vol. 127, No. 1, pp. 30-40. https://doi.org/10.1061/(ASCE)0733-9496(2001)127:1(30)
  35. Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, London.
  36. Sklar, A. (1959). "Fonctions de repartition a n dimensions et leurs marges." Publ. Inst. Statist. Univ. Paris 8, pp. 11.
  37. Smakhtin, V.U. (2001). "Low flow hydrology: a review." Journal of Hydrology, Vol. 240, No. 3-4, pp. 147-186. https://doi.org/10.1016/S0022-1694(00)00340-1
  38. Thomas, H.A., and Fiering, M.B., (1962). "Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation" Design of Water Resources Systems, (Ed. by A. Maas et al.) Chapter 12. Harvard University Press, Cambridge.
  39. Ünal, N., Aksoy, H., and Akar, T. (2004). "Annual and monthly rainfall data generation schemes." Stochastic Environmental Research and Risk Assessment, Vol. 18, No. 4, pp. 245-257.
  40. Wilhite, D.A. (2000). "Drought as a natural hazard: concepts and definitions." Drought, A Global Assessment, Routledge Publishers, UK.
  41. Wong, G., Lambert, M.F., Leonard, M., and Metcalfe, A.V. (2010). "Drought analysis using trivariate Copulas conditional on climatic states." Journal of Hydrologic Engineering, Vol. 15, No. 129.
  42. Yevjevich, V. (1967). "On objective approach to definitions and investigations of continental hydrologic droughts." Hydrology Paper, No. 23, Colorado State University, Fort Collins, pp. 4-18.
  43. Yoo, C., and Ryoo, S. (2003). "Analysis of drought return and duration characteristics at Seoul." Journal of Korea Water Resources Association, Vol. 36, No. 4, pp. 561-573. https://doi.org/10.3741/JKWRA.2003.36.4.561
  44. Yue, S., Ouarda, T.B.M.J., Bobee, B., Legendre, P., and Bruneau, P. (1999). "The Gumbel mixed model for flood frequency analysis." Journal of Hydrology, Vol. 226, No. 1-2, pp. 88-100. https://doi.org/10.1016/S0022-1694(99)00168-7
  45. Zhang, L., and Singh, V.P. (2006). "Bivariate flood frequency analysis using the copula method." Journal of Hydrologic Engineering, Vol. 11, No. 2, pp. 150-164. https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(150)

Cited by

  1. Estimation and Assessment of Bivariate Joint Drought Index based on Copula Functions vol.47, pp.2, 2014, https://doi.org/10.3741/JKWRA.2014.47.2.171
  2. Non-Parametric Low-Flow Frequency Analysis Using RCPs Scenario Data : A Case Study of the Gwangdong Storage Reservoir, Korea vol.34, pp.4, 2014, https://doi.org/10.12652/Ksce.2014.34.4.1125
  3. Estimation of drought risk through the bivariate drought frequency analysis using copula functions vol.49, pp.3, 2016, https://doi.org/10.3741/JKWRA.2016.49.3.217
  4. A development of trivariate drought frequency analysis approach using copula function vol.49, pp.10, 2016, https://doi.org/10.3741/JKWRA.2016.49.10.823
  5. Application of Streamflow Drought Index using Threshold Level Method vol.47, pp.5, 2014, https://doi.org/10.3741/JKWRA.2014.47.5.491
  6. Seasonal Drought Damage Prediction Method Based On the Climate Forecasting Data in Geum River Basin vol.16, pp.1, 2016, https://doi.org/10.9798/KOSHAM.2016.16.1.83
  7. Forecasting Quarterly Inflow to Reservoirs Combining a Copula-Based Bayesian Network Method with Drought Forecasting vol.10, pp.2, 2018, https://doi.org/10.3390/w10020233