Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
권호 표지
DOI QR코드

DOI QR Code

Application of the Beta Distribution for the Temporal Quantification of Storm Events

호우사상의 시간적 정량화를 위한 베타분포의 적용

  • Jun, Chang-Hyun (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University) ;
  • Yoo, Chul-Sang (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University)
  • 전창현 (고려대학교 대학원 건축사회환경공학부) ;
  • 유철상 (고려대학교 공과대학 건축사회환경공학부)
  • Received : 2011.09.06
  • Accepted : 2012.03.08
  • Published : 2012.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This study suggested the parameter estimation method for given rainfall events to be properly expressed by the beta distribution. For this purpose, this study compared the characteristics of probability density function with the parameter proposed considering the cases with and without addition to the rainfall peak, and the cases of using the real hyetograph and the rearranged hyetograph about the rainfall peak. As an example, this study analyzed the independent rainfall events at Seoul in 2010 and the annual maximum independent rainfall events from 1961 to 2010. The results derived are as follows. First, this study confirmed the necessity of additional consideration on rainfall peak to mimic the real hyetograph of rainfall events by the beta distribution. Second, this study confirmed the case of using rearranged hyetograph about the rainfall peak derived a better beta distribution to well mimic the characteristics of real rainfall than the case using the real hyetograph.

본 연구에서는 주어진 호우사상을 베타분포로 적절히 표현하기 위한 매개변수의 결정 방법을 제시하였다. 이를 위해 첨두에 대한 고려를 추가한 경우와 그렇지 않은 경우, 실제 우량주상도 및 첨두를 중심으로 재배열된 수정 우량주상도를 사용하는 경우 등을 고려하여 그 특성을 비교 검토하였다. 본 연구는 서울 지점의 2010년 독립 호우사상과 1961~2010년 사이의 연 최대치 독립 호우사상을 대상으로 베타분포를 적용하고, 그 결과를 분석하였다. 그 결과를 정리하면 다음과 같다. 첫째, 베타분포를 이용하여 실제 호우사상의 우량주상도 형태를 유사하게 표현하기 위해서는 첨두에 대한 추가적인 고려가 필요한 것으로 확인되었다. 둘째, 첨두를 중심으로 시간강우를 좌우 순차적으로 재배열한 수정 우량주 상도를 이용하는 경우가 실제 우량주상도를 이용하는 경우보다 실제 강우의 시간분포 특성에 보다 가까운 베타분포를 유도함을 확인하였다.

Keywords

References

  1. 권재호, 박무종, 김중훈 (2004). "비점오염원 산정을 위한 강우 분석." 한국수자원학회 학술발표회 논문집, 한국수자원학회, pp. 666-670.
  2. 김남원(1998). 강우의시.공간분포특성: 점강우모형매개변수 추정. 한국건설기술연구원.
  3. 오규창 (2005). "유역종합치수계획 수립 현황 및 문제점." 한국수자원학회 학술발표회 기획세션II, 한국수자원학회.
  4. 박철순 (2012). 독립 호우사상의 빈도해석 및 유출해석. 석사학위논문, 고려대학교.
  5. 박철순, 유철상 (2012). "Freund 이변량 지수분포의 매개변수 추정과정 검토." 한국수자원학회논문집, 한국수자원학회, 제45권, 제2호, pp. 191-201.
  6. 윤용남 (2009). 수문학, 청문각.
  7. 윤용남, 장수형, 강성규, 박민석 (2004). "설계홍수량 산정을 위한 적정 설계강우시간분포의 개발." 한국수자원학회 학술발표회 논문집, 한국수자원학회, pp. 54.
  8. 이동률, 정상만 (1992). "한강유역 강우의 시.공간적 특성." 한국수자원학회지, 한국수자원학회, 제25권, 제4호, pp. 75-85.
  9. 이상렬 (2005). "유역종합치수계획의 바람직한 방향설정." 한국수자원학회 학술발표회 기획세션II, 한국수자원학회.
  10. 정종호, 윤용남 (2005). 수자원설계실무, 구미서관.
  11. Beran, M.A., and Sutcliffe, J.V. (1972). "An index of flood-producing rainfall based on rainfall and soil moisture deficit." Journal of Hydrology, Vol. 17, pp. 229-236. https://doi.org/10.1016/0022-1694(72)90006-6
  12. Bhunya, P.K., Mishra, S.K., Ojha, C.S.P., and Ronny Berndtsson (2004). "Parameter Estimation of Beta Distribution for Unit Hydrograph Derivation." Journal of Hydrologic Engineering, Vol. 9, Issue. 4, pp. 325-332. https://doi.org/10.1061/(ASCE)1084-0699(2004)9:4(325)
  13. Bhunya, P.K., Berndtsson, R., Ojha, C.S.P., and Mishra, S.K. (2007). "Suitability of Gamma, Chi-square, Weibull, and Beta distributions as synthetic unit hydrographs." Journal of Hydrology, Vol. 334, pp. 28-38. https://doi.org/10.1016/j.jhydrol.2006.09.022
  14. Bogardi, J., Duckstein, L., and Rumambo, O. (1988). "Practical generation of synthetic rainfall event time series in a semi-arid climatic zone." Journal of Hydrology, Vol. 103, pp. 357-373. https://doi.org/10.1016/0022-1694(88)90144-8
  15. Brubaker, K.L., and Menoes, M. (2001). "A technique to estimate snow depletion curves from time-series data using the beta distribution." Proceedings of the Eastern Snow Conference, Vol. 58, pp. 343-346.
  16. Cooke, R.A., Mostaghimi, S., and Woeste, F. (1995). "Effect of hydraulic conductivity probability distribution function on simulated solute leaching." Water Environment Research, Vol. 67, No. 2, pp. 159-168. https://doi.org/10.2175/106143095X131303
  17. Ferreira, V. (1990). Temporal characteristics of arid land rainfall events. In: French, R. (Ed.), Hydraulics/Hydrology of Arid Lands, ASCE, pp. 584-589.
  18. Hafley, W.L., and Schreuder, H.T. (1977). Statistical distributions for fitting diameter and height data in even-aged stands." Canadian Journal of Forest Research, Vol. 4, pp. 481-487.
  19. Hogg, W. (1980). Time distribution of short duration storm rainfall in Canada. In: Proc. Canadian Hydrology Symposium: 80, NRCC, Ottawa, pp. 53-63.
  20. Huff, F.A. (1967). "Time distribution of rainfall in heavy storms." Water Resources Research, Vol. 3, No. 4, pp. 1007-1019. https://doi.org/10.1029/WR003i004p01007
  21. Huff, F.A. (1986). "Urban hydrology review." Bulletin of the American Meteorological Society, Vol. 67, No. 6, pp. 703-712.
  22. Knapp, H.V., and Terstriep, M.L. (1981). Effects of basin rainfall estimates on dam safety design in illinois. Illinois State Water Survey Contract Report, 253, pp. 57.
  23. Maltamo, M., Puumalainen, J., and Paivinen, R. (1995). "Comparison of beta and Weibull functions for modelling basal area diameter distribution in stands of Pinun sylvestris and Picea abies." Scandinavian Journal of Forest Research, Vol. 10, pp. 284-295. https://doi.org/10.1080/02827589509382895
  24. Mays, L. (2001). General characteristics of arid and semiarid regions. Urban drainage in specific climates, vol. III: urban drainage in arid and semi-arid climates, IHP-V, Technical Documents in Hydrology, pp. 40-159.
  25. Nouh, M. (1985). "Effects of rainfall runoff model assumptions on optimal storm sewer system design." The Arabial Journal for Science and Engineering, Vol. 12, No. 1, pp. 19-35.
  26. Pearson, K. (1934). Tables of the Incomplete Beta-Function. Biometrika Office, University College, London.
  27. Pilgrim, D., and Cardery, I. (1975). "Rainfall temporal patterns for design floods." Journal of Hydraulics Division, ASCE, Vol. 101, No. HY1, pp. 81-95.
  28. Ricciardi, K.L., Pinder, G.F., and Belitz, K. (2005). "Comparison of the log-normal and beta distribution functions to describe the uncertainty in permeability." Journal of Hydrology, Vol. 313, pp. 248-256. https://doi.org/10.1016/j.jhydrol.2005.03.007
  29. Sabol, G., and Stevens, K. (1990). Comparison of design rainfall criteria for the southwest. In: French, R. (Ed.), Hydraulics/Hydrology of Arid Lands, ASCE, pp. 102-107.
  30. SCS. (1972). National Engineering Handbook, Section 4. Hydrology. Soil Conservation Service, US Department of Agriculture: Washington, DC.
  31. Ward, A.B., Bridges, T., and Barfield, B. (1980). An evaluation of hydrologic modeling techniques for determining a design storm hydrograph. Proc., International Symposium on Urban Storm Runoff, pp. 59-69.

Cited by

  1. Estimating Cumulative Distribution Functions with Maximum Likelihood to Sample Data Sets of a Sea Floater Model vol.37, pp.5, 2013, https://doi.org/10.5394/KINPR.2013.37.5.453
  2. Evaluation of the Concept of Critical Rainfall Duration by Bivariate Frequency Analysis of Annual Maximum Independent Rainfall Event Series in Seoul, Korea vol.21, pp.1, 2016, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001259
  3. Analysis on the Characteristics about Representative Temporal-distribution of Rainfall in the Annual Maximum Independent Rainfall Events at Seoul using Beta Distribution vol.46, pp.4, 2013, https://doi.org/10.3741/JKWRA.2013.46.4.361
  4. Comparative Analysis of Estimation Methods for Basin Averaged Effective Rainfall Using NRCS-CN Method vol.34, pp.2, 2014, https://doi.org/10.12652/Ksce.2014.34.2.0493