Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Temporal distritution analysis of design rainfall by significance test of regression coefficients

회귀계수의 유의성 검정방법에 따른 설계강우량 시간분포 분석

  • Park, Jin Heea (Department of Civil Engineering, Kumoh National Institute of Technology) ;
  • Lee, Jae Joon (Department of Civil Engineering, Kumoh National Institute of Technology)
  • 박진희 (금오공과대학교 토목공학과) ;
  • 이재준 (금오공과대학교 토목공학과)
  • Received : 2022.02.28
  • Accepted : 2022.03.17
  • Published : 2022.04.30
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Abstract

Inundation damage is increasing every year due to localized heavy rain and an increase of rainfall exceeding the design frequency. Accordingly, the importance of hydraulic structures for flood control and defense is also increasing. The hydraulic structures are designed according to its purpose and performance, and the amount of flood is an important calculation factor. However, in Korea, design rainfall is used as input data for hydrological analysis for the design of hydraulic structures due to the lack of sufficient data and the lack of reliability of observation data. Accurate probability rainfall and its temporal distribution are important factors to estimate the design rainfall. In practice, the regression equation of temporal distribution for the design rainfall is calculated using the cumulative rainfall percentage of Huff's quartile method. In addition, the 6th order polynomial regression equation which shows high overall accuracy, is uniformly used. In this study, the optimized regression equation of temporal distribution is derived using the variable selection method according to the principle of parsimony in statistical modeling. The derived regression equation of temporal distribution is verified through the significance test. As a result of this study, it is most appropriate to derive the regression equation of temporal distribution using the stepwise selection method, which has the advantages of both forward selection and backward elimination.

국지성 호우 및 설계빈도 이상 강우의 증가로 침수피해가 매년 증가하고 있으며 이에 따라 홍수 조절 및 방어를 위한 수공구조물의 중요성이 증가하고 있다. 수공구조물은 목적과 성능에 따른 설계가 이루어지고 있고 홍수량이 중요한 산정 요소이나 국내에서는 관측자료의 신뢰성 부족 및 데이터의 부족으로 인하여 수공구조물 설계를 위한 수문해석 입력자료로 사용되는 설계강우량은 정확한 확률강우량의 산정과 시간분포가 중요한 요소로 작용한다. 실무에서는 Huff의 4분위 방법의 누가우량백분율을 이용하여 설계강우량의 시간분포 회귀식을 산정하고 있으며 분위별 곡선에 대한 회귀식은 전반적으로 정확도가 높게 나타나는 6차 다항회귀식을 일률적으로 사용하고 있다. 본 연구에서는 실무에서 일반적으로 설계강우량의 시간분포를 위해 사용하고 있는 Huff의 4분위 방법의 누가우량백분율을 이용하여 통계 모델링에서 간결함의 원리에 따라 변수선택법을 이용하여 시간분포 회귀식을 유도하였으며, 유의성 검정을 통한 시간분포 회귀식의 검증을 실시하였다. 변수선택법과 유의성 검정을 통한 시간분포 회귀식 산정 결과 전진선택법과 후방제거법의 장점을 모두 가지고 있는 단계선택법을 이용하여 시간분포 회귀식을 유도하는 것이 가장 적합한 것으로 분석되었다.

Keywords

Acknowledgement

이 연구는 금오공과대학교 대학 학술연구비로 지원되었음 (2019년).

References

  1. Allen, D.M. (1971). The prediction sum of squares as a criterion for selecting predictor variables. Technical Report no.23, Department of Statistics, University of Kentucky, KY, U.S.
  2. Draper, N.R., and Smith, H. (1981). Applied regression analysis. 2nd edition, John Wiley & Sons, NY, U.S.
  3. 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
  4. Jang, S.H., Yoon, J.Y., and Yoon, Y.N. (2006a). "A study on the improvement of Huff's method in Korea: I. Review of applicability of Huff's method in Korea." Journal of Korea Water Resources Association, Vol. 39, No. 9, pp. 767-777. https://doi.org/10.3741/JKWRA.2006.39.9.767
  5. Jang, S.H., Yoon, J.Y., and Yoon, Y.N. (2006b). "A study on the Improvement of Huff's method in Korea: II. Improvement of Huff's method." Journal of Korea Water Resources Association, Vol. 39, No. 9, pp. 779-786. https://doi.org/10.3741/JKWRA.2006.39.9.779
  6. Keifer, C.J., and Chu, H.H. (1957). "Synthetic storm pattern for drainage design." Journal of the Hydraulics Division, ASCE, Vol. 83, No. HY4, pp. 1-25.
  7. Lee, J.S., and Kim, G.D. (2005). An analysis of temporal and spatial distribution of urban rainfall. Research Report, FFC04-06. Urban Flood Disaster Management Research Center.
  8. Ministry of Environment (ME) (2019). Standard guidelines for flood estimation.
  9. Ministry of Land, Transport and Maritime Affairs (MLTMA) (2011). Study of improvement and supplement of probability rainfall.
  10. Ministry of Land, Transport and Maritime Affairs (MLTMA) (2012). Design flood calculation tips.
  11. Park, C.Y., and Lee, W.H. (1980). "A study on rainfall-pattern analysis for determination of dsign flow in small watershed." Journal of Korea Association of Hydrological sciences, Vol. 14, No. 4, pp. 13-18.
  12. Park, J.H., Lee, J.J., and Lee, S.H. (2018). "Statistical significance test of polynomial regression equation for Huff's quartile method of design rainfall." Journal of Korea Water Resources Association, Vol. 51, No. 3, pp. 263-272. https://doi.org/10.3741/JKWRA.2018.51.3.263
  13. Pilgrim, D.H., and Cordery, I. (1975). "Rainfall temporal patterns for design floods." Journal of the Hydraulics Division, ASCE, Vol. 101, No. HY1, pp. 81-95. https://doi.org/10.1061/JYCEAJ.0004197
  14. Salas, J.D., Delleur, J.W., Yevjevich, V., and Lane, W.L. (1980). Applied modeling of hydrologic time series. Water Resources Publications, CO, U.S.
  15. Seo, B.H., and Kim, N.W. (1989). Analysis of temporal variations for determining the local design storms. Korea Institute of Civil Engineering and Building Technology.
  16. Seo, S.D. (1965). "A study on temporal pattern of storms." Magazine of the Korean Society of Agricultural Engineers, Vol. 7, No. 2, pp. 972-977.
  17. Seong., W.H., and Lee, S.C. (2001). Regression analysis, Bobmunsa.
  18. Yen, B.C., and Chow, V.T. (1977). Feasibility study on research of local design storms. Report No. FHW A-RD-78-65, U.S. Department of Transportation, Federal Highway Administration, Washington, D. C., U.S.