비편향 회귀분석모형을 이용한 낙동강 본류 부유사량 산정방법의 신뢰도 향상

Improvement of Suspended Solid Loads Estimation in Nakdong River Using Minimum Variance Unbiased Estimator

  • 한수희 (부경대학교 환경시스템공학부) ;
  • 강두기 (부산대학교 토목공학과) ;
  • 신현석 (부산대학교 토목공학과) ;
  • 유재정 (국립환경과학원 낙동강물환경연구소) ;
  • 김상단 (부경대학교 환경시스템공학부)
  • Han, Suhee (Department of Environmental System Engineering, Pukyong National University) ;
  • Kang, Du Kee (Department of Civil Engineering, Pusan National University) ;
  • Shin, Hyun Suk (Department of Civil Engineering, Pusan National University) ;
  • Yu, Jae-Jeong (Nakdong River Water Environmental Research Center, National Institute of Environmental Research) ;
  • Kim, Sangdan (Department of Environmental System Engineering, Pukyong National University)
  • 투고 : 2007.01.15
  • 심사 : 2007.02.26
  • 발행 : 2007.03.30

초록

In this study three log-transformed linear regression models are compared with the focus of bias correction problem. The models are the traditional simple linear regression estimator (SL), the quasi maximum likelihood estimator (QMLE) and the minimum variance unbiased estimator (MVUE). Using such models, suspended solid loads can be estimated using the discharge - suspended solid data set that has been measured by NIER Nakdong River Water Environment Laboratory. As a result, SL shows negative bias for most values of the measured discharge range. QMLE is nearly unbiased for moderate values of the measured discharge range, but shows increasingly positive bias for either large or small value of the measured discharge range. MVUE is unbiased. It is also analyzed how the estimated regression coefficient and exponent are distributed along Nakdong river main stream.

키워드

과제정보

연구 과제번호 : 낙동강 하천수리특성분석 및 수리모의예측기법 개발

참고문헌

  1. 김상단, 송미영, 이기영, 이성룡, 단순회귀모형을 이용힌 인구와 도시적 토지이용이 팔당호 수질에 미치는 영향분석, 수질보전 한국물경학회지, 20, pp. 703-707 (2004)
  2. 낙동강물환경연구소, 2006년 유량측정사업, 국립환경과학원 (2006)
  3. Aitchison, J. and Brown, J. A. C, The Lognormal Distribution With Special Referance to Its Uses in Economics, Cambridge University Press, New York (1981)
  4. Bradu, D. and Mundlak, Y., Estimation in Lognormal Linear Models. J. Am. Stat. Assoc, 65(329), pp. 198-211 (1970) https://doi.org/10.2307/2283587
  5. Colin, T. A., Del.ong, L. L., and Gilroy, E. J., Estimating Constituent Loads. Water Resour. Res., 25(5), pp. 937-942 (1989) https://doi.org/10.1029/WR025i005p00937
  6. DeLong, L. L., Water Qualih of Streams and Springs. Green River Basin, Wyoming, U.S. Goel. Surv., Water Resour. Invest. Rep., 82-4008. p. 36 (1982)
  7. DeLong, L. L. and Wells, D. K., Estimating Average Dissolved-solids Yields from Basins Drained by Ephemeral and Intermittent Streams-Green River Basin. Wyoming, U.S. Goel. Surv., Water Resour. Invest. Rep., 87-4222, p. 29 (1987)
  8. Draper, N. and Smith. H, Applied Regression Analysis. 2nd ed., 709, John Wiley, New York (1981)
  9. Duan, N.. Smearing Estimate: A Nonparametric Retransformation .Method, J. Am. Stat. Assoc, 78(383). pp. 605-610 (1983) https://doi.org/10.2307/2288126
  10. Ferguson. R. I, River Loads Underestimated by Rating Curves, Water Resour. Res., 22(1), pp. 74-76 (1986) https://doi.org/10.1029/WR022i001p00074
  11. Ferguson, R. I, Accuracy and Precision of Methods for Estimating River Loads, Earth Surf. Processes Landforms, 12, pp. 95-104 (1987) https://doi.org/10.1002/esp.3290120111
  12. Finney, D. J., On the Distribution of a Variate Whose Logarithm Normally Distributed, J. R. Stat. Soe. Suppl., 7, pp. 155-161 (1941) https://doi.org/10.2307/2983663
  13. Gilroy, E. J., Hirsch, R. M. and Cohn. T. A., Mean Square Error of Regression-based Constituent Transport Estimates, Water Resour. Res., 26(9), pp. 2069-2077 (1990) https://doi.org/10.1029/WR026i009p02069
  14. Koch. R. W. and Smillic. G. M., Biased in Hydrologic Prediction Using Log-transformed Regression Models, Water Resour. Bull., 22(5), pp. 717-723 (1986) https://doi.org/10.1111/j.1752-1688.1986.tb00744.x
  15. Landwehr, J. M.. Some Properties of the Geometric Mean and Its Use in Water Quality Standards, Water Resour. Res. 14(3), pp. 467-473 (1987)
  16. Lane. W. L., Extraction of Information on Inorganic Water Quality, Hyclrol. Pap.. 73, Colo. State Univ.. Ft. Collins (1975)
  17. Lee. C. Y., Comparison of Two Correction Methods for the Bias due to the Logarithmic Transformation in the Estimation of Biomass, Can. J. Forest Res. 12. pp. 326-331 (1982) https://doi.org/10.1139/x82-047
  18. Likes. J., Variance of the MVUE for Lognormal Variance. Techno metrics, 22(2). pp. 253-258 (1980)
  19. Richards, R. P. and Holloway, J. Monte Carlo Studies of Sampling Strategies for Fstimating Tributary Loads, Water Resour. Res., 23(10). pp. 1939-1948 (1987) https://doi.org/10.1029/WR023i010p01939
  20. Rukhin, A. L., Improved Estimation in I.ognormal Models, J. Am. Stat. Assoc, 81(396), pp. 1046-1049 (1986) https://doi.org/10.2307/2289081
  21. Sichel. H. S., New Methods in the Statistical Evaluation of Minor Sampling Data. Inst. Min. Metall. Trans.. 61. pp. 261-288 (1952)
  22. Thomas. R. B.. Estimating Total Suspended Sediment Yield with Probability Sampling. Water Resour. Res., 21(9), pp. 1381-1388 (1985) https://doi.org/10.1029/WR021i009p01381
  23. Young, T. C. DePinto. J. V. and Ueidtke. T. H. factors Affecting the Efficiency of Some Estimators of Fluvial Total Phosphorus Load. Water Resour. Res., 24(9). pp. 535-1540 (1988)