Analysis of BOD Mean Concentration and Confidence Interval using Bootstrap Technique

Bootstrap 기법을 이용한 BOD 평균 농도 및 신뢰구간 분석

  • Kim, Kyung Sub (Department of Environmental Engineering, Hankyong National University)
  • 김경섭 (국립한경대학교 환경공학과)
  • Received : 2009.10.21
  • Accepted : 2010.01.14
  • Published : 2010.03.30

Abstract

It is very important to know mean and confidence interval of water-quality constituents such as BOD for water-quality control and management of rivers and reservoirs effectively. The mean and confidence interval of BOD at Anseong2 and Hwangguji3 sampling stations which are located at the border of local governments in Anseong Stream were estimated and analyzed in this paper using Bootstrap technique which is one of non-parametric statistics. The results of Bootstrap were compared with arithmetic mean, geometric mean, Biweight method mean as a point estimator and distribution mean came from the appropriate probability distribution of Log-normal. In Bootstrap technique 12 data set was randomly selected in each year and 1000 samples was produced to get parameter of population. Visual Basic for Applications (VBA) of Microsoft Excel was utilized in Bootstrap. It was revealed that the Bootstrap technique can be used to explain more rigorously and robustly the achievement or violation of BOD target concentration in Total Maximum Daily Load (TMDL).

Keywords

References

  1. 김경섭, 안태진(2009). 안성천 유역의 BOD농도 확률분포 특성. 수질보전 한국물환경학회지, 25(3), pp. 425-431.
  2. 김병식, 김형수, 서병하(2002). Bootstrap 방법에 의한 하천 유출량 모의와 왜곡도. 한국수자원학회논문집, 35(3), pp. 275-284.
  3. 이명우, 이충성, 김형수, 심명필(2005). Bootstrap방법과 SIR 알고리즘을 이용한 확률강우량 결정과 위험도 분석. 대한토목학회논문집, 25(5B), pp. 365-373.
  4. 전명식(1990). 통계적 데이터 분석방법을 위한 컴퓨터의 활용 I: 붓스트랩 이론과 응용. 응용통계연구, 3(1), pp. 121-141.
  5. 전영두, 박종천, 정의승(2008). 부트스트랩 기법을 이용한 소음진동 스펙트럼 분석법 소개. 2008년 춘계학술대회논문집, 한국소음진동공학회, pp. 185-188.
  6. 정석근, 최일수, 장대수(2008). 부트스트랩과 베이지안 방법으로 추정한 수자원관리에서의 생물학적 기준점의 신뢰구간. 한국수산학회지, 41(2), pp. 107-112.
  7. 환경부(2009). 물환경정보시스템. http://water.nier.go.kr/.
  8. Chang, K. Y., Hong, K. O., and Pak, S. I. (2007). Bootstrap simulation for quantification of uncertainty in risk assessment. Korean J. Vet. Res., 47(2), pp. 259-263.
  9. Efron, B. (1979). Bootstrap Method: Another Look at the Jackknife. The Annuals of Statistics, Institute of Mathematical Statistics, 7(1), pp. 1-26.
  10. Kim, K. S., Kim, B., and Kim, J. H. (2002). Robust measures of location in water-quality data. Water Engineering Research, 3(3), pp. 195-202.
  11. Manly, B. F. J. (2006). Randomization, Bootstrap and Monte Carlo methods in Biology, CRC, Boca Ranton, FL.
  12. Novotny, V. (2004). Simplified Databased Total Maximum Daily Loads, or the World is Log-Normal. J. Environ. Eng., 130(6), pp. 674-683. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:6(674)
  13. Schwarz, G. E., Hoos, A. B., Alexander, R. B., and Smith, R. A. (2006). The SPARROW Surface Water-Quality Model: Theory. Application and User Documentation, U.S. Geological Survey, Reston, Virginia.
  14. Tung, Y. K. and Hathhorn, W. E. (1988). Assessment of probability distribution of dissolved oxygen deficit. Journal of Environmental Engineering. ASCE, 114(6), pp. 1421-14.15. https://doi.org/10.1061/(ASCE)0733-9372(1988)114:6(1421)