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Development of Rating Curves Using a Maximum Likelihood Model  

Kim, Gyeong-Hoon (Department of Civil Engineering, Gyeongsang National University)
Park, Jun-Il (Department of Civil Engineering, Gyeongsang National University)
Shin, Chan-Ki (Nakdong River Environment Research Center National Institute of Environmental Research)
Publication Information
Journal of environmental and Sanitary engineering / v.23, no.4, 2008 , pp. 83-93 More about this Journal
Abstract
The non-linear least squares model(NLSM) has long been the standard technique used by hydrologists for constructing rating curves. The reasons for its adaptation are vague, and its appropriateness as a method of describing discharge measurement uncertainty has not been well investigated. It is shown in this paper that the classical method of NLSM can model only a very limited class of variance heterogeneity. Furthermore, this lack of flexibility often leads to unaccounted heteroscedasticity, resulting in dubious values for the rating curve parameters and estimated discharge. By introducing a heteroscedastic maximum likelihood model(HMLM), the variance heterogeneity is treated more generally. The maximum likelihood model stabilises the variance better than the NLSM approach, and thus is a more robust and appropriate way to fit a rating curve to a set of discharge measurements.
Keywords
Rating curve; Heteroscedasticity; Non-linear least square model; Maximum likelihood model;
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1 건설교통부 수문조사연보, 수위편, 유량편, 2004
2 Lambie, J.C. Measurement of flow-velocity-area methods. In: Herschy, R.W., (Ed.), Hydrometry: Principles and Practices, Wiley, Chichester, Chapter 1, 1978
3 Ackers, P., White, W.R., Perkins, J.A., Harrison, J.M. Weirs and Flumes for Flow Measurement, Wiley, Chichester, 1978
4 Herschy, R.W. Accuracy. In: Herschy, R.W., (Ed.), Hydrometry: Principles and Practices, Wiley, Chichester, Chapter 10, 1978
5 서혜선, 양경숙, 김나영, 김희영, 김미정 SPSS를 활용한 회귀분석, SPSS 아카데미, pp. 233-262, 2003
6 Clarke, R.T. Uncertainty in the estimation of mean annual flood due to rating curve indefinition, J. Hydrol. 222, 185-190, 1999   DOI   ScienceOn
7 Huet, S., Bouvier, A., Gruet, M.A., Jolivet, E. Statistical Tools for Nonlinear Regression, Springer, London, 1996
8 김원, 윤광석 등. 하천유량측정지침, 수자원의 지속적 확보기술개발사업단 기술보고서(TR 2004-01), pp. 73-82, 2004
9 건교부 수자원국 하천관리과 수문조사 선진화 5개년 계획(하천관리과-1147, 2005. 6. 1), 2005
10 Seber, G.A.F., Wild, C.J. Nonlinear Regression, Wiley, Chichester, 1989
11 김경훈, 김문수 등 낙동강수계 T/M유량과 실측유량의 비교분석, 한국물환경학회. 대한상하수도학회 공동춘계학술발표회 논문집, pp. 629-632, 2005
12 Yu, B. A systematic over-estimation of flows. J. Hydrol. 233, 258-262, 2000   DOI   ScienceOn
13 Clarke, R.T., Mendiondo, E.M., Brusa, I.C. Uncertainties in mean annual discharge from two large South American rivers due to rating curve variability, Hydrol. Sci. 45, 221-236, 2000   DOI   ScienceOn
14 Gawne, K.D., Simonovic, S.P. A computer based system of modelling the stage-discharge relationships in steady state conditions, Hydrol. Sci. J. 39(5), 487-506, 1994   DOI   ScienceOn
15 Efron, B., Tibshirani, R.J. An Introduction to the Bootstrap, Chapman & Hall, London, 1993
16 Huet, S., Bouvier, A., Gruet, M.A., Jolivet, E. Statistical Tools for Nonlinear Regression. Springer, London, 1996
17 건교부 수자원관리기법 개발연구조사 보고서, 1994
18 Asgeir Petersen-Overleir Accounting for heteroscedasticity in rating curve estimates, J. Hydrol. 292, 173-181, 2004   DOI   ScienceOn
19 ISO Technical Corrigendum 1 to International Standard ISO 1100-2:1998. Prepared by Technical Committee ISO/TC 113. Hydrometric Determinations, Sub-committee SC 1. Velocity Area Methods, 1998