A development of rating-curve using Bayesian Multi-Segmented model

Jin-Young Kim; Jin-Guk Kim; Jae Chul Lee; Hyun-Han Kwon

doi:10.3741/JKWRA.2016.49.3.253

All Issue

2016 Vol.49, Issue 3 Preview Page Next Page

A development of rating-curve using Bayesian Multi-Segmented model Bayesian 기반 Multi-Segmented 곡선식을 활용한 수위-유량 곡선의 불확실성 분석

31 March 2016. pp. 253-262

PDF XML

Abstract

A Rating curve is a regression equation of discharge versus stage for a given point on a stream where the stream discharge is measured across the stream channel with a stage and discharge measurement. The curve is generally used to calculate discharge based on the stage. However, the existing approach showed problems in terms of estimating uncertainty associated with regression parameters including the separation parameter for low and high flow. In this regard, this study aimed to develop a new method for the aforementioned problems based on Bayesian approach, which can better estimate the parameter and its uncertainty. In addition, this study used a Bayesian Multi-Segmented (Bayesian M-S) model which is provided a comparison between the existing and proposed scheme. The proposed model showed better results for the parameter estimation than the existing approach, and provided better performance in terms of estimating uncertainty range.

Keywords

Rating curve

Bayesian

Multi-Segmented

Uncertainty

수위-유량 관계곡선(rating curve)은 수위표에서 관측된 수위 및 유량을 이용하여 만들어진 회귀분석식을 의미하며, 하천의 수위를 유량으로 환산하는 방법으로 일반적으로 활용되고 있다. 그러나 수위-유량 관계곡선식에서 저수위와 고수위와 분리 및 매개변수 추정에 있어 불확실성을 고려한 해석은 이루어지지 않고 있다. 이러한 이유로 본 연구에서는 수위-유량 관계곡선식에서 매개변수 추정 및 저·고수위 분리시 발생하는 문제점을 개선하기 위해 Bayesian 기법을 도입하였으며, 수위-유량 관계곡선식의 매개변수의 추정과 더불어 불확실성을 정량화 하는데 목적을 두었다. 이와 더불어 Bayesian 모형 기반 Multi-Segmented 수위-유량 관계곡선(Bayesian M-S)을 활용하여 저·고수위를 분리할 수 있는 새로운 수위-유량 관계곡선을 개발하고 기존 수위-유량 관계곡선과 비교·분석을 실시하였다. 그 결과 본 연구에서 개발한 Bayesian M-S 기법이 기존 수위-유량 관계곡선식 보다 개선된 결과를 도출할 수 있었으며, 수위-유량 관계곡선식의 신뢰구간을 제시하는데 유리한 것을 확인할 수 있었다.

키워드

수위-유량 관계곡선

Bayesian

Multi-Segmented

불확실성

References

Block, P.J., Filho, F.A.S., and Kwon, H.-H. (2009). “A Streamflow Forecasting Framework using Multiple Climate and Hydrological Models.” Journal of The American Water Resources Association, Vol. 45, No. 4, pp. 828-843.

Kim, J.-Y., Kwon, H.-H., and Lim, J.-Y. (2014). “Development of Hierarchical Bayesian Spatial Regional Frequency Analysis Model Considering Geographical Characteristics.” Journal of Korea Water Resources Association, KWRA, Vol. 47, No. 5, pp. 469-482.

Kim, S.U., and Lee,. K.S. (2008). “Identification of Uncertainty in Fitting Rating Curve with Bayesian Regression.” Journal of Korea Water Resources Association, KWRA, Vol. 41, No. 9, pp. 943-958.

Kwon, H.-H., Filho, F., Block, P., Sun, L., Lall, U., and Reis Jr, D. S. (2012a). “Uncertainty Assessment of Hydrologic and Climate Forecast Models in Northeatern Brazil.” Hydrological Processes, Vol. 26, pp. 3875-3885.

Kwon, H.-H., Kim, J.-G., Lee, J.S., and Na, B.-K. (2012b). “Uncertainty Assessment of Single Event Rainfall-Runoff Model using Bayesian Model.” Journal of Korea Water Resources Association, KWRA, Vol. 45, NO. 5, pp. 505- 516.

Kwon, H.-H., Moon, Y.-I., Kim, B.-S., and Yoon, S-Y. (2008). “Parameter Optimization and Uncertainty Analysis of the NWS-PC Rainfall-Runoff Model Coupled with Bayesian Markov Chain Monte Carlo Inference Scheme.” Journal of Korean Society of Civil Engineer, Vol. 28 No. 4B, pp. 363-467.

Lee, W.S., Kim, S.U., Chung, E.-S., and Lee, K.S. (2008). “Improvement of Rating Curve Fitting Considering Variance Function with Pseudo-likelihood Estimation.” Journal of Korea Water Resources Association, KWRA, Vol. 41, No. 8, pp. 807-823.

Li, P.-H., Kwon, H.-H., Sun, L., Lall, U., and Kao, J.-J. (2010). “A Modified Support Vector Machine based Prediction Model on Streamflow at the Shihmen Reservoir, Taiwan.” International Journal of Climatology, Vol. 30, pp. 1256- 1268.

Ministry of Land, Infrastructure and Transport. (2010). “Korea Annual hydrological report.”

Ministry of Land, Infrastructure and Transport. (2011). “Korea Annual hydrological report.”

Ministry of Land, Infrastructure and Transport. (2012). “Korea Annual hydrological report.”

Nash, J.E., and Sutcliffe, J.V. (1970). “River Flow Forecasting through Conceptual Models Part I-A Discussion of Principles.” Journal of Hydrology, Vol. 10, pp. 282-290.

Petersen-Øverleir, A. (2005). “A Hydraulics Perspective on the Power-law Stage-discharge Rating Curve.” NVE report 05-05, Norwegian Water Resources and Energy Directorate, pp. 28.

Petersen-Øverleir, A. and Reitan, T. (2005) “Objective Segmentation in Compound Rating Curves.” Journal of Hydrology, Vol. 311, Issues 1-4, pp. 188-201.

Reitan, T., and Petersen-Øverleir, A. (2006). “Existence of the Frequentistic Regression Estimate of a Power-law with a Location Parameter, with Applications for Making Discharge Rating Curves.” Stoch. Environ. Res. Risk Asses/, Vol. 20, No. 6, pp. 445-453.

Reitan, T., and Petersen-Øverleir, A. (2008). “Bayesian methods for estimating multi-segment discharge rating curves”, Stochastic Environmental Research and Risk Assessment, Vol. 23, No. 5, pp. 627-642.

Seber, G.A.F., and Wild, C.J. (1989). “Nonlinear Regression.” New York: John Wiley and Sons.

White, H. (1980). “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica, Vol. 48, No. 4, pp. 817-838.

Xu, K., Brown, C., Kwon, H.-H., Lall, U., Zhang, J., Hayashi, S., and Chen, Z. (2007). “Climate Teleconnections to Yangtze River Seasonal Steamflow at the Three Gorges Dam, China.” International Journal of Climatology, Vol. 27, pp. 771-780.

Yoon, Y.N. (2007). “Hydrology - Basics and Application.” CheongMoonGak

Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 49
No :3
Pages :253-262
Received Date : 2016-01-04
Revised Date : 2016-01-28
Accepted Date : 2016-02-05
DOI :https://doi.org/10.3741/JKWRA.2016.49.3.253

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

All Issue