KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Re-Analysis of Clark Model Based on Drainage Structure of Basin

배수구조를 기반으로 한 Clark 모형의 재해석

  • 박상현 (금강유역환경청 측정분석과) ;
  • 김주철 (충남대학교 국제수자원연구소) ;
  • 정동국 (한남대학교 건설시스템공학과) ;
  • 정관수 (충남대학교 토목공학과)
  • Received : 2013.06.17
  • Accepted : 2013.08.21
  • Published : 2013.11.30
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Abstract

This study presents the width function-based Clark model. To this end, rescaled width function with distinction between hillslope and channel velocity is used as time-area curve and then it is routed through linear storage within the framework of not finite difference scheme used in original Clark model but analytical expression of linear storage routing. There are three parameters focused in this study: storage coefficient, hillslope velocity and channel velocity. SCE-UA, one of the popular global optimization methods, is applied to estimate them. The shapes of resulting IUHs from this study are evaluated in terms of the three statistical moments of hydrologic response functions: mean, variance and the third moment about the center of IUH. The correlation coefficients to the three statistical moments simulated in this study against these of observed hydrographs were estimated at 0.995 for the mean, 0.993 for the variance and 0.983 for the third moment about the center of IUH. The shape of resulting IUHs from this study give rise to satisfactory simulation results in terms of the mean and variance. But the third moment about the center of IUH tend to be overestimated. Clark model proposed in this study is superior to the one only taking into account mean and variance of IUH with respect to skewness, peak discharge and peak time of runoff hydrograph. From this result it is confirmed that the method suggested in this study is useful tool to reflect the heterogeneity of drainage path and hydrodynamic parameters. The variation of statistical moments of IUH are mainly influenced by storage coefficient and in turn the effect of channel velocity is greater than the one of hillslope velocity. Therefore storage coefficient and channel velocity are the crucial factors in shaping the form of IUH and should be considered carefully to apply Clark model proposed in this study.

본 연구에서는 유역의 배수구조를 설명할 수 있는 폭 함수 기반의 Clark 모형을 제안하였다. 시간-면적곡선으로는 지표면과 하천에 대하여 개별적인 동수역학적 특성을 적용한 재조정된 폭 함수를 이용하였다. 선형저수지 추적의 경우 기존의 Clark 모형과 같이 차분화된 형태가 아니라 해석식을 적용하여 수행하였다. 본 연구에서 고려한 주요한 매개변수들로는 지표면평균이송속도 및 하천평균이송속도와 저류상수를 들 수 있다. 실제 매개변수의 추정 과정에는 전역최적화 기법 중의 하나인 SCE-UA 기법을 적용하였다. 또한 Clark 모형으로부터 유도된 순간단위도의 형상은 원점에 대한 1차모멘트와 면적중심에 대한 2, 3차 모멘트로 구분하여 평가하였다. 관측 수문사상의 통계모멘트들과 본 연구에서 추정된 통계모멘트들의 상관계수는 1차모멘트의 경우 0.995, 2차모멘트는 0.993, 3차모멘트는 0.983로 산정되었다. 평균과 분산에 대해서는 추정값과 관측값이 대체로 일치하는 경향을 보여주었다. 그러나 추정된 3차모멘트에 대한 결과는 다소 과대 평가되는 경향을 나타내었다. 제안된 Clark 모형은 순간단위도의 형상을 평균과 분산만을 고려하여 적용한 방법보다 수문곡선의 왜곡 및 첨두좌표의 모의와 관련된 한계점을 개선하였다. 이러한 결과로부터 본 연구에서 제시한 방법론은 배수경로의 이질성과 동적매개변수들의 영향을 적절하게 반영할 수 있음을 확인할 수 있었다. 본 연구에서 고려한 모멘트들의 변동성은 주로 저류상수의 영향이 크게 나타나고 있으며, 지표면평균이송속도보다는 하천평균이송속도가 크게 영향을 미치는 것을 확인할 수 있었다. 이로부터 저류상수와 하천평균이송속도가 Clark 모형으로부터 유도되는 순간단위도의 형상을 결정하는데 지배적인 역할을 하는 것으로 확인되었다. 따라서 두 매개변수는 모형의 적용 과정에서 중요하게 고려되어야 할 것으로 판단된다.

Keywords

References

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