Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Hack's Law and the Geometric Properties of Catchment Plan-form

Hack의 법칙과 집수평면의 기하학적 특성

  • 김주철 (한국수자원공사 수자원연구원) ;
  • 이상진 (한국수자원공사 수자원연구원)
  • Published : 2009.09.30
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Abstract

This study makes a systematic approach to Hack's law considering self-affinity and self-similarity of natural basins as well as the elongation of corresponding catchment-plan forms. Catchment-plan forms extracted from DEM appear to be the population come from the interactions of 2 hypotheses on Hack's law. It is judged that the elongation measures based on inertia moments are more intuitive than the ones based on main channel lengths. The exponent of Hack's law, h, seems to be similar to the result of Gray's study (1961). However Hurst exponent, H, being 0.96 imply that catchment-plan forms considered in this study have isotropic increasing properties with scale. From this point of view it is inferred that the shapes of the basins in this study would be more affected from self-similarity of main channel lengths than self-affinity of catchment-plan forms.

본 연구에서는 집수평면의 신장도에 대한 검토와 함께 자연유역의 자기유사성 및 자기상사성을 고려하여 Hack의 법칙에 대한 체계적인 접근을 수행하여 보았다. DEM으로부터 추출된 대상유역의 집수평면들은 Hack의 법칙에 대한 두 가설이 상호작용을 할 경우 나타날 수 있는 유역 형상들에 대한 모집단처럼 나타났다. 유역면적에 따른 집수평면 신장도의 변화를 도시해 본 결과 유로연장을 기반으로 한 고전적인 지형인자들보다는 관성적률을 기반으로 한 신장도가 보다 직관적인 결과를 줄 수 있을 것으로 판단되었다. Hack의 법칙에 대한 지수 h는 Gray (1951)의 연구결과와 유사하게 산정됨을 확인할 수 있었다. 하지만 대상유역들에 대한 Hurst의 지수 H는 0.96으로 나타나 본 연구에서 고려한 집수평면들은 규모에 따라 등방성 성장률을 가지고 있는 것으로 사료되었다. 이로부터 본 연구의 대상유역들의 형상은 집수평면의 자기유사성보다는 유로연장의 자기상사성에 더 영향을 받는 것으로 추론할 수 있었다.

Keywords

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