Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Estimation of fractal dimension for Seolma creek experimental basin on the basis of fractal tree concept

Fractal 나무의 개념을 기반으로 한 설마천 시험유역의 Fractal 차원 추정

  • Kim, Joo-Cheol (International Water Resources Research Institute, Chungnam National University) ;
  • Jung, Kwan Sue (Department of Civil Engineering, Chungnam National University)
  • 김주철 (충남대학교 국제수자원연구소) ;
  • 정관수 (충남대학교 토목공학과)
  • Received : 2020.06.12
  • Accepted : 2020.12.01
  • Published : 2021.01.31
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Abstract

This study presents a methodology to estimate two distinct fractal dimensions of natural river basin by using fractal tree concept. To this end, an analysis is performed on fractal features of a complete drainage network which consists of all possible drainage paths within a river basin based on the growth process of fractal tree. The growth process of fractal tree would occur only within the limited drainage paths possessing stream flow features in a river basin. In the case of small river basin, the bifurcation process of network is more sensitive to the growth step of fractal tree than the meandering process of stream segment, so that various bifurcation structures could be generated in a single network. Therefore, fractal dimension of network structure for small river basin should be estimated in the form of a range not a single figure. Furthermore, the network structures with fractal tree from this study might be more useful information than stream networks from a topographic or digital map for analysis of drainage structure on small river basin.

본 연구에서는 Fractal 나무의 개념을 이용하여 자연유역의 두 가지 개별적 Fractal 차원을 추정하는 방법을 제시하고자 한다. 이를 위하여 Fractal 나무의 성장 과정을 기반으로 유역 내부에서 발생 가능한 모든 배수 경로를 추출하여 완전한 배수망을 구성하고 이에 해당하는 Fractal 특성을 분석해 보고자 한다. 유역 내부에서 Fractal 나무의 성장 과정은 하천 유동의 특성을 가지는 배수 경로에서만 제한적으로 나타날 수 있다. 소규모 유역의 경우 Fractal 나무의 성장 단계에 따라 망상 구조의 분기 특성이 단일 하천 구간의 사행 특성에 비하여 민감하게 변화하여 단일한 망상 구조 속에서도 다양한 분기 구조가 생성될 수 있다. 따라서 소규모 유역을 대상으로 한 망상 구조에 대한 Fractal 차원은 단일한 수치의 고정된 형태보다는 범위의 형태로 취급되어야 하는 것이 타당한 것으로 판단된다. 또한, 소규모 유역의 배수 구조에 대한 분석에는 지형도나 수치지도로부터 추출한 하천망보다 본 연구에서 제시한 Fractal 나무의 성장에 따른 망상 구조와 같은 정보가 더 유용할 수 있을 것으로 판단된다.

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