• Journal of Korea Water Resources Association
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• v.54 no.1
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• pp.49-60
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• 2021

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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.97-106
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• 1992

Total length of stream networks and main stream length vary with topographic map scales, and the stream length of drainage basin on topographic map can be viewed as a fractal. Total length of stream network and main stream length are represented as only stream area ratio($R_a$) based on Horton's laws, thereafter the fractal dimensions of stream network and main stream length are derived as a simple function of stream length($R_L$) and stream area ratios($R_a$) respectively. The derived equations of fractal dimension are applied to Sansung basin in Kum River and compared with the equations already existed. The stream network appeared as space filling with fractal dimension near 2 as map scale increases, while main stream length shows near 1. The results of this study are expected to be helpful in the quantitative analysis of drainage network composition with map scale.

• Journal of Korea Water Resources Association
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• v.32 no.5
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• pp.565-577
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• 1999

The geometric patterns of a stream network in a drainage basin can be viewed as a "fractal" with fractal dimensions. Fractals provide a mathematical framework for treatment of irregular, ostensively complex shapes that show similar patterns or geometric characteristics over a range of scale. GIUH (Geomorphological Instantaneous Unit Hydrograph) is based on the hydrologic response of surface runoff in a catchment basin. This model incorporates geomorphologic parameters of a basin using Horton's order ratios. For an ordered drainage system, the fractal dimensions can be derived from Horton's laws of stream numbers, stream lengths and stream areas. In this paper, a fractal approach, which is leading to representation of a 2-parameter Gamma distribution type GIUH, has been carried out to incorporate the self similarity of the channel networks based on the high correlations between the Horton's order ratios. The shape and scale parameter of the GIUH-Nash model of IUH in terms of Horton's order ratios of a catchment proposed by Rosso(l984J are simplified by applying the fractal dimension of main stream length and channel network of a river basin. basin.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.142-142
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• 2023

Humans inevitably and continuously produce wastewater in daily life worldwide. To decrease the degradation of river water bodies and aquatic ecosystem therein, humans have built systems at different scales to collect, drain, and treat household-produced wastewater. Particularly, municipal wastewater treatment plants (WWTPs) with centralized controls have played a key role in reducing loads of nutrients in domestic wastewater for the last few decades. Notwithstanding such contributions, impaired rivers regarding water quality and habitat integrity still exist at the whole river basin scale. It is highly attributable to the absence of dilution capacity of receiving streams and/or the accumulation of the pollutant loads along flow paths. To improve the perspective for individual WWTPs assessment, the first crucial step is to achieve systematic understanding on spatial distribution characteristics of all WWTPs together in a given river basin. By taking the initiative, our former study showed spatial hierarchical distributions of WWTPs in three large urbanized river basins in Germany. In this study, we uncover how municipal WWTPs in the contiguous United States are distributed along river networks in a give river basin. The extended spatial scope allows to deal with wide ranges in geomorphological attributes, hydro-climatic conditions, and socio-economic status. Furthermore, we identify the relation of the findings with multiple factors related to human activities, such as the spatial distribution of human settlements, the degree of economy development, and the fraction of communities served by WWTPs. Generalizable patterns found in this study are expected to contribute to establishing viable management plans for recent water-environmental challenges caused by WWTP-discharges to river water bodies.