• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.552-556
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• 2004

프랙탈 이송확산방정식은 정수 차수의 미분연산자로 구성된 고전적인 이송확산방정식과 비교하여 프랙탈 차수의 미분연산자로 구성된 보다 상위개념의 방정식으로써 정의된다. 지금까지의 프랙탈 이송확산방정식은 추계학적인 기법을 동원하여 푸리에-라플라스 공간에서 주로 해석되었으나, 본 연구에서는 실제 공간에서 유한차분개념을 도입하여 보다 직접적으희 하천에서의 오염물 이송확산에 관한 지배방정식을 유도하였다. 이러한 개념의 유도방법은 프랙탈 차수 및 관련 확산계수의 물리적인 추정에 관한 실마리를 제공할 수 있다. 고전적인 이송확산방정식과는 달리 프랙탈 이송확산방정식은 실제 하천에서 관측되는 오염물의 시간-농도 분포곡선의 왜곡현상과 분포곡선의 전후방부 농도를 보다 실제에 가깝게 모의할 수 있을 것으로 기대되어진다.

• Journal of Korea Water Resources Association
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• v.37 no.11
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• pp.889-896
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• 2004

The fractal advection-diffusion equation (ADE) is a generalization of the classical AdE in which the second-order derivative is replaced with a fractal order derivative. While the fractal ADE have been analyzed with a stochastic process In the Fourier and Laplace space so far, in this study a fractal ADE for describing solute transport in rivers is derived with a finite difference scheme in the real space. This derivation with a finite difference scheme gives the hint how the fractal derivative order and fractal diffusion coefficient can be estimated physically In contrast to the classical ADE, the fractal ADE is expected to be able to provide solutions that resemble the highly skewed and heavy-tailed time-concentration distribution curves of contaminant plumes observed in rivers.

• 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.

• Journal of Korea Water Resources Association
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• v.31 no.5
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• pp.587-597
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• 1998

Researchers have suggested that the fractal dimension of the stream length is uniform in all the streams of the basin and the estimates of the fractal dimension are in between 1.09 and 1.13 which may be considerably large values. In this study, the fractal dimension for the Ieemokjung subbasin streams in the Pyungchang River basin which is one of the IHP representative basins in Korea are estimated for each stream order using three scale maps of a 1/50,000, 1/25,000, and 1/5,000. As a result, the fractal dimension of the stream length is different by stream order and the fractal dimension of all streams shows a lower value in comparison to that of the previous studies. As a result of the fractal dimension estimation for the Ieemokjung subbasin streams, we found that the fractal dimension of the stream length shows different estimates in stream orders. The fractal dimension of 1st and 2nd order stream is 1.033, and the fractal dimension of 3rd and 4th order stream is 1.014. This result is different from the previous studies that the fractal dimension of the stream length is uniform in all streams of the basin. The fractal dimension for a whole stream length is about 1.027. Therefore, the previous estimates of 1.09 and 1.13 suggested as the fractal dimension of the stream length may be overestimated in comparison with estimated value in this study.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.291-300
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• 1999

The Snyder's synthetic unit hydrograph method is selected to apply the concept of the fractal dimension by stream order for the practicable rainfall-runoff generation, and fourth types of the Snyder's relation are derived from topographic and observed unit hydrograph data of twenty-nine basins. As a result of the analysis of twenty-nine basins and the verification of two basins, the Snyder's relation which considers the fractal dimension of the stream length and uses calculated unit hydrograph data shows the best result. The concept of the fractal dimension by stream order is applied to the Snyder's synthetic unit hydrograph method. The topographic factors, used in the Snyder's synthetic unit hydrograph method, which have a property of the stream length like $L_{ma}$ (mainstream length) and $L_{ca}$ (length along the mainstream to a point nearest the watershed centroid) were considered. In order to simplify the fractal property of stream length, it is supposed that $L_{ma}$ has not the fractal dimension and the stream length between $L_{ma}$ and ($L_{ma}\;-\;L_{ca}$) has the fractal dimension of 1.027. From the utilization of this supposition, a new Snyder's relation which consider the fractal dimension of the stream length occurred by the map scale used was finally suggested.

• Journal of the Korean Geographical Society
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• v.40 no.3 s.108
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• pp.253-273
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• 2005

In recent years, there are strong social demands to characterize the spatial distribution of mountains in Korea. This study aims to develop a 'Sanjulgi-Jido(mountain ridge map)' that might be used not only to satisfy these social demands but also to effectively present the spatial distribution of mountains and drainage basins in the Korean Peninsular. The 'Sanjulgi-Jido' developed in this study is a map that presents the continuity of mountains based on the drainage divides that are delineated by a pre-defined drainage basin size and elevation. This study first validated the Bakdudaegan system through the analyses of a digital elevation model. The Bakdudaegan system has long been recognized as the Koreans traditional conceptual framework to characterize the spatial distribution of mountains. The analyses showed that the Bakdudaegan system has several problems to represent the mountain systems in Korea, which includes 1) the lack of the representativeness of drainage basins, 2) inaccuracy to depict the boundary of drainage basins, 3) the lack of representativeness of mountains, and 4) geo-polical issue that confines the spatial extent of mountain systems within the Korean Peninsular. In order to represent the mountains system in a more quantitative manner, we applied several terrain analysis techniques to understand the spatial distribution of mountains and drainage basins. Based on these analyses, we developed an hierarchical system to classify the continuity (If mountains, which are presented as the spatial distribution of drainage divides with a certain elevation. The first-order Sanjulgi is the drainage divides whose drainage basin are bigger than $5,000km^2$ and the point elevation is above 100m. The next order Sanjulgi is delineated as the size of drainage basin is successively divided by two. This kind of design is able to provide a logical framework to present the mountain systems at different details, depending on the purpose and scale of maps. We also provide several empirical functions to calculate various geomorphological indices for each order of Sanjulgi. The 'Sanjulgi Jido' is similar with the Bakdudaegan system, since it characterizes the continuity of mountains based on the spatial distribution of the drainage divide. It, however, has more scientific criteria to define the scale and continuity of mountains. It should be also noted that the 'Sanjulgi Jido' proposed has different logical and methodological background, compared with the mountain range map that explains the genesis of mountain systems in addition to the continuity of mountains.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.731-736
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• 2004

강우-유출과정의 수문학적 현상을 보다 정확히 분석하고 예측하는 기법으로 강우에 의한 유출의 반응을 나타내는 지체시간, 도달시간 등 수문학적 반응시간을 유역의 지형형태학적 인자들과 연계하는 방법이 많이 이용되고 있다. 이에 본 연구에서는 Clark방법과 지형형태학적 순간단위도(GIUH)를 이용하여 계측유역의 강우-유출반응을 모의하였고, 이를 관측된 값과 비교하여 미계측유역의 적용성 여부를 검토해보았다. 대상 유역의 하상지형인자 및 지형형태학적 특성은 Arc-View를 이용하여 구하였으며, 이를 기존의 문헌자료와 비교해보았다. Clark방법의 매개변수의 결정에 있어서 시간-면적곡선은 HEC-1의 무차원 식을 이용하였고, 도달시간은 Kirpich 공식을 이용하여 구하였으며, 저류상수는 Clark방법에 의해 추정된 순간단위도의 첨두유량이 Horton의 차수비의 함수로 구한 철두유량과 같아지는 값으로 결정하였다. 본 연구는 전적비교를 출구점으로하는 유역면적 $8.5km^2$인 설마천을 대상유역으로 하였으며, 모의된 강우-유출반응과 비교하기 위해 사용된 강우사상은 2002년의 8월 4일과 2002년 10월 6일의 10분 단위 우량이다. Clark방법과 GIUH를 이용하여 모의한 유출곡선과 관측된 유출곡선을 비교해본 결과 첨두유량은 8월의 강우사상 때는 $21\%$크게, 10월의 강우사상 때는 $35\%$작게 나타났다. 첨두시간은 모의된 경우가 각각 10분, 20분 빨리 도달하였다. 또한 이러한 결과는 유역의 도달시긴에 가장 민감하게 반응함을 알 수 있었다. 따라서, 유역의 도달시간 산정에 주의를 요한다면 프랙탈 차원이 유사한 미계측유역의 수문곡선 산정에 있어서 Clark방법과 GIUH를 이용하는 방법도 유용하다고 사료된다. 주는 각 수문인자 중 강우시간분포와 유효우량 산정방법 그리고 유출모형에 대해 자자 검토하였으며, 최종적으로 면적에 따른 임계지속기간과 유출량의 변화를 검토해 보았다.이를 각각의 경우의 해석해 결과와 비교${\cdot}$분석하였다. 후방추적 퍼프모형은 전방추적 퍼프모형에 비하여 사용된 퍼프수와 관계없이 작은 오차를 발생하였으며, 전체적으로 퍼프 모형이 입자모형보다는 훨씬 적은 수의 계산을 통해서도 작은 오차를 나타낼 수 있다는 것을 알 수 있었다. 그러나 Gaussian 분포를 갖는 퍼프모형은 전단흐름에서의 긴 유선형 농도분포를 모의할 수 없었고, 이에 관한 오차는 전단계수가 증가함에 따라 비선형적으로 증가하였다. 향후, 보다 다양한 흐름영역에서 장${\cdot}$단점 분석 및 오차해석을 수행한 후에 각각의 Lagrangian 모형의 장점만을 갖는 모형결합 방법을 제시할 수 있을 것으로 판단된다.mm/$m^{2}$로 감소한 소견을 보였다. 승모판 성형술은 전 승모판엽 탈출증이 있는 두 환아에서 동시에 시행하였다. 수술 후 1년 내 시행한 심초음파에서 모든 환아에서 단지 경등도 이하의 승모판 폐쇄 부전 소견을 보였다. 수술 후 조기 사망은 없었으며, 합병증으로는 유미흉이 한 명에서 있었다. 술 후 10개월째 허혈성 확장성 심근증이 호전되지 않아 Dor 술식을 시행한 후 사망한 예를 제외한 나머지 6명은 특이 증상 없이 정상 생활 중이다 결론: 좌관상동맥 페동맥이상 기시증은 드물기는 하나, 영유아기에 심근경색 및 허혈성 심근증 또는 선천성 승모판 폐쇄 부전등을 초래하는 심각한 선천성 심질환이다. 그러나 진단 즉시 직접 좌관상동맥-대동맥 이식술로 수술적 교정을 해줌으로써 좋은 성적을 기대할 수 있음을 보여주었다.특히 교사들이 중요하

• Journal of Korean Society of Environmental Engineers
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• v.28 no.3
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• pp.337-344
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• 2006

Characteristics of flocculent aggregates have great effects on membrane fouling. Floc from kaolin particles gave higher permeate throughputs than floc from natural particles at the same conditions. Therefore, the objectives of this study are to thoroughly analyze characteristics of flocculated aggregates and to investigate effects of flocculated aggregates on membrane fouling. Image analysis, specific rake resistance and cake compressibility were used for characterization of flocs. Different flocculent aggregates formed with natural and kaolin particles were employed in this study. The fractal dimensions from the image analysis were $D_2=1.79{\pm}0.07$ for floc from natural particles and $D_2=1.84{\pm}0.06$ for floc from kaolin particles. The lower fractal dimension($D_2$) of floc from natural particles indicated that the aggregates were more porous and less compact than floe from kaolin particles. In addition, both the specific cake resistances and compressible degrees of flocs from natural particles showed greater values than those of flocs from kaolin particles. The results implied that the porous and loose flocs from natural particles were more easily compressed on membrane surface than the dense and compact flocs from kaolin particles. The compressed flocs yielded the great hydraulic resistances by hindering the water flow through the cake layer.