• 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.

• The Journal of Engineering Geology
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• v.20 no.2
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• pp.137-146
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• 2010

To estimate the accumulated infiltration, Horton's and Green-Ampt's equations are usually applied. Because the real infiltration is penetrated into the soil continuously, to cover the problems of the conventional equations derived from the discontinuous infiltration system, new infiltration equation is derived from the concepts of continuous infiltration system. Furthermore, infiltration tests were done to compare the results from the conventional Horton's and Green-Ampt's equations and newly derived equation. Unsaturated permeability is the function of water content ratio or saturation degree, which affects directly to the infiltration capacity and accumulated infiltration. Therefore, the variation term of unsaturated permeability is inserted into the new equation to estimate the proper infiltration capacity and accumulated infiltration. It will make the more accurate analysis for the safety of structure and the behavior of groundwater.

• Magazine of the Korean Society of Agricultural Engineers
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• v.24 no.2
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• pp.76-88
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• 1982

The stream morphological characteristics of a basin have important influence upon the analysis of runoff. In this study, the laws of stream morphology-the law of average stream fall and the law of least rate of potential energy expenditure-which were derived based on the analogy of entropy in thermodynamics are introduced and their validity is analysised with the data taken from the topographic maps covering the whole Geum River system. The first law is the Law of Average Stream Fall which states that under the dynamic equilibrium condition the ratio of average fall between any two different order stream in the same river basin in unity. The second law is the law of least rate of energy expenditure which states that all natural streams are intended to choose their own course of flow such that the rate of potential energy loss per unit mass of water this course is a minimum. The parameters representing the morphological characteristics of 13 tributaries in the Geum River system such as stream bifurcation ratio and stream concavity were Computed from the Horton-Strahler's laws and are used to check the law of average stream fall. The result showed that the law of average stream fall agrees reasonably well with law of Horton-Strahler. Concavity of a river basin is shown to be the determinative factor to the formation of a stream system. Concavity of a river basin is shown to be the determinative factor to the formation of a stream system. Based on Horton's Law and the law of average stream fall, longitudinal stream profiles can be calculated.

• Journal of the Korean Institute of Landscape Architecture
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• v.36 no.4
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• pp.111-119
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• 2008

The runoff coefficient for a block paved area is determined with regional rainfall distribution. The Rational Method is a basic equation of a drainage system design and is a function of runoff coefficient, rainfall intensity and area. A runoff coefficient is the ratio of rainfall intensity and runoff. The rainfall intensity which is a function of the return period and rainfall duration differs by region. Therefore the runoff coefficient varies regionally even though there is the same return period and rainfall duration. The ratio of rainfall intensity and rainfall duration is decided by the loss of rainfall. The constant infiltration capacity of Horton's equation is adopted to determine the loss of rainfall. As time passed, the joint of the block paved area through which the infiltration occurs is covered by pollution material, sandy dust, pollen and is hardened by foot pressure, so the constant infiltration capacity may decrease. Six different sites were selected to verify the assumption of the constant infiltration capacity decrease and 10 year return period. 10, 20, and 30 minute rainfall duration were applied to calculate rainfall intensity. The results indicate that the Horton's constant infiltration capacity decreases over time and the minimum constant infiltration capacity is selected to compute runoff coefficients. The runoff coefficients varied by region ranging from $0.94{\sim}0.84$ for 10 minute of rainfall duration.

• 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.

• Water for future
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• v.14 no.1
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• pp.39-49
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• 1981

The purpose of this study is to examine the meander charactericstics for the rivers in Korea..In this study, the new characteristics factors of meander are proposed, and the relationships among the factors proposed in this study and the existing factors are derived. An attempt is made to find considerable relation among meander characteristics, but width and meander belt did not show any defined trend and considerable scatter of points was observed. Relationships among the meander length, belt and flowrate, etc., which are factors of meander characteristics, are analyzed the 67 rivers above 30km in length. Channel shape factor which is the ratio of the length from the starting point to the end to the channel lenght, tortuosity which is the ratio of the curved channel length against the channel length are suggested for a new characteristics factor of meander. They are well correlated with channel length, Horton's shape facotr and meander gradient, consequently have to be important measures of river meander. The result of the detailed comparison and the analysis of degree of sinuosity, velocity and water surface slop are brought light on the fact show that the curved reach is morestable than the straight one. The ratio of the meander length to the meander belt and its accumulative frequency showed excellent correlationship when plotted on the semi-log paper. The results of regression analysis of meander belt and meander length show linear for the South Han river branches and power curve for the Geum river and the Nakdong river branches.

• Journal of the Korean Society of Hazard Mitigation
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• v.6 no.1 s.20
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• pp.49-58
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• 2006

Rainfall-runoff characteristics are analysed based on the geomorphological instantaneous unit hydrograph(GIUH) derived by geomorphological parameters using geographical information system in watershed ungaged or deficient of field data. Observed data of Seom river experiment watershed at upstream of Hoengseong dam and variable slope method for hydrograph separating of direct non are used. The 4th stream order of Seom river experimental watershed is developed with a regular correlation referred to the Horton-Strahler's law of stream order. The characteristic velocity to determine shape parameter of GIUH is 1.0m/s and its equation is modified for accurate results. Hydrograph at the outlet of 4th stream order of Maeil gage station and at the outlets of 3rd stream order of Sogun and Nonggeori gage stations show a little differences in falling limb of hydrograph but agree well to the observed data in general. The results by hydrological routing with HEC-HMS to the outlet of 4th stream order of Maeil gage station which the hydrograph by GIUH obtained at Sogun and Nonggeori gage stations of 3rd stream oder are applied as upstream inputs give better agreement with observed data than those by hydrograph by GIUH obtained at Maeil gage station of 4th stream order. In general, the rainfall-runoff by GIUH has applicability to the watershed routing of ungaged project regions.

• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.1
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• pp.85-91
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• 2011

RV-GIUH must be applied at an outlet or a junction of highest order stream of a subbasin because the model was derived for basins following Horton's ordering system. However hydrograph is calculated at various locations which does not fit to the desirable points. Therefore, some guideline is required for RV-GIUH application in practice. This study would like to suggest the outlet location criteria for appling RV-GIUH at un-gauged basin. Locations were selected by moving to upstream from outlet of Sanganmi basin and unit hydrograph using derived and simple RV-GIUH were estimated at each location. As the results, the peaks of RV-GIUH in upstream were exaggerated because of distortion of length ratio and total stream length. To avoid this error, the location must be selected at 60% downstream of highest stream length. To apply RV-GIUH at various places, equations correcting distortion of total stream length were suggested. With the correcting equations, it can be possible that RV-GIUH is applied at 20% downstream of highest stream length. Application and precision of RV-GIUH will be improved through this research.

• Magazine of the Korean Society of Agricultural Engineers
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• v.32 no.3
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• pp.87-101
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• 1990

The purpose of this study is to estimate the flood discharge and runoff volume at a stream by using geomorphologic parameters obtained from the topographic maps following the law of stream classification and ordering by Horton and Strahier. The present model is modified from Cheng' s model which derives the geomorphologic instantaneous unit hydrograph. The present model uses the results of Laplace transformation and convolution intergral of probability density function of the travel time at each state. The stream flow velocity parameters are determined as a function of the rainfall intensity, and the effective rainfall is calculated by the SCS method. The total direct runoff volume until the time to peak is estimated by assuming a triangular hydrograph. The model is used to estimate the time to peak, the flood discharge, and the direct runoff at Andong, Imha. Geomchon, and Sunsan basin in the Nakdong River system. The results of the model application are as follows : 1.For each basin, as the rainfall intensity doubles form 1 mm/h to 2 mm/h with the same rainfall duration of 1 hour, the hydrographs show that the runoff volume doubles while the duration of the base flow and the time to peak are the same. This aggrees with the theory of the unit hydrograph. 2.Comparisions of the model predicted and observed values show that small relative errors of 0.44-7.4% of the flood discharge, and 1 hour difference in time to peak except the Geomchon basin which shows 10.32% and 2 hours respectively. 3.When the rainfall intensity is small, the error of flood discharge estimated by using this model is relatively large. The reason of this might be because of introducing the flood velocity concept in the stream flow velocity. 4.Total direct runoff volume until the time to peak estimated by using this model has small relative error comparing with the observed data. 5.The sensitivity analysis of velocity parameters to flood discharge shows that the flood discharge is sensitive to the velocity coefficient while it is insensitive to the ratio of arrival time of moving portion to that of storage portion of a stream and to the ratio of arrival time of stream to that of overland flow.