• Journal of Korea Water Resources Association
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• v.46 no.6
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• pp.597-611
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• 2013

This paper presents the methodology for construction of time-area curve via the width function and thereby rational estimation of time of concentration and storage coefficient of Clark model within the framework of method of moments. To this end time-area curve is built by rescaling the grid-based width function under the assumption of pure translation and then the analytical expressions for two parameters of Clark model are proposed in terms of method of moments. The methodology in this study based on the analytical expressions mentioned before is compared with both (1) the traditional optimization method of Clark model provided by HEC-1 in which the symmetric time-area curve is used and the difference between observed and simulated hydrographs is minimized (2) and the same optimization method but replacing time-area curve with rescaled width function in respect of peak discharge and time to peak of simulated direct runoff hydrographs and their efficiency coefficient relative to the observed ones. The following points are worth of emphasizing: (1) The optimization method by HEC-1 with rescaled width function among others results in the parameters well reflecting the observed runoff hydrograph with respect to peak discharge coordinates and coefficient of efficiency; (2) For the better application of Clark model it is recommended to use the time-area curve capable of accounting for irregular drainage structure of a river basin such as rescaled width function instead of symmetric time-area curve by HEC-1; (3) Moment-based methodology with rescaled width function developed in this study also gives rise to satisfactory simulation results in terms of peak discharge coordinates and coefficient of efficiency. Especially the mean velocities estimated from this method, characterizing the translation effect of time-area curve, are well consistent with the field surveying results for the points of interest in this study; (4) It is confirmed that the moment-based methodology could be an effective tool for quantitative assessment of translation and storage effects of natural river basin; (5) The runoff hydrographs simulated by the moment-based methodology tend to be more right skewed relative to the observed ones and have lower peaks. It is inferred that this is due to consideration of only one mean velocity in the parameter estimation. Further research is required to combine the hydrodynamic heterogeneity between hillslope and channel network into the construction of time-area curve.

• Journal of Korean Society on Water Environment
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• v.27 no.5
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• pp.661-669
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• 2011

The purpose of this study is quantitative analysis of the effects of the interactions between stream network and hillslope to hydrologic response functions. To this end general formulation of hydrologic response function is performed based on width function and grid framework. Target basins are Ipyeong and Tanbu basins. From the results of width function estimation even similar sized and closely located basins could have very different hydrologic response function. It is found out that the interactions between stream network and hillslope are essential factors of rainfall-runoff processes because their difference can make the hydrologic response function with positive skewness. The change of velocities of stream network and hillslope might influence the magnitude of peak but time to peak tends to more sensitively respond to velocities of stream network. Lag time of basin would be the result of complex interaction between drainage structures and dynamic properties of river basin.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1B
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• pp.47-55
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• 2011

This study suggests new synthetic unit hydrograph method considering hydrodynamic characteristic on the basin. The suggested method based on width function GIUH, and the procedure is summarized as follows; 1) Draw up a travel distance distribution map (width function) which is raster of length between from center of individual cells to the outlet by GIS. 2) Calculation of travel time distribution map (rescaled width function) by hydrodynamic parameters and travel distance distribution map. 3) Derivation of IUH and Duration UH from rescaled width function. 4) Comparison of shape of UH between suggested method and existing synthetic unit hydrograph methods. The target basins are selected Ipyeong and Tanbu subwatershed in the Bocheong Basin. The target basins are similar scale (watershed area), but different drainage structure (drainage density et al.). Therefore we anticipate that there are different hydrologic response functions because different hydrodynamic characteristics. As a result of derivation of UH, existing synthetic unit hydrograph methods are similar shape of UHs about Ipyeong and Tanbu watersheds, but the suggested method is different shape of ones. As a result of application to observed data, the peak discharge by suggested method is similar to existing synthetic unit hydrograph methods, but the peak time is well correspondence between those. Henceforth, if the suggested method combines with the rational velocity estimation method, it is useful method for synthetic of UH in ungauged watershed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2255-2265
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• 2013

This study presents the width function-based Clark model. To this end, rescaled width function with distinction between hillslope and channel velocity is used as time-area curve and then it is routed through linear storage within the framework of not finite difference scheme used in original Clark model but analytical expression of linear storage routing. There are three parameters focused in this study: storage coefficient, hillslope velocity and channel velocity. SCE-UA, one of the popular global optimization methods, is applied to estimate them. The shapes of resulting IUHs from this study are evaluated in terms of the three statistical moments of hydrologic response functions: mean, variance and the third moment about the center of IUH. The correlation coefficients to the three statistical moments simulated in this study against these of observed hydrographs were estimated at 0.995 for the mean, 0.993 for the variance and 0.983 for the third moment about the center of IUH. The shape of resulting IUHs from this study give rise to satisfactory simulation results in terms of the mean and variance. But the third moment about the center of IUH tend to be overestimated. Clark model proposed in this study is superior to the one only taking into account mean and variance of IUH with respect to skewness, peak discharge and peak time of runoff hydrograph. From this result it is confirmed that the method suggested in this study is useful tool to reflect the heterogeneity of drainage path and hydrodynamic parameters. The variation of statistical moments of IUH are mainly influenced by storage coefficient and in turn the effect of channel velocity is greater than the one of hillslope velocity. Therefore storage coefficient and channel velocity are the crucial factors in shaping the form of IUH and should be considered carefully to apply Clark model proposed in this study.