• 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.

• Korean Journal of Mineralogy and Petrology
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• v.35 no.1
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• pp.41-50
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• 2022

To study the properties of Sr²⁺ exchange into zeolite A with increasing the molar concentration of Na⁺ in given exchange solution, four single crystals of fully dehydrated Sr²⁺- and Na⁺- exchanged zeolite A were prepared by the bath method using mixed ion-exchange solutions. The Sr(NO₃)₂:NaNO₃ molar rations of the ion exchange solution were 1:1(crystal 1), 1:100(crystal 2), 1:250(crystal 3), and 1:500 (crystal 4), respectively, with a total concentration of 0.05 M. The single-crystals were then vacuum dehydration at 623 K and 1×10^-4 Pa for 2 days. Their single-crystal structures were determined by single-crystal synchrotron X-ray diffraction techniques in the cubic space group Pm3-m, at 100(1) K, and were then refined to the final error indices of R₁/wR₂=0.047/0.146, 0.048/0.142, 0.036/0.128, and 0.040/0.156 for crystals 1, 2, 3, and 4, respectively. In crystals 1 and 2, the 6 Sr²⁺ ions are found at three different crystallographic sites. In crystal 3, 1 Sr²⁺ and 10 Na⁺ ions are found in large cavity and sodalite unit. In crystal 4, only 12 Na⁺ ions occupy three equipoints. The degree of Sr²⁺ ion-exchange decreased sharply from 100 to 16.7 to 0% as the initial Na⁺ concentration increase and the Sr²⁺ concentration decrease. In addition, the unit cell constant of the zeolite framework decreased with this lower level of Sr²⁺ exchange.