초록
This study was conducted to derive an Instantaneous Unit Hydrograph for the accurate and reliable unitgraph which can be used to the estimation and control of flood for the development of agricultural water resources and rational design of hydraulic structures. Eight small watersheds were selected as studying basins from Han, Geum, Nakdong, Yeongsan and Inchon River systems which may be considered as a main river systems in Korea. The area of small watersheds are within the range of 85 to 470$\textrm{km}^2$. It is to derive an accurate Instantaneous Unit Hydrograph under the condition of having a short duration of heavy rain and uniform rainfall intensity with the basic and reliable data of rainfall records, pluviographs, records of river stages and of the main river systems mentioned above. Investigation was carried out for the relations between measurable unitgraph and watershed characteristics such as watershed area, A, river length L, and centroid distance of the watershed area, Lca. Especially, this study laid emphasis on the derivation and application of Instantaneous Unit Hydrograph (IUH) by applying Nash's conceptual model and by using an electronic computer. I U H by Nash's conceptual model and I U H by flood routing which can be applied to the ungaged small watersheds were derived and compared with each other to the observed unitgraph. 1 U H for each small watersheds can be solved by using an electronic computer. The results summarized for these studies are as follows; 1. Distribution of uniform rainfall intensity appears in the analysis for the temporal rainfall pattern of selected heavy rainfall event. 2. Mean value of recession constants, Kl, is 0.931 in all watersheds observed. 3. Time to peak discharge, Tp, occurs at the position of 0.02 Tb, base length of hlrdrograph with an indication of lower value than that in larger watersheds. 4. Peak discharge, Qp, in relation to the watershed area, A, and effective rainfall, R, is found to be {{{{ { Q}_{ p} = { 0.895} over { { A}^{0.145 } } }}}} AR having high significance of correlation coefficient, 0.927, between peak discharge, Qp, and effective rainfall, R. Design chart for the peak discharge (refer to Fig. 15) with watershed area and effective rainfall was established by the author. 5. The mean slopes of main streams within the range of 1.46 meters per kilometer to 13.6 meter per kilometer. These indicate higher slopes in the small watersheds than those in larger watersheds. Lengths of main streams are within the range of 9.4 kilometer to 41.75 kilometer, which can be regarded as a short distance. It is remarkable thing that the time of flood concentration was more rapid in the small watersheds than that in the other larger watersheds. 6. Length of main stream, L, in relation to the watershed area, A, is found to be L=2.044A0.48 having a high significance of correlation coefficient, 0.968. 7. Watershed lag, Lg, in hrs in relation to the watershed area, A, and length of main stream, L, was derived as Lg=3.228 A0.904 L-1.293 with a high significance. On the other hand, It was found that watershed lag, Lg, could also be expressed as {{{{Lg=0.247 { ( { LLca} over { SQRT { S} } )}^{ 0.604} }}}} in connection with the product of main stream length and the centroid length of the basin of the watershed area, LLca which could be expressed as a measure of the shape and the size of the watershed with the slopes except watershed area, A. But the latter showed a lower correlation than that of the former in the significance test. Therefore, it can be concluded that watershed lag, Lg, is more closely related with the such watersheds characteristics as watershed area and length of main stream in the small watersheds. Empirical formula for the peak discharge per unit area, qp, ㎥/sec/$\textrm{km}^2$, was derived as qp=10-0.389-0.0424Lg with a high significance, r=0.91. This indicates that the peak discharge per unit area of the unitgraph is in inverse proportion to the watershed lag time. 8. The base length of the unitgraph, Tb, in connection with the watershed lag, Lg, was extra.essed as {{{{ { T}_{ b} =1.14+0.564( { Lg} over {24 } )}}}} which has defined with a high significance. 9. For the derivation of IUH by applying linear conceptual model, the storage constant, K, with the length of main stream, L, and slopes, S, was adopted as {{{{K=0.1197( {L } over { SQRT {S } } )}}}} with a highly significant correlation coefficient, 0.90. Gamma function argument, N, derived with such watershed characteristics as watershed area, A, river length, L, centroid distance of the basin of the watershed area, Lca, and slopes, S, was found to be N=49.2 A1.481L-2.202 Lca-1.297 S-0.112 with a high significance having the F value, 4.83, through analysis of variance. 10. According to the linear conceptual model, Formular established in relation to the time distribution, Peak discharge and time to peak discharge for instantaneous Unit Hydrograph when unit effective rainfall of unitgraph and dimension of watershed area are applied as 10mm, and $\textrm{km}^2$ respectively are as follows; Time distribution of IUH {{{{u(0, t)= { 2.78A} over {K GAMMA (N) } { e}^{-t/k } { (t.K)}^{N-1 } }}}} (㎥/sec) Peak discharge of IUH {{{{ {u(0, t) }_{max } = { 2.78A} over {K GAMMA (N) } { e}^{-(N-1) } { (N-1)}^{N-1 } }}}} (㎥/sec) Time to peak discharge of IUH tp=(N-1)K (hrs) 11. Through mathematical analysis in the recession curve of Hydrograph, It was confirmed that empirical formula of Gamma function argument, N, had connection with recession constant, Kl, peak discharge, QP, and time to peak discharge, tp, as {{{{{ K'} over { { t}_{ p} } = { 1} over {N-1 } - { ln { t} over { { t}_{p } } } over {ln { Q} over { { Q}_{p } } } }}}} where {{{{K'= { 1} over { { lnK}_{1 } } }}}} 12. Linking the two, empirical formulars for storage constant, K, and Gamma function argument, N, into closer relations with each other, derivation of unit hydrograph for the ungaged small watersheds can be established by having formulars for the time distribution and peak discharge of IUH as follows. Time distribution of IUH u(0, t)=23.2 A L-1S1/2 F(N, K, t) (㎥/sec) where {{{{F(N, K, t)= { { e}^{-t/k } { (t/K)}^{N-1 } } over { GAMMA (N) } }}}} Peak discharge of IUH) u(0, t)max=23.2 A L-1S1/2 F(N) (㎥/sec) where {{{{F(N)= { { e}^{-(N-1) } { (N-1)}^{N-1 } } over { GAMMA (N) } }}}} 13. The base length of the Time-Area Diagram for the IUH was given by {{{{C=0.778 { ( { LLca} over { SQRT { S} } )}^{0.423 } }}}} with correlation coefficient, 0.85, which has an indication of the relations to the length of main stream, L, centroid distance of the basin of the watershed area, Lca, and slopes, S. 14. Relative errors in the peak discharge of the IUH by using linear conceptual model and IUH by routing showed to be 2.5 and 16.9 percent respectively to the peak of observed unitgraph. Therefore, it confirmed that the accuracy of IUH using linear conceptual model was approaching more closely to the observed unitgraph than that of the flood routing in the small watersheds.