Resumen
In this study, the time?area curve of an ellipse is analytically derived by considering flow velocities within both channel and hillslope. The Clark IUH is also derived analytically by solving the continuity equation with the input of the derived time?area curve to the linear reservoir. The derived Clark IUH is then evaluated by application to the Seolmacheon basin, a small mountainous basin in Korea. The findings in this study are summarized as follows. (1) The time?area curve of a basin can more realistically be derived by considering both the channel and hillslope velocities. The role of the hillslope velocity can also be easily confirmed by analyzing the derived time?area curve. (2) The analytically derived Clark IUH shows the relative roles of the hillslope velocity and the storage coefficient. Under the condition that the channel velocity remains unchanged, the hillslope velocity controls the runoff peak flow and the concentration time. On the other hand, the effect of the storage coefficient can be found in the runoff peak flow and peak time, as well as in the falling limb of the runoff hydrograph. These findings are also confirmed in the analysis of rainfall?runoff events of the Seolmacheon basin. (3) The effect of the hillslope velocity varies considerably depending on the rainfall events, which is also found to be mostly dependent upon the maximum rainfall intensity.