Abstract
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.
Highlights
Flow velocity in a river basin is one of the key components that determine the overall shape of the basin’s response function
The analytically-derived Clark instantaneous unit hydrograph (IUH) in Section 2 is a function of the channel velocity, hillslope velocity, and storage coefficient
Yoo et al (2014) showed that the concentration time and the storage coefficient of the Clark IUH could be estimated by analyzing the observed rainfall–runoff data [37]
Summary
Flow velocity in a river basin is one of the key components that determine the overall shape of the basin’s response function. The hillslope velocity or the travel time across hillslopes is assumed to be insignificant, compared to that in streams [1]. Most hydrologic models assume flow velocity over the entire basin to be uniform [5,6,7,8]. This assumption has been proven valid, especially in channel systems [9,10,11]. Along with the assumption of a linear system, including the linear reservoir and linear channel, the assumption of uniform velocity plays a key role in developing various unit hydrograph models, like the geomorphological instantaneous unit hydrograph (GIUH) model [12,13,14] and the Clark model [15]
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