Relative Roles of Time-Area Curve and Storage Coefficient on the Shape of Clark's Instantaneous Unit Hydrograph: Analytical Approach

The Clark's instantaneous unit hydrograph (IUH) has been developed to transform excess precipitation into a runoff hydrograph, dependent on basin characteristics with flow velocity in a basin. In this study, the relative effects of the time-area curve and storage coefficient on the shape of the Clark IUH are analytically evaluated under hypothetical conditions of an elliptical-shaped basin and a straight flow direction of raindrops throughout total travel lengths. The time-area curve of an ellipse is derived by considering constant flow velocity in the basin, which is then used as input to the linear reservoir with a given storage coefficient to derive the Clark IUH by solving the continuity equation. The derived Clark IUH is evaluated with various shapes of elliptical basins and different storage coefficients. The time-area curve of a basin is found to be the dominant factor influencing the shape of the Clark IUH. The storage coefficient controls the steepness of the curve, while maintaining the overall shape of the Clark IUH unchanged.