Investigation of the profile curvature effect on the hydrologic response of the parallel hillslopes with the kinematic wave model

Hydrologic response of hillslopes is affected by their geometric characteristics including the profile curvature. In the previous studies، in order to investigate the effect of profile curvature a single equation، Evans’ (1980) equation، was used to produce convex and concave hillslopes corresponding response of which were compared. In this paper، first، it is shown that in the previous studies the convex and concave hillslopes were not equivalent and comparable. Next، some criteria for producing pairs of equivalent hillslopes are suggested. Based on these criteria a new profile model is derived. Evans’ (1980) profile model with the new one can be employed in producing pairs of comparable hillslopes. Finally، the equilibrium time equations and the dimensionless equations corresponding to the rising limb of the resulting hydrographs for equivalent hillslopes are derived and compared. The results showed that time to equilibrium for concave slope is shorter than that of convex slope. In addition، ignoring slope variation in the determination of time to equilibrium in convex slopes may potentially cause an underestimation by up to 25%. Time to equilibrium for concave slopes is close to that of straight slopes. Thus، the error due to assuming a uniform slope is negligible for this case.