Effects of geometry on runoff time characteristics and time-area histogram of hillslopes

•We addressed the KW-based lag time and time to equilibrium in complex hillslopes.•We changed the lag time equation form to the new one applicable for complex hillslopes.•A new topography model was introduced by combining two existing models.•We derived ratio of equilibrium time to lag time as a function of geometric features.•Lag time and equilibrium time response to geometric parameters variation inversely.

SummaryGeometry (plan curvature and profile curvature) of hillslopes affects the time characteristics of overland flow such as lag time (tl) and time to equilibrium (te). The results of previous studies on the response time of overland flow over complex hillslopes express diversity of conclusions in some cases. In this research, the effects of hillslope geometry on tl and te are investigated for complex hillslopes, and the ratio of te/tl is defined as a function of the geometric characteristics of hillslopes and flow regime type. To this aim, a new topography model is first introduced and kinematic wave-based equations for computing te and tl which can consider the convergence/divergence and concavity/convexity parameters of the complex hillslopes are presented. Using the derived te equations, the location of isochrones and then the time-area histograms of the complex hillslopes are derived and compared. It is concluded that the average te for divergent hillslopes is 33% more than that for convergent ones. Convex hillslopes have longer te relative to the concave hillslopes, and the mean te of the former is 13% more than that of the latter. Although the te of convergent hillslopes is longer than that of equivalent divergent ones (with the same degree of plan curvature), the tl of the convergent hillslopes is always shorter than that of the divergent ones.