Overland Flow Times of Concentration for Hillslopes of Complex Topography

The time of concentration is an important parameter for predicting peak discharge at the basin outlet and for designing urban infrastructure facilities. In studying the hillslope response, employing hydraulic equations of flow, the shape of the hillslope geometry has often been assumed as rectangular and planar. However, natural hillslopes have complex topographies whose shapes are characterized by irregularly spaced contour lines. Recently, kinematic wave time of concentration has been derived for rectangular and curved parallel hillslopes. This paper extends this work to hillslopes of complex planform geometry, considering the degree of divergence or convergence of the hillslope. The extended formulation consists of only one equation that is valid for both divergent/convergent surfaces and for concave/convex hillslope profile, and is compared with the formulations for plane convergent and plane divergent surfaces previously introduced. Results are compared with those already available in the literature, which were obtained by using the nonlinear storage model applied to the same complex hillslopes.