Abstract. The travel time of subsurface flow in complex hillslopes (hillslopes with different plan shape and profile curvature) is an important parameter in predicting the subsurface flow in catchments. This time depends on the hillslopes geometry (plan shape and profile curvature), soil properties and climate conditions. The saturation capacity of hillslopes affect the travel time of subsurface flow. The saturation capacity, and subsurface travel time of compound hillslopes depend on parameters such as soil depth, porosity, soil hydraulic conductivity, plan shape (convergent, parallel or divergent), hillslope length, profile curvature(concave, straight or convex) and recharge rate to the groundwater table. An equation for calculating subsurface travel time for all complex hillslopes was presented. This equation is a function of the saturation zone length (SZL) on the surface. Saturation zone length of the complex hillslopes was calculated numerically by using the hillslope-storage kinematic wave equation for subsurface flow, so an analytical equation was presented for calculating the saturation zone length of the straight hillslopes and all plan shapes geometries. Based on our results, the convergent hillslopes become saturated very soon and they showed longer SZL with shorter travel time compared to the parallel and divergent ones. The subsurface average flow rate in convergent hillslopes is much less than the divergent ones in the steady state conditions. Concerning to subsurface travel time , convex hillslopes have more travel time in comparison to straight and concave hillslopes. The convex hillslopes exhibit more average flow rate than concave hillslopes and their saturation capacity is very low. Finally, the effects of recharge rate variations, average bedrock slope and soil depth on saturation zone extension were investigated.

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Abstract. The travel time of subsurface flow in complex hillslopes (hillslopes with different plan shape and profile curvature) is an important parameter in predicting the subsurface flow in catchments. This time depends on the hillslopes geometry (plan shape and profile curvature), soil properties and climate conditions. The saturation capacity of hillslopes affect the travel time of subsurface flow. The saturation capacity, and subsurface travel time of compound hillslopes depend on parameters such as soil depth, porosity, soil hydraulic conductivity, plan shape (convergent, parallel or divergent), hillslope length, profile curvature (concave, straight or convex) and recharge rate to the groundwater table. An equation for calculating subsurface travel time for all complex hillslopes was presented. This equation is a function of the saturation zone length (SZL) on the surface. Saturation zone length of the complex hillslopes was calculated numerically by using the hillslope-storage Boussinesq (hsB) model in the steady state conditions, so an analytical equation was presented for calculating the saturation zone length of the straight hillslopes and all plan shapes geometries. Based on our results, the convergent hillslopes become saturated very soon and they showed longer SZL with shorter travel time compared to the parallel and divergent ones. The subsurface average flow rate in convergent hillslopes is much less than the divergent ones in the steady state conditions. Concerning to subsurface travel time, convex hillslopes have more travel time in comparison to straight and concave hillslopes. The convex hillslopes exhibit more average flow rate than concave hillslopes and their saturation capacity is very low. Finally, the effects of recharge rate variations, average bedrock slope and soil depth on saturation zone extension were investigated.

Abstract. Time of concentration (TC) of surface flow in watersheds depends on the coupled response of hillslopes and stream networks. The important point in this background is to study the effects of the geometry and the shape of complex hillslopes on the time of concentration considering the degree of flow convergence (convergent, parallel or divergent) as well as the profile curvature (concave, straight or convex). In this research, the shape factor of complex hillslopes as introduced by Agnese et al. (2007) is generalized and linked to the TC. A new model for calculating TC of complex hillslopes is presented, which depends on the plan shape, the type and degree of profile curvature, the Manning roughness coefficient, the flow regime, the length, the average slope, and the excess rainfall intensity. The presented model was compared to that proposed by Singh and Agiralioglu (1981a,b) and Agiralioglu (1985). Moreover, the results of laboratory experiments on the travel time of surface flow of complex hillslopes were used to calibrate the model. The results showed that TC for convergent hillslopes is nearly double those of parallel and divergent ones. TC in convex hillslopes was very close to that in straight and concave hillslopes. While the effect of convergence on TC is considerable, the curvature effect confirmed insignificant. Finally, in convergent hillslopes, TC increases with the degree of convergence, but in divergent hillslopes, it decreases as degree of divergence increases.

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