Abstract
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.
Highlights
Subsurface flow is percolating water that encounters an impending horizon in shallow soil, where the water is diverted horizontally and reaches the stream channel
We proved the hillslope-storage kinematic wave model is suitable for investigating the response of the complex hillslopes and some of our results are similar to the Aryal et al (2005) results in the steady state condition but the hillslope-storage Boussinesq (hsB) model can be extended for unsteady state condition
The main aim of the present study is to benefit from its results for the modeling saturation zone extension in unsteady-state condition based on temporal distributions of rainfall during storms in hillslopes in future studies
Summary
Subsurface flow is percolating water that encounters an impending horizon in shallow soil, where the water is diverted horizontally and reaches the stream channel. Aryal (2005) and O’Loughlin (2005) have shown that the hillslope travel time in subsurface flow is dependent on hillslope length, hydraulic conductivity, plan shape, profile curvature and recharge rate They demonstrated equations of saturation zone boundary for hillslope in steady state and introduced three equations for calculating complex hillslopes travel time based on Zaslavsky and Rogowski (1969) geometry equations. The objectives of this paper are: (i) introduce an equation for subsurface travel time of all complex hillslopes with regard to parameters such as the saturation zone length , total length, soil porosity, profile curvature, soil hydraulic conductivity , and average bedrock slope, (ii) calculate the saturation zone length of nine basic hillslopes in steady-state conditions, (iii) explore the effects of different factors such as the soil depth, the recharge rate, bedrock slope angle on travel time and saturation zone length, (iv) present analytical expressions for calculating saturation zone length in straight hillslopes for different shape functions (convergent, parallel, divergent) and (v) compare the drainage capacity of all complex hillslopes based on their average discharge rates
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