Prediction of saturated zone length and subsurface travel time of hillslopes based on three saturation models of complex hillslopes

Hillslopes of natural catchments have a complex geometry. In complex hillslopes, the plan shape (convergence, parallelity and the amount of profile curvature (concave, straight and convex) create nine different shapes of complex hillslopes. To examine the amount of surface and subsurface runoff of hillslopes based on Dunne-Black mechanism, the saturated and unsaturated zones of hillslopes must be first separated. Travel time of surface and subsurface flow is a key parameter in runoff prediction of most rainfall-runoff models like time-dependent hydrograph models. In this research, a new simple saturation model, called Gamma, was employed with simpler geometry and equations. In this model, analytical equations were introduced to calculate saturation zone length (SZL) and subsurface travel time (STT). Results of Gamma saturation model and travel time of the proposed model were compared with other complex saturation models like W model and Sigma model by using two criteria of root mean square error (RMSE) and Nash efficiency factor (CE). The mean of RMSE for SZL prediction according to Gamma and Sigma models are 0.84 and 0.82 respectively. The mean CE for STT prediction according to Gamma and Sigma models are 0.79 and 0.72 respectively that were evaluated well. The main goal of this study is the examination of the efficiency of three models in estimation of saturated zone length and subsurface travel time. According to the results, Gamma model results were very close to those of Sigma model but for the straight divergent and convex divergent hillslopes, the Gamma model is not recommended.