Does watershed size affect simple mathematical relationships between flow velocity and discharge rate at watershed outlets on the Loess Plateau of China

Abstract

Summary An empirical power function model of V = kQ m has been used worldwide to describe the relationship between flow velocity ( V , m s −1 ) and discharge rate ( Q , m 3 s −1 ) for rill and open channel flows. However, it has seldom been applied to watershed outlet channels taking into account the impacts of watershed size. In this study, observed data from four experimental watersheds of different sizes, ranging from about 1 to 100 km 2 , were used to verify the stability of the power function model for use at a watershed level on the Loess Plateau. An alternative logarithmic function model of V = e ln Q + d was also tested. Results showed that the constant parameters in both model types were impacted by watershed size, which are inherently directly related to the size of the outlet channels. The constants k and d , which represent flow velocity for unit discharge rate, were negatively correlated with watershed size. However, the exponential constants m and e , which determine the rate of change in flow velocity with respect to discharge rate, were shown to be independent of watershed size. Furthermore, soil and water conservation land use management on the Loess Plateau was also shown to indirectly affect the flow velocity–discharge rate relationship in the smallest watersheds (1 km 2 ). The study indicated that, although the performance of the logarithmic function model was acceptable, the power function model generally performed better over a larger range of flow velocity values and was better able to represent the flow velocity–discharge rate relationship in the unique context of the Loess Plateau.