Estimating Manningʹs n for steep slopes

Hydrological and soil erosion models require calculations of flow velocity, for which either the Darcy-Weisbach or the Manning equation is generally used. A series of field experiments was carried out in a small catchment on the Chinese Loess Plateau to obtain reliable values of Manningʹs n. The soils are typically erodible loess soils. The experiments were conducted for a range of land uses as well as for different slope angles (6–64%). Measurements were performed on a 2.5×0.4 m plot, on which flow was allowed to find its own path. Water was evenly applied to the top of the plot and discharge, surface velocity, flow width and slope were measured. The results show that Manningʹs n can, just like Darcy-Weisbach f, be estimated from Reynolds number. Furthermore, for croplands, there is an apparent linear increase in Manningʹs n (and f) with increasing slope angle (R2=0.70). As Manningʹs n is usually assumed to be constant, this must mean that either velocity increases with slope or hydraulic radius decreases. The measurements showed virtually no increase in velocity and a minor increase in hydraulic radius with slope, as flow was more concentrated on steeper slopes. Possible explanations for this lack of increase in velocity include increased roughness [Water Resour. Res. 37 (2001) 791], decreased effective slope angle because of the development of vertical head cuts and a shift in energy use. All three hypotheses only apply to situations involving erosion. The trend of Manningʹs n with slope implies that, in soil erosion models using Manningʹs equation (or Darcy-Weisbach), the value of n (or f) should be a function of the slope for erodible soils. For non-erodible soil (as in woodland), no increase in Manningʹs n with slope was observed.