Research papersModelling sheet erosion on steep slopes in the loess region of China

- Sheet erosion rate (SE) can be predicted using power function equation of slope gradient and rainfall intensity.
- SE can be well predicted with flow velocity (V), shear stress (τ) and stream power (Ω) except unit stream power (P).
- Stream power (Ω) is a preferred hydraulic parameter for estimating SE.

The relationship of sheet erosion rate (SE), slope gradient (S) and rainfall intensity (I), and hydraulic parameters, such as flow velocity (V), shear stress (τ), stream power (Ω) and unit stream power (P), was investigated to derive an accurate experimental model. The experiment was conducted at slopes of 12.23%, 17.63%, 26.8%, 36.4%, 40.4% and 46.63% under I of 48, 60, 90, 120, 138 and 150 mm h−1, respectively, using simulated rainfall. Results showed that sheet erosion rate increased as a power function with rainfall intensity and slope gradient with R2 = 0.95 and Nash-Sutcliffe model efficiency (NSE) = 0.87. Sheet erosion rate was more sensitive to rainfall intensity than to slope gradient. It increased as a power function with flow velocity, which was satisfactory for predicting sheet erosion rate with R2 = 0.95 and NSE = 0.81. Shear stress and stream power could be used to predict sheet erosion rate accurately with a linear function equation. Stream power (R2 = 0.97, NSE = 0.97) was a better predictor of sheet erosion rather than shear stress (R2 = 0.90, NSE = 0.89). However, a prediction based on unit stream power was poor. The new equation (i.e. SE=7.5×1012S1.43I3.04 and SE=0.06Ω-0.0003 and SE=0.011τ-0.01) would improve water erosion estimation on loess hillslopes of China.