Quantifying interactions between slope gradient, slope length and rainfall intensity on sheet erosion on steep slopes using Multiple Linear Regression

Understanding the interactions between influencing factors on sheet erosion is crucial for model development and mechanism elucidation. Simulation rainfall tests using a full-factorial design were conducted in 0.4 m wide flumes with five slope lengths (0.4, 0.8, 1.2, 1.6, and 2 m), five slope gradients (17.63, 26.79, 36.40, 46.63 and 57.74 %) and five rainfall intensities (48.0, 62.4, 102.0, 148.5, and 170.1 mm·h-1) to quantity interactions between these factors on sheet erosion and runoff rate by using Multiple Linear Regression. The results revealed that adding all two-way interaction terms into the equation, such as Rainfall intensity ∗ Slope length (IL), Slope gradient ∗ Rainfall intensity (SI) and Slope gradient ∗ Slope length (SL), significantly improved the interpretation of erosion and runoff rate. Under various slope gradients, the interaction item IL had a negative impact on erosion rate with an average slope of -0.86, but a positive impact on runoff rate with an average slope of 4.33, which improved the interpretation of regression equations for erosion and runoff rate by 0.86 %-1.83 % and 0.21 %-0.47 %. SI exhibited a positive effect on both erosion and runoff rate with an average slope of 4.36 and 8.44, and enhanced the interpretation for erosion and runoff rate by 0.70 %-3.54 % and 0.02 %-0.32 % under various slope lengths. SL had a negative effect on both erosion and runoff rate with an average slope of -3.55 and -6.93, and increased the interpretation of erosion and runoff rate by 1.15 %-6.84 % and 0.10 %-2.26 % under various rainfall intensities. The roles of I and S on erosion and runoff are both mutually promoting, of S and L are both mutually hindering, and of I and L on erosion are mutually hindering but on runoff are mutually promoting. Additionally, the interactions between I, L and S were even higher than that of a single influencing factor in some cases. Our findings highlight the need to consider the two-way interactions between influencing factors when predicting soil loss and provide methodological guidance for quantifying the interactions on soil erosion.