In terms of the strongest correlations, 17 rainstorm erosion events include linear, power, logarithmic and exponential functions. The logarithmic function is the upper convex curve, which is characterized by sediment yield increasing sharply with increased runoff (Figs 3–9). Representative rainstorm events are 7 July 2000, 23 June 1998, and 16 August 2001. The erosion amount of the three rainstorms roughly lies between 3000–5000 t. The power function can be divided into the upper convex or lower convex type according to the size of the index. Representative rainfall events are 26 July 2000, 14 July 2000, 28 June 2008 and 21 August 1998. The sediment yield rate with increased runoff is lower than the logarithmic function during the initial runoff yield period. The sediment yield rate of the linear regression relation is between power function and logarithmic function. Representative rainfall events are 28 July 1997, 11 August 2000, 11 August 2010 and 7 July 2009. The regression relationships on 6 May 1997 and 26 July 2001 were the weakest. The 26 July 2001 was a heavy rainfall erosion event. The 6 May 1997 was a prolonged rainfall event. Because the project of returning farmland to forest in 1997 was in the primary stage, the relationship between sediment yield and runoff was unstable. In 2009, with the effectiveness of soil and water conservation measures, the sediment yield of small rainstorm events was linearly correlated with runoff. A representative rainfall event was 7 July 2009. These results also validated that the surface conditions on the loess slope significantly affected runoff and sediment yield processes46. The above analysis is of great significance for further summarizing relationships between runoff and sediment yield, and understanding the variation of sediment yield associated with different rainstorm events.