The loess hilly region is a typical infiltration-excess runoff area. The main factors affecting runoff and sediment yield are rainfall intensity, rainfall duration and surface conditions (slope, gully density and antecedent moisture condition). Among them, the surface condition is a more deterministic factor, while rainfall is a stochastic factor58. Rainfall intensity in the loess hilly region plays a decisive role in runoff yield amount, while antecedent soil water content takes second place. Each stage of soil loss by unit runoff for a given mean rainfall intensity was significantly different among rainstorm patterns59. Besides, because the climate of the Loess Plateau is arid and semi-arid, the thickness of loess soil is often 50–80 m and the thickest is 150–180 m, the water storage capacity of the whole vadose zone is very large, low intensity rainfall often does not produce runoff, only intense rainstorms produce surface runoff. Due to the uneven spatio-temporal distribution of rainstorms, runoff yield from catchments is local, and extensive simultaneous runoff is extremely rare. Therefore, the flood process is often sudden rise and sudden fall, and the peak volume is small. Under the same conditions, if rainfall is large, runoff is generally large, and runoff erosion capacity and sediment transport capacity are also large. The more uneven the distribution of rainfall in time and space, the more concentrated the sediment yield in different periods, the greater the amount of runoff and sediment yield in the same rainfall event60.