Background Antecedent soil moisture and rainfall (ASAM) are the main influencing factors on runoff occurring in a loess slope at northern Shaanxi. There have been many models for the coupling relationship between runoff and factors of antecedent soil moisture and rainfall, but they are based on regression analysis, their practicality and universality are limited, especially on the forecast of runoff erosion.

Methods Based on the basic principle of runoff occurring under excess infiltration and introduced 2 indicators of antecedent soil moisture and rainfall, the model for the rainfall threshold while runoff occurs for a loess slope was deduced based on the coupling relationship between antecedent soil moisture and rainfall. Then according to this model and combined with the measured soil moisture, the rainfall threshold while runoff occurs was simulated, calculated and analyzed during the drought year, normal year and wet year in the typical vegetation community in the Wuqi county of northern Shaanxi loess region.

Results 1) Rainfall thresholds while runoff occurred differed significantly between wet years and dry years as well as normal years in the loess slope of northern Shaanxi. The required rainfall for runoff occurring in wet years was little and the theoretical rainfall for runoff occurring was the lowest at 5.6 mm. There were no significant difference in rainfall thresholds for runoff occurring between dry years and normal years, but rainfall required in dry years for runoff occurring was large. 2) The minimum rainfall for runoff occurring at different vegetation types was different, while the rainfall threshold for runoff occurring in Pinus tabulaeformis forest land was the least, i.e., the runoff in the P. tabulaeformis forest land easily occurred. The rainfall for runoff occurring in Hippophae rhamnoides forest land was the most, i.e., it was difficult for H. rhamnoides forest land to have runoff occurring. There was a significant difference in the rainfall thresholds for runoff occurring between these two vegetation types. 3) When vegetation and other topographical conditions were the same, the lower the rainfall intensity was, the longer the time required for runoff occurring was; the more the amount of rainfall loss was, the longer the time required for runoff occurring was. 4) When the surface soil of a slope had high saturated water content and the antecedent soil moisture content was small, the field rainfall required for runoff occurring was high; when the soil density on a soil slope was large, the rainfall required for runoff occurring was also large. When the depth of soil infiltration on the slope surface was shallow, the amount of rainfall required for runoff occurring was also small.

Conclusions Studying the coupling relationship between the ASMA and the critical rainfall threshold of loess slope runoff is of great significance to prevent soil erosion and to effectively utilize water and soil resources in this area.