Soil erosion by water is one of the most widespread and major ecological environmental problems worldwide, which results in reduced agricultural productivity, increased water pollution, and unsustainable development1–5. Soil erosion is a complex physical process, the fundamental explanations are the comprehensive interaction between precipitation and the surface of watersheds6,7. In a mathematical sense, it is a highly non-linear mapping relationship from the watershed surface and rainfall conditions to runoff and sediment transport8,9. Generally, the main factors affecting rainfall erosion and sediment yield include: rainfall intensity, rainfall duration, rainfall spatio-temporal characteristics, soil properties, geological conditions, vegetation, land use and antecedent soil wetting condition10,11. Rainfall is one of the most important active agents of soil erosion, due to its potential to breakdown aggregates, detach soil particles, and produce runoff12–14. At present, many scholars have conducted experimental and modelling studies in runoff and sediment yield characteristics under the conditions of different soil types, rainfall intensity, slope gradient, land use types, vegetation coverage, and water conservation measures15. However, most studies mainly explored runoff and sediment loss on runoff plots16,17. On the other hand, other studies focused on rainfall, runoff and sediment relationships at basin scales. They mainly analysed relationships between rainfall runoff and sediment yield on annual time scales18. Besides, some scholars have also constructed different rainstorm runoff-sediment models, but they did not reveal the pulsed runoff-sediment relationship of the typical loess hilly watershed, due to local characteristics19,20.