| Soil erosion is severely intensive in hilly loess region on the Loess Plateau. Because of soil loosening and short-duration storm rainfall, erosion happens mainly in several torrential rains and rill erosion has the great contribution to total erosion. Many researchers have studied the law of slope erosion and built many slope erosion models. In this paper, firstly, the relationship between rainfall and soil erosion, especially the rainfall erosive index are analyzed; secondly, the topography, vegetation, soil water content on soil erosion are also analyzed; thirdly, rill erosion on slope and the critical judgments of rill erosion are studied; Finally, the mixed model of soil erosion and construct rainfall, erosion model of erosive rainfall, rainfall rill erosion model are built. Generally, all the conclusions are based on data observed at Chabagou experimental watershed and few data observed at Wangjiagou experimental watershed. Main results concluded are follows:(1) It seems that both linear and power functions can be used to express the relationship between It or EIt and erosion intensity with reasonable results, so It or EIt can be used either power function form or linear function form in soil erosion model. Only form the correlation can not select rainfall erosivity index, must be differences between the correlation analysis of numerical. Statistical test shows that the correlation coefficients of It or EIt and erosion intensity also do not show significantly difference. In this sense, from the EI10 to EI60 all EIt can be used as rainfall erosivity on the Loess Plateau. Because It is a reflection of the concentration of rainfall, Concentration of different type rainfall is very different, then rainfall type influence correlation coefficients between EIt and erosion. This suggests that every EIt can be considered to be representative of rainfall erosivity index and used for soil erosion prediction. There is no significant difference form rEI10 to rEI30 of highly concentrated short thunderstorm (A rain pattern), however, there is significant difference between rEI10 and rEI40. There is no significant difference form rEI10 to rEI100 of frontal rain mixed short thunderstorm (B rain pattern); there is no significant difference form rEI10 to rEI100 of prolonged frontal rain(C rain pattern). Soil erosion mainly concentrated in high-intensity short-duration thunderstorms on the Loess Plateau. To improve forecast accuracy of short thunderstorm. Therefore, every EIt form EI10 to EI30 can be used as the rainfall erosivity, and can be substitute for the corresponding simple factor PIt.(2) Slope have a great impact on soil erosion. So, when rainfall intensity is different, the relationship between slope length and soil erosion is different. When the rainfall is intensive, such as I30≥0.31mm/min, there is a power function between slope and erosion modulus.Slope length have a great impact on soil erosion. There is the same tendency of soil erosion modulus and runoff modulus changes according to changing slope length that soil erosion modulus decreased with the increase in slope length form 20m to 60m, when I30 was less than 0.21mm/min; There is the same tendency of soil erosion modulus change and runoff sediment change according to changing slope length that soil erosion modulus increased with the increase in slope length form 20m to 60m at first and then was stabilized,when I30 more than 0.21mm/min; The critical slope gradient of soil erosion was non-fixed value, which was a function of I30.(3) Crop cover degree increased first and then decreased from May to September in Chabagou watershed. They remain their relative peak annually form late July to late August. Vegetation cover significantly impact on soil erosion. Soil erosion intensity decreases with the increase in vegetation coverage. Vegetation cover can effectively decrease erosion on the Loess Plateau. Soil moisture significantly impacts on soil erosion. The last 11 days to 15 days rainfall can be well reflected in soil moisture content.(4) Rill erosion on a great contribution to surface erosion in Chabagou Watershed. The critical judgments of rill erosion, laws of water and sediment in rill erosion, are the basis of rill erosion model. When the I30≤0.31mm/min, splash and sheet erosion are dominant on slopes. When slopes are dominated by splash-sheep erosion, there is a critical gradient less than 31°with the same tendency of soil erosion modulus and runoff modulus changes according to gradient that soil erosion modulus increases first and then decreases with the slope changes from 9°to 31°. When the I30≥0.31mm/min, rill erosion is dominant on slopes. When slopes dominated by rill erosion, there is no critical gradient, with the same tendency of soil erosion modulus change and runoff sediment change according to changing gradient that soil erosion modulus increase with the increase of slope from 9°to 31°.(5) In this paper, the accuracy of rainfall erosion model, erosive rainfall erosion model, rill erosion model are all very high. There is high prediction accuracy to large erosion events. The high sensitivity factor of rainfall erosion model and erosive rainfall erosion model is S, C, I10 or PI10; The high sensitivity factor of rill erosion model is S, I10 or PI10. Vegetation cover can only decrease less degree erosion when slopes are dominated by rill erosion.
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