Introduction

Soil erosion is one of the most severe ecological and environmental challenges worldwide1,2,3, and rainfall characteristics are closely linked to both the magnitude and spatial patterns of soil erosion. However, not all rainfall events trigger erosion; only those capable of generating sufficient runoff with sediment transport capacity are considered erosive4. Consequently, identifying erosive rainfall remains a central focus and challenge in soil erosion research5,6. The Revised Universal Soil Loss Equation (RUSLE) is a widely accepted empirical model for soil erosion assessment7. Thresholds of erosive factors represent a major source of uncertainty in RUSLE predictions, while site-specific erosive rainfall thresholds can effectively reduce model uncertainty8. Moreover, establishing threshold criteria for erosive rainfall can simplify calculations in practice, enhance the efficiency of identifying erosive rainfall events, and thus improve the assessment of rainfall-induced erosion hazards in specific regions. Therefore, the determination of erosive rainfall thresholds has long been a research priority9,10.

Numerous scholars have extensively investigated erosive rainfall thresholds11,12,13. Among these, one of the most influential standards was proposed by Wischmeier et al.14, who defined erosive rainfall in the Universal Soil Loss Equation (USLE) as events with a total rainfall depth of ≥ 12.7 mm, or with a 15-min rainfall depth exceeding 6.4 mm. Wang and Jiao15 summarized erosive rainfall standards across different regions of China and concluded that a threshold of 10 mm is commonly adopted nationwide. Currently, three main approaches are employed to determine erosive rainfall thresholds: (i) frequency analysis, where cumulative frequency curves of selected rainfall characteristics are plotted, and characteristic values corresponding to cumulative frequencies such as 80%4,16,15 or 90%17 are taken as thresholds. Using this approach, Chinese scholars have established erosive rainfall thresholds for the Loess Plateau, northeast Yunnan, northern Jiangxi red-soil region, and purple hill regions, reported as 10 mm, 9.2 mm, 11.2 mm, and 11.3 mm, respectively4,16,17,18,19. However, this method is subject to considerable subjectivity since frequency parameters are artificially defined15. (ii) Rainfall erosivity deviation coefficient method, which involves ranking all rainfall events by erosivity from largest to smallest, then cumulatively summing erosivity values. The characteristic rainfall corresponding to the point at which cumulative erosivity approaches the total erosivity of all erosive rainfall events is defined as the threshold20. This method has been applied to establish erosive rainfall depth and intensity thresholds for regions including the Longdong Loess Plateau, Zizhou in northern Shaanxi, Beijing, and karst areas21,22,23,24. Although this method incorporates erosive dynamic factors, the determination of the threshold still relies on an empirical “approximate point” on the cumulative curve, which limits its objectivity and precision. (iii) Regression analysis method, which uses selected rainfall characteristics as independent variables and runoff depth as the dependent variable to construct linear regression equations, where the intercept on the x-axis represents the erosive rainfall threshold. Li et al.25 applied this method to calculate erosive rainfall thresholds for nine types of artificial catchments. Huang et al.26 applied this method to calculate slope-scale erosive rainfall thresholds under four underlying surface conditions and further developed a multiparameter nonlinear erosive rainfall threshold model. In contrast, the regression analysis method is more objective, as the erosive rainfall threshold is derived directly from the statistical relationships in the observed data, without relying on subjectively defined empirical parameters. This method has a clear mechanistic basis, as it establishes a quantitative relationship between rainfall characteristics and runoff depth, thereby providing the threshold with a more explicit hydrodynamic interpretation. Moreover, the approach is highly flexible, allowing both the construction of linear models to obtain single-parameter thresholds and the further development of multi-parameter nonlinear models to more comprehensively capture the influence of underlying surface conditions on the critical processes governing erosion initiation.

The erosive rainfall threshold is influenced by multiple factors, including geomorphology, soil type, vegetation cover, land use, slope gradient, and rainfall intensity. A study revealed distinct differences in erosive rainfall thresholds between karst and non-karst slopes, with values ranging from 35.4 to 45.6 mm for karst slopes and from 11.8 to 18.8 mm for non-karst slopes27. Wang et al.28 conducted experiments in Fangshan District, Beijing, across five typical soil types representing China’s secondary water erosion regions. The results showed that erosive rainfall thresholds were highest for black soil and cinnamon soil (both 10.0 mm), followed by loess soil (9.5 mm), while purple soil and red soil exhibited relatively lower thresholds of 5.4 mm and 6.1 mm, respectively. A long-term study (2006–2022) in the karst yellow soil region, based on 10 experimental stations and 69 plots, further indicated that erosive rainfall thresholds varied across land-use types: 12.66 mm for forest, 10.57 mm for grassland, 9.94 mm for cropland, and 8.93 mm for fallow land. Moreover, croplands with slopes of 13°, 15°, 20°, 23°, and 25° exhibited thresholds of 10.41 mm, 10.28 mm, 9.66 mm, 9.52 mm, and 9.15 mm, respectively11. In addition, rainfall characteristics such as intensity exert significant control over erosive rainfall thresholds29. At present, thresholds are often defined either as a fixed rainfall depth or as a fixed rainfall intensity. However, laboratory simulations have demonstrated substantial variations in rainfall depth thresholds under different rainfall intensities30. This suggests that the variability of erosive rainfall thresholds across rainfall intensities is also an important aspect warranting further investigation.

Since 1999, large-scale ecological restoration programs such as the Grain for Green Program (GFGP) and the Three-North Shelterbelt Forest Program (TNSFP) have contributed to mitigating soil erosion31,32. However, soil erosion remains a persistent threat to ecosystem recovery in China33. To improve the efficiency of soil erosion monitoring and control, the Ministry of Water Resources34 classified hydraulic erosion intensity into five grades. Due to the distinct topography and climatic conditions across regions, significant spatial heterogeneity exists in soil erosion. Among these, the Loess Plateau in Northwest China represents one of the most severely eroded landscapes worldwide and has long been a focal area for soil erosion research. Nevertheless, limited attention has been given to the variability of erosive rainfall thresholds under different rainfall intensities. Therefore, this study utilizes long-term runoff plot observations from three representative monitoring stations on the Loess Plateau, applying an improved regression analysis to examine how erosive rainfall thresholds vary with rainfall intensity. Furthermore, a nonlinear regression approach is employed to develop predictive models of erosive rainfall thresholds under different land cover types. The results aim to provide scientific support for regional soil erosion prediction and soil and water conservation planning.

Materials and methods

Overview of the study area

The Loess Plateau is recognized as one of the most severely eroded regions worldwide. Soil erosion in this area results from the combined effects of rainfall, runoff, and soil properties. Li et al.35 reported that the soils of the Loess Plateau exhibit both consistency in particle composition36 and distinct zonal distribution. The consistency is reflected in the high proportion of silt particles (0.05–0.001 mm), which generally account for 60–75% of the total soil content, with limited variation across different subregions. Among these, coarse silt particles (0.05–0.01 mm) contribute approximately 50%. The zonal distribution is characterized by a gradual fining of loess particles from northwest to southeast, most evident in the changes of sand and clay fractions. Specifically, Suide soils are classified as sandy loam, whereas Tianshui and Xifeng soils are predominantly clay loam.

Fig. 1
Fig. 1
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Schematic diagram of field runoff plot stations—created using ArcGIS (version 10.8, https://www.esri.com/en-us/home).

Data sources

The field observation data were obtained from soil and water conservation monitoring stations established by the Yellow River Conservancy Commission in Suide, Xifeng, and Tianshui (Fig. 1). The rainfall data used in this study were obtained entirely from field observations based on individual natural rainfall events. In Suide, the runoff plots are located at the Xindian Gully and Yejia Slope experimental fields, representing the first subregion of the hilly–gully area, with a total of 158 plots under different land cover conditions. In Xifeng, the plots are situated in the Nanxiaohe Gully experimental field, characteristic of the Loess Tableland geomorphology, where 62 runoff plots with various land cover types were established over time. In Tianshui, the runoff plots are distributed across the Daliushu Gully and Luoyu Gully experimental fields, representing the third subregion on the hilly–gully area, with 40 plots under different vegetation covers. The detailed information of runoff plots at the three stations is provided in Table 1.

Table 1 Conditions of runoff plots at observation stations.
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Analytical methods

The erosive rainfall threshold was determined using the linear regression method adopted by Fink et al.37,38,39. When the linear form is expressed as R = A + B*P = B*(P–C), where R denotes the runoff for a single rainfall event, P the corresponding rainfall amount, and A and B the regression coefficients, then C = –A/B is defined as the erosive rainfall threshold, while B represents the event runoff coefficient. The rainfall–runoff linear model performs well when runoff is substantially greater than zero; however, errors increase when runoff approaches zero, as in the case of natural catchments and natural catchments with weed removal in this study. This limitation can be addressed using Diskin’s37 parameter estimation procedure. Specifically, rainfall observations are first arranged in ascending order, and different candidate threshold rainfall values (P0) are selected. For events with P > P0, runoff is predicted using R = A + BP, while for events with P ≤ P0, runoff is considered negligible. The residual sum of squares between observed and predicted runoff is then calculated, establishing a functional relationship S = f(P0). The erosive rainfall threshold is defined as the P0 value corresponding to the minimum residual sum of squares. In addition, rainfall events separated by more than three days were assumed to be unaffected by antecedent rainfall.

For further categorization and analysis, rainfall events were classified according to the Standards for Classification and Gradation of Soil Erosion (SL190-2007) (Table 2)34. Within this framework, the variations in event-based runoff depth, rainfall depth, and erosive rainfall thresholds with rainfall intensity were quantified. To distinguish the effect of rainfall intensity on thresholds, rainfall events of the same intensity were retained only if the coefficient of determination between rainfall and runoff exceeded 0.90 (R2 ≥ 0.90); otherwise, they were reassigned to a lower intensity class until no runoff was generated. Finally, nonlinear regression analysis was applied to construct predictive models of erosive rainfall thresholds under different land cover conditions.

The geographic data of the Loess Plateau used in this study were obtained from the Loess Plateau Sub-Center of the National Earth System Science Data Center (http://loess.geodata.cn), and spatial mapping was carried out using ArcGIS 10.8 (https://www.esri.com/en-us/home). Data analysis of long-term field observation datasets was performed using IBM SPSS Statistics 27 (https://www.ibm.com), and the final figures were generated using Origin 2022 (https://www.originlab.com).

Table 2 Classification criteria for areal erosion.
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Results

Rainfall thresholds for soil erosion under different land cover types

Rainfall thresholds for soil erosion on farmland slopes

In the experiment, the main crops in Suide farmland were sorghum and cowpea. The four slope classes of 8°–15°, 15°–25°, 25°–35°, and > 35° corresponded to moderate, strong, very strong, and severe erosion intensity grades, respectively, according to the Standards for Classification and Gradation of Soil Erosion (SL190-2007). In Xifeng, millet and broomcorn millet were the dominant crops, and the two slope classes of 8°–15° and 15°–25° were classified as moderate and strong erosion intensities, respectively. In Tianshui, the main crop was wheat, and the three slope classes of 5°–8°, 8°–15°, and 15°–25° were categorized as slight, moderate, and strong erosion intensities, respectively.

Taking Suide as an example, scatterplots of event runoff depth versus rainfall amount under different erosion grades are shown in Fig. 2, with regression results summarized in Table 3. The results indicate a strong linear relationship between event rainfall and runoff across varying rainfall intensities. For farmland in Suide, the erosive rainfall thresholds (ERT) under four slope classes (8°–15°, 15°–25°, 25°–35°, > 35°) were 1.3, 10.0, 20.9, 5.5, 11.5, 18.4, 30.6, 7.1, 13.0, 20.7, 8.5, and 14.4 mm. In Xifeng, farmland with two slope classes (8°–15°, 15°–25°) exhibited erosive rainfall thresholds (ERT) of 2.9, 4.2, 18.0, 30.8, 3.6, 8.8, 11.0, and 13.0 mm under different rainfall intensities. For farmland in Tianshui, the erosive rainfall thresholds (ERT) under three slope classes (5°–8°, 8°–15°, 15°–25°) were 3.9, 14.6, 4.5, 14.3, 3.1, and 4.6 mm, respectively.

A regression analysis was conducted between erosive rainfall thresholds and mean rainfall intensity (i.e., the mean of the maximum rainfall intensity for each rainfall event). For Suide, the relationships under severe and extremely severe erosion grades were expressed as y = 60.591e–2.268x (R2 = 0.92, n = 12), while for Xifeng, the relationships under intense and moderate erosion grades were expressed as y = 54.844e–2.14x (R2 = 0.97, n = 8). A comparison of the two regions indicates that the variation trends of erosive rainfall thresholds with mean rainfall intensity in farmland slopes of Xifeng and Suide are generally consistent.

The relationship between erosive rainfall thresholds and mean rainfall intensity under different erosion intensity classes in Suide and Xifeng was fitted to an exponential function, expressed as y = 59.986e–1.888x (R2 = 0.65, n = 20). When combining Suide, Xifeng, and Tianshui, the relationship was expressed as y = 27.693e–1.35x (R2 = 0.43, n = 27). These results indicate that in Suide and Xifeng, the relationship between erosive rainfall thresholds and mean rainfall intensity can still be described by an exponential function, although the fitting accuracy decreases. In contrast, the relationship in Tianshui differs markedly from that in Suide and Xifeng. Moreover, it can be observed that with the southwestward shift of the study area, the rate of decline in erosive rainfall thresholds with increasing mean rainfall intensity becomes less pronounced.

Fig. 2
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Trends of erosive rainfall thresholds with mean rainfall intensity on farmland slopes.

Table 3 Relationships between erosive rainfall thresholds and rainfall intensity under different erosion intensity classes on farmland slopes across the study regions.
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Rainfall thresholds for soil erosion on forest land slopes

In the different study areas, the dominant forest land species was Robinia pseudoacacia. In Suide, vegetation cover was categorized into four levels: <30%, 30%–45%, 45%–60%, and > 60%. The corresponding slope classes were 25°–35°, 25°–35° & 8°–25°, 15°–35°, and > 25°, which were classified as extremely severe, severe & moderate, moderate, and moderate erosion intensity levels, respectively. In Xifeng, vegetation cover was grouped into three levels: 30%–45%, 45%–60%, and > 60%. The associated slope classes were 25°–35°, 15°–35°, and > 25°, corresponding to severe, moderate, and moderate erosion intensity levels, respectively. In Tianshui, vegetation cover ranged between 61% and 85%, with slopes greater than 43°, which were classified as moderate erosion intensity.

Taking Suide as an example, scatter plots of event runoff depth versus event rainfall depth under different erosion severity classes are presented in Fig. 3. Across different rainfall intensities, event runoff depth and event rainfall depth exhibited strong linear relationships, with the regression results summarized in Table 4. In Suide, the erosive rainfall thresholds (ERT) for forest land under four vegetation cover and slope classes were 8.0, 17.7, 30.3, 8.1, 9.4, 19.1, 36.7, 4.0, 13.8, 24.8, 37.3, 8.9, 15.4, 25.9, and 38.5 mm across different rainfall intensities. In Xifeng, the erosive rainfall thresholds for forest land under three vegetation cover and slope classes were 4.4, 16.8, 37.0, 19.2, 32.2, 8.7, 20.9, and 34.1 mm. In Tianshui, the erosive rainfall thresholds for forest land under one vegetation cover and slope class were 6.4, 15.2, and 24.2 mm.

By fitting the relationship between erosive rainfall thresholds and mean rainfall intensity under different erosion severity classes, it was found that, for the moderate erosion class, the relationships for Xifeng and Suide were expressed as y = 48.434e–1.097x (R2 = 0.94, n = 5) and y = 88.885e–2.19x (R2 = 0.97, n = 9), respectively. When combining the moderate and strong erosion classes, the corresponding relationships were y = 50.019e–1.367x (R2 = 0.86, n = 8) for Xifeng and y = 81.482e–2.121x (R2 = 0.96, n = 12) for Suide. A comparison of the trends revealed that, under the same erosion severity class, the erosive rainfall thresholds in Suide decreased more rapidly with increasing mean rainfall intensity than those in Xifeng.

By fitting the relationship between erosive rainfall thresholds and mean rainfall intensity for Suide and Xifeng, the function was expressed as y = 58.943e–1.668x (R2 = 0.84, n = 3). When incorporating data from Suide, Xifeng, and Tianshui, the fitted function was y = 47.227e–1.487x (R2 = 0.67, n = 26). These results indicate that the relationship between ERTs and mean rainfall intensity across regions and erosion severity classes can still be described using an exponential function, although the fitting accuracy gradually decreases. Moreover, it was observed that with the southwestward shift of the study area (accompanied by a finer soil texture), the erosive rainfall thresholds on forested slopes progressively decreased, and the rate of decline with increasing rainfall intensity became less pronounced.

Fig. 3
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Trends of erosive rainfall thresholds with mean rainfall intensity on forest land slopes.

Table 4 Relationships between erosive rainfall thresholds and rainfall intensity under different erosion intensity classes on forest land slopes across the study regions.
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Rainfall thresholds for soil erosion on grassland slopes

In the Suide region, the main pasture species included Medicago sativa (alfalfa), Melilotus spp., and Bothriochloa ischaemum. Vegetation cover was categorized into four classes: <30%, 30–45%, 45–60%, and > 60%. The corresponding slope gradients were 25–35°, 8–25°, 15–35°, and > 25°, respectively, which fall into the categories of extremely severe, moderate, moderate, and moderate erosion intensity according to the Standards for Classification and Gradation of Soil Erosion (SL190-2007). In the Xifeng region, the main pasture species were Melilotus spp. and Medicago sativa. Vegetation cover was divided into two classes, 30–45% and 45–60%, with slope gradients of 15–25° and 5–15°, corresponding to severe and slight erosion intensity, respectively. In the Tianshui region, the pastures mainly consisted of Medicago sativa, Coronilla varia, Onobrychis viciifolia, and Bothriochloa ischaemum. Vegetation cover ranged from 60% to 95%, and slopes varied from 7.4° to 25°, corresponding to slight erosion intensity according to the same classification standard.

Taking the Suide region as an example, scatterplots of event-based runoff against rainfall under different erosion intensity classes are shown in Fig. 4. Across different rainfall intensities, event runoff exhibited a strong linear relationship with event rainfall, with regression results summarized in Table 5. In Suide, the erosive rainfall thresholds (ERT) of pastureland under five cover–slope classes were 5.1, 13.4, 30.4, 7.5, 13.2, 15.9, 40.2, 11.3, 21.7, 27.7, 5.5, 10.0, 19.4, 26.6, 3.0, 9.8, 15.8, and 23.2 mm across different rainfall intensities. In Xifeng, the erosive rainfall thresholds for pastureland under two cover–slope classes were 7.6, 17.1, 22.5, 39.9, and 10.8 mm. In Tianshui, the erosive rainfall thresholds for pastureland under two cover–slope classes were 4.7, 16.0, and 15.5 mm.

By fitting the relationship between erosive rainfall thresholds and rainfall intensity under different erosion intensity classes, the functional expressions for Xifeng (severe and slight erosion) and Suide (very severe, severe, and moderate erosion) were obtained as y = 56.026e–1.636x (R2 = 0.93, n = 5), y = 71.142e–2.222x (R2 = 0.79, n = 18), respectively. A comparison of the trends indicates that the erosive rainfall threshold in Suide declines more rapidly with increasing mean rainfall intensity than in Xifeng.

The relationship between erosive rainfall thresholds and mean rainfall intensity under different erosion intensity classes for Suide and Xifeng was fitted as y = 64.596e–2.034x (R² = 0.83, n = 23), while for Suide, Xifeng, and Tianshui it was fitted as y = 53.56e–1.889x (R2 =0. 72, n = 26). These results indicate that the relationship between erosive rainfall thresholds and mean rainfall intensity under different erosion intensity classes across regions can still be described by an exponential function, although the fitting accuracy gradually decreases. Moreover, on grassland slopes, the erosive rainfall threshold gradually decreases with finer soil texture, and the rate of decline slows with increasing rainfall intensity.

Fig. 4
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Trends of erosive rainfall thresholds with mean rainfall intensity on grassland slopes.

Table 5 Relationships between erosive rainfall thresholds and rainfall intensity under different erosion intensity classes on grassland slopes across the study regions.
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Rainfall thresholds for soil erosion on abandoned land slopes

In Suide, the vegetation in the abandoned land mainly consists of Artemisia scoparia, Stipa bungeana, Artemisia capillaris, Setaria viridis, and other species. Vegetation cover is categorized into two levels, < 30% and 30%–45%, with corresponding slope gradients all > 35°, classified as severe and extremely severe erosion intensity according to the “Soil Erosion Classification and Grading Standard.” In Xifeng, the abandoned land are dominated by Artemisia, Bothriochloa ischaemum, Agropyron cristatum, and Cleistogenes, with three vegetation cover levels: 30%–45%, 45%–60%, and > 60%, all with slope gradients of 25°–35°, corresponding to strong, moderate, and moderate erosion intensity levels, respectively, based on the same standard.

Taking Suide as an example, the scatter plots of event-based runoff versus event rainfall under different erosion intensity levels are shown in Fig. 5. Across varying rainfall intensities, event runoff exhibits a strong linear relationship with event rainfall, with the fitting results detailed in Table 6. In Suide, the erosion rainfall thresholds (ERT) for abandoned land under two vegetation cover and slope classes are 3.6, 13.0, 25.6, 37.2, 7.9, 16.1, and 29.6 mm. In Xifeng, the erosive rainfall thresholds for abandoned land under three vegetation cover and slope classes are 5.3, 13.1, 25.1, 5.8, 23.9, 31.6, 5.7, 17.1, and 29.9 mm.

Fitting the erosion rainfall thresholds against rainfall intensity under different erosion levels, the relationships for Xifeng under strong and moderate erosion intensity and for Suide under severe and extreme erosion intensity are expressed as y = 78.32e–2.482x (R2 = 0.76, n = 9) and y = 77.973e–2.235x (R2 = 0.88, n = 7), respectively. A comparison of the trends indicates that the erosion rainfall thresholds for wasteland slopes in Xifeng and Suide decrease with increasing average rainfall intensity in a nearly consistent manner.

The relationship between erosion rainfall thresholds and mean rainfall intensity for different erosion intensity levels in Suide and Xifeng was fitted using the function y = 74.809e–2.308x (R2 = 0.80, n = 16), indicating that the relationship across different regions and erosion intensity levels can still be expressed using an exponential function.

Fig. 5
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Trends of erosive rainfall thresholds with mean rainfall intensity on abandoned land slopes.

Table 6 Relationships between erosive rainfall thresholds and rainfall intensity under different erosion intensity classes on abandoned land slopes across the study regions.
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Influence of land cover types on rainfall thresholds for soil erosion

Rainfall thresholds for soil erosion in the suide region

In this study, the linear regression method was used to estimate the slope erosive rainfall thresholds. It was found that in the Suide, under different land cover types, the rainfall thresholds for slope soil erosion decreased exponentially with increasing rainfall intensity.

Slope vegetation cover is a key factor influencing the slope erosive rainfall thresholds. The variation of erosion rainfall thresholds with mean rainfall intensity under different land cover types in Suide is shown in Fig. 6. Here, the fitted curves represent erosive rainfall thresholds across all erosion classes defined in China’s “Soil Erosion Classification and Grading Standard” (SL190-2007). The fitted equations for forest land, grassland, abandoned land, and farmland are y = 68.15e–1.907x (R2 = 0.83, n = 15), y = 71.142e–2.222x (R2 = 0.79, n = 18), y = 77.973e–2.235x (R2 = 0.87, n = 7), and y = 60.248e–2.256x (R2 = 0.92, n = 15), respectively. Comparison of the fitted coefficients indicates that the rainfall threshold for soil erosion decreases most rapidly on abandoned land, followed by grassland and forest land, while farmland decreases most slowly. Due to these differences in decline rates among land cover types, Fig. 6 shows that for rainfall intensities below 0.4 mm/min, the threshold order is forest land > abandoned land ≈ grassland > farmland; for rainfall intensities above 0.4 mm/min, the order becomes forest > abandoned land > grassland > farmland. The soil erosion rainfall thresholds under different rainfall intensities in Suide are listed in Table 7.

Fig. 6
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Variation of erosive rainfall thresholds with mean rainfall intensity under different land cover types in Suide.

Table 7 Variation of erosive rainfall thresholds with rainfall intensity under different land cover types in Suide.
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Rainfall thresholds for soil erosion in the Xifeng region

In this study, the erosive rainfall threshold for slope surfaces was determined using the linear regression method. Similarly, it was found that in the Xifeng, the slope erosive rainfall thresholds under different land cover types decreased exponentially with increasing rainfall intensity.

The variation trends of slope erosive rainfall thresholds under different land cover types in Xifeng are shown in Fig. 7. The fitted curves of erosion rainfall thresholds with average rainfall intensity for forest land, grassland, abandoned land, and farmland are expressed as y = 50.022e–1.367x (R2 = 0.86, n = 8), y = 56.026e–1.636x (R2 = 0.93, n = 5), y = 78.32e–2.482x (R2 = 0.76, n = 9), and y = 82.922e–1.776x (R2 = 0.83, n = 8), respectively. Comparing the fitted coefficients shows that the erosive rainfall thresholds on farmland decreases most rapidly with increasing rainfall intensity, followed by abandoned land and grassland, while forest land decreases the slowest. Due to the differing rates of decline in erosive rainfall thresholds among land cover types, Fig. 7 shows that for rainfall intensities below 0.4 mm/min, the trend of soil erosion rainfall thresholds is abandoned land > grassland > forest land > farmland; for rainfall intensities above 0.4 mm/min, the trend is forest land > grassland ≈ abandoned land > farmland. The rainfall thresholds for soil erosion under different rainfall intensities in Xifeng are listed in Table 8.

Fig. 7
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Variation of erosive rainfall thresholds with mean rainfall intensity under different land cover types in Xifeng.

Table 8 Variation of erosive rainfall thresholds with rainfall intensity under different land cover types in Xifeng.
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Discussion

The erosive rainfall thresholds serve as fundamental parameters for studies on slope runoff regulation and soil erosion prediction. In this study, the erosive rainfall thresholds were estimated using a linear regression approach, revealing that the erosive rainfall thresholds decrease exponentially with increasing rainfall intensity under different land cover types. This pattern may be attributed to the loess soil’s loose structure and well-developed porosity, which make it highly susceptible to raindrop impact and particle dispersion. Under high-intensity rainfall, the kinetic energy of raindrops can rapidly destroy soil aggregates, causing fine particles to clog pores and form a dense surface crust. This process nonlinearly, and even exponentially, reduces soil infiltration capacity. Once infiltration falls below rainfall intensity, surface water rapidly accumulates, significantly shortening the time to runoff initiation and, consequently, to soil erosion, resulting in an exponential decline of erosive rainfall thresholds with increasing rainfall intensity. Huang et al.40 analyzed the relationship between individual rainfall events and runoff depth in eight experimental plots (forest + understory shrub-grass) in the Pearl River Basin and found a linear decrease of erosive rainfall thresholds with increasing rainfall intensity, which differs slightly from the present study. The discrepancy may be due to their rainfall intensity classification, where the highest categories were 30–35 mm/h and > 35 mm/h, lacking data on high-intensity rainfall events; under such conditions, slope runoff occurs rapidly, and the decrease in erosive rainfall thresholds with increasing intensity is less pronounced. Overall, on loess slopes, short-duration, high-volume rainfall events can rapidly generate surface runoff and enhance sediment transport capacity, causing severe soil erosion. Furthermore, studies have shown that the Revised Universal Soil Loss Equation (RUSLE) tends to overestimate soil erosion under vegetation recovery conditions8, likely because RUSLE uses fixed erosion thresholds that do not account for variations with vegetation cover or erosion intensity, nor the response of thresholds to rainfall intensity. The predictive models of erosive rainfall thresholds under different land cover types developed in this study can provide useful references for RUSLE-based soil erosion prediction and help reduce its calculation uncertainties.

Slope vegetation cover is a critical factor influencing the slope erosive rainfall thresholds. Vegetation can delay crust formation by intercepting raindrops, increasing surface roughness, and improving soil structure41,42, thereby raising erosion rainfall thresholds. Different vegetation measures effectively mitigated soil erosion, with the annual mean soil loss ranked as follows: natural vegetation restoration < cropland < bare land43. Therefore, different slope cover conditions exhibit varying capacities to increase the slope erosive rainfall thresholds. Wang Wanzhong4 suggested that the basic erosive rainfall thresholds in the Loess Plateau are: farmland 8.1 mm < artificial grassland 10.9 mm < forest land 14.6 mm, with the required rainfall intensities generally exceeding 0.26 mm/min, 0.32 mm/min, and 0.32 mm/min for the respective land covers (based on average intensity of individual rainfall events). In the present study, at a rainfall intensity of 0.8 mm/min, the slope erosive rainfall thresholds in Suide were: farmland 9.9 mm < grassland 12.0 mm < barren land 13.0 mm < forest land 14.8 mm, and in Xifeng: farmland 10.2 mm < barren land 10.8 mm < grassland 15.1 mm < forest land 16.8 mm. In terms of rainfall amounts, these results are roughly consistent with Wang Wanzhong’s findings. Regarding the corresponding rainfall intensities, this study used the mean of the maximum intensities of individual rainfall events, whereas Wang used the mean rainfall intensity, which may explain why the rainfall intensities corresponding to similar thresholds are higher in this study. Differences may also arise from variations in vegetation types, coverage, slope, and soil texture between the experimental plots in this study and those in Wang’s work. Wang et al. reported erosive rainfall thresholds at a single rainfall intensity, whereas this study presents curves of rainfall thresholds for different cover types as a function of rainfall intensity, further improving the precision of threshold estimation. Both this study and previous research11 indicate that forested slopes have higher soil erosion rainfall thresholds than grassland or farmland. This is likely because soil erosion is primarily driven by surface runoff, and erosion under forest canopies is mitigated by the canopy intercepting rainfall44, filtering raindrops, and enhancing soil stability through root structures45,46. Modeste et al.47 found that, in non-karst regions, infiltration capacity follows the order: forest land > farmland > bare land; the higher infiltration capacity of forest soils also contributes to their larger erosion rainfall thresholds.

Soil texture is also an important factor influencing runoff generation on slopes. In this study, it was observed that on forest, grassland, and barren slopes, as the study area shifts southwestward (i.e., with increasingly fine-textured soils), the rate of decline in erosive rainfall thresholds with increasing mean rainfall intensity gradually slows. Zhou Peihua and Wang Zhanli48 reported from farmland plots on clay loess, sandy loess, and loessial soils that soil texture had no significant effect on runoff initiation time, arguing that tillage of farmland masks the role of soil texture. Frequent tillage increases macropores in the topsoil, which may lead to higher erosive rainfall thresholds—likely explaining the relatively large erosive rainfall thresholds for farmland observed in Xifeng. However, quantitatively evaluating the influence of soil properties on the proposed thresholds is not straightforward. For instance, erosive rainfall thresholds generally increase with clay content49. Yet, in some cases—such as soils with high exchangeable sodium percentage (ESP) or sodium adsorption ratio (SAR)13—clay can behave very differently, reducing soil structural stability and increasing susceptibility to erosion processes.

At the same time, rainfall characteristics vary markedly across regions. de Almeida et al.50 demonstrated that for rainfall events with equivalent erosive power, differences in rainfall intensity and duration can alter both the onset time of runoff and the runoff volume. Regional variations in rainfall characteristics are therefore one of the key reasons for the differences in erosive rainfall thresholds between Suide and Xifeng. In addition, differences in topography and climatic conditions across regions result in distinct standards for erosive rainfall. Findings from this study, together with previous research, support this perspective. For instance, some scholars define erosive rainfall in the Loess Plateau as events with rainfall amounts greater than 10 mm18; in northeastern Heilongjiang, the threshold for soil erosion is 9.8 mm51; in the northeastern mountainous regions of Yunnan Province, it is 9.2 mm19; whereas in the Poyang Lake Basin, the standard for erosive rainfall is 14 mm52. Such erosive rainfall thresholds provide an effective criterion for distinguishing rainfall events capable of generating soil erosion in specific regions or catchments.

Other factors, such as antecedent rainfall and baseline conditions (e.g., soil moisture content and organic matter content), may also influence the threshold of erosive rainfall. For instance, antecedent soil moisture has a significant effect on runoff generation and soil loss53,54,55; compared with dry soils, wet soils can exhibit a twofold increase in runoff coefficients and shortened runoff initiation times56. Organic matter content governs the stability of soil aggregates3, and stable aggregates are critical for enhancing soil infiltration capacity and reducing erosion. This study has certain limitations. For example, the availability of key data (such as antecedent rainfall and soil moisture) was limited, and other potentially important factors (e.g., the effects of soil organic matter) were not fully considered. The mechanisms through which these factors influence the thresholds of erosive rainfall will be explored in future studies using more comprehensive spatiotemporal datasets. Moreover, because of limited data availability for the Tianshui region, the influence of land cover types on erosive rainfall thresholds there was not evaluated. Despite these limitations, this study provides novel insights by analyzing the variation of erosive rainfall thresholds with rainfall intensity and developing predictive models of erosive rainfall thresholds under different land cover conditions. Nonetheless, it did not account for alternative approaches or regional heterogeneity. Future research should integrate additional methodologies, address data constraints, and explore broader environmental conditions to enhance threshold accuracy and improve predictions of soil erosion and water loss.

Conclusions

Based on long-term runoff plot observations from farmland, forest land, grassland, and abandoned land in representative regions of the Loess Plateau (Suide, Xifeng, and Tianshui), this study applied an improved regression analysis to determine erosive rainfall thresholds under different erosion grades. The variation of erosive rainfall thresholds with rainfall intensity was analyzed, along with the effects of land cover and soil texture. Furthermore, nonlinear regression analysis was employed to establish predictive models of erosive rainfall thresholds for different land cover types. The results indicate that the rainfall threshold for soil erosion on slopes decreases exponentially with increasing rainfall intensity. The regression models are as follows: forest land, y = 58.943e–1.668x (R2 = 0.84, n = 23); grassland, y = 64.596e–2.034x (R2 = 0.83, n = 23); abandoned land, y = 74.809e–2.308x (R2 = 0.80, n = 16); and farmland, y = 59.986e–1.888x (R2 = 0.65, n = 20). Soil texture was identified as a key factor influencing erosive rainfall thresholds, with finer textures associated with lower thresholds on forest land, grassland, and abandoned land, while the rate of decline with rainfall intensity became more gradual. Threshold trends also varied by rainfall intensity and region. In Suide, thresholds followed the order forest land > abandoned land ≈ grassland > farmland when rainfall intensity < 0.4 mm/min, and forest land > abandoned land > grassland > farmland when rainfall intensity > 0.4 mm/min. In Xifeng, thresholds followed the order abandoned land > grassland > forest land > farmland when rainfall intensity < 0.4 mm/min, and forest land > grassland ≈ abandoned land > farmland when rainfall intensity > 0.4 mm/min. Soil texture, land cover type, and rainfall characteristics exert significant influences on the effectiveness of vegetation in controlling runoff and soil erosion. These findings advance the understanding of the role of rainfall characteristics in soil erosion processes and provide a scientific basis for erosion forecasting and soil and water conservation planning.