Effects of Content of Soil Rock Fragments on Soil Erodibility in China

Soil erosion is serious in China—the soil in plateau and mountain areas contain a large of rock fragments, and their content and distribution have an important influence on soil erosion. However, there are still no complete results for calculating soil erodibility factor (K) that have corrected rock fragments in China. In this paper, the data available on rock fragments in the soil profile (RFP); rock fragments on the surface of the soil (RFS); and environmental factors such as elevation, terrain relief, slope, vegetation coverage (characterised by normalised difference vegetation index, NDVI), land use, precipitation, temperature, and soil type were used to explore the effects of content of soil rock fragments on calculating of K in China. The correlation analysis, typical sampling area analysis, and redundancy analysis were applied to analyse the effects of content of soil rock fragments on calculating of K and its relationship with environment factors. The results showed that (1) The rock fragments in the soil profile (RFP) increased K. The rock fragments on the surface (RFS) of the soil reduced K. The effect of both RFP and RFS reduced K. (2) The effect of rock fragments on K was most affected by elevation, followed by terrain relief, NDVI, slope, soil type, temperature, and precipitation, but had little correlation with land use. (3) The result of redundancy analysis showed elevation to be the main predominant factor of the effect of rock fragments on K. This study fully considered the effect of rock fragments on calculating of K and carried out a quantitative analysis of the factors affecting the effect of rock fragments on K, so as to provide necessary scientific basis for estimating K and evaluating soil erosion status in China more accurately.


Introduction
Soil is a finite natural resource that controls biological, hydrological, erosive, and geochemical cycles [1]. It not only provides survival guarantee for life on earth, but also carries the indispensable material foundation of ecosystems [2]. However, soil erosion has become one of the biggest threats to soil destruction today [3,4]. Soil erosion is one of the world's environmental problems, and it is also an incentive for many other environmental problems [5]. Due to the influence of China's special physical geography, social economy, and human factors, land resources are increasingly damaged to meet the needs of human social development, and soil erosion has become more serious [6], making China one of the countries with the most severe soil erosion in the world [7]. According to the bulletin of 2020 Soil and Water Conservation in China, the total area of soil erosion in China is more than 26.9 million km 2 , accounting for 28.14% of the monitored area [8]. Large-scale soil erosion has become an important factor restricting economic development and destroying the health of the ecosystem. Soil erodibility factor (hereinafter referred to as the K), as a quantitative index that characterises the intrinsic properties of soil, is a necessary parameter for soil erosion prediction models [9], and has been widely used in models such as universal Meteorological station data of 338 prefecture-level cities Note: 1 RFS-rock fragments on the surface of the soil; 2 RFP-rock fragments in the soil profile; 3 soil typerefer to the world reference base for soil resources based on food and Agriculture Organisation of the United Nations; 4 ISRIC-International Soil Reference and Information Centre SoilGrids: https://files.isric.org/soilgrids/ former/2017-03-10/data/ (accessed on 1 October 2021); 5 https://www.resdc.cn/ (accessed on 1 October 2021); 6 http://data.cma.cn/ (accessed on 1 October 2021).

Data Pre-Processing
Spatial interpolation: Interpolation is a procedure that depends on the spatial and/or statistical properties of the analysed variable(s) [41]. The inverse distance weighting (IDW) interpolation is the widely used spatial interpolation method, which has the advantages of simple principle and fast calculation, and conforms to the first law of geography. It has been widely used in DEM construction, meteorological analysis, hydrological analysis, and so on [42]. IDW estimates values at un-sampled points by the weighted average of observed data at surrounding points. Thus, this can be defined as a distance reverse function of each point from neighbouring points [43]. That means by using a linear combination of values at a known sampled point, values at un-sampled points can be calculated. IDW relies on the theory that the unknown value of a point is more influenced by closer points than by points further away [42].
Regarding the spatial interpolation of meteorological data, Dirks et al. [44] recommended the use of IDW for interpolations for spatially dense networks. In this paper, the annual average total precipitation and annual average temperature were prepared using the IDW method for map generation (Geographic Information System software (GIS) ArcGIS™ 10.5 invented by ESRI (Environmental Systems Research Institute in Redlands, CA, USA) and its extension Geostatistical Analyst) according to the monthly average precipitation and temperature data of 338 cities above the prefecture level in China from 2010 to 2017. Spatial distribution maps of the annual average total precipitation and annual average temperature were constructed according to the coordinates and sample data by using IDW method.
Calculation of slope and terrain relief : Derived from elevation data with a resolution of 250 m in China to obtain terrain relief and slope data with a resolution of 250 m based on the ArcGIS 10.5.

Calculation of the Effect of Rock Fragments on K
The effect of RFS on K: Poesen [26] proposed an algorithm for calculating attenuation coefficients of rock fragment. This method was used to analysis the effect of RFS on K in this study, through calculating the rock fragment reduction coefficient St, which represents the influence coefficient of RFS (Equation (1)).
where R c is the rock fragments on the surface of the soil (%), and the larger St is, the more obvious the weakening effect of RFS on K.
The effect of RFP on K: The USLE algorithm, proposed by Wischmeier [11,45], is a commonly used algorithm to calculate the K [12,46]. This study used the USLE-K algorithm as an example to discuss the effect of RFP on K. The equation for the USLE-K is where M c is the clay content (%), M silt is the silt content (%), M vfs is the very fine sand content (%), OM is the soil organic carbon content (%), s is the soil structure class, and p is the soil profile permeability class. The K affected by RFP (Kc) and K without considering the rock fragments (Kf) were calculated by Equations (4) and (5). Calculate the difference between the Kc and Kf to obtain the influence coefficient of RFP (K cf ). The larger the K cf , the more obvious the enhancement effect of the RFP on K.
K pf is the permeability coefficient that does not consider the effect of RFP, and K pc is the permeability coefficient that considers the effect of RFP. P f is the permeability class without considering the RFP; P c is the permeability class considering the RFP.
The effect of both RFP and RFS on K: Multiplying St and Kc to calculate the K considering the effect of both RFP and RFS (K cs ).
Calculate the difference between Kf and K cs to obtain the comprehensive influence coefficient of both RFP and RFS (K f-cs ). The effect of rock fragments on K (hereinafter referred to as the E R_K ) is expressed by the influence coefficient of RFS (St), the influence coefficient of RFP (K cf ), and the comprehensive influence coefficient of both RFP and RFS (K f-cs ).

Sampling Statistics and Typical Sampling Area Analysis
E R_K (St, K cf , K f-cs ) and terrain relief, slope, elevation, NDVI, precipitation, and temperature were sampled at the central point of 1:50,000 standard map (latitude difference is 10 , longitude difference is 15 ). A total of 638 samples were collected in China, which were evenly distributed and had certain representativeness. The relationship between the E R_K and terrain relief, slope, elevation, NDVI, precipitation, and temperature was obtained by fitting analysis of the values of sampling points. The correlation between influencing factors and E R_K was compared, and their significance was tested. When analysing the effect of land use and soil type, the mean values of E R_K of different land use and soil type were counted, and the reasons for the high and low values were analysed. For the selection of typical sampling areas, from the low value of influencing factors to the high value, we selected five small sampling areas with different gradients (very low, low, medium, high, and very high) of terrain relief, slope, elevation, NDVI and land use, and their regular patterns and correlations were analysed to discuss the influence of different factors on E R_K .

Redundancy Analysis
Redundancy analysis (RDA) is a well-known multivariate method that models the information flow between two datasets by maximising the redundancy index between explanatory and response variables; thus, RDA measures the effect of the explanatory dataset on the response dataset [47]. RDA describes the relationships between datasets by finding a linear combination of the explanatory variables that explain the most variance of the response variables. RDA is a kind of constrained sequencing, similar to multiple regression analysis, which is a direct gradient analysis method. It neither combines several variables into a virtual complex variable nor simply analyses groups of variables. Its biggest advantage is that it can independently maintain the contribution rate of each explanatory variable. The statistical characteristics of a single explanatory variable can be described under different combinations of explanatory variables, and then the choice of explanatory variables can be decided.
RDA's conceptual model was already described by Wollenberg [48] and has been widely used in fields such as geology [49,50], ecology [51], and psychology [52]. RDA was used to evaluate the effect of influencing factors on spatial differentiation of E R_K , and to identify the main predominant factor affecting spatial variation of E R_K in this study. Influencing factors were selected as indicators to measure the effect of rock fragments, and St, K cf , and K f-cs values were selected as response variables in RDA analysis. Eight influencing factors, namely, terrain relief, elevation, slope, NDVI, land use, precipitation, temperature, and soil type, were selected as explanatory variables. The RDA was analysed using CANOCO 5.0 software.

The Effect of Rock Fragments on K (E R_K )
The average value of the influence coefficient of RFS (St) was 0.292 (Figure 1c), which has a significant weakening effect on K, reducing K by 0.0094 (t·hm 2 ·h)·(hm −2 ·MJ −1 ·mm −1 ). The reason is that RFS slows down raindrop splashes and reduces surface water flow, reducing runoff, thus alleviating soil erosion [9,34,36]. RFP increases K by 0.0011 (t·hm 2 ·h)·(hm −2 ·MJ −1 ·mm −1 ) on average in China, because the increase of RFP reduces soil porosity, thus reducing infiltration and increasing surface runoff, soil erosion, and sediment yield [20,21,26,31]. The effect of both RFP and RFS reduced K by an average of 0.0013 (t·hm 2 ·h)·(hm −2 ·MJ −1 ·mm −1 ), which occurs in Yunnan-Guizhou Plateau, Qinghai-Tibet Plateau, and Tianshan Mountains with high rock fragment coverage. The protective effect of RFS is greater than RFP in those areas. However, in the eastern multi-plain area, the effect of both RFS and RFP is weak. In general, the effect of RFS on the whole is greater.  By comparing the relationship between E R_K and terrain relief (Figure 2a), we found that St, K cf , and K f-cs were significantly correlated with terrain relief, with correlation coefficients of 0.802, 0.646, and 0.820, respectively (Figure 3), indicating a high correlation between E R_K and terrain relief. St, K cf , and K f-cs increase with the increase of terrain relief, indicating that rock fragment has greater influence on soil erosion with the increase of terrain relief. The reason is that areas with large terrain relief ( Figure 2a) have higher terrain ( Figure 2c) mainly distributed in mountains and some hilly areas. The soil parent material in these areas is mostly bedrock, and the degree of soil development is low, which makes the RFS and RFP are large (Figure 1a,b), and therefore it has a greater impact on soil erosion ( Figure 1).

Relationship between the Effect of Rock Fragments on K (ER_K) and Slope
Comparing the relationship between ER_K and slope, we found that St, Kcf, and Kf-cs were all significantly correlated with slope, and the correlation coefficients were 0.577, 0.454, and 0.562, respectively ( Figure 4). When the slope increased, St, Kcf, and Kf-cs also showed an upward trend. The reason was that the greater the slope, the more mountains and grassland were distributed, and they were more affected by rock fragments. However, when the slope was greater than 6°, the upward trend of St, Kcf, and Kf-cs slowed down significantly. The reason was that areas with a slope greater than 6° are mainly distributed on the border of the Qinghai-Tibet Plateau, as shown in the red area in Figure 2b. These places have better hydrothermal conditions, higher vegetation coverage, and welldeveloped soil. Moreover, the content of rock fragments in these places is also within a certain threshold range, and therefore the trend of ER_K will tend to be gentle and will not increase indefinitely only because of the increase in slope.

Relationship between the Effect of Rock Fragments on K (E R_K ) and Slope
Comparing the relationship between E R_K and slope, we found that St, K cf , and K f-cs were all significantly correlated with slope, and the correlation coefficients were 0.577, 0.454, and 0.562, respectively ( Figure 4). When the slope increased, St, K cf , and K f-cs also showed an upward trend. The reason was that the greater the slope, the more mountains and grassland were distributed, and they were more affected by rock fragments. However, when the slope was greater than 6 • , the upward trend of St, K cf , and K f-cs slowed down significantly. The reason was that areas with a slope greater than 6 • are mainly distributed on the border of the Qinghai-Tibet Plateau, as shown in the red area in Figure 2b. These places have better hydrothermal conditions, higher vegetation coverage, and well-developed soil. Moreover, the content of rock fragments in these places is also within a certain threshold range, and therefore the trend of E R_K will tend to be gentle and will not increase indefinitely only because of the increase in slope.

Relationship between the Effect of Rock Fragments on K (ER_K) and Elevation
Comparing the relationship between ER_K and elevation, we found that St, Kcf, and Kfcs were all significantly correlated with elevation, and the correlation coefficients were 0.902, 0.934, and 0.900, respectively ( Figure 5). When the elevation increased, St, Kcf, and Kf-cs also showed an upward trend, and the correlation was extremely high. The reason was that in mountainous areas with large terrain relief and slopes, such as the Qinghai-Tibet Plateau, Tianshan Mountains, and Himalayas, there are mainly distributed relatively infertile soils such as Leptosols and Cryosols, with large content of rock fragments. Moreover, the hydrothermal conditions at different elevations also have an indirect impact on the physical and chemical properties of the soil, and thus the higher the elevation, the greater the effect on soil erosion.

Relationship between the Effect of Rock Fragments on K (E R_K ) and Elevation
Comparing the relationship between E R_K and elevation, we found that St, K cf , and K f-cs were all significantly correlated with elevation, and the correlation coefficients were 0.902, 0.934, and 0.900, respectively ( Figure 5). When the elevation increased, St, K cf , and K f-cs also showed an upward trend, and the correlation was extremely high. The reason was that in mountainous areas with large terrain relief and slopes, such as the Qinghai-Tibet Plateau, Tianshan Mountains, and Himalayas, there are mainly distributed relatively infertile soils such as Leptosols and Cryosols, with large content of rock fragments. Moreover, the hydrothermal conditions at different elevations also have an indirect impact on the physical and chemical properties of the soil, and thus the higher the elevation, the greater the effect on soil erosion. cs were all significantly correlated with elevation, and the correlation coefficients were 0.902, 0.934, and 0.900, respectively ( Figure 5). When the elevation increased, St, Kcf, and Kf-cs also showed an upward trend, and the correlation was extremely high. The reason was that in mountainous areas with large terrain relief and slopes, such as the Qinghai-Tibet Plateau, Tianshan Mountains, and Himalayas, there are mainly distributed relatively infertile soils such as Leptosols and Cryosols, with large content of rock fragments. Moreover, the hydrothermal conditions at different elevations also have an indirect impact on the physical and chemical properties of the soil, and thus the higher the elevation, the greater the effect on soil erosion.

Typical Sampling Areas of Topography
Five typical sampling areas with different gradients (very low, low, medium, high, and very high) of terrain relief, slope, and elevation were selected, as shown in Figure 2. By calculating the mean values of St, Kcf, and Kf-cs in different regions ( Figure 6), we found that the mean values of St, Kcf, and Kf-cs gradually increased with the increase of terrain relief, slope, and elevation, which is consistent with the regular pattern mentioned above. This means that when calculating the effect of rock fragment on K, terrain relief, slope, and elevation factors need to be considered.

Typical Sampling Areas of Topography
Five typical sampling areas with different gradients (very low, low, medium, high, and very high) of terrain relief, slope, and elevation were selected, as shown in Figure 2. By calculating the mean values of St, K cf , and K f-cs in different regions ( Figure 6), we found that the mean values of St, K cf , and K f-cs gradually increased with the increase of terrain relief, slope, and elevation, which is consistent with the regular pattern mentioned above. This means that when calculating the effect of rock fragment on K, terrain relief, slope, and elevation factors need to be considered.

Relationship between the Effect of Rock Fragments on K (ER_K) and Land Use
Analysing the average values of St, Kcf, and Kf-cs of bare land, grassland, forest, cropland, and other land, we found that rock fragment had the greatest effect on bare land, followed by grassland and forest, and had the least effect on cropland (Figure 7). The reason is that cropland is usually distributed in relatively flat terrain. The slope and terrain relief of cropland are small-the mean values were 2.534° and 115.965 m, respectively (Table 2). Bare land areas are usually arid, with weak biological activities, and strong winds lead to more content of rock fragments in the soil. The slope and terrain relief of forest and grassland are relatively large. In general, the effect of rock fragments on bare land, grassland, and forest is greater, and the effect of rock fragments on cropland is relatively small ( Table 2).

Relationship between the Effect of Rock Fragments on K (E R_K ) and Land Use
Analysing the average values of St, K cf , and K f-cs of bare land, grassland, forest, cropland, and other land, we found that rock fragment had the greatest effect on bare land, followed by grassland and forest, and had the least effect on cropland (Figure 7). The reason is that cropland is usually distributed in relatively flat terrain. The slope and terrain relief of cropland are small-the mean values were 2.534 • and 115.965 m, respectively ( Table 2). Bare land areas are usually arid, with weak biological activities, and strong winds lead to more content of rock fragments in the soil. The slope and terrain relief of forest and grassland are relatively large. In general, the effect of rock fragments on bare land, grassland, and forest is greater, and the effect of rock fragments on cropland is relatively small ( Table 2).
terrain relief of cropland are small-the mean values were 2.534° and 115.965 m, respectively (Table 2). Bare land areas are usually arid, with weak biological activities, and strong winds lead to more content of rock fragments in the soil. The slope and terrain relief of forest and grassland are relatively large. In general, the effect of rock fragments on bare land, grassland, and forest is greater, and the effect of rock fragments on cropland is relatively small ( Table 2).     Figure 8 shows that the relationship between NDVI and E R_K generally presented a concave quadratic curve. The minimum value was about 0.4. When the NDVI was less than 0.4, the larger the NDVI, the smaller the St, K cf , and K f-cs , indicating the smaller impact of NDVI on rock fragments. The reason is that the areas with NDVI less than 0.4 were mainly distributed in the western regions with lower coverage grassland (Figure 9a). The NDVI increased from northwest to southeast, but the content of rock fragments showed the opposite trend, and therefore St, K cf , and K f-cs all showed a downward trend. When the NDVI was greater than 0.4, the three figures (Figure 8a-c) all had inflection points, and St, K cf , and K f-cs all showed an upward trend. The possible reason was that the areas with small NDVI were mainly cropland, and the content of rock fragments were both small and the effect was small. However, the areas with larger NDVI were mainly distributed in the steep low hills with larger content of rock fragments, and thus the effect was greater.  Figure 8 shows that the relationship between NDVI and ER_K generally presented a concave quadratic curve. The minimum value was about 0.4. When the NDVI was less than 0.4, the larger the NDVI, the smaller the St, Kcf, and Kf-cs, indicating the smaller impact of NDVI on rock fragments. The reason is that the areas with NDVI less than 0.4 were mainly distributed in the western regions with lower coverage grassland (Figure 9a). The NDVI increased from northwest to southeast, but the content of rock fragments showed the opposite trend, and therefore St, Kcf, and Kf-cs all showed a downward trend. When the NDVI was greater than 0.4, the three figures (Figure 8a-c) all had inflection points, and St, Kcf, and Kf-cs all showed an upward trend. The possible reason was that the areas with small NDVI were mainly cropland, and the content of rock fragments were both small and the effect was small. However, the areas with larger NDVI were mainly distributed in the steep low hills with larger content of rock fragments, and thus the effect was greater.

Typical Sampling Areas of Land Cover
Five typical sampling areas with different gradients (very low, low, medium, high, and very high) of NDVI ( Figure 9a) were selected to calculate the mean values of St, Kcf, Kf-cs and NDVI. It was found that the higher the mean value of NDVI in the selected sampling area, the smaller the mean variation of St, Kcf, and Kf-cs (Figure 10a). It shows that

Typical Sampling Areas of Land Cover
Five typical sampling areas with different gradients (very low, low, medium, high, and very high) of NDVI (Figure 9a) were selected to calculate the mean values of St, K cf , K f-cs and NDVI. It was found that the higher the mean value of NDVI in the selected sampling area, the smaller the mean variation of St, K cf , and K f-cs (Figure 10a). It shows that the higher the vegetation coverage, the more protective effect on the soil, and the effect of rock fragments on K will be reduced. In this research, a typical sampling area of bare land, cropland, forest, grassland, and other land was selected (Figure 9b), and the mean values of St, K cf , and K f-cs were calculated. It was found that when the selected typical sampling area was cropland, the mean variation of St, K cf , and K f-cs were small; when the selected typical sampling area was grassland, the mean values of St, K cf , and K f-cs varied greatly (Figure 10b), which is consistent with the regular pattern mentioned above. Therefore, the effect of NDVI and different land use should be considered when considering the effect of rock fragments on K. the higher the vegetation coverage, the more protective effect on the soil, and the effect of rock fragments on K will be reduced. In this research, a typical sampling area of bare land, cropland, forest, grassland, and other land was selected (Figure 9b), and the mean values of St, Kcf, and Kf-cs were calculated. It was found that when the selected typical sampling area was cropland, the mean variation of St, Kcf, and Kf-cs were small; when the selected typical sampling area was grassland, the mean values of St, Kcf, and Kf-cs varied greatly (Figure 10b), which is consistent with the regular pattern mentioned above. Therefore, the effect of NDVI and different land use should be considered when considering the effect of rock fragments on K.

Relationship between the Effect of Rock Fragments on K (ER_K) and Soil Type
This study calculated the average values of St, Kcf, and Kf-cs under different soil types, finding that when the soil types were Leptosols, Cryosols, Gypsisols, Solonchaks, Gypsisols, Luvisols and Calcisols (Table 3), the average values of St, Kcf, and Kf-cs were higher, indicating that the rock fragment has a greater effect on K in this condition. The reason is that this kind of soil is mainly distributed in the west of China. In arid or semi-arid environment, it is mostly shallow soil, which has higher soluble salt content and secondary

Relationship between the Effect of Rock Fragments on K (E R_K ) and Soil Type
This study calculated the average values of St, K cf , and K f-cs under different soil types, finding that when the soil types were Leptosols, Cryosols, Gypsisols, Solonchaks,

Relationship between the Effect of Rock Fragments on K (E R_K ) and Temperature
Compared with the relationship between E R_K and temperature (Figure 11a), St, K cf , and K f-cs were significantly correlated with temperature, with correlation coefficients of 0.393, 0.229, and 0.515, respectively; the overall trend of St, K cf , and K f-cs decreased with the increase of temperature ( Figure 12). The reason was that temperature changes soil structure mainly through affecting microbial community, which has great influence on soil spatial distribution and soil physical and chemical properties, thus affecting soil erodibility. The temperature gradually decreases from northwest to southeast, which is opposite to the content of rock fragments and slope distribution. The higher the temperature, the better the hydrothermal conditions, the gentler the terrain, and the better the soil conditions; therefore, the effect of rock fragments will be relatively small.

Relationship between the Effect of Rock Fragments on K (E R_K ) and Precipitation
Compared with the relationship between E R_K and precipitation (Figure 11b), St, K cf , and K f-cs were significantly correlated with precipitation, with correlation coefficients of 0.411, 0.214, and 0.596, respectively; the overall trend of St, K cf , and K f-cs decreased with the increase of precipitation ( Figure 13). The reason is was the areas with high precipitation are mainly distributed in the southeast of China, where the terrain is low and NDVI is high. The soil types are mainly Fluvisols, Phaeozems, and Chernozems, etc. This kind of soil is deep and nutritive, and has less content of rock fragments, and therefore it has less influence on E R_K. and Kf-cs were significantly correlated with temperature, with correlation coefficients of 0.393, 0.229, and 0.515, respectively; the overall trend of St, Kcf, and Kf-cs decreased with the increase of temperature (Figure 12). The reason was that temperature changes soil structure mainly through affecting microbial community, which has great influence on soil spatial distribution and soil physical and chemical properties, thus affecting soil erodibility. The temperature gradually decreases from northwest to southeast, which is opposite to the content of rock fragments and slope distribution. The higher the temperature, the better the hydrothermal conditions, the gentler the terrain, and the better the soil conditions; therefore, the effect of rock fragments will be relatively small.

Relationship between the Effect of Rock Fragments on K (ER_K) and Precipitation
Compared with the relationship between ER_K and precipitation (Figure 11b), St, Kcf, and Kf-cs were significantly correlated with precipitation, with correlation coefficients of 0.411, 0.214, and 0.596, respectively; the overall trend of St, Kcf, and Kf-cs decreased with the increase of precipitation ( Figure 13). The reason is was the areas with high precipitation are mainly distributed in the southeast of China, where the terrain is low and NDVI is high. The soil types are mainly Fluvisols, Phaeozems, and Chernozems, etc. This kind of soil is deep and nutritive, and has less content of rock fragments, and therefore it has less influence on ER_K.

Relationship between the Effect of Rock Fragments on K (ER_K) and Precipitation
Compared with the relationship between ER_K and precipitation (Figure 11b), St, Kcf, and Kf-cs were significantly correlated with precipitation, with correlation coefficients of 0.411, 0.214, and 0.596, respectively; the overall trend of St, Kcf, and Kf-cs decreased with the increase of precipitation ( Figure 13). The reason is was the areas with high precipitation are mainly distributed in the southeast of China, where the terrain is low and NDVI is high. The soil types are mainly Fluvisols, Phaeozems, and Chernozems, etc. This kind of soil is deep and nutritive, and has less content of rock fragments, and therefore it has less influence on ER_K.

Impact of Influencing Factors on the Effect of Rock Fragments on K (ER_K)
In order to further clarify the quantitative impact of influencing factors on ER_K, this research selected St, Kcf, and Kf-cs values as the response variables in the RDA analysis; eight environmental factors, namely, soil type, elevation, slope, terrain relief, land use, NDVI, precipitation, and temperature were used as explanatory variables. The RDA anal-

Impact of Influencing Factors on the Effect of Rock Fragments on K (E R_K )
In order to further clarify the quantitative impact of influencing factors on E R_K , this research selected St, K cf , and K f-cs values as the response variables in the RDA analysis; eight environmental factors, namely, soil type, elevation, slope, terrain relief, land use, NDVI, precipitation, and temperature were used as explanatory variables. The RDA analysis results showed that eight influencing factors can explain 75.98% of the total information about the spatial variation of E R_K ; the first axis explained the variation information by 75.98%, and the second axis had no explanation for the variation information. On the axis, the correlation between the response variable and the explanatory variable was 87.17%, and the correlation on the second axis was 49.25%.
In the sequence diagram of RDA (Figure 14), the length of each influencing factor arrow indicates the relative magnitude of the influencing factor's explanation of E R_K . The angle between the two arrows indicates the degree of correlation between the two. When the angle is less than 90 • , it indicates that the relationship between the two is positively correlated; when the angle is between 90 • and 180 • , it indicates that the two are negatively correlated. When it is 90 • , it indicates that there is no correlation between the two. Therefore, according to the result of RDA, the values of E R_K were negatively correlated with temperature, precipitation, and NDVI. The values of E R_K were positively correlated with elevation, slope, terrain relief, land use, and soil type. This indicates that there is a correlation between the selected eight influencing factors and E R_K . It can be seen from the length of each factor arrow that elevation has the largest amount of explanation, followed by terrain relief, NDVI, slope, soil type, temperature, and precipitation, and land use had a smaller amount of explanation. In the sequence diagram of RDA (Figure 14), the length of each influencing factor arrow indicates the relative magnitude of the influencing factor's explanation of ER_K. The angle between the two arrows indicates the degree of correlation between the two. When the angle is less than 90°, it indicates that the relationship between the two is positively correlated; when the angle is between 90° and 180°, it indicates that the two are negatively correlated. When it is 90°, it indicates that there is no correlation between the two. Therefore, according to the result of RDA, the values of ER_K were negatively correlated with temperature, precipitation, and NDVI. The values of ER_K were positively correlated with elevation, slope, terrain relief, land use, and soil type. This indicates that there is a correlation between the selected eight influencing factors and ER_K. It can be seen from the length of each factor arrow that elevation has the largest amount of explanation, followed by terrain relief, NDVI, slope, soil type, temperature, and precipitation, and land use had a smaller amount of explanation. On the basis of the above correlation analysis results, we found that all influencing factors were correlated with the values of St, Kcf, and Kf-cs, but the highest correlation was elevation, which was able to explain 74.7% of the values of St, Kcf, and Kf-cs, indicating that the elevation is the main predominant factor affecting the spatial variation of ER_K, followed by terrain relief, NDVI, slope, soil type, temperature, and precipitation. Therefore, clarifying the spatial distribution of various influencing factors and discussing the variation of the values of St, Kcf, and Kf-cs are of great significance for estimating the soil erodibility factor (K).

The Source and Classes of Rock Fragments
The rock fragment in the soil is a product of weathering and disintegration of rocks; rock fragments may be produced in chemical weathering and root penetration processes that transform rocks into soil [53]; tectonic movement [54]; physical weathering, land- On the basis of the above correlation analysis results, we found that all influencing factors were correlated with the values of St, K cf , and K f-cs , but the highest correlation was elevation, which was able to explain 74.7% of the values of St, K cf , and K f-cs , indicating that the elevation is the main predominant factor affecting the spatial variation of E R_K , followed by terrain relief, NDVI, slope, soil type, temperature, and precipitation. Therefore, clarifying the spatial distribution of various influencing factors and discussing the variation of the values of St, K cf , and K f-cs are of great significance for estimating the soil erodibility factor (K).

The Source and Classes of Rock Fragments
The rock fragment in the soil is a product of weathering and disintegration of rocks; rock fragments may be produced in chemical weathering and root penetration processes that transform rocks into soil [53]; tectonic movement [54]; physical weathering, landslides, and debris flows [55]; and water selective erosion of soil fine particles [37].
Particle sizes of rock fragments are divided into seven classes in the USDA (United States Department of Agriculture) [56]. For simulated rainfall experiments [57] and typical studies of larger particle sizes in small areas [58], the particle size can be distinguished into varied classes. However, for regional calculations and analysis, there is no available data yet. Thus, this study only considers the rock fragments 2 mm in diameter or larger [56].
Due to the lack of a complete set of the coverage of rock fragment data except that rock fragment in special areas or under specific scenarios was reported in some special studies (e.g., Qian et al. [59]; Cao et al. [60]), the data of RFS and RFP used in this paper are SoilGrid dataset from ISRIC (International Soil Reference and Information Centre) data. This dataset provides global predictions for coarse fragments at depths of 0 and 15 cm. Predictions were based on around 150,000 soil profiles used for training and a stack of 158 remote sensing-based soil covariates, which were used to fit an ensemble of machine learning methods [61]. These data have high accuracy and availability. It is expected that in the future, on the basis of high-resolution imaging and UAV (unmanned aerial vehicle) technology, it is possible to distinguish particle sizes in typical areas and analyse the effects of different particle sizes on the erodibility (K factor) or the cover and management factor.

The Influencing Factors of the Effect of Rock Fragment on K
In China, elevation has the greatest influence on St, K cf , and K f-cs. The reason is that the terrain in China varies greatly, and the elevation is distributed in a three-step pattern [62]. The first step is the Qinghai-Tibet Plateau and the Qaidam Basin, with an average altitude of more than 4000 m. The second step is distributed with large basins and plateaus, with an average elevation between 1000 and 2000 m. The third step covers a vast plain with hills and low mountains in between, including the northeast plain; the North China plain; the plains of the middle and lower Yangtze River; and the hills of Liaodong, Shandong, and Southeast, with elevations below 500 m. Areas with higher elevation are more arid and colder, dominated by physical weathering, and the soil-forming process is weak. Therefore, the soil surface has large content of rock fragments, and the impact of rock fragment is also greater.
Studies have shown that differences in the size, shape, void type, and particle size of rock fragment have important effects on soil physical and chemical properties, hydrological processes, etc. [26,63,64], thereby affecting soil erosion. The impact of rock fragment is related to tillage measure, soil depth, topographic curvature, physical and chemical properties of parent materials, etc. [53,[65][66][67]. However, it is difficult to obtain and apply these data in the whole country. In the future, the environmental factor data and the content of rock fragments can be measured for further discussion when analysing in small watershed, so as to obtain more accurate results of soil erosion evaluation.

The Effect of Rock Fragments on Regional Soil Erosion Evaluation
The effect of rock fragments should be fully considered in the calculation of K. If the effect of RFS is not taken into account, the rate of soil erosion is overestimated. If the effect of RFP is not taken into account, the rate of soil erosion is underestimated. Thus, if the effect of rock fragments not considered, the analysis and evaluation of soil erosion obtained will not be accurate. Take the Yunnan-Guizhou Plateau, Qinghai-Tibet Plateau, the Himalayas, and Karakoram Mountains as an example, these areas have high elevation and high terrain relief. The surface is dominated by physical weathering, with large content of rock fragments (Figure 1), and soil erosion is relatively weak. However, the soil erosion evaluation results of Borrelli et al. [46] (Figure 15) show that the soil erosion rate in Himalayas and Karakoram Mountains is significantly higher than that of neighbouring areas. Wang et al. [68] found that the Yunnan-Guizhou Plateau is a hotspot of erosion in southwestern China. In the study of Teng et al. [69], the soil erodibility factor in the eastern part of the Qinghai-Tibet Plateau was overestimated. We suspect that the possible reason was that the effect of rock fragments is not fully considered in their research, and the analysis and evaluation of soil erosion were not complete and accurate. This study fully considered the impact of rock fragments in the calculation of soil erodibility factors, carrying out a quantitative analysis of the influencing factors of the effect of rock fragments on K. Therefore, in the systematic soil erosion evaluation in China, especially in areas with large slopes and insufficient soil water and heat conditions, as well as deserts with low rainfall, the impact of rock fragments should be fully considered in order to have a more comprehensive and accurate understanding of the intensity and spatial differentiation of water erosion in China. slopes and insufficient soil water and heat conditions, as well as deserts with low rainfall, the impact of rock fragments should be fully considered in order to have a more comprehensive and accurate understanding of the intensity and spatial differentiation of water erosion in China. As for the influencing factors of the effect of rock fragments on K, Zhu and Shao [36] showed that rock fragments were mainly distributed in areas with large slope. Marshall et al. [13] and Nyssen et al. [35] found that rock fragments were more distributed in areas with high altitude and relatively cold and arid mountains and deserts. Although the conclusion of this study was consistent with their understanding, they ignored the influence of land use, soil type, and climate. However, the difference between spatial pattern of rock fragment and vegetation cover is correlated with land use factors [33]. The distribution characteristics of rock fragment are also affected by physical and chemical properties, temperature, and rainfall of parent material [53]. Thus, this study quantified and analysed a variety of influencing factors and can help us understand the effect of rock fragment on K more comprehensively.

Implications for Production Practice
Gravel and sand mulched field (hereinafter referred to as the GSMF) is a kind of farmland covered with a layer of rock fragments on the soil surface. It is a unique droughtresistant farming form in the arid and semi-arid areas of northwest China with annual precipitation of 200-300 mm, and it has a history of more than 300 years [19]. GSMF are mainly distributed in the central part of Gansu Province, as well as parts of Qinghai, Xinjiang, and Ningxia provinces [70]. Rock fragment covering technology has been widely used in the field of agricultural production because of its significant effects of water storage, temperature, and yield increase. Rock fragments on the surface of farmland are beneficial in improving hydrothermal condition and yield. They allow water to infiltrate and store in the soil, effectively maintaining soil moisture and temperature, and can significantly increase crop yields [71][72][73]. Farmers are generally reluctant to remove smaller rock fragments from their land [35] because they believe that they have a positive effect on soil moisture retention and protection of topsoil from erosion. The research of Li et al. [28]  As for the influencing factors of the effect of rock fragments on K, Zhu and Shao [36] showed that rock fragments were mainly distributed in areas with large slope. Marshall et al. [13] and Nyssen et al. [35] found that rock fragments were more distributed in areas with high altitude and relatively cold and arid mountains and deserts. Although the conclusion of this study was consistent with their understanding, they ignored the influence of land use, soil type, and climate. However, the difference between spatial pattern of rock fragment and vegetation cover is correlated with land use factors [33]. The distribution characteristics of rock fragment are also affected by physical and chemical properties, temperature, and rainfall of parent material [53]. Thus, this study quantified and analysed a variety of influencing factors and can help us understand the effect of rock fragment on K more comprehensively.

Implications for Production Practice
Gravel and sand mulched field (hereinafter referred to as the GSMF) is a kind of farmland covered with a layer of rock fragments on the soil surface. It is a unique droughtresistant farming form in the arid and semi-arid areas of northwest China with annual precipitation of 200-300 mm, and it has a history of more than 300 years [19]. GSMF are mainly distributed in the central part of Gansu Province, as well as parts of Qinghai, Xinjiang, and Ningxia provinces [70]. Rock fragment covering technology has been widely used in the field of agricultural production because of its significant effects of water storage, temperature, and yield increase. Rock fragments on the surface of farmland are beneficial in improving hydrothermal condition and yield. They allow water to infiltrate and store in the soil, effectively maintaining soil moisture and temperature, and can significantly increase crop yields [71][72][73]. Farmers are generally reluctant to remove smaller rock fragments from their land [35] because they believe that they have a positive effect on soil moisture retention and protection of topsoil from erosion. The research of Li et al. [28] showed that rock fragment provides a better growth environment for plant growth in the Loess Plateau. The experiment of Pang Lei et al. [19] showed that soil moisture and the soil microbial quantity all increase when mulched by rock fragment. It is especially beneficial to actinomycete when mulched by bigger diameter gravels. It is optimum for microbial developing when the thickness of gravel-sand is in the range of 7-9 cm. However, these understandings have not been fully considered in soil erosion survey and research in China.

Conclusions
On the basis of the data of rock fragments and eight environmental factors in China, we used correlation analysis, typical sampling area analysis, and redundancy analysis to explore the effect of content of soil rock fragments on calculating of soil erodibility (K) and its influencing factors. The major conclusions are as follows: (1) The rock fragments in the soil profile (RFP) increased soil erodibility (K) by 0.0011 (t·hm 2 ·h)·(hm −2 ·MJ −1 ·mm −1 ), the rock fragments on the surface (RFS) of the soil reduced soil erodibility (K) by 0.0094 (t·hm 2 ·h)·(hm −2 ·MJ −1 ·mm −1 ), and the effect of both RFP and RFS reduced soil erodibility (K) by 0.0013 (t·hm 2 ·h)·(hm −2 ·MJ −1 ·mm −1 ). (2) This effect of rock fragments had the highest correlation with elevation, followed by terrain relief, vegetation coverage (NDVI), slope, soil type, temperature, and precipitation. The higher the elevation, terrain relief, and slope, the greater the effect of rock fragments on K, and the smaller the precipitation, temperature, and vegetation coverage (NDVI), the less the effect of rock fragments on K. When the soil types were Leptosols, Cryosols, Gypsisols, Solonchaks, Gypsisols, Luvisols, and Calcisols, the influence was greater. The effect of rock fragments on K (E R_K ) had little correlation with land use. (3) The results of RDA analysis showed that the elevation was the main predominant factor affecting E R_K , and the elevation had the greatest influence on St, K cf , and K f-cs. The reason is that the topography of China varies greatly, with high elevation mountains and plateaus being widely distributed. These mountainous and plateau areas are usually cold and dry, and the soil erosion is mainly wind erosion. Due to the weak soil-forming process, the content of rock fragments is large, and the effect of rock fragments is also great.
In the systematic evaluation of soil erosion in China, the effect of rock fragments should be fully considered, and the effect of rock fragments should be paid more attention to the higher elevation areas such as Qinghai-Tibet Plateau, Yunnan-Guizhou Plateau, and Tianshan Mountains, so as to have a more comprehensive and accurate understanding of the current situation and regular pattern of soil erosion in China.  Data Availability Statement: All data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.