2.3. Research Methods

Since the 1980s, Chinese scholars proposed some regional models for soil erosion estimation based on the Universal Soil Loss Equation (USLE) and combined with local topographical features [31]. Among these models, the Chinese Soil Loss Equation (CSLE) fully considers the impact of biological, engineering, and tillage measures on the process and results of soil erosion, making it more suitable and widely used in the soil erosion estimation in China [32]. The CSLE model expression is as follows:

where A is the average annual soil erosion modulus in t/(hm²·a); R is the rainfall erosivity factor in MJ·mm/(hm²·a); K is the soil erodibility factor in t·h/(MJ·mm); L and S are dimensionless factors of slope length and slope steepness, respectively; and B, E, T are dimensionless factors of biological-control, engineering-control, and tillage practices, respectively. The dimensionless factors of slope and soil conservation measures were defined as the ratio of soil erosion amounts from unit plot to actual plot with the aimed factor changed but the same sizes of other factors as the unit plot [32].

Based on the CSLE model and the control variable method, this study calculated the soil erosion modulus in the Ansai Watershed from 2000 to 2015 under two land use scenarios (the initial and current scenarios of vegetation restoration). The effect of vegetation restoration on soil erosion during the study period was identified by comparing the differences of average soil erosion modulus under two scenarios among 16 years. It should be noted that for the soil erosion modulus calculation under the two scenarios in the same year, the R, K, L, S, E, and T factors remained unchanged, while the B factor related to vegetation restoration was calculated based on the land use maps and remote sensing images in 2000 and 2015, respectively. Furthermore, the calculation method of each factor is as follows.

Rainfall erosivity (R) factor reflects the influence of rainfall on soil erosion [33]. In this study, we calculated the R factor according to the method proposed by Zhang et al. (2002) [34], a method that has been widely used in China [34,35]. The R factor, based on aggradations of half-month rainfall erosivity, was estimated using daily rainfall data obtained from the Hydrological Yearbook of the People’s Republic of China from 2000 to 2015. The calculation method is as follows:

where M_i is the half-month rainfall erosivity in MJ·mm/(hm²·h·a), k refers to the number of days in a half-month, and D_j represents the effective rainfall for day j in one half-month. D_j is equal to the actual rainfall if the actual rainfall is greater than the threshold value of 12 mm, which is the standard for China’s erosive rainfall. Otherwise, D_j is equal to zero [34]. The terms α and β are the undetermined parameters of the model and are calculated as follows:

where P¯d12 is the daily average rainfall that is greater than 12 mm, and P¯y12 is the yearly average rainfall for days with rainfall more than 12 mm.

Soil erodibility (K) factor indicates both the susceptibility of soil to erosion and the amount and rate of runoff, as measured under standard plot conditions [36]. Previous studies found that the existing foreign K factor estimation models cannot be directly applied to the K factor calculation in China, and their estimated values are far greater than the actual measured values, while there is a certain linear relationship among them [37]. To this end, based on soil data obtained from the soil survey conducted in the Ansai Watershed, the K factor was calculated according to the Equations (5) and (6) [37,38].

where D_g is the geometric mean diameter of soil grains, and K_shirazi is the K value estimated by the Equation (5) proposed by Shirazi et al. (1988) [38].

Topography is an important factor that directly affects soil erosion. The slope length factor (L) and slope steepness factor (S) represent the effects of slope length and slope gradient on soil erosion, respectively [39]. The L factor and S factor can be calculated using the following equations:

where λ is the length of the slope, m is the variable length-slope exponent, β is a factor that varies with slope gradient, and θ is slope gradient calculated based on DEM.

Biological-control (B) factor refers to the ratio of the soil erosion amounts of land with vegetation cover or field management, and that of continuously fallowed land under certain conditions [40,41]. In this study, we extracted NDVI values and calculated the vegetation coverage by using Equation (11) according to Li et al. (2020) [42] based on remote sensing images captured from June to September during 2000 to 2015; B factor was obtained according to the relationship between B factor and the land use types, and vegetation coverage (Table 1) [43]. The vegetation coverage was calculated as follows:

where f is the vegetation coverage, and NDVI_min and NDVI_max are the minimum and maximum NDVI values.

B factor under different land use types and different vegetation coverage.

Engineering-control (E) factor refers to the ratio of the soil erosion amounts occurring under certain engineering measures to that occurring without engineering measures under the same conditions [32]. The engineering-control practices in the Ansai Watershed mainly include silting dams and terraces. Considering the difficulty of collecting data on engineering measures, this study obtained terrace and silting dam data based on the Statistical Yearbook of Ansai County and calculated the E factor by referring to Equation (12) proposed by Xie et al. (2009) [44]:

where S_t is the terrace area, S_d is the area controlled by silting dams, S is the total land area, and α and β refer to the sediment reduction coefficients of terrace and silting dam and are 0.836 and 1, respectively.

Tillage (T) factor refers to the ratio of the soil erosion amounts occurring under a specific tillage measure to that occurring under consistent flat cropping or slope tillage [45]. In this study, the slope gradient was extracted based on the DEM, and T factor was calculated according to the relationship between the slope gradient and the T factor (Table 2).

T factor under different slope gradient.