• Rainfall erosivity factor (R)

The R factor in USLE is calculated by 30-min maximum rainfall intensity and rainfall kinetic energy [6]. Since the R factor of USLE is complicated to calculate, Chen et al. [48] estimated the R factor for TUSLE by the regression equation developed by the U.S. Department of Agriculture, Agriculture Research Service (Equation (10)) [48].

$$\mathbf{R\_{eq}} = -823.8 + 5.213 \mathbf{P\_r} \tag{10}$$

where Req is rainfall erosivity factor; Pr is annual precipitation (mm).

In MUSLE, the rainfall erosivity factor is replaced by the runoff factor as the runoff factor could better represent the surface runoff and overland sediment transport characteristics [7]. Thus, in this study, we calculated the runoff factor (R) in MUSLE, instead of the rainfall erosivity factor (Req).

$$\mathbf{R} = 11.8(\mathbf{Q} \cdot \mathbf{q} \cdot \mathbf{A})^{0.56} \tag{11}$$

where R is runoff factor; Q is surface runoff (mm/ha); q is peak runoff (m3/s); A is the area of catchment (ha).

• Cover and management factor (C)

The C factor was estimated by non-linear equation with the normalized difference vegetation index (NDVI) to avoid overestimating the C values of area with low soil erosion rate [51] (Table 3).

$$\text{NDVI} \ge 0, \quad \mathbb{C} = \left(\frac{1 - \text{NDVI}}{2}\right)^{1 + \text{NDVI}} \tag{12}$$

$$\text{NDVI} < 0, \quad \left( \begin{array}{c} \text{Buildingormon} - \text{expposedground}, \text{ C} = 0.01\\ \text{Barren}, \text{ C} = 1.0 \end{array} \right) \tag{13}$$


**Table 3.** Normalized difference vegetation index (NDVI)-calculated weighted C value for different land uses.

• Topographic factor (LS)

Wischmeier and Smith [52] established the LS equation (Equation (14)) as the product of L factor (Equation (15)) and S factor. In the SWAT model, the exponential factor (m) in the L factor equation is defined as Equation (16) [44], while TUSLE adopted the classification suggested by [52] that the exponential factor (m) varies with the slope, where m = 0.5, 0.4, 0.3 and 0.2 is used for the average slope greater than 5%, between 3–5%, between 1–3%, and less than 1%, respectively. Thus, TUSLE can increase the underestimated L factor at flatter slope and reduce the overestimated L factor at a steeper slope (Figure 5a). McCool et al. [53] indicated that Wischmeier and Smith's [52] topographic factor equation could only be suitable for the slope from 0.1% to 18%, and developed S factor equation (Equations (17) and (18)) to more reasonably predict soil loss at steep topography. The comparison of S factor by [52,53] (Figure 5b) showed that the equation would overestimate S factor in areas of steeper slope. Therefore, we combined the L factor equation with m values from TUSLE and the S factor equation by [53] to calculate the LS factor.

$$\text{LS} = \left(\frac{\chi}{22.13}\right)^{\text{m}} \left(0.0654 + 4.56\sin\theta + 65.4\sin^2\theta\right) \tag{14}$$

$$\mathbf{L} = \left(\frac{\chi}{22.13}\right)^{\mathbf{m}}\tag{15}$$

$$\mathbf{m} = 0.6 \times \left( \mathbf{1} - \mathbf{e}^{-35.835 \ast \mathbf{0}} \right) \tag{16}$$

where X = slope length (m), m = exponential factor.

$$\mathbf{S} = 10.8\sin\theta + 0.03\,\theta < 9\% \tag{17}$$

$$\mathbf{S} = \left(\frac{\sin\theta}{0.0896}\right)^{0.6}, \theta \ge 9\% \tag{18}$$

where S is the slope factor of HRUs in MUSLE, θ is the slope of HRUs.
