Topographic Factor (LS)
The (LS) factor reflects the combined effect of slope length and slope steepness on erosion. The empirical equation developed by Wischmeier & Smith (1978) as follow.
LS = (L/22.15) × (65.41 sin2S +4.56 sin S+0.065) (2)
For practical reasons of calculation under GIS, we have adopted the following formula: LS = Pow ([flowacc] * resolution / 221.04) * Pow (Sin [slope] * 0.01745 / 0.09,1.4) * 1.4 where ”flowacc” is the flow accumulation, ”resolution” is the spatial resolution of the numerical model of terrain used and ”slope” is the slope gradient in degree (°).

Cropping management factor (C)

The C factor is a most important factor that controls soil erosion risk (Knijff et al., 2000) and it reflects the effect of cropping and management practices on the soil erosion rate (Jong, 1994; Biesemans et al., 2000; Patil & Sharma, 2013). For our case, the land use classes were digitized by photo-interpretation based on the very high spatial resolution satellite image with provided by ESRI © servers.

Rainfall-runof f erosivity (R) factor

Rainfall-runoff erosivity is defined as the intrinsic capacity of the rain to cause soil erosion, and amount, intensity, terminal velocity, drop size and drop size distribution of rain are the variables affecting total erosivity of a rain event ( Blanco-Canqui and Lal , 2008). According to Wischmeier and Smith (1978) and Renard et al. (1997), estimation of R factor requires total rainfall energy (E) and maximum 30 min rainfall intensity (I30) of storm events for at least 20 years. With the lack of sufficient return period climate data in the study area, the R factor was calculated adopting the modified formula of Rango and Arnoldus (1987). Which is defined as Eq (3 ).
\(logR=1.74.log\sum_{i=1}^{12}{\left(Pi\hat{}2/P\right)+1.29}\)(3)

Support practice (P) factor

The P factor indicates the significance of support practices, which reduce soil loss by modifying the flow pattern, grade or direction of surface runoff and by reducing the rate of runoff (Wischmeier and Smith, 1978; Renard and Foster, 1983). It varies from 0 to 1, according to the practice adopted and slope. In our case, the value assigned to the factor P is 1 for the whole watershed, since the anti-erosion measures are absent.

Soil Erodibility Factor (K)

The soil erodibility factor K represents the susceptibility of soil particles to be detached (Renard and al., 1997). K is strongly related to the physical properties of the soil and plays an important role in soil conservation strategies (Shabani, Kumar, & Esmaeili, 2014). All of the K factor equations are related to the soil texture, soil organic matter, and percentage of sand, silt, and clay in the soil (Millward & Mersey, 1999). It is expressed in t.haMJ-1.mm-1, and determined according to the following formula (Eq. 4).
K = 2.77M 1,14. 10-7(12 − OM) + 4.28 (10-3) (SS − 2) + 3.29 (10-3) (PP − 3) (4)
Where OM is the soil organic matter content, M is the indicator of the soil textural class ((%fine sand+silt) × (100–%clay)), SS and PP represent the soil structure and permeability classes.