Factor

Algorithms

Rainfall factor

$R=-8.12+\left(0.56\times P\right)$

R is the rainfall factor and P is the mean annual rainfall [17]

Soil erodibility factor

$K=27.66m^{1.14}\times {10}^{-8}\times \left(12-a\right)+0.0043\times \left(b-2\right)+0.0033\times \left(c-3\right)$

K = Soil erodability factor (ton・hr⁻¹・ha⁻¹・MJ・mm), m = (Silt% + Sand%) × (100 ? clay%), a = % organic matter, b = structure code: 1) very structured or particulate, 2) fairly structured, 3) slightly structured, and 4) solid, c = profile Permeability code: 1) rapid, 2) moderate to rapid, 3) moderate, 4) moderate to slow, 5) slow, 6) very slow [7]

Equation used to derive soil organic matter

$SOM=1.72\times OC$

SOM is the soil organic matter and OC is the soil percentage organic carbon content [20]

Slope length factor

$\begin{array}{l}LS={\left(\left[\text{Flowaccumulation}\right]\times \left[\text{cellsize}\right]/22.1\right)}^{0.4}\\ \times {\left[\sin \left(\text{localslope}\left(\text{degrees}\right)\right)\times 0.0896/0.0896\right]}^{1.3}\end{array}$

LS is the length slope factor; flow accumulation is the number of cells contributing to flow into a given cell. Cell size is the ground resolution of 30 meters [22] [23]

Land cover factor

Equation used to calculate landsat image reflectance value:

$\rho \lambda =M\rho Qcal+A\rho$

Where ρλ is the TOA planetary reflectance, Mρ is band multiplicative rescaling factor, Qcal is quantized and calibrated standard product pixel values (DN) and Aρ is the band specific additive rescaling factor

Equation used to correct reflectance for the sun angle:

$\rho \lambda =\rho \lambda /\cos \Phi \text{SZ}=\rho \lambda /\sin \Phi \text{SE}$

where ρλ is the Top of Atmosphere (TOA) planetary reflectance, FSE is the local sun elevation angle (Sun Elevation), FSZ is the local solar zenith angle (FSZ = 90˚ − FSE)

Equation used to calculate the Normalized Difference Vegetation Index (NDVI)

$\text{NDVI}=\frac{\text{Band5}-\text{Band4}}{\text{Band5}+\text{Band4}}$

Where band 4 is the red band while band 5 is the infra-red band

Equation used to estimate the land cover factor

$C_r=\left[\left(-\text{NDVI}+\frac{1}{2}\right)\right]$

where C_r is the land cover factor [24] [25]

Practice factor

This was derived through a process outlined below

Soil loss

The five RUSLE factors were overlaid to derive the soil loss

$A=R\times K\times LS\times C\times P$

where A is the soil loss, R is the rainfall, K is the soil, LS is the slope length, C is the crop and P is the practice factors