Table 4 Table of topographic factors formula for different studies

\({\mathbf{LS}} = 1.4\left[ {\frac{{\varvec{As}}}{22.13}} \right]^{0.4} *\left( {\frac{{\sin \left(\varvec{\beta}\right)}}{0.0896}} \right)^{1.3}\)

As = the specific area defined as the upslope contributing area for overland grid per unit width normal to flow direction, and β is the slope gradient in degrees

Kavian et al. (2017)

Iran

\({\mathbf{LS}} = \left[ {\frac{{ {\varvec{\upbeta \upchi }} }}{22.13}} \right]^{0.5} *\left( {\frac{{\sin \left( {0.01745\varvec{s}} \right)}}{0.0896}} \right)^{1.3}\)

β is flow accumulation, χ is grid cell size (30 m), 22.13 is the RUSLE standard plot length; 0.5 is the exponent of slope length; s is Slope of DEM in degrees

Asnake and Amare (2019), Fenta et al. (2016)

Blue Nile Basin

\({\mathbf{LS}} = \left[ {\frac{{ {\mathbf{fac}}*{\mathbf{DEM}} {\mathbf{resolution}} }}{22.13}} \right]^{0.4} *\left( {\frac{{\sin \left( \varvec{s} \right)}}{0.0896}} \right)^{1.3}\)

fac is flow accumulation, s is slope in degree

Habtamu et al. 2020

West Shoa Ethiopia

\({\mathbf{LS}} = \left( {\frac{{{\varvec{\uplambda}}^{0.3} }}{22.1}} \right)*\left( {\frac{{\mathbf{S}}}{9}} \right)^{1.3}\)

λ is Flow length and S is Slope in percent

Wolka et al. (2015)

CRV of Ethiopia

\({\mathbf{LS}} = \left( {\frac{{\varvec{\uplambda}}}{22.1}} \right)^{\varvec{m}} *(0.065 + 0.045{\mathbf{x}} + 0.0065\left( {\mathbf{x}} \right)^{2}\)

λ is flow length, m is an exponent that depends on slope steepness

Bewket and Teferi (2009)

Blue Nile Basin