# Topographic Factor

The topographic factor, $$LS\_{USLE}$$, is the expected ratio of soil loss per unit area from a field slope to that from a 22.1-m length of uniform 9 percent slope under otherwise identical conditions. The topographic factor is calculated:

$$LS\_{USLE}=(\frac{L\_{hill}}{22.1})^m\*(65.41*sin^2(\alpha\_{hill})+4.56*sin\alpha\_{hill}+0.065)$$     4:1.1.12

          where $$L\_{hill}$$ is the slope length ($$m$$), $$m$$ is the exponential term, and $$\alpha\_{hill}$$ is the angle of the slope. The exponential term, $$m$$, is calculated:

$$m=0.6\*(1-exp\[-35.835\*slp])$$                                                           4:1.1.13

         where $$slp$$ is the slope of the HRU expressed as rise over run (m/m). The relationship between $$\alpha\_{hill}$$ and $$slp$$ is:

      $$slp=tan\alpha\_{hill}$$                                                                                          4:1.1.14