Unit stream power is defined as the energy expended per unit channel length (Bagnold, 1960). It is an index of erosion for hillslopes.
Ω = gQS
Ω = Stream power
ρ = Density of water (1000 g/m-3)
g = Acceleration due to gravity (9.81 m/s-2)
Q = Discharge, which can be substituted for with m3s-1 for each cell with a precipitation-weighted flow accumulation for a given flow network
S = Unitless parameter defining the steepest drop between each cell and any of its neighboring cells
The Q value assumes all precipitation falling on the land surface becomes surface runoff (no infiltration, evaporation, or transpiration). “Hillslope erosion potential” (HEP) is mean annual precipitation multiplied by slope for every cell (pixel) in a DEM. Precipitation rasters for the U.S. are found at the PRISM Climate Group at Oregon State University. It is an index that reveals spatial differences in erosion, but values generated are relative and not actual bedrock erosion rates or stream power.
HEP = Mean Annual Precip * Slope
Areas of steep slopes and high rainfall will yield higher HEP values for a given bedrock type. Hillslope erosion potential increases in a non-linear way as slopes steepen. Hillslope erosion may take place as landslides, debris flows, soil creep, and rainsplash.
Mitchell and Montgomery (2006)