The term stream power law describes a semi-empirical family of equations used to predict the rate of erosion of a river into its bed.
These combine equations describing conservation of water mass and momentum in streams with relations for channel hydraulic geometry (width-discharge scaling) and basin hydrology (discharge-area scaling) and an assumed dependency of erosion rate on either unit stream power or shear stress on the bed to produce a simplified description of erosion rate as a function of power laws of upstream drainage area, A, and channel slope, S: where E is erosion rate and K, m and n are positive.
However, observations of the hydraulic scaling of real rivers believed to be in erosional steady state indicate that the ratio m/n should be around 0.5, which provides a basic test of the applicability of each formulation.
Typically, the equation is used to simulate propagating incision pulses creating discontinuities or knickpoints in the river profile.
Commonly used first order finite difference methods to solve the stream power law may result in significant numerical diffusion which can be prevented by the use of analytical solutions [3] or higher order numerical schemes .