What is Channel steepness and concavity indices?

When the gradient of a river follows $S = k_s A^{-\theta}$, the exponent $\theta$ is the concavity index and the coefficient $k_s$ the channel steepness index. To compare rivers, $\theta$ is set to a common reference value $\theta_{\mathrm{ref}}$, and $k_{sn} = S A^{\theta_{\mathrm{ref}}}$ is the normalised steepness.