Scaling and elevation in river networks
Water Resources Research
The analysis of large river networks obtained from digital elevation models has given insight into the variation of channel slope with scale. Investigators have recently suggested that channel slopes are self-similar with magnitude or area as a scaling parameter. Our data indicates otherwise; in particular, the variance of channel slope is larger than that predicted by simple self-similarity. This suggests multiscaling. The scaling exponent for the standard deviation is approximately half the corresponding exponent in the relationship of the slope mean to magnitude or area. A model for channel slopes based on a point process of elevation drops along the channel is presented. The model reproduces observed multiscaling properties when the density of elevation increments is related to area (or magnitude) as A^−θ.
Tarboton, David G.; Bras, Rafael L.; and Rodriguez-Iturbe, Ignacio, "Scaling and elevation in river networks" (1989). Civil and Environmental Engineering Faculty Publications. Paper 2522.