Catchment drainage network scaling laws found experimentally in overland flow morphologies

The scaling relation between the drainage area and stream length (Hack's law), along with exceedance probabilities of drainage area, discharge, and upstream flow network length, is well known for channelized fluvial regions. We report here on a laboratory experiment on an eroding unconsolidated sediment for which no channeling occurred. Laser scanning was used to capture the morphological evolution of the sediment. High-intensity, spatially nonuniform rainfall ensured that the morphology changed substantially over the 16-hr experiment. Based on the surface scans and precipitation distribution, overland flow was estimated with the D8 algorithm, which outputs a flow network that was analyzed statistically. The above-mentioned scaling and exceedance probability relationships for this overland flow network are the same as those found for large-scale catchments and for laboratory experiments with observable channels. In addition, the scaling laws were temporally invariant, even though the network dynamically changed over the course of experiment.