Basin self-similarity, Hack's law, and the evolution of experimental rill networks

While the hierarchical organization of river basins has been well described, little physical evidence exists on how such signatures change in time as a function of drainage network evolution. Using a soil-mantled experimental landscape, a fourth-order rill network was developed in response to applied rainfall and base-level lowering. Drainage basin area and tributary length scales were determined at discrete times during the evolution of the rill network. Results show that rill basin area exhibited self-similarity across rill order (space) and as the network grew in time, and that the coefficient of Hack's law, once the network began to grow, also was invariant with time. This experimental evidence strongly supports the use of scaling arguments for drainage basin evolution and for the prediction of rill network development and organization on hillslopes and agricultural fields.