Characteristic lengths of stream networks in porous terrain

The conditions for sediment transport of particles in streams has previously been found to give a relationship between the stream's slope and flux. Using this relationship, we establish a lower bound on the size of features in a stream network. Tributaries that violate this lower bound do not receive groundwater and dry up. This technique also gives bounds on a network's drainage density, which is its total length divided by the area it drains; this is the inverse of a characteristic length. These bounds obey scaling laws with respect to physical constants that describe the hydrological environment of the network, such as grain size, porosity, and water table depth, and we observe the effects of these scaling laws in a real-world network.