Three Growth Models for Stream Channel Networks

Abstract

Three models that specify allowable branching events during the growth of stream channel networks through time are introduced. These models identify the possible topologie "growth paths" that may be followed as a network grows from a single link to one of magnitude n. The probability of occurrence of channel networks is calculated for magnitudes 2 to 6. One model has probabilities identical with those for Shreve's model of topologically random channel networks. The three models are compared with published data on 12 topologic studies of stream networks of magnitudes 4 to 6. The model with Shreve's probabilities fits 7 of the 12 data sets, a second model also fits 7 of them, and the third model does not fit any. Only one data set is not fit by at least one model. The results suggest that network growth by branching of exterior links alone is not adequate for development of the topologie diversity observed in natural stream channel networks. This conclusion conflicts with the prevalent view of contemporary geomorphology that headword growth is more rapid than sideward growth in dendritic drainage basins of small magnitude.