A novel probabilistic model to explain drainage network evolution

Abstract

River channels self-organize to form tree-like networks that follow certain statistical laws, such as Horton's laws and Hack's law, which is perhaps the reason why simple statistical models are often used to explain river network evolution. However, statistical models generally do not attempt to explain the differences between network structures. Here we address this issue by incorporating certain physically meaningful variables in a statistical modeling framework. The model allows the network to grow in a headward direction via probabilistic decisions based on two free parameters. Simulations performed over a planar matrix result in tree-like networks exhibiting power-law scaling relationships as displayed by real river networks. The two parameters are shown to be capable of explaining the variation of key network characteristics such as compactness coefficient and Hack's exponent. The uniqueness of the model thus lies in its ability to generate networks with different shapes and characteristics.