Relation between grid, channel, and Peano networks in high‐resolution digital elevation models

Abstract The topological interconnection between grid, channel, and Peano networks is investigated by extracting grid and channel networks from high‐resolution digital elevation models of real drainage basins, and by using a perturbed form of the equation describing how the average junction degree varies with Horton‐Strahler order in Peano networks. The perturbed equation is used to fit the data observed over the Hortonian substructures of real networks. The perturbation parameter, denoted as “uniformity factor,” is shown to indicate the degree of topological similarity between Hortonian and Peano networks. The sensitivities of computed uniformity factors and drainage densities to grid cell size and selected threshold for channel initiation are evaluated. While the topological relation between real and Peano networks may not vary significantly with grid cell size, these networks are found to exhibit the same drainage density only for specific grid cell sizes, which may depend on the selected threshold for channel initiation.