Universal features of mountain ridge networks on Earth

Abstract

Compared to the heavily studied surface drainage systems, the mountain ridge systems have been a subject of less attention even on the empirical level, despite the fact that their structure is richer. To reduce this deficiency, we analyze different mountain ranges by means of a network approach and grasp some essential features of the ridge branching structure. We also employ a fractal analysis as it is especially suitable for describing properties of rough objects and surfaces. As our approach differs from typical analyses that are carried out in geophysics, we believe that it can initialize a research direction that will allow to shed more light on the processes that are responsible for landscape formation and will contribute to the network theory by indicating a need for the construction of new models of the network growth as no existing model can properly describe the ridge formation. We also believe that certain features of our study can offer help in the cartographic generalization. Specifically, we study structure of the ridge networks based on the empirical elevation data collected by SRTM. We consider mountain ranges from different geological periods and geographical locations. For each mountain range, we construct a simple topographic network representation (the ridge junctions are nodes) and a ridge representation (the ridges are nodes and the junctions are edges) and calculate the parameters characterizing their topology. We observe that the topographic networks inherit the fractal structure of the mountain ranges but do not show any other complex features. In contrast, the ridge networks, while lacking the proper fractality, reveal the power-law degree distributions with the exponent $1.6\le \beta \le 1.7$. By taking into account the fact that the analyzed mountains differ in many properties, these values seem to be universal for the earthly mountainous terrain.