The geometry and complexity of spatial patterns of terrestrial channel networks: Distinctive fingerprints of erosional regimes

The morphology of channel networks related to long-term erosion reflects the mechanisms involved in their formation. This study aims to identify quantitative metrics, drawn from topographic data and satellite imagery, that are diagnostic of the distinctive styles of erosion by rivers, glaciers, subglacial meltwater, and groundwater sapping. From digital elevation models, we identify three geometric metrics: the minimum channel width, channel aspect ratio (longest length to channel width at the outlet), and tributary junction angle. We also characterize channel network complexity in terms of its stream order and fractal dimension. To validate our approach, we perform a principal component analysis (PCA) on measurements of these five metrics on 70 channel networks. We build understanding of these results, in turn using scaling analyses of appropriate physical models. We show that rivers, glaciers, and groundwater sapping erode the landscape in rigorously distinguishable ways. Whereas rivers are characterized by nearly constant minimum width, variable aspect ratio, and high stream orders, glaciers have highly variable minimum widths and aspect ratios and much smaller stream orders. Erosion by subglacial meltwater remains poorly understood, and we argue that we require an additional metric to fully characterize these systems. Our methodology can more generally be applied to identify the contributions of different processes involved in carving a channel network. In particular, we are able to identify transitions from fluvial to glaciated landscapes or vice versa.