Mark Melton in 1957 found that climate, basin morphometry, and surficial variables control drainage density (Dd), but differences observed between field surveyed channels and those mapped on topographic contours or blue lines left doubts on these results. Later, several landscape evolution model and observational studies analyzed the behavior of Dd. However, only a few studies have been performed over a large number of landscapes of different characteristics and have relied on high resolution topography data.
We revisit Melton’s hypothesis by using meter-resolution digital terrain models (DTMs) in 101 subbasins in the USA. We first propose a dimensionless drainage density (Ddd) metric based on the ratio of likely channelized pixels to total number of basin pixels, which has the advantage of eliminating the computation of the channel network. Our analysis shows that Ddd is a weak scaling function of the input DTM resolution compared to the classic dimensional Dd metric (ratio of total channel length to total basin area). We analyze the correlation of Ddd and mean annual precipitation (MAP) with a Gaussian mixture model which identifies two sub-groups displaying different correlation; negative in arid and semi-arid environments, and positive in humid environments. The transition in correlation is around 1100 ± 100 mm/yr of MAP and is accompanied by the occurrence of thick soil layers and high available water capacity that promote dense vegetation cover (Vcov) and low Ddd. While small variation in Ddd is observed across vegetation types, increasing Vcov corresponds to decreasing Ddd. We also explore the relationship between Ddd and relief R , and Ddd and lithology. Ddd and R are weakly correlated in arid and semi-arid environments, while they have strong positive correlation in humid environments. No significant correlation is found between Ddd and lithology although the results are likely affected by our sample choice.
