Universality and variability in basin outlet spacing: implications for the two-dimensional form of drainage basins

It has been observed that the distance between the outlets of transverse basins in orogens is typically half of the distance between the main divide and the range front irrespective of mountain range size or erosional controls. Although it has been suggested that this relationship is the inherent expression of Hack's law, and/or possibly a function of range widening, there are cases of notable deviations from the typical half‐width average spacing. Moreover, it has not been demonstrated that this general relationship is also true for basins in morphologically similar nonorogenic settings, or for those that do not extend to the main drainage divide. These issues are explored by investigating the relationship between basin outlet spacing and the 2‐dimensional geometric properties of drainage basins (basin length, main valley length and basin area) in order to assess whether the basin outlet spacing‐range width ratio is a universal characteristic of fluvial systems. We examined basins spanning two orders of magnitude in area along the southern flank of the Himalayas and the coastal zone of southeast Africa. We found that the spacing between basin outlets (L_os) for major transverse basins that drain the main divide (range‐scale basins) is approximately half of the basin length (L_b) for all basins, irrespective of size, in southeast Africa. In the Himalayas, while this ratio was observed for eastern Himalayan basins (a region where the maximum elevations coincided with the main drainage divide), it was only observed in basins shorter than ～30 km in the western and central Himalayas. Our analysis indicates that basin outlet spacing is consistent with Hack's law, apparently because the increase in basin width (represented by outlet spacing) with basin area occurs at a rate similar to the increase in main stream length (L_v) with basin area. It is suggested that most river systems tend towards an approximately diamond‐shaped packing arrangement, and this applies both to the nonorogenic setting of southeast Africa as well as most orogenic settings. However, in the western Himalayas shortening associated with localised rock uplift appears to have occurred at length scales smaller than most the basins examined. As a result rivers in basins longer than ～30 km have been unable to erode in a direction normal to the range front at a sufficiently high rate to sustain this form and have been forced into an alternative, and possibly unstable, packing arrangement.