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

Abstract

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 £uvial systems.We examined basins spanning two orders of magnitude in area along the southern £ank 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 su⁄ciently high rate to sustain this form and have been forced into an alternative, and possibly unstable, packing arrangement.

Morphometric properties of the trans-Himalayan river catchments: Clues towards a relative chronology of orogen-wide drainage integration

“…This consistency among spacing ratios has been attributed to an expression of Hack's Law (Hovius, 1996), which states that the length of the trunk stream maintains a power law relationship with the drainage area (Hack, 1957) during the growth of the drainage network. Despite being more or less regularly spaced, unlike other orogens the spacing ratio of outlets of the trans-Himalayan drainages has been found to be much less, about 1.7 (Hovius, 1996;Walcott and Summerfield, 2009). This would indicate that the catchment-evolution process, in this case, is different.…”

“…The long time interval over which these processes interact, and the low preservation potential of the morphological signatures in a high-denudation setting, together tend to obscure the evidence (Walcott and Summerfield, 2009). …”

“…It is expected that, in such cases, additional factors and mechanisms will affect drainage development (Friend et al, 1999;Castelltort and Simpson, 2006;Gupta, 1997). It has been argued that drainage reorganization induced by currently ongoing tectonic deformation at the frontal part of this active orogen produces an unstable arrangement of the basins (Walcott and Summerfield, 2009), which gives rise to a computed spacing ratio smaller than 2. However, the mechanics of catchment evolution that might explain the present-day shape and organization of the trans-Himalayan basins remains to be fully investigated.…”

“…It has been also noted that the outlet spacing (s) maintains a consistent relationship with the width of the orogen (w). For many orogens, the spacing ratio (w/s) takes a value of about 2 (Hovius, 1996;Walcott and Summerfield, 2009). This consistency among spacing ratios has been attributed to an expression of Hack's Law (Hovius, 1996), which states that the length of the trunk stream maintains a power law relationship with the drainage area (Hack, 1957) during the growth of the drainage network.…”

“…4 Global surveys of the drainage networks in linear orogens and footwall uplands (Hovius, 1996, Talling et al, 1997Purdie and Brook, 2006;Walcott and Summerfield, 2009) indicate that the drainage outlets of the range-scale catchments are regularly spaced along the mountain front irrespective of scale, slope, lithology, climate or tectonic setting. It has been also noted that the outlet spacing (s) maintains a consistent relationship with the width of the orogen (w).…”