Regular spacing of drainage outlets from linear mountain belts

Straight sections of many actively uplifting mountain belts have simple patterns of drainage, transverse to their main structural trend. Streams rising near or beyond the topographic ridgepole of these sections are spaced at seemingly regular intervals. To test whether this regularity exists, morphometric aspects of drainage networks were measured in 11 mountain belts. The spacing of drainage basins can be expressed using a spacing ratio, which in effect is the ratio of the length and the width of the catchments under consideration. Average spacing ratios for most linear mountain belts are within a narrow range of values between 1.91 and 2.23. A linear relationship exists between the spacing of catchment outlets and the distance between the main divide and the front of the mountain belt in which they have developed. The Nepalese Himalaya form an exception to this regular pattern. In this mountain belt drainage is blocked and diverted by structures that have developed in relation to the Main Boundary Thrust. Structural complications cause drainage patterns to become less regular, introducing important nontransverse components. The linear relationship between spacing of catchment outlets and half-width of the mountain belt may be expressed in an equation of the same general form as Hack's law of stream length and drainage basin area. It seems likely that the mechanism underlying Hack's law also explains the consistent regularity of drainage spacing in active mountain belts. However, no generally accepted explanation for Hack's law has been offered. The narrow range of spacing ratios found for drainage networks in active orogens may represent an optimal catchment geometry that embodies a 'most probable state' in the uplift-erosion system of a linear mountain belt. The linear relationship between the half-width of a mountain belt and spacing of catchment outlets has profound implications for the modelling of erosion of orogenic topography, and for the formation and filling of foreland basins.