Impact of Changing Concavity Indices on Channel Steepness and Divide Migration Metrics

Abstract

The concavity index, (Formula presented.), describes how quickly river channel gradient declines downstream. It is used in calculations of normalized channel steepness index, (Formula presented.), a metric for comparing the relative steepness of channels with different drainage area. It is also used in calculating a transformed longitudinal coordinate, (Formula presented.), which has been employed to search for migrating drainage divides. A (Formula presented.) value of 0.45 is typically assumed in studies. Here we quantify the variability in (Formula presented.) across multiple landscapes distributed across the globe. We describe the degree to which both the spatial distribution and magnitude of (Formula presented.) and (Formula presented.) can be distorted if (Formula presented.) is assumed rather than constrained. Differences between constrained and assumed (Formula presented.) of 0.1 or less are unlikely to affect the spatial distribution and relative magnitude of (Formula presented.) values, but larger differences can change the spatial distribution of (Formula presented.) and in extreme cases invert differences in relative steepness: relatively steep reaches can appear relatively gentle as quantified by (Formula presented.). These inversions are function of the range of drainage area in the considered watersheds. We also demonstrate that the (Formula presented.) coordinate, and therefore the detection of migrating drainage divides, is sensitive to varying values of (Formula presented.). The median of most likely (Formula presented.) across a wide range of mountainous and upland environments is 0.425. This wide range of variability suggests workers should not assume any value for (Formula presented.), but should instead calculate a representative (Formula presented.) for the landscape of interest, and exclude basins for which this value is a poor fit.