Abstract
Abstract. Quantitative tectonic geomorphology hinges on the analysis of longitudinal river profiles. The model behind almost all approaches in this field originates from an empirical relationship between channel slope and catchment size, often substantiated in the form of the stream-power model for fluvial incision. Significant methodological progress was recently achieved by introducing the χ transform. It defines a nonlinear length coordinate in such a way that the inherent curvature of river profiles due to the increase of catchment sizes in the downstream direction is removed from the analysis. However, the limitation to large catchment sizes inherited from the stream-power approach for fluvial incision persists. As a consequence, only a small fraction of all nodes of a digital elevation model (DEM) can be used for the analysis. In this study we present and discuss some empirically derived extensions of the stream power law towards small catchment sizes in order to overcome this limitation. Beyond this, we introduce a simple method for estimating the adjustable parameters in the original χ method as well as in our extended approaches. As a main result, an approach originally suggested for debris flow channels seems to be the best approximation if both large and small catchment sizes are included in the same analysis.
Highlights
The vast majority of the approaches used to derive information on tectonic processes from topography are based on the analysis of longitudinal river profiles
Analyzing the migration of drainage divides quantitatively requires a χ transform free of any bias at small catchment sizes induced by the limited applicability of the stream-power law
All digital elevation model (DEM) nodes without valid elevation data or where the surface elevation had to be increased when filling local depressions were disregarded
Summary
The vast majority of the approaches used to derive information on tectonic processes from topography are based on the analysis of longitudinal river profiles. Based models of bedrock incision suggest that the concavity index θ of a steady-state bedrock river under homogeneous conditions depends on the constitutive laws of the erosion process and on the crosssectional geometry of the channels (e.g., Whipple, 2004; Whipple et al, 2013; Lague, 2014). Analyzing channel slopes at constant catchment sizes, Hergarten et al (2010) found a strong positive correlation between surface elevation and slope in several orogens, suggesting a correlation between uplift rate and elevation This correlation will lead to a higher apparent concavity index when following individual rivers, which may explain why the majority of the values of θ found in nature are greater than θref = 0.45. If such changes are discontinuous, they result in distinct knickpoints propagating in the upstream direction
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