A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis

Abstract

[1] We present a statistical technique for analyzing longitudinal channel profiles. Our technique is based on the integral approach to channel analysis: Drainage area is integrated over flow distance to produce a transformed coordinate, χ, which has dimensions of length. Assuming that profile geometry is conditioned by the stream power law, defined as E = KA m S n where E is erosion rate, K is erodibility, A is drainage area, S is channel gradient, and m and n are constants, the slope of a transformed profile in χ-elevation space should reflect the ratio of erosion rate to channel erodibility raised to a power 1/n; this quantity is often referred to as the channel steepness and represents channel slope normalized for drainage area. Our technique tests all possible contiguous segments in the channel network to identify the most likely locations where channel steepness changes and also identifies the most likely m/n ratio. The technique identifies locations where either erodibility or erosion rates are most likely to be changing. Tests on a simulated landscape demonstrate that the technique can accurately retrieve both the m/n ratio and the correct number and location of segments eroding at different rates where model assumptions apply. Tests on natural landscapes illustrate how the method can distinguish between spurious channel convexities due to incorrect selection of the m/n ratio from those which are candidates for changing erodibility or erosion rates. We also show how, given erosion or uplift rate constraints, the method can be used to constrain the slope exponent, n.

Tectonic geomorphology at small catchment sizes – extensions of the stream-power approach and the <i>χ</i> method

“…However, this may lead to systematic bias for transient topographies. An extension based on fitting piecewise linear functions was recently suggested by Mudd et al (2014), but this algorithm may become numerically expensive, in particular if applied to a large number of catchments or if two adjustable parameters are involved.…”

Patterns of Quaternary uplift of the Corinth rift southern border (N Peloponnese, Greece) revealed by fluvial landscape morphometry

“…In this respect, Mudd et al (2014) present a framework to identify the statistically most meaningful partition of a chi profile in segments of different steepness. However, we do not follow this approach because it allows only distinction of segments of varying steepness but the same concavity, whereas varying concavity is expected to be as important an attribute of the transient profiles we investigate.…”

Bumps in river profiles: uncertainty assessment and smoothing using quantile regression techniques

“…The geometry of a river, specifically its longitudinal profile, reflects climatic and tectonic forcing, variations in base level and sediment transport processes, and differences in bedrock erodibility. Gradients along rivers, for example, reflect spatial variations in uplift rates (Whipple et al, 2013;Mudd et al, 2014;Scherler et al, 2014) and indicate the extent of past glaciations (Brardinoni and Hassan, 2006). Moreover, they can act as predictors for the zones of erosion and sediment accumulation during extreme events (Devrani et al, 2015) and reflect the repeated impact of mass-wasting events (Korup, 2006).…”