Importance of concavity for interpreting rates and patterns of landscape evolution from river profiles
Authors: Gailleton Boris , Mudd Simon , Clubb Fiona , Hurst Martin , Grieve Stuart 
Published: March 2020

&lt;p&gt;The analysis of river profiles is a fundamental tool in modern quantitative geomorphology. Since the 1960's, workers have demonstrated a systematic power-law relationship between river gradient and discharge, or its proxy drainage area, predicting a steepening of rivers towards the headwaters. This relationship provides means of quantitatively describing river profiles by extracting a concavity index (&lt;em&gt;&amp;#952;&lt;/em&gt;), the rate at which slope decreases as a function of drainage area, and steepness index (&lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;), the steepness of river reaches independent of changes in drainage area. Recent developments have provided an alternative representation of the slope-area relationship, aiming to circumvent its high sensitivity to topographic noise and to the branching nature of fluvial networks by directly integrating drainage area normalised to a concavity index into a transformed coordinate (&lt;em&gt;&amp;#967;&lt;/em&gt;). These parameters can be easily extracted from digital elevation models, resulting in their widespread application to detect tectonic, climatic, and autogenic signals from landscape morphology, such as active faulting, stream piracy, drainage divide migration or sea-level changes.&lt;/p&gt;&lt;p&gt;River profile concavity, or &lt;em&gt;&amp;#952;&lt;/em&gt;, is an essential metric to constrain, as it is necessary to fix a reference value &lt;em&gt;&amp;#952;&lt;sup&gt;ref&lt;/sup&gt;&lt;/em&gt; in order to compare &lt;em&gt;&amp;#967;&lt;/em&gt; or &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; values between different drainage basins. This exposes a key problem with the slope-area relationship: the watersheds within a study area do not necessarily all have the same optimal &lt;em&gt;&amp;#952;&lt;/em&gt;, potentially leading to incorrect interpretations of the relative distribution of &lt;em&gt;&amp;#967;&lt;/em&gt; and &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; within a landscape. This problem is enhanced over large spatial scales, such as over the width of an orogen, where the probability of &lt;em&gt;&amp;#952;&lt;/em&gt; heterogeneity increases drastically. However, the distortion of &lt;em&gt;&amp;#967;&lt;/em&gt; and &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; linked to a &lt;em&gt;&amp;#952;&lt;sup&gt;ref&lt;/sup&gt;&lt;/em&gt; being different than the local best-fit has been poorly explored: we currently do not know how much these concavity variations influence channel steepness interpretations.&lt;/p&gt;&lt;p&gt;In this contribution, we explore the extent of the effect of varying concavity on channel steepness using analytical and numerical methods both on landscape evolution models and real landscapes. We show that (i) relative values of &lt;em&gt;&amp;#967;&lt;/em&gt; and &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;, i.e location of local maxima, minima and variations, can be significantly and non-linearly impacted as a function of their &lt;em&gt;&amp;#916;&amp;#952;&lt;/em&gt; from optimal &lt;em&gt;&amp;#952;&lt;/em&gt; and drainage area; (ii) we identify cases where asymmetries in &lt;em&gt;&amp;#952;&lt;/em&gt; can cause incorrect interpretations of changes in channel steepness (iii) present tools to quantify the extent and therefore the risk of misinterpretation.&lt;/p&gt;