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Quantitative tectonic geomorphology hinges on the analysis of longitudinalriver profiles. The model behind almost all approaches in this field originatesfrom an empirical relationship between channel slope and catchment size, oftensubstantiated in the form of the stream-power model for fluvial incision.Significant methodological progress was recently achievedby introducing the <i>χ</i> transform. It defines a nonlinear length coordinatein such a way that the inherent curvature of river profiles due to theincrease of catchmentsizes 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 streampower law towards small catchment sizes in order to overcome this limitation.Beyond this, we introduce a simple methodfor estimating the adjustable parameters in the original <i>χ</i> method as wellas in our extended approaches. As a main result, an approach originally suggestedfor debris flow channels seems to be the best approximation if both large andsmall catchment sizes are included in the same analysis

Tectonic geomorphology at small catchment sizes – extensions of the stream-power approach and the &lt;i&gt;χ&lt;/i&gt; method

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