Scale-dependence of lithological control on topography; bedrock channel geometry and catchment morphometry in western Scotland

We propose that a scale-dependent topographic signature of erodibility arises due to fluvial and glacial erosion acting on different parts of the landscape at different times.  For 14 catchments in western Scotland, we define three levels of substrate erodibility in order of decreasing resistance: quartzite rocks, non-quartzite rocks, and zones of fault-related fracture.  Then, using digital topographic and planimetric data coupled with field measurements, we identify regression-based scaling relationships between substrate erodibility and morphometric parameters at two spatial scales.  Catchment-scale morphometry shows a weak to variable relationship with substrate metrics overall.  Erodibility can be inferred from catchment steepness indices (i.e., channel steepness index and relief ratio), but the existence of multiple exceptions could confound a more general application of this approach.  Nonetheless, major valley troughs trace fault zones and non-quartzite rocks, leaving much of the higher and steeper ground formed in quartzite.  At the reach-scale, bedrock channel slope is far more sensitive to substrate erodibility than is channel width.  Quartzite outcrops steepen bedrock channels by a factor of 1.5 to 6.0 and, in terms of unit stream power, channels increase their erosional capacity by a factor of 2.7 to 3.5.  Yet only 4 to 13% of this increase is due to channel narrowing.  Based on a large dataset of bedrock channel width (n=5825) from 4 rivers, we find that width scales with drainage area (in m2) as W=0.01 A0.28.  Our results are consistent with the view that width-area scaling is similar in all single-thread rivers subject to transport-limited conditions, but for increasingly sediment supply-limited settings erosional thresholds at the channel boundary are the key determinants of bedrock channel width.