Topographic Metrics Many Topographic metrics have been proposed. We’ll examine the three most common –Channel Steepness Index –Hillslope Gradients –Local Relief at Various Scales What are the relationships among these? Which are most useful for gaging the influence of tectonics on topography?

80-90% Relief is on Bedrock Channels Blue lines: drainage area > 1km 2

80-90% Relief is on Bedrock Channels Threshold hillslope gradients dominate – no tectonic info

Now in 3D The Same Drainage Basin in Taiwan

Beware: Many authors use “hillslope relief” and “local relief” (measured over up to 5km radius) as interchangeable

Empirical data for well-adjusted fluvial systems around the globe yield the following scaling: S = k s A -  Fluvial Scaling – Empirical Data Linear relationship between log(S) and log(A) k s is the channel steepness;  is the concavity

Flint’s Law: Mixed Bedrock-Alluvial Stream (Appalachians, VA)

S = k s A -  k s is a more-general equivalent to the SL index: No dependence on basin shape colluvial reach ksks --

Duvall, Kirby, and Burbank, 2004, JGR-ES  ksks S = k s A - 

Concavity invariant with U Steepness varies with U Debris-flow chutes expand with U

Question: What Sets Erosion Rate?

E = KA m S n Transient systems Knickpoint in long profile Break in slope-area scaling