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 > 1km2

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 = ksA-

Fluvial Scaling – Empirical Data

• Linear relationship between log(S) and log(A)

• ks is the channel steepness; is the concavity

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

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

S = ksA-

ks is a more-general equivalent to the SL index:No dependence on basin shape

colluvialreach ks-

Duvall, Kirby, and Burbank, 2004, JGR-ES

ks

S = ksA-

Concavity invariant with U

Steepness varies with U

Debris-flow chutesexpand with U

Question: What Sets Erosion Rate?

E = KAmSnTransient systems• Knickpoint in long profile• Break in slope-area scaling