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Topographic Metrics

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?.

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Topographic Metrics

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  1. 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?

  2. 80-90% Relief is on Bedrock Channels Blue lines: drainage area > 1km2

  3. 80-90% Relief is on Bedrock Channels Threshold hillslope gradients dominate – no tectonic info

  4. Now in 3D The Same Drainage Basin in Taiwan

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

  6. Fluvial Scaling – Empirical Data • Empirical data for well-adjusted fluvial systems around the globe yield the following scaling: S = ksA-q • Linear relationship betweenlog(S) and log(A) • ks is the channel steepness; q is the concavity

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

  8. Flint’s Law: Mixed Bedrock-Alluvial Stream (Appalachians, VA) S = ksA-q colluvial reach ks -q ks is a more-general equivalent to the SL index: No dependence on basin shape

  9. Duvall, Kirby, and Burbank, 2004, JGR-ES q S = ksA-q ks

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

  11. Question: What Sets Erosion Rate?

  12. Transient systems • Knickpoint in long profile • Break in slope-area scaling E = KAmSn

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