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Analyzing Topographic Metrics: Insights into Relief, Steepness, and Erosion in Tectonic Landscapes

This article explores three crucial topographic metrics: Channel Steepness Index, Hillslope Gradients, and Local Relief at various scales. We examine their interrelationships and evaluate their effectiveness in understanding the impact of tectonics on topography. Empirical data reveals significant insights about fluvial scaling and erosion rates. The analysis includes a focus on bedrock channels and transient systems, highlighting essential metrics for geomorphological studies. With practical examples from regions like Taiwan and the Appalachians, we aim to enhance the understanding of topographic influences.

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Analyzing Topographic Metrics: Insights into Relief, Steepness, and Erosion in Tectonic Landscapes

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Presentation Transcript

  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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