GSA Short Course: Tectonic Geomorphology

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GSA Short CourseTectonic Geomorphology
Acknowledgements Cam Wobus Ben Crosby Eric
Kirby Daniel Sheehan Kelin Whipple Noah
Snyder Will Ouimet Nicole Gasparini Roman
DiBiase Funding NSF GLD
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Topographic Metrics

• Many Topographic metrics have been proposed.
  Well 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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Course Outline

• Presentation I why rivers determining channel
  steepness
• Analysis of Model Topographies
• Discussion
• Presentation II relations among erosion rate,
  channel steepness, hillslope gradients, and local
  relief
• Analysis of Real Topography
• Discussion
• Presentation III distinguishing spatial from
  temporal effects

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80-90 Relief is on Bedrock Channels
Blue lines drainage area gt 1km2
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80-90 Relief is on Bedrock Channels
Threshold hillslope gradients dominate no
tectonic info
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Now in 3D

• The Same Drainage Basin in Taiwan

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Historical Context

• River profiles generally smooth, concave-up
• Debate z(x) power law, logarithmic, semi-log
• Hack semi-log
• Hack Gradient Index SL (slopelength)
• Differentiate once evaluate at x L

Deviations from constant gt lithologic, tectonic
effects
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Historical Context

• Hacks Law (1957)
• Flints Law (1974)
• Generalization of Hacks semi-log profile
  thus ks replaces SL index
• Combine above relations
• IFF

Integrate Once
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SL index Can Vary Downstream simply due to Basin
Shape
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Fluvial Scaling Empirical Data

• Empirical data for well-adjusted fluvial systems
  around the globe yield the following scaling
• S ksA-q

• Linear relationship between log(S) and log(A)
• ks is the channel steepness q is the concavity

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Flints Law Mixed Bedrock-Alluvial Stream
(Appalachians, VA)
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Flints 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
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Duvall, Kirby, and Burbank, 2004, JGR-ES
q
S ksA-q
ks
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King Range Concavity Invariant with Rock Uplift
Rate
Snyder et al, 2000, GSABDirectly Contradicts
Earlier Finding of Merritts and Vincent, 1989,
GSAB
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Steepness varies with U
Concavity invariant with U
Debris-flow chutes expand with U
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1. Extract raw channel profile data
Source USGS 10 m DEM (Free!)
Solution Original Contour Crossings
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Raw Pixel-to-Pixel Slopes, USGS 10m
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2. Resample at a constant contour interval and
regress on linear segment
Grey raw data Black 30m contour crossings
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Similar scaling from a variety of data sources
Blue USGS 10 m DEM
Red SRTM 90 m DEM (720 m downstream moving
average)
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Problem Co-variation of ks and q

• Can not compare ks among streams with even
  slightly different concavities
• Solution Need a Normalized Steepness Index
  determined with a reference concavity (use
  regional mean)

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ksn
Sklar and Dietrich, 1998
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Estimating ksn Uncertainty

• The Integral Method
• integrate once
• Regress z on c, slope of line is ksn
• Uncertainty on ksn fit by regression is best
  measure of goodness of fit (2s reported)

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Variation in Concavity Index

• Blind regression from headwaters to outlet,
  concavity varies widely
• 0.2 1.2, and locally up to very high 6
• Recognizing interpretable spatial and transient
  effects
• 0.4 0.6 captures most data
• Effects debris-flow chutes lithology (x)
  uplift (x) transient response to uplift (t) or
  climate (t)

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Flints 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
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• Transient systems
• Knickpoint in long profile
• Break in slope-area scaling

E KAmSn
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Channel Steepness Index Spatial Information
about Relative Rock Uplift Rate

• Siwalik Hills, Nepal
• San Gabriel Mountains, CA

Nepal Himalaya (Wobus et al.) Olympic Mountains,
WA (Gasparini and Brandon) Bolivian Andes (Safran
et al) Santa Ynez Mtns, CA (Duvall et al) King
Range, CA (Snyder et al) Eastern Margin, Tibetan
Plateau (Ouimet et al)
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Siwalik Hills, Nepal
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Bagmati Transect
Bakeya Transect
Data from Lave and Avouac, 2000, JGR
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Siwalik Hills Anticline Himalaya Foreland, Nepal
Strike-Parallel Uniform Uplift Along Stream
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Strike-Parallel Normal, uniform concavity
14 mm/yr
7 mm/yr
Strike-Parallel Steepness varies with U
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Siwalik Hills, Nepal
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Transverse U(x) Reflected in Concavity
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Eastern margin of the Tibetan Plateau A
Transient Landscape deep river gorges cut into
an uplifted, slowly eroding, low-relief relict
landscape. fluvial dissection has not
propagated through the entire landscape. rivers
typically transition from the relict landscape
into dissected gorges bounded by steep hillslopes.
Patches of low-relief, relict landscape preserved
in eastern Tibet (Clark, 2003).
Mean, high elevation relict topography
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Slope map from SRTM 90 m DEM
Transient Hillslopes
Hillslopes, following incision, display zones
of adjustment with steepest values in the
lowermost reaches of individual basins
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• Zhong Qing River Transient hillslope and river
  profile response
• Tributary of the Dadu River
• 70 km long, 1500 m of fluvial relief
• Total Area 930 km2

A
B
Google Earth
Longitudinal River Profile from 90 m SRTM
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Transient Morphology Photos from the Zhong Qing
and Li Qui Rivers
2 Initial Dissection
1 Relict Landscape
3 Transition (Gentle)
6 Gorge Landscape
5 Transition (Steep)
4 Transition (Intermediate)
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125 km
Ouimet, Whipple, Granger Tues 8am 63 Basin Wide
Erosion Rates Mean Drainage Area 38 km2
Erosion Rate (m/Ma)
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35 Erosion Rates (out of 70 total) 4 samples are
greater than 1km/Ma (1mm/yr) Plotted here are
all samples (31) less than 600 m/Ma, 0.6 mm/yr
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63 Basins ------------------- 2 rates 3000 m/Ma
Gonga Shan ------------------- Rate error Bars 1s
Snyder et al, 2003 Theoretical Curve
Roering et al, 2001 Theoretical Curve
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Example Tectonic Geomorphology of the San
Gabriel Mountains
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Shaded Relief with Color Elevation
Active FaultsThickness Most Recent Known Slip
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San Gabriel Mountains Shaded Relief
Preliminary Detrital Cosmogenic 10Be Sample
Catchments Transparent Overlay
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Hillslope Gradient (30x30m)
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Beware Many authors use hillslope relief and
local relief (measured over up to 5km radius)
as interchangeable
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Local Relief (r 100m)
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Hillslope Gradient (30x30m)
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Slope calculated as Relief/diameter (R/200)
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Local Relief (r 1km)
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Local Relief (r 2.5km)
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Background Color Elevation, Streams by
Normalized Steepness Index
Note abrupt steepness breaks across active
faults, no break where inactive/slow