Extracting longitudinal profiles from side canyons of Colorado River through Grand Canyon NP
Leif KarlstromEPS 209 Final Project
Basic science questions: • Is the differential incision history of Grand
Canyon recorded in variable response of tributary erosion to main stem downcutting?
• Is substrate strength (rock type) a first-order control on channel incision rates?
• How does channel width respond to transient uplift?
Warning: I have not yet gotten far enough on this to answer any of these!
The hypothesis: Colorado plateau uplift causes fault-controlled knickpoints to form and migrate upstream
Pederson et al. 2002, Karlstrom et al. 2008
Tectonics Nonequilibrium river profiles Knickpoint propagation
Basic knickpoint physics (Whipple and Tucker 1999):
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dzdt=U − E,
E =KAmSn =KAmSn−1dzdx
A = kx h
Evolution of channel height balances uplift and erosion
Hack’s Law to relate drainage area A to channel length x
“Stream power” model for detachment limited erosion – depends on slope and drainage area
Knickpoints are kinematicWaves!
(caveat: aren’t a feature inTransport limited systems)
My goal: exctract long profiles from ALL tributaries to the Colorado river from 10 m NED DEM. My Hypotheses:1) Distribution of side canyon knickpoints/channel width reflects spatial variability in uplift2) Substrate strength (rock type) determines a minimum drainage area size that can
respond to main-stem base level fall
Established result: Long profile Colorado River main stem has “knick zones”, some major tributaries have over-steepened profiles and and smaller knick points
Cook et al., 2009
Exercise: Segmentation, edge detection and massaging of DEM images to automate the extraction of long profiles
Problem: the data set is large.
Smaller subset of total DEM to learn techniques with.
Image processing techniques I tried: Entropy, edge detection, curvature based, steepest descent
One decent method: Curvature + diffusion-based smoothing
Original topographyAfter median filter + laplacian-of-gaussian (rotationally symmetric) filteringThreshold to just positive curvature: ridges have negative curvature,
Valleys have positive curvature (in current reference frame)Make binary
Skeletonize, overlay on original image: problem lots of loops, very small channels
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One possible solution: apply curvature evolution to DEM.
Diffusion equation is actually similar to real hillslope evolution
And has nice property that is preserves the sign of curvature while smoothingHigh frequency variation
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dz(x,y)dt
=∇2z(x,y)
Compare Skeletonized channels before and after hillslope diffusion:Some improvement but STILL are loops… this method is not the best…
Original DEM + curvature based skeleton Diffused DEM + curvature based skeleton
Another approach: Steepest descent (track maximum slope to find channels)
Flow accumulation direction and channels
Just channels, in “Strahler order”
Next step: extract meaningful profiles, using drainage area cutoff (larger DEM example)
Unfinished ...
OK profile, but are the steps artifacts of DEM or my extraction procedure?