Extracting longitudinal profiles from side canyons of Colorado River through Grand Canyon NP

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?