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?