Extracting longitudinal profiles from side canyons of Colorado River through Grand Canyon NP Leif Karlstrom EPS 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): Evolution of channel height balances uplift and erosion “Stream power” model for detachment limited erosion – depends on slope and drainage area Hack’s Law to relate drainage area A to channel length x Knickpoints are kinematic Waves! (caveat: aren’t a feature in Transport limited systems)
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 My goal: exctract long profiles from ALL tributaries to the Colorado river from 10 m NED DEM. My Hypotheses: Distribution of side canyon knickpoints/channel width reflects spatial variability in uplift 2) Substrate strength (rock type) determines a minimum drainage area size that can respond to main-stem base level fall
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 topography Make binary After median filter +laplacian-of-gaussian (rotationally symmetric) filtering Skeletonize, overlay on original image: problem lots of loops, very small channels Threshold to just positive curvature: ridges have negative curvature, Valleys have positive curvature (in current reference frame)
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 smoothing High frequency variation N
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?