Numerical landscape modeling page

I have written into code a couple of the published landscape evolution models out there (Howard, 1994; Chase, 1991), to get some sense of the kind of erosional behavior one might expect from them. I modified Howard's model to my own ends...Some of the changes are to the numerical lattice boundaries. I set a single outlet for eroded material to exit the lattice, and enforced a planform boundary to the lattice similar to my physical sandbox epxeriment. I also modified processes operating on the numerical lattice, such as erosion based on stream curvature, hillslope failure, and directional diffusion. For more details on erosional processes, see information on the model used to make these animations.

Model animations (time series of gray scale elevation fields)

R2 upstream area + diffusion + periodic uplift (gif animation 414 kb)(input parameters)

R9 upstream area +diffusion (gif animation 475 kb)(input parameters)

R12 upstream area +diffusion (gif animation 664 kb)(input parameters)

R13 upstream area +slope failure (gif animation 682 kb)(input parameters)

R 18 upstream area + stream curvature (gif animation 681 kb)(input parameters)

R22 slope failure only (gif animation 376 kb)(input parameters)

R27 upstream area + stream curvature (gif animation 670 kb)(input parameters)

R29 upstream area + asymmetric diffusion (gif animation 662 kb)(input parameters)

R30 upstream area + asymmetric diffusion (gif animation 645 kb and 304 kb-4_color)(input parameters)

A few conclusions...

• While the numerical simulations exhibit lateral migration of ridges/streams, this behavior dies out as some (for lack of a better term) optimal network is achieved. All of the simulations I have run are driven to this stable form (though some of the simulations clearly were not run long enough...). Stability is achieved shortly after a balance between erosion and uplift has been established, and usually not more than a relief's worth of erosion beyond complete dissection of the initial surface (Howard notes a limit of 3 reliefs to achieve stability).
• When ridges do migrate, they appear to 'close' from the upstream to the downstream end.
• Adding additional terms to the erosion law, such as for stream curvature, for threshold slope driven slope failures, or general diffusion, does not lead to self-sustaining migration.

page last modified June 11, 2001 by Les Hasbargen