Landscape evolution: Coupling hillslope diffusion with the stream-power law

By coupling equations for hillslope diffusion and bedrock-river incision and adding in tectonic uplift, we can derive a straightforward and broadly-used expression for landscape evolution.

Learning Goals

• Appreciate how simple it can be to combine the pieces of knowledge into something that describes rich and complex – though still straightforwrad – topographic evolution.

Derivation

Here I derive the equation for landscape evolution in one dimension:

\[\frac{\partial z}{\partial t} = k_h \frac{\partial^2 z}{\partial x^2} - K A^m {\left|\frac{\partial z}{\partial x}\right|}^n + U.\]

This is my derivation (in PDF), written in xournal++, as it appears after creating the video lecture (below).

Examples

Basic landscape evolution model

Creating an erosional river network and diffusive hillslopes from near-featureless flat surface. It isn’t totally realistic, but it’s simple to set up on a computer. This could relate, for example, to incision of a ancient abandoned lake bed.

Landscape evolution on a volcanic island

Note the steep valley walls: this indicates that hillslope processes may be slow relative to fluvial processes.

Eurpoean Geosciences Union medal to Jean Braun

If you’re really into this, Jean Braun is one of the leading experts in landscape evolution. You’ll see the exact equation that you’ve just learned in an international scientific society medalist lecture!

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