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Earth and Space Sciences · Glossary

What is Hillslope diffusion?

Definition 18.1 University Earth and Space Sciences — Year 3 · Chapter 18 — Quantitative Geomorphology

Hillslope diffusion is the slow downslope transport of soil whose volume flux per unit width of slope, q⃗\vec q, is proportional to the gradient of the surface elevation zz: q⃗=−κ ∇z\vec q = -\kappa\,\nabla z. The coefficient κ\kappa, in m2/yr\mathrm{m}^{2}/\mathrm{yr}, is the hillslope diffusivity.

Left, a scarp of 5\, m offset on a slope of 0.05, diffusing with = 5 × 10-3\, m2/ yr: the initial step (dashed) and the profiles after 2, 10 and 40\, kyr. Right, steady hills of half-width 150\, m with the same (height above the channels), lowering at 0.0215, 0.043 and 0.086\, mm/ yr: parabolas whose relief and hilltop curvature are proportional to the erosion rate.
Left, a scarp of 5 m5\,\mathrm{m} offset on a slope of 0.05, diffusing with κ=5×10−3 m2/yr\kappa = 5 \times 10^{-3}\,\mathrm{m}^{2}/\mathrm{yr}: the initial step (dashed) and the profiles after 2, 10 and 40 kyr40\,\mathrm{kyr}. Right, steady hills of half-width 150 m150\,\mathrm{m} with the same κ\kappa (height above the channels), lowering at 0.0215, 0.043 and 0.086 mm/yr0.086\,\mathrm{mm}/\mathrm{yr}: parabolas whose relief and hilltop curvature are proportional to the erosion rate.
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