Biogenic transport—slope dependent Assume qs(x) = -kDh/Dx tree throw h x burrowing For the areas being studied, the dominant method of soil transport is due to mantle creep and biogenic disturbance in the form of tree throw and burrowing by pocket gophers. Both methods of transport can be thought of as ‘diffusive,’ in that the sediment flux qs is slope dependent as shown in the equation above. Some things to think about… The equation above implies that sediment is always being moved downslope (the negative z direction) and that sediment flux will be greater when the topographic gradient is steeper. Similar conditions and equations define the diffusion of heat, among other things. How might the development of soil mantles be different in the absence of life? (slope) http://wdfw.wa.gov/wlm/living/gophers.htm Modified from DiBiase, 2006

Slope dependent transport law qs(x) Sediment flux k Dh/Dx (slope) Soil creep Biogenic processes (burrowing, other animal induced disturbances) Rainsplash, etc. Thus, qs(x) = kDh/Dx Assume k constant in time and space

Example of quarters Simple mass continuity for a hillslope element 1 2 3 Simple mass continuity for a hillslope element

Consider pile #2 # quarters = 8 Rate of input = 2 # quarters = 10 Rate of output = 2 # quarters = 8 Net change = 0 1 2 3

Consider pile #2 # quarters = 8 Rate of input =1 # quarters = 9 Rate of output = 7 # quarters = 2 Net change = -6 1 2 3

->Production or detachment limited! Consider pile #2 # quarters = 2 Rate of input =1 # quarters = 3 Potential rate of output = 10 Actual rate of output = 3 ->Production or detachment limited! # quarters = 0; bedrock exposed 1 2 3

Combine continuity and transport rule     “diffusion” erosion Modified Sept 27

Simple scarp diffusion: Vertical initial form B = “fan” slope a = half-offset “analytic solution”

Simple scarp diffusion: finite slope initial form q = initial scarp slope “analytic solution”

A = 1 and 5 m total half offset; kt = 1 m2 Simple scarp diffusion: continuous vertical offset A = half offset rate “analytic solution”