Hillslope steady state profiles — hillslope

Compute hillslope topography steady state profiles, in the case of linear and nonlinear sediment flux

hillslope_profile(x, E, K, L, beta, Sc = NULL)

Arguments

x	Horizontal position along the hillslope (x=0 at hilltop, m)
E	Denudation rate (m/a)
K	Diffusion coefficient (m2/a)
L	hillslope length (m)
beta	rock to teglith density ratio (dimensionless)
Sc	Critical hillslope gradient (optional, m/m)

Value

Hillslope elevation (relative to base of hillslope) at the position specified in `x`.

Details

If the threshold hillslope gradient `Sc` is specified the profile is computed in the non-linear case, otherwise linear.

Examples

x = seq(0,100,by=1)
L =  max(x) # hillslope length
E = 100/1e6 # erosion rate (m/Ma -> m/a)
K = 0.01 # diffusion coefficient (m2/a)
beta = 2
Sc = 0.8 # (m/m)
znl = hillslope_profile(x,E,K,L,beta,Sc)
plot(x,znl,type="l",lwd=3,
xlab="Distance from hilltop (m)",ylab="Elevation (m)")
zl = hillslope_profile(x,E,K,L,beta)
lines(x,zl,col="blue")