Smoothing function applied to initial glacier geometry

[facusapienza21]

We are using the smooth!() function defined in utils.jl to smooth the initial ice thickness of all the glaciers following what it seems to be one step in a diffusivity equation solver.

"""
    smooth!(A)
Smooth data contained in a matrix with one time step (CFL) of diffusion.
"""
@views function smooth!(A)
    A[2:end-1,2:end-1] .= A[2:end-1,2:end-1] .+ 1.0f0./4.1f0.*(diff(diff(A[:,2:end-1], dims=1), dims=1) .+ diff(diff(A[2:end-1,:], dims=2), dims=2))
    A[1,:]=A[2,:]; A[end,:]=A[end-1,:]; A[:,1]=A[:,2]; A[:,end]=A[:,end-1]
    return
end

function smooth(A)
    A_smooth = A[2:end-1,2:end-1] .+ 1.0f0./4.1f0.*(diff(diff(A[:,2:end-1], dims=1), dims=1) .+ diff(diff(A[2:end-1,:], dims=2), dims=2))
    @tullio A_smooth_pad[i,j] := A_smooth[pad(i-1,1,1),pad(j-1,1,1)] # Fill borders 
    return A_smooth_pad
end

This is currently just been used in get_initial_geometries(), which in principle shouldn't have effects in the UDE behavior. However, this could induce instabilities and it is not clear this transformation is mathematically correct.

[mauro3]

What is the purpose of the smoothing? If it is physics related, it should probably be formulated in terms of a multiple of local ice thickness.