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Dashed line = 1: erosion exactly balances uplift (steady state). Above 1 the landscape is shrinking (e.g. after clear-cutting), below 1 it is still growing.
The science
Uplift versus erosion. Elevation z changes as ∂z/∂t = U - K Am S + D ∇²z. The first term is rock uplift (m/yr). The second is stream-power incision: erosion grows with the upstream drainage area A (a proxy for discharge) and the local channel slope S. The third is hillslope diffusion (soil creep and rain splash) with diffusivity D.
Steady state. When uplift and erosion balance, S = (U/K) A-m: slopes get gentler downstream in a power law (Flint's law) and the total sediment leaving the basin equals U × area. Doubling U doubles the slopes; halving K does the same. The page tests both statements numerically.
Numerics. Flow is routed over the grid by a priority-flood algorithm (depressions are filled) and each cell drains to its lowest neighbour (D8). Incision is solved with the implicit scheme of Braun and Willett (2013) for n = 1, which is stable for any time step; diffusion uses explicit sub-steps. The edges are fixed at base level 0 and carry all sediment away.
Cover, rain and terraces. The effective erodibility is Keff = K0 · Prain · C · Pt with the RUSLE-style cover factor C = 1 - 0.95 · cover and terrace practice factor Pt = 1 - 0.5 · terraces. The readout "Soil loss" uses the empirical RUSLE formula A = R K LS C P (t/ha/yr) with R = 500 · rain, K = 0.03 and LS = (L/22.13)0.5 (0.065 + 4.56 s + 65.41 s²) for the mean hillslope slope s and a 50 m slope length. It is a separate empirical estimate, not computed from the landscape model.
Honest simplifications. Detachment-limited, no sediment transport or deposition, single-direction flow, one rock type, no landslides, no climate variability; time per step is a numerical choice; elevations are exaggerated two times, trees and the hut are not to scale. Constants are typical orders of magnitude (K near 10-5 per year, D near 0.01 m²/yr), not calibrated to a real catchment.