  We find that watersheds in real and artificial landscapes can be strongly
affected by small, local perturbations like landslides or tectonic motions. We
observe power-law scaling behavior for both the distribution of areas enclosed
by the original and the displaced watershed as well as the probability density
to induce, after perturbation, a change at a given distance. Scaling exponents
for real and artificial landscapes are determined, where in the latter case the
exponents depend linearly on the Hurst exponent of the applied fractional
Brownian noise. The obtained power-laws are shown to be independent on the
strength of perturbation. Theoretical arguments relate our scaling laws for
uncorrelated landscapes to properties of invasion percolation.
