Impact of Perturbations on Watersheds

TL;DR

This paper investigates how small local perturbations like landslides or tectonic shifts can significantly alter watersheds in both real and artificial landscapes, revealing universal power-law behaviors and scaling laws.

Contribution

It introduces a comprehensive analysis of watershed perturbations, establishing power-law scaling laws and linking them to invasion percolation theory, with dependence on landscape correlations.

Findings

Power-law distribution of affected watershed areas

Scaling exponents depend linearly on Hurst exponent in artificial landscapes

Power-laws are independent of perturbation strength

Abstract

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.