Percolation Framework of the Earth's Topography

TL;DR

This paper introduces a percolation theory-based framework to analyze Earth's topography, revealing potential discontinuous transitions and the influence of long-range correlations, with implications for understanding climate change vulnerability.

Contribution

It develops a novel percolation-based approach to study Earth's relief, incorporating fractional Brownian motion models and finite-size scaling to identify phase transitions and critical nodes.

Findings

Evidence of abrupt, possibly discontinuous, transitions in Earth's relief network.

Long-range correlations influence the nature of topographical phase transitions.

Identification of critical nodes vulnerable to climate change.

Abstract

Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on high-resolution, 1 arc min, ETOPO1 global relief records.We find some evidence for abrupt transitions that occurred during the evolution of the Earth's relief network, indicative of a continental/cluster aggregation. We apply finite-size-scaling analysis based on a coarse-graining procedure to show that the observed transition is most likely discontinuous. Furthermore, we study the percolation on two-dimensional fractional Brownian motion surfaces with Hurst exponent $H$ as a model of long-range correlated topography, which suggests that the long-range correlations may play a key role in the observed discontinuity on Earth. Our framework presented here provides a theoretical model to better understand the geometrical phase transition on Earth, and it also identifies the critical nodes that will be more exposed to global climate change in the Earth's relief network.