Topological Data Analysis Detects Percolation Thresholds in Arctic Melt-Pond Evolution

TL;DR

This paper applies topological data analysis, specifically the signed Euclidean distance transform, to Arctic melt pond images to detect percolation thresholds and characterize pond evolution with multiscale shape metrics.

Contribution

It introduces a novel topological shape analysis method for melt ponds, adapting the SEDT to provide detailed shape and percolation insights beyond traditional fractal techniques.

Findings

Identification of percolation thresholds in melt pond networks

Rich shape characterization of ponds using topological metrics

Distinction of different melt pond evolution models

Abstract

During the summer melt period, ponds form on the surface of Arctic sea ice as it melts, with important consequences for ice evolution and marine ecology. Due to the ice-albedo feedback, these melt ponds experience uneven heat absorption, and exhibit complex patterns, which has motivated the development of modelling and data analysis to understand their particular dynamics. We provide a multiscale shape analysis using tools from computational algebraic topology, simultaneously capturing convexity, proximity, integrity, and feature size complementing existing single-scale quantification. Of particular interest in modelling the ponds is a percolation threshold at which local pond structure begins merging into macroscopic features. This percolation threshold has previously been observed using fractal dimension techniques. The signed Euclidean distance transform (SEDT) is a topological encoding of heterogeneous shape in binary images, and has been previously applied to porous media for percolation as well as other material behaviours. Here we adapt the SEDT for Arctic melt pond data to give a rich characterization and computation of shape, quantifying overall melt pond development in several complementary ways, and from which classical percolation and dimension results can be extracted. This orientation-invariant topological approach distinguishes different dynamical network models of melt pond evolution of varying complexity.