A topological perspective on weather regimes

TL;DR

This paper proposes a topological approach using persistent homology to identify and analyze weather regimes in atmospheric dynamics, providing a new perspective on their existence and structure.

Contribution

It introduces a novel topological data analysis method to define and detect weather regimes based on attractor structure in dynamical systems.

Findings

Persistent homology effectively identifies regime structures.

The approach is computationally feasible and practically informative.

It offers a clear topological criterion for regimes in atmospheric models.

Abstract

It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as `weather regimes', loosely categorised as regions of phase space with above-average density and/or extended persistence. Their existence and behaviour has been extensively studied in meteorology and climate science, due to their potential for drastically simplifying the complex and chaotic mid-latitude dynamics. Several well-known, simple non-linear dynamical systems have been used as toy-models of the atmosphere in order to understand and exemplify such regime behaviour. Nevertheless, no agreed-upon and clear-cut definition of a `regime' exists in the literature. We argue here for an approach which equates the existence of regimes in a dynamical system with the existence of non-trivial topological structure of the system's attractor. We show using persistent homology, an algorithmic tool in topological data analysis, that this approach is computationally tractable, practically informative, and identifies the relevant regime structure across a range of examples.