Improving Topological Detection of Weather Regimes in climate dynamical systems

TL;DR

This paper introduces a topological data analysis approach to identify weather regimes in climate systems, avoiding the need to predefine the number of regimes and addressing limitations of traditional methods.

Contribution

It applies persistent homology to topologically characterize weather regimes, providing a unified framework that overcomes the constraints of existing techniques.

Findings

Topological methods reveal weather regimes without predefining their number.

Persistent homology captures large-scale atmospheric variability.

The approach addresses over-smoothing issues in density estimation.

Abstract

Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather regimes. Recent work has shown that weather regimes can be interpreted geometrically as topological structures in the phase space of the atmospheric system. In this approach, regimes are identified using a density--radius bifiltration combined with persistent homology, a well-established tool from Topological Data Analysis (TDA). This topological perspective provides a unifying view of regimes and, unlike traditional methods, does not require the number of regimes to be specified in advance. However, the method relies on density estimation techniques (typically Gaussian kernel density estimation), which can over--smooth weakly populated but dynamically important regions of the phase space.