Improving Topological Detection of Weather Regimes in climate dynamical systems

TL;DR

Weather regimes are difficult to define with fixed-clustering; this paper leverages a two-parameter density–distance bifiltration with persistent homology to detect regime-like topological structures in atmospheric data without pre-specifying the number of regimes. To overcome KDE over-smoothing, the authors introduce a local centrality measure based on the distance-to-measure function $d_k$, yielding centrality $C_k$ that remains robust to noise and captures thin or sparse features. Across four datasets (Lorenz–63, Lorenz–96, Charney–DeVore, JetLat), the centrality-based approach detects regime-related connected components and loops more reliably and often earlier in the filtration than KDE, including the southern JetLat regime; it also improves computation, scalability, and interpretability. The method provides a unifying geometric perspective for atmospheric regime analysis and is readily applicable to high-dimensional observational data, with potential extensions to incorporate temporal dynamics and data-driven parameter selection.

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.

Figures (19)

• Figure 1: Lorenz–63 attractor simulated with 40,000 data points.
• Figure 2: Lorenz–96 attractor projected onto the first onto the first three principal components using 40,000 data points.
• Figure 3: CdV attractor projected onto the first three principal components (40,000 data points).
• Figure 4: JetLat dataset from reanalysis, comprising about 9,800 data points.
• Figure 5: Vietoris--Rips filtration of a noisy circle. For small radius values, edges connect only nearby points, forming small clusters. As the radius grows, these clusters merge and a loop appears. The loop later fills in as the complex becomes fully connected.