Topological Structure of the Cyclonic-Anticyclonic Interactions

TL;DR

The paper develops a topological data analysis framework based on persistent homology to quantify cyclonic–anticyclonic interactions in North Atlantic sea-level pressure anomalies from 1950–2022. By treating SLP anomaly fields as cubical complexes and applying sublevel- and superlevel-set filtrations, it identifies $1$-hole features corresponding to anticyclones and cyclones, encoded in persistence diagrams and summarized by total persistence $\mathrm{TP}$. Temporal evolution is tracked with optimal matching and the $1$-Wasserstein distance between diagrams, revealing robust seasonal patterns with winter maxima and longer, more numerous cyclone trajectories. The approach yields an objective, filtering-free characterization of pressure-field organization, recovers known climatology (e.g., Icelandic Low, blocking episodes), and offers a topological framework for analyzing mid-latitude circulation and other atmospheric fields.

Abstract

We investigate the large-scale structure and temporal evolution of cyclonic and anticyclonic systems in the North Atlantic using persistent homology applied to daily sea-level pressure anomalies from the ERA5 reanalysis (1950-2022). By interpreting the pressure field as a cubical complex and computing its sublevel- and superlevel-set filtrations, we identify degree-1 topological features corresponding respectively to anticyclones surrounded by low pressure and cyclones surrounded by high pressure. We quantify their intensity through total persistence and track their evolution over time using optimal matchings and Wasserstein distances between consecutive persistence diagrams. The method captures coherent, long-lived structures without requiring feature-tracking heuristics and reveals robust seasonal patterns: both cyclonic and anticyclonic 1-holes exhibit strong winter maxima and summer minima in total persistence, lifetime, and frequency. Cyclonic features are more persistent, more numerous, and longer-lived than their anticyclonic counterparts, consistent with the climatological dominance of the Icelandic Low in winter and the weaker, more transient nature of anticyclonic highs. Long trajectories correspond to known large-scale structures such as winter cyclonic deepening and blocking episodes. These results demonstrate that persistent homology provides an objective, filtering-free characterization of pressure-field organization and offers a topological framework to analyze the dynamics and variability of mid-latitude circulation.

Figures (12)

• Figure 1: A hollow torus with two non-equivalent 1-holes (respectively blue and red circles).
• Figure 2: A grayscale image and its representation as a grid which is obtained after tesselation by congruent squares. Each square has a number associated to it corresponding to the intensity of the light.
• Figure 3: Filtered cubical complexes and their corresponding persistence diagrams. In all diagrams, birth and death values correspond to intensity. (b) Persistence diagram corresponding to the filtration in (a). (d) Persistence diagram corresponding to the filtration in (c).
• Figure 4: (a) Sequence of gray scale images. (b) Sequence of persistence diagrams with 1-holes tracked across timeline using optimal matching. Birth and death values correspond to intensity. (c) Sequence of gray scale images with the regions tracking the 1-holes in orange and green contours.
• Figure 5: Sea level pressure (SLP) anomalies over the North Atlantic on 31 December 2022. Blue shading indicates cyclonic regions, and red shading indicates anticyclonic regions.

Theorems & Definitions (15)

• Definition 2.1: Sublevel and Superlevel Set Filtrations
• Definition 2.2
• Definition 2.3
• Definition 2.4: Persistence
• Definition 2.5: Total Persistence
• Definition 2.6
• Definition 2.7
• Definition 2.8
• Definition A.1
• Definition A.2