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A Topological Framework for Atmospheric River Interaction Using Framed Braids

Ioannis Diamantis

TL;DR

ARs are analyzed with a topological framework that treats multiple filaments as interacting strands whose time-ordered crossings are captured by oriented braids and whose internal moisture evolution is encoded by integer framings. By extracting braid words from ERA5 AR track data in sliding windows and attaching framing via a moisture integral around cross-sections, the authors generate framed braid representations that couple geometry and transport strength. Case studies in the North Pacific demonstrate that braid-based indicators reveal structural reorganizations and moisture intensification not evident from centroid geometry or IVT alone, offering a potential topological early-warning perspective. The work discusses limitations and outlines future directions including braidoids for birth/dissipation, pseudo crossings for uncertainty, and integration with forecasting workflows.

Abstract

Atmospheric Rivers (ARs) are filamentary moisture pathways responsible for a large fraction of extreme precipitation and often occur as interacting filament bundles within the same synoptic regime. Existing diagnostics typically analyze ARs in isolation, despite the frequent coexistence and interaction of multiple filaments. We introduce a topological framework for AR analysis based on framed braids and framed braidoids, which encodes both the geometric interaction of AR centroids and the internal evolution of moisture transport. In this approach, AR filaments are represented as strands whose time-ordered crossings form braid words, while moisture-based framing captures internal intensification or weakening along each filament. Applying this framework to reanalysis-derived Atmospheric River track data, we construct braid and framed braid representations over sliding time windows and analyze a strongly interacting multi-filament AR episode in the North Pacific. The results show that braid-based indicators capture structural reorganizations and moisture intensification episodes that are not apparent from centroid geometry or IVT magnitude alone, offering a complementary structural perspective on atmospheric moisture transport.

A Topological Framework for Atmospheric River Interaction Using Framed Braids

TL;DR

ARs are analyzed with a topological framework that treats multiple filaments as interacting strands whose time-ordered crossings are captured by oriented braids and whose internal moisture evolution is encoded by integer framings. By extracting braid words from ERA5 AR track data in sliding windows and attaching framing via a moisture integral around cross-sections, the authors generate framed braid representations that couple geometry and transport strength. Case studies in the North Pacific demonstrate that braid-based indicators reveal structural reorganizations and moisture intensification not evident from centroid geometry or IVT alone, offering a potential topological early-warning perspective. The work discusses limitations and outlines future directions including braidoids for birth/dissipation, pseudo crossings for uncertainty, and integration with forecasting workflows.

Abstract

Atmospheric Rivers (ARs) are filamentary moisture pathways responsible for a large fraction of extreme precipitation and often occur as interacting filament bundles within the same synoptic regime. Existing diagnostics typically analyze ARs in isolation, despite the frequent coexistence and interaction of multiple filaments. We introduce a topological framework for AR analysis based on framed braids and framed braidoids, which encodes both the geometric interaction of AR centroids and the internal evolution of moisture transport. In this approach, AR filaments are represented as strands whose time-ordered crossings form braid words, while moisture-based framing captures internal intensification or weakening along each filament. Applying this framework to reanalysis-derived Atmospheric River track data, we construct braid and framed braid representations over sliding time windows and analyze a strongly interacting multi-filament AR episode in the North Pacific. The results show that braid-based indicators capture structural reorganizations and moisture intensification episodes that are not apparent from centroid geometry or IVT magnitude alone, offering a complementary structural perspective on atmospheric moisture transport.
Paper Structure (47 sections, 1 theorem, 51 equations, 23 figures, 1 algorithm)

This paper contains 47 sections, 1 theorem, 51 equations, 23 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Atmospheric Rivers: Geometry, Dynamics, and Moisture Structure
  3. Geometric description of ARs
  4. Cross-sectional structure and the band model
  5. Dynamical evolution and interactions
  6. Moisture accumulation and the role of framing
  7. Why ARs admit a topological model
  8. Framed Braids and Braidoids: Mathematical Background
  9. Classical braids
  10. Framed braids
  11. Physical interpretation of framing
  12. Framed isotopy and atmospheric interpretation
  13. Framed braidoids: the correct setting for finite AR filaments
  14. Braidoids and knotoids.
  15. Generators and atmospheric interpretation.
  16. ...and 32 more sections

Key Result

Theorem 3.2

The closures of two braids are isotopic if and only if one braid can be taken to another by finite sequence of the following moves (for an illustration see Figure beq):

Figures (23)

  • Figure 1: Anatomy of an Atmospheric River. (a) Plan-view geometry showing the centroid and IVT-defined band. (b) Cross-sectional IVT profile illustrating the moisture-rich core and AR width.
  • Figure 2: Distribution of AR lifetimes within the North Pacific domain. Longer-lived filaments are more likely to undergo interactions and structural reorganization.
  • Figure 3: Seasonal cycle of AR track occurrences within the selected regional domain, showing the mean number of detected AR filaments per month.
  • Figure 4: Examples of a 2--strand and a 3--strand braid. Time increases upward.
  • Figure 5: Closure of a 2-strand and a 3-strand braid producing two links.
  • ...and 18 more figures

Theorems & Definitions (13)

  • Definition 2.1: Moisture load along an AR filament
  • Remark 2.2
  • Remark 2.3
  • Remark 3.1
  • Theorem 3.2: Markov
  • Remark 3.3
  • Definition 3.4
  • Remark 3.5
  • Remark 3.6
  • Remark 4.1
  • ...and 3 more