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Topology of The Polar Vortex and Montana Weather

Joshua Dorrington, Sushovan Majhi, Atish Mitra, James Moukheiber, Demi Qin, Jacob Sriraman, Kristian Strommen

TL;DR

The paper addresses how to detect and interpret polar-vortex dynamics using topology. By applying Takens' time-delay embedding to a one-dimensional wind time series, it constructs a higher-dimensional point cloud in $\mathbb{R}^{M+1}$ and computes $H_1$ persistence diagrams via Vietoris–Rips filtrations, enabling robust, noise-resistant insights into the vortex's dynamical structure. The authors observe clear seasonal changes in topological activity, with pronounced persistence during extreme cold events and potential signatures of vortex splitting, notably around early 2016, and demonstrate cross-regional correlations with Montana temperatures. This work illustrates the potential of Topological Data Analysis to illuminate complex climate dynamics and offers a framework that could generalize to other weather regimes.

Abstract

This paper explores the use of Topological Data Analysis (TDA) to investigate patterns in zonal-mean zonal winds of the Arctic, which make up the polar vortex, in order to better explain polar vortex dynamics. We demonstrate how TDA reveals significant topological features in this polar vortex data, and how they may relate these features to the collapse of the stratospheric vortex during the winter in the northern hemisphere. Using a time series representation of this data, we build a point cloud using the principles of Takens' Embedding theorem and apply persistent homology to uncover nontrivial topological structures that provide insight into the dynamical system's chaotic and periodic behaviors. These structures can offer new perspectives on the dynamics of the polar vortex, and perhaps other weather regimes, all of which have a global impact. Our results show clear transitions between seasons, with substantial increases in topological activity during periods of extreme cold. This is particularly evident in the historically strong polar vortex event of early 2016. Our analysis captures the persistence of topological features during such events and may even offer insights into vortex splitting, as indicated by the number of distinct persistent features. This work highlights the potential of TDA in climate science, offering a novel approach to studying complex dynamical systems.

Topology of The Polar Vortex and Montana Weather

TL;DR

The paper addresses how to detect and interpret polar-vortex dynamics using topology. By applying Takens' time-delay embedding to a one-dimensional wind time series, it constructs a higher-dimensional point cloud in and computes persistence diagrams via Vietoris–Rips filtrations, enabling robust, noise-resistant insights into the vortex's dynamical structure. The authors observe clear seasonal changes in topological activity, with pronounced persistence during extreme cold events and potential signatures of vortex splitting, notably around early 2016, and demonstrate cross-regional correlations with Montana temperatures. This work illustrates the potential of Topological Data Analysis to illuminate complex climate dynamics and offers a framework that could generalize to other weather regimes.

Abstract

This paper explores the use of Topological Data Analysis (TDA) to investigate patterns in zonal-mean zonal winds of the Arctic, which make up the polar vortex, in order to better explain polar vortex dynamics. We demonstrate how TDA reveals significant topological features in this polar vortex data, and how they may relate these features to the collapse of the stratospheric vortex during the winter in the northern hemisphere. Using a time series representation of this data, we build a point cloud using the principles of Takens' Embedding theorem and apply persistent homology to uncover nontrivial topological structures that provide insight into the dynamical system's chaotic and periodic behaviors. These structures can offer new perspectives on the dynamics of the polar vortex, and perhaps other weather regimes, all of which have a global impact. Our results show clear transitions between seasons, with substantial increases in topological activity during periods of extreme cold. This is particularly evident in the historically strong polar vortex event of early 2016. Our analysis captures the persistence of topological features during such events and may even offer insights into vortex splitting, as indicated by the number of distinct persistent features. This work highlights the potential of TDA in climate science, offering a novel approach to studying complex dynamical systems.

Paper Structure

This paper contains 14 sections, 1 equation, 3 figures.

Table of Contents

  1. Introduction
  2. Dynamical Systems and weather regimes
  3. Polar Vortices
  4. TDA and Time Delay Embeddings
  5. Introduction to TDA
  6. Time-delay Embeddings
  7. Data
  8. Polar Vortex Data
  9. Computation
  10. Persistent Homology
  11. Visualizing Persistent Homology
  12. Conclusion
  13. Persistent Homology
  14. Additional Figures

Figures (3)

  • Figure 1: Left: A stable polar vortex. Right: Warm air from the south disrupts the vortex butler_understanding_2021.
  • Figure 2: A time series plot of the persistence norms of the polar wind data (blue) compared to aggregate temperature values for Montana, USA, over the period $2015$--$2020$.
  • Figure 3: