SuPerPoV: Score and evolution of the stratospheric polar vortex via persistent homology

TL;DR

This paper addresses the lack of a robust, threshold-free definition for the stratospheric polar vortex and SSWs by introducing SuPerPoV, which uses persistent homology and a superlevel-set filtration on geopotential height to derive two interpretable scores: Split and Displacement. The method computes the two longest $H_1$-lifespans from grid-to-circular coordinate representations, yielding a threshold-free, continuous measure of vortex state that interpolates previous classifications. SuPerPoV is demonstrated on ERA5 NH winter data across 10, 50, and 100 hPa, with open-source code and clear interpretation of outputs, including visualizations and comparisons with historical definitions. The work advances the study of polar vortex dynamics by providing an objective, evolutive framework that can reveal precursors to SSWs and facilitate exploration of vertical coupling in the stratosphere, while remaining accessible to non-experts.

Abstract

Classifying the stratospheric polar vortex provides predictability for surface weather on extended-range timescales definitions of these events proposed in over 60 years of study depend on empirically chosen parameters and yield different results when one of them changes. Moreover, as previous definitions are based on static thresholds, it is not straightforward to use them to study the spatiotemporal evolution of the vortexe introduce SuPerPoV, a score system that computes displacement and split ratiossing tools from applied topology. The computation is entirely threshold-free, open source, and does not require familiarity with applied topology. The scores generally recovers previous definitions and are output for a user-defined number of days, thus showing the evolution of the event. SuPerPoV offers a paradigm shift in the study of the polar vortex, hopefully bringing a deeper understanding of the polar vortex and related extreme events, such as sudden stratospheric warmings.

Figures (6)

• Figure 1: Grid (top row) and cylindrical (bottom row) plots for a normal vortex (a), a displaced one (b), and a split one (c). The red line/dot denotes the North Pole, and the green lines in the grid plot are identified in the cylindrical one.
• Figure 2: A visualization of superlevel-set filtration on the grid (top row) and cylindrical (bottom row) plot for the date 1965-12-23. The value at the bottom of each column is the height we have reached going downward (so, everything above it is included).
• Figure 3: SuPerPoV output of the 1987-12-5, with 5 days prior and 6 days after. Grid and cylindrical plots of the day in the top left corner, lifespans of the two longest $H_1$ for each day in the bottom left, split and displacement scores on the right. In the latter two, red points denote negative zonal-mean wind speed. In all plots, the chosen input day is highlighted in bold.
• Figure 4: SuPerPoV scores of the whole winter 1976-1977. The red points represent a negative zonal-mean wind speed, to facilitate the comparison with other methods.
• Figure 5: Scatter plot with the displacement (horizontal axis) and split (vertical axis) score, where each point is a collection of days where at least one of the definitions from the literature finds a major event occurring. "Multi" stands for days that were classified as major events by multiple definitions.