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Hyperbolicity and Southern Hemisphere Persistent Synoptic Events
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  • Andrew Richard Axelsen,
  • Terence John O'Kane,
  • Courtney Quinn,
  • Andrew Bassom
Andrew Richard Axelsen
University of Tasmania

Corresponding Author:[email protected]

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Terence John O'Kane
Commonwealth Scientific and Industrial Research Organisation (CSIRO)
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Courtney Quinn
Commonwealth Scientific and Industrial Research Organisation
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Andrew Bassom
University of Tasmania
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Abstract

Predicting the occurrence of coherent blocking structures in synoptic weather systems remains a challenging problem that has taxed the numerical weather prediction community for decades. From a mathematical perspective, the underlying factor behind this difficulty is the so-called “loss of hyperbolicity” known to be linked with the alignment of dynamical vectors characterizing the growth and decay of flow instabilities. We introduce measures that utilize the close link between hyperbolicity, the alignment of Lyapunov vectors, and their associated growth and decay rates to characterize the dynamics and lifecycles of persistent synoptic events in the mid-troposphere of the Southern Hemisphere. These measures reveal a general loss of hyperbolicity that typically occurs during onset and decay of a given event, and a gain of hyperbolicity during the persistent mature phase. Facilitating this analysis in a typically high dimensional system first requires the extraction of the relevant observed coherent structures, i.e. feature space, and the generation of a reduced-order model for constructing the tangent space necessary for dynamical analysis. We achieve this through the combination of principal component analysis and a non-parametric, temporally regularized, vector auto-regressive clustering method. Analysis of the primary blocking sectors reveals hyperbolic dynamics that are consistent between metastable states and whose dynamics span the tangent subspace defined by the leading physical modes. The insights from this work are not only important for dynamical approaches applicable to high dimensional multi-scale systems, but are also of direct relevance to the development of modern operational ensemble numerical weather prediction systems.
10 Jul 2024Submitted to ESS Open Archive
14 Jul 2024Published in ESS Open Archive