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.