Hyperbolicity and Southern Hemisphere Persistent Synoptic Events

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. 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 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 high-dimensional system first requires the extraction of the relevant observed coherent structures, 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. We show that these diverse synoptic features are manifest via common spatially dependent attractors as determined by tangent space dynamics. Our results are not only important for dynamical approaches applicable to high-dimensional multi-scale systems, but are also relevant for the development of modern operational ensemble numerical weather prediction systems.