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.

Regime dependencies and Granger causal relationships between tropical and extratropical teleconnections are inferred using Bayesian structure learning. Using ERA5 data, an examination of the differences between the learned causal structures during particular phases of the Interdecadal Pacific Oscillation (IPO) are used to infer the role of the background state on interactions between the major climate teleconnections and in particular the dependence of the ENSO autocorrelation on the phase of the background state, and the role of the Madden Julian Oscillation as being key to link the extratropical tropospheric modes (PNA, NAO) and the equatorial surface ocean forced convective modes (IOD, ENSO). These relationships are presented as posterior distributions over possible graphical representations in terms of Dynamic Bayesian Network (DBN) models constructed from time series of empirical climate indices. General circulation model simulations are used to sample from a larger distribution of possible IPO periods and their phase dependencies.

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.

A document by Terence John O'Kane. Click on the document to view its contents.

An examination of the dynamics of the middle atmosphere as reconstructed in the NASA Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) reveals the formation of large scale three dimensional vortices in the tropical stratosphere following both the vernal and autumnal equinoxes at times where the jet associated with the westerly phase of the semi-annual oscillation (SAO) is maximal and extratropical influences from planetary waves are weakest. An empirical orthogonal function (EOF) analysis of the second matrix invariant of the velocity gradient tensor applied to the shear zones about the SAO reveals statistically stationary wave-5 vortex structures that span more than 3200km in length and up to 40km in the vertical. Eliassen-Palm fluxes suggests the vortices are maintained by a combination of local (shear zones) and remote (vertically propagating tropical) sources of momentum. These large scale coherent features appear to be unique to the stratopause.

We apply a Bayesian structure learning approach to study interactions between global teleconnection modes, illustrating its use as a framework for developing process-based diagnostics with which to evaluate climate models. Homogeneous dynamic Bayesian network models are constructed for time series of empirical indices diagnosing the activity of major tropical, Northern and Southern Hemisphere modes in the NCEP/NCAR and JRA-55 reanalyses. The resulting probabilistic graphical models are comparable to Granger causal analyses that have recently been advocated. Reversible jump Markov Chain Monte Carlo is employed to provide a quantification of the uncertainty associated with the selection of a single network structure. In general, the models fitted from the NCEP/NCAR reanalysis and the JRA-55 reanalysis are found to exhibit broad agreement in terms of associations for which there is high posterior confidence. Differences between the two reanalyses are found that involve modes for which known biases are present or that may be attributed to seasonal effects, as well as for features that, while present in point estimates, have low overall posterior mass. We argue that the ability to incorporate such measures of confidence in structural features is a significant advantage provided by the Bayesian approach, as point estimates alone may understate the relevant uncertainties and yield less informative measures of differences between products when network-based approaches are used for model evaluation.