A new mathematical framework for atmospheric blocking events

Abstract

We use a simple yet Earth-like hemispheric atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated with conditions featuring anomalously high instability. Longer-lived blockings are very rare and have typically higher instability. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking event, while a relative increase of predictability is found in the mature phase. The opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. Blockings are realised when the trajectory of the system is in the neighbourhood of a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor the system. UPOs corresponding to blockings have, indeed, a higher degree of instability compared to UPOs associated with zonal flow. Our results provide a rigorous justification for the classical Markov chains-based analysis of transitions between weather regimes. The analysis of UPOs elucidates that the model features a very severe violation of hyperbolicity, due to the presence of a substantial variability in the number of unstable dimensions, which explains why atmospheric states can differ a lot in term of their predictability. The resulting lack of robustness might be a fundamental cause contributing to the difficulty in representing blockings in numerical models and in predicting how their statistics will change as a result of climate change. This corresponds to fundamental issues limiting our ability to construct very accurate numerical models of the atmosphere, in term of predictability of the both the first and of the second kind in the sense of Lorenz.

On Temporal Scale Separation in Coupled Data Assimilation with the Ensemble Kalman Filter

“…Along these lines, using an idealised multi-scale system made up of coupled copies of the Lorenz 3-variables model, the authors of [50] demonstrate that weakly stable directions are needed in situations of strong nonlinear dynamics and intermittent error growth. Similarly, the authors of [39] have suggested that the variability in the number of unstable modes associated to unstable periodic orbits in a simple Earth system model, can explain the observed very different predictability of individual atmospheric blocking events, and have argued that DA must thus cautiously incorporate stable modes too.…”

The physics of climate variability and climate change

“…Certain spatial features of the phases of this mode do present striking similarities to the blocked and zonal flows that appear not just as the two stable equilibria in the highly idealized model of Charney and DeVore (1979), but also as unstable, though long-lived, patterns in much more realistic models, like the three-level, quasigeostrophic (QG3) model originally formulated by Marshall and Molteni (1993). The latter model is still widely used to study the nonlinear dynamics of large-scale, midlatitude atmospheric flows (e.g., Kondrashov et al, 2004;Lucarini and Gritsun, 2020).…”

“…This coarse-graining of the LFV's phase space and Markov chain representation of the dynamics continues to inform current efforts at understanding what atmospheric phenomena can be predicted beyond 10-15 days and how. Recently, analyses based on dynamical systems theory have associated blocked flow configurations with higher instability of the atmosphere as a whole (Faranda et al, 2017;Lucarini and Gritsun, 2020;Schubert and Lucarini, 2016), as predicted by Legras and Ghil (1985).…”

“…Furthermore, multiple regimes and intraseasonal oscillations can coexist in a two-layer model on the sphere within the scenario of "chaotic itinerancy" Kimoto, 1996, 1997). Lucarini and Gritsun (2020) observed that blockings occur when the system's trajectory is in the neighborhood of a specific class of unstable periodic orbits (UPOs). UPOs in general are natural modes of variability that cover a chaotic system's attractor (Cvitanović, 1988;Cvitanovíc and Eckhardt, 1991).…”

Detecting Regime Transitions in Time Series Using Dynamic Mode Decomposition

“…More recently methods from dynamical systems theory have been employed. In particular, covariant Lyapunov vectors and unstable periodic orbits were shown to capture blocking events [43,28]. More closely related to our approach of DMD, methods based on the transfer operator, the formal L 2 -adjoint of the Koopman operator, and the behaviour of its point spectrum were used to study transitions to individual blocking event [44].…”