Lyapunov Analysis of Strange Pseudohyperbolic Attractors: Angles Between Tangent Subspaces, Local Volume Expansion and Contraction

Kuptsov, Pavel V.; Кузнецов, С. П.

doi:10.1134/s1560354718070079

Cited by 21 publications

(26 citation statements)

References 38 publications

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“…Nonetheless, the system does not have regions where we have return of skill: if, instead we plot the daily averages of the largest covariant or backward FTLE we find a broad distribution with exclusively positive support (not shown). Note that the problem of assessing whether a system is uniformly hyperbolic is usually addressed by studying whether the unstable and stable tangent spaces have tangencies (see e.g.. Ginelli et al 2007;Kuptsov and Kuznetsov 2018). We will address this matter using the formalism of UPOs, see Sect.…”

Section: Dynamical Heterogeneity Of the Attractormentioning

confidence: 99%

A New Mathematical Framework for Atmospheric Blocking Events

Lucarini

2021

Preprint

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We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events, which are associated with low frequency, large scale waves in the atmosphere. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with conditions of anomalously high instability of the atmosphere. Additionally, the lifetime of a blocking is positively correlated with the intensity of such an anomaly, against intuition. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking, while a relative increase of predictability is found in the mature phase, while the opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. We associate blockings to a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor of the system. The UPOs differ substantially in terms of instability, which explains the diversity of the atmosphere in terms predictability. The UPOs associated to blockings are indeed anomalously unstable, which leads to them being rarely visited. The onset of a blocking takes place when the trajectory of the system hops into the neighbourhood of one of these special UPOs. The decay takes place when the trajectory hops back to the neighbourhood of usual, less unstable UPOs associated with zonal flow. This justifies the classical Markov chains-based analysis of transitions between weather regimes. The existence of UPOs differing in the dimensionality of their unstable manifold indicates a very strong violation of hyperbolicity in the model, which leads to a lack of structural stability. We propose that this is could be a generic feature of atmospheric models and might be a fundamental cause behind difficulties in representing blockings for the current climate and uncertainties in predicting how their statistics will change as a result of climate change. References: V. Lucarini, A. Gritsun, A. A new mathematical framework for atmospheric blocking events. Climate Dynamics 54, 575&#8211;598 (2020).&#160;https://doi.org/10.1007/s00382-019-05018-2 M. Ghil, V. Lucarini, The Physics of Climate Variability and Climate, Rev. Modern Physics, 92, 035002 (2020). https://link.aps.org/doi/10.1103/RevModPhys.92.035002 &#160; S. Schubert, V. Lucarini, Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors. Q. J. R. Meteorol. Soc. 142, 2143-2158 (2016).&#160;https://doi.org/10.1002/qj.2808

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Section: Dynamical Heterogeneity Of the Attractormentioning

confidence: 99%

A New Mathematical Framework for Atmospheric Blocking Events

Lucarini

2021

Preprint

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“…Note that the problem of assessing whether a system is uniformly hyperbolic is usually addressed by studying whether the unstable and stable tangent spaces have tangencies (see e.g.. Ginelli et al 2007;Kuptsov and Kuznetsov 2018). We will address this matter using the formalism of UPOs, see Sect We can better appreciate how heterogeneous the tangent space is by noting -see Fig.…”

Section: Dynamical Heterogeneity Of the Attractormentioning

confidence: 99%

A new mathematical framework for atmospheric blocking events

Lucarini

Gritsun

2019

Clim Dyn

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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.

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“…While the FTCLEs give the relative growth and decay rates of tangent vectors to the subspaces, the angle between the CLVs (otherwise known as alignment) gives an idea of transversality of the subspaces (Kuptsov and Kuznetsov 2018). High alignment of CLVs, or a vanishing angle between subspaces, has been suggested to be an indicator of transitions and catastrophic events (Beims and Gallas 2016;Sharafi et al 2017).…”

Section: B Alignment Of Clvsmentioning

confidence: 99%

“…When applied to the atmospheric circulation in the Atlantic sector, the FEM-BV-VAR method yields a set of states consistent with differing phases of the NAO. By treating the clustering as a non-smooth linear delay system, it is possible to directly compute the Lyapunov spectrum and CLVs of the model, as well as dynamical indicators of transitions such as increased finite-time instability (Norwood et al 2013) and alignment of CLVs (Beims and Gallas 2016;Sharafi et al 2017;Kuptsov and Kuznetsov 2018). The relationship between these dynamical quantities and the particular regime transitions can then be compared to assess whether the reduced-order model exhibits non-trivial dynamics.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a reduced model for the North Atlantic Oscillation

Quinn¹,

Harries²,

O’Kane³

2020

Preprint

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We apply a regularized vector autoregressive clustering technique to identify recurrent and persistent states of atmospheric circulation patterns in the North Atlantic sector (110 • W-0 • E, • N-90 • N) associated with the Atlantic Ridge (AR) and the North Atlantic Oscillation (NAO). The technique additionally provides the temporal behavior in terms of a time-dependent switching between the respective cluster states. Using the resulting cluster affiliations for each day, we set the switchingsequence a priori to define a non-smooth linear delayed map that we use to analyze the dynamics associated with the resulting cluster-based model. We compute the time-dependent covariant Lyapunov vectors (CLVs) and their associated finite-time covariant Lyapunov exponents (FTCLEs), with a particular focus on indicators of transitions between the states. We find that the window chosen to compute the CLVs acts as a filter on the dynamics. For short windows, CLV alignment and changes in FTCLE growth rates are indicative of individual transitions between persistent states. For long windows, we observe an emergent annual signal manifest in the alignment of the CLVs characteristic of the observed seasonality in the respective NAO and AR indices. Analysis of the average finite-time dimension reveals the NAO − as the most unstable state relative to the NAO + , with persistent AR states largely stable.

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Lyapunov Analysis of Strange Pseudohyperbolic Attractors: Angles Between Tangent Subspaces, Local Volume Expansion and Contraction

Cited by 21 publications

References 38 publications

A New Mathematical Framework for Atmospheric Blocking Events

A New Mathematical Framework for Atmospheric Blocking Events

A new mathematical framework for atmospheric blocking events

Dynamical analysis of a reduced model for the North Atlantic Oscillation

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