Exploring the Lyapunov instability properties of high-dimensional
atmospheric and climate models

Cruz, Lesley De; Schubert, Sebastian; Demaeyer, Jonathan; Lucarini, Valerio; Vannitsem, Stéphane

doi:10.5194/npg-2017-76

Cited by 7 publications

(15 citation statements)

References 89 publications

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“…In Fig. 5a, in agreement with previous investigations performed using both more complex (De Cruz et al 2018) and simpler (Vannitsem and Lucarini 2016) models, we find that the daily value of the first FTLE fluctuates substantially along the trajectory, with mean value corresponding to the asymptotic value for the first LE given in Table 1. Note that, by construction, the first FTLEs is the same whether we use the covariant or the backward definition.…”

Section: Dynamical Heterogeneity Of the Attractorsupporting

confidence: 90%

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 Attractorsupporting

confidence: 90%

A New Mathematical Framework for Atmospheric Blocking Events

Lucarini

2021

Preprint

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Section: Dynamical Heterogeneity Of the Attractorsupporting

confidence: 90%

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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“…The longer time step allows faster integration, which is useful for ensemble experiments. De Cruz et al () adopted a time step of 0.2 time units for even higher‐resolution versions of the model. Our experiments indicate that the general behavior of the model, for example, as characterized by the Lyapunov spectrum, does not significantly change within this parameter range.…”

Section: Methodsmentioning

confidence: 99%

“…The coupling between the two components includes momentum transfer (wind forcing), as well as radiative and heat exchanges. Examinations of the Lyapunov spectrum of the coupled configuration of the MAOOAM were conducted by Vannitsem et al (), Vannitsem and Lucarini (), Vannitsem (), and De Cruz et al (). Vannitsem and Lucarini () also examined MAOOAM's covariant Lyapunov vectors.…”

Section: Introductionmentioning

confidence: 99%

Strongly Coupled Data Assimilation in Multiscale Media: Experiments Using a Quasi‐Geostrophic Coupled Model

Penny

Bach

Bhargava

et al. 2019

J Adv Model Earth Syst

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Strongly coupled data assimilation (SCDA) views the Earth as one unified system. This allows observations to have an instantaneous impact across boundaries such as the air‐sea interface when estimating the state of each individual component. Operational prediction centers are moving toward Earth system modeling for all forecast timescales, ranging from days to months. However, there have been few studies that examine fundamental aspects of SCDA and the transition from traditional approaches that apply data assimilation only to a single component, whether forecasts were derived from a coupled model or an uncoupled forced model. The SCDA approach is examined here in detail using numerical experiments with a simple coupled atmosphere‐ocean quasi‐geostrophic model. The impact of coupling is explored with respect to its impact on the Lyapunov spectrum and on data assimilation system stability. Different data assimilation methods are compared within the context of SCDA, including the 3‐D and 4‐D Variational methods, the ensemble Kalman filter, and the hybrid gain method. The impact of observing system coverage is also investigated. We find that SCDA is generally superior to weakly coupled or uncoupled approaches. Dynamically defined background error covariance estimates are essential for SCDA to achieve an accurate coupled state estimate as the observing system becomes sparser. As a clarification of seemingly contradictory findings from previous studies, it is shown that ocean observations can adequately constrain atmospheric state estimates provided that the analysis‐observing frequency is sufficiently high and the ensemble size determining the background error covariance is sufficiently large.

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Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

Cited by 7 publications

References 89 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

Strongly Coupled Data Assimilation in Multiscale Media: Experiments Using a Quasi‐Geostrophic Coupled Model

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