Lyapunov analysis of multiscale dynamics

the slow bundle of the two-scale Lorenz 96 model

Mallory Carlu (Corresponding Author), Francesco Ginelli, Valerio Lucarini, Antonio Politi

Research output: Contribution to journalArticle

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Abstract

We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models.
Original languageEnglish
Pages (from-to)73-89
Number of pages17
JournalNonlinear Processes in Geophysics
Volume26
Issue number2
DOIs
Publication statusPublished - 7 May 2019

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degrees of freedom
ensemble forecasting
Climate models
climate models
assimilation
Prisms
tangents
weather
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forecasting
prisms
set theory
climate modeling
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timescale
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Lyapunov analysis of multiscale dynamics : the slow bundle of the two-scale Lorenz 96 model. / Carlu, Mallory (Corresponding Author); Ginelli, Francesco; Lucarini, Valerio; Politi, Antonio.

In: Nonlinear Processes in Geophysics, Vol. 26, No. 2, 07.05.2019, p. 73-89.

Research output: Contribution to journalArticle

Carlu, Mallory ; Ginelli, Francesco ; Lucarini, Valerio ; Politi, Antonio. / Lyapunov analysis of multiscale dynamics : the slow bundle of the two-scale Lorenz 96 model. In: Nonlinear Processes in Geophysics. 2019 ; Vol. 26, No. 2. pp. 73-89.
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abstract = "We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models.",
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