Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model

Carlu, M., Ginelli, F., Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 and Politi, A. (2019) Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model. Nonlinear Processes in Geophysics, 26 (2). pp. 73-89. doi: 10.5194/npg-26-73-2019

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/83568
Identification Number/DOI	10.5194/npg-26-73-2019
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE)
Publisher	EGU
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