Logarithmic bred vectors in spatiotemporal chaos: structure and growth

Abstract

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth- rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector. This fact allows us to deduce a scaling law for the bred vector growth rate as a function of their amplitude. In addition, we relate growth rates with the spectrum of Lyapunov exponents corresponding to the most expanding directions. We illustrate our results with simulations of the Lorenz '96 model.

8 pages, 8 figures

References in corpus (3)

• Predictability: a way to characterize Complexity
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos
• Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices

Cited by in corpus (11)

• A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings
• Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model
• A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model
• Stochastic perturbations to dynamical systems: a response theory approach
• Ensemble Dynamics and Bred Vectors
• Lyapunov analysis of multiscale dynamics: The slow bundle of the two-scale Lorenz 96 model
• Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere
• Heterogeneity of the Attractor of the Lorenz '96 Model: Lyapunov Analysis, Unstable Periodic Orbits, and Shadowing Properties
• Maximizing the statistical diversity of an ensemble of bred vectors by using the geometric norm
• On finite-size Lyapunov exponents in multiscale systems
• Avalanches, Breathers and Flow Reversal in a Continuous Lorenz-96 Model