Computation of covariant lyapunov vectors using data assimilation

TL;DR

This paper introduces a data assimilation-based method to compute covariant Lyapunov vectors from partial and noisy data, analyzing their sensitivity and stability relative to the true underlying system.

Contribution

It presents a novel approach combining data assimilation with Lyapunov vector computation and studies the sensitivity of these vectors to trajectory perturbations.

Findings

Approximate Lyapunov vectors' errors relate to trajectory perturbations.

Oseledets' subspaces are less sensitive than individual vectors.

Sensitivity analysis explains the errors in approximate vectors.

Abstract

Computing Lyapunov vectors from partial and noisy observations is a challenging problem. We propose a method using data assimilation to approximate the Lyapunov vectors using the estimate of the underlying trajectory obtained from the filter mean. We then extensively study the sensitivity of these approximate Lyapunov vectors and the corresponding Oseledets' subspaces to the perturbations in the underlying true trajectory. We demonstrate that this sensitivity is consistent with and helps explain the errors in the approximate Lyapunov vectors from the estimated trajectory of the filter. Using the idea of principal angles, we demonstrate that the Oseledets' subspaces defined by the LVs computed from the approximate trajectory are less sensitive than the individual vectors.