Preprints
https://doi.org/10.5194/egusphere-2023-2168
https://doi.org/10.5194/egusphere-2023-2168
15 Nov 2023
 | 15 Nov 2023

Computation of covariant lyapunov vectors using data assimilation

Shashank Kumar Roy and Amit Apte

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.

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Shashank Kumar Roy and Amit Apte

Status: closed (peer review stopped)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2168', Anonymous Referee #1, 10 Dec 2023
    • AC1: 'Comment on egusphere-2023-2168', Shashank Kumar Roy, 02 Jun 2024
  • RC2: 'Comment on egusphere-2023-2168', Anonymous Referee #2, 15 Dec 2023
    • AC1: 'Comment on egusphere-2023-2168', Shashank Kumar Roy, 02 Jun 2024
  • AC1: 'Comment on egusphere-2023-2168', Shashank Kumar Roy, 02 Jun 2024

Status: closed (peer review stopped)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2168', Anonymous Referee #1, 10 Dec 2023
    • AC1: 'Comment on egusphere-2023-2168', Shashank Kumar Roy, 02 Jun 2024
  • RC2: 'Comment on egusphere-2023-2168', Anonymous Referee #2, 15 Dec 2023
    • AC1: 'Comment on egusphere-2023-2168', Shashank Kumar Roy, 02 Jun 2024
  • AC1: 'Comment on egusphere-2023-2168', Shashank Kumar Roy, 02 Jun 2024
Shashank Kumar Roy and Amit Apte

Model code and software

Mr-Markovian/Reconstruct_CLV_via_enkf: Published version of the code Shashank Kumar Roy https://zenodo.org/record/8396549

Shashank Kumar Roy and Amit Apte

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Short summary
We focus on the computation of Lyapunov vectors for dynamical systems using partial and noisy observations using data assimilation. We study how the errors in the approximated LVs are implicitly affected by the errors in the estimated trajectory. Our results reveal the difference in sensitivity of the individual vectors in low and high dimensions. Additionally, we find that the subspaces defined by the LVs computed from the approximate trajectory are less sensitive than the individual vectors.