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.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Shashank Kumar Roy and Amit Apte

Status: final response (author comments only)

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
  • RC2: 'Comment on egusphere-2023-2168', Anonymous Referee #2, 15 Dec 2023
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

Viewed

Total article views: 187 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
121 54 12 187 11 10
  • HTML: 121
  • PDF: 54
  • XML: 12
  • Total: 187
  • BibTeX: 11
  • EndNote: 10
Views and downloads (calculated since 15 Nov 2023)
Cumulative views and downloads (calculated since 15 Nov 2023)

Viewed (geographical distribution)

Total article views: 187 (including HTML, PDF, and XML) Thereof 187 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 
Latest update: 18 May 2024
Download
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.