Projected Shadowing-based Data Assimilation

TL;DR

This paper introduces a shadowing-based data assimilation algorithm leveraging time-dependent stable/unstable splitting, which improves state and parameter estimation in chaotic systems by utilizing Lyapunov exponents and vectors.

Contribution

It develops a novel shadowing refinement and synchronization method for data assimilation that adapts to partial observations and extends to parameter estimation.

Findings

Effective in Lorenz models for state estimation

Comparable or superior to existing variational methods

Handles partial and noisy observations well

Abstract

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on Assimilation in the Unstable Subspace (AUS) and Pseudo-orbit Data Assimilation (PDA). The algorithm utilizes time dependent projections onto the non-stable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.