Shadowing-based data assimilation method for partially observed models

TL;DR

This paper introduces a shadowing-based data assimilation algorithm for partially observed dynamical systems, utilizing a regularized Gauss-Newton method, with proven convergence and demonstrated effectiveness on Lorenz models.

Contribution

It develops a new shadowing refinement algorithm for data assimilation that handles partial observations and proves its local convergence properties.

Findings

Algorithm converges to the solution manifold.

Preconditioning improves orbit recovery accuracy.

Method compares favorably with existing variational and shadowing techniques.

Abstract

In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on regularized Gauss-Newton method. We prove local convergence to the solution manifold and provide a lower bound on the algorithmic time step. We use numerical experiments with the Lorenz 63 and Lorenz 96 models to illustrate convergence of the algorithm and show that the results compare favourably with a variational technique (weak-constraint four-dimensional variational method) and a shadowing technique (pseudo-orbit data assimilation). Numerical experiments show that a preconditioner chosen based on a cost function allows the algorithm to find an orbit of the dynamical system in the vicinity of the true solution.