A framework for interpreting regularized state estimation

TL;DR

This paper presents a novel framework for long-term 4D-Var data assimilation that interprets the problem as controlling unstable modes in coupled chaotic systems, improving stability and applicability.

Contribution

It introduces a new interpretation of 4D-Var as managing unstable modes via synchronized chaotic systems, enabling extended assimilation periods.

Findings

Stable tangent linear and adjoint models can be achieved.

The approach effectively tracks persistent signals in ocean models.

Method extends the feasible period for 4D-Var assimilation.

Abstract

Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled by adjusting initial conditions to bring all stable modes closer to observations and by using a continuous guide to direct unstable modes toward a reference time series. This interpretation provides a consistent and effective procedure for solving problems of long-term state estimation. By applying this approach to an ocean general circulation model with a parameterized vertical diffusion procedure, it is demonstrated that tangent linear and adjoint models in this framework should have no unstable modes and hence be suitable for tracking persistent signals. This methodology is widely applicable to extend the assimilation period in 4D-Var.