Effective Actions for Ensemble Data Assimilation

TL;DR

This paper introduces effective actions and equations of motion for ensemble data assimilation, incorporating measurement errors and correlations to improve the estimation of dynamical system trajectories.

Contribution

It develops a novel approach using statistical physics methods to derive effective actions for ensemble data assimilation with error and correlation considerations.

Findings

Incorporates measurement error correlations naturally

Provides equations of motion for mean orbits in data assimilation

Enhances understanding of uncertainty in dynamical models

Abstract

Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in statistical physics, we present effective actions and equations of motion for the mean orbits associ- ated with the temporal development of a dynamical model when it has errors, there is uncertainty in its initial state, and it receives informa- tion from measurements. If there are correlations among errors in the measurements they are naturally included in this approach.