Conditions for successful data assimilation

TL;DR

This paper investigates the conditions under which data assimilation is successful, emphasizing the importance of effective problem dimension and analyzing various algorithms like particle filters and variational methods.

Contribution

It introduces criteria based on effective dimension for successful data assimilation and compares the capabilities of particle filters and variational methods.

Findings

Effective dimension influences data assimilation success.

Well-designed particle filters can solve many data assimilation problems.

Variational methods succeed under similar conditions to particle filters.

Abstract

We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically reasonable problems it can be moderate even when the number of variables is huge. We then analyze several data assimilation algorithms, including particle filters and variational methods. We show that well-designed particle filters can solve most of those data assimilation problems that can be solved in principle, and compare the conditions under which variational methods can succeed to the conditions required of particle filters. We also discuss the limitations of our analysis.