Model Error in Data Assimilation

TL;DR

This chapter explores the impact of model error, especially from unresolved scales, in data assimilation, discussing theoretical foundations, existing methods, and challenges in applying stochastic parameterizations and nonparametric approaches.

Contribution

It classifies and analyzes existing methods for handling model error, emphasizing stochastic parameterizations and providing theoretical justification for their effectiveness.

Findings

Stochastic parameterizations effectively mitigate model error in data assimilation.

Existing methods are classified into statistical and stochastic approaches.

Challenges in applying these methods to real-world problems are discussed.

Abstract

This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of model error from unresolved scales. In particular, connection to related subjects under different names in applied mathematics, such as the Mori-Zwanzig formalism and the averaging method, were discussed with the hope that the existing methods can be more accessible and eventually be used appropriately. We will classify existing methods into two groups: the statistical methods for those who directly estimate the low-order model error statistics; and the stochastic parameterizations for those who implicitly estimate all statistics by imposing stochastic models beyond the traditional unbiased white noise Gaussian processes. We will provide theory to justify why stochastic parameterization, as one of the main theme in this book, is an adequate tool for mitigating model error in data assimilation. Finally, we will also discuss challenges in lifting this approach in general applications and provide an alternative nonparametric approach.