# Data Assimilation

## The Ensemble Kalman Filter

• GeirĀ Evensen
Book

1. Front Matter
Pages i-xxi
2. Pages 1-4
3. Pages 5-12
4. Pages 13-25
5. Pages 27-45
6. Pages 47-69
7. Pages 71-93
8. Pages 95-101
9. Pages 103-117
10. Pages 119-137
11. Pages 139-155
12. Pages 157-174
13. Pages 175-194
14. Pages 195-205
15. Pages 207-229
16. Pages 231-237
17. Pages 239-248
18. Back Matter
Pages 249-279

### Introduction

Data Assimilation comprehensively covers data assimilation and inverse methods, including both traditional state estimation and parameter estimation. This text and reference focuses on various popular data assimilation methods, such as weak and strong constraint variational methods and ensemble filters and smoothers. It is demonstrated how the different methods can be derived from a common theoretical basis, as well as how they differ and/or are related to each other, and which properties characterize them, using several examples.

It presents the mathematical framework and derivations in a way which is common for any discipline where dynamics is merged with measurements. The mathematics level is modest, although it requires knowledge of basic spatial statistics, Bayesian statistics, and calculus of variations. Readers will also appreciate the introduction to the mathematical methods used and detailed derivations, which should be easy to follow, are given throughout the book. The codes used in several of the data assimilation experiments are available on a web page.

The focus on ensemble methods, such as the ensemble Kalman filter and smoother, also makes it a solid reference to the derivation, implementation and application of such techniques. Much new material, in particular related to the formulation and solution of combined parameter and state estimation problems and the general properties of the ensemble algorithms, is available here for the first time.

### Keywords

Data assimilation Derivation Ensemble Kalman Filter Ensemble Kalman Smoother algorithm algorithms calculus inverse methods mathematics model optimization parameter estimation statistics

#### Authors and affiliations

• GeirĀ Evensen
• 1
• 2
1. 1.Hydro Research Centre, BergenBergenNorway
2. 2.Mohn-Sverdrup Center for Global Ocean Studies and Operational Oceanography at Nansen Environmental and Remote Sensing CenterBergenNorway