Data Assimilation for the Geosciences: From Theory to Application, Second Edition brings together all of the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place. It includes practical exercises enabling readers to apply theory in both a theoretical formulation as well as teach them how to code the theory with toy problems to verify their understanding. It also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to land surface, the atmosphere, ocean and other geophysical situations. The second edition of Data Assimilation for the Geosciences has been revised with up to date research that is going on in data assimilation, as well as how to apply the techniques. The new edition features an introduction of how machine learning and artificial intelligence are interfacing and aiding data assimilation. In addition to appealing to students and researchers across the geosciences, this now also appeals to new students and scientists in the field of data assimilation as it will now have even more information on the techniques, research, and applications, consolidated into one source.
Table of Contents
1. Introduction2. Overview of Linear Algebra
3. Univariate Distribution Theory
4. Multivariate Distribution Theory
5. Introduction to Calculus of Variation
6. Introduction to Control Theory
7. Optimal Control Theory
8. Numerical Solutions to Initial Value Problems
9. Numerical Solutions to Boundary Value Problems
10. Introduction to Semi-Lagrangian Advection Methods
11. Introduction to Finite Element Modeling
12. Numerical Modeling on the Sphere
13. Tangent Linear Modeling and Adjoints
14. Observations
15. Non-variational Sequential Data Assimilation Methods
16. Variational Data Assimilation
17. Subcomponents of Variational Data Assimilation
18. Observation Space Variational Data Assimilation Methods
19. Kalman Filter and Smoother
20. Ensemble-Based Data Assimilation
21. Non-Gaussian Variational Data Assimilation
22. Markov Chain Monte Carlo and Particle Filter Methods
23. Machine Learning Artificial Intelligence with Data Assimilation
24. Applications of Data Assimilation in the Geosciences
25. Solutions to Select Exercise
