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.

1. Introduction2. Overview of Linear Algebra3. Univariate Distribution Theory4. Multivariate Distribution Theory5. Introduction to Calculus of Variation6. Introduction to Control Theory7. Optimal Control Theory8. Numerical Solutions to Initial Value Problems9. Numerical Solutions to Boundary Value Problems10. Introduction to Semi-Lagrangian Advection Methods11. Introduction to Finite Element Modeling12. Numerical Modeling on the Sphere13. Tangent Linear Modeling and Adjoints14. Observations15. Non-variational Sequential Data Assimilation Methods16. Variational Data Assimilation17. Subcomponents of Variational Data Assimilation18. Observation Space Variational Data Assimilation Methods19. Kalman Filter and Smoother20. Ensemble-Based Data Assimilation21. Non-Gaussian Variational Data Assimilation22. Markov Chain Monte Carlo and Particle Filter Methods23. Machine Learning Artificial Intelligence with Data Assimilation24. Applications of Data Assimilation in the Geosciences25. Solutions to Select Exercise