Data assimilation for the geosciences : from theory to application Steven J Fletcher

Includes bibliographical references and index.

Chapter 1. Introduction -- Chapter 2. Overview of Linear Algebra -- Chapter 3. Univariate Distribution Theory -- Chapter 4. Multivariate Distribution Theory -- Chapter 5. Introduction to Calculus of Variation -- Chapter 6. Introduction to Control Theory -- Chapter 7. Optimal Control Theory -- Chapter 8. Numerical Solutions to Initial Value Problems -- Chapter 9. Numerical Solutions to Boundary Problems -- Chapter 10. Introduction to Semi-Langrangian Advection Methods -- Chapter 11. Introduction to Finite Element Modeling -- Chapter 12. Numerical Modeling of the Sphere -- Chapter 13. Tangent Linear Modeling and Adjoints -- Chapter 14. Observations -- Chapter 15. Non-variational Sequential Data Assimilation Methods -- Chapter 16. Variational Data Assimilation -- Chapter 17. Subcomponents of Variational Data Assimilation -- Chapter 18. Observation of Space Variation Data Assimilation Methods -- Chapter 19. Kalman Filter and Smoother -- Chapter 20. Ensemble-Based Data Asssimilation -- Chapter 21. Non-Gaussian Variational Data Assimilation -- Chapter 22. Markov Chain Monte Carlo and Particle Filter Methods -- Chapter 23. Applications of Data Asssimilation in the Geosciences -- Chapter 24. Solutions to Select Exercise -- Bibliography -- Index.