Description
Data Assimilation for the Geosciences: From Theory to Application brings together all of the mathematical,statistical, and probability background knowledge needed to formulate data assimilation systems in one place. It includes practical exercises for understanding theoretical formulation and presents some aspects of coding the theory with a toy problem.The book also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to the atmosphere, oceans, as well as the land surface and other geophysical situations. It offers a comprehensive presentation of the subject, from basic principles to advanced methods, such as Particle Filters and Markov-Chain Monte-Carlo methods. Additionally, Data Assimilation for the Geosciences: From Theory to Application covers the applications of data assimilation techniques in various disciplines of the geosciences, making the book useful to students, teachers, and research scientists.- Includes practical exercises, enabling readers to apply concepts in a theoretical formulation- Offers explanations for how to code certain parts of the theory- Presents a step-by-step guide on how, and why, data assimilation works and can be used
Table of Contents
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. Applications of Data Assimilation in the Geosciences24. Solutions to Select Exercise
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