Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to make predictions about how a complex physical system will behave. This book is designed to be a basic one-stop reference for graduate students and researchers. It is based on graduate courses taught over a decade to mathematicians, scientists, and engineers, and its modular structure accommodates the various audience requirements. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints. Computation is encouraged: algorithms are liberally scattered throughout the text. Accompanying refresher material - in many areas of mathematics including vector spaces, optimization and probability theory - will be available from www.cambridge.org/0521851556. The book ends with a comprehensive bibliography.
• A comprehensive and self-contained introduction to data assimilation, with background material available from www.cambridge.org/0521851556 • A wide spectrum of scientific views of data assimilation including problems from atmospheric chemistry, oceanography, astronomy, fluid dynamics and meteorology • Rich set of problems, with instructive hints, at the end of each chapter
Contents
1. Synopsis; 2. Pathways into data assimilation: illustrative examples; 3. Applications; 4. Brief history of data assimilation; 5. Linear least squares estimation: method of normal equations; 6. A geometric view: projection and invariance; 7. Nonlinear least squares estimation; 8. Recursive least squares estimation; 9. Matrix methods; 10. Optimization: steepest descent method; 11. Conjugate direction/gradient methods; 12. Newton and quasi-Newton methods; 13. Principles of statistical estimation; 14. Statistical least squares estimation; 15. Maximum likelihood method; 16. Bayesian estimation method; 17. From Gauss to Kalman: sequential, linear minimum variance estimation; 18. Data assimilation-static models: concepts and formulation; 19. Classical algorithms for data assimilation; 20. 3DVAR - a Bayesian formulation; 21. Spatial digital filters; 22. Dynamical data assimilation: the straight line problem; 23. First-order adjoint method: linear dynamics; 24. First-order adjoint method: nonlinear dynamics; 25. Second-order adjoint method; 26. The ADVAR problem: a statistical and a recursive view; 27. Linear filtering - Part I: Kalman filter; 28. Linear filtering-part II; 29. Nonlinear filtering; 30. Reduced rank filters; 31. Predictability: a stochastic view; 32. Predictability: a deterministic view; Bibliography; Index.
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