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. Designed as a basic one-stop reference for graduate students and researchers, the book is based on graduate courses taught over a decade to mathematicians, scientists, and engineers. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints. Accompanying refresher material - in many areas of mathematics - is available from www.cambridge.org/0521851556.…mehr
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. Designed as a basic one-stop reference for graduate students and researchers, the book is based on graduate courses taught over a decade to mathematicians, scientists, and engineers. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints. Accompanying refresher material - in many areas of mathematics - is available from www.cambridge.org/0521851556.
John M. Lewis is a Research Scientist at the National Severe Storms Laboratory in Oklahoma, and the Desert Research Institute in Nevada.
Inhaltsangabe
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. Optimisation: 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.
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. Optimisation: 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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