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Dynamic Data Assimilation

Dynamic Data Assimilation
A Least Squares Approach


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521851558

£ 160.00

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About the Authors
  • Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about the system's behaviour. The topic has assumed increasing importance in fields such as numerical weather prediction where conscientious efforts are being made to extend the term of reliable weather forecasts beyond the few days that are presently feasible. 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. Thus Part I is a broad introduction to the history, development and philosophy of data assimilation, illustrated by examples; Part II considers the classical, static approaches, both linear and nonlinear; and Part III describes computational techniques. Parts IV to VII are concerned with how statistical and dynamic ideas can be incorporated into the classical framework. Key themes covered here include estimation theory, stochastic and dynamic models, and sequential filtering. The final part addresses the predictability of dynamical systems. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints.

    • A comprehensive and self-contained introduction to data assimilation, with background material available from
    • 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
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    Product details

    • Date Published: August 2006
    • format: Hardback
    • isbn: 9780521851558
    • length: 680 pages
    • dimensions: 239 x 165 x 39 mm
    • weight: 1.1kg
    • contains: 29 tables 208 exercises
    • availability: Available
  • Table of 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. 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

  • Resources for

    Dynamic Data Assimilation

    John M. Lewis, S. Lakshmivarahan, Sudarshan Dhall

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  • Authors

    John M. Lewis, National Severe Storms Laboratory, Oklahoma
    John M. Lewis is a Research Scientist at the National Severe Storms Laboratory in Oklahoma, and the Desert Research Institute in Nevada.

    S. Lakshmivarahan, University of Oklahoma
    S. Lakshmivarahan is a George Lynn Cross Research Professor at the School of Computer Science, University of Oklahoma.

    Sudarshan Dhall, University of Oklahoma
    Sudarshan K. Dhall is a Professor at the School of Computer Science, University of Oklahoma.

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