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By John M. Lewis
By S. Lakshmivarahan
By Sudarshan Dhall
Publisher: Cambridge University Press
Print Publication Year:2006
Online Publication Date:December 2009
Online ISBN:9780511526480
Hardback ISBN:9780521851558
Book DOI: http://dx.doi.org/10.1017/CBO9780511526480
Subjects: Numerical analysis and computational science , Atmospheric Science and Meteorology
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.
Reviews:
pp. i-vi
pp. vii-xii
pp. xiii-xx
pp. xxi-xxii
PART 1 - GENESIS OF DATA ASSIMILATION: Read PDF
pp. 1-2
pp. 3-26
2 - Pathways into data assimilation: illustrative examples: Read PDF
pp. 27-50
pp. 51-80
4 - Brief history of data assimilation: Read PDF
pp. 81-96
PART II - DATA ASSIMILATION: DETERMINISTIC/STATIC MODELS: Read PDF
pp. 97-98
5 - Linear least squares estimation: method of normal equations: Read PDF
pp. 99-120
6 - A geometric view: projection and invariance: Read PDF
pp. 121-132
7 - Nonlinear least squares estimation: Read PDF
pp. 133-140
8 - Recursive least squares estimation: Read PDF
pp. 141-146
PART III - COMPUTATIONAL TECHNIQUES: Read PDF
pp. 147-148
pp. 149-168
10 - Optimization: steepest descent method: Read PDF
pp. 169-189
11 - Conjugate direction/gradient methods: Read PDF
pp. 190-208
12 - Newton and quasi-Newton methods: Read PDF
pp. 209-224
PART IV - STATISTICAL ESTIMATION: Read PDF
pp. 225-226
13 - Principles of statistical estimation: Read PDF
pp. 227-239
14 - Statistical least squares estimation: Read PDF
pp. 240-253
15 - Maximum likelihood method: Read PDF
pp. 254-260
16 - Bayesian estimation method: Read PDF
pp. 261-270
17 - From Gauss to Kalman: sequential, linear minimum variance estimation: Read PDF
pp. 271-282
PART V - DATA ASSIMILATION: STOCHASTIC/STATIC MODELS: Read PDF
pp. 283-284
18 - Data assimilation – static models: concepts and formulation: Read PDF
pp. 285-299
19 - Classical algorithms for data assimilation: Read PDF
pp. 300-321
20 - 3DVAR: a Bayesian formulation: Read PDF
pp. 322-339
21 - Spatial digital filters: Read PDF
pp. 340-362
PART VI - DATA ASSIMILATION: DETERMINISTIC/DYNAMIC MODELS: Read PDF
pp. 363-364
22 - Dynamic data assimilation: the straight line problem: Read PDF
pp. 365-381
23 - First-order adjoint method: linear dynamics: Read PDF
pp. 382-400
24 - First-order adjoint method: nonlinear dynamics: Read PDF
pp. 401-421
25 - Second-order adjoint method: Read PDF
pp. 422-444
26 - The 4DVAR problem: a statistical and a recursive view: Read PDF
pp. 445-460
PART VII - DATA ASSIMILATION: STOCHASTIC/DYNAMIC MODELS: Read PDF
pp. 461-462
27 - Linear filtering – part I: Kalman filter: Read PDF
pp. 463-484
28 - Linear filtering: part II: Read PDF
pp. 485-508
29 - Nonlinear filtering: Read PDF
pp. 509-533
30 - Reduced-rank filters: Read PDF
pp. 534-560
PART VIII - PREDICTABILITY: Read PDF
pp. 561-562
31 - Predictability: a stochastic view: Read PDF
pp. 563-580
32 - Predictability: a deterministic view: Read PDF
pp. 581-627
pp. 628-629
pp. 630-647
pp. 648-654