Dynamic Data Assimilation: A Least Squares Approach, Volume 13

Front Cover
Cambridge University Press, Aug 3, 2006 - Mathematics - 654 pages
0 Reviews
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Brief history of data assimilation
81
method of normal equations
99
projection and invariance
121
Nonlinear least squares estimation
133
Recursive least squares estimation
141
Matrix methods
149
steepest descent method
169
Conjugate directiongradient methods
190
the straight line problem
365
linear dynamics
382
nonlinear dynamics
401
Secondorder adjoint method
422
a statistical and a recursive view
445
Kalman filter
463
part II
485
Nonlinear filtering
509

Newton and quasiNewton methods
209
Principles of statistical estimation
227
Statistical least squares estimation
240
Maximum likelihood method
254
Bayesian estimation method
261
sequential linear minimum
271
concepts and formulation
285
Classical algorithms for data assimilation
300
a Bayesian formulation
322
Spatial digital filters
340
Reducedrank filters
534
a stochastic view
563
a deterministic view
581
Epilogue
628
Preface page
xiii
Appendix A Finitedimensional vector space
xviii
Acknowledgements
xxi
illustrative examples
636
3
642
Copyright

Common terms and phrases

References to this book

All Book Search results »

About the author (2006)

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

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

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