Dynamic Data Assimilation: A Least Squares Approach, Nide 13Cambridge University Press, 3.8.2006 - 654 sivua 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. |
Sisältö
ek as a linear combination of v s that | 30 |
If ek+ is much larger than e in magnitude then it implies that there exists an index | 112 |
λε 1 λ +1 1 6 | 129 |
and the first r eigenvectors V1 V2 V define the unstable manifold local | 136 |
two initial conditions x and x such that xo x0 ɛ and if k 0 is the first | 373 |
then k is the predictability limit of the model | 454 |
Muita painoksia - Näytä kaikki
Dynamic Data Assimilation: A Least Squares Approach John M. Lewis,S. Lakshmivarahan,Sudarshan Dhall Esikatselu ei käytettävissä - 2009 |
Yleiset termit ja lausekkeet
adjoint method algorithm analysis Appendix approximation assumed called Chapter columns components compute conjugate gradient conjugate gradient method constraint convergence covariance matrix data assimilation data assimilation problem define denote derivation descent direction deterministic diagonal discrete dynamical system eigenvalues eigenvectors error Example Exercise first-order forecast function given grid point Hence Hessian initial condition inverse iterative Kalman filter known least squares estimate linear least squares linear system Lyapunov M(xk minimization Newton's noise nonlinear observations obtain optimal parameter perturbation Pk+1 positive definite matrix prediction probability density properties quadratic quasi-Newton methods random Recall recursive recursive filters Rm×n scalar Section sequence singular vectors solution solving space Step Substituting symmetric and positive symmetric matrix term trajectory unbiased uncorrelated variable verified Wk+1 Xk+1 zero ди
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