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Open access
Title
Data assimilation fundamentals : a unified formulation of the state and parameter estimation problem / Geir Evensen, Femke C. Vossepoel, Peter Jan van Leeuwen.
ISBN
9783030967093 (electronic bk.)
3030967093 (electronic bk.)
9783030967086 (print)
Published
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource (xix, 245 pages) : illustrations (some color).
Item Number
10.1007/978-3-030-96709-3 doi
Call Number
QA276.8
Dewey Decimal Classification
519.5/44
Summary
This open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it difficult to compare them. Thus, it is unclear which assumptions are made to derive an assimilation method and sometimes even which problem it aspires to solve. The book's top-down approach allows categorizing data-assimilation methods based on the approximations used. This approach enables the user to choose the most suitable method for a particular problem or application. Have you ever wondered about the difference between the ensemble 4DVar and the "ensemble randomized likelihood" (EnRML) methods? Do you know the differences between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers to several such questions. The book provides the basis for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation.
Bibliography, etc. Note
Includes bibliographical references and indexes.
Access Note
Open access.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 27, 2022).
Series
Springer textbooks in earth sciences, geography and environment, 2510-1315
Introduction
Part I Mathematical Formulation: Problem formulation
Maximum a posteriori solution
Strong-constraint 4DVar
Weak constraint 4DVar
Kalman filters and 3DVar
Randomized-maximum-likelihood sampling
Low-rank ensemble methods
Fully nonlinear data assimilation
Localization and inflation
Methods’ summary
Part II Examples and Applications: A Kalman filter with the Roessler model
Linear EnKF update
EnKF for an advection equation
EnKF with the Lorenz equations
3Dvar and SC-4DVar for the Lorenz 63 model
Representer method with an Ekman-flow model
Comparison of methods on a scalar model
Particle filter for seismic-cycle estimation
Particle flow for a quasi-geostrophic model
EnRML for history matching petroleum models
ESMDA with a SARS-COV-2 pandemic model
Final summary
References
Index.
