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Data assimilation fundamentals = a u...

Evensen, Geir.

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Data assimilation fundamentals = a unified formulation of the state and parameter estimation problem /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Data assimilation fundamentals/ by Geir Evensen, Femke C. Vossepoel, Peter Jan van Leeuwen.
其他題名:	a unified formulation of the state and parameter estimation problem /
作者:	Evensen, Geir.
其他作者:	Vossepoel, Femke Cathelijne.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xix, 245 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Estimation theory. -
電子資源:	https://doi.org/10.1007/978-3-030-96709-3
ISBN:	9783030967093

Data assimilation fundamentals = a unified formulation of the state and parameter estimation problem /
Evensen, Geir.

Data assimilation fundamentalsa unified formulation of the state and parameter estimation problem /[electronic resource] :by Geir Evensen, Femke C. Vossepoel, Peter Jan van Leeuwen. - Cham :Springer International Publishing :2022. - xix, 245 p. :ill. (some col.), digital ;24 cm. - Springer textbooks in earth sciences, geography and environment,2510-1315. - Springer textbooks in earth sciences, geography and environment..

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.

Open access.

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.

ISBN: 9783030967093

Standard No.: 10.1007/978-3-030-96709-3doiSubjects--Topical Terms:

565962
Estimation theory.

LC Class. No.: QA276.8 / .E84 2022

Dewey Class. No.: 519.544

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505 0 $a 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.
506 $a Open access.
520 $a 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.
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650 0 $a Kalman filtering. $3 544465
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650 2 4 $a Methodology of Data Collection and Processing. $3 3598081
650 2 4 $a Bayesian Inference. $3 3386929
700 1 $a Vossepoel, Femke Cathelijne. $3 3598080
700 1 $a Leeuwen, Peter Jan van. $3 2157943
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