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Data Assimilation Fundamentals

- A Unified Formulation of the State and Parameter Estimation Problem

Data Assimilation Fundamentals

- A Unified Formulation of the State and Parameter Estimation Problem
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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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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.


Produktdetaljer
Sprog: Engelsk
Sider: 245
ISBN-13: 9783030967116
Indbinding: Paperback
Udgave:
ISBN-10: 3030967115
Udg. Dato: 23 apr 2023
Længde: 17mm
Bredde: 234mm
Højde: 156mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 23 apr 2023
Forfatter(e) Geir Evensen, Femke C. Vossepoel, Peter Jan van Leeuwen


Kategori Bayesiansk statistik


ISBN-13 9783030967116


Sprog Engelsk


Indbinding Paperback


Sider 245


Udgave


Længde 17mm


Bredde 234mm


Højde 156mm


Udg. Dato 23 apr 2023


Oplagsdato 23 apr 2023


Forlag Springer Nature Switzerland AG

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