Data Assimilation: Mathematical Concepts and Instructive Examples
This book endeavours to give a concise contribution to understanding the data assimilation and related methodologies. The mathematical concepts and related algorithms are fully presented, especially for those facing this theme for the first time.&nbs
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Rodolfo Guzzi
Data Assimilation: Mathematical Concepts and Instructive Examples 123
SpringerBriefs in Earth Sciences
More information about this series at http://www.springer.com/series/8897
Rodolfo Guzzi
Data Assimilation: Mathematical Concepts and Instructive Examples
123
Rodolfo Guzzi System Biology Group University La Sapienza Rome Italy
ISSN 2191-5369 SpringerBriefs in Earth Sciences ISBN 978-3-319-22409-1 DOI 10.1007/978-3-319-22410-7
ISSN 2191-5377
(electronic)
ISBN 978-3-319-22410-7
(eBook)
Library of Congress Control Number: 2015948730 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
Data Assimilation is a set of mathematical techniques allowing us to use all the information available within a time frame. This includes observational data, any a priori information we may have and a deterministic or stochastic model describing our system, and encapsulating our theoretical understanding. The mathematical basis is the estimation theory or theory of the inverse problem that is an organized set of mathematical techniques for obtaining useful information about the physical world on the basis of observation. In a conventional problem one would use a set of known prior parameters to predict the state of the physical system. This approach is usually called a “forward problem.” In the “inverse problem” one attempts to use available observation of the state of the system to estimate poorly known parameters of the state itself. In both these cases Data Assimilation can be treated as a Bayesian system. The Bayesian theorem or the law of inverse probability allows us to combine a priori information about the parameters with the information contained into observations to guide the statistical inference process. The reason why the Data Assimilation is s
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