Model Calibration and Parameter Estimation For Environmental and Wat
This three-part book provides a comprehensive and systematic introduction to the development of useful models for complex systems. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part
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Ne-Zheng Sun • Alexander Sun
Model Calibration and Parameter Estimation For Environmental and Water Resource Systems
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Ne-Zheng Sun Department of Civil and Environmental Engineering University of California at Los Angeles Los Angeles California USA
Alexander Sun Bureau of Economic Geology, Jackson School of Geosciences University of Texas at Austin Austin Texas USA
ISBN 978-1-4939-2322-9 ISBN 978-1-4939-2323-6 (eBook) DOI 10.1007/978-1-4939-2323-6 Library of Congress Control Number: 2015931547 Mathematics Subject Classification (2010): 97Mxx, 93A30, 93B11, 93B30, 90Cxx, 65Kxx, 86A05, 15A29, 35R30, 86A22, 65M32, 65N21, 81T80, 62P12, 65Cxx Springer New York Heidelberg Dordrecht London © Springer Science+Business Media, LLC 2015 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 New York is part of Springer Science+Business Media (www.springer.com)
To Rachel, Albert, Adam, and Jacob
Preface
A mathematical model constructed for a real system must be calibrated by data and its uncertainty must be assessed before used for prediction, decision making, and management purposes. After more than a half century of study, however, the construction of a reliable model for complex systems is still a challenging task. In mathematical modeling, the “prediction problem” or the “forward problem” (inputs → outputs) uses as model inputs a fixed model structure, known model parameters, given system controls, and other necessary information to find the system states (as model outputs). Unless all properties of the modeled system can be measured directly, model inputs tend to always contain unknowns or uncertainties that have to be determined indirectly. Model calibration (outputs → inputs) uses the measured system states and other available information to identify or estimate the unknown model inputs. Thus, in a certain sense it is the “inverse problem” of model prediction. The history of studying model calibration is probably as long as the
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