A Guide to Empirical Orthogonal Functions for Climate Data Analysis
Climatology and meteorology have basically been a descriptive science until it became possible to use numerical models, but it is crucial to the success of the strategy that the model must be a good representation of the real climate system of the Earth.
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Antonio Navarra
•
Valeria Simoncini
A Guide to Empirical Orthogonal Functions for Climate Data Analysis
123
Dr. Antonio Navarra Ist. Nazionale di Geofisica e Vulcanologia Via Gobetti, 101 40100 Bologna Italy [email protected]
Prof. Valeria Simoncini Università di Bologna Dip. to Matematica Piazza di Porta San Donato, 5 40126 Bologna Italy
Additional material to this book can be downloaded from http://extra.springer.com. ISBN 978-90-481-3701-5 e-ISBN 978-90-481-3702-2 DOI 10.1007/978-90-481-3702-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010920466 c Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: Boekhorst Design b.v. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
1
Introduction . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
1
2
Elements of Linear Algebra.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.1 Introduction . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.2 Elementary Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.3 Scalar Product .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.4 Linear Independence and Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.5 Matrices . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.6 Rank, Singularity and Inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.7 Decomposition of Matrices: Eigenvalues and Eigenvectors .. . . . . . . . . . . 2.8 The Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 2.9 Functions of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
5 5 5 6 10 12 16 17 19 21
3
Basic Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 3.1 Introduction . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 3.2 Climate Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 3.3 The Sample and the Po
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