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Scientific descriptions of the climate have traditionally been based on the study of average meteorological values taken from different positions around the world. In recent years however it has become apparent that these averages should be considered with other statistics that ultimately characterize spatial and temporal variability. This book is designed to meet that need. It is based on a course in computational statistics taught by the author that arose from a variety of projects on the design and development of software for the study of climate change, using statistics and methods of random functions.
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Computational Statistics in Climatology This page intentionally left blank Computational Statistics in Climatology Ilya Polyak New York Oxford OXFORD UNIVERSITY PRESS 1996 Oxford University Press Oxford New York Athens Auckland Bangkok Bogota Bombay Buenos Aires Calcutta Cape Town Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto and associated companies in Berlin Ibadan Copyright © 1996 Oxford University Press, Inc. Published by Oxford University Press, Inc., 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Polyak, Ilya. Computational statistics in climatology / Ilya Polyak. p. cm. Includes bibliographical references and index. ISBN 0-19-509999-0 1. Climatology—Statistical methods. I. Title. QC981.P63 1996 551.5'01'176—dc20 95-35132 987654321 Printed in the United States of America on acid-free paper Preface The range of statistical applications in the atmospheric sciences is so wide and diverse that it is difficult to mention even the most important areas of study. The proceedings of the Conferences on Probability and Statistics in the Atmospheric Sciences and of the Meetings on Statistical Climatology number in the dozens, and several books were published more than a decade ago (Gandin, 1965; Panofsky and Brier, 1968; Kagan, 1979; Epstein, 1985). Recently published textbooks (Thiebaux, 1994; Wilks, 1995) basically contain an introduction to the statistical methods, and an interesting monograph by R. Daley (1991) shows the possibility of the mutual physical and statistical analysis and modeling of atmospheric data. There are also a monograph, Applied Statistics in Atmospheric Sciences, by Essenwanger (1989) and a book by Preisendorfer and Mobley (1988) devoted solely to the principal component analysis in meteorology and oceanography. Although much work has been done in developing statistical climatology, many important topics remain to be studied—for instance, topics in the field of computational statistics and its climatological applications. This book presents the advanced course on computational statistics that I have taught for some years to Ph.D. students and scientists in the Main Geophysical Observatory, Hydrological Institute, and Civil Engineering Institute at St. Petersburg, Russia. The main objective of the course is to progress from univariate modeling and spectral and correlation analysis to multivariate modeling and multidimensional spectral and correlation analysis. The course developed as a result of my many years of involvement in a variety of projects dealing with design and development of software for climate change studies by using statistic and random functions methods. The elaboration of the corresponding algorithms, their application to analyzing and modeling climati