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January 24, 2004 12:0 Elsevier/AID aid An Introduction to Dynamic Meteorology FOURTH EDITION January 24, 2004 12:0 Elsevier/AID aid This is Volume 88 in the INTERNATIONAL GEOPHYSICS SERIES A series of monographs and textbooks Edited by RENATADMOWSKA, JAMES R. HOLTON and H.THOMAS ROSSBY A complete list of books in this series appears at the end of this volume. January 24, 2004 12:0 Elsevier/AID aid AN INTRODUCTION TO DYNAMIC METEOROLOGY Fourth Edition JAMES R. HOLTON Department of Atmospheric Sciences University of Washington Seattle,Washington Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo January 24, 2004 12:0 Elsevier/AID aid Senior Editor, Earth Sciences Frank Cynar Editorial Coordinator Jennifer Helé Senior Marketing Manager Linda Beattie Cover Design Eric DeCicco Composition Integra Software Services Printer/Binder The Maple-Vail Manufacturing Group Cover printer Phoenix Color Corp Elsevier Academic Press 200 Wheeler Road, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobald’s Road, London WC1X 8RR, UK This book is printed on acid-free paper. Copyright c 2004, Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: [email protected]. You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting “Customer Support” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 0-12-354015-1 CD-Rom ISBN: 0-12-354016-X For all information on all Academic Press publications visit our Web site at www.academicpressbooks.com PRINTED IN THE UNITED STATES OF AMERICA 0405060708987654321 January 24, 2004 12:0 Elsevier/AID aid CONTENTS Preface xi Chapter 1 Introduction 1.1 The Atmospheric Continuum 1 1.2 Physical Dimensions and Units 2 1.3 Scale Analysis 4 1.4 Fundamental Forces 4 1.5 Noninertial Reference Frames and “Apparent” Forces 10 1.6 Structure of the Static Atmosphere 19 Problems 24 MATLAB Exercises 26 Suggested References 27 Chapter 2 Basic Conservation Laws 2.1 Total Differentiation 29 2.2 The Vectorial Form of the Momentum Equation in Rotating Coordinates 33 2.3 Component Equations in Spherical Coordinates 34 2.4 Scale Analysis of the Equations of Motion 38 2.5 The Continuity Equation 42 2.6 The Thermodynamic Energy Equation 46 2.7 Thermodynamics of the Dry Atmosphere 49 v January 24, 2004 12:0 Elsevier/AID aid vi contents Problems 54 MATLAB Exercises 55 Suggested References 56 Chapter 3 Elementary Applications of the Basic Equations 3.1 Basic Equations in Isobaric Coordinates 57 3.2 Balanced Flow 60 3.3 Trajectories and Streamlines 68 3.4 The Thermal Wind 70 3.5 Vertical Motion 75 3.6 Surface Pressure Tendency 77 Problems 79 MATLAB Exercises 83 Chapter 4 Circulation and Vorticity 4.1 The Circulation Theorem 86 4.2 Vorticity 91 4.3 Potential Vorticity 95 4.4 The Vorticity Equation 100 4.5 Vorticity in Barotropic Fluids 106 4.6 The Baroclinic (Ertel) Potential Vorticity Equation 108 Problems 111 MATLAB Exercises 113 Suggested References 114 Chapter 5 The Planetary Boundary Layer 5.1 Atmospheric Turbulence 116 5.2 Turbulent Kinetic Energy 120 5.3 Planetary Boundary Layer Momentum Equations 122 5.4 Secondary Circulations and Spin Down 131 Problems 136 MATLAB Exercises 137 Suggested References 138 Chapter 6 Synoptic-Scale Motions I: Quasi-geostrophic Analysis 6.1 The Observed Structure of Extratropical Circulations 140 6.2 The Quasi-Geostrophic Approximation 146 6.3 Quasi-geostrophic Prediction 155 6.4 Diagnosis of the Vertical Motion 164 6.5 Idealized Model of a Baroclinic Disturbance 174 Problems 176 MATLAB Exercises 178 Suggested References 180 January 24, 2004 12:0 Elsevier/AID aid contents vii Chapter 7 Atmospheric Oscillations: Linear Perturbation Theory 7.1 The Perturbation Method 183 7.2 Properties of Waves 183 7.3 Simple Wave Types 188 7.4 Internal Gravity (Buoyancy) Waves 196 7.5 Gravity Waves Modified by Rotation 204 7.6 Adjustment to Geostrophic Balance 208 7.7 Rossby Waves 213 Problems 220 MATLAB Exercises 224 Suggested References 226 Chapter 8 Synoptic-Scale Motions II: Baroclinic Instability 8.1 Hydrodynamic Instability 229 8.2 Normal Mode Baroclinic Instability: A Two-Layer Model 230 8.3 The Energetics of Baroclinic Waves 242 8.4 Baroclinic Instability of a Continuously Stratified Atmosphere 250 8.5 Growth and Propagation of Neutral Modes 260 Problems 264 MATLAB Exercises 266 Suggested References 267 Chapter 9 Mesoscale Circulations 9.1 Energy Sources for Mesoscale Circulations 269 9.2 Fronts and Frontogenesis 269 9.3 Symmetric Baroclinic Instability 279 9.4 Mountain Waves 284 9.5 Cumulus Convection 289 9.6 Convective Storms 298 9.7 Hurricanes 304 Problems 309 MATLAB Exercises 310 Suggested References 311 Chapter 10 The General Circulation 10.1 The Nature of the Problem 314 10.2 The Zonally Averaged Circulation 316 10.3 The Angular Momentum Budget 329 10.4 The Lorenz Energy Cycle 337 10.5 Longitudinally Dependent Time-Averaged Flow 343 10.6 Low-Frequency Variability 349 10.7 Laboratory Simulation of the General Circulation 354 10.8 Numerical Simulation of the General Circulation 360 Problems 366 January 24, 2004 12:0 Elsevier/AID aid viii contents MATLAB Exercises 368 Suggested References 369 Chapter 11 Tropical Dynamics 11.1 The Observed Structure of Large-Scale Tropical Circulations 371 11.2 Scale Analysis of Large-Scale Tropical Motions 387 11.3 Condensation Heating 391 11.4 Equatorial Wave Theory 394 11.5 Steady Forced Equatorial Motions 400 Problems 403 MATLAB Exercises 404 Suggested References 406 Chapter 12 Middle Atmosphere Dynamics 12.1 Structure and Circulation of the Middle Atmosphere 408 12.2 The Zonal-Mean Circulation of the Middle Atmosphere 411 12.3 Vertically Propagating Planetary Waves 421 12.4 Sudden Stratospheric Warmings 424 12.5 Waves in the Equatorial Stratosphere 429 12.6 The Quasi-biennial Oscillation 435 12.7 Trace Constituent Transport 440 Problems 445 MATLAB Exercises 446 Suggested References 447 Chapter 13 Numerical Modeling and Prediction 13.1 Historical Background 449 13.2 Filtering Meteorological Noise 450 13.3 Numerical Approximation of the Equations of Motion 452 13.4 The Barotropic Vorticity Equation in Finite Differences 462 13.5 The Spectral Method 464 13.6 Primitive Equation Models 470 13.7 Data Assimilation 475 13.8 Predictability and Ensemble Prediction Systems 481 Problems 485 MATLAB Exercises 487 Suggested References 490 January 24, 2004 12:0 Elsevier/AID aid contents ix Appendix A Useful Constants and Parameters 491 Appendix B List of Symbols 493 Appendix C Vector Analysis 498 Appendix D Moisture Variables 501 Appendix E Standard Atmosphere Data 504 Appendix F Symmetric Baroclinic Oscillations 506 Answers to Selected Problems 509 Bibliography 513 Index 519 International Geophysics Series 531 January 24, 2004 12:0 Elsevier/AID aid January 24, 2004 12:0 Elsevier/AID aid PREFACE In this fourth edition of An Introduction to Dynamic Meteorology I have retained the basic structure of all chapters of the previous edition.A number of minor correc- tions, pedagogical improvements, and updates of material are included throughout. The major departure from previous editions, however, is inclusion of a variety of computer-based exercises and demonstrations utilizing the MATLABr program- ming language at the end of each chapter (MATLABr is a registered trademark of The MathWorks, Inc.). These will, I hope, provide students with an opportunity to visualize and experiment with various aspects of dynamics not readily accessible through analytic problem solving. I have chosen MATLAB because it is a high-level language with excellent graphing capabilities and is readily available to most university students. The ability within MATLABto animate wave fields is particularly valuable as a learning aid in dynamic meteorology. It is not necessary to have much experience with MATLAB to solve most of the problems provided. In most cases MATLAB scripts (M-files) are provided on the accompanying CD, and the student need only run the scripts for various parameter choices or make minor revisions. Through studying the various examples, students should gradually be able to gain the confidence to program their own MATLAB scripts. xi January 24, 2004 12:0 Elsevier/AID aid xii preface Much of the material included in this text is based on a two-term course sequence for seniors majoring in atmospheric sciences at the University of Washington. It would also be suitable for first-year graduate students with little previous back- ground in meteorology. As in the previous editions the emphasis in the text is on physical principles rather than mathematical elegance. It is assumed that the reader has mastered the fundamentals of classical physics and has a thorough knowledge of elementary calculus. Some use is made of vector calculus. In most cases, how- ever, the vector operations are elementary in nature so that the reader with little background in vector operations should not experience undue difficulties. The fundamentals of fluid dynamics necessary for understanding large-scale atmospheric motions are presented in Chapters 1–5. These have undergone only minor revisions from the previous edition. The development of the Coriolis force in Section 1.5 has been substantially improved from previous editions. The dis- cussion of the barotropic vorticity equation in Section 4.5 now introduces the streamfunction.
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