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Atmospheric Modeling, Data Assimilation and Predictability This page intentionally left blank Atmospheric modeling, data assimilation and predictability This comprehensive text and reference work on numerical weather prediction covers for the first time, not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important new science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. This includes discussions of ensemble forecasting, El Ni˜no events, and how various methods contribute to improved weather and climate prediction. In each of these areas the emphasis is on clear and intuitive explanations of all the fundamental concepts, followed by a complete and sound development of the theory and applications. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book which can also form the basis of one or more graduate-level courses. It will appeal to professionals modeling the atmosphere, weather and climate, and to researchers working on chaos, dynamical systems, ensemble forecasting and problems of predictability. Eugenia Kalnay was awarded a PhD in Meteorology from the Massachusetts Institute of Technology in 1971 (Jule Charney, advisor). Following a position as Associate Professor in the same department, she became Chief of the Global Modeling and Simulation Branch at the NASA Goddard Space Flight Center (1983–7). From 1987 to 1997 she was Director of the Environmental Modeling Center (US National Weather Service)and in 1998 was awarded the Robert E. Lowry endowed chair at the University of Oklahoma. In 1999 she became the Chair of the Department of Meteorology at the University of Maryland. Professor Kalnay is a member of the US National Academy of Engineering and of the Academia Europaea, is the recipient of two gold medals from the US Department of Commerce and the NASA Medal for Exceptional Scientific Achievement, and has received the Jule Charney Award from the American Meteorological Society. The author of more than 100 peer reviewed papers on numerical weather prediction, data assimilation and predictability, Professor Kalnay is a key figure in this field and has pioneered many of the essential techniques. Atmospheric modeling, data assimilation and predictability Eugenia Kalnay University of Maryland Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521791793 © Eugenia Kalnay 2003 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2002 - ---- eBook (NetLibrary) - --- eBook (NetLibrary) - ---- hardback - --- hardback - ---- paperback - --- paperback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. I dedicate this book to the Grandmothers of Plaza de Mayo for their tremendous courage and leadership in defense of human rights and democracy Contents Foreword xi Acknowledgements xv List of abbreviations xvii List of variables xxi 1 Historical overview of numerical weather prediction 1 1.1 Introduction 1 1.2 Early developments 4 1.3 Primitive equations, global and regional models, and nonhydrostatic models 10 1.4 Data assimilation: determination of the initial conditions for the computer forecasts 12 1.5 Operational NWP and the evolution of forecast skill 17 1.6 Nonhydrostatic mesoscale models 24 1.7 Weather predictability, ensemble forecasting, and seasonal to interannual prediction 25 1.8 The future 30 2 The continuous equations 32 2.1 Governing equations 32 2.2 Atmospheric equations of motion on spherical coordinates 36 2.3 Basic wave oscillations in the atmosphere 37 2.4 Filtering approximations 47 2.5 Shallow water equations, quasi-geostrophic filtering, and filtering of inertia-gravity waves 53 2.6 Primitive equations and vertical coordinates 60 vii viii Contents 3 Numerical discretization of the equations of motion 68 3.1Classificationofpartialdifferentialequations(PDEs) 68 3.2 Initial value problems: numerical solution 72 3.3 Space discretization methods 91 3.4 Boundary value problems 114 3.5 Lateral boundary conditions for regional models 120 4 Introduction to the parameterization of subgrid-scale physical processes 127 4.1 Introduction 127 4.2 Subgrid-scale processes and Reynolds averaging 129 4.3 Overview of model parameterizations 132 5 Data assimilation 136 5.1 Introduction 136 5.2 Empirical analysis schemes 140 5.3 Introduction to least squares methods 142 5.4 Multivariate statistical data assimilation methods 149 5.5 3D-Var, the physical space analysis scheme (PSAS), and their relation to OI 168 5.6 Advanced data assimilation methods with evolving forecast error covariance 175 5.7 Dynamical and physical balance in the initial conditions 185 5.8 Quality control of observations 198 6 Atmospheric predictability and ensemble forecasting 205 6.1 Introduction to atmospheric predictability 205 6.2 Brief review of fundamental concepts about chaotic systems 208 6.3 Tangent linear model, adjoint model, singular vectors, and Lyapunov vectors 212 6.4 Ensemble forecasting: early studies 227 6.5 Operational ensemble forecasting methods 234 6.6 Growth rate errors and the limit of predictability in mid-latitudes and in the tropics 249 6.7 The role of the oceans and land in monthly, seasonal, and interannual predictability 254 6.8 Decadal variability and climate change 258 Contents ix Appendix A The early history of NWP 261 Appendix B Coding and checking the tangent linear and the adjoint models 264 Appendix C Post-processing of numerical model output to obtain station weather forecasts 276 References 283 Index 328 Foreword During the 50 years of numerical weather prediction the number of textbooks dealing with the subject has been very small, the latest being the 1980 book by Haltiner and Williams. As you will soon realize, the intervening years have seen impressive devel- opment and success. Eugenia Kalnay has contributed significantly to this expansion, and the meteorological community is fortunate that she has applied her knowledge and insight to writing this book. Eugenia was born in Argentina, where she had exceptionally good teachers. She had planned to study physics, but was introduced to meteorology by a stroke of fate; her mother simply entered her in a competition for a scholarship from the Argentine National Weather Service! But a military coup took place in Argentina in 1966 when Eugenia was a student, and the College of Sciences was invaded by military forces. Rolando Garcia, then Dean of the College of Sciences, was able to obtain for her an assistantship with Jule Charney at the Massachusetts Institute of Technology. She was the first female doctoral candidate in the Department and an outstanding student. In 1971, under Charney’s supervision, she finished an excellent thesis on the circulation of Venus. She recalls that an important lesson she learned from Charney at that time was that if her numerical results did not agree with accepted theory it might be because the theory was wrong. What has she written in this book? She covers many aspects of numerical weather prediction and related areas in considerable detail, on which her own experience enables her to write with relish and authority. The first chapter is an overview that introduces all the major concepts discussed later in the book. Chapter 2 is a pre- sentation of the standard equations used in atmospheric modeling, with a concise xi xii Foreword but complete discussion of filtering approximations. Chapter 3 is a roadmap to nu- merical methods providing a student without background in the subject with all the tools needed to develop a new model. Chapter 4 is an introduction to the pa- rameterization of subgrid-scale physical processes, with references to specialized textbooks and papers. I found her explanations in Chapter 5 of data assimilation methods and in Chapter 6 on predictability and ensemble forecasting to be not only inclusive but thorough and well presented, with good attention to historical devel- opments. These chapters, however, contain many definitions and equations. (I take this wealth as a healthy sign of the technical maturity of the subject.)This complex- ity may be daunting for many readers, but this has obviously been recognized by Eugenia. In response she has devised many simple graphical sketches that illustrate the important relations and definitions. An added bonus is the description in an ap- pendix of the use of Model Output Statistics by the National Weather Service, its successes, and the rigid constraints that it imposes on the forecast
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