Fundamentals of Numerical Weather Prediction

363 Pages·2012·5.283 MB·English

by  Jean Coiffier

Fundamentals of Numerical Weather Prediction
Numerical models have now become essential tools in environmental science, parti­
cularly in weather forecasting and climate prediction. This book provides a compre­
hensive overview of the techniques used in these fields, with emphasis on the design
of the most recent numerical models of the atmosphere. It presents a short history
of numerical weather prediction and its evolution, before providing step­by­step
descriptions of the various model equations and how to solve them numerically. It
outlines the main elements of a meteorological forecast suite, and the theory is illus­
trated throughout with practical examples of operational models and parameteriza­
tions of the main physical processes.
This book is founded on the author’s many years of experience, working as a scientist
at Météo­France and teaching university­level courses. It is a practical and accessible
textbook for graduate courses and is a handy resource for researchers and profession­
als in atmospheric physics, meteorology, and climatology, as well as the related discip­
lines of fluid dynamics, hydrology, and oceanography.
Jean Coiffier is now retired from Météo­France, where he was Ingénieur en Chef des
Ponts et Chaussées, and is a member of the Société Météorologique de France. His
involvement in meteorological science began in 1968 at the new Algerian Meteorological
Service, implementing elements of a modest meteorological forecast suite on a small
computer, before joining the Direction de la Météorologie Nationale (later Météo­
France) where he took part in the development and implementation of operational
models. In 1989, he became the head of the General Forecast Office. He worked there
until his retirement, also giving regular lectures on numerical weather prediction to
students of the École Nationale de la Météorologie and training courses to profes­
sional forecasters. He also played an active role in realizing Computer Aided Learning
modules devoted to numerical modelling and forecasting methods.

Fundamentals of Numerical
Weather Prediction
Jean Coiffier
formerly at Météo-France
Translated by
Christopher sut Cliffe
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town,
Singapore, São Paulo, Delhi, Tokyo, Mexico City
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9781107001039
© Jean Coiffier 2011
Original French edition:
© Météo­France, Paris, 2009
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published by Météo­France, Paris as Les bases de la prévision numérique du temps, 2009
This edition in English 2011
Ouvrage publié avec le concours du Centre national du livre – ministère français chargé de la Culture
This edition published with the support of the Centre national du livre – French Ministry of Culture
Printed in the United Kingdom at the University Press, Cambridge
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Coiffier, Jean.
[Bases de la prévision numérique du temp. English]
Fundamentals of numerical weather prediction / Jean Coiffier ; translated by Christopher Sutcliffe.
p. cm.
Includes bibliographical references and index.
ISBN 978­1­107­00103­9
1. Numerical weather forecasting. 2. Weather forecasting – Mathematical models. I. Title.
QC996.C65 2011
551.634–dc23 2011026294
ISBN 978­1­107­00103­9 Hardback
Cambridge University Press has no responsibility for the persistence or
accuracy of URLs for external or third­party internet websites referred to
in this publication, and does not guarantee that any content on such
websites is, or will remain, accurate or appropriate.
Contents
Foreword to the French edition Olivier Talagrand page viii
Foreword to the English edition Andrew Staniforth x
Preface xi
Acknowledgments xiii
Partial list of symbols xv
1 Half a century of numerical weather prediction 1
1.1 Introduction 1
1.2 The early days 2
1.3 Half a century of continual progress 3
1.4 Developments in computing 11
2 Weather prediction equations 15
2.1 Introduction 15
2.2 The simplifications and the corresponding models 16
2.3 The equations in various systems of coordinates 24
2.4 Some typical conformal projections 29
3 Finite differences 39
3.1 Introduction 39
3.2 The finite difference method 39
3.3 The grids used and their properties 46
3.4 Conclusion 55
4 Spectral methods 57
4.1 Introduction 57
4.2 Using series expansions in terms of functions 57
4.3 Spectral method on the sphere 61
4.4 Spectral method on a doubly periodic domain 73
5 The effects of discretization 79
5.1 Introduction 79
5.2 The linearized barotropic model 79
5.3 Effect of horizontal discretization 82
5.4 Various time integration schemes 87
v
vi Contents
5.5 Time filtering 102
5.6 Effect of spatial discretization on stability 103
6 Barotropic models 106
6.1 Barotropic models using the vorticity equation 106
6.2 The shallow water barotropic model 114
6.3 Spectral processing of the shallow water model 127
6.4 Practical use of the shallow water model 135
7 Baroclinic model equations 136
7.1 Introduction 136
7.2 Introducing a general vertical coordinate 136
7.3 Application to the primitive equations 137
7.4 Various vertical coordinates 140
7.5 Generalization to nonhydrostatic equations 146
7.6 Conservation properties of the equations 151
7.7 Conclusion 155
8 Some baroclinic models 157
8.1 Introduction 157
8.2 The context of discretization 157
8.3 Vertical discretization of the equations 160
8.4 A sigma coordinate and finite difference model 166
8.5 Formalization of the semi­implicit method 179
8.6 A variable resolution spectral model 182
8.7 Lagrangian advection in baroclinic models 190
9 Physical parameterizations 192
9.1 Introduction 192
9.2 Equations for a multi­phase moist atmosphere 194
9.3 Radiation 199
9.4 Boundary layer and vertical diffusion 213
9.5 Precipitation resolved at the grid scale 225
9.6 Convection 231
9.7 Effect of sub­grid orography 237
9.8 Horizontal diffusion 241
9.9 Validation of physical parameterizations 243
10 Operational forecasting 245
10.1 Introduction 245
10.2 Meteorological observations 245
10.3 Objective analysis and data assimilation 248
10.4 Initialization of data on starting the model 259
10.5 Coupled models 263
vii Contents
10.6 Post­processing of model output 266
10.7 Local forecasting 268
10.8 The forecasting process 270
10.9 Forecast verification 271
10.10 Ensemble forecasting 276
10.11 International cooperation 280
10.12 Future prospects 281
Appendix A Examples of nonhydrostatic models 285
A.1 Introduction 285
A.2 The AROME model 285
A.3 The WRF/ARW model 296
Further reading 315
References 318
Index 337
Foreword to the French Edition
It is a pleasure to present this book by Jean Coiffier. After many years of teaching at
the École Nationale de la météorologie, he wanted to give a lasting form to the work
at which he had laboured so long. The result is what is probably the first book (at any
rate it is the first in French) to present the fundamentals and the current methods of
numerical weather prediction in a comprehensive and consistent way.
Numerous books, some of them excellent, deal with dynamic meteorology, the sci­
ence of the moving atmosphere. But although numerical modelling has become a fun­
damental tool not just for weather forecasting but also for dynamic meteorology itself
as well as for oceanography and climate studies, there is no one book that presents the
methods and techniques in a systematic manner. New users of numerical models of
the atmosphere, whether students on placement or experienced scientists making car­
eer changes, find it hard to make their way into the world of numerical modelling. It
is not that documentation is lacking; most models now come with detailed guides to
help users take their first steps; and copious academic literature including some out­
standing papers is also readily available.
What is lacking is an overview of the techniques and methods; and that is what
Fundamentals of Numerical Weather Prediction provides. Without requiring from read­
ers more knowledge than the standard science graduate should have acquired, Jean
Coiffier guides them with pragmatism and pedagogy. The main points are explained in
simple but, at the same time, clear and rigorous terms. A few years ago, I proposed to
a group of students at the École Polytechnique to develop a general circulation model
of the atmosphere from scratch as a shared coursework project. It was Jean Coiffier’s
lecture notes (those on which this book is based) that appeared to me the most suitable
document to take them straight to the crux of what they needed to learn.
Numerical weather prediction is now more than 50 years old. One might wonder
what its pioneers would make of what it has become. Perhaps they would be surprised
at how the definition of initial conditions and data assimilation have grown steadily
more important over the years. Jean Coiffier deals with all these aspects of numerical
modelling, introducing the essential points of assimilation methods (although so very
different from what he describes elsewhere) with the same precision and the same rig­
our as he presents the discretization algorithms.
Jean Coiffier is perhaps a little too modest. He confines the title of his book to
‘numerical weather prediction,’ but the methods set out in it are the same as are used
for numerical modelling of the climate, which is now so crucial for forecasting the
changes in store for us and for preventing or at least mitigating their harmful effects.
viii
ix olivier talagrand
This book is aimed at students and it will be very helpful to them. But I am sure that
a number of engineers and experienced scientists too will be using it, for they can be
sure to find in it clear answers to precise questions. I am confident that many will join
me in thanking Jean Coiffier for his Fundamentals of Numerical Weather Prediction.
Olivier Talagrand – 25 September 2007