Fundamentals of Numerical Weather Prediction

Numerical models have become essential tools in environmental science, particularly in weather forecasting and climate prediction. This book provides a comprehensive 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 describing the various model equations and how to solve them numerically. It outlines the main elements of a meteorological forecast suite, and the theory is illustrated throughout with practical examples of operational models and parameterizations of physical processes. This book is founded on the author's many years of experience, as a scientist at M t o-France and teaching university-level courses. It is a practical and accessible textbook for graduate courses and a handy resource for researchers and professionals in atmospheric physics, meteorology and climatology, as well as the related disciplines of fluid dynamics, hydrology and oceanography.

Jean Coiffier is now retired from Mto-France, where he was Ingnieur en Chef des Ponts et Chausses, and is a member of the Socit Mtorologique 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 Mtorologie Nationale (later Mto-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 cole Nationale de la Mtorologie and training courses to professional forecasters. He also played an active role in realizing Computer Aided Learning modules devoted to numerical modelling and forecasting methods.

Foreword to the French edition Olivier Talagrand	p. viii
Foreword to the English edition Andrew Staniforth	p. x
Preface	p. xi
Acknowledgments	p. xiii
Partial list of symbols	p. xv
Half a century of numerical weather prediction	p. 1
Introduction	p. 1
The early days	p. 2
Half a century of continual progress	p. 3
Developments in computing	p. 11
Weather prediction equations	p. 15
Introduction	p. 15
The simplifications and the corresponding models	p. 16
The equations in various systems of coordinates	p. 24
Some typical conformal projections	p. 29
Finite differences	p. 39
Introduction	p. 39
The finite difference method	p. 39
The grids used and their properties	p. 46
Conclusion	p. 55
Spectral methods	p. 57
Introduction	p. 57
Using series expansions in terms of functions	p. 57
Spectral method on the sphere	p. 61
Spectral method on a doubly periodic domain	p. 73
The effects of discretization	p. 79
Introduction	p. 79
The linearized barotropic model	p. 79
Effect of horizontal discretization	p. 82
Various time integration schemes	p. 87
Time filtering	p. 102
Effect of spatial discretization on stability	p. 103
Barotropic models	p. 106
Barotropic models using the vorticity equation	p. 106
The shallow water barotropic model	p. 114
Spectral processing of the shallow water model	p. 127
Practical use of the shallow water model	p. 135
Baroclinic model equations	p. 136
Introduction	p. 136
Introducing a general vertical coordinate	p. 136
Application to the primitive equations	p. 137
Various vertical coordinates	p. 140
Generalization to nonhydrostatic equations	p. 146
Conservation properties of the equations	p. 151
Conclusion	p. 155
Some baroclinic models	p. 157
Introduction	p. 157
The context of discretization	p. 157
Vertical discretization of the equations	p. 160
A sigma coordinate and finite difference model	p. 167
Formalization of the semi-implicit method	p. 179
A variable resolution spectral model	p. 182
Lagrangian advection in baroclinic models	p. 190
Physical parameterizations	p. 192
Introduction	p. 192
Equations for a multi-phase moist atmosphere	p. 194
Radiation	p. 199
Boundary layer and vertical diffusion	p. 213
Precipitation resolved at the grid scale	p. 225
Convection	p. 231
Effect of sub-grid orography	p. 237
Horizontal diffusion	p. 241
Validation of physical parameterizations	p. 243
Operational forecasting	p. 245
Introduction	p. 245
Meteorological observations	p. 245
Objective analysis and data assimilation	p. 248
Initialization of data on starting the model	p. 259
Coupled models	p. 263
Post-processing of model output	p. 266
Local forecasting	p. 268
The forecasting process	p. 270
Forecast verification	p. 271
Ensemble forecasting	p. 276
International cooperation	p. 280
Future prospects	p. 281
Examples of nonhydrostatic models	p. 285
Introduction	p. 285
The AROME model	p. 285
The WRF/ARW model	p. 296
Further reading	p. 315
References	p. 318
Index	p. 337
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Fundamentals of Numerical Weather Prediction

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