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### Summary

### Summary

Lewis Fry Richardson dreamt that scientific weather prediction would one day become a practical reality. Before his ideas could bear fruit several advances were needed: better understanding of the dynamics of the atmosphere; stable computational algorithms to integrate the equations; regular observations of the free atmosphere; and powerful automatic computer equipment. By 1950 advances in all these fronts were sufficient to permit the first computer forecast to be made. Over the ensuing fifty years progress in numerical weather prediction has been dramatic. Weather prediction and climate modelling have now reached a high level of sophistication. This book, first published in 2006, tells the story of Richardson's trial forecast, and the fulfilment of his dream of practical numerical weather forecasting. It includes a complete reconstruction of Richardson's forecast, and analyses in detail the causes of his failure. This will appeal to everyone involved in numerical weather forecasting, from researchers and graduate students to professionals.

### Author Notes

Peter Lynch is the vice-chairman of Fidelity Management and Research.

Lynch wrote "One Up on Wall Street," "Beating the Street," and "Learning to Earn," all of which are guides to investing, tracking, and reading the stock market.

(Bowker Author Biography)

### Table of Contents

Guiding signs | p. viii |

Preface | p. ix |

Acknowledgements | p. xi |

1 Weather Prediction by Numerical Process | p. 1 |

1.1 The problem | p. 1 |

1.2 Vilhelm Bjerknes and scientific forecasting | p. 4 |

1.3 Outline of Richardson's life and work | p. 10 |

1.4 The origin of Weather Prediction by Numerical Process | p. 14 |

1.5 Outline of the contents of WPNP | p. 18 |

1.6 Preview of remaining chapters | p. 25 |

2 The fundamental equations | p. 29 |

2.1 Richardson's general circulation model | p. 30 |

2.2 The basic equations | p. 31 |

2.3 The vertical velocity equation | p. 39 |

2.4 Temperature in the stratosphere | p. 42 |

2.5 Pressure co-ordinates | p. 44 |

3 The oscillations of the atmosphere | p. 47 |

3.1 The Laplace tidal equations | p. 48 |

3.2 Normal modes of the atmosphere | p. 49 |

3.3 Atmospheric tides | p. 55 |

3.4 Numerical solution of the Laplace tidal equations | p. 56 |

4 The barotropic forecast | p. 63 |

4.1 Richardson's model and data | p. 63 |

4.2 The finite difference scheme | p. 65 |

4.3 Richardson's conclusions | p. 68 |

4.4 The global numerical model | p. 70 |

4.5 Extending the forecast | p. 72 |

4.6 Non-divergent and balanced initial conditions | p. 75 |

4.7 Reflections on the single layer model | p. 77 |

5 The solution algorithm | p. 79 |

5.1 The finite difference method | p. 79 |

5.2 Integration in time | p. 81 |

5.3 The Courant-Friedrichs-Lewy stability criterion | p. 85 |

5.4 The Richardson grid | p. 87 |

5.5 The equations for the strata | p. 89 |

5.6 The computational algorithm | p. 92 |

6 Observations and initial fields | p. 97 |

6.1 Aerological observations | p. 97 |

6.2 Dines' meteorograph | p. 100 |

6.3 The Leipzig charts | p. 104 |

6.4 Preparation of the initial fields | p. 109 |

7 Richardson's forecast | p. 117 |

7.1 What Richardson actually predicted: 20 numbers | p. 117 |

7.2 Scaling the equations of motion | p. 120 |

7.3 Analysis of the initial tendencies | p. 125 |

7.4 The causes of the forecast failure | p. 131 |

7.5 Max Margules and the 'impossibility' of forecasting | p. 133 |

8 Balance and initialisation | p. 137 |

8.1 Balance in the atmosphere | p. 137 |

8.2 The slow manifold | p. 140 |

8.3 Techniques of initialisation | p. 142 |

8.4 The swinging spring | p. 146 |

8.5 Digital filter initialisation | p. 152 |

9 Smoothing the forecast | p. 159 |

9.1 Reconstruction of the forecast | p. 159 |

9.2 Richardson's five smoothing methods | p. 162 |

9.3 Digital filtering of the initial data | p. 164 |

9.4 Extension of the forecast | p. 175 |

10 The ENIAC integrations | p. 181 |

10.1 The 'Meteorology Project' | p. 182 |

10.2 The filtered equations | p. 187 |

10.3 The first computer forecast | p. 190 |

10.4 The barotropic model | p. 196 |

10.5 Multi-level models | p. 199 |

10.6 Primitive equation models | p. 202 |

10.7 General circulation models and climate modelling | p. 206 |

11 Numerical weather prediction today | p. 209 |

11.1 Observational data | p. 209 |

11.2 Objective analysis | p. 213 |

11.3 Progress in computing | p. 219 |

11.4 The European Centre for Medium-Range Weather Forecasts | p. 221 |

11.5 Meso-scale modelling | p. 228 |

11.6 Chaos, predictability and ensemble forecasting | p. 231 |

12 Fulfilment of the dream | p. 243 |

12.1 Richardson's explanation of his glaring error | p. 243 |

12.2 The 'forecast factory' | p. 246 |

12.3 Richardson's dream | p. 248 |

Appendix 1 Table of notation | p. 251 |

Appendix 2 Milestones in Richardson's life and career | p. 254 |

Appendix 3 Laplace tidal equations: separation of variables | p. 256 |

Appendix 4 Richardson's forecast factory: the $64 000 question | p. 259 |

References | p. 262 |

Index | p. 274 |