Book contents
- Frontmatter
- Contents
- Foreword to the French Edition
- Foreword to the English Edition
- Preface
- Acknowledgments
- Partial list of symbols
- 1 Half a century of numerical weather prediction
- 2 Weather prediction equations
- 3 Finite differences
- 4 Spectral methods
- 5 The effects of discretization
- 6 Barotropic models
- 7 Baroclinic model equations
- 8 Some baroclinic models
- 9 Physical parameterizations
- 10 Operational forecasting
- Appendix A Examples of nonhydrostatic models
- Further reading
- References
- Index
5 - The effects of discretization
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Foreword to the French Edition
- Foreword to the English Edition
- Preface
- Acknowledgments
- Partial list of symbols
- 1 Half a century of numerical weather prediction
- 2 Weather prediction equations
- 3 Finite differences
- 4 Spectral methods
- 5 The effects of discretization
- 6 Barotropic models
- 7 Baroclinic model equations
- 8 Some baroclinic models
- 9 Physical parameterizations
- 10 Operational forecasting
- Appendix A Examples of nonhydrostatic models
- Further reading
- References
- Index
Summary
Introduction
The effect of the various discretizations in space and time may be studied systematically in the context of a linearized model (Grotjhan and O’Brien, 1976). With such a model, it is possible to determine analytical solutions both for the system of equations under consideration and for the system obtained after discretization and therefore, by straightforward comparison, to appraise the effect of the chosen numerical schemes. The shallow water barotropic model is used as a study tool, as it has as solutions the two types of waves described by the primitive equation models: slow waves associated with advection terms and fast inertia-gravity waves associated with the Coriolis terms and the adaptation terms (pressure force in the equations of motion and divergence in the continuity equation). Moreover, it can be shown that a primitive equation model with n levels may be considered, once linearized, as the superposition of n shallow water barotropic models of decreasing equivalent heights.
The linearized barotropic model
5.2.1 The equations for the perturbations
- Type
- Chapter
- Information
- Fundamentals of Numerical Weather Prediction , pp. 79 - 105Publisher: Cambridge University PressPrint publication year: 2011