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1. Historical overview; 2. The continuous equations; 3. Discretization of the equations; 4. Introduction to the parameterizations of subgrid-scale physical processes; 5. Data assimilation; 6. Atmospheric predictability and ensemble forecasting; References; Appendix A. The early history of numerical weather prediction; Appendix B. List of acronyms; Appendix C. Coding and checking the linear tangent and adjoint models; Appendix D. Post processing of numerical model output to obtain station weather forecasts.

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