Fundamentals of numerical weather prediction by Jean Coiffier

By Jean Coiffier

''Numerical types became crucial instruments in environmental technology, fairly in climate forecasting and weather prediction. This publication presents a finished evaluate of the recommendations utilized in those fields, with emphasis at the layout of the latest numerical types of the ambience. It provides a quick background of numerical climate prediction and its evolution, earlier than describing some of the model Read more...

content material: computer generated contents observe: Foreword to the French version; Foreword to the English variation; Preface; Acknowledgements; checklist of symbols; 1. part a century of numerical climate prediction; 2. climate prediction equations; three. Finite changes; four. Spectral equipment; five. the consequences of discretization; 6. Barotropic types; 7. Baroclinic version equations; eight. a few baroclinic versions; nine. actual parameterizations; 10. Operational forecasting; Appendix A. Examples of non-hydrostatic versions; additional studying; References; Index.

a pragmatic, available evaluate of climate forecasting and weather modeling thoughts for graduate scholars, researchers and execs in atmospheric science. Read more...

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While methods using series expansion in terms of functions now compete with the finite difference method for the horizontal processing of meteorological fields, vertical discretization, to some extent, and time discretization still utilize finite differences. This presentation of finite differences is not designed to demonstrate the basic results that can be found in books on numerical analysis but rather to show in concrete terms how the finite difference method is applied to numerical weather prediction models.

M’ O ρ^ ρ^ M’ x O a’λ Weather prediction equations 32 Choosing the Cartesian axes in an appropriate way on the projection plane, with the equator as x-axis and with the y-axis set on the origin meridian, makes it easy to identify a point on the projection map from its coordinates as follows: x = a′ λ , y = ρ , where ρ ̂ represents here the distance of the point M ′ to the equator on the cylinder and λ the longitude. The map scale factor along a parallel is given by: a ′d λ a cos ϕ d λ while along a meridian it reads: d ρ a dϕ , .

The resulting simplified form of the equations can also be obtained directly by deducing the momentum equation from the Lagrange equations when replacing the initial metrics: dr 2 = r 2 cos 2 ϕ d λ 2 + r 2 d ϕ 2 + dr 2 ( where λ is the longitude), by the metrics consistent with the thin layer approximation (Hinkelmann, 1969): dr 2 = a 2 cos 2 ϕ d λ 2 + a 2 d ϕ 2 + dr 2 . Weather prediction equations 18 Therefore, these equations verify the principle of conservation of angular momentum in a way that is consistent with the thin layer approximation (Phillips, 1966; Lorenz, 1967; Müller, 1989).

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