By Jean Coiffier
''Numerical types became crucial instruments in environmental technological know-how, really in climate forecasting and weather prediction. This booklet offers a finished evaluate of the options utilized in those fields, with emphasis at the layout of the latest numerical versions of the ambience. It provides a brief historical past of numerical climate prediction and its evolution, earlier than describing a few of the model equations and the way to unravel them numerically. It outlines the most components of a meteorological forecast suite, and the idea is illustrated all through with useful examples of operational versions and parameterizations of actual tactics. This e-book is based at the author's a long time of expertise, as a scientist at Me;te;o-France and instructing university-level classes. it's a useful and available textbook for graduate classes and a convenient source for researchers and execs in atmospheric physics, meteorology and climatology, in addition to the similar disciplines of fluid dynamics, hydrology and oceanography''-- Read more...
content material: laptop generated contents observe: Foreword to the French version; Foreword to the English version; Preface; Acknowledgements; checklist of symbols; 1. part a century of numerical climate prediction; 2. climate prediction equations; three. Finite alterations; four. Spectral tools; five. the results of discretization; 6. Barotropic types; 7. Baroclinic version equations; eight. a few baroclinic types; nine. actual parameterizations; 10. Operational forecasting; Appendix A. Examples of non-hydrostatic types; additional examining; References; Index.
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Additional resources for Fundamentals of numerical weather prediction
9) This system of equations is relevant for simulating atmospheric motion whose horizontal space scale is greater than about 10 km, which excludes its use for the explicit modelling of convection. It allows us to take into account Rossby waves and inertiagravity waves; but nevertheless, it eliminates sound waves because of the hydrostatic relation which has a filtering effect on them. The primitive equations are the basis of most numerical models used by meteorological services for weather forecasting (at any rate up to the late 1990s).
By using the vector identity: ( V · ∇p ) V = ∇ p V2 + ζ k × V, 2 where ζ = k · (∇p × V) is the vorticity (vertical component of curl) and V2/2 the kinetic energy per unit mass for the horizontal wind (noted K), we get the equation for the horizontal wind: ∂V ∂t = −ω ∂V ∂p − ( f + ζ ) k × V − ∇p ( Φ + K ) . This formulation is said to be semi-invariant, because it involves vorticity ζ and kinetic energy K, two quantities that are independent of the system of coordinates. 3) can be written: d (ln ρ) dt ∂w = − ∇z · V + .
3 The polar stereographic projection. ρ^ sin λ P’ ρ^ cos λ λ x y ρ^ M’ Weather prediction equations 30 x and y. By making the x-axis coincide with the origin meridian (λ = 0), the Cartesian coordinates are obtained from the polar coordinates by the relations: x = ρ cos λ , y = ρ sin λ , ρ = L tan (θ/2) in which θ is the co-latitude, defined by θ = π/2−ϕ, and L = a (1+sin ϕ0) is the distance between the South Pole and the projection plane. Based on the geometrical construction, the map scale factor is easily calculated from a displacement along a meridian and is: m=− dρ a dϕ = − L 1 + tan 2 θ dθ 2 −2 a d θ .