The spherical polar components of the Coriolis force consist of terms in sin ϕ and terms in cos ϕ, where ϕ is latitude (referred to the frame‐rotation vector as polar axis). The cos ϕ Coriolis terms are not retained in the usual hydrostatic primitive equations of numerical weather prediction and climate simulation, their neglect being consistent with the shallow‐atmosphere approximation and the simultaneous exclusion of various small metric terms. Scale analysis for diabatically driven, synoptic‐scale motion in the tropics, and for planetary‐scale motion, suggests that the cos ϕ Coriolis terms may attain magnitudes of order 10% of those of key terms in the hydrostatic primitive equations. It is argued that the cos ϕ Coriolis terms should be included in global simulation models.A global, quasi‐hydrostatic model having a complete representation of the Coriolis force is proposed. Conservation of axial angular momentum and potential vorticity, as well as energy, is achieved by a formulation in which all metric terms are retained and the shallow‐atmosphere approximation is relaxed. Distance from the centre of the earth is replaced by a pseudo‐radius which is a function of pressure only. This model is put forward as a more accurate alternative to the traditional hydrostatic primitive equations; it preserves the desired conservation laws and may be integrated by broadly similar grid‐point methods.
When this book was first published in 1976; it consisted, like Gaul, of three parts, one setting out the basic mathematical and physical concepts that are used in atmospheric dynamics, another constructing the necessary equations, and a third discussing the application of the equations to the atmosphere. In this new paperback edition the author has added a chapter on mathematical modeling of the atmosphere, and he has taken the opportunity to make some corrections and revisions. There have been many advances in meteorology in the decade since publication of the first edition, but this edition includes hardly any of them. This is essentially a book about theorectical rather than observational meteorology, so perhaps it is understandable that no account is given of recent satellite data for the stratosphere or for the southern hemisphere. However, to read the sections on the global energy budget, one might think that the Global Weather Experiment had never taken place. Only a few theoretical topics have been added, while others, such as cyclogenesis, have been left unaltered, with the result that what little attention they receive seems to be distinctly old‐fashioned. The new material at the end of the book includes a study of the possible flow regimes of the (global) atmosphere. This starts out in promising fashion and sets up some useful working approximations, but instead of going on to apply these in real situations, the discussion turns away to examine a set of canonical equations that owes as much to statistical mechanics as to meteorology. These additions are not made any easier to appreciate by the rather baffling decision to add an extra index for the new chapter. The reader may now have the pleasure of looking u p one subject in two indexes before discovering that it was never there in the first place.
The linearized two-dimensional equations of motion on an f plane arc solved for a localized perturbation using Local polar coordinates, and a general solution involving Bessel functions is found which can be fitted to any initial conditions. Three types of perturbation are used as examples; they show the formation of an external gravity wave which propagates outward leaving a geostrophically balanced residual flow as r + m. The divergent component of the initial wind field has no cffcct on this residual flow. Experiments in which the same perturbations were applied to all levels of a numerical model showed good agreement with the analytical solutions.Using an isentropic temperature profile as an example, the theory is extended to three-dimensional perturbations. As well as the gravity waves and geostrophic residual flow found in two dimensions, a third component of the solution is found, namely, an inertial oscillation originating in the deviation of the wind perturbation from its vertical mean. This oscillation continues indefinitely with the Coriolia frequency. Numerical model experiments show good agreement with the solutions in the early stages of adjustment though the inertial oscillation slowly decays through internal gravity wave generation. Finally, the analytical solutions are discussed in the light of the results of research on the design and performance of analysis schemes. No. 41, Met. 0. 979 Geostrophic adjustment. Rev. Geophys. Space Phys., 10,485-528 An investigation of the free oscillations of a simple current system. J . Meteorol., 2, 113-119 On the optimal specification of the initial state for deterministic forecasting. Mon. Weather Reu., 108, 1719-1735 Four-dimensional data assimilation and the slow manifold. ibid., 108, 85-99 Tables of integral transforms. McGraw-Hill Book Co. The 15-level weather prediction model. MeteoroI. Mag., 114, Some simple solutions for heat-induced tropical circulation. Q. J. R. Meteorol. SOC., 106, 447-462 Experiments in the four-dimensional assimilation of Nimbus 4 SIRS data. 1. Appl. Meteorol., 12, 425-436 Some simple analytical solutions to the problem of forced equatorial long waves. Q. J. R. Meteorol. Soc., 110,203-217 The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field. Tellus, %A, 111-136 Nonlinear normal mode initialization and quasi-geostrophic theory. J. Atmos. Sci., 37, 958-968 222-226
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