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Brian J. Hoskins

Abstract

From spectral analyses of the 1° terrain heights of Gates and Nelson (1975), the representation of the earth topography by truncated series of spherical harmonics is obtained. Rhomboidal and triangular truncations at various wavenumbers are exhibited.

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Brian J. Hoskins

Abstract

Consideration of flows in which the rate of change of momentum is much smaller than the Coriolis force suggests that the advected quantity momentum may be approximated by its geostrophic value but that trajectories cannot be so approximated. The resulting set of equations imply full forms of the equations for potential temperature, three-dimensional vorticity, potential vorticity and energy. A transformation of horizontal coordinates products the “semi-geostrophic” system in which conservation of potential vorticity and potential temperature suffice to determine the motion. The system is capable of describing the formation of fronts, jets, and the growth of baroclinic waves into the nonlinear regime. It sheds some light on the success and failure of the quasi-geostrophic equations.

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Brian J. Hoskins and Ion Draghici

Abstract

It has been shown previously how a transformation of coordinates applied to the primitive equations with the geostrophic momentum approximation produces the quite simple semi-geostrophic equations. Here the connection with quasi-geostrophic theory and the role of ageostrophic motions are clarified. The cross-frontal circulation equation of Eliassen (1962) is shown to be applicable in a modified form in three dimensions, and a simple “ω equation” in obtained.

A similar analytical development is possible in isentropic coordinates. As an example of the diagnostic use of the equations derived, a study of the formation of an upper air front in a numerical model is given.

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Frederick Sanders and Brian J. Hoskins

Abstract

It is shown how to estimate the directions and relative magnitudes of Q-vectors from a map of isobars and isotherms. The divergence of this vector field represents the forcing function in the quasi-geostrophic omega-equation. The direction of the Q-vector at a point is determined by the rate of change of the geostrophic wind vector taken along the isotherms, with the colder air to the left in the Northern Hemisphere. Its direction is 90° to the right of this vector change of wind. The strength of the Q-vector is proportional to the magnitude of the rate of vector wind change, and to the magnitude of the temperature gradient.

Application to an actual situation is shown and compared with the traditional inferences from advections of temperature and vorticity. General agreement is found. Patterns of Q-vectors and associated vertical motion are sketched for idealized patterns of surface lows and highs and for upper-level troughs and ridges. Examples of confluent frontogenesis are shown, for a lower-tropospheric col and for a upper-level jet entrance. Patterns of Q-vectors and vertical circulations are noted for frontogenetical and frontolytical situations.

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Masaru Inatsu and Brian J. Hoskins

Abstract

Atmospheric general circulation model experiments have been performed to investigate how the significant zonal asymmetry in the Southern Hemisphere (SH) winter storm track is forced by sea surface temperature (SST) and orography. An experiment with zonally symmetric tropical SSTs expands the SH upper-tropospheric storm track poleward and eastward and destroys its spiral structure. Diagnosis suggests that these aspects of the observed storm track result from Rossby wave propagation from a wave source in the Indian Ocean region associated with the monsoon there. The lower-tropospheric storm track is not sensitive to this forcing. However, an experiment with zonally symmetric midlatitude SSTs exhibits a marked reduction in the magnitude of the maximum intensity of the lower-tropospheric storm track associated with reduced SST gradients in the western Indian Ocean. Experiments without the elevation of the South African Plateau or the Andes show reductions in the intensity of the major storm track downstream of them due to reduced cyclogenesis associated with the topography. These results suggest that the zonal asymmetry of the SH winter storm track is mainly established by stationary waves excited by zonal asymmetry in tropical SST in the upper troposphere and by local SST gradients in the lower troposphere, and that it is modified through cyclogenesis associated with the topography of South Africa and South America.

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Stephanie Waterman and Brian J. Hoskins

Abstract

This manuscript revisits a study of eddy–mean flow interactions in an idealized model of a western boundary current extension jet using properties of the horizontal velocity correlation tensor to diagnose characteristics of average eddy shape, orientation, propagation, and mean flow feedback. These eddy characteristics are then used to provide a new description of the eddy–mean flow interactions observed in terms of different ingredients of the eddy motion. The diagnostics show patterns in average eddy shape, orientation, and propagation that are consistent with the signatures of jet instability in the upstream region and wave radiation in the downstream region. Together they give a feedback onto the mean flow that gives the downstream character of the jet and drives the jet's recirculation gyres. A breakdown of the eddy forcing into contributions from individual terms confirms the expected role of cross-jet gradients in meridional eddy tilt in stabilizing the jet to its barotropic instability; however, it also reveals important roles played by the along-jet evolution of eddy zonal–meridional elongation. It is the mean flow forcing derived from these patterns that acts to strengthen and extend the jet downstream and forces the time-mean recirculation gyres. This understanding of the dependence of mean flow forcing on eddy structural properties suggests that failure to adequately resolve eddy elongation could underlie the weakened jet strength, extent, and changed recirculation structure seen in this idealized model for reduced spatial resolutions. Further, it may suggest new ideas for the parameterization of this forcing.

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Brian J. Hoskins and Anthony Hollingsworth

Abstract

The simplest example of possibly unstable Rossby wave motion is reexamined. The necessary and sufficient condition for instability is shown to be that the tendency of the, β effect to produce different phase speeds for different wavelengths may be balanced by the interaction effect.

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Feifei Jin and Brian J. Hoskins

Abstract

The global response to tropical heating is studied by performing a time integration of a 15-level primitive equation model, starting with a basic flow maintained by a constant forcing. The direct, quasi-steady response to the tropical heating is seen during the first 20 days before baroclinic instability dominates. This technique enables the investigation of a variety of basic flows, from a resting state to a December–February 3D time-mean flow; of the timescales for establishing remote responses; and of nonlinear effects. It also allows the determination of timescales for the establishment of the response. The Gill-type response is seen in the lower troposphere in all cases. In the upper troposphere, depending on the basic conditions, the simple tropical quadrupole response of the Gill model shows considerable modification. The anticyclonic pair can be centered over the heating and can vary substantially in magnitude and vertical extent. The Rossby wave source and the upper-tropospheric divergence above the beating region is always found, but the existence and relative magnitudes of local Hadley and Walker cells as measured by upper-tropospheric convergence are strong functions of the flow. Both the Rossby wave source and the Rossby wave propagation are also strongly influenced by the ambient flow. Wave patterns extend to the equator in the regions in which the basic westerlies extend to the equator. Significant tropical zonal flow variations, which are also very dependent on the basic flow and the position of the heating, are also produced. The tropical and midlatitude response are generally established within a week. In an additional week the high-latitude pattern is determined and the subtropical wave pattern propagates back into the Tropics in the westerly wind regions. Nonlinear effects are found to be minor in all cases before the middle-latitude transients develop. On the two-week timescale of interest here, the sensitivity of steady-state models to the dissipations employed and to the existence of low-frequency modes is not found.

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Brian J. Hoskins and Tercio Ambrizzi

Abstract

The response of a barotropic model, linearized about a climatological 300-mb December–February time-mean flow to localized forcing, is considered. In order to aid the design of the experiments and interpretation of the results, a simplified analysis is made of the basic flow in terms of zonal wind, meridional vorticity gradient, and stationary wavenumber. From the analysis the possible existence of a strong waveguide in the Asian jet and weaker waveguides in the North Atlantic and Southern Hemisphere jets is deduced. The possibility of propagation into the equatorial east Pacific and Atlantic oceans and even across these regions is also suggested. These features are confirmed by barotropic model integrations for a variety of perturbation vorticity source positions and shapes. These integrations also show preferred propagation regions arching across North America, from Europe to the Arabian Gulf and, in the Southern Hemisphere, into the equatorial Indian Ocean and Indonesian regions. They also show a tendency to produce a low-wavenumber, fast westward-moving “tail” along the Asian jet. Many of the features found in this study are remarkably consistent with observational teleconnection studies.

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Paul J. Valdes and Brian J. Hoskins

Abstract

Traditionally, stationary wave models have been linearized about a zonal-mean flow and the response calculated to various fixed orographic and thermal forcings. In this paper it is shown that the inclusion of nonlinear interactions can significantly modify the solution for orographic forcing. This arises primarily from the improved boundary condition that allows the flow to be deflected around the mountain as well as over it. In this context a useful conceptual model is obtained by linearization based on the smallness of the latitudinal extent of a mountain. The nonlinear model is considerably less sensitive to the zonal-mean surface flow and, in some instances, the perturbation amplitude decreases with increasing surface flow. The nonlinear, hemispheric solutions for full orography and wintertime basic state are shown for both the Northern and Southern hemispheres. They suggest that the direct effect of orographic forcing alone accounts for less than one-half of the observed time mean asymmetries.

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