The Effects of Spherical Geometry on the Evolution of Baroclinic Waves

Jeffrey S. Whitaker National Center for Atmospheric Research, Boulder, Colorado

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Chris Snyder National Center for Atmospheric Research, Boulder, Colorado

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Abstract

The effects of spherical geometry on the nonlinear evolution of baroclinic waves are investigated by comparing integrations of a two-layer primitive equation (PE) model in spherical and Cartesian geometry. To isolate geometrical effects, the integrations use basic states with nearly identical potential vorticity (PV) structure.

Although the linear normal modes are very similar, significant differences develop at finite amplitude. Anticyclones (cyclones) in spherical geometry are relatively stronger (weaker) than those in Cartesian geometry. For this basic state, the strong anticyclones on the sphere are associated with anticyclonic wrapping of high PV in the upper layer (i.e., high PV air is advected southward and westward relative to the wave). In Cartesian geometry, large quasi-barotropic cyclonic vortices develop, and no anticyclonic wrapping of PV occurs. Because of their influence on the synoptic-scale flow, spherical geometric effects also lead to significant differences in the structure of mesoscale frontal features.

A standard midlatitude scale analysis indicates that the effects of sphericity enter in the next-order correction to β-plane quasigeostrophic (QG) dynamics. At leading order these spherical terms only affect the PV inversion operator (through the horizontal Laplacian) and the advection of PV by the nondivergent wind. Scaling arguments suggest, and numerical integrations of the barotropic vorticity equation confirm, that the dominant geometric effects are in the PV inversion operator. The dominant metric in the PV inversion operator is associated with the equatorward spreading of meridians on the sphere, and causes the anticyclonic (cyclonic) circulations in the spherical integration to become relatively stronger (weaker) than those in the Cartesian integration.

This study demonstrates that the effects of spherical geometry can be as important as the leading-order ageostrophic effects in determining the structure of evolution of dry baroclinic waves and their embedded mesoscale structures.

Abstract

The effects of spherical geometry on the nonlinear evolution of baroclinic waves are investigated by comparing integrations of a two-layer primitive equation (PE) model in spherical and Cartesian geometry. To isolate geometrical effects, the integrations use basic states with nearly identical potential vorticity (PV) structure.

Although the linear normal modes are very similar, significant differences develop at finite amplitude. Anticyclones (cyclones) in spherical geometry are relatively stronger (weaker) than those in Cartesian geometry. For this basic state, the strong anticyclones on the sphere are associated with anticyclonic wrapping of high PV in the upper layer (i.e., high PV air is advected southward and westward relative to the wave). In Cartesian geometry, large quasi-barotropic cyclonic vortices develop, and no anticyclonic wrapping of PV occurs. Because of their influence on the synoptic-scale flow, spherical geometric effects also lead to significant differences in the structure of mesoscale frontal features.

A standard midlatitude scale analysis indicates that the effects of sphericity enter in the next-order correction to β-plane quasigeostrophic (QG) dynamics. At leading order these spherical terms only affect the PV inversion operator (through the horizontal Laplacian) and the advection of PV by the nondivergent wind. Scaling arguments suggest, and numerical integrations of the barotropic vorticity equation confirm, that the dominant geometric effects are in the PV inversion operator. The dominant metric in the PV inversion operator is associated with the equatorward spreading of meridians on the sphere, and causes the anticyclonic (cyclonic) circulations in the spherical integration to become relatively stronger (weaker) than those in the Cartesian integration.

This study demonstrates that the effects of spherical geometry can be as important as the leading-order ageostrophic effects in determining the structure of evolution of dry baroclinic waves and their embedded mesoscale structures.

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