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  • Author or Editor: RAFFAELE FERRARI x
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Malte Jansen and Raffaele Ferrari

Abstract

A major question for climate studies is to quantify the role of turbulent eddy fluxes in maintaining the observed atmospheric mean state. Both the equator-to-pole temperature gradient and the static stability of the extratropical atmosphere are set by a balance between these eddy fluxes and the radiative forcing. Much attention has been paid to the adjustment of the isentropic slope, which relates the static stability and the meridional temperature gradient. It is often argued that the extratropical atmosphere always equilibrates such that isentropes leaving the surface in the subtropics reach the tropopause near the poles. However, recent work challenged this argument. This paper revisits scaling arguments for the equilibrated mean state of a dry atmosphere, which results from a balance between the radiative forcing and the along-isentropic eddy heat flux. These arguments predict weak sensitivity of the isentropic slope to changes in the radiative forcing, consistent with previous results. Large changes can, however, be achieved if other external parameters, such as the size and rotation rate of the planet, are varied. The arguments are also extended to predict both the meridional temperature gradient and the static stability independently. This allows a full characterization of the atmospheric mean state as a function of external parameters.

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Malte Jansen and Raffaele Ferrari

Abstract

Observations suggest that the time- and zonal-mean state of the extratropical atmosphere adjusts itself such that the so-called “criticality parameter” (which relates the vertical stratification to the horizontal temperature gradient) is close to one. T. Schneider has argued that the criticality parameter is kept near one by a constraint on the zonal momentum budget in primitive equations. The constraint relies on a diffusive closure for the eddy flux of potential vorticity (PV) with an eddy diffusivity that is approximately constant in the vertical.

The diffusive closure for the eddy PV flux, however, depends crucially on the definition of averages along isentropes that intersect the surface. It is argued that the definition favored by Schneider results in eddy PV fluxes whose physical interpretation is unclear and that do not satisfy the proposed closure in numerical simulations. An alternative definition, first proposed by T.-Y. Koh and R. A. Plumb, is preferred. A diffusive closure for the eddy PV flux under this definition is supported by analysis of the PV variance budget and can be used to close the near-surface zonal momentum budget in idealized numerical simulations. Following this approach, it is shown that O(1) criticalities are obtained if the eddy diffusivity decays from its surface value to about zero over the depth of the troposphere, which is likely to be the case in Earth’s atmosphere. Large criticality parameters, however, are possible if the eddy diffusivity decays only weakly in the vertical, consistent with results from quasigeostrophic models. This provides theoretical support for recent numerical studies that have found supercritical mean states in primitive equation models.

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Malte Jansen and Raffaele Ferrari

Abstract

A major question for climate studies is to quantify the role of turbulent eddy fluxes in maintaining the observed ocean–atmosphere state. It has been argued that eddy fluxes keep the midlatitude atmosphere in a state that is marginally critical to baroclinic instability, which provides a powerful constraint on the response of the atmosphere to changes in external forcing. No comparable criterion appears to exist for the ocean. This is particularly surprising for the Southern Ocean, a region whose dynamics are very similar to the midlatitude atmosphere, but observations and numerical models suggest that the currents are supercritical.

This paper aims to resolve this apparent contradiction using a combination of theoretical considerations and eddy-resolving numerical simulations. It is shown that both marginally critical and supercritical mean states can be obtained in an idealized diabatically forced (and thus atmosphere-like) Boussinesq system, if the thermal expansion coefficient is varied from large atmosphere-like values to small oceanlike values. The argument is made that the difference in the thermal expansion coefficient dominantly controls the difference in the deformation scale between the two fluids and ultimately renders eddies ineffective in maintaining a marginally critical state in the limit of small thermal expansion coefficients.

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Jörn Callies, Oliver Bühler, and Raffaele Ferrari

Abstract

Spectral analysis is applied to infer the dynamics of mesoscale winds from aircraft observations in the upper troposphere and lower stratosphere. Two datasets are analyzed: one collected aboard commercial aircraft and one collected using a dedicated research aircraft. A recently developed wave–vortex decomposition is used to test the observations’ consistency with linear inertia–gravity wave dynamics. The decomposition method is shown to be robust in the vicinity of the tropopause if flight tracks vary sufficiently in altitude. For the lower stratosphere, the decompositions of both datasets confirm a recent result that mesoscale winds are consistent with the polarization and dispersion relations of inertia–gravity waves. For the upper troposphere, however, the two datasets disagree: only the research aircraft data indicate consistency with linear wave dynamics at mesoscales. The source of the inconsistency is a difference in mesoscale variance of the measured along-track wind component. To further test the observed flow’s consistency with linear wave dynamics, the ratio between tropospheric and stratospheric mesoscale energy levels is compared to a simple model of upward-propagating waves that are partially reflected at the tropopause. For both datasets, the observed energy ratio is roughly consistent with the simple wave model, but wave frequencies diagnosed from the data draw into question the applicability of the monochromatic theory at wavelengths smaller than 10 km.

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