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Tapio Schneider

Abstract

While it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in potential vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean balance of zonal momentum and of potential vorticity on isentropes, including the near-surface isentropes that sometimes intersect the surface. Integrated vertically, the mean zonal momentum or potential vorticity balance leads to a balance condition that relates the mean meridional mass flux along isentropes to eddy fluxes of potential vorticity and surface potential temperature. The isentropic-coordinate balance condition formally resembles balance conditions well known in quasigeostrophic theory, but on near-surface isentropes it generally differs from the quasigeostrophic balance conditions. Not taking the intersection of isentropes with the surface into account, quasigeostrophic theory does not adequately represent the potential vorticity dynamics and mass fluxes on near-surface isentropes—a shortcoming that calls into question the relevance of quasigeostrophic theories for the macroturbulence and global circulation of the atmosphere.

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Tapio Schneider

Abstract

A dynamical constraint on the extratropical tropopause height and thermal stratification is derived by considerations of entropy fluxes, or isentropic mass fluxes, and their different magnitudes in the troposphere and stratosphere. The dynamical constraint is based on a relation between isentropic mass fluxes and eddy fluxes of potential vorticity and surface potential temperature and on diffusive eddy flux closures. It takes baroclinic eddy fluxes as central for determining the extratropical tropopause height and thermal stratification and relates the tropopause potential temperature approximately linearly to the surface potential temperature and its gradient.

Simulations with an idealized GCM point to the possibility of an extratropical climate in which baroclinic eddy fluxes maintain a statically stable thermal stratification and, in interaction with large-scale diabatic processes, lead to the formation of a sharp tropopause. The simulations show that the extratropical tropopause height and thermal stratification are set locally by extratropical processes and do not depend on tropical processes and that, across a wide range of atmospheric circulations, the dynamical constraint describes the relation between tropopause and surface potential temperatures well. An analysis of observational data shows that the dynamical constraint, derived for an idealized dry atmosphere, can account for interannual variations of the tropopause height and thermal stratification in the extratropics of the earth's atmosphere.

The dynamical constraint implies that if baroclinic eddies determine the tropopause height and thermal stratification, an atmosphere organizes itself into a state in which nonlinear interactions among eddies are inhibited. The inhibition of nonlinear eddy–eddy interactions offers an explanation for the historic successes of linear and weakly nonlinear models of large-scale extratropical dynamics.

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Tapio Schneider

Abstract

Estimating the mean and the covariance matrix of an incomplete dataset and filling in missing values with imputed values is generally a nonlinear problem, which must be solved iteratively. The expectation maximization (EM) algorithm for Gaussian data, an iterative method both for the estimation of mean values and covariance matrices from incomplete datasets and for the imputation of missing values, is taken as the point of departure for the development of a regularized EM algorithm. In contrast to the conventional EM algorithm, the regularized EM algorithm is applicable to sets of climate data, in which the number of variables typically exceeds the sample size. The regularized EM algorithm is based on iterated analyses of linear regressions of variables with missing values on variables with available values, with regression coefficients estimated by ridge regression, a regularized regression method in which a continuous regularization parameter controls the filtering of the noise in the data. The regularization parameter is determined by generalized cross-validation, such as to minimize, approximately, the expected mean-squared error of the imputed values. The regularized EM algorithm can estimate, and exploit for the imputation of missing values, both synchronic and diachronic covariance matrices, which may contain information on spatial covariability, stationary temporal covariability, or cyclostationary temporal covariability. A test of the regularized EM algorithm with simulated surface temperature data demonstrates that the algorithm is applicable to typical sets of climate data and that it leads to more accurate estimates of the missing values than a conventional noniterative imputation technique.

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Junjun Liu
and
Tapio Schneider

Abstract

The giant planet atmospheres exhibit alternating prograde (eastward) and retrograde (westward) jets of different speeds and widths, with an equatorial jet that is prograde on Jupiter and Saturn and retrograde on Uranus and Neptune. The jets are variously thought to be driven by differential radiative heating of the upper atmosphere or by intrinsic heat fluxes emanating from the deep interior. However, existing models cannot account for the different flow configurations on the giant planets in an energetically consistent manner. Here a three-dimensional general circulation model is used to show that the different flow configurations can be reproduced by mechanisms universal across the giant planets if differences in their radiative heating and intrinsic heat fluxes are taken into account. Whether the equatorial jet is prograde or retrograde depends on whether the deep intrinsic heat fluxes are strong enough that convection penetrates into the upper troposphere and generates strong equatorial Rossby waves there. Prograde equatorial jets result if convective Rossby wave generation is strong and low-latitude angular momentum flux divergence owing to baroclinic eddies generated off the equator is sufficiently weak (Jupiter and Saturn). Retrograde equatorial jets result if either convective Rossby wave generation is weak or absent (Uranus) or low-latitude angular momentum flux divergence owing to baroclinic eddies is sufficiently strong (Neptune). The different speeds and widths of the off-equatorial jets depend, among other factors, on the differential radiative heating of the atmosphere and the altitude of the jets, which are vertically sheared. The simulations have closed energy and angular momentum balances that are consistent with observations of the giant planets. They exhibit temperature structures closely resembling those observed and make predictions about as yet unobserved aspects of flow and temperature structures.

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Simona Bordoni
and
Tapio Schneider

Abstract

Steady-state and time-dependent Hadley circulations are investigated with an idealized dry GCM, in which thermal forcing is represented as relaxation of temperatures toward a radiative-equilibrium state. The latitude ϕ 0 of maximum radiative-equilibrium temperature is progressively displaced off the equator or varied in time to study how the Hadley circulation responds to seasonally varying forcing; axisymmetric simulations are compared with eddy-permitting simulations. In axisymmetric steady-state simulations, the Hadley circulations for all ϕ 0 approach the nearly inviscid, angular-momentum-conserving limit, despite the presence of finite vertical diffusion of momentum and dry static energy. In contrast, in corresponding eddy-permitting simulations, the Hadley circulations undergo a regime transition as ϕ 0 is increased, from an equinox regime (small ϕ 0) in which eddy momentum fluxes strongly influence both Hadley cells to a solstice regime (large ϕ 0) in which the cross-equatorial winter Hadley cell more closely approaches the angular-momentum-conserving limit. In axisymmetric time-dependent simulations, the Hadley cells undergo transitions between a linear equinox regime and a nonlinear, nearly angular-momentum-conserving solstice regime. Unlike in the eddy-permitting simulations, time tendencies of the zonal wind play a role in the dynamics of the transitions in the axisymmetric simulation. Nonetheless, the axisymmetric transitions are similar to those in the eddy-permitting simulations in that the role of the nonlinear mean momentum flux divergence in the zonal momentum budget shifts from marginal in the equinox regime to dominant in the solstice regime. As in the eddy-permitting simulations, a mean-flow feedback—involving the upper-level zonal winds, the lower-level temperature gradient, and the poleward boundary of the cross-equatorial Hadley cell—makes it possible for the circulation fields to change at the transition more rapidly than can be explained by the steady-state response to the thermal forcing. However, the regime transitions in the axisymmetric simulations are less sharp than those in the eddy-permitting simulations because eddy–mean flow feedbacks in the eddy-permitting simulations additionally sharpen the transitions.

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Yohai Kaspi
and
Tapio Schneider

Abstract

Transient and stationary eddies shape the extratropical climate through their transport of heat, moisture, and momentum. In the zonal mean, the transports by transient eddies dominate over those by stationary eddies, but this is not necessarily the case locally. In particular, in storm-track entrance and exit regions during winter, stationary eddies and their interactions with the mean flow dominate the atmospheric energy transport. Here it is shown that stationary eddies can shape storm tracks and control where they terminate by modifying local baroclinicity. Simulations with an idealized aquaplanet GCM show that zonally localized surface heating alone (e.g., ocean heat flux convergence) gives rise to storm tracks, which have a well-defined length scale that is similar to that of Earth's storm tracks. The storm tracks terminate downstream of the surface heating even in the absence of continents, at a distance controlled by the stationary Rossby wavelength scale. Stationary eddies play a dual role: within about half a Rossby wavelength downstream of the heating region, stationary eddy energy fluxes increase the baroclinicity and therefore contribute to energizing the storm track; farther downstream, enhanced poleward and upward energy transport by stationary eddies reduces the baroclinicity by reducing the meridional temperature gradients and enhancing the static stability. Transports both of sensible and latent heat (water vapor) play important roles in determining where storm tracks terminate.

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Tapio Schneider
and
Simona Bordoni

Abstract

In a simulation of seasonal cycles with an idealized general circulation model without a hydrologic cycle and with zonally symmetric boundary conditions, the Hadley cells undergo transitions between two regimes distinguishable according to whether large-scale eddy momentum fluxes strongly or weakly influence the strength of a cell. The center of the summer and equinox Hadley cell lies in a latitude zone of upper-level westerlies and significant eddy momentum flux divergence; the influence of eddy momentum fluxes on the strength of the cell is strong. The center of the cross-equatorial winter Hadley cell lies in a latitude zone of upper-level easterlies and is shielded from the energy-containing midlatitude eddies; the influence of eddy momentum fluxes on the strength of the cell is weak. Mediated by feedbacks between eddy fluxes, mean zonal winds at upper levels, and the mean meridional circulation, the dominant balance in the zonal momentum equation at the center of a Hadley cell shifts at the transitions between the regimes, from eddies dominating the momentum flux divergence in the summer and equinox cell to the mean meridional circulation dominating in the winter cell. At the transitions, a feedback involving changes in the strength of the lower-level temperature advection and in the latitude of the boundary between the winter and summer cell is responsible for changes in the strength of the cross-equatorial winter cell. The transitions resemble the onset and end of monsoons, for example, in the shift in the dominant zonal momentum balance, rapid shifts in the latitudes of maximum meridional mass flux and of maximum convergence at lower levels, rapid changes in strength of the upward mass flux, and changes in direction and strength of the zonal wind at upper and lower levels. In the monsoonal regime, the maximum upward mass flux occurs in an off-equatorial convergence zone located where the balance of the meridional geopotential gradient in the planetary boundary layer shifts from nonlinear frictional to geostrophic. Similar dynamic mechanisms as at the regime transitions in the simulation—mechanisms that can act irrespective of land–sea contrasts and other inhomogeneities in lower boundary conditions—may be implicated in large-scale monsoon dynamics in Earth’s atmosphere.

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Tapio Schneider
and
Junjun Liu

Abstract

The zonal flow in Jupiter’s upper troposphere is organized into alternating retrograde and prograde jets, with a prograde (superrotating) jet at the equator. Existing models posit as the driver of the flow either differential radiative heating of the atmosphere or intrinsic heat fluxes emanating from the deep interior; however, they do not reproduce all large-scale features of Jupiter’s jets and thermal structure. Here it is shown that the difficulties in accounting for Jupiter’s jets and thermal structure resolve if the effects of differential radiative heating and intrinsic heat fluxes are considered together, and if upper-tropospheric dynamics are linked to a magnetohydrodynamic (MHD) drag that acts deep in the atmosphere and affects the zonal flow away from but not near the equator. Baroclinic eddies generated by differential radiative heating can account for the off-equatorial jets; meridionally propagating equatorial Rossby waves generated by intrinsic convective heat fluxes can account for the equatorial superrotation. The zonal flow extends deeply into the atmosphere, with its speed changing with depth, away from the equator up to depths at which the MHD drag acts. The theory is supported by simulations with an energetically consistent general circulation model of Jupiter’s outer atmosphere. A simulation that incorporates differential radiative heating and intrinsic heat fluxes reproduces Jupiter’s observed jets and thermal structure and makes testable predictions about as yet unobserved aspects thereof. A control simulation that incorporates only differential radiative heating but not intrinsic heat fluxes produces off-equatorial jets but no equatorial superrotation; another control simulation that incorporates only intrinsic heat fluxes but not differential radiative heating produces equatorial superrotation but no off-equatorial jets. The proposed mechanisms for the formation of jets and equatorial superrotation likely act in the atmospheres of all giant planets.

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Yohai Kaspi
and
Tapio Schneider

Abstract

The Northern Hemisphere storm tracks have maximum intensity over the Pacific and Atlantic basins; their intensity is reduced over the continents downstream. Here, simulations with an idealized aquaplanet general circulation model are used to demonstrate that even without continents, storm tracks have a self-determined longitudinal length scale. Their length is controlled primarily by the planetary rotation rate and is similar to that of Earth’s storm tracks for Earth’s rotation rate. Downstream, storm tracks self-destruct: the downstream eddy kinetic energy is lower than it would be without the zonal asymmetries that cause localized storm tracks. Likely involved in the downstream self-destruction of storm tracks are the energy fluxes associated with them. The zonal asymmetries that cause localized storm tracks enhance the energy transport through the generation of stationary eddies, and this leads to a reduced baroclinicity that persists far downstream of the eddy kinetic energy maxima.

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Junjun Liu
and
Tapio Schneider

Abstract

In rapidly rotating planetary atmospheres that are heated from below, equatorial superrotation can occur through convective generation of equatorial Rossby waves. If the heating from below is sufficiently strong that convection penetrates into the upper troposphere, then the convection generates equatorial Rossby waves, which can induce the equatorward angular momentum transport necessary for superrotation. This paper investigates the conditions under which the convective generation of equatorial Rossby waves and their angular momentum transport lead to superrotation. It also addresses how the strength and width of superrotating equatorial jets are controlled.

In simulations with an idealized general circulation model (GCM), the relative roles of baroclinicity, heating from below, and bottom drag are explored systematically. Equatorial superrotation generally occurs when the heating from below is sufficiently strong. However, the threshold heating at which the transition to superrotation occurs increases as the baroclinicity or the bottom drag increases. The greater the baroclinicity is, the stronger the angular momentum transport out of low latitudes by baroclinic eddies of extratropical origin. This competes with the angular momentum transport toward the equator by convectively generated Rossby waves and thus can inhibit a transition to superrotation. Equatorial bottom drag damps both the mean zonal flow and convectively generated Rossby waves, weakening the equatorward angular momentum transport as the drag increases; this can also inhibit a transition to superrotation. The strength of superrotating equatorial jets scales approximately with the square of their width. When they are sufficiently strong, their width, in turn, scales with the equatorial Rossby radius and thus depends on the thermal stratification of the equatorial atmosphere.

The results have broad implications for planetary atmospheres, particularly for how superrotation can be generated in giant planet atmospheres and in terrestrial atmospheres in warm climates.

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