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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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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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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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Cheikh Mbengue and Tapio Schneider

Abstract

Earth’s storm tracks are instrumental for transporting heat, momentum, and moisture and thus strongly influence the surface climate. Climate models, supported by a growing body of observational data, have demonstrated that storm tracks shift poleward as the climate warms. But the dynamical mechanisms responsible for this shift remain unclear. To isolate what portion of the storm track shift may be accounted for by large-scale dry dynamics alone, disregarding the latent heat released in phase changes of water, this study investigates the storm track shift under various kinds of climate change in an idealized dry general circulation model (GCM) with an adjustable but constant convective stability. It is found that increasing the mean surface temperature or the convective stability leads to poleward shifts of storm tracks, even if the convective stability is increased only in a narrow band around the equator. Under warming and convective stability changes roughly corresponding to a doubling of CO2 concentrations from a present-day Earthlike climate, storm tracks shift about 0.8° poleward, somewhat less than but in qualitative agreement with studies using moist GCMs. About 63% (0.5°) of the poleward shift is shown to be caused by tropical convective stability variations. This demonstrates that tropical processes alone (the increased dry static stability of a warmer moist adiabat) can account for part of the poleward shift of storm tracks under global warming. This poleward shift generally occurs in tandem with a poleward expansion of the Hadley circulation; however, the Hadley circulation expansion does not always parallel the storm track shift.

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Florent Brient and Tapio Schneider

Abstract

Physical uncertainties in global-warming projections are dominated by uncertainties about how the fraction of incoming shortwave radiation that clouds reflect will change as greenhouse gas concentrations rise. Differences in the shortwave reflection by low clouds over tropical oceans alone account for more than half of the variance of the equilibrium climate sensitivity (ECS) among climate models, which ranges from 2.1 to 4.7 K. Space-based measurements now provide an opportunity to assess how well models reproduce temporal variations of this shortwave reflection on seasonal to interannual time scales. Here such space-based measurements are used to show that shortwave reflection by low clouds over tropical oceans decreases robustly when the underlying surface warms, for example, by −(0.96 ± 0.22)% K−1 (90% confidence level) for deseasonalized variations. Additionally, the temporal covariance of low-cloud reflection with temperature in historical simulations with current climate models correlates strongly (r = −0.67) with the models’ ECS. Therefore, measurements of temporal low-cloud variations can be used to constrain ECS estimates based on climate models. An information-theoretic weighting of climate models by how well they reproduce the measured deseasonalized covariance of shortwave cloud reflection with temperature yields a most likely ECS estimate around 4.0 K; an ECS below 2.3 K becomes very unlikely (90% confidence).

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Cheikh Mbengue and Tapio Schneider

Abstract

Zonal-mean storm-track shifts in response to perturbations in climate occur even in idealized simulations of dry atmospheres with axisymmetric forcing. Nonetheless, a generally accepted theory of the mechanisms controlling the storm-track shifts is still lacking. Here, mean available potential energy (MAPE), a general measure of baroclinicity that is proportional to the square of the Eady growth rate, is used to understand storm-track shifts. It is demonstrated that, in dry atmospheres, the eddy kinetic energy (EKE) in a storm track is linearly related to the mean available potential energy, relative to a local reference state, and that maxima of the two are generally collocated in latitude. Changes in MAPE with climate are then decomposed into components. It is shown that in simulations of dry atmospheres, changes in the latitude of maximum MAPE are dominated by changes in near-surface meridional temperature gradients. By contrast, changes in the magnitude of MAPE are primarily determined by changes in static stability and in the depth of the troposphere. A theory of storm-track shifts may build upon these findings and primarily needs to explain changes in near-surface meridional temperature gradients. The terminus of the Hadley circulation often shifts in tandem with storm tracks and is hypothesized to play an important role in triggering the storm-track shifts seen in this idealized dry context, especially in simulations where increases only in the convective static stability in the deep tropics suffice to shift storm tracks poleward.

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Tobias Bischoff and Tapio Schneider

Abstract

The intertropical convergence zone (ITCZ) can shift meridionally on seasonal and longer time scales. Previous studies have shown that the latitude of the ITCZ is negatively correlated with cross-equatorial atmospheric energy transport. For example, the ITCZ shifts southward as the Northern Hemisphere cools and the northward cross-equatorial energy transport strengthens in response. It has remained unclear what controls the sensitivity of the ITCZ position to cross-equatorial energy transport and what other factors may lead to shifts of the ITCZ position. Here it is shown that the sensitivity of the ITCZ position to cross-equatorial energy transport depends on the net energy input to the equatorial atmosphere: the net radiative energy input minus any energy uptake by the oceans. Changes in this energy input can also lead to ITCZ shifts. The cross-equatorial energy transport is related through a series of approximations to interhemispheric asymmetries in the near-surface temperature distribution. The resulting theory of the ITCZ position is tested in idealized general circulation model simulations with a slab ocean as lower boundary condition. In the simulations, cross-equatorial energy transport increases under global warming (primarily because extratropical latent energy fluxes strengthen), and this shifts the ITCZ poleward. The ITCZ shifts equatorward if primarily the tropics warm in response to an increased net energy input to the equatorial atmosphere. The results have implications for explaining the varied response of the ITCZ to global or primarily tropical changes in the atmospheric energy balance, such as those that occur under global warming or El Niño.

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Tapio Schneider and Adam Sobel
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