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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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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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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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Sebastian Schemm and Tapio Schneider

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The wintertime evolution of the North Pacific storm track appears to challenge classical theories of baroclinic instability, which predict deeper extratropical cyclones when baroclinicity is highest. Although the surface baroclinicity peaks during midwinter, and the jet is strongest, eddy kinetic energy (EKE) and baroclinic conversion rates have a midwinter minimum over the North Pacific. This study investigates how the reduction in EKE translates into a reduction in eddy potential vorticity (PV) and heat fluxes via changes in eddy diffusivity. Additionally, it augments previous observations of the midwinter storm-track evolution in both hemispheres using climatologies of tracked surface cyclones. In the North Pacific, the number of surface cyclones is highest during midwinter, while the mean EKE per cyclone and the eddy lifetime are reduced. The midwinter reduction in upper-level eddy activity hence is not associated with a reduction in surface cyclone numbers. North Pacific eddy diffusivities exhibit a midwinter reduction at upper levels, where the Lagrangian decorrelation time is shortest (consistent with reduced eddy lifetimes) and the meridional parcel velocity variance is reduced (consistent with reduced EKE). The resulting midwinter reduction in North Pacific eddy diffusivities translates into an eddy PV flux suppression. In contrast, in the North Atlantic, a milder reduction in the decorrelation time is offset by a maximum in velocity variance, preventing a midwinter diffusivity minimum. The results suggest that a focus on causes of the wintertime evolution of Lagrangian decorrelation times and parcel velocity variance will be fruitful for understanding causes of seasonal storm-track variations.

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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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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

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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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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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