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Isaac M. Held and Ngar-Cheung(Gabriel) Lau
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Michael Winton, Ken Takahashi, and Isaac M. Held

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This article proposes a modification to the standard forcing–feedback diagnostic energy balance model to account for 1) differences between effective and equilibrium climate sensitivities and 2) the variation of effective sensitivity over time in climate change experiments with coupled atmosphere–ocean climate models. In the spirit of Hansen et al. an efficacy factor is applied to the ocean heat uptake. Comparing the time evolution of the surface warming in high and low efficacy models demonstrates the role of this efficacy in the transient response to CO2 forcing. Abrupt CO2 increase experiments show that the large efficacy of the Geophysical Fluid Dynamics Laboratory’s Climate Model version 2.1 (CM2.1) sets up in the first two decades following the increase in forcing. The use of an efficacy is necessary to fit this model’s global mean temperature evolution in periods with both increasing and stable forcing. The intermodel correlation of transient climate response with ocean heat uptake efficacy is greater than its correlation with equilibrium climate sensitivity in an ensemble of climate models used for the third and fourth Intergovernmental Panel on Climate Change (IPCC) assessments. When computed at the time of doubling in the standard experiment with 1% yr−1 increase in CO2, the efficacy is variable amongst the models but is generally greater than 1, averages between 1.3 and 1.4, and is as large as 1.75 in several models.

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Olivier Pauluis, V. Balaji, and Isaac M. Held
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Aiko Voigt, Isaac M. Held, and Jochem Marotzke

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The Hadley cell of a virtually dry snowball Earth atmosphere under equinox insolation is studied in a comprehensive atmospheric general circulation model. In contrast to the Hadley cell of modern Earth, momentum transport by dry convection, which is modeled as vertical diffusion of momentum, is important in the upper branch of the snowball Earth Hadley cell. In the zonal momentum balance, mean meridional advection of mean absolute vorticity is not only balanced by eddies but also by vertical diffusion of zonal momentum. Vertical diffusion also contributes to the meridional momentum balance by decelerating the Hadley cell through downgradient mixing of meridional momentum between its upper and lower branches. When vertical diffusion of momentum is suppressed in the upper branch, the Hadley cell strengthens by a factor of about 2. This is in line with the effect of vertical diffusion in the meridional momentum balance but in contrast with its effect in the zonal momentum balance. Neither axisymmetric Hadley cell theories based on angular momentum conservation nor eddy-permitting Hadley cell theories that neglect vertical diffusion of momentum are applicable to the snowball Earth Hadley cell. Because the snowball Earth Hadley cell is a particular realization of a dry Hadley cell, these results show that an appropriate description of dry Hadley cells should take into account vertical transport of momentum by dry convection.

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William J. Randel and Isaac M. Held

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Tropospheric zonal mean eddy fluxes of heat and momentum, and the divergence of the Eliassen-Palm flux, are decomposed into contributions from different zonal phase speeds. Data analyzed are ECMWF operational global analyses covering 1980–87. Eastward moving medium-scale waves (zonal waves 4–7) dominate the spectra of lower tropospheric heat fluxes in both hemispheres and all seasons. Upper tropospheric wave flux spectra are similar to the low level spectra in midlatitudes, but shift to slower zonal phase speeds as low latitudes are approached. The cause of this shift is the selective absorption of faster moving components in midlatitudes as the waves propagate meridionally. Latitude-phase speed distributions of eddy fluxes are constructed and compared to the zonal mean wind structure. These results demonstrate that upper tropospheric eddies break and decelerate the zonal mean flow approximately 10°–20° in latitude away from their critical line (where phase speed equals zonal wind speed). Comparisons are also made with results from the middle stratosphere.

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Isaac M. Held and Peter J. Phillips

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An example of the barotropic decay of wavelike midlatitude disturbance in the presence of a shear flow on the sphere is examined. The linear theory for the evolution of the disturbance is first described, with emphasis on the importance of the pseudomomentum spectrum for the resulting drag on the mean flow. After a brief discussion of the ways in which this linear theory can break down, a high-resolution nonlinear numerical model is used to examine the dependence of the mean-flow modification and the qualitative character of the decay on the amplitude of the initial disturbance.

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Vitaly D. Larichev and Isaac M. Held

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A horizontally homogeneous two-layer quasigeostrophic model with imposed environmental vertical shear is used to study eddy energies and fluxes in the regime in which an inverse barotropic energy cascade excites eddies of much larger scale than the deformation radius. It is shown that the eddy potential vorticity flux, “thickness” flux, and the extraction of energy from the background flow are dominated by the largest eddies excited by the cascade, and not by deformation-scale eddies. The role of the latter is a catalytic one of transferring the baroclinic energy cascading downscale into the barotropic mode, thereby energizing the inverse cascade.

Based on this picture, scaling arguments are developed for the eddy energy level and potential vorticity flux in statistical equilibrium. The potential vorticity flux can be thought of as generated by a diffusivity of magnitude Ukd/k20, where U is the difference between the mean currents in the two layers, kd is the inverse of the deformation radius, and k 0 is the wavenumber of the energy-containing eddies. This result is closely related to that proposed by Green, although the underlying dynamical picture is different.

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In-Sik Kang and Isaac M. Held

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The upper tropospheric circulation during northern summer produced by a general circulation model (GCM) is studied using linear and nonlinear barotropic models and by analysing a streamfunction budget. The model experiments and the budget calculations both show a simple Sverdrup balance to he a useful first approximation for the largest scales during this season. In this Sverdrup balance, the advection of planetary vorticity by the divergent component of the flow is found to be significant, particularly in the Southern Hemisphere tropics.

Nonlinear barotropic models improve the simulation of regional structures. The correct position of the Tibetan high is explained by Sverdrup balance, but its amplitude and structure are reasonably well simulated only with the nonlinear models. With climatological forcing, the time-averaged solutions of the nonlinear model are insensitive to the strength of the damping included in the model. The difference between the GCM's climatology and the GCM's flow in a particular summer is more difficult to model because of the large contribution of anomalous transients to the maintenance of the flow. However, strongly damped models produce simulations that bear some resemblance to the anomalous flow, at least in the tropics.

To estimate the potential importance of vertical transport of momentum during moist convection, a damping proportional to the precipitation rate in the GCM is added in the nonlinear model. The estimated damping time scale for the eddy streamfunction is ∼5 days in the northern tropics, but the changes in the predicted stationary eddy streamfunction are modest.

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David B. Stephenson and Isaac M. Held

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The response of the Geophysical Fluid Dynamics Laboratory (GFDL) coupled ocean-atmosphere R15, 9-level GCM to gradually increasing C02 amounts is analyzed with emphasis on the changes in the stationary waves and storm tracks in the Northern Hemisphere wintertime troposphere. A large part of the change is described by an equivalent-barotropic stationary wave with a high over eastern Canada and a low over southern Alaska. Consistent with this, the Atlantic jet weakens near the North American coast.

Perpetual winter runs of an R15, nine-level atmospheric GCM with sea surface temperature, sea ice thickness, and soil moisture values prescribed from the coupled GCM results are able to reproduce the coupled model's response qualitatively. Consistent with the weakened baroclinicity associated with the stationary wave change, the Atlantic storm track weakens with increasing C02 concentrations while the Pacific storm track does not change in strength substantially.

An R15, nine-level atmospheric model linearized about the zonal time-mean state is used to analyze the contributions to the stationary wave response. With mountains, diabatic heating, and transient forcings the linear model gives a stationary wave change in qualitative agreement with the change seen in the coupled and perpetual models. Transients and diabatic heating appear to be the major forcing terms, while changes in zonal-mean basic state and topographic forcing play only a small role. A substantial part of the diabatic response is due to changes in tropical latent heating.

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Isaac M. Held and David G. Andrews

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The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However. some exceptions to this general rule exist.

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