In rapidly rotating atmospheres, the Rossby number in the extratropics is small, and geostrophic balance is the dominant balance in the horizontal momentum equations. In the zonal mean, zonal pressure gradients vanish, but meridional pressure gradients do not, so if the dominant momentum balance is geostrophic, winds are anisotropic with , where denotes a zonal mean. Variations in the planetary vorticity with latitude, β, are central to vorticity mixing arguments [e.g., Rhines, 1994; Held, 2000], which can account for the generation of atmospheric zonal jets: When a Rossby wave packet stirs the atmosphere in a region bounded by a polar cap, highvorticity fluid moves equatorward and low-vorticity fluid moves poleward. This reduces the vorticity in the polar cap. By Stokes' Theorem, the reduced vorticity in the polar cap means that the zonal wind at the latitude of the bounding cap decreases; if angular momentum is conserved, the zonal wind outside the polar cap increases. Irreversible vorticity mixing (wave-breaking or dissipation) is necessary to maintain the angular momentum fluxes in the time mean. Thus, the larger planetary vorticity gradients of the rapidly rotating planet allow zonal jets to form provided there is a source of wave activity that leads to vorticity stirring.
 We return to the analysis of Charney  to estimate temperature variations in the free atmosphere. For rapidly rotating planets, geostrophic balance holds in the horizontal momentum equations: δp/(ρL) ∼ fU. Combining the scaling from the momentum equation with the hydrostatic relation, the pressure, density, and (potential) temperature variations scale like the ratio of the Froude number to the Rossby number,
Where the Rossby number is small (in the extratropics), the temperature variations will be a factor of order inverse Rossby number (Ro−1 ∼ 10) larger than in the slowly rotating simulation for similar values of U, g, and H. Thus, we expect larger horizontal temperature and pressure variations away from the equator in the rapidly rotating simulation.
4.1. Surface Temperature and Outgoing Longwave Radiation
 In the rapidly rotating simulation, the surface temperature on the day side of the planet is maximal off of the equator and does not bear a close resemblance to the insolation distribution; the night side of the planet has relatively warm regions in western high latitudes (Figure 1). Compared to the slowly rotating simulation, the surface temperature is more substantially modified by the atmospheric circulation; however, the temperature contrasts between the day and night side are similar.
 The outgoing longwave radiation of the rapidly rotating simulation has substantial variations (Figure 1). Some of the structures in the surface temperature are echoed in the OLR distribution. Compared to the slowly rotating simulation, OLR variations have smaller spatial scales and occupy a wider range of values.
4.2. Hydrological Cycle
 Surface evaporation rates mimic the insolation distribution (Figure 2). This is one of the most similar fields between the slowly and rapidly rotating simulations, as expected from the gross similarity in surface temperature and the smallness of the Bowen ratio at these temperatures (Figure 3). This might not be the case if the model included the radiative effects of clouds since the amount of shortwave radiation reaching the surface would be shaped by variations in cloud albedo, which, in turn, depend on the atmospheric circulation.
 Precipitation rates are large in a crescent-shaped region on the day side of the planet; the night side of the planet generally has small but nonzero precipitation rates (Figure 2). The evaporation minus precipitation field has substantial structure: there are large amplitude changes from the convergence zones (P > E) to nearby areas of significant net drying (E > P). Comparing the slowly and rapidly rotating simulations shows that precipitation and E – P on the night side of the planet are sensitive to the atmospheric circulation.
 An interesting aspect of the climate is that the precipitation maximum (near ∼15° latitude) is not co-located with the off-equatorial surface temperature maximum (near ∼40° latitude). The simulation provides an example of precipitation and deep convection that are not locally thermodynamically controlled: the precipitation is not maximum where the surface temperature is maximum; the column static stability (e.g., Figure 13), and therefore the convective available potential energy, are not markedly different between the maxima in precipitation and temperature. However, if the surface climate is examined latitude-by-latitude instead of examining the global maxima, the region of large precipitation is close to the maximum surface temperature (as well as surface temperature curvature) at a given latitude. The structure of the surface winds, discussed next, and the associated moisture convergence are key for determining where precipitation is large. Sobel  provides a review of these two classes of theories for tropical precipitation (thermodynamic control vs. momentum control) and the somewhat inconclusive evidence of which class of theory better accounts for Earth observations.
 The global precipitation is ∼10% larger in the rapidly rotating simulation than in the slowly rotating simulation. This suggests that radiative-convective equilibrium cannot completely describe the strength of the hydrological cycle.
4.3. General Circulation of the Atmosphere
 In the rapidly rotating simulation, the atmospheric circulation has several prominent features: there are westerly jets in high (∼65°) latitudes, the mid-tropospheric zonal wind exhibits equatorial superrotation, and the surface winds converge in a crescent-shaped region near the subsolar point (Figure 11). The equatorial superrotation and westerly jets are evident in the zonal-mean zonal wind (Figure 6).
Figure 11. Zonal wind (left) and meridional wind (right) of ΩE simulation on the σ = 0.28 (a), 0.54 (b), and 1.0 (c) surfaces. The contour interval is 5 m s−1, and the zero contour is not shown.
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 The existence of the high-latitude jets can be understood from the temperature field and eddy angular momentum flux convergence (Figures 13 and 6). There are large meridional temperature gradients, which give rise to zonal wind shear by thermal wind balance and provide available potential energy for baroclinic eddies that transport angular momentum into the jets. In the vertical average, the eddy angular momentum transport into an atmospheric column is balanced by surface stress (provided the Rossby number is small), so surface westerlies appear underneath high-latitude regions of angular momentum flux convergence.
 The equatorial superrotation is a consequence of angular momentum flux convergence (Figure 6). Saravanan  and Suarez and Duffy  describe the emergence of superrotation generated by large-scale, zonally asymmetric heating anomalies in the tropics. As in their idealized models, the zonal asymmetry in the low-latitude heating (in our simulation, provided by insolation) generates a stationary Rossby wave. Consistent with a stationary wave source, in the rapidly rotating simulation, the horizontal eddy angular momentum flux convergence in low latitudes is dominated by the stationary eddy component. This aspect of the simulation is sensitive to horizontal resolution and the subgrid-scale filter. With higher resolution or weaker filtering, the superrotation generally extends higher into the troposphere and has a larger maximum value.
 There is a crescent-shaped region where the surface zonal wind is converging. This is where the precipitation (Figure 2) and upward vertical velocity (Figure 5) are largest. The horizontal scale of the convergence zone is similar to the equatorial Rossby radius, (c/β)1/2, where β is the gradient of planetary vorticity and c is the gravity wave speed. If moisture effects are neglected, the gravity wave speed is estimated using a characteristic tropospheric value for the Brunt-Väisälä frequency on the day side of the planet, the equatorial Rossby radius corresponds to ∼10° latitude, which is of the same order as the scale of the convergence zone. The surface zonal wind can be qualitatively understood as the equatorially-trapped wave response to stationary heating: equatorial Kelvin waves propagate to the east of the heating and generate easterlies; equatorial Rossby waves propagate to the west of the heating and generate westerlies [Gill, 1980].
 The shape of the zero zonal wind line and its horizontal scale are similar to those of the Gill  model, which describes the response of damped, linear shallow-water waves to a prescribed heat/mass source. For the prescribed heat source in the original Gill model, the crescent-shape zero zonal wind line extends over ∼2 Rossby radii and, as in the GCM simulation, is displaced to the east of the heating maximum on the equator.
 A complicating factor in the analogy between the GCM's low-latitude surface winds and those of the Gill model is that the heating is prescribed in the Gill model, while it interacts with the flow in the GCM. As previously mentioned, the precipitation is strongly shaped by the winds. To see if the analogy between the winds in the GCM and in the Gill model breaks down because of the more complex structure of the latent heating, we force a variant of the Gill model with the GCM's precipitation field following the formulation of Neelin  (see Appendix for details). The results of this calculation are compared with the GCM output in Figure 12. The direction, large-scale structure, and, in the case of the zonal component, magnitude of the mass fluxes are similar between the GCM and precipitation-forced Gill model, though it is clear that there are quantitative differences. Better quantitative agreement particularly in the meridional component could be achieved by using anisotropic damping (different damping coefficients in the zonal and meridional direction) in the Gill model, as is common in studies of Earth's atmosphere [e.g., Stevens et al., 2002].
Figure 12. Zonal (left column) and meridional (right column) near-surface mass fluxes for the GCM (top row, averaged between the surface and σ = 0.73 model level) and the Gill model forced by the GCM's precipitation (bottom row, see Appendix for Gill model equations and parameters). The contour interval is 2 × 104 kg m−1 s−1.
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 In contrast to the zonal wind, which has larger magnitude, the meridional wind is diverging at the surface and converging aloft near the subsolar point (right panel of Figure 11a,c). As discussed by Gill , the reasons for this lie in the vorticity balance: for a Sverdrup vorticity balance, the vortex stretching caused by the overall convergence near the surface near the equator must be balanced by poleward motion, toward higher planetary vorticity, and vice versa at higher levels; hence, the meridional wind is poleward near the surface and equatorward aloft.
 The Eulerian mean mass streamfunction (Figure 6) has the opposite sense as Earth's Hadley cells: in the zonal mean, there is descent at the equator, poleward flow near the surface, ascent near 15°, and equatorward flow near the surface and in the mid-troposphere. If the dominant balance in the zonal momentum equation is between Coriolis acceleration and eddy angular momentum flux divergence, [i.e., small local Rossby number as defined in Walker and Schneider ], then the angular momentum flux convergence that establishes the superrotating zonal wind also leads to equatorward mean meridional wind in the free troposphere, as in Earth's Ferrel cells [e.g., Held, 2000]. This can lead to a dynamical feedback that enhances superrotation [Schneider and Liu, 2009]: as superrotation emerges, the mean meridional circulation can change direction with a concomitant change in the direction of mean-flow angular momentum fluxes (changing from exporting angular momentum from the deep tropics to importing it), which enhances the superrotation.
 The instantaneous, upper tropospheric zonal wind in the rapidly rotating simulation is shown in Figure 7, and a corresponding animation is available at doi: 10.3894/JAMES.2010.2.13.S2. The large-scale features of the general circulation such as the high-latitude jets and divergent zonal wind in the tropical upper troposphere are clear in the instantaneous winds. The eddies in the animation generally have larger spatial scales and longer timescales than in the corresponding slowly rotating animation.
 The vertically and globally integrated eddy kinetic energy is 1.0 × 106 J m−2. This is about 20% larger than in the slowly rotating case. The eddy kinetic energy spectrum has a typical n−3 shape in spherical wavenumber n, up to the smallest resolved wavenumber. But the integrated eddy kinetic energy hides an important difference in synoptic variability between the rapidly and slowly rotating simulations: in the extratropics, for zonal wavenumbers between ∼3–6, the rapidly rotating simulation has a factor of 2–3 times more velocity variance (Figure 8) than the slowly rotating simulation.
4.4. Atmospheric Stratification and Energy Transports
 The tropospheric temperature distribution on the day side of the planet (Figure 13) resembles the surface temperature distribution: the temperature field has a local maximum near ∼40° latitude and is relatively uniform up to high latitudes (up to ∼50°). In the free troposphere on the day side, the lapse rates are close to the moist adiabatic lapse rate, computed using the local temperature and pressure, over a region roughly within the 300 K contour of the surface temperature. Note that 300 K does not have a particular physical significance, e.g., as a deep convection threshold—we are simply using it to describe a feature of the simulation. There is a local minimum of temperature on the equator which may be related to the downward vertical velocity there (Figure 5). In low latitudes, there is a near-surface inversion on the night side of the rapidly rotating simulation that, as in the slowly rotating simulation, is the result of weak temperature gradients in the free troposphere and the substantial radiative cooling owing to the small optical thickness of the atmosphere.
Figure 13. Temperature section of antisolar longitudes (a) and subsolar longitudes (b) in ΩE simulation. Averages are taken over 10° of longitude. The contour interval is 10 K.
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 As in the slowly rotating simulation, the moist static energy flux diverges on the day side and converges on night side of the planet (solid curves in Figure 10); there is substantial cancellation between the dry static energy flux and the latent energy flux divergence near the subsolar point. Though the hydrological cycle is more active on the night side of the rapidly rotating simulation than in the slowly rotating simulation, the dry static energy component still dominates (≳ 80% of total) the moist static energy advection on the night side of the planet.
 The two simulations are more similar in this respect than might have been anticipated given the differences in their flow characteristics, although there are regional differences that are obscured by averaging over latitude. The broad similarities can be understood by considering the moist static energy budget. In the time mean, denoted by [·], neglecting kinetic energy fluxes and diffusive processes within the atmosphere, the mass-weighted vertical integral 〈·〉of the moist static energy flux divergence is balanced by surface energy fluxes Fs and radiative tendencies Qrad,
 As a result of the gross similarity of the two simulations in evaporation and low-latitude stratification (in part due to the smaller dynamical role that rotation plays near the equator), and hence the gross similarity in radiative cooling, the divergence of the moist static energy flux is also similar, at least in low latitudes and in the meridional mean. Locally in the extratropics, however, considering the sources and sinks of moist static energy does not provide a useful constraint because the stratification is dynamically determined and not moist adiabatic [e.g., Schneider, 2007], and there can be geostrophically balanced temperature gradients in rapidly rotating atmospheres. As a consequence, the radiative cooling, through dynamical influences on temperature, is determined by the flow, so the moist static energy flux divergence will generally depend on the rotation rate. Indeed, the warm regions on the night side of the rapidly rotating simulation have larger moist static energy flux divergence than the corresponding regions in the slowly rotating simulation.