5.1. The Global Response
 We begin with brief summary of the fast global response of SP-CAM to CO2 quadrupling. We will then focus on the tropical response for the remainder of the paper.
 The global and tropical mean (30S-30N) values for the control run and their changes with 4xCO2 are shown in Table 1. The radiative impact of the 4xCO2 perturbation is dominated by a shift of effective emission to space of longwave radiation to colder temperatures, reducing the net emission. At the top of the atmosphere, global net outgoing longwave radiation is reduced by 6.7 W m−2 and the clear-sky net outgoing longwave is reduced by 8.0 W m−2, while net incoming all-sky and clear-sky shortwave radiation increases only 0.1 W m−2 and 0.2 W m−2, respectively. The reduction of clear-sky TOA net longwave radiation is about 8% larger in SP-CAM than the estimated model-ensemble mean value in the 4xCO2 experiments of Gregory and Webb .
 There is a significant slowing of the hydrological cycle with global-mean reduction in precipitation and surface latent heat flux. The fast impact of increased CO2 on the global hydrological cycle has been the focus of many recent modeling studies [e.g., Bala et al., 2009; Andrews et al., 2009; Wu et al., 2010; Andrews and Forster, 2010; Cao et al., 2011]. SP-CAM's 4% reduction in precipitation is similar to the precipitation reduction of 3.6% in the Community Atmosphere Model (CAM) 3.1 reported by Bala et al.  (based on doubling the response of their 2xCO2 experiment). It is substantially less than the 7% global precipitation reduction in the UK Met office Hadley Center model (HadCM3L) reported by Cao et al. .
 There is a slight increase in total cloud fraction (0.5%) led by modest increases in high and low clouds, and partially offset by a loss of middle clouds. The global mean total condensed water in the troposphere changes only slightly; the small 0.2 g m−2 increase in liquid water path (LWP) is offset by a 0.2 g m−2 decrease of ice water path (IWP).
 Global maps of mean change of LWCF and SWCF are shown in Figure 2, corrected by cloud mask (LWCF and SWCF of the control simulation are very similar to those presented in an earlier version of SP-CAM shown by Khairoutdinov et al. ). There are very large regional changes in LWCF and SWCF, especially in the tropics due to local cloud changes. However the corrected global mean changes of LWCF and SWCF are each only about −0.2 W m−2.
 Tropical-mean changes in Table 1 are qualitatively similar to global-mean changes in most regards - cloud cover changes only slightly and the strength of the hydrological cycle is reduced. For the remainder of the paper we shift our focus to tropical changes.
5.2. Tropical-Mean 4xCO2 Changes in Radiation and Precipitation
 Here we analyze the response of salient cloud-related variables in both tropical-mean (30S-30N), and partitioned between tropical land and ocean. Since both land and ocean encompass a wide variety of dynamical regimes, we use similar methodology to Bony et al.  to sort tropical column-months (land, ocean, or both) using monthly-mean pressure velocity at 500 hPa, ω500, and examine the responses in this dynamically binned framework.
 Table 1 includes statistics computed separately over tropical land and ocean regions. As tropical land coverage is only about 25%, the overall statistics are heavily influenced by the ocean regions. However the mean changes over land due to 4xCO2 are stronger and almost always of opposite sign to the changes over ocean, so the changes over land regions prove to also be important to the tropical mean. Colman and McAvaney  also discuss some opposing fast responses over ocean and land in their experiments.
 The overall net outgoing longwave (LW) flux at the top of the tropical atmosphere is reduced by 8.0 W m−2 (Table 1) due to a higher and colder effective CO2 emission level. There is also reduced LW surface cooling over both tropical ocean and land, but this mean reduction is smaller (3.3 W m−2). Therefore the atmospheric column-integrated LW cooling is reduced by 4.7 W m−2. There are much smaller increases in net downward SW fluxes at the TOA (0.4 W m−2) and at the surface (0.1 W m−2) which slightly further reduce the net tropospheric radiative cooling.
 Radiative cooling is present throughout the troposphere, but it is particularly strong (1.7 K day−1) near the top of the boundary layer between 800 and 900 hPa due to the strong vertical gradient of water vapor mixing ratio. With the increase of CO2, radiative cooling is reduced by 0.1–0.2 K day−1 in most of the lower troposphere, especially at the top of the boundary layer (Figure 3, magenta dashed line). We also performed offline calculations of the clear-sky radiative heating rates using the mean ω-sorted and averaged temperature and moisture profiles. These are averaged over all ω's and also plotted in Figure 3 (light blue dot-dashed line). Above 900 hPa, the clear-sky changes are similar to the full model radiative cooling changes. This implies that the decrease in lower to mid-tropospheric radiative cooling is primarily a clear-sky phenomenon, and not mainly a result of fast cloud changes. In the layer near the surface (900–1000 hPa) the reduction of SP-CAM radiative cooling is much weaker than predicted from the clear-sky change, presumably due to the effects of boundary layer cloud.
Figure 3. SP-CAM tropical mean heating rates in K day−1 for control (black solid), 4xCO2 (magenta dashed), and control-plus-clear-sky change due to 4xCO2 (light blue dot-dashed, computed offline).
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 Accompanying the reduction in tropospheric radiative cooling is a reduction in tropical-mean precipitation by 0.13 mm day−1 (Table 1), or 3.8%, and a reduction in condensational heating of 3.8 W m−2. The surface latent heat flux is similarly reduced by 3.9 W m−2.
 The precipitation and its change can usefully be analyzed using dynamical ω500-binning. Figure 4a shows the expected strong linear relationship between precipitation and ω in ascent regions over both land and oceans, with strongest precipitation in regions of strongest mid-tropospheric ascent. With the quadrupling of CO2 precipitation is reduced across almost all tropical ω regimes (Figure 4b), especially in most regions of strong ascent.
Figure 4. (a) Surface precipitation in mm day−1 for ocean (blue dot-dashed), land (red dashed), and tropics-wide (black solid) sorted by ω500. (b) Precipitation changes due to 4xCO2 with error bars estimated from precipitation differences for simulation year 1 and year 2 considered separately. Omega percentiles are indicated in green at the top of the figure.
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 There is also a positive ‘dynamic’ contribution to the precipitation response (in the terminology of Bony et al. ) due to a slight shift in the tropics-wide ω PDF toward more mean ascent (see next section), but it has only about 15% of the amplitude of the sum of the ‘thermodynamic’ contribution plotted here.
5.3. Shifts Between Ocean and Land
 One key feature of the perturbed climate is the change in land surface temperature, as shown in Figure 5. Over most of the globe, the land-surface temperature increases with a global land-mean increase of 0.87 K. An ensemble average of 10 climate models by Andrews et al.  gives a fast global land surface warming of 0.49 K for a 2xCO2 perturbation, so the SP-CAM land warming response is a little weaker than most of these models. The tropical-mean land temperature increase is SP-CAM is 0.50 K, with especially strong surface warming in tropical deserts. The land temperature increase is primarily caused by the greenhouse effect of the added CO2. That is, even before any change in atmospheric temperature or moisture, the downward flux of infrared radiation increases. The land surface temperature warms rapidly because of its weak thermal inertia until a new radiative balance is reached. This surface warming is reduced by the tropospheric export of moist static energy from land columns to ocean columns [see Lambert et al., 2011]. Additional mechanisms for land-sea surface temperature contrast in both transient and equilibrium climate perturbatio'n experiments are considered by Joshi et al. , Dong et al. , and Lambert et al. .
 With increased CO2 in SP-CAM, there is a general tropospheric warming, particularly over land (Figure 6), where it increases with height reaching a maximum in the upper troposphere at about 280 hPa. Over the ocean, the warming profile also has a second maximum at 820 hPa discussed further in Section 5.4.
Figure 6. SP-CAM mean potential temperature change in K for all tropical columns (black solid), ocean (blue dash-dotted), land (red dashed), and regions with stable MBL's (green dotted) to be discussed in section 5.4. Note that temperature changes at each pressure level are computed only for above-surface points, so the population of columns represented varies with pressure level near the surface. The land profile is plotted only to about 960 hPa, the median tropical land surface pressure.
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 A consequence of the warming of land surfaces relative to fixed SSTs and relatively stronger warming of the troposphere near the land surface is a shift of convection from ocean to land regions. There is an increase of mean ascent in the mid-troposphere (−ω500) over land by almost 3 hPa day−1, and the fraction of overall tropical precipitation that falls over land areas increases 18%. The shift to land is further examined in Figure 7 which shows PDFs of ω500 for the control climate and their changes with increased CO2. Here the column-months are sorted into bins of 20 hPa day−1 from −190 hPa day−1 to 150 hPa day−1. This sorting is done separately for land regions (red dashed line), ocean regions (blue dash-dotted line), and the entire tropics (black solid line). In the control climate (Figure 7a), the ω500 PDFs for ocean and land are fairly similar. The dominant feature of the changes over land (Figure 7b) is a shift in PDF from regions of mean subsidence to those where mean upward motion is already strong (from −50 to −130 hPa day−1). The PDF changes over ocean regions are generally the opposite in sign but much weaker. The overall response of the tropics-wide PDF is a slight shift away from extreme values of ω500 (a slowdown of the overturning circulation) and also a slight shift toward mean ascent. A similar shift in circulation is also noted in HadAM3 2xCO2 experiments by Lambert et al. .
Figure 7. (a) PDF of tropical monthly pressure velocity ω at 500 hPa and (b) its change due to 4xCO2 for SP-CAM. Separate PDF's are plotted for ocean (blue dash-dotted), land (red dashed) and all points (black solid). Error bars are estimated from PDF changes of years one and two considered separately.
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 Figure 8 shows a conceptual diagram of these changes. Increasing downward longwave radiation leads to warmer land surface temperatures and a larger land-ocean thermal contrast (due to the fixed SSTs). This in turn leads to more upward motion and convection, more clouds at all vertical levels, and more precipitation over land with opposite effects over the oceans. While the fixed SSTs in the 4xCO2 experiment are somewhat unrealistic, even in a coupled ocean-atmosphere GCM the larger thermal inertia of the ocean relative to land would lead to much slower warming of the ocean surface than the land surface and a larger land-ocean thermal contrast. As a result, the changes seen here would likely be present in the early years of experiments with instantaneous increases of CO2 in coupled models.
Figure 8. Conceptual picture of rapid tropical cloud changes due to increasing CO2 shown together with mean tropical SP-CAM changes.
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 We now examine some elements of this conceptual picture in more detail, beginning with land-ocean shifts in precipitation due to increasing CO2. Land precipitation increases strongly (+0.25 mm day−1) and ocean precipitation decreases strongly (−0.25 mm day−1) (Table 1) associated with the shift of strong ascent and deep convection from ocean to land regions.
 The 4xCO2 liquid water path (LWP) and ice water path (IWP) respond to this shift of convection, increasing sharply over land and decreasing more modestly over ocean (Table 1). These effects largely cancel in the tropical mean. The tropical mean LWP is reduced by only about 1.2 g m−2 or 1.6% and the tropical mean IWP increases by only 0.1 g m−2 or 0.6%.
 The combined land and ocean cloud fraction sorted by ω are presented in Figure 9. Henceforth in the paper we follow W09 and use percentile binning. The advantage of this method is that each bin represents an equal surface area, so an unweighted average across bins gives the tropical mean. Since the omega values at the bin-boundaries are free to shift when using percentile-binning, changes of bin-mean quantities represent a combination of dynamic and thermodynamic contributions computed when using specified ω-valued bins. For most variables of interest in this study, the thermodynamic contributions (in this case, cloud profile changes at constant ω) are dominant (not shown).
 The control cloud fraction (Figure 9a) is dominated by high clouds in the strongest ascent regions where precipitation is strongest. In the lower troposphere, vertical profiles of low cloud peak at around the 900 hPa level, with peak single-level cloud fractions >0.1 in regions of moderate to strong subsidence. The changes in cloud fraction (Figure 9b) indicate a general increase (and perhaps a slight lifting) of high clouds in the ascent regions associated with the IWP increase. Cloud fractions in the lower troposphere are reduced tropics-wide from 800 to 900 hPa, but this is compensated by an increase in cloud fraction nearer to the surface, particularly in moderate to strong subsidence regions. In these subsidence regions, the vertical dipole pattern of decreasing cloud fraction near cloud top and increasing cloud fraction below is suggestive of a shallowing of the boundary layer and will be further explored in Section 5.4.
 The tropics-wide ocean and land changes in cloud fraction at various tropospheric levels (Table 1) mirror the circulation changes and largely cancel in tropical-mean. Over ocean, there is a weak mean decrease in cloudiness at all levels, while over land cloudiness increases at all levels, with an especially strong 0.02 increase in high clouds. The total tropical cloud cover increases only by about 0.002 or a relative increase of 0.4%.
 The overall radiative impact of these cloud changes is similarly small. Figure 10a presents ω500 percentile-binned tropical-mean simulated LWCF and SWCF for the control simulation. At all percentiles, the shortwave cooling effect of clouds is larger than the longwave heating effect. The amplitudes of both LWCF and SWCF increase to the left, towards increasing deep convection and associated high and middle clouds. Net cloud forcing in subsiding regions, where high cloud is minimal, is controlled by low clouds, which cause negative SWCF by reflecting shortwave radiation, and only slightly influence LWCF.
 The respective changes to SWCF and LWCF (Figure 10b) due to 4xCO2 are generally weakly positive and negative, with tropical mean changes of +0.3 W m−2 and −1.2 W m−2 (Table 1) (A similar weak cloud forcing response is seen in the HadAM3 GCM experiments of Lambert et al. ). When corrected by cloud masking, the tropical changes are only 0.2 W m−2 and −0.1 W m−2, respectively.
 Hence the inferred SP-CAM 4xCO2 tropical-mean longwave and shortwave cloud radiative feedbacks are both very small, consistent with the very small simulated tropical-mean cloud cover changes and the cancelation of compensating longwave effects of slight boundary layer cloud height decreases and tropopause cirrus cloud height increases.
5.4. Marine Low Cloud Response
 In discussing Figure 9, we noted a change in the vertical profile of cloud fraction suggestive of a tropical-mean lowering of boundary-layer cloud. In low latitudes, boundary-layer clouds are concentrated over the cooler parts of the oceans. As the final part of this study, we analyze why CO2 quadrupling might lead to a overall lowering of MBL cloud heights in these regions. We argue for two possible mechanisms. One is the enhancement of downwelling longwave radiation in the free troposphere with increased CO2. This results in less radiative destabilization of marine cloud-topped boundary layers, lower turbulent entrainment, and hence a shallower boundary layer top. This mechanism was introduced by Caldwell and Bretherton  mixed-layer-model study of subtropical stratocumulus response to climate change. The second mechanism is a general warming of the low-latitude lower troposphere due to reduced longwave cooling. In combination with fixed SST, this causes a strengthening of the trade inversion and thereby also inhibits turbulent entrainment.
 To test the links implied in this argument, we start by analyzing SP-CAM monthly climatology in grid columns over ocean regions between 30S and 30N. We bin column-months using the lower tropospheric stability (LTS), defined here as the difference between potential temperature at 700 hPa and the SST. LTS is a skillful predictor of climatological marine low cloud amount [Klein and Hartmann, 1993] that differentiates marine low cloud regimes more effectively than ω500. Within 30S-30N, LTS depends mainly on SST, with low LTS corresponding to high SST and vice versa. LTS-sorted ω and cloud fraction for the SP-CAM control and perturbation cases are shown in Figure 11. In the control case, we see as expected that in higher LTS regions, there is stronger tropospheric subsidence, more low cloud with a slightly lower typical altitude, and less high cloud. Because of the strong association of LTS with subsidence, it is not surprising that the general shape of the control cloud fraction distribution (Figure 11b) is similar to the tropics-wide ω-sorted distribution shown in Figure 9 (note different color scale).
Figure 11. Monthly-mean tropical ocean profiles sorted by LTS for the SP-CAM. Control case (a) 500-hPa pressure velocity ω and (b) cloud fraction, and (c and d) corresponding 4xCO2 changes.
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 In response to the CO2 perturbation, the tropospheric radiative cooling rate decreases (Figure 3) so mean subsidence over the cooler oceans, which is predominantly radiatively driven, is also weakened (Figure 11c) (In these regions fast changes in tropospheric lapse rate and their impact on subsidence warming are small). For the top 50% of LTS column-months, a vertical dipole in MBL cloud change is apparent (Figure 11d) similar to the dipole seen in Figure 9b. That is, the mean height of MBL cloud is lowered, though the vertically integrated change in marine low cloud fraction is slight. It is hard to precisely estimate the boundary layer depth reduction from the cloud profile change, but the height of the 50% relative humidity level, a proxy for the boundary layer capping inversion, drops about 80 m averaged across these LTS percentiles.
 Another important change is the warming of the lower troposphere above the MBL also possibly caused by the CO2-induced reduction in radiative cooling. Figure 6 (green dotted line) shows the LTS80-90 composite change in potential temperature, which has a maximum of about 0.6 K at 800 hPa. One significant contributor to this is just the lowering of the trade inversion itself. However, even at 600–700 hPa, well above the mean inversion height, temperature increases much more than near-surface temperature, which is tightly coupled to the fixed SST. This suggests that the trade inversion not only lowers but also strengthens by 0.3–0.5 K.