In all outputs of the 1% yr −1 increase in CO 2 climate model experiments archived under the World Climate Research Programme’s (WCRP) phase 5 of the Coupled Model Intercomparison Project (CMIP5), regions exist in the low latitudes where both the clear-sky and all-sky OLR decrease with surface warming. These are identified as regions of positive longwave feedback and are regions of a super greenhouse effect (SGE). These SGE regions are identified from feedback analysis of the 4 × CO 2 abrupt experiments of CMIP5, and despite their existence, there is little agreement across models as to the magnitude of the effect. The general effects of clouds on the SGE are to amplify the clear-sky SGE, but there is also poor agreement on the magnitude of the amplification that varies by an order of magnitude across models. Sensitivity analyses indicate that localized SGE regions are spatially aligned with a large moistening of the upper troposphere. The reduction in clear-sky OLR arises from a reduction in emission in the far IR with nonnegligible contributions from mid-IR emission from the midtroposphere. When viewed in the broader context of meridional heat transport, it is found that of the 1.03-PW rate of heat gained globally, 0.8 PW is absorbed in the tropics and is contributed almost equally by reductions in clear-sky longwave emission (i.e., the clear-sky SGE) and increased absorbed clear-sky solar radiation associated with increased water vapor. The processes that define the clear-sky SGE are shown to be fundamental to the way models accumulate heat and then transport it poleward.

While past studies infer (3) from spatiotemporal changes in SST using natural modes of variability such as ENSO, the SGE of this study is introduced here in a slightly different way. The SGE is not simply defined by an SST threshold as in Hallberg and Inamdar (1993) or from gradients of SST as in Valero et al. (1997) , but rather it is derived from changes in the OLR that result in response to a surface warming induced by increased greenhouse gases. The model experiments used to analyze this SGE are described in the next section, and the SGE is defined from the feedback analysis of the 4 × CO 2 abrupt experiments archived under the World Climate Research Programme’s (WCRP) phase 5 of the Coupled Model Intercomparison Project (CMIP5) ( Taylor et al. 2012 ). The results of this feedback analysis are described in section 3 and followed in section 4 by a discussion of the feedback factors that shape the changes in OLR observed in the 1% yr −1 increase in CO 2 transient experiments. Sensitivity analyses outlined in section 5 are used to point to the processes responsible for the clear-sky component of the SGE. Since the SGE is a property of climate change, the implications of the SGE to climate change projected by climate models are discussed in section 6 .

where SST is the sea surface temperature, σ is the Stefan–Boltzmann constant, and ε is the emissivity of the sea surface. According to this definition, the SGE is present in those regions where the increase in G with SST exceeds the increase in surface emission εσSST 4 :

The term “super greenhouse” has been used in a number of contexts. Super greenhouse gas was coined to refer to those gases like hydrofluorocarbons ( IPCC 2013 ) that are deemed to be disproportionately strong absorbers of infrared radiation on a molecule-by-molecule basis compared to, for instance, carbon dioxide (e.g., Hong et al. 2013 ). The term super greenhouse climate is used in a paleoclimate context to describe periods of great warmth like the Cretaceous Thermal Maximum about 90 million years ago when it is estimated that the surface temperatures of tropical oceans reached 35°C and sea levels elevated, all coinciding with a more extreme carbon cycle with much higher levels of carbon dioxide in the atmosphere than today ( Bornemann et al. 2008 ). The super greenhouse effect (SGE) has also been used to describe a particular characteristic of the greenhouse effect mostly in tropical regions ( Raval and Ramanathan 1989 ; Valero et al. 1997 ; Hallberg and Inamdar 1993 ) based on the observed relation between spatiotemporal patterns of longwave fluxes and sea surface temperatures. In this context, the SGE refers to those regions where the emission to the surface [the downward longwave radiation (DLR)] increases with increasing SSTs at a rate that exceeds changes to the outgoing longwave radiation emitted to space (OLR) as SSTs increase (e.g., Stephens and Greenwald 1991 ). Valero et al. (1997) introduce the SGE in terms of the following measure of the earth’s greenhouse G:

The fundamental importance of the earth’s greenhouse effect to the earth’s climate has been appreciated for some time. Fourier (1824) first proposed its existence and Tyndall (1861) made the first quantitative measurements of the strength of greenhouse absorbers in the laboratory. Arrhenius (1896) , influenced by the works of Fourier and Tyndall, produced the first calculations of how changes to the levels of carbon dioxide in the atmosphere alter the surface temperature through changes in the greenhouse effect.

Differences of quantities averaged over the years 136–140 (1999) and 0–4 (1860) of the CMIP5 1% yr −1 increased CO 2 transient experiment. Quantities shown are the (top left) SAT, (top right) OLR, (bottom left) clear-sky OLR, and (bottom right) the change in the longwave cloud radiative effects (the difference between and the clear- and all-sky OLRs). The results shown are for the HadGEM2-ES.

Differences of quantities averaged over the years 136–140 (1999) and 0–4 (1860) of the CMIP5 1% yr −1 increased CO 2 transient experiment. Quantities shown are the (top left) SAT, (top right) OLR, (bottom left) clear-sky OLR, and (bottom right) the change in the longwave cloud radiative effects (the difference between and the clear- and all-sky OLRs). The results shown are for the HadGEM2-ES.

The CMIP5 data used in this study are summarized in Table 1 . Data from three sets of experiments are analyzed: the abrupt 4 × CO 2 experiments as mentioned, the preindustrial control experiments that are subtracted from the abrupt experiment to remove drift following the approach of DeAngelis et al. (2015) , and the transient climate change experiment with the model forced by a 1% yr −1 increase in CO 2 . The transient experiment is used to examine the more realistic changes that might be expected to occur in an evolving climate system. Results of the transient experiment for one model (HadGEM2-ES) are shown in Fig. 1 mostly for the purpose of illustration and framing the later discussion. For this one example, differences between the averages over the final 5 years of the experiment (years 136–140, or 1999) and the first 5 years (years 0–4, or 1860) are shown. Over the period of time that elapses between these two 5-yr averages, the CO 2 of the model approximately quadrupled and the modeled earth warmed everywhere as indicated by the change in near-surface air temperature (SAT; Fig. 1 , top left). Changes in OLR ( Fig. 1 , top right) and clear-sky OLR ( Fig. 1 , bottom left) reveal that, unlike SAT, neither the all-sky nor the clear-sky OLR increases systematically everywhere with warming. These regions of reduced emission tend to be offset by enhanced emission to space in the middle-to-higher latitudes, most notably over the warmed landmasses of the NH. This pattern of negative changes in OLR at low latitudes and positive changes at higher latitudes is largely a manifestation of the feedbacks involving an enhanced greenhouse associated with upper-tropospheric water vapor at low latitudes and the so-called Planck feedback associated with a warmed atmosphere at higher latitudes. The general effect of clouds on the OLR, indicated by the clear-sky minus all-sky OLR differences in the bottom-right panel of Fig. 1 , at least for HadGEM2-ES, amplifies the clear-sky pattern of change. This amplification of the pattern is also apparent in the multimodel results of Andrews et al. (2015) and is discussed in the following section.

where α is a measure of all climate feedbacks. This linear analysis assumes these feedbacks are constant over time and is estimated from model experiments in which F is held constant, such as occurs in the abrupt 4 × CO 2 climate model experiments. This linear analysis can also be applied to each of the additive components of the net flux change, thereby determining the feedback strengths of the processes that shape these respective components. For example, analysis of clear-sky OLR provides a joint measure of Planck and water vapor longwave (LW) feedbacks, and analysis of the clear-sky solar absorption includes combinations of surface albedo and water vapor feedbacks (e.g., Andrews and Ringer 2014 ). In this study, as in Andrews et al. (2015) , we regress changes in local TOA fluxes onto global mean ΔT to obtain local values of α. The SGE then follows as those regions where

The SGE is an important consequence of feedbacks that occur as the earth warms. The SGE is defined here using the forcing–response analysis introduced by Gregory et al. (2004) as implemented regionally by Andrews et al. (2015) . This framework is underpinned by a simple linear relation between global radiative forcing F (W m −2 ), the change in net TOA radiative flux ΔN (W m −2 ), and surface temperature change ΔT (K):

Zonal averaged feedback for (a) all sky, (b) clear sky, and (c) their differences. Bold lines are the 26-model ensemble average with years 1–20 (red) and 21–150 (blue); individual model results are presented as thin lines. Clouds are largely a source of positive feedback on OLR. (d) Box-and-whisker plot of area-weighted all-sky feedback (W m −2 K −1 ) divided by clear-sky feedback within SGE regions, showing that clouds amplify the clear-sky SGE.

Zonal averaged feedback for (a) all sky, (b) clear sky, and (c) their differences. Bold lines are the 26-model ensemble average with years 1–20 (red) and 21–150 (blue); individual model results are presented as thin lines. Clouds are largely a source of positive feedback on OLR. (d) Box-and-whisker plot of area-weighted all-sky feedback (W m −2 K −1 ) divided by clear-sky feedback within SGE regions, showing that clouds amplify the clear-sky SGE.

Figures 4a–c summarize the LW feedbacks in zonally averaged form for both epochs and for all sky, clear sky, and the difference between them. In the bulk sense and at most latitudes, the LW cloud feedbacks are all positive acting to reduce the clear-sky feedbacks at all latitudes except those that straddle the tropical heating region of the SGE. The maps of Figs. 2 and 3 clearly show an enhanced all-sky negative feedback response both poleward and to the west of the enhanced positive SGE feedback, which is very analogous to the dynamical response to an equatorial heating described by Gill (1980) . Figure 4d also provides the ratio of all sky to clear sky of the accumulated heat calculated by integrating over regions of positive α for latitudes between 20°N and 20°S. The ratio is presented for the two epochs (years 0–20 in red and 21–150 in blue). Clouds substantially enhance the SGE effect by a factor of 10.7 in years 1–20 and 7.4 in years 21–150. The model-to-model range of this amplification is large, suggesting that the magnitude of the cloud feedback is also highly uncertain.

An assumption inherent to (5) is that feedbacks are constant over the time period analyzed. Andrews et al. (2015) showed how the feedbacks, although largely linear, vary in time and appear to separate into a relatively fast response epoch (up to the first 20 years) and a slower response epoch from years 21 to 150. Feedback analyses are applied to data from each of these two epochs as well as to the total time period and are summarized in Fig. 2 for the HadGEM2-ES model and Fig. 3 for the multimodel mean. Figures 2 and 3 are constructed as six panels showing the all-sky LW feedbacks (top panels) and clear-sky LW regional feedbacks (bottom panels). In all cases, the pattern of feedback is similar, although the magnitude and areal extent of the SGE region varies. The pattern of positive feedback in Fig. 3 closely resembles the regions of negative OLR change noted in Fig. 1 , which is expected because these regions of negative OLR change in the transient experiment are primarily set by feedbacks.

Figure 5d is analogous to Fig. 5b except the water vapor difference from 1999 to 1860 is shown with temperatures held at 1860. The clear-sky OLR is reduced everywhere with the largest reductions in the most convectively active areas of the tropics. Figure 5e shows the sum of Figs. 5b and 5d , and negative regions represent the SGE with respect to the temperature and water vapor feedbacks only. Figure 5f is similar to Fig. 5e but includes the contributions of 4 × CO 2 forcing added to the feedbacks. Negative regions show the SGE regions with respect to the sum of forcing and feedbacks together. Comparison of Figs. 5e and 5f reveals the dominance of the water vapor feedbacks on shaping the spatial patterns of the OLR differences everywhere and especially in the moist tropical regions. Even over the Southern Ocean regions where the CO 2 forcing is important to the OLR response, the water vapor feedback is also an important contributor. The CO 2 forcing increases the spatial coverage of the SGE regions where the temperature and water vapor feedback contributions to clear-sky OLR changes are similar in magnitude.

Figure 5b presents the OLR calculated for 1 × CO 2 and the atmospheric state of 1860 but with the temperatures replaced by the 1999 distribution minus the 1860 OLR. This difference thus represents the effects of the 4 × CO 2 temperature increase alone on OLR. The changes in OLR are positive everywhere, especially over NH landmasses, and are significantly larger than the OLR decrease associated with the CO 2 forcing as was shown in Andrews and Ringer (2014) . Figure 5c shows the sum of the temperature and 4 × CO 2 impacts on the OLR. The patterns are generally similar to temperature alone ( Fig. 5b ) but are reduced in magnitude. Figure 5c confirms the dominance of temperature change over the CO 2 forcing except in the region of the Southern Ocean where the CO 2 forcing remains a significant contributor to the derived OLR change.

Clear-sky OLR differences: (a) the 4 × CO 2 minus 1 × CO 2 OLR difference calculated for the 1860 model climate state; (b) as in (a), but with the temperature replaced with 1999 values; (c) the sum of (a) and (b); (d) as in (b), but for water vapor; (e) OLR change from feedbacks only; (f) OLR change from feedbacks and forcing. All results apply to HadGEM2-ES and were calculated with an offline radiative transfer model.

Clear-sky OLR differences: (a) the 4 × CO 2 minus 1 × CO 2 OLR difference calculated for the 1860 model climate state; (b) as in (a), but with the temperature replaced with 1999 values; (c) the sum of (a) and (b); (d) as in (b), but for water vapor; (e) OLR change from feedbacks only; (f) OLR change from feedbacks and forcing. All results apply to HadGEM2-ES and were calculated with an offline radiative transfer model.

Several sets of calculations of clear-sky OLR were performed. First the clear-sky OLR was calculated using atmospheric profiles from the 1860 period assuming two different concentrations of CO 2 , one corresponding to the initial 280 ppm and the second corresponding to its quadrupled value ( Fig. 5a ). The 4 × CO 2 minus 1 × CO 2 OLR calculated difference is the instantaneous radiative forcing and closely matches the forcing calculated from the abrupt 4 × CO 2 experiments reported in Andrews et al. (2015) . The distribution of this flux difference in Fig. 5a essentially reproduces the multimodel instantaneous forcing summarized in Zhang and Huang (2014) . The distribution of the OLR difference from CO 2 exhibits distinct structure that, among other factors, reflects the pattern of upper-tropospheric humidity, with the largest values aligning with the drier regions of the subtropics and smaller values in the moist tropics. This is to be expected because the changes in emission associated with a CO 2 increase overlap with water vapor emission from the strongly absorbing water rotation band. Thus, changes in emission by CO 2 are more highly masked by the emission from water vapor in the moister regions of the tropics.

The quadrupling of CO 2 through the course of the model integrations imposes an influence on the OLR that is implicit in the OLR differences shown in Fig. 1 . To determine this contribution, calculations were performed with an offline radiation model ( Stephens et al. 2001 ) that has been verified against observations (e.g., L’Ecuyer et al. 2008 ) and has served as the basis of the CloudSat fluxes product ( Henderson et al. 2013 ). The radiation model is a derivative of the widely used Fu and Liou scheme ( Fu and Liou 1992 ). Monthly mean temperature, moisture, and profile data from both the initial and end periods of the 1% yr −1 experiment for HadGEM2-ES served as input to this offline model.

We show below how the clear-sky SGE is a fundamental source of heating of the climate system. Here we examine the factors that are largely responsible for the changes to the clear-sky OLR depicted in Fig. 1. For this purpose, we adopt a simple sensitivity analysis similar to that described in Dessler et al. (2008). The sensitivity of the clear-sky OLR to changes in altitude-resolved atmospheric temperature T a and water vapor q, expressed as ∂OLR/∂T a and ∂OLR/∂q, are given in Fig. 6. In constructing this plot, T a and q profiles from the Atmospheric Infrared Sounder (AIRS; Chahine et al. 2006) collected in 2012 were averaged into 1-K sea surface temperature T s bins. These profiles were then used as input into the same radiation model used to produce the CO 2 flux difference plots described above. Of the 12 longwave infrared bands of the model, 8 are located in the mid IR (λ < 15 µm) with the remaining four bands located in the far IR (λ > 15 µm). The bin-averaged T a and q profiles were then respectively perturbed by +1 K and +10% in each 100-hPa-thick layer, and a new OLR was then calculated for perturbations to each 100-hPa layer of mean pressure p and for each surface temperature bin T s . In this way, the OLR sensitivities are created as functions of p and T s and are also calculated separately for broadband OLR (OLR bb ; λ > 4 µm), the sum of the four far-IR OLR bands OLR far (λ > 15 µm), and the sum of the eight mid-IR OLR bands OLR mid (λ < 15 µm).

Fig . 6. View largeDownload slide (left)–(right) The broadband-, mid-, and far-IR sensitivity of the OLR as a function of sea surface temperature T sfc . These sensitivities are derived from calculations for (top) 1-K atmospheric temperature T a and (bottom) 10% water vapor mixing ratio q perturbations applied to 100-hPa layers. The perturbations are from a mean climatological state taken from the AIRS clear-sky retrievals during 2012. Superimposed on the far-IR sensitivities are contours of the fractional contributions of the far IR to the total OLR sensitivity. Fig . 6. View largeDownload slide (left)–(right) The broadband-, mid-, and far-IR sensitivity of the OLR as a function of sea surface temperature T sfc . These sensitivities are derived from calculations for (top) 1-K atmospheric temperature T a and (bottom) 10% water vapor mixing ratio q perturbations applied to 100-hPa layers. The perturbations are from a mean climatological state taken from the AIRS clear-sky retrievals during 2012. Superimposed on the far-IR sensitivities are contours of the fractional contributions of the far IR to the total OLR sensitivity.

The top panels of Fig. 6 are the OLR sensitivities to T a , and the bottom panels show sensitivities to q. The sensitivities of spectral and broadband OLR to increased T a are positive everywhere. The maximum T a sensitivity of the mid IR occurs in the lower atmosphere over regions of highest T s . By contrast, the maximum temperature sensitivity of the far IR is located in the upper troposphere and also in regions of higher T s . These two factors combine to produce a broadband sensitivity (viz., ∂OLR bb /∂T a ) that is bimodal in altitude at these higher surface temperatures.

In contrast to the T a sensitivities, the sensitivities of broadband, mid, and far IR to changes in q are negative everywhere with a structure that is similar to the temperature sensitivities. For example, the maximum q sensitivity in the mid IR occurs in the lower atmosphere and over warmer surfaces, whereas the maximum in far-IR sensitivity, like temperature, occurs in the upper troposphere, although the peak sensitivity of q is located at slightly higher altitudes than are the T a sensitivities. The assumed moistening (+10%) and warming (+1 K) applied in Fig. 6 demonstrate the relative response across a range of T s and altitude. With a much larger relative increase in q compared to T a , which is a more realistic representation in the heart of the tropical SGE regions, the reduction in OLR will be much larger and well explains the patterns observed in Figs. 1, 2, 3, 5e, and 5f.

In a warming planet, increased temperatures occur synchronously with increased water vapor, so the net OLR response is some weighted combination of the sensitivities shown in Fig. 6. Consequently, the spatial distribution of change is more complex than that given by simple and separate perturbations of +1 K in T a and +10% in q as used for Fig. 6. This complexity is seen in both satellite observations of multiyear variability and climate model simulations of multidecadal trends. Gambacorta et al. (2008) used ENSO variations of AIRS T a and q soundings as a proxy for present-day climate variability and showed regions of drying, as well as moistening, within many tropical and subtropical upper-tropospheric regions that are several times higher than predicted by the Clausius–Clapeyron relation (7% K−1). Similar regional variations that deviate strongly from the global mean in the long-term rate of upper-tropospheric moistening are also observed in climate model simulations (Sherwood et al. 2010). The nature of this complication is revealed in Fig. 7 showing the difference profiles of 1999–1860 for the 1% yr−1 HadGEM2-ES experiments. The difference in the mean T a and q fields indicates that some regions of the lower and middle subtropical and tropical troposphere dry and warm in contrast to the more dramatic moistening and warming found in the upper troposphere. The combination of T a and q perturbations and their effect on OLR is presented in Fig. 8, symbolically ∂OLR/∂T a + ∂OLR/∂q, calculated from the respective joint T a and q perturbations of individual layers obtained. The combined sensitivities for the broadband, mid, and far IR are presented and emphasize how synchronous changes in T a and q combine to affect the clear-sky OLR. The results of Figs. 6 and 8 suggests that the SGE that can be readily identified in Figs. 1, 2, and 3 is a consequence of the moistening of the upper troposphere (e.g., Fig. 6, bottom) over the warmest regions of the planet that is shaped by emission changes in the far IR (Fig. 8, right) but with nonnegligible contributions in mid-IR emission from the midtroposphere over the warmest regions of the planet where SAT > 300 K. Furthermore, Figs. 6 and 8, in addition to Fig. 5, illustrate that the increased OLR at higher latitudes is largely a consequence of temperature changes in these regions.

Fig . 7. View largeDownload slide (top) The difference profiles of T a and (bottom) the relative difference of q for 1999–1860 of the 1% yr−1 HadGEM2-ES experiments. Fig . 7. View largeDownload slide (top) The difference profiles of T a and (bottom) the relative difference of q for 1999–1860 of the 1% yr−1 HadGEM2-ES experiments.