Interpretation of the positive low-cloud feedback predicted by a climate model under global warming

2.1 Brief description of the IPSL-CM5A-LR OAGCM

The IPSL-CM5A-LR OAGCM is the low-resolution version of the IPSL-CM5A model version used in CMIP5. Its atmospheric component, referred to as LMDZ4 (Hourdin et al. 2006), is largely similar to the one used in the IPSL-CM4 OAGCM of CMIP3 (Marti et al. 2005, 2010), except that both the vertical and horizontal resolutions have been improved (from 19 vertical levels and 3.7° × 2.5° longitude/latitude resolution in IPSL-CM4 to 39 vertical levels including 8 levels below 2 km- and 2.5° × 1.875° longitude/latitude resolution in IPSL-CM5A-LR, respectively), and that it can now be coupled to biogeochemical components so as to form the IPSL Earth System Model. ¹ More information about the IPSL-CM5A-LR (or IPSL-CM4) OAGCM can be found in Dufresne et al. (submitted).

Clouds are parameterized through a statistical cloud scheme describing the subgrid-scale variability of total water within each mesh of the model through a generalized log-normal Probability Density Function (PDF) bounded by zero on the lower side (Bony and Emanuel 2001). In (deep and shallow) convective situations, the statistical moments of this PDF are diagnosed from the in-cloud water content predicted in convective updrafts by the Emanuel parameterization (Emanuel 1991), modified by Grandpeix et al. (2004) and from the large-scale relative humidity field (Bony and Emanuel 2001). The skewness of the generalized log-normal PDF, which depends on the ratio between the variance and the mean of total water, is close to zero at low levels (therefore the PDF is close to a gaussian) but becomes more and more positive as height increases. A non-convective cloudiness is also predicted by the model using the same PDF but by computing the statistical moments of this PDF in a more ad-hoc fashion, by assuming that the total water variance is proportional to the mean total water, with a proportionality coefficient that varies linearly with pressure from 0.05 near the surface to 0.33 at 300 hPa (Hourdin et al. 2006). Two cloud schemes are called at each time step, and the maximum cloud fraction of the two schemes is used in radiation calculations. More information about the model physics can be found in Hourdin et al. (2006).

2.2 Overview of the cloud response to climate change

The climate sensitivity of the IPSL-CM5A-LR OAGCM is similar to that of IPSL-CM4. With an Equilibrium Climate Sensitivity of 4.4 K and a Transient Climate Response of 2.1 K (Fig. 1), this model ranges among the highest-sensitivity climate models of CMIP3 (Randall et al. 2007). A quantitative analysis of its radiative forcing and feedbacks shows that this high climate sensitivity stems from a strongly positive cloud feedback (Soden and Held 2006; Dufresne and Bony 2008). This strong feedback is associated with a large increase (in absolute sense) of the global NET (longwave + shortwave) Cloud Radiative Forcing (CRF) at the top of the atmosphere (by 0.5 W/m²/K, Table 1), which is dominated by the change in the shortwave (SW) component of the CRF (+1.3 W/m²/K). This weakening of the cooling effect of clouds as climate gets warmer arises mostly from low-latitudes (the change in SW CRF is more than two times larger in the tropics than in the extratropics) and is associated with a decrease of the cloudiness, especially of low-level clouds (Fig. 2).

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Table 1

Global, tropical (30°S–30°N), and extra-tropical (90°S–30°S + 30°N–90°N) averages of changes in surface temperature, CRF components and low-level cloudiness predicted by the IPSL-CM5A-LR coupled model under climate change (changes correspond to the difference between the end and the beginning of the 1pctCO2 simulation)

IPSL-CM5A-LR	Global	Tropical	Extra-tropical
\(\Updelta\)Temperature (K)	2.3	2.2	2.5
\(\Updelta\)CRF Net (W/m2/K)	0.5	0.8	0.3
\(\Updelta\)CRF SW (W/m2/K)	1.3	1.8	0.9
\(\Updelta\)CRF LW (W/m2/K)	−0.8	−1.0	−0.6
\(\Updelta\) Low cloud (%/K)	−0.9	−1.1	−0.7

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Many cloud regimes, ranging from deep convective to stratiform low-level clouds, may contribute to this change in tropically-averaged SW CRF. To determine their relative contribution, we use a simple compositing methodology (Bony et al. 2004) which consists in decomposing the large-scale atmospheric circulation in a series of dynamical regimes defined from the monthly large-scale vertical velocity at 500 hPa (ω). Within this framework, positive (negative) values of ω correspond to regimes of large-scale subsidence (convective regimes, respectively), and the PDF of ω is a measure of the statistical weight of each regime within the tropics (30°S–30°N). If C _ω is a composite of a geophysical field C (e.g. the SW CRF) in a regime defined by ω, and P _ω the PDF for this regime, the tropically-averaged C, noted \(\bar{C}\), may then be defined as: \(\bar{C} = \int_\omega P_\omega C_\omega d\omega\). The change in \(\bar{C}\) may thus be linearly decomposed into three terms: a “dynamic” component related to the change in the large-scale atmospheric circulation (\(\int_\omega C_\omega \delta P_\omega d\omega\)), a “thermodynamic” component related to the change in C _ω for a given circulation regime (\(\int_\omega P_\omega \delta C_\omega d\omega\)), and a term of co-variation. The quantification of these different terms shows that, as in other models (e.g. Bony et al. 2004; Medeiros et al. 2008), the thermodynamic component largely dominates the tropically-averaged change in SW and NET CRF. This component accounts for the change in radiative cloud properties in each dynamical regime weighted by the PDF of this regime. As discussed in Bony et al. (2004), since the PDF is maximum in regimes of weak subsidence (for ω around 20 hPa/day), small changes in cloud properties within this regime can influence very strongly the tropically-averaged radiation budget owing to their large statistical weight.

The vertical profile of cloud fraction simulated by the IPSL-CM5A-LR OAGCM in regimes of weak subsidence (ω = 20 hPa/day), and its change under global warming are shown in Fig. 3. The model simulates a maximum cloud fraction (about 20 %) around 950 hPa, i.e. 0.6 km, thus well below the top of the PBL which occurs around 1 km. It is also at this level that the model predicts the largest decrease of the cloud fraction (and cloud water, now shown) in coupled simulations where CO₂ increases by 1 %/year. The aim of the following sections will be to analyze and to understand the origin of this change in low-level cloudiness.

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3.1 Idealized atmospheric GCM experiments

The response of clouds to CO₂ increase and associated global warming in coupled ocean-atmosphere experiments may result from the interaction of a myriad of physical and dynamical processes, purely atmospheric and/or involving coupled interactions between the ocean and the atmosphere. To simplify the analysis and identify the dominant processes, we now analyze the response of clouds to a range of prescribed perturbations in model experiments run with exactly the same physical package but using different configurations.

One configuration consists in atmosphere-only experiments following the protocol of CMIP5 experiment #3.3.² In this experiment, commonly referred to as Atmospheric Model Intercomparison Project (AMIP) experiment (Gates 1992), the atmospheric component of the coupled ocean-atmosphere model is used in isolation using Sea Surface Temperatures (SST) prescribed from observations over the period 1979–2008. To distinguish the relative role of CO₂ increase and global warming in cloud changes, additional atmospheric experiments forced either by a globally uniform 4 K increase in SST (CFMIP2/CMIP5 experiment #6.8 referred to as AMIP4K) or by a prescribed quadrupling of the atmospheric CO₂ concentration (CFMIP2/CMIP5 experiments #6.5 referred to as AMIP4xCO2) are also performed.³

Aqua-planet experiments are also performed, in which the atmospheric model is run in perpetual equinox conditions using a specified, time-invariant distribution of SST zonally-uniform and symmetrical to the equator [the so-called “QOBS” distribution proposed by Neale and Hoskins (2000)]. These experiments run without any season nor land-atmosphere or ocean-atmosphere interactions, allow us to examine the response of clouds in a highly idealized framework and thus to assess the robustness of some predicted features. Aquaplanet experiments in which CO₂ is quadrupled ("Aqua4xCO2”) or in which the SST is uniformly increased by 4 K (“Aqua4K”) are also performed. These experiments correspond to the CFMIP2/CMIP5 experiments #6.7a, #6.7b and #6.7c, respectively.

The tropically-averaged change in CRF associated with the different experiments is given in Table 2. As in the OAGCM experiment, the change in NET CRF is dominated by the change in SW CRF. In all experiments, the change in SW CRF is also dominated by the thermodynamic component, which is itself dominated by the change in cloudiness that occurs in weak subsidence regimes (not shown). The vertical profile of cloud fraction simulated by the model in weak subsidence regimes in AMIP and aqua-planet configurations (Fig. 4) resemble very much that predicted in the OAGCM (Fig. 3), with however a slightly smaller cloud fraction at 950 hPa (about 13 vs. 20%), and a slightly larger cloudiness around 800 hPa in the aqua-planet configuration than in the more realistic AMIP or OAGCM configurations. The change in cloudiness between +4K and control experiments in AMIP and aqua-planet configurations are of same order as those found in OAGCM experiments (once normalized by the temperature change, which is roughly twice as large in +4K experiments than in the 1% CO₂ experiment at the time of CO₂ doubling), and occur at the same level. Note that these absolute changes are relative to their current climatological cloud profiles, which are slightly different in the three model configurations. In all configurations, the relative humidity decreases within the cloud layer and increases at the top of the boundary layer and above (Fig. 5), in association with an enhanced shallow convective activity. The response of clouds to the CO₂ radiative effect largely differs from the response to temperature change: both in AMIP and aqua-planet experiments, the cloud fraction changes little with CO₂, and exhibits only a weak increase around 950 hPa and a weak decrease around 800 hPa (Fig. 4).

Table 2

Tropically-averaged change in ocean surface temperature, CRF components and low-level cloudiness predicted by the atmospheric component of the IPSL-CM5A-LR climate model in AMIP and a aqua-planet simulations in uniform surface warming (+4K) experiments and in 4xCO2 experiments

	AMIP	Aqua	AMIP	Aqua
\(\Updelta\)Temperature (K)	4	4	0	0
CO 2 (−)	1×	1×	4×	4×
\(\Updelta\)CRF Net (W/m2)	+4.1	+4.8	−1.2	−0.9
\(\Updelta\)CRF SW (W/m2)	+3.7	+6.7	+2.7	+2.1
\(\Updelta\)CRF LW (W/m2)	+0.3	−1.9	−3.9	−3.0
\(\Updelta\) Low cloud (%)	−6.0	−6.1	+0.7	+1.0

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Three main conclusions arise from this series of experiments: (1) the response of low-level clouds to temperature and CO₂ is similar in AMIP and aqua-planet experiments, suggesting that it is controlled by robust physical processes independent on their exact geographical distribution, and independent on land-surface processes at first order; (2) low-level clouds exhibit opposite responses to surface ocean warming and CO₂ radiative forcing: the former induces a decrease of low-level clouds and a weakening of their radiative effects while the latter induces an increase of low-level clouds and an enhanced cooling effect of clouds on climate (3) the response of clouds to climate change experiments performed with ocean-atmosphere coupling and associated with both surface warming and CO₂ increase is qualitatively and quantitatively much more consistent with the response of clouds to SST change, than to the response to CO₂ increase. It suggests that in the IPSL model, and contrary to some other models (Gregory and Webb 2008), the tropospheric adjustment to CO₂ radiative forcing exerts a much weaker impact on boundary-layer clouds than surface temperature changes. The sensitivity of low-level clouds to SST changes may stem from local and/or remote influences. To examine how much local processes may be responsible for this sensitivity, we now go one step further in the model hierarchy by considering Single Column Model (SCM) simulations forced by large-scale forcings representative of weak subsidence conditions. These simulations are run with exactly the same physical parameterizations as GCM experiments previously discussed.

3.2 Idealized Single-Column Simulations

To investigate the response of tropical low-clouds to climate change, we use the CFMIP-GCSS Intercomparison of Large Eddy Models and Single Column Models (CGILS) framework: the aim of this community project is to evaluate subtropical marine boundary layer cloud feedback processes in GCMs and in high-resolution process models using a set of idealized large-scale dynamical conditions.⁴ CGILS focuses on three cases of boundary-layer clouds occurring along a transect ranging from California to Hawaii (Teixeira et al. 2011) and representative of stratus, stratocumulus and shallow cumulus cloud types (Karlsson et al. 2010). For each case, idealized large-scale conditions representative of the present-day climate are derived from European Centre for Medium-Range Weather Forecasts (ECMWF) analysis, and idealized large-scale forcings representative of global warming conditions are derived by prescribing a +2 K SST increase and by assuming that the tropical temperature profile follows a moist adiabat, that the relative humidity remains constant, that profiles of horizontal heat and moisture advection are unchanged, and that large-scale subsidence is changed so as to balance the radiative cooling above the boundary layer (Zhang and Bretherton 2008). Climate change conditions are thus associated with a warmer, more stable atmosphere and a weakened vertical motion.

In this study, we focus on the so-called “S6” CGILS case, which corresponds to large-scale conditions very similar to those of the ω = 20 hPa/day dynamical regime (especially in terms of SST and vertical velocity profile). SCM simulations are performed for an SST of 298.8 K, a surface pressure of 1,014 hPa and a mean solar irradiance of 448.1 W/m², and they are initialized by specified temperature, humidity and wind conditions. As recommended by CGILS, a relaxation towards a specified temperature profile is applied to the predicted temperature profile between 600 hPa and the top of the atmosphere. The simulations are run for 200 days but a steady state is reached after about 20 days.

The time evolution of the vertical profile of cloud fraction predicted by the IPSL SCM is shown in Fig. 6a, together with the mean profile for present-day condition and its change under idealized climate warming. The SCM simulation exhibits a maximum cloud fraction (of about 25%) around 850 hPa with a secondary maximum around 950 hPa, and the cloud response to SST increase consists in a decrease of both cloud layers by a few percent. Although corresponding to similar large-scale conditions on the monthly time scale, these results thus differ considerably from the robust GCM characteristics associated with weak subsidence regimes (Fig. 4). How to interpret this difference?

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3.3 Stochastic forcing

The examination of the time evolution of aquaplanet simulations in single geographical points belonging to the weak subsidence regime (monthly ω = 20 hPa/day) reveals a large high-frequency variability, with an alternance of shallow (and sometimes even deep) convection and suppressed conditions (Fig. 7). This variability, related to some internal synoptic variability of the atmosphere such as tropical waves, induces an alternance of cloud layers between 1,000 and 750 hPa, with a maximum occurence and amount at 950 hPa. The high-frequency variance of the GCM large-scale vertical velocity in regimes of weak subsidence is maximum in the upper troposphere, in agreement with NCEP2 meteorological reanalyses (Fig. 8). To investigate the influence that this high-frequency variability might have on the mean state, and also to reduce the proneness of the model to “grid-locking” the simulated cloud layers at particular vertical levels, especially near the trade inversion, we apply at each time step a stochastic forcing on the prescribed CGILS vertical velocity profile. For this purpose, we impose a white noise (of zero mean) that has the same variance as the vertical velocity profile of aqua-planet simulations in weak subsidence regimes, and we assume that stochastic fluctuations of the large-scale vertical velocity are vertically coherent (Fig. 8).

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These results show that SCM simulations forced by CGILS large-scale forcings together with a white stochastic forcing qualitatively reproduce main features of the vertical cloud distribution predicted by the GCM, both under present-day conditions and climate change. In the rest of this study, we thus use stochastically-forced SCM simulations to further interpret the physical mechanisms that control the low-cloud response to external perturbations in the IPSL model.

4.1 Relative influence of the different forcings

In the CGILS framework, idealized climate change conditions are expressed through a change in SST, in the large-scale velocity profile, and in horizontal large-scale advections of temperature and moisture. In addition, the free-tropospheric temperature profile is relaxed towards a pre-defined, prescribed temperature profile. This relaxation of the free-trospospheric temperature in subtropical regions is meant to mimic the effect of gravity waves on the horizontal homogeneization of the tropical temperature above the boundary layer. To perform sensitivity tests aimed at unraveling the influence of different physical mechanisms on the subtropical low-cloud response, we deliberately remove it. However, the mean vertical profile of cloud fraction (Fig. 6b) obtained with and without temperature relaxation, as well as its response to climate change, are very close to each other (not shown).

A series of experiments is performed, in which individual climate change perturbations are applied one by one, and compared with the “Control” experiment (a SCM simulation forced by CGILS idealized forcings associated with present-day conditions, together with stochastic forcing and without temperature relaxation in the free troposphere). The radiative cloud response to these different forcings is quantified through the change in top-of-atmosphere (TOA) CRF and in atmospheric CRF (ACRF), defined as the difference between the CRF at TOA and at the surface. When all climate change forcings are applied (experiment A), the TOA CRF is weakened by about 13 W/m² (the TOA CRF being negative in the current climate, a positive anomaly corresponds to a weakening), and the ACRF (which is also negative in the current climate) is also weakened by about half as much (Table 3). When applying only the +2K SST perturbation (experiment B), the cloud radiative response is very close, albeit slightly weaker, to that obtained in experiment A. Applying only the change in vertical velocity (experiment C) also contributes to weaken the CRF and ACRF, but to a much lesser extent than in experiments A and B. Changes in horizontal temperature and moisture advections have either an opposite influence on CRF and ACRF (experiment D), or a weak influence (experiment E) comparable to that of experiment C. These results suggest that the change in SST constitutes the primary driver of the cloud radiative response in this subtropical cloud regime, and that other forcings related to dynamical changes have a secondary influence. These findings confirm that in our model, the subtropical cloud response to climate change is more driven by thermodynamical processes associated with SST changes, than by dynamical changes.

Two main physical processes dependent on surface temperature are likely to contribute to the response of clouds to SST: turbulence and radiation. Since both are related to each other through energy conservation (for given large-scale forcings, the source of energy of the atmosphere comes from surface turbulent fluxes, and the sink of energy is ensured by radiative cooling), we will focus on one of them only: the effect of SST changes on atmospheric radiative cooling, and its impact on the cloud distribution.

4.2 Influence of clear-sky radiative cooling changes

The increase in SST induces a warming and a moistening of the troposphere, which lead to an enhanced cooling of the atmosphere by clear-sky radiation (Fig. 9). To examine how much this change in clear-sky radiative cooling might contribute to the cloud response to SST, we repeat control and climate change SCM experiments by using a prescribed, stationary clear-sky radiative cooling (referred to as R ₀ and R′₀ for present-day and +2K climate conditions, respectively) instead of an interactive clear-sky radiative cooling. R ₀ and R′₀ are set to the time-averaged values of the clear-sky radiative cooling predicted in “Control” (Fig. 6b) and “Experiment A” (Table 3) SCM experiments, respectively.

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The cloud-radiative response predicted by the SCM when substituting the time-varying clear-sky radiative cooling by a prescribed, time-invariant radiative cooling (R ₀ in present-day conditions and R′₀ in climate change), is fairly similar to that predicted by using an interactive clear-sky radiative cooling (compare experiments A and F in Table 3). Another experiment (G) identical to the “Control” experiment (present-day SST, horizontal advections, vertical velocity, etc) but imposing the clear-sky radiative cooling rate of the +2K experiment (R′₀) instead of R ₀ also predicts a cloud radiative response qualitatively similar to that obtained in actual climate change experiment (experiment A or F) when all forcings are applied. It seems therefore that the enhanced clear-sky radiative cooling associated with +2K conditions be sufficient to induce a low-cloud decrease and a low-cloud radiative response similar to that predicted by the IPSL model under climate change conditions. A similar conclusion is reached when considering the effect of 4xCO2 radiative forcing on low-level clouds and radiation (Table 3, experiment O). The reasons for the influence of the clear-sky radiative cooling on subtropical low-clouds is examined below.

The response of the clear-sky radiative cooling to global warming or 4xCO2 radiative forcing is shown in Fig. 9 for SCM and GCM (AMIP or aqua-planet) experiments: for each type of perturbation, both the vertically-integrated value and the vertical profile of the clear-sky radiative cooling change. To investigate the relative sensitivity of clouds to these two types of change, a series of experiments is performed in which a given perturbation of the vertically-integrated clear-sky radiative cooling (\(\Updelta[R_0]\)) is applied to the model, but distributed in different ways along the vertical (Table 3), localized either in the Upper Troposphere (UT, 100–400 hPa), in the Free Troposphere (FT, 400–700 hPa), in the Upper Cloud Layer (UCL, 900–700 hPa) or in the Cloud Layer (CL, surface-900 hPa). Experiments H and I show that the radiative response of clouds is as sensitive to the change in the vertically-averaged value (\(\Updelta[R_0]\)) as to the change in the vertical profile, and experiments J to M show that the response strongly depends on the altitude at which the perturbation is applied: low-level clouds decrease all the more that the clear-sky radiative perturbation is applied high in the troposphere. A perturbation applied within the boundary layer even enhances the low-level cloud fraction. These results suggest that the response of low-level clouds to a given radiative perturbation strongly depends on the change in the vertical atmospheric stratification associated with this perturbation. The reason for this influence is examined below by analyzing the energy budget of the troposphere.

5.1 Moist static energy budget

Boundary-layer clouds exert a radiative cooling on the troposphere, which can be quantified through the so-called Atmospheric Cloud Radiative Forcing (ACRF). The ACRF is defined as the difference between the CRF at TOA and at the surface or, equivalently, as the vertically-integrated cloud perturbation of the tropospheric radiative cooling (defined as the all-sky minus clear-sky radiative heating rates) [R]−[R₀]:

$$ [ACRF] = [R] - [R_0] = \int\limits_{P_{SFC}}^{P_{toa}} (R-R_0) {\frac{dP} {g}} = CRF_{TOA} - CRF_{SFC} $$

(1)

The change in ACRF induced by different perturbations being strongly correlated with the change in SW CRF at the top of the atmosphere (Fig. 10, Table 3) and with the change in low-level cloud fraction (not shown), it may be used as a proxy for the cloud-radiative response that we aim to interpret.

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Figure 11 compares the perturbations of the different terms of Eq. 3 in SCM experiments (G, J, K, L and M) in which a given vertically-averaged clear-sky radiative cooling is applied to the model with different vertical distributions (Sect. 2). In response to an increased [R ₀], surface fluxes always increase, all the more that the radiative cooling is applied near the surface (experiment M). However, the vertical advection term of MSE substantially depends on the vertical distribution of the clear-sky radiative perturbation and appears to be primarily responsible for differences in the cloud response among the different experiments: when the radiative cooling perturbation is applied in the upper troposphere, the change in the vertical stratification of MSE (the vertical velocity profile remains unchanged in this experiment but the MSE strongly decreases above the PBL) induces a strong negative anomaly of the vertical advection term which is not compensated by the increase in surface fluxes and is associated with a decreased low-cloud cover and a weakened ACRF (positive anomaly) to ensure energy conservation. At the other extreme, when the increased clear-sky radiative cooling perturbation is applied within the low-cloud layer, the vertical gradient of MSE in the lower troposphere weakens, which makes the vertical advection of MSE less negative in the PBL and leads to an enhanced low-level cloud cover and cloud radiative cooling. These experiments suggest that the impact of an external perturbation on the low-cloud cover strongly depends on how this perturbation affects the MSE vertical gradient within the PBL.

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5.2 Physical understanding of the relationship between MSE advection term and low-level clouds

To understand physically the correlation between changes in the vertical gradient of MSE and changes in the low-level cloud cover, we examine the vertical profile of MSE normalized by the near-surface MSE value (Fig. 12) in SCM and GCM experiments. In the subsidence regimes of the tropics, the atmosphere exhibits a minimum MSE above the PBL (around 700 hPa) and thus a negative vertical advection term of MSE (−ω ∂h/∂P) below this minimum and a positive term above. In a warmer climate (SCM experiment A), the PBL deepens, the minimum MSE occurs higher in altitude and the MSE contrast between the near-surface and minimum MSE values increases: this induces a change in the MSE vertical advection term which maximizes between 900 and 700 hPa. A similar behaviour is found in GCM experiments, both in realistic (AMIP) and aqua-planet configurations.

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Equation 3 and SCM sensitivity experiments (Fig. 11) suggest some correlation between the low-cloud radiative response and the change in vertical MSE advection. Since the sensitivity of the latter to climate change perturbations is maximum at the top of the PBL, we consider the vertically-integrated MSE vertical advection term between 900 and 700 hPa, an index hereafter referred to as boundary-layer vertical advection term or BVA (BVA = \(\int_{900\,{\rm hPa}}^{700\,{\rm hPa}} -\omega {\frac{\partial h}{\partial P}} {\frac{dP} {g}}\)). Figure 13 shows that across the range of SCM and GCM experiments, the change in low-level cloudiness (characterized by the change in PBL cloud fraction at the vertical level where the cloud fraction is maximum, which typically occurs around 950 hPa) is well correlated with the change in BVA (R ² = 0.55 with point M and R ² = 0.81 without). In response to a large range of perturbations (including changes in SST, CO₂ or large-scale subsidence), the change in BVA thus appears to be the term of Eq. 3 that correlates best with the change in ACRF, both in SCM and GCM experiments (Fig. 13).

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The vertical advection of MSE being dependent on both the vertical velocity profile and the vertical gradient in MSE, it may be perturbed both by local (e.g. surface temperature changes) and remote changes. Those latters may be associated with a change in the large-scale atmospheric dynamics (change in ω) or with a change in the free-tropospheric temperature profile, which is mainly controlled by deep convective processes. To clarify the origin of the change in low-level clouds, we thus examine in the next section the reasons for the change in BVA in GCM experiments.

5.3 Interpretation of low-cloud changes in GCM experiments

The robust change in the MSE vertical gradient and in BVA in surface warming experiments (Fig. 12) results from two factors. On the one hand, the deepening of the PBL, which is consistent with the expected growth of a marine shallow cumulus boundary layer in response to increased surface turbulent fluxes (Medeiros et al. 2005; Stevens 2007), rises the height of minimum MSE and then makes the vertical advection term of MSE more negative around the top of the PBL. However, a second and even more robust explanation is related to the non-linearity of the thermodynamic relationship of Clausius-Clapeyron, which increases the specific humidity (and thus MSE) with temperature at a larger rate near the surface than at altitude (changes in relative humidity play a secondary role, Fig. 12b). This enhances the MSE vertical gradient between the surface and the height of minimum MSE and then strengthens the import by large-scale subsidence of low-MSE from the free troposphere down to the surface. This effect, together with the deepening of the PBL, make BVA more negative and decreases the low-cloud fraction.