1. Introduction

For nearly three decades, the large spread of cloud feedbacks among climate models has been considered a major source of uncertainty for climate sensitivity estimates (e.g., Cess et al. 1990, 1996; Zhang et al. 2005; Soden and Held 2006; Webb et al. 2006; Gettelman et al. 2012). The representation of convective and boundary layer processes, in addition to the parameterization of cloud properties, is known to be critical for the prediction of cloud response to climate change, and it differs widely among models. Intermodel comparison studies suggest that tropical low clouds are at the heart of tropical cloud feedback uncertainties in global climate models (GCMs) (e.g., Bony et al. 2004; Bony and Dufresne 2005; Bretherton 2006; Wyant et al. 2006). Clearly needed is more process-level investigation and understanding of what treatment of GCM physics parameterizations is responsible for the differences in the tropical low cloud response to warming.

The two recently developed Geophysical Fluid Dynamics Laboratory (GFDL) atmospheric models—GFDL Atmospheric Model, version 3 (AM3) (Donner et al. 2011; Golaz et al. 2011), and the High Resolution Atmospheric Model (HIRAM) (Zhao et al. 2009; I. Held et al. 2014, unpublished manuscript), both used for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5)—exhibit marked increases in climate sensitivity compared to the earlier GFDL model [GFDL Atmospheric Model, version 2 (AM2) (Anderson et al. 2004)]. Since these models share considerable common formulations in dynamics and physics, they provide a desirable case for a process-level investigation of the dependence of cloud feedback on physical parameterizations. In this study, we explore one aspect of the connections among convection, clouds, and cloud feedback by varying the physics representation of subgrid moist convection in GFDL HIRAM. A simple diagnostic approach is constructed to understand these physics perturbation experiments. Below we provide some rationale for our model exploration.

Moist convection occurs as a population of cumulus clouds with varying vertical extent that interact strongly with each other and with their environment. Individually, each convective cloud moistens its upper environment through detrainment of condensate and vapor and dries and warms its lower environment through its compensating environmental subsidence. Through these processes, convective clouds together control most of tropospheric mixing of water and heat, regulate the atmospheric vertical distribution of moisture and temperature, and impact the large-scale cloudiness and associated radiation field. These processes are expected to depend crucially on the nature of cumulus mixing dynamics (cumulus macrophysical processes) and the details of convective cloud precipitation microphysics.

Current GCMs try to mimic some aspects of convective cloud processes using ensembles of plumes/drafts with different lateral mixing rates and some crude representations of cumulus precipitation microphysics and detrainment (e.g., Arakawa 2004). Despite some success, the detailed representation of cumulus mixing and convective cloud microphysics remains highly uncertain due partly to the lack of observational constraints (e.g., Mapes and Neale 2011). As a result, it is a common practice for GCM modelers to use these parameterizations to optimize some aspects of their simulation results. In this regard, we note that the analysis of the climateprediction.net (http://climateprediction.net/) ensemble suggests that cumulus entrainment rates are very important for climate sensitivity in that set of models (Benjamin et al. 2008).

Using Cess experiments [i.e., 2-K uniform sea surface temperature (SST) warming, Cess et al. (1990)] as an assessment tool, the estimated climate sensitivity parameter is respectively 0.58, 0.73, and 0.79 K W⁻¹ m² for AM2, AM3, and HIRAM. The increase of climate sensitivity in both AM3 and HIRAM is due primarily to an increase of positive feedback from tropical low clouds. A change in climate sensitivity in AM3 may not be too surprising since it differs from AM2 in many ways: shallow as well as deep convection, interactive chemistry, aerosol prediction, and aerosol–cloud interaction. However, HIRAM exhibits a similar change in climate sensitivity despite its more limited physics modifications from AM2, which are nearly entirely confined to moist physical processes. While the default configuration of HIRAM is a model with 0.5° horizontal resolution, HIRAM physics produces climate simulations comparable in quality with AM2 and AM3 at a coarse (2°) resolution. Both low- and high-resolution HIRAM models produce a similar increase of climate sensitivity compared to AM2.

Through a set of experiments with incremental modifications in physics parameterizations from AM2 to HIRAM, we have identified that replacing the relaxed Arakawa–Schubert (RAS) convection scheme (Moorthi and Suarez 1992) with a modified version of the University of Washington shallow cumulus (UWShCu) scheme (Bretherton et al. 2004) causes the increase in climate sensitivity. Since AM3 shares the same UWShCu scheme, this suggests that use of the UWShCu scheme may also be the cause of the increased climate sensitivity in AM3. The analysis of Gettelman et al. (2012) also found that a new version of the UWShCu scheme (Park and Bretherton 2009) is partly responsible for the increase in climate sensitivity from version 4 to version 5 of the Community Atmosphere Model (CAM4 and CAM5, respectively). Because of the much simpler alteration in physics from AM2 to HIRAM, we use a low resolution (same as AM2 and AM3) for the HIRAM as our base model for studying the connections among process-level modeling of convection and GCM simulated clouds, cloud feedback, and climate sensitivity.

Section 2 describes HIRAM and the simulation setup with a special emphasis on the representation of cumulus mixing and convective microphysics. Section 3 presents the analysis approach. Section 4 displays the results from present-day simulations using a control model and eight perturbed-physics models with alterations in cumulus mixing and convective microphysics. Section 5 explores the cloud response to global warming. Section 6 discusses the response of convective precipitation efficiency to warming and what formulation differences in cumulus mixing and convective microphysics between UWShCu and RAS may have led to the increased positive cloud feedback in HIRAM. Section 7 provides a summary and discussion.

2. The model, formulation of cumulus mixing and convective cloud microphysics, and simulation setup

A version of the HIRAM with 50-km resolution (C180HIRAM2.1) has been used extensively in simulating and predicting hurricane statistics and their response to global warming (Zhao et al. 2009, 2010; Held and Zhao 2011; Zhao and Held 2012). With only a few modifications in the treatment of mountain gravity wave drag, and the cumulus mixing rate over land, we constructed a lower resolution version of HIRAM. We refer to this model as C48HIRAM (C48 refers to a model with a cubed sphere dynamical core with 48 × 48 grid points on each face of the cube, resulting in grid sizes of roughly 2°). The climate simulated by C48HIRAM is broadly similar to that from C180HIRAM, including the higher climate sensitivity as compared to AM2.

The main change from AM2 to C48HIRAM is a switch of convection scheme from RAS to the UWShCu scheme. For details about the formulations and descriptions in UWShCu, we refer to Bretherton et al. (2004). Some differences in our implementation of the UWShCu in HIRAM as well as the simulated mean climate are documented in Zhao et al. (2009). Below we focus on a description of two important processes and associated parameters in this scheme: cumulus mixing and convective cloud microphysics.

The UWShCu scheme assumes a single bulk plume that can both entrain and detrain at each layer as it ascends through the column atmosphere. The model distinguishes between lateral mixing, entrainment, and detrainment rate at the boundary of the plume. In each layer, an equal amount of updraft air (expressed as a fraction of the updraft mass flux) and environmental air are assumed to mix and generate a full spectrum of mixtures with differing fraction of environmental air. Since a mixture’s buoyancy does not linearly depend on the mixing fraction owing to the evaporation of updraft condensate, negatively buoyant mixtures can result from the mixing process. The model then utilizes a buoyancy-sorting algorithm (e.g., Raymond and Blyth 1986; Kain and Fritsch 1990; Emanuel 1991; Zhao and Austin 2003; Bretherton et al. 2004) to determine which portions of the mixtures are entrained into (or detrained out of) the updraft. The entrained environmental air is further assumed to be homogenized within the updraft so that the plume can march upward and continue the mixing process until cloud top.

While the actual plume lateral entrainment and detrainment rates at each layer are dynamically and thermodynamically determined based on the property of environmental sounding, a key parameter in modulating the overall efficiency in cumulus mixing and entrainment/detrainment rate in this scheme is the fractional lateral mixing rate ϵ₀, which is parameterized as

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where c₀ is a specified empirical nondimensional parameter and H is the convective depth at the previous model time step. The scaling of fractional mixing rate by the convective depth allows plumes to penetrate deeper in a deep convective region and therefore offer a possibility for a single bulk plume to represent both shallow and deep convection. We choose a smaller c₀ [c₀ = 10 instead of 15 in Bretherton et al. (2004)] in HIRAM to optimize the performance of UWShCu in representing both shallow and deep convection. The mixing rate c₀ is one of the key parameters that we vary in the sensitivity study.

The second parameter explored in this study is related to convective cloud precipitation microphysics. In UWShCu, for a given updraft-mean total condensate (q_c = liquid + ice), we assume a symmetric triangular distribution of total condensate with a width of δq_c [δq_c = min(q_c, 0.5 g kg⁻¹)]. We then follow Emanuel and Zivkovic-Rothman (1999) by converting all cloud condensate in excess of a threshold value to precipitation. Ice processes are crudely accounted for by allowing to be temperature dependent:

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where q₀ is a warm cloud autoconversion threshold and T_crit a critical temperature (°C) below which all cloud condensate is converted to precipitation. In HIRAM, our default values for q₀ and T_crit are respectively 1 g kg⁻¹ and −60°C. In UWShCu, both cloud condensate and precipitation are partitioned into liquid and ice phase based solely on temperature.

The detailed formulations in cumulus mixing and convective microphysics processes can be quite different among different GCMs. In this study, we choose c₀ and q₀ as two key parameters to vary for studying the impact of the assumptions in cumulus mixing and convective microphysics on simulated clouds and cloud feedback. We generate eight perturbed-physics models by increasing and decreasing each parameter to check for the linearity of the cloud response to each parameter. For the control and the eight perturbed-physics models, we conducted both present-day and global warming experiments. The present-day simulations are forced by seasonally varying climatological SST (1981–2005 average) with prescribed present-day (1990) radiative gases. The global warming simulations are identical to the present-day simulations except SSTs are uniformly warmed by 2 K (Cess et al. 1990). The models are integrated for a total of 16 years and the last 15 years of output is used for analysis. Table 1 provides a list of the perturbed-physics models with their c₀ and q₀ values. The model ID numbers (1–4 for c₀ perturbation and 5–8 for q₀ perturbation) are used for plotting the figures below. We will explore the extent that the simulated clouds and cloud feedback sensitivity may be understood through our proposed bulk diagnostic quantities in section 3.

Table 1.

A list of the C48HIRAM control and the eight perturbed-physics models with their c₀ and q₀ values. The model ID numbers (0: control, 1–4: c₀ perturbation, 5–8: q₀ perturbation) are used for plotting figures.

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3. The diagnostic approach

While GCM-simulated clouds may exhibit complicated spatial structures and seasonal cycles, we shall take a rather simple approach here and frame the global and/or tropical (30°S–30°N) atmosphere as a single box, with all variables defined as horizontal and time averaged values. We formulate our diagnostics starting with a global (or tropical) cloud condensate budget associated with atmospheric water phase change. In equilibrium state, a global or tropical (assuming meridional transport of condensate from the tropics is negligible; this will be verified using simulation results) condensate budget associated with atmospheric water phase change can be written as

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where all variables are in water mass flux unit (kg m⁻² s⁻¹); C is the vertically integrated condensation/deposition rate and P the precipitation flux reaching the earth’s surface in association with C. Not all condensate precipitates out of the atmosphere; some is detrained from the condensation/deposition processes, forming clouds that travel with the atmosphere and are eventually recycled into the atmosphere. The production rate for the leftover condensate (C − P) may be referred to as condensate detrainment rate. In equilibrium state, it must be balanced by condensate evaporation/sublimation rate E.

Although the global and tropical mean P is well defined and is strongly constrained by the atmospheric radiative cooling rate, the boundary between C and E may not always be clearly defined. For example, it is difficult to isolate C and E inside cumulus clouds because cumulus mixing and associated E occurs simultaneously with C. Nevertheless, it may be conceptually useful to idealize the atmospheric water vapor going through two distinct paths along with their phase change to provide heating to the atmosphere. One is a rare and/or fast process in which water vapor condenses/deposits, releases latent heat, and precipitates out quickly without significant impact on atmospheric radiation budget. The second is a frequent and/or slow process in which water vapor condenses/deposits and forms clouds, which occur frequently enough and/or last for a long enough time that they can strongly interact with atmospheric radiative transfer. These clouds are eventually recycled back into the atmosphere through evaporation/sublimation. This idealization allows us to define a bulk precipitation efficiency e,

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which measures the efficiency of the fast and/or rare process in global and tropical hydrological cycle. We can alternatively define a condensate detrainment efficiency κ as

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κ measures the rate of condensate detrainment per unit surface precipitation and is directly related to precipitation efficiency e as shown in (5). Given a fixed global and tropical P, a less efficient precipitation system (smaller e) would require a larger C to produce that P, yielding a larger κ, and therefore an additional source for cloud condensate. It is sometimes more convenient to work with κ than e.

In typical GCMs with relatively coarse spatial resolutions, precipitation results from both a parameterization of subgrid-scale convection and an explicit representation of stratiform/large-scale clouds. Therefore, it is necessary to define e and κ separately for each parameterization module. We first define a global or tropical mean convective precipitation efficiency e_c and the corresponding condensate detrainment efficiency κ_c as

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where C_c and P_c are respectively the vertically integrated condensation/deposition rate and surface precipitation rate from the subgrid-scale convection parameterization module in a GCM. If using energy unit C_c can be directly estimated through a vertically integrated convective heat rate. Thus, e_c is readily diagnosed in GCMs. The bulk convective precipitation efficiency e_c is controlled by the assumptions of cumulus mixing and convective cloud microphysics in a convection scheme.

Similar to e_c and κ_c, we also define an explicit/large-scale cloud precipitation efficiency e_l and the corresponding condensate detrainment efficiency κ_l as

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where C_l and P_l are respectively the vertically integrated condensational/depositional rate and surface precipitation rate from the explicit cloud module in a GCM. This definition of e_l is not as clean as e_c since convective detrainment of condensate is also a source term for the explicit/large-scale cloud condensate, which ultimately leads to P_l. Therefore, it would be difficult to single out the part of precipitation due solely to the explicit/large-scale condensation/deposition. However, in HIRAM, the condensate detrained from the parameterized convection is generally small and most of it is reevaporated into the atmosphere as it travels through the atmosphere as cloud condensate. Thus, e_l defined in (7) will provide a good estimate for global and tropical (not necessarily local) large-scale cloud precipitation efficiency in these models: e_l would depend on the parameterizations of large-scale cloud microphysics and macrophysics (cloudiness assumptions).

Given the definitions of e_c, κ_c, e_l, and κ_l, we can obtain the total precipitation efficiency e and total detrainment efficiency κ in a GCM as

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where C = C_c + C_l, P = P_c + P_l, and f_l = P_l/P; f_l is the fraction of total precipitation that comes from the explicit cloud module. It is clear that the decomposition of κ into individual components has a simpler form than e especially if one is trying to analyze the difference in κ with respect to a climate change scenario. Depending on the details of implementation, e_c and e_l may vary considerably in a given GCM and among different GCMs. We propose e_c, e_l, and f_l as useful diagnostic quantities for characterizing and understanding some aspects of our GCM simulated hydrological cycle, clouds, and cloud feedback in relation to convection and cloud parameterizations.

4. Cloud sensitivity in present-day simulations

As shown in (3), the mean dissipation rate (E) for condensate over the entire globe must balance the condensate generation (detrainment) rate (C − P). In the tropics, a direct calculation of E through a summation of individual terms of condensate evaporation/sublimation rate yields a value very close (1.2% difference in the control simulation) to C − P. This indicates that the net meridional transport of condensate from the tropics is negligible. Hence, for both the tropics and the globe we can simply obtain E = C_c + C_l − P_c − P_l where C and P are replaced by the sum of convective and large-scale components. Both C_c and C_l are computed at each model physics time step and they are accumulated and averaged online and outputted at monthly frequency.

In a GCM as well as the real world, E should depend on both the nature of atmospheric turbulence and the total amount of condensate in the system. One may approximate E by a simple relaxation of a global or tropical mean total condensate path Q_c [sum of liquid water path (LWP) and ice water path (IWP)] to a fixed value of Q_c0 with a condensate dissipation (or residence) time scale of τ:

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We will demonstrate that (9) provides a good fit for our simulation results and τ and Q_c0 can be empirically determined by a linear regression of Q_c and E among the models. Combining (9), (3), and (5), Q_c can be written as

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Equation (10) suggests that the global and tropical mean cloud condensate in a given GCM may be primarily determined by the cloud dissipation time scale τ, the total precipitation P, and the total condensate detrainment efficiency (or cloudy efficiency) κ, with κ further depending on κ_c, κ_l, and f_l (see 8b). While the details in the parameterizations of convection and clouds in GCMs are complicated and their interactions with each other and with the large-scale dynamics are difficult to understand, (10) and (8b) might provide useful guidance for understanding some of the connections between process models and broad aspects of our GCM simulated clouds. These variables might be used to characterize and compare GCMs. Physically, these variables can be readily traced back to a model’s formulation and parameter settings.

To demonstrate the linear relationship between Q_c and E, Fig. 1 shows scatterplots of Q_c versus their corresponding E for each perturbed-physics experiment for both the tropics and entire globe. That all the perturbation experiments follow well along a single line suggests that τ and Q_c0 do not vary significantly among the models, consistent with the fact that our perturbed physics parameters are not directly related to cloud dissipation processes. A linear regression yields a slope of τ ≈ 1.5 h and a y-intercept Q_c0 ≈ 0.01 kg m⁻² for the globe. The small τ suggests a rapid recycling of global and tropical cloud condensate, which may be dominated by tropical convective clouds. The variations in global and tropical mean precipitation are also small (≤0.3%) among these prescribed SST experiments.

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Scatterplots of tropical (black) and global (gray) mean total condensate path Q_c (= LWP + IWP) vs corresponding condensate dissipation rate E from the control (0), the c₀-perturbation (1–4), and the q₀-perturbation experiments (5–8). See Table 1 for model ID numbers. Lines show linear regressions; legend shows correlation coefficients.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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For a GCM with fixed P, τ, and Q_c0, which is approximately true for the perturbation experiments in Fig. 1, (10) suggests that Q_c should depend only on κ and therefore κ_c, κ_l, and f_l. Figure 2 shows scatterplots of κ versus various measures of cloud properties including not only cloud condensate but also cloud fraction and cloud radiative forcing. Both liquid and ice water path increase roughly linearly with κ (Figs. 2a,b). Despite the two distinct perturbations in the parameterized processes (mixing versus microphysics), all experiments collapse onto a single straight line. This signifies that, at least for cloud condensate, details of the convection parameterization may not be important as long as their impact on κ is captured. The steeper slopes for the tropical component are consistent with a larger impact of convection in the tropics.

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As in Fig. 1, but for scatterplots of (a) LWP, (b) IWP, (c) low (below 700 hPa) cloud fraction (CFL), (d) middle (400–700 hPa) cloud fraction (CFM), (e) high (above 400 hPa) cloud fraction (CFH), (f) longwave cloud radiative forcing (LCRF), (g) shortwave cloud radiative forcing (SCRF), and (h) total cloud radiative forcing (TCRF), vs the corresponding total condensate detrainment efficiency κ.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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Low and middle cloud fractions increase substantially with κ (Figs. 2c,d). Low cloud fraction also reveals two discernible slopes with the variation of the mixing parameter c₀ (1–2–0–3–4) producing a larger sensitivity especially in the tropics. In contrast, middle cloud fraction does not display such a distinction. In comparison, κ appears to exert a much smaller impact on the high-level cloudiness in this model, especially for the c₀-perturbation experiments and for the global means (Fig. 2e). This is likely due to the compensating effects of fewer deep convective events with each being more efficient in producing high-level cloudiness as κ increases.

The asymmetric impact of κ on low and high clouds shows up more clearly in the longwave and shortwave components of cloud radiative forcing (CRF). Figures 2f–h display that globally, as κ increases from 0.4 to 0.65, longwave CRF increases by ~4 W m⁻² while shortwave CRF decreases by ~12 W m⁻², resulting in ~8 W m⁻² decrease (more negative) in total CRF. This large cloud sensitivity to κ (or e) may have important implications for cloud feedback to warming in a GCM since any significant response of κ (or e) to warming would likely affect the magnitude or sign of cloud feedback and therefore model estimates of climate sensitivity. We will explore this in section 5.

The high correlation between κ and different measures of cloud properties in Fig. 2 suggests that κ has good explanatory power for our modeled cloud sensitivity in relation to convection parameterizations. At the process level, we know that our alterations of cumulus mixing and convective precipitation microphysics should affect directly the parameterized convective precipitation (detrainment) efficiency e_c (κ_c). Figure 3 confirms that changes in κ for all of the perturbed-physics models are indeed dominated by their convective component δκ_c with the scatterplots of δκ and (1 − f_l)δκ_c closely following the identity line.

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Scatterplots of changes in total condensate detrainment efficiency δκ vs their convective component (1 − f_l)δκ_c for each perturbed-physics model (1–8) for the tropics (black) and the globe (gray): δ denotes the difference between a perturbed-physics model and the control model. See (8b) for definitions of κ, κ_c, and f_l.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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Why does κ_c (e_c) decrease (increase) as the lateral mixing rate parameter c₀ or the microphysics parameter q₀ decreases? Why does a decrease (increase) in κ_c (e_c) result in a large reduction in low cloud fraction but only a small change in high cloud fraction in this model? To better understand these two questions, we further examine the changes in vertical profile of the parameterized convective updraft velocity averaged over the tropics (Fig. 4a). As c₀ decreases (1 and 2), the parameterized updraft velocity increases. This is due to multiple effects of the reduction in plume lateral mixing/entrainment on updraft buoyancy and velocity, including the reduction in updraft condensate evaporative cooling, the enhancement in precipitation fallout, and the reduction in the direct drag from lateral mixing of vertical momentum. In the cases of decreasing q₀ (5 and 6), Fig. 4a also shows an increase in plume vertical velocity although the increase is weaker at upper levels. This is because a smaller q₀ converts more updraft condensate to precipitation (raising e_c directly) and reduces condensate loading. When most of the condensate is depleted at upper levels, the effect becomes weaker. In both cases, the enhancement of updraft buoyancy and velocity would allow shallow plumes to convect deeper, resulting in a shift of convective cloud population from shallow to deeper plumes and therefore increasing the overall convective precipitation efficiency e_c (or decreasing κ_c).

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Difference in the vertical profile of tropical mean (a) parameterized convective updraft velocity and (b) total (parameterized + explicit) convective mass flux between each physics perturbation model (1–8) and the control model (0). Parameterized updraft velocities are averaged at a level only when parameterized convection exist and reach that level. Explicit upward mass fluxes are computed online at each model physics time step.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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The shift in tropical convective cloud population can be seen in Fig. 4b. Since a significant amount of explicit convection also occurs in the tropics in these models, we include both parameterized and explicit convection in the mass flux calculation in Fig. 4b. Changes in total convective mass flux are dominated by the parameterized component. As c₀ or q₀ decreases, there is an increase in deep convective mass flux. The enhancement in deep convection suppresses shallower convection by drying and warming the lower troposphere, resulting in a large reduction in shallower convection with the greatest diminishment below 700 hPa. At high levels, the effects of an increase in deep convective clouds are largely compensated by their reduced efficiency in detraining water. They together produce only a modest impact on high-level cloudiness, explaining the lack of sensitivity of high cloud fraction to κ_c in this model. Finally, Fig. 4 also shows that the convection responses to increasing c₀ or q₀ are generally opposite to those of decreasing c₀ or q₀, consistent with our interpretation. These results suggest that the choice of assumptions in cumulus mixing and convective cloud microphysics affect the height distribution of convective clouds. A shift of convective cloud population from shallow to deeper clouds has a strong impact on GCM simulated clouds, especially in the lower troposphere. The effect may be captured through a simple bulk convective precipitation (detrainment) efficiency e_c (κ_c). Therefore, κ_c may serve as an important connection between convective parameterization and GCM simulated clouds.

5. Cloud response to uniform SST warming

The large sensitivity of net top-of-atmosphere (TOA) CRF to κ, shown in section 4, suggests that a response in κ to warming might play an important role in GCM simulated cloud feedback and climate sensitivity. We investigate this possibility in this section. We begin our analysis of the global warming experiments by showing that the intermodel differences in estimates of climate sensitivity are, indeed, due to model variations in cloud response in these models. Following Cess et al. (1990), we can estimate a model’s climate sensitivity parameter λ, which is defined as the difference in global SST (denoted as T_s below) divided by changes in net TOA radiative flux between a warming and a control experiment: λ = ΔT_s/G, where G = Δ(OLR − SWABS); Δ denotes the difference between warming and present-day simulations, and OLR and SWABS are respectively the net outgoing longwave radiative flux and the net shortwave downward (absorption) flux at TOA. The effect of clouds on λ can be measured by the ratio of the all-sky (λ) to clear-sky (λ_c) sensitivity, and is related to changes in total cloud radiative forcing (ΔTCRF) and G, that is, λ/λ_clr = ΔTCRF/G + 1 [Cess et al. 1990, Eq. (9)]. The literature tends to associate ΔTCRF/G with cloud feedback although caveats about this metric have been pointed out by Soden et al. (2004).

Figure 5a shows scatterplots of λ versus ΔTCRF/G from the C48HIRAM control and the eight perturbed-physics models. For comparison, the results from a pair of control and warming AM2 experiments are also plotted. There is a very high correlation between λ and ΔTCRF/G, confirming that the intermodel differences in λ are, indeed, due to model variations in cloud feedback in these models. The linear regression yields a slope and a y intercept about 0.55 K m² W⁻¹, which is well in agreement with a direct calculation of λ_clr (0.54 K m² W⁻¹). Thus, all models produce a positive (λ/λ_clr > 1) cloud feedback with λ/λ_clr ranging from 1.23 to 1.54 for the perturbed C48HIRAM models. Despite the significant variability, even the least sensitive C48HIRAM-perturbed model produces a larger positive cloud feedback than AM2 (λ/λ_clr = 1.07).

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(a) Scatterplot of climate sensitivity parameter λ vs cloud feedback parameter ΔTCRF/G from the control (0), the perturbed C48HIRAM (1–8) models, and AM2 (star). The line shows linear regression and legend shows correlation coefficient. (b) As in (a), but showing changes in total cloud radiative forcing (ΔTCRF) vs changes in total condensate detrainment efficiency (Δκ). Changes are for the globe and are normalized for per degree warming.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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Much of the intermodel variations in changes of total CRF can be explained by changes in total condensate detrainment efficiency Δκ. This can be seen in Fig. 5b, which shows a high correlation between ΔTCRF and Δκ (correlation drops from 0.96 to 0.87 if the AM2 result is omitted). In contrast to a slight increase in κ in AM2, all C48HIRAM-perturbed models produce a large decrease in κ, which leads to an overall increase in positive cloud feedback among the models. We will come back to this in section 6.

To help us understand the intermodel variation in cloud response among the perturbed-physics models we take the derivative of (10) with respect to T_s and make use of (9) and E = Pκ. Then we can write the fractional change in Q_c, P, κ, and τ as

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Equation (11) suggests that the fractional change of global or tropical mean condensate with warming may be understood through a decomposition into three components: fractional changes in total precipitation, total condensate detrainment efficiency, and cloud dissipation time scale τ. This decomposition helps to distinguish the processes that are important for the cloud response to warming. For example, unlike the results in section 4, as the global SST increases, it is expected that global mean precipitation will increase due to enhanced atmospheric radiative cooling. All other things being equal, this component alone would lead to an increase in global mean condensate. However, it is not obvious how other components respond to warming. Below we explore the response of each term to warming for all nine models.

We first verify that a nearly linear relationship between total condensate path Q_c and condensate evaporation rate E holds well for the warmer climate simulations. Figure 6 shows scatterplots of Q_c versus E for both present-day and warmer-climate simulations. As SST warms, the global mean Q_c increases for all models. The slope of linear regression is steeper for the warmer climate simulations, especially for global means. This suggests that it takes a longer time (larger τ) for a given condensate to dissipate in warmer climate in these models. In the tropics, changes in Q_c are subtle among the models, with E generally decreasing with warming. The linear regression exhibits only a slight increment in τ in the tropics. From Fig. 6, we can estimate Δτ/τ in (11) as respectively 2.34% and 0.56% K⁻¹ for the globe and the tropics.

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As in Fig. 1, but also including the results from the global warming simulations (red).

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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The fractional changes of global and tropical P, κ, τ, and Q_c − Q_c0 to warming are shown in Fig. 7 for all models. As the climate warms, the models produce on average 3.7% K⁻¹ increase in P for both the tropics and the globe. [This increase in strength of the global hydrological cycle is larger than that in Held and Soden (2006) due partly to the fixed greenhouse gas concentration in the Cess type of experiments (Cess et al. 1990).] This should contribute to an increase in Q_c. However, this increase is overcompensated by Δκ/κ, which exhibits a larger reduction (−4.5% K⁻¹) in the tropics in these models. Further, the intermodel variation in Δκ/κ is roughly 4 times larger (measured by standard deviation) than that from ΔP/P, with ΔP/P being negatively correlated with Δκ/κ (r ≈ −0.9) for both the tropics and the globe. Globally, the fractional change in condensate dissipation time scale contributes significantly to the increase in Q_c although this does not add to the intermodel variability. For both the globe and the tropics, the sum of the three individual components reproduces reasonably well the simulated response in Q_c for the models.

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Fractional changes in total precipitation P, total condensate detrainment efficiency κ, and condensate dissipation time scale τ from each model for (a) the globe and (b) the tropics. The sum of the three terms and fractional changes in Q_c − Q_c0 [see (11)] are plotted for comparison.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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While (11) is derived based on the total condensate budget, we find it is also useful for explaining simulated intermodel differences in the response of other cloud properties. To demonstrate this, we denote an arbitrary measure of cloud property as X and pursue a linear regression between each X and E for both present-day and global warming experiments. The correlations are high for all X with the lowest correlation (~0.8) from the high cloud fraction. We then rewrite (11) in terms of X as

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Here we choose to explicitly retain the ΔX₀ term since we find that a linear regression between X and E across the models does not always lead to a negligible x-intercept X₀ and ΔX₀ can be significant for cloud fractions. Although Δτ_X and ΔX₀ in (12) may vary with different cloud properties, they are constant across the models by construction (i.e., they are a function of X but not a function of the models). They constitute a component of the cloud response shared among the models and therefore do not contribute to the intermodel spreads in ΔX. In contrast, the Δκ and ΔP terms vary among models but not among different cloud properties (i.e., they are a function of models but not of X). By factoring out the effect of the Δτ_X and ΔX₀ terms, we would like to focus our analysis on the extent to which the intermodel variation in response of X can be explained by the Δκ and ΔP terms. Further, we point out that, when X₀ is subtracted from X in the denominator, the ΔX/(X − X₀) term can be significantly different from the actual fractional change in X when X₀ is large. Therefore, one needs to be careful about a quantitative interpretation of ΔX/(X − X₀). For notational convenience we also refer to the sum of the rhs of (12) as I_X.

We show in Fig. 8 scatterplots of ΔX/(X − X₀) versus I_X for total condensate Q_c, low cloud fraction, and shortwave and total CRF. The constant values of the corresponding X₀, ΔX₀, and Δτ_X/τ_X are listed in Table 2; the correlation coefficients between ΔX/(X − X₀) and Δκ/κ across the models are also listed. As expected, the intermodel differences in response of Q_c (Fig. 8a) to warming are well explained by model variations in with correlation exceeding 0.98. Both Q_c0 and ΔQ_c0 are small. The intermodel variation in is due nearly entirely to the Δκ/κ term. In contrast to an increase of global condensate, all models produce a reduction of low cloud fraction CFL to warming (Fig. 8b) with the intermodel variation being well explained by I_CFL. Differing from condensate, the ΔCFL₀ term adds significantly to the mean reduction in I_CFL that is further contributed by the Δτ_CFL/τ_CFL term (see Table 2). The reductions in I_CFL in the tropics are systematically larger than those for the globe. Despite the complication of ΔCFL₀, most intermodel spread in I_CFL is still accounted for by model variations in Δκ/κ (see correlations in Table 2). Similar to low cloud fractions, middle and high cloud fractions also decrease with warming for all models with intermodel spread being well explained by their corresponding I_X (not shown).

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Scatterplots of ΔX(X − X₀) vs I_X [see (12)] for both the tropics (red) and the globe (blue) from the control (0) and the perturbed-physics model (1–8): X includes (a) total condensate Q_c, (b) low cloud fraction (CFL), (c) SW cloud radiative forcing (SCRF), and (d) total cloud radiative forcing (TCRF). The constant values of X₀, ΔX₀, and Δτ_X/τ_X for each cloud property are listed in Table 2. Lines show linear regressions; the legend displays correlation coefficients.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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Table 2.

List of X₀, ΔX₀, and Δτ_X/τ_X for the four cloud properties (X) shown in Fig. 8. The units of X₀ and ΔX₀ are given in the left column. The correlation coefficients between ΔX/(X − X₀) and Δκ/κ across the models are listed in the right column. See text and (12) for the definitions of variables. Numbers within parentheses are for the globe.

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Consistent with the reductions in low cloud fraction, all models produce a decrease in the magnitude of shortwave CRF (SCRF) (Fig. 8c). The intermodel variation in ΔSCRF/(SCRF − SCRF₀) is also highly correlated to Δκ/κ with a coefficient greater than 0.95 (Table 2). Owing to a decline of high cloud fraction longwave CRF also decreases but with a significantly smaller magnitude so that the total CRF is dominated by the shortwave component. Figure 8d shows that all models generate a reduction in TCRF. ΔTCRF₀ is small for both the tropics and the globe (Table 2). Hence, I_TCRF is determined primarily by Δκ/κ, ΔP/P, and Δτ/τ. The intermodel variation in ΔTCRF/(TCRF − TCRF₀) is again well explained by Δκ/κ with correlation r = 0.93 for the globe. To summarize, Fig. 8 and Table 2 suggest that intermodel variations in the response of not only cloud condensate but also low cloud fraction, and associated shortwave and total cloud radiative forcing are well explained by their corresponding I_X, whose variation is dominated by model variations in response of total condensate detrainment efficiency.

6. Response of convective precipitation efficiency and its sensitivity to convective parameterization

The results in section 5 suggest that much of the model differences in cloud response to warming that result from diversity in formulations of cumulus mixing and convective microphysics may be encapsulated and understood through model response in the total condensate detrainment efficiency κ. Despite some intermodel variations, all C48HIRAM perturbed models produce a reduction of κ in response to warming, which is partly responsible for the overall positive cloud feedback across the models. A significant fraction of the reduction in κ is due to its convective component κ_c, which also exhibits a reduction for all models (Fig. 9). The intermodel variation in Δκ is dominated by Δκ_c for the set of q₀-perturbation experiments (5–6–0–7–8) although this does not appear to be true for the c₀-perturbation experiments (1–2–0–3–4) owing to a weaker intermodel variation in Δκ_c and a compensating effect in model variations in 1 − f_l (not shown). Figure 9 also shows that the different response in κ between AM2 and C48HIRAM is due to their different response in κ_c. Despite significant variability, the values of Δκ_c and Δκ in the perturbed C48HIRAM models are broadly similar to each other compared to AM2. In contrast to a large decrease in κ_c, AM2 produces a slight increase in κ_c, causing a slight increase in κ.

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A comparison of the response in global total (Δκ) and convective (Δκ_c) condensate detrainment efficiency for the control (0), the perturbed C48HIRAM models (1–8), and AM2.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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a. Conceptual model

Since the increase in convective precipitation efficiency e_c, or reduction in κ_c, constitutes an essential part of the overall positive cloud feedback in all C48HIRAM-perturbed models, it is more imperative to understand why these models produce an increase in e_c in response to warming. To help us understand this, it may be useful to think about a heuristic model of tropical convection consisting of an idealized parcel that ascends through the atmosphere. The parcel is allowed to mix with environmental air and evaporate some in-cloud condensate. However, an equal amount of the mixed air is assumed to be detrained back into the environment so that the parcel maintains the same amount of mass as it ascends. The depth of the convection would depend on the mixing efficiency. We now assume that the parcel produces total condensate q_c = αq_b, where q_b denotes boundary layer specific humidity and α represents the fraction of q_b being condensed over the convective layer. The parcel then loses αq_b − q_c0 as surface precipitation at cloud top, where q_c0 is a threshold value of condensate above which precipitation occurs. This idealization yields the parcel’s precipitation efficiency e_c = 1 − q_c0/(αq_b) and the climate response of e_c can be written as

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For simplicity, let us first assume q_c0 does not change with warming so that we can neglect the last term. It is well known that Δq_b/q_b roughly follows the Clausius–Clapeyron scaling (~7% K⁻¹) (e.g., Held and Soden 2006). For the deepest convective parcels, which mix so little and condense virtually all vapor content so that α ≈ 1 and Δα/α ≈ 0, Δe_c would be (q_c0/q_b)Δq_b/q_b. For a choice of q_c0 ≈ 1 g kg⁻¹ and a typical value of q_b (~20 g kg⁻¹) in the tropical deep convective region, q_c0/q_b is ~0.05 and Δe_c ≈ 0.0035 K⁻¹, which is at the lower end of our model simulated ranges in Δe_c (0.004–0.014 K⁻¹). For shallower convective parcels with α smaller than 1, q_c0/(αq_b) can be significantly larger than q_c0/q_b, which could lead to much increased Δe_c if Δα/α is still negligible. However, it is unclear what Δα will be since it depends on the response of cumulus mixing to warming. If shallow convection mixes less and penetrates deeper in a warmer climate, Δα/α will produce a sizable positive contribution to Δe_c. On the other hand, if shallow convection mixes more and does not penetrate as deep in warmer climate, Δα/α will contribute negatively to Δe_c. Last, but not least, the Δq_c0/q_c0 term is sensitive to model assumptions for convective cloud microphysics. We will return to this later.

Despite the idealization of moist convection, (13) provides several implications. First, it indicates that e_c is likely to increase with warming at the limit of deepest convective updrafts (assuming Δq_c0/q_c0 is negligible). Second, since q_c0/(αq_b) = 1 − e_c, (13) suggests that Δe_c should scale with the present-day value of 1 − e_c if Δq_b/q_b + Δα/α − Δq_c0/q_c0 is independent of 1 − e_c. Figure 10 shows a scatterplot of Δe_c versus 1 − e_c for the globe. As 1 − e_c increases (or e_c decreases), Δe_c increases roughly linearly (r = 0.98) with a slope of ~0.04 K⁻¹ among the models. This indicates Δq_b/q_b + Δα/α − Δq_c0/q_c0 is roughly 4% K⁻¹ although there appears a distinguishable difference between the c₀- and q₀-perturbation experiments. The high correlation suggests that most of the intermodel variations in Δe_c in the two sets of physics perturbation experiments are due to their variations in present-day e_c. Third, (13) predicts that Δq_b/q_b + Δα/α − Δq_c0/q_c0 being equal, Δe_c (Δκ_c) should increase (decrease) with q_c0. This is entirely consistent with the results of q₀-perturbation experiments (5–6–0–7–8) in Fig. 9. Finally, (13) suggests that parameterizations of cumulus mixing and convective microphysics processes can affect Δe_c through the Δα/α and Δq_c0/q_c0 terms. Below we explain why they are the causes for the different responses in e_c between HIRAM and AM2.

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Scatterplot of global Δe_c vs 1 − e_c from the control (0) and the perturbed-physics models (1–8). The line shows a linear regression and legend shows the correlation coefficient.

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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b. Implications

What differences in the formulations of the two convective parameterization schemes (i.e., UWShCu versus RAS) are responsible for the different response in e_c between HIRAM and AM2? There are many subtle differences in the implementation details between AM2 RAS and HIRAM UWShCu. For instance, RAS utilizes multiple entraining plumes with each detraining only at cloud-top while UWShCu employs a single bulk plume with entrainment and detrainment at each level. The definition and physical meaning of e_c allows us to trace back to two important differences in assumptions of cumulus mixing and convective cloud precipitation microphysics. The first is the way that the cumulus mixing/entrainment rate is formulated and computed. RAS calculates the entrainment rate of each plume inversely so that individual plume tops are locked to model levels: at each model level, it finds an entrainment rate so that a plume originating from the boundary layer with that entrainment rate can reach the model level with a neutral buoyancy. While this is a clever way to avoid an unnecessary number of plumes in a coarse vertical resolution model, it may have an unintended consequence when considering the response of plume entrainment in a warmer climate. For example, if the buoyancy of a plume with constant entrainment rate increases in a warmer climate (most models included in the IPCC Fourth Assessment Report produce an increase of CAPE in the tropics), this inverse calculation will generate an increase in entrainment rate for that plume since more entrainment would be needed for it to reach the same model level with neutral buoyancy. As we discussed before, everything else being equal, additional mixing/entrainment should reduce α, making Δα/α [see (13)] negatively contribute to Δe_c.

In contrast to AM2 RAS, the HIRAM UWShCu plume assumes a lateral mixing rate inversely proportional to convective depth. If convective depth increases in a warmer climate (as it does in HIRAM), this should lead to reduced lateral mixing and entrainment. A reduction in cumulus mixing/entrainment should increase α, making Δα/α positively contribute to Δe_c. A reduction in cumulus mixing should also increase updraft buoyancy, velocity, and e_c as we discussed in section 4. Indeed, Fig. 11a shows that, as the climate warms, all C48HIRAM-perturbed models produce an increase in updraft velocity, which helps to make shallower plumes ascend deeper. Figure 11b shows an increase of the parameterized convective mass flux above 500 hPa with a larger reduction below 600 hPa, indicating on average an increase of convective depth to warming in these models. In comparison, AM2 RAS produces large reductions in mass flux from cloud base up to 200 hPa. To separate changes in the vertical distribution of mass flux from the changes in cloud-base mass flux, Fig. 11c presents differences in a normalized convective mass flux. The normalized (divided by cloud-base mass flux) mass flux is essentially the cumulative distribution function of vertical mass flux, with cloud-base value 1 decreasing to 0 at the maximum cloud height. Hence, Fig. 11c provides an estimate of changes in parameterized convective cloud height distribution. While RAS produces large reductions of plumes with cloud top above 500 hPa, the perturbed-C48HIRAM models produce an increase for these deep plumes and large reductions of shallow plumes with cloud top between 600 and 800 hPa. This difference in response of convective cloud height distribution may be conveniently measured by changes in the bulk convective precipitation efficiency Δe_c (or Δκ_c) and is ultimately responsible for the increase in positive cloud feedback in HIRAM compared to AM2.

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Difference in vertical profiles of tropical (30°S–30°N) (a) convective updraft velocity, (b) convective mass flux, and (c) normalized (by cloud-base mass flux) convective mass flux, between a global warming and a present-day simulation from the control (0) and each perturbed-physics model (1–8). Convective updraft velocity at each level is averaged only when parameterized convection occurs at that level. Changes in parameterized convective mass flux from AM2 are also plotted for comparison (AM2 RAS does not compute updraft velocity).

Citation: Journal of Climate 27, 5; 10.1175/JCLI-D-13-00145.1

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The difference in Δe_c and the associated response in convective cloud height distribution between HIRAM and AM2 are also partly due to their formulation difference in convective microphysics. AM2 RAS utilizes a fractional removal of condensate (i.e., a fraction β of total condensate at each plume top is removed as precipitation), while the UWShCu employs a threshold removal of condensate (i.e., condensate exceeding a threshold value q_c0 is removed as precipitation). The actual implementation in each scheme also contains many subtle details. For example, in RAS different precipitation efficiencies β are explicitly specified for plumes with different heights, while in our UWShCu a temperature dependency of q_c0 is used for ice phase clouds and a probability density function of cloud condensate distribution is assumed to roughly account for the inhomogeneity of in-cloud condensate. Despite these complications, the broad difference between a fractional and a threshold removal scheme for treatment of convective precipitation is likely an important source for the different response in e_c to warming as can be seen in (13). For instance, in the limit of an undiluted parcel with deep penetration, plume condensate increases roughly following the Clausius–Clapeyron scaling. A fixed threshold removal gives Δq_c0/q_c0 = 0. In contrast, a fractional removal produces a positive Δq_c0/q_c0 ≈ (1 − β)Δq_b/q_b, counteracting the increase in Δq_b/q_b, and hence reduces a potential increase in Δe_c (see 13).

Finally, cumulus mixing and convective microphysics do not act independently: they are strongly coupled in the plume calculation in UWShCu. For instance, compared to using a fractional removal scheme for convective precipitation, our choice of a threshold removal scheme would allow a plume to develop larger buoyancy in a warmer climate due to less condensate loading and evaporative cooling. The increase in plume buoyancy should result in stronger updrafts and deeper penetration. Deeper convective depth is allowed to positively feed back to plume buoyancy by reducing plume lateral mixing and entrainment (see 1). This positive feedback can strengthen the initial increase in e_c due to the microphysics scheme alone. Therefore, the interaction between the cumulus mixing and convective microphysics schemes in UWShCu further enhances the increase in e_c to warming compared to AM2.

7. Summary and discussion

Uncertainty in cloud feedback is a leading cause of disagreement in GCM predictions of climate change. The differences in parameterizations of convection, clouds, and boundary layer processes are known to be critical. Yet, there is still a lack of in-depth investigation and understanding of what processes are responsible for the difference and how/why the different schemes may have led to the diversity of cloud feedback. This is partly due to the variety of differences coexisting among models, making it difficult to isolate the effect of individual processes. One way to get around this problem is to run a single model with systematic perturbations of many parameters one at a time in searching for those responsible for a change in cloud feedback and climate sensitivity (e.g., Benjamin et al. 2008; Mauritsen et al. 2012). A large number of perturbation experiments may be required to identify those key parameters. Further, cloud feedback and climate sensitivity may be more sensitive to changes in structure or formulation of a parameterization than to changes in the parameters. Another potential way to make progress is to analyze a sequence of models of different versions along the path of model development assuming a significant change in climate sensitivity exists among the different versions (e.g., Soden et al. 2004; Gettelman et al. 2012). The incremental advancement between model versions may help to identify key physical processes accountable for the change in climate sensitivity.

This study combines the two approaches with a goal of providing a process-level understanding of the connections between convection parameterization and GCM simulated clouds and cloud feedback. The two recently developed GFDL models (HIRAM and AM3) were found to acquire considerable increase in climate sensitivity compared to the earlier AM2 model. The replacement of the RAS convection scheme by the UWShCu is found to be the cause. Owing to the simpler change from AM2 to HIRAM, we use the HIRAM model as a base model to explore sensitivity of clouds and cloud feedback to perturbations of cumulus mixing and convective microphysics processes through well-controlled cases (i.e., varying parameters one at a time).

In the present-day simulations, we have explored cloud sensitivity in the control and eight perturbed-physics models. A novel bulk diagnostic approach is constructed to help us understand the simulation results. A set of diagnostic variables is derived and demonstrated to be useful in explaining the simulated relationship. In particular, a simple bulk convective precipitation efficiency e_c, or equivalently a convective detrainment efficiency κ_c, is found to be useful to understand the connections between the convective parameterization and our GCM-simulated clouds and cloud feedback. The e_c and κ_c are two inversely related variables and are used interchangeably in the analysis for the sake of mathematical simplicity and physical clarity. Not only can the two variables be readily diagnosed at global and tropical scales in a GCM, they are also fundamentally related to process-level quantities that can be perceived through process models. As e_c increases, or κ_c decreases, both liquid and ice water path decrease, with low and middle cloud fractions diminishing at a faster rate than high cloud fractions. Together, they produce a larger decrease in the magnitude of shortwave cloud radiative forcing than that of the longwave CRF in these models. This asymmetric impact of e_c on low and high clouds leads to a strong sensitivity of total CRF to changes in e_c. This result indicates that any possible response of e_c to warming could significantly alter the magnitude of cloud feedback and climate sensitivity in a GCM.

For the global warming experiments, our analysis reveals that the fractional change in global and tropical mean cloud condensate can be very well understood through a decomposition into changes in three individual components: total precipitation P, total condensate detrainment efficiency κ, and condensate dissipation time scale τ. In particular, the intermodel variation in condensate response to warming is nearly entirely explained by model variations in response of κ in these models. While the responses in cloud fractions are not fully explained by these three components, our results in Fig. 8, Table 2, and Fig. 5b suggest that most of the intermodel variations in changes of low cloud fractions and associated changes in CRF are still well accounted for by model differences in Δκ. Moreover, Δκ also explains the large difference in cloud feedback between the various C48HIRAM-perturbed models and AM2 (Fig. 5b). Since the climate sensitivity parameter λ depends strongly on cloud feedback (Fig. 5a), which in turn depends on Δκ (Fig. 5b), a comprehension of Δκ and its variability among the models would be important to understand the model uncertainties in climate sensitivity in relation to convection and cloud parameterization.

Despite significant intermodel variation in the magnitude of Δκ, all C48HIRAM-perturbed models produce a substantial reduction in κ to warming. Much of this is due to its convective component Δκ_c. In addition, the slight increase of Δκ in AM2 is also due to a slight increase of Δκ_c (Fig. 9). This suggests that the difference in response of convection is the primary cause for the difference in cloud feedback among these models. Since κ_c (or e_c) is fundamentally related to process-level models of convection, we use an idealized parcel model to help us understand possible responses of e_c to warming. Our analysis indicates that Δe_c is sensitive to details in assumptions of cumulus mixing and convective microphysics [see (13)] through their impact on both present-day e_c and their response to warming. This analysis further allows us to identify two important formulation differences between the UWShCu in HIRAM and the RAS in AM2 that explain the different response in Δe_c (or Δκ_c). In particular, the formulation of cumulus mixing rate to be inversely dependent on convective depth and the use of a threshold removal scheme for cumulus precipitation microphysics tend to reduce entrainment and enhance plume buoyancy in a warmer climate. They result in an increase in updraft velocity and a shift of convective cloud population from shallow to deeper plumes (Fig. 11), which ultimately give rise to a broad increase in e_c and a strong positive cloud feedback in the warmer climate in HIRAM. In contrast, the inverse calculation of plume entrainment rate and the use of a fractional removal scheme in RAS lead to an enhanced cumulus mixing and a muted response in plume buoyancy in the warmer climate in AM2. They counteract a potential increase in e_c, resulting in a slight reduction in e_c and a weaker positive cloud feedback in AM2.

While it is our hope through this study to provide an in-depth analysis of possible connections between the parameterized convective processes and GCM-simulated clouds and climate sensitivity, it is beyond our goal to answer which parameterization (UWShCu versus RAS) is more realistic. Convective parameterizations in current GCMs are still in a primitive stage. Many problems exist and they are major sources of GCM biases. Nevertheless, our results do suggest that any moist convective turbulent process and associated cloud microphysics important for determining the bulk convective precipitation efficiency would be critical to the broad issue of clouds and cloud feedback on climate sensitivity. These processes include the cumulus mixing dynamics, the formation and evolution of cloud and precipitating hydrometeors, the fall of precipitation, and associated downdrafts and precipitation reevaporation. These processes are tightly coupled under the envelope of moist convective turbulence with a broad range of scales. An adequate representation of these processes is challenging. Continued efforts through large-eddy simulations of moist convection, intensive field observation, and refined process models will be required to achieve a new level of confidence for our convection parameterization, without which it would be difficult to narrow the uncertainties in modeling cloud feedback and climate sensitivity.

Finally, one caveat of the present study is that we investigate only a narrow range of models varying in convection parameterizations from a single institution (GFDL). Despite the general diagnostic framework and some broad implications, the usefulness of our proposed diagnostic quantities is only validated in a limited context in this paper. Its possible generality for explaining other convection schemes in other models will require further evaluations by the community. This will also beg the questions as to how much diversity among GCMs can be explained by focusing on bulk measures of convection although the experience from the perturbed parameter experiments suggest that the sensitivity is strong. Further, our results and conclusions do not exclude the possibility that other processes (e.g., boundary layer turbulence, radiative properties of clouds, and stratiform clouds) and their representations may also be important in affecting GCM-simulated clouds and cloud feedback. Continued efforts through various isolated cases would be helpful to identify and understand the connections between parameterization details and uncertainties in GCM cloud feedback and climate sensitivity.