1. Introduction
Clouds cool the earth–atmosphere system by reflecting incoming shortwave (SW) radiation and warm it by absorbing outgoing longwave (LW) radiation from the surface. Satellite observations reveal that the net radiative effect of clouds on the earth–atmosphere system is a cooling of 20–24 W m−2 in the global annual average (SW cooling of 47–54 W m−2; LW warming of 26–30 W m−2), about 6 times larger than the radiative forcing associated with doubled CO2 (Ramanathan et al. 1989; Loeb et al. 2009). To the first order, SW radiation reflected by clouds and LW radiation absorbed by clouds are proportional to the cloud fraction and in-cloud optical thickness that is (inversely) proportional to the in-cloud condensate amount (cloud droplet radius). Clouds are central to the global hydrological cycle. In the global annual mean, the sink of atmospheric moisture by precipitation should balance the upward moisture flux from the earth’s surface. If evaporation is neglected, the global-mean precipitation rate at the surface is the product of the cloud fraction and in-cloud production rate of precipitation that is proportional to the in-cloud condensate amount and cloud droplet radius. Clouds also play an important role in the vertical transport of heat, moisture, momentum, and aerosols. The formation and dissipation of clouds that regulate the global radiation budget and the hydrological cycle is controlled by this vertical transport, which in turn is strongly influenced by the radiative and hydrological properties of clouds. This indicates the existence of complex feedback processes among cloud dynamics, radiation, and precipitation. To correctly assess future climate change, we need a good representation of global cloud properties (cloud fraction, in-cloud condensate, and cloud droplet radius), the factors that control the variations of cloud properties, and the feedback between cloud properties and controlling factors.
We have worked on developing a new version of the Community Atmosphere Model (CAM5) that provides the community with a state-of-the-art GCM that can simulate cloud–aerosol–climate interactions in a physically reasonable way. Compared to the previous versions, CAM5 contains many new physics parameterizations, including the following: 1) a moist turbulence scheme (Bretherton and Park 2009) that performs subgrid vertical transport by both dry and moist turbulent eddies throughout the whole atmosphere, replacing CAM3’s dry PBL scheme (Holtslag and Boville 1993); 2) a shallow convection scheme (Park and Bretherton 2009) that performs subgrid vertical transport by a convective inhibition (CIN)-based, ensemble-mean updraft plume with a penetrative entrainment closure at the cumulus top, replacing CAM3’s shallow convection scheme (Hack 1994); 3) a deep convection scheme that has a dilute convective available potential energy (CAPE)-based closure (Neale et al. 2008), with vertical transport of horizontal momentum (Richter and Rasch 2008); 4) a double-moment stratiform microphysics scheme (Morrison and Gettelman 2008), replacing CAM3’s single-moment stratiform microphysics scheme (Rasch and Kristjansson 1998); 5) a modal aerosol model that computes the mass and number conversion rates between various prognostic aerosol species and performs droplet activation and ice nucleation (Liu et al. 2012), replacing CAM3’s bulk aerosol model; and 6) an improved radiation scheme (Iacono et al. 2008). Altogether, CAM5 is designed to improve simulation of the global radiation budget and hydrological cycle; the subgrid vertical transport of heat, moisture, momentum, and aerosols; and complex feedbacks among cloud dynamics, radiation, and precipitation processes. This is achieved by improving the subgrid representation of cumulus and stratus and the interactions between different physics parameterizations associated with the clouds and aerosols (see Fig. 1).
A diagram illustrating interactions among various physics and dynamic processes in CAM5. Thick arrows denote a sequence of process splitting at each time step with a flow of normal grid-mean state variables of ϕ = T, qυ, ql, qi, u, υ, ζi, and ζc, where ζi and ζc are the mass and number concentrations of 15 interstitial (i.e., outside of cloud liquid droplets and ice crystals) and stratus-borne aerosol species, respectively. Thin arrows denote the flows of additional variables [turbulent kinetic energy (TKE), PBL top height (PBLH); eddy diffusivity for heat and moisture Kh; A, ql, qi, nl, ni, rl, and ri are cloud fraction and condensate mass, number concentration, and radius of cloud liquid droplets and ice crystals; subscripts dp, sh, st, and tot denote deep cumulus, shallow cumulus, stratus, and total clouds; the overbar and hat denote grid-mean and in-cloud average, respectively; QR,L is LW radiative cooling rate; P and E are precipitation production and evaporation; M is convective mass flux; and 
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
Compared with the previous versions, the cloud parameterizations in CAM5 are more consistent and physically based. Several key aspects of CAM5 cloud parameterizations are as follows:
a consistent cloud macrophysical formulation;
stratus–radiation–turbulence interactions;
prognostic treatment of stratus droplet number and aerosol species; and
radiatively active cumulus and snow.
This paper describes the CAM5 cloud macrophysics scheme, which provides a framework for the horizontal and vertical distribution of clouds (see Fig. 2). Section 2 provides a detailed description of the cloud macrophysical structure in CAM5, including how CAM5 computes cloud fraction, in-cloud condensate amount, and the droplet number concentration for deep and shallow cumulus and stratus clouds, and a description of how to impose consistency between the diagnosed stratus fraction and prognosed in-stratus condensate in appendix A. Section 3 contrasts CAM5-simulated cloud properties compared with CAM3/CAM4 and observations, with discussion on the source of improvements from CAM3/CAM4 and the source of discrepancies against observations at the process level. A summary and conclusion is provided in section 4.
A diagram illustrating cloud macrophysical structures in CAM5 that have nonoverlapped deep cumulus, shallow cumulus, and stratus in each layer: each of which has its own cloud fraction, mass, and number concentration of cloud droplets. A single stratus fraction (Ast) is obtained by assuming maximum overlap between liquid stratus (Al,st) and ice stratus (Ai,st), and then in-stratus LWC/IWC are uniformly distributed over Ast. In this figure, Ai,st is located within Al,st, so that Ast = max(Al,st, Ai,st) = Al,st. CAM5 assumes that any stratus in the vertical path of convective updraft (either shallow or deep) is displaced by the convective updraft, resulting in the horizontal nonoverlap between stratus and cumulus, as shown above. The tilde denotes the average over the clear portion. Thick arrows denote convective condensate detrained into the environment randomly without preferred spots. See the caption of Fig. 1 for the meaning of each variable.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
2. Cloud structures in CAM5
Cloud is a volume containing hydrometeors suspended in the atmosphere. CAM5 has two types of clouds: cumulus and stratus. Cumulus consists of deep and shallow cumulus, while stratus consists of liquid and ice stratus. In contrast to CAM3/CAM4, CAM5 does not have a stability-based stratiform cloud but has a relative humidity (RH)-based stratiform cloud that is referred to as stratus throughout this paper. In the case that the horizontal grid size G ≡ ΔxΔy (where Δx and Δy are the zonal and meridional width of the model grid) is comparable to or larger than the size of the compensating subsidence induced by a typical convective updraft observed in nature, CAM5-simulated cumulus and stratus are analogous to the observed cumulus and stratus, respectively. If G becomes small, however, such analogy is broken, and special attention is necessary in comparing the simulated and observed cloud components and associated precipitation rates (Park 2014a,b).
CAM5 defines the following five quantities for each cloud type in each layer: cloud fraction (A), in-cloud liquid water content 
a. Cumulus
CAM5 has separate deep and shallow convection schemes, where each of which computes a cloud fraction A, and in-cloud condensate amount 
1) Deep cumulus
Deep cumulus below the lifting condensation level (LCL) is empty (i.e., in-cumulus condensate 
For radiative treatment, CAM5 assumes in-cumulus condensate has the same droplet radius and size distribution parameters as in-stratus condensate in the same layer. If stratus does not exist in the same layer, CAM5 specifies an effective diameter of 50 μm for cumulus ice crystals and shape and slope parameters of a gamma distribution of 5.3 and (5.3 + 1)/25 μm−1 for cumulus liquid droplets, respectively. For detrained cumulus condensate, the effective volume radius is set to 8 (25) μm for liquid droplets (ice crystals) at all heights.
2) Shallow cumulus
In contrast to deep cumulus, there is no empty shallow cumulus since ash is computed from the LCL. If 
The droplet size distributions of in-cloud and detrained shallow cumulus condensates are specified in the same way as deep cumulus, except for the use of 10 (50) μm as the effective volume radius of detrained shallow cumulus liquid droplets (ice crystals).
b. Stratus
Both CAM3 and CAM4 diagnosed a single-phase stratus fraction (ast) as a quadratic function of grid-mean RH 
1) Liquid stratus
In principle, both al,st and 
Once consistent values of al,st and 
CAM5 prognoses the number concentrations (
2) Ice stratus
Rather than using saturation equilibrium constraints for ice stratus with 
CAM5 prognoses 
c. Cloud overlap
Within each grid layer, CAM5 diagnoses four independent cloud fractions for deep and shallow cumulus and liquid and ice stratus (0 ≤ adp ≤ 0.6, 0 ≤ ash ≤ 0.2, 0 ≤ al,st, and ai,st ≤ 1, respectively) and the associated in-cloud condensate mass and number concentration (
1) Horizontal overlap
2) Vertical overlap
In CAM5, the following physical processes make use of the vertical overlap structure of clouds and precipitation areas: 1) deep and shallow convection schemes to compute evaporation rates of convective precipitation, 2) aerosol activation, 3) stratiform microphysics to compute production and evaporation rates of stratiform precipitation, 4) wet scavenging (or deposition) of aerosols by convective and stratiform precipitation, and 5) the radiation scheme. While the methods used to compute cloud properties 
For computing evaporation rates of convective precipitation, the deep and shallow convection schemes assume that the convective precipitation area is 1.
The aerosol activation routine assumes a maximum vertical overlap of Ast between any adjacent layers.
Stratus microphysics assumes that 1) Ast is maximally overlapped in the vertical regardless of vertical separation distance and 2) the stratiform precipitation area Ap,st, with nonzero stratiform precipitation flux, is the maximum Ast in the layers above the current layer: that is, Ap,st(k) = max[Ast(1), Ast(2), …, Ast(k − 1)], where k = 1 is the model top layer.
Wet scavenging of aerosols consists of two processes: 1) scavenging of activated aerosols within cloud droplets (i.e., cloud-borne aerosols) by precipitation production and 2) scavenging of the remaining nonactivated aerosols (i.e., interstitial aerosols) by precipitation flux falling into the layer. These two processes are separately applied for each form of convective and stratiform precipitation. For the purpose of wet scavenging of aerosols, CAM5 assumes that 1) the convective precipitation area Ap,cu is the vertical integral of Acu in the layers above, weighted by the net production rate of convective precipitation, with similar computation for the stratiform precipitation area, and 2) for computing wet scavenging of nonactivated aerosols, Ap,cu and Ap,st are randomly overlapped with clouds in the layer below. When precipitation is evaporated, some aerosols within the precipitation are redeposited into the atmosphere in proportion to the ratio of the evaporation rate to the precipitation flux falling into the layer.
Within each grid layer, the CAM5 radiation scheme sees a single total cloud fraction (Atot) and horizontally homogeneous
In principle, all of the above five processes should use the same vertical overlap structure of cloud and precipitation areas. Because of the contrasting nature of the associated turbulent eddies, cumulus and stratus are likely to have different vertical cloud overlap: if vertical shear of the horizontal wind is neglected, cumulus fractions are likely to be maximally overlapped over the entire depth of convective updrafts, while the vertical distance over which stratus is maximally overlapped is likely to be much smaller than for the cumulus. We hope to include these improvements in future versions of CAM.
3. Simulations
Two types of global simulations—1) a stand-alone simulation forced by the observed climatological sea surface temperature (SST) and sea ice fraction with an annual cycle in the year 2000 for 10 yr and 2) a fully coupled simulation without any flux correction between atmosphere and underlying surfaces for 156 yr from 1850 to 2005—are performed at a horizontal resolution of 1.9° latitude × 2.5° longitude with a model physics time step Δt = 1800 s for both CAM5 at L30 (where L denotes the number of vertical layers) and CAM4 at L26. The fully coupled models (or simulations) with CAM5 and CAM4 will be referred to as the Community Earth System Model, version 1 (CESM1) and the Community Climate System Model, version 4 (CCSM4), respectively. The detailed configurations of the stand-alone and fully coupled simulations as well as other frequently used global simulations [i.e., Atmospheric Model Intercomparison Project (AMIP) and slab-ocean model (SOM) simulations] are described in appendix B. [Except for Figs. 11 and 12, which are from the fully coupled simulations (note that computation of the surface heat flux feedback parameter in Fig. 12 requires the fully coupled simulations), we use the stand-alone simulations for all the analysis in this paper.]
a. CRF
Figure 3 shows CAM5-simulated SW and LW cloud radiative forcings (CRFs) at the top of atmosphere (TOA) compared with the Clouds and the Earth’s Radiant Energy Systems Energy Balanced and Filled (CERES-EBAF; Loeb et al. 2009) satellite observations. CRF is the difference of net downward radiative flux between all sky and clear sky, and can be defined at any height, with positive (negative) CRF indicating that the cloud warms (cools) the underlying atmosphere and surface. For references, CAM5-simulated global annual-mean net downward SW radiation at TOA and upward LW radiation at the top of the model are 242.2 and 237.7 W m−2, respectively.
Annual-mean (left) SW and (right) LW CRF at the TOA from (top) CAM5 and (middle) observations (OBS). (bottom) The difference maps between CAM5 and OBS obtained by converting the CAM5 simulation into the horizontal grid of the observation with appropriate area weighting. The area-weighted global-mean value is denoted by mean at the top left of individual plots with corresponding unit and color scales at the top right and bottom of each plot, respectively. In (bottom), r and rmse at the top of each plot denote global pattern correlation and root-mean-square error between CAM5 and OBS. The observation is the 10-yr climatology of CRF from CERES-EBAF (March 2000–February 2010; Loeb et al. 2009). The same global-mean statistics of CRFs at SFC from CAM5 and the ISCCP-derived surface radiative flux data (January 1984–December 2007: 17 yr; Zhang et al. 2004) are also denoted in the parenthesis at the top of each plot. Similar plotting rules are used in the following horizontal 2D plots.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
One important caveat in comparing CAM5-simulated CRFs with the observations is that CAM5-simulated CRFs are computed by assuming that all thermodynamic variables (e.g., water vapor, temperature, and concentrations of gases and aerosols), except the mass and number concentration of cloud condensates are horizontally uniform within each grid layer. This assumption inevitably overestimates qυ,clr (water vapor in the clear portion that is set to the grid-mean 
CAM5-simulated global annual-mean SW CRF at TOA is −48.8 W m−2, which is within the range of available satellite observations [−47.1 W m−2 from CERES-EBAF as shown in Fig. 3c and −54.2 W m−2 from the Earth Radiation Budget Experiment (ERBE; Harrison et al. 1990)]. Overall, CAM5 successfully captures the observed regional maxima of SW CRFs over the following three main cloud regimes with a global pattern correlation r = 0.91 between CAM5 and observations: 1) the tropical deep convection regime, 2) subtropical marine stratocumulus decks on the west of the major continents, and 3) midlatitude oceans. As shown in Fig. 3e, CAM5 has systematic regional biases of SW CRF at TOA [root-mean-square error (rmse) = 14.0 W m−2], although they are smaller than the corresponding biases in CAM4 (rmse = 17 W m−2): 1) substantial overestimation (i.e., more cooling) in the tropical deep convection regime, especially over the continents; 2) underestimation over the eastern subtropical oceans downstream of marine stratocumulus decks and over the portion of midlatitude oceans with strong meridional SST gradient, where downwind transition between stratocumulus and cumulus widely occurs; 3) underestimation over the Southern Hemispheric circumpolar ocean (SHC) poleward of 55°S mainly during December–February (DJF); and 4) underestimation by more than 20 W m−2 over the Arctic during June–August (JJA; although not so evident in the annual mean). CAM5-simulated global annual-mean SW CRF at the surface (SFC) is nearly identical to observations (Δmean = −0.4 W m−2) and the regional bias patterns at SFC are very similar to those at TOA (not shown).
The CAM5 tuning strategy is to minimize the overall climate bias score measured by the average time–space rmse errors of several semi-independent key thermodynamic variables (see Park and Bretherton 2009) while satisfying a couple of mandatory conditions (global energy balance at the top of the model and stable coupled simulation) and improving specific phenomena that are important for climate research but are not well simulated (e.g., ENSO and an acceptable magnitude of aerosol direct and indirect effects). Because CAM5’s physics–dynamics schemes are not perfect, some aspects such as SW CRF are inevitably biased under our tuning strategy.
CAM5-simulated global annual-mean LW CRF at TOA is 22.4 W m−2, significantly smaller than the available observations (26.5 W m−2 from CERES-EBAF as shown in Fig. 3d and 30.4 W m−2 for ERBE). A similar underestimate can be seen in the LW CRF at SFC 
With this caveat in mind, CAM5 overestimates LW CRF in the tropical deep convection regimes over the western coast of Central America and the intertropical convergence zone (ITCZ), the western Indian Ocean, and Africa. With opposite signs, these regional biases are roughly consistent with the biases in the SW CRF at TOA, implying that CAM5 simulates too much (or too optically thick or too high) upper-level clouds in the tropical deep convection regimes. The biases of LW CRF at TOA over the eastern subtropical stratocumulus-to-cumulus transition regimes and the SHC ocean are much weaker than the corresponding biases in SW CRF, implying that CAM5 simulates too few (or too optically thin) low-level clouds there. In section 3j, we discuss possible sources of these regional biases in SW and LW CRFs at the process level. The net radiative impact of clouds on the global atmospheric column (not the sum of the atmospheric column and underlying surface) is a warming, with a global annual mean of 2.1 W m−2 in CAM5 (SW warming = 4.8; LW cooling = 2.7) and 2.9 W m−2 from observations (SW warming = 6.1; LW cooling = 3.2).
b. Cloud fraction and cloud condensate amount
SW CRF is a function of cloud fraction and cloud optical thickness, which in turn is a function of cloud LWC/IWC and cloud droplet radius. Cloud-top temperature also plays an important role in LW CRF. To obtain insight into the biases of CAM5-simulated CRFs, we plot the total cloud fraction (CLDTOT) and column-integrated LWC (TGCLDLWP; which includes both stratus and cumulus LWPs) in Fig. 4.
As in Fig. 3, but for the annual-mean (left) CLDTOT and (right) TGCLDLWP. The observations are the 19-yr climatology of infrared-based total cloud fraction from the ISCCP D2 (July 1983–December 2001; Rossow and Schiffer 1991) and the 12-yr climatology of column-integrated grid-mean cloud LWC over the ocean from the NVAP (January 1988–December 1999; Randel et al. 1996). The global-mean statistics are only over the ocean in (d),(f). Note that vertical overlapping assumptions used for computing CLDTOT as well as the definition of cloud in each layer differ between CAM5 and OBS.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
Overall, CAM5-simulated CLDTOT is similar to the International Satellite Cloud Climatology Project (ISCCP; Rossow and Schiffer 1991) observations with a global annual-mean CLDTOT of 63% (observation = 66.8%), r = 0.94, and rmse = 10.5%. Both CAM5 and observations show maximum CLDTOTs in the tropical deep convection and midlatitude oceans, which project onto both SW and LW CRFs. However, the maximum CLDTOT over the eastern subtropical oceans are projected only onto SW CRF and not LW CRF, indicating lower-tropospheric clouds. The maximum CLDTOT in the Arctic is not evident in either CRF, probably because the underlying surface (sea ice or snow) is as reflective as clouds and the typical cloud-top temperature is comparable to that of the surface. CAM5-simulated CLDTOT is 1) overestimated over the tropical deep convection regime, 2) underestimated over the eastern subtropical oceans downstream of marine stratocumulus decks, and 3) overestimated over the polar regions. These biases exist throughout the year with the first (second) bias being projected on both CRFs (SW CRF). Over the Arctic in JJA, CAM5 overestimates CLDTOT by 15%, but underestimates SW CRF cooling more than 20 W m−2 (CAM5-simulated clear-sky surface albedo is smaller than the observations). Over the SHC ocean during DJF, CAM5-simulated CLDTOT is similar to observations, but SW CRF cooling is underestimated by more than 50 W m−2. This indicates that over the summer Arctic and the SHC ocean, CAM5-simulated in-cloud condensate is much smaller (or droplet radius is much larger) than the observations, as is also reflected in the negative biases of TGCLDLWP in the SHC ocean (Fig. 4f).
CAM5-simulated global annual-mean TGCLDLWP is 43.3 g m−2 with distinctively high values over tropical land areas and China. Since TGCLDLWP is a function of cloud fraction, the global pattern of TGCLDLWP is roughly similar to CLDTOT, but with larger values in the midlatitude oceans, where stratus LWP in the lower and midtroposphere mostly contributes (Figs. 8g and 9h). When averaged over the ocean, CAM5-simulated TGCLDLWP is only half of the observed 77.5 g m−2 from the National Aeronautics and Space Administration (NASA) Water Vapor Project (NVAP; Randel et al. 1996). Except near the coasts, CAM5 underestimates TGCLDLWP all over the oceans throughout the year, with pronounced maximum negative biases over the eastern subtropical oceans and a portion of midlatitude oceans where meridional SST gradient is large. The biases over the subtropical and midlatitude oceans are consistent with the corresponding biases of CLDTOT and SW CRF, indicating CAM5 does not generate enough cloud condensate there. Section 3j will provide a discussion on the sources of these biases of CLDTOT and TGCLDLWP.
c. Precipitation rate at the surface
Figure 5 shows the CAM5-simulated annual-mean total (convective + stratiform) precipitation rate at the surface compared with the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP; Xie and Arkin 1996). The observed climatologies and CAM5 biases of total precipitation rates in DJF and JJA are shown in the middle and bottom panels of Fig. 6, respectively.
As in Fig. 3, but for the annual-mean precipitation rate at the surface. The observations are 20-yr climatologies of surface precipitation rates from CMAP (January 1979–December 1998; Xie and Arkin 1996).
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
(top) CAM5-simulated annual-mean convective and stratiform precipitation rates at the surface; (middle) observed precipitation rates at the surface from CMAP in DJF and JJA; and (bottom) the difference maps of surface precipitation rates between CAM5 and OBS in DJF and JJA.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
The CAM5-simulated global annual-mean total precipitation rate is 3.01 mm day−1, about 12%–15% larger than the satellite-derived observational estimates [2.69 mm day−1 for CMAP during 1979–98 and 2.61 mm day−1 for the Global Precipitation Climatology Project (GPCP; Huffman et al. 2009) during 1979–2003]. Stephens et al. (2012) suggested these satellite estimates may be biased low, which would reduce most of the discrepancy. While the overall patterns are similar (r = 0.93), systematic regional biases can be identified in CAM5 simulation (and also in the CAM4 simulation): 1) too strong precipitation along the ITCZ extending to the west coast of Central America, especially in DJF; 2) a double ITCZ over the eastern tropical Pacific Ocean south of the equator, especially in DJF; 3) too strong precipitation over the great mountain areas of the Himalayas (especially in JJA), the Andes (especially in DJF), and the Rockies; 4) anomalous precipitation over the desertlike southern portion of the Arabian peninsula in JJA; 5) a meridional shift of the Atlantic ITCZ extending into Africa; 6) complex regional biases over the western tropical Pacific warm pool and Indian Ocean with strong seasonality; and 7) positive biases over the midlatitude storm track, especially during boreal winter. The same comparison against the GPCP instead of the CMAP observation shows similar bias patterns, except that the positive biases in the tropical (extratropical) regions are enhanced (reduced) (not shown).
In CAM5, two types of precipitation exist: convective precipitation (a sum of deep and shallow convective precipitation) generated by single-moment convective microphysics and stratiform precipitation generated by double-moment stratiform microphysics. In this 1.9° latitude × 2.5° longitude horizontal resolution simulation, CAM5-simulated precipitation in the tropics (midlatitude storm track) is mostly convective (stratiform), with similar contributions from both convective and stratiform precipitation over the Himalayas and the Andes (top panels of Fig. 6). The global ratio of the shallow convective precipitation rate to the deep convective precipitation rate simulated by CAM5 is about 0.2 (not shown).
d. The frequencies of deep and shallow cumulus
Figure 7 shows the CAM5-simulated annual-mean frequency of occurrence (FQ) of deep and shallow cumulus compared with surface observations estimated using the methodology described in Park and Leovy (2004). The definitions of individual cumulus FQs from CAM5 and surface observations are given in the caption of Fig. 7. We repeated the same analysis by changing the definitions of CAM5-simulated shallow and deep cumulus (e.g., 0.001 instead of 0.01 as the threshold of saturated updraft fraction, 880 and 850 hPa instead of 900 hPa as the reference level of shallow cumulus, and 450 and 350 hPa instead of 400 hPa as the reference level of deep cumulus), but the results were qualitatively similar to those shown in Fig. 7.
As in Fig. 3, but for the annual-mean frequencies of (left) deep cumulus and (right) shallow cumulus (FQ). The observations are the 53- and 26-yr climatologies of low-cloud FQs over ocean/land at 5° latitude × 5° longitude computed from the Extended Edited Cloud Report Archive (EECRA; Hahn and Warren 1999). In the case of simulations, deep (shallow) cumulus FQ is defined as the fractional occurrence of saturated deep (shallow) cumulus with updraft fractional area larger than 0.01 at 400 (900) hPa. The observed deep (shallow) cumulus FQs are defined as the ratio of the number of observations that reported low-cloud type of CL = 3 or 9 (CL = 1, 2, 4, and 8) to the total number of observations that reported any low-cloud-type information. The method used for computing the observed climatological FQs of various cloud types from individual surface observations is detailed in Park and Leovy (2004). In (c)–(f), grid boxes without enough observations to form a reasonable climatology are regarded as missing and denoted with a dot and global-mean statistics are computed using only the nonmissing grids.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
The global pattern correlations between CAM5 and observations are r = 0.64 for deep cumulus FQ and r = 0.81 for shallow cumulus FQ. CAM5-simulated deep cumulus is mostly concentrated in the tropics, with a negative bias over the subtropical trade cumulus region throughout the year, the northeastern Atlantic and northwestern Pacific Oceans in DJF, and northern Asia and the SH midlatitude ocean during JJA. In the tropical deep convection regions, CAM5 overestimates deep cumulus FQ substantially over land during boreal summer. Some care is needed in the interpretation of these biases because of differences in the method used to produce the FQs between the model and observations. However, from the consistent positive biases of the tropical CRFs (Fig. 3), we speculate that overly frequent tropical deep convective frequency in CAM5 may be real. This may be associated with the assumption that deep convection occurs whenever CAPE exceeds a threshold, and the specification of a CAPE relaxation time scale of τ = 1 h (greater than the model integration time step Δt = 1800 s), which requires more frequent convective events to neutralize atmospheric static instability. This aspect should be explored more in the future.
Except for some regions of the trade cumulus region and the SH midlatitude ocean during DJF, CAM5-simulated shallow cumulus FQ is smaller than the observed estimates with significant negative biases in the tropical deep convection regimes and over summer continents (e.g., over the central United States in JJA, the observed shallow cumulus FQ is about 30% while CAM5 is less than 10%). This may be an artifact of the process splitting in CAM5 described in Fig. 1. Because the deep convection parameterization stabilizes the column before the shallow convection parameterization is invoked, shallow convection will occur less often than it would otherwise. On the other hand, the higher reporting priority given to deep cumulus (CL = 3 and 9) over shallow cumulus (CL = 1, 2, 4, and 8; see Park and Leovy 2004) makes the shallow cumulus FQ reported by surface observers smaller than reality. Since there is no way to quantify the effects of these two artificial factors (e.g., process splitting versus reporting priority), we avoid further interpretation of the negative biases of shallow cumulus FQ in the tropical convective systems that usually accompany both deep and shallow cumulus. However, the negative biases of shallow cumulus FQ over North America during summer may be real, reflecting that CAM5 fails to capture forced convection [i.e., convective updrafts that reach the LCL but not to the level of free convection (LFC)] since both the CIN closure in the shallow convection scheme and the CAPE closure in the deep convection scheme are designed to simulate only the positively buoyant convective updrafts growing above the LFC (i.e., free convection). In the subtropical trade cumulus regime, CAM5-simulated shallow cumulus FQ is roughly similar to observations, even though substantial negative biases of SW CRF, CLDTOT, and TGCLDLWP exist there.
e. LWP and IWP from individual cloud types
Within each grid layer, CAM5 generates deep and shallow cumulus and stratus, which are assumed to occupy horizontally nonoverlapped regions, each with its own cloud fraction, in-cloud LWC/IWC and droplet radius [Eq. (5)]. Figure 8 shows the contribution of each of these three cloud types to TGCLDLWP (left panels) and TGCLDIWP (right panels). In this plot, cumulus LWP/IWP are not the detrained convective condensate but the in-cumulus condensate within the quasi-steady convective updraft plumes that are used only for radiation computation, without being advected by grid-mean flow. In the global annual average, 65% (23% and 12%) of LWP comes from stratus (deep cumulus and shallow cumulus) with similar partitioning for IWP (62%, 22%, and 16%, respectively) but with slightly larger (smaller) contribution from shallow cumulus (stratus).
CAM5-simulated annual-mean (left) column-integrated LWC and (right) column-integrated IWC from (a),(b) all types (deep cumulus + shallow cumulus + stratus) of clouds (TGCLDLWP and TGCLDIWP); (c),(d) deep cumulus; (e),(f) shallow cumulus; and (g),(h) stratus.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
In the tropical regions, deep cumulus LWP/IWP over land are generally larger than over ocean, due partly to the use of smaller autoconversion efficiency (c0) of deep cumulus condensate into convective precipitation over land (c0,lnd = 0.0059 m−1 and c0,ocn = 0.045 m−1), although this may be also due to the stronger buoyancy flux over land tied to the diurnal cycle. Some in-cumulus condensate within deep convective updrafts is detrained in the layers above the level of minimum grid-mean moist static energy and becomes a part of stratus condensate after evaporation and sublimation. Larger stratus LWP/IWP over tropical land than ocean partially reflects the larger amount of detrained deep cumulus condensate over land. However, very large stratus LWP over China might also be enhanced with abundant surface aerosol emission that suppresses stratiform precipitation by reducing the radius of stratus liquid droplets there. A sensitivity simulation with the preindustrial aerosol emission produced smaller LWP than the simulation with the present-day aerosol emission over China (not shown).
Although shallow cumulus LWP is small, it is broadly distributed over subtropical and midlatitude oceans and exerts radiative impacts. At (20°N, 150°W), east of Hawaii, CAM5-simulated shallow cumulus FQ is at a maximum (Fig. 7b), and shallow cumulus LWP is 20 g m−2, larger than stratus LWP (<10 g m−2). Even with the inclusion of the radiative effects of the cumulus updrafts, however, CAM5-simulated SW CRF is smaller than observations (Fig. 3e) in association with negative biases of CLDTOT and TGCLDLWP there (Figs. 4e,f). This implies that penetrative entrainment drying at the cumulus top is stronger than upward moisture transport from the sea surface, resulting in the dissipation of overlying stratocumulus. The sensitivity of the CAM5 cloud system to the penetrative entrainment efficiency will be discussed in section 3j. Shallow cumulus LWP is also at a maximum on the northern flank of the SST cold tongue over the eastern equatorial Pacific Ocean. During August–October along 95°W, stratus, shallow cumulus, and deep cumulus LWP reaches a maximum at 3°, 5°, and 7°N, respectively, in response to the changes of PBL structures in the vicinity of the SST cold tongue and grid-mean vertical velocity.
In the extratropical regions, most TGCLDLWP comes from stratus with some contribution from shallow cumulus. Along the midlatitude oceanic storm track during boreal winter, shallow cumulus IWP is as large as stratus IWP, indicating the importance of convective updrafts in postfrontal cold air outbreaks. The CAPE closure that is mainly designed for simulating tropical deep convection inhibits the triggering of frontal deep convection in the midlatitude regions (Fig. 7a); therefore, the shallow convection scheme is active instead.
f. Zonal-mean cross sections of cloud properties
Figure 9 shows CAM5-simulated zonal-mean cross sections of in-cloud (with hat) and grid-mean (with overbar) LWC (
CAM5-simulated annual zonal-mean cross sections of cloud condensates (color shading) and cloud fractions (solid lines) from (left) cumulus (Acu), (center) stratus (Ast), and (right) cumulus + stratus (Atot,). Shown are in-cloud (a)–(c) liquid and (d)–(f) ice condensates and grid-mean (g)–(i) liquid and (j)–(l) ice condensates. In (a)–(f), white color denotes the area without corresponding clouds.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
CAM5-simulated annual zonal-mean cross sections of (left) grid-mean LWC and IWC from shallow and deep cumulus (color shading) and (right) effective radius and number concentrations of stratus liquid droplets and ice crystals (color shading). In each plot, cloud fraction—(a),(c) Ash; (e),(g) Adp; (b),(f) Al,st; and (d),(h) Ai,st— is overlaid as solid lines. In (right), white color denotes the area without corresponding clouds.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
CAM5-simulated annual zonal-mean 
The composite cloud properties provided to the radiation scheme are shown in Figs. 9c,f (Atot = Acu + Ast, 
Cumulus exists in a wide range of regions from the tropics to the midlatitudes and from the lower to the upper troposphere (Figs. 9g,j). In the tropics, deep convection grows up to the upper troposphere and stabilizes the atmospheric column, which inhibits shallow cumulus growing above ~800 hPa in the process-splitting CAM5 (Fig. 10a). In the midlatitudes where CAM5-simulated deep convective activity is weak, however, shallow cumulus grows up to ~600 hPa and contributes more than 50% of the 
Most of the CAM5-simulated 
CAM5 simulates a maximum 
(left) Diagnostic PBLH in JJA from (top) CESM1, (bottom) CCSM4, and (middle) CESM1 minus CCSM4. (right) Fog amount in JJA from (top) CESM1, (bottom) CCSM4, and (middle) EECRA observations. Simulated fog amount is defined as Atot in the lowest model layer located at z = 67 m over the ocean. Observed fog amount is defined as total cloud fraction when surface observer reported fog [ww = 10–12 and 40–49 where ww is a present weather code defined from WMO (1975)]. In CAM4, PBLH is defined as the lowest interpolated height, where the dry bulk Richardson number computed upward from the lowest model layer is larger than 0.3, with additional adjustment if surface buoyancy flux (Bs) is positive. A minimum value of 700 × u* meters (u* is surface frictional velocity) is imposed on the diagnosed PBLH. In CAM5, if Bs < 0 (Bs > 0), PBLH is defined as zH, the layer midpoint height just below the lowest model interface (as the height of the lowest model interface) where the moist gradient Richardson number is >0.19. When Bs > 0, PBLH is allowed to rise into the next model interface as detailed in Bretherton and Park (2009). No minimum value is imposed on the diagnosed PBLH in CAM5 but by construction PBLH is always larger than the midpoint height of the lowest model layer.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
As expected from Eq. (3), the pattern of Al,st (Fig. 10b) is similar to the pattern of grid-mean RH (not shown), but the pattern of Ai,st (Fig. 10d) more closely resembles 
In the entire globe, 
From the above analysis, the CAM5-simulated cloud systems can be grouped into the following six categories: 1) deep cumulus mainly in the tropics; 2) shallow cumulus between the tropics/subtropics and the midlatitude regions; 3) thick stratus in the midlatitude storm track throughout the whole troposphere, especially during boreal winter; 4) cirrus in the tropical–extratropical upper troposphere; 5) marine stratocumulus over the midlatitude oceans, eastern subtropical oceans on the west of the major continents, and the northern flank of the SST front in the eastern equatorial Pacific Ocean; and 6) optically thin Arctic low-level clouds. These cloud features are in fact quite similar to what is observed in nature.
g. PBL top height, fog, and low-cloud amount
Figure 11 shows CESM1 and CCSM4-simulated PBL top heights and the amount of fog during JJA. Low-cloud amount (LCA) is plotted as solid lines on the left panel of Fig. 12. CAM5/CAM4 produced similar results as the ones from CESM1/CCSM4 (not shown). In the subtropical stratocumulus decks west of the major continents, CESM1 simulates a much deeper PBL than CCSM4. This deepening feature extends westward into the midlatitude oceans including the 60°S latitude band and also into the SST frontal region over the eastern equatorial Pacific Ocean, although it is offset by other factors that force CESM1 to simulate a shallower PBL than the CCSM4 (e.g., in contrast to CAM3/CAM4, CAM5 uses turbulent mountain stress that may decrease surface wind speed and the PBL top height; as detailed in the caption of Fig. 11, in defining PBL top height, 1) CAM4 uses 0.3 while CAM5 uses the more strict value of 0.19 for the critical Richardson number; 2) CAM4 imposes a certain minimum PBL top height while CAM5 does not; and 3) in cases of decoupling, the CAM5 PBL top height is defined as the top interface of surface-based convective layers). The deeper PBL in CESM1 over the marine stratocumulus deck is partly due to strong cloud-top entrainment driven by cloud-top radiative cooling that is explicitly incorporated into the computation of buoyancy production at the PBL top. Strong entrainment at the PBL top dries the PBL by bringing warmer and drier free air into the PBL.
(left) Interannual correlation coefficient (r) between LTS (θ700hPa − θ1000hPa) and LCA. (right) Surface heat flux feedback parameter for SW radiation (λSW) computed from (top) CESM1, (middle) observations, and (bottom) CCSM4 in JJA. Climatological LCA during JJA is overlaid as solid lines in each plot. Simulated r is computed using 156 yr (January 1850–December 2005) of detrended monthly output from twentieth-century coupled simulations while observed LCA and LTS are from the detrended 53 (ocean) and 26 yr (land) of EECRA surface observations and detrended National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis product (Kalnay et al. 1996), respectively. Only the grid boxes with statistically significant r at the 95% confidence level from the two-sided t test (assuming independent samples) are shaded either by red or blue colors. The λSW is estimated using the lagged covariance between monthly SST anomalies and net upwelling SW radiative flux anomalies at the surface, following Park et al. (2005). Physically, negative (positive) λSW indicates the increase (decrease) of net downwelling SW radiative flux at the surface when underlying SST increases by 1 K, implying positive (negative) feedback between the surface temperature and net downwelling SW radiative flux at the surface. The grid boxes with yellow shading denote the area with statistically nonsignificant monthly persistency of underlying surface temperature, so no feedback estimation is performed there.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
The drier air in the lower PBL in CESM1 is clearly reflected in the simulated fog amount in Fig. 11. During JJA, observations show the maximum fog amount on the northwestern flank of the subtropical high where warm and moist air is advected over the cold ocean across the SST front, forming advection fog. CCSM4 roughly captures the spatial distribution of observed fog but the magnitude is much larger than the observations, with anomalous fog over the subtropical stratocumulus decks west of the major continents, over the southwestern Arabian Sea and over the SST cold tongue along the equator in the eastern equatorial Pacific Ocean. CESM1 does a much better job: the fog amount over the northwestern flank of the subtropical high is smaller than in CCSM4, and anomalous fog over the subtropical stratocumulus decks and western Arabian Sea has completely disappeared, with better simulation along the SST cold tongue. This improvement in CESM1 is due to enhanced turbulent mixing and drying of the lower PBL, as a result of the simulation of cloud–radiation–turbulence interactions in CAM5.
Over some portions of the Antarctic sea ice area during JJA (e.g., at around 180° and 50°W along 75°S), however, CESM1 simulates more fog than CCSM4. We speculate that the changes of the horizontal advection, synoptic storm activity, and surface wind speed may be responsible for this increase of fog from CCSM4 to CESM1 during boreal winter.
h. Lower-tropospheric stability versus LCA
Because of the explicit parameterization of cloud–radiation–turbulence interaction, CESM1 does not need a separate parameterization for stability-based stratus fraction. However, if the simulated cloud–radiation–turbulence interactions are realistic, CESM1 should be able to reproduce the observed relationship between lower-tropospheric stability (LTS; LTS ≡ θ700hPa − θ1000hPa) and stratus fraction (Klein and Hartmann 1993) that was built into CCSM4.
Figure 12 shows the interannual correlation coefficient between LTS and LCA from the observations, CESM1, and CCSM4 during JJA. For comparison, climatological LCA from the observations and individual simulations is also plotted as solid lines in each figure. Observations show a maximum in LCA over the subtropical stratocumulus decks west of the major continents, midlatitude oceans, SST front in the eastern equatorial Pacific Ocean, and the Arctic. CCSM4 captures the observed maxima of LCA partly with the help of the stability-based stratus fraction. Even without the stability-based stratus, however, CESM1 successfully simulates the observed LCA maxima over the aforementioned areas, including the local minimum LCA along the equator slightly north of the SST cold tongue in the eastern equatorial Pacific Ocean.
Observations also show significant positive correlation between LTS and LCA over the subtropical stratocumulus decks, over midlatitude oceans in the NH, and in the vicinity of the SST cold tongue in the eastern equatorial Pacific Ocean. By construction, CCSM4 simulates a strong positive correlation between LTS and LCA. Without stability-based stratus, CESM1 successfully captures the observed significant positive correlations. This figure demonstrates that the cloud–radiation–turbulence interactions simulated in CESM1 realistically reproduce complex feedback processes that control the observed positive relationship between LTS and LCA over the marine stratocumulus decks. However, simulated positive correlations are generally stronger and more ubiquitous than the observations, especially over the tropics and the major continents. This implies possible model deficiencies, although sampling noise in the relatively sparse observations may contribute to this difference. Both CCSM4 and CESM1 simulate significant negative correlations over the Arctic and Antarctic, with stronger negative correlation in CESM1 over the Arctic in summer.
i. Radiative feedback of marine stratocumulus at the surface
Marine stratocumulus (MSC) reflects incoming solar radiation and cools the underlying sea surface. In turn, cold SST favors the formation of MSC by increasing the degree of vertical coupling of thermodynamic variables within the PBL. During the tuning process of CAM5–CESM1, we found that a version of CAM5 with excessive SW CRF over the North Pacific Ocean would drift toward very cold SSTs after dynamical ocean coupling, even though fixed SST simulations produced a good global energy balance at TOA. This drift in the coupled system was eventually solved by retuning CAM5 to produce closer agreement with the observed SW CRF over the North Pacific Ocean. Correct simulation of future climate critically depends on how the model accurately simulates the positive feedback between SST and MSC (Bodas-Salcedo et al. 2012; Williams et al. 2013).
Park et al. (2005) quantitatively estimated the strength of this positive MSC–SST feedback by computing surface heat flux feedback (i.e., the response of surface heat flux to sea surface temperature anomalies) using the observed monthly SST and the surface radiative flux dataset. They showed that positive MSC–SST feedback is strong along the SST gradient zone over the subtropical and midlatitude oceans where the transition between stratocumulus and cumulus occurs. Using a stochastically forced ocean mixed layer model, Park et al. (2006) also showed that positive MSC–SST feedback can substantially enhance the persistence of SST anomalies during late spring and early summer over the North Pacific Ocean.
The right panels of Fig. 12 show surface SW radiative feedback during JJA estimated following the methodology of Park et al. (2005) to produce observed and model estimates. With a change in sign, the surface SW radiative feedback measures how much net downwelling SW radiation at the surface changes when the underlying SST increases by 1 K. Observations show strong positive SW feedback along the SST gradient zone in the midlatitudes and eastern subtropical Pacific Ocean in association with the transition of stratocumulus to cumulus when the underlying SST increases. The maximum magnitude of SW radiative feedback at the surface amounts to 40 W m−2 K−1 over the northwestern flank of the Namibian stratocumulus deck during September–November (SON; not shown). Both CCSM4 and CESM1 reproduce the observed SW radiative feedback. The success of CCSM4, mainly due to the empirical parameterization for stability-based stratus fraction, is somewhat surprising since CAM3/CAM4 do not generate in-cloud condensate within the stability-based stratus. Without the stability-based stratus, CESM1 successfully reproduces the observed positive MSC–SST feedback at the right location and magnitude, because of the explicit parameterization of cloud–radiation–turbulence interactions. Strong positive feedback over the summer Arctic, both in CESM1 and CCSM4, reflects the melting of sea ice and the decrease of clear-sky surface albedo in association with the increase of surface temperature, rather than the effects of clouds which are optically thin there.
j. Sensitivity of the cloud system to key uncertain parameters
This section provides insight into the sensitivity of CAM5-simulated clouds to several key parameters that were optimized during the tuning process, rather than being strictly constrained against observations. Figures 13 and 14 show the changes of SW CRF at TOA (color in Fig. 13), LW CRF at TOA (line in Fig. 13), condensate water path (CWP; CWP = TGCLDLWP + TGCLDIWP; color in Fig. 14), and CLDTOT (line in Fig. 14) from the control simulation when individual parameter values are perturbed from the CAM5 default value as indicated at the top of each figure. The physical meaning of each of the eight parameters is as follows: a2l is the evaporative enhancement factor of entrainment rate at the top of cloud-topped convective layers (Fig. 13a); rpen is the penetrative entrainment efficiency at the top of shallow convective updraft (Fig. 13b); co is the autoconversion efficiency of deep convective condensate into precipitation (Fig. 13c); qi,st,min is the minimum in-stratus IWC that stratus can hold (Fig. 13d); Rdet,dp is the effective radius of detrained deep convective condensate (Fig. 13e); Rdet,sh is the effective radius of detrained shallow convective condensate (Fig. 13f); Dc,s is the critical diameter of ice crystals at which stratus ice condensate starts to be converted into snow (Fig. 13g); and wice,max is the maximum subgrid vertical velocity for the activation of stratus ice nuclei (Fig. 13h).
Sensitivity of CAM5 cloud system to several uncertain model parameters. The plots show the changes of SW CRF (color shading) and LW CRF (solid–dashed black lines, where the dashed line is for a negative value) at TOA, when the individual parameter is perturbed from the default value as denoted at the top of each plot. The values at the top left of individual plots are the global-mean values of ΔSW CRF (ΔLW CRF). Contour interval is 5 W m−2. See the text for the physical meaning of the perturbed parameters.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
As in Fig. 13, but the changes of CWP (color shading) and TCA (solid–dashed black lines, where a dashed line is for negative values). The values at the top left of individual plots are the global-mean values of ΔCWP (ΔTCA). Contour interval is 0.05 for the first contour and 0.1 for the other contours.
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
If a2l is reduced, the top-of-stratocumulus-topped PBL becomes moister because of the reduction of entrainment warming and drying, resulting in increases of LCA, TGCLDLWP, and SW CRF cooling over the subtropical and midlatitude stratocumulus decks over the ocean (Figs. 13a and 14a). The parameter rpen has a similar effect to a2l except that the effect of rpen is stronger in the downstream portion of the subtropical stratocumulus deck in which shallow cumulus lies underneath stratocumulus (Figs. 13b and 14b). The negative regional biases of SW CRF (Fig. 3e), CLDTOT (Fig. 4e), and TGCLDLWP (Fig. 4f) in the eastern subtropical ocean west of the major continents can be adjusted by reducing a2l and rpen.
If the production rate of deep convective precipitation decreases because of the decrease of c0, deep convective updrafts can hold more in-cumulus condensate: some of which is detrained and forms the stratiform condensate in the tropics, which in turn is transported into the extratropical regions by the Hadley circulation and resolved eddy motions, resulting in substantial increases of CWP, SW CRF cooling, and LW CRF warming, in both the tropical and extratropical regions (Figs. 13c and 14c). Some of the negative biases of TGCLDLWP (Fig. 4f) can be offset by reducing c0, but the negative bias of SW CRF (Fig. 3e) in the tropical deep convection regime will be degraded. If qi,st,min increases, CAM5 decreases the fractional amount of optically thin ice stratus without changing the grid-mean IWC of stratus. The largest decrease in ice stratus fraction can be seen in the tropical upper troposphere and polar regions, without much change to CWP and CRFs (Fig. 14d). The positive biases of CLDTOT in the polar regions (Fig. 4e) can be offset by increasing qi,st,min.
The CAM5 cloud system is surprisingly insensitive to the specified sizes of detrained deep convective condensates. Deep convective condensate is detrained mostly in the tropics (Figs. 8c,d and 10e,g), where convective precipitation is dominant over stratiform precipitation (Figs. 6a,b). In addition, in-cloud LWC/IWC of deep cumulus in CAM5 is very low because of the use of a very large autoconversion efficiency (Figs. 9a,d). Thus, the change in Rdet,dp does not have much impact on the hydrological cycle, CWP (Fig. 14e), and CRFs (Fig. 13e). In contrast to deep convection, the size of detrained shallow convective condensate has a large influence on the midlatitude cloud system. Detrained shallow convective IWC serves as an important source of ice stratus IWC in the midlatitudes (Figs. 10c,h), where stratiform precipitation is dominant over convective precipitation (Figs. 6a,b). As a result, small Rdet,sh decreases stratiform precipitation, resulting in an increase of CWP and SW CRF cooling in the midlatitude storm track. This change would reduce the SWCF bias in the SH storm track. In fact, smaller Rdet,sh is more comparable with the satellite estimates (King et al. 2013).
If Dc,s decreases, more in-stratus IWC can be converted into snow, resulting in a decrease of TGCLDIWP and the associated ice stratus fraction (Fig. 14g). In the tropics, both SW and LW CRFs become consistently weaker, but SW CRF cooling increases in the midlatitude storm track, even though CWP decreases there (Fig. 13g). This is partly due to the increase of diagnostic snow amount and its radiative impact: CAM5 explicitly includes the SW radiative effect of snow. If wice,max decreases, the nucleation rate of aerosols into cloud ice droplet decreases [at z = 200-hPa height in the tropical deep convection region, the frequency of wice ≥ wice,max = 0.2 m s−1 (so that wice is reset to wice,max for the aerosol nucleation) is about 0.15–0.3 (not shown)], resulting in a decrease of ice stratus fraction, SW CRF cooling, and LW CRF warming, mostly in the tropical deep convection regimes (Figs. 13h and 14h).
4. Summary and conclusions
This paper provides a description of the integrated representation for cloud processes in CAM5. Compared with the previous versions, the cloud parameterizations in CAM5 are more consistent and physically based, due to inclusion of more realistic and complex parameterizations and much attention given to the interactions among them within a more consistent framework. Several key aspects of CAM5 cloud parameterizations are 1) a consistent cloud macrophysical formulation, 2) stratus–radiation–turbulence interactions, 3) prognostic treatment of stratus droplet number and aerosol species, and 4) radiatively active cumulus and snow.
Within each grid layer, CAM5 has nonoverlapped deep cumulus, shallow cumulus, and stratus, where each of which has its own cloud fraction, in-cloud mass, and number concentration of cloud droplets. Deep and shallow convection schemes diagnose vertical profiles of cumulus properties. Liquid and ice stratus fractions are diagnosed as a function of grid-mean RH over water and ice, respectively, and a single stratus fraction is diagnosed by assuming maximum horizontal overlap between the two. The saturation equilibrium constraint (i.e., RH over water within liquid stratus is 1, and liquid stratus condensate does not exist outside of liquid stratus) allows CAM5 to compute the net condensation rate of water vapor into liquid stratus. By performing pseudo condensation–evaporation (adjusting the ice stratus fraction), consistency is imposed between the diagnosed cloud fraction and the prognosed condensate amount of liquid (ice) stratus at the end of stratus macrophysics, which removes empty (i.e., zero in-stratus condensate) and dense (i.e., very large in-stratus condensate) stratus. On the other hand, CAM4 allows horizontal overlap without occupancy priority among the three clouds, only diagnoses a single-phase stratus fraction, uses stability-based empty stratus as well as RH-based stratus, and frequently generates empty and dense stratus.
The CAM5 moist turbulence scheme handles both the dry and saturated turbulent processes throughout the whole atmosphere, while the CAM4 PBL scheme handles only dry turbulent processes within the PBL. By incorporating cloud-top LW cooling into the computation of eddy diffusivity, CAM5 explicitly simulates stratus–radiation–turbulence interactions that can sustain a saturated PBL top over the ocean by enhancing turbulent vertical mixing. As a result, CAM5 simulates marine stratocumulus (MSC) at the PBL top solely from the grid-mean RH without relying on separate empirical stability-based prescription of stratus cloud fraction. With stratus–radiation–turbulence interaction, MSC is a dynamic driver of the climate system as well as the controller of the global radiation budget and hydrological cycle. Parameterization of stratus–radiation–turbulence interaction imposes direct interaction among stratiform macrophysics, radiation, and moist turbulence schemes (Fig. 1) that are absent in CAM4.
As well as the mass, CAM5 prognoses number concentration of stratus droplets. The two main sources of stratus droplet numbers are activated aerosols and detrained in-cumulus condensates, while the main sinks are evaporation, sedimentation, and precipitation of stratus condensates. Both deep and shallow convection schemes only diagnose the mass of in-cumulus condensate. CAM5 specifies the mean volume radius of detrained in-cumulus condensate and derives condensate number from the condensate mass and size. Through the activation process, aerosol controls the stratus droplet size, which affects the radiation and the production rate of stratiform precipitation. In other words, CAM5 simulates various aerosol indirect effects associated with stratus. Since aerosol activation occurs when subsaturated turbulent eddies are delivered into the saturated stratus portion, direct interaction among stratiform macrophysics, aerosol activation, and moist turbulence schemes are included in the CAM5 processes (Fig. 1). Grid-scale advection and moist PBL schemes transport stratus droplets, assuming that they are conserved during transport. Instead of prognosing droplet number concentration, CAM4 specifies a fixed radius of stratus droplets over land and ocean with a ramp between them.
CAM5 explicitly handles the radiative effects of cumulus and snow by assuming that in-cumulus condensate (not the detrained condensate) has the same droplet radius and size distribution parameters as the in-stratus condensate in the same layer. However, internal thermodynamic properties of cumulus are not advected by the large-scale advection scheme.
In addition to the more comprehensive and consistent model physics, CAM5–CESM1 has improved climate fidelity. However, several systematic biases were also identified in the simulated cloud fields in CAM5. Through a set of parameter sensitivity simulations and a detailed review of model parameterizations, we could identify (or speculate on) the source of the discrepancies down to the process level, which can be grouped into the following three categories: 1) deficient regional tuning, 2) inconsistency between various physics parameterizations, and 3) incomplete model physics.
Parameter sensitivity simulations provided potential pathways to address the following biases:
negative biases of CLDTOT and associated CRFs in the eastern subtropical oceans can be reduced by reducing penetrative entrainment efficiency at the shallow cumulus top;
positive biases of CLDTOT over polar regions can be reduced by increasing minimum in-stratus IWC thresholds;
negative biases of TGCLDLWP can be partially addressed by reducing autoconversion efficiency of deep cumulus condensate or by reducing the effective radius of detrained shallow cumulus condensate;
weak SW CRF over the SH storm track can be reduced by decreasing the effective radius of detrained shallow cumulus condensate;
some of the overly strong SW CRF and LW CRF in the tropics can be addressed by reducing the deep cumulus fraction; and
too frequent deep convective activity might be addressed by reducing the CAPE consumption time scale.
One example of the inconsistency between different parameterizations is the aerosol activation performed in the middle of stratiform microphysics rather than at the beginning, resulting in overestimation of stratus droplet size used for the computation of stratiform precipitation production and the negative bias of TGCLDLWP.
The biases possibly associated with incomplete model physics are as follows:
underestimation of LW CRF due to the horizontal heterogeneity assumption of water vapor within each grid layer in the radiation scheme;
overly strong SW CRF and LW CRF in the tropics due to the use of a single-type cloud within the radiation scheme; and
underfrequent shallow convective activity over summer continents due to the neglect of forced convection.
In summary, CAM5 provides the community with a unique opportunity to explore cloud–aerosol–climate interactions in a physically reasonable way. While substantially improved from its predecessors, many aspects of CAM5 can and should be improved in the future, upon which we are continuously working with collaborators.
Acknowledgments
Sungsu Park is supported by the National Science Foundation. Part of this work was supported by the Regional and Global Climate Modeling Program (RGCM) of the U.S. Department of Energy, Office of Science (BER), Cooperative Agreement DE-FC02-97ER62402.
APPENDIX A
Cloud Macrophysics for Liquid Stratus
This section provides information on the CAM5 cloud macrophysics for liquid stratus. Cloud macrophysics is a set of physical processes used to compute cloud fraction and net condensation rate of water vapor into cloud water. On the other hand, cloud microphysics is a set of processes used to generate precipitation from cloud water. We will explain how CAM5 computes diagnostic liquid stratus fraction (al,st) and prognostic grid-mean net condensation rate of water vapor into liquid stratus water 
a. Liquid stratus fraction
(top) Triangular PDF of total liquid specific humidity (qt,l) used for computing liquid stratus fraction (al) in CAM5. Liquid stratus fraction is the area on the rhs of the dashed line of qt,l = qs,w where qs,w is saturation specific humidity over water. In principle, in-stratus LWC
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
CAM5 generates slightly smaller al than CAM3/CAM4. As al → 1, CAM5 satisfies 
In principle, triangular PDF can be used to diagnose 
b. Grid-mean net condensation rate of water vapor into liquid stratus condensate 
To compute 
Although Al,st is explicitly used in computing 
c. Imposing consistency between liquid stratus fraction and liquid stratus condensate
To reduce numerical instability due to the use of a long model integration time step (Δt = 1200 s for the Eulerian dynamic core or 1800 s for the finite-volume dynamic core), CAM has used process splitting: that is, in each time step, successive parameterizations operate on the updated state resulting from the previous parameterization, as shown in Fig. 1. This process splitting allows for the use of separate shallow and deep convection schemes, because, in the case of time splitting (in which all parameterizations are operating on the same input state), a simultaneous use of two separate convection schemes can cause overstabilization of the atmospheric column because of double counting of the convective adjustment. However, since multiple values of stratus fraction can be computed in each time step because of continuous updates of grid-mean RH after individual parameterization, process splitting raises a question on what is the best stratus fraction that all parameterizations should commonly use at each time step. During CAM5 development procedure, we found that CAM3 frequently generated unreasonably large 
To elucidate this problem, we pick the initial equilibrium state of p = 900 hPa, 
Figure A2 shows the scatterplot of Δal,st and 
Changes of liquid stratus fraction (Δal,st) and in-stratus LWC 
Citation: Journal of Climate 27, 18; 10.1175/JCLI-D-14-00087.1
APPENDIX B
Description of the Various Simulations
This section provides a brief description of the configurations of various CAM5 simulations. The basic settings common to all simulations, detailed below, are as follows:
model physics time step of Δt = 1800 s, radiation time step of Δt = 3600 s, and dynamic sub–time step of Δt = 225 s;
horizontal resolution of 1.9° latitude × 2.5° longitude; and
30 vertical layers with the midpoint height of the lowest model layer [z(1)] at the sigma pressure level of σ = 0.9926, corresponding to ~67 m over the ocean, and the highest model interface at σ = 0.00225.
a. Stand-alone CAM5 simulation forced by climatological SST in the year 2000
This simulation is forced by observed climatological SST and sea ice fraction with annual cycle (Hurrell et al. 2008). One-dimensional ice thermodynamics (i.e., vertical exchanges of heat and moisture) is active assuming sea ice thickness is 2 (1) m over the Arctic (Antarctic) and ocean temperature below sea ice is fixed at −1.8°C. Snow fraction over ice is a function of snow depth, which is controlled by snowfall rate from the atmosphere. Snow albedo, which is generally larger than the sea ice albedo at the clean state, can decrease when atmospheric aerosols (e.g., black carbon) are deposited onto the snow. The land model is fully interactive with the atmosphere. The atmospheric concentration of individual greenhouse gases is specified as a fixed value over the entire atmosphere without annual cycle (CO2 = 367, CH4 = 1760 × 10−3, N2O = 316 × 10−3, CFC-11 = 653.45 × 10−6, and CFC-12 = 535 × 10−6; all in units of ppmv). Atmospheric concentration of ozone is also specified as a function of (x, y, z) with a specified annual cycle. Solar constant is specified as a fixed value without annual cycle. Surface fluxes of various aerosol species are also specified in the year 2000. No major volcanic aerosols are added in this simulation.
b. CAM5–AMIP
This simulation is identical to the above stand-alone CAM5 simulation, except that
all of the specified SST, sea ice fraction, greenhouse gases, ozone, solar constant, and surface flux of aerosols have interannual variations derived from the observations and
atmospheric concentrations of the major volcanic aerosols are specified as a function of (y, z, t) with annual cycle with specified effective radii.
c. CAM5–SOM
This is a CAM5 simulation coupled with an SOM with adjustive surface fluxes of heat and moisture designed to mimic the effects of oceanic horizontal advection in the fully coupled CESM1 simulation. A long-term CAM5–SOM is run (with the configurations of the above stand-alone CAM5 but in the year 1850 with constant CO2 = 284.7, CH4 = 791.6 × 10−3, N2O = 275.68 × 10−3, CFC-11 = 12.48 × 10−6, and CFC-11 = 0; all in units of ppmv) without the specifications of SST and sea ice fraction, until it reaches the stable equilibrium state.
d. CESM1
This is a fully coupled simulation without any flux correction between atmosphere and underlying surfaces. The specifications of greenhouse gases, ozone, solar constant, surface fluxes of aerosols, and major volcanic aerosols are identical to the CAM5–AMIP, except that full interannual variations from 1850 to 2005 are included.
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