Improved Low-Cloud Simulation from the Community Atmosphere ...

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Improved Low-Cloud Simulation from the Community Atmosphere Model with an Advanced Third-Order Turbulence Closure ANNING CHENG Science Systems and Applications, Inc., and Climate Science Branch, NASA Langley Research Center, Hampton, Virginia

KUAN-MAN XU Climate Science Branch, NASA Langley Research Center, Hampton, Virginia (Manuscript received 13 November 2014, in final form 19 February 2015) ABSTRACT In this study, a simplified intermediately prognostic higher-order turbulence closure (IPHOC) is implemented in the Community Atmosphere Model, version 5 (CAM5), to provide a consistent treatment of subgrid-scale cloud processes, except for deep convection. The planetary boundary layer (PBL) height is prognosticated to better resolve the discontinuity of temperature and moisture above the PBL top. Singlecolumn model tests show that fluxes of liquid water potential temperature and total water, cloud fraction, and liquid water content are improved with this approach. The simplified IPHOC package replaces the boundary layer dry and moist turbulence parameterizations, the shallow convection parameterization, and the liquid-phase part of the cloud macrophysics parameterization in CAM5. CAM5-IPHOC improves the simulation of the low-level clouds off the west coasts of continents and the storm track region in the Southern Hemisphere (SH). The transition from stratocumulus to cumulus clouds is more gradual. There are also improvements on the cloud radiative forcing, especially shortwave, in the subsidence regime. The improvements in the relationships among low cloud amount, surface relative humidity, lower tropospheric stability, and PBL depth are seen in some stratocumulus regions. CAM5-IPHOC, however, produces weaker precipitation at the South Pacific convergence zone than CAM5 because of less energy flux into the SH atmosphere. The more downward surface shortwave radiative cooling and the less top-of-theatmosphere longwave cloud radiative heating in the SH relative to the Northern Hemisphere explains the anomalous cooling and the lesser energy flux into the SH, which is related to the underestimate of extratropical middle/high clouds in the SH.

1. Introduction Low-level clouds, shallow cumuli, and stratocumuli play a crucial role in Earth’s radiation balance, owing to their high reflectivity to incoming shortwave radiation and their large areal coverage (e.g., Randall et al. 1984; Slingo 1990). The surface fluxes, radiative cooling/heating, turbulence mixing, cloud-top entrainment, microphysics, and large-scale processes are interactive in the formation, maintenance, and dissipation of the low-level clouds and exert complex

Corresponding author address: Dr. Anning Cheng, Climate Science Branch, NASA Langley Research Center, Mail Stop 420, Hampton, VA 23681. E-mail: [email protected] DOI: 10.1175/JCLI-D-14-00776.1 Ó 2015 American Meteorological Society

feedbacks on the climate system (Stephens 2005; Wood 2012). It is challenging to simulate the low-level clouds realistically in climate models owing to the fact that they are responsible for most of the spread in model-based estimates of equilibrium and transient climate (Randall et al. 2007; Dufresne and Bony 2008; Boucher et al. 2013). The lack of coastal low-level clouds is a well-known problem in a number of general circulation models (GCMs; e.g., Schmidt et al. 2006; Donner et al. 2011) and even in multiscale modeling framework (MMF), in which a cloud-resolving model (CRM) is embedded in each atmospheric grid column of the host GCM to represent cloud physical processes (Grabowski 2001; Khairoutdinov and Randall 2001). When an MMF or a GCM was coupled to an ocean model, the underestimate of low-level clouds led to

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warm biases in sea surface temperature (SST) in the eastern subtropical oceans (e.g., Ma et al. 1996; Yu and Mechoso 1999; Stan et al. 2010) because of the excessive amount of solar radiation reaching the ocean surface. In the past decade, there is an increasing trend to represent low-level clouds as a part of unified parameterizations of the planetary boundary layer (PBL) mixing and stratocumulus and shallow cumulus clouds. This approach is attractive because of the internal consistency on the treatments of the subgrid-scale processes. For example, the eddy diffusion mass flux (EDMF) approach (Siebesma et al. 2007; Neggers et al. 2009), unifying the traditionally used diffusion scheme in the PBL and the commonly used mass flux approach to parameterize shallow convection, has shown a strong ability to simulate various boundary layer clouds. The higher-order turbulence closure (HOC) approach is a unified boundary layer turbulence and cloud parameterization by design. This approach determines lowand higher-order moments of thermodynamic and dynamic variables, which are used to determine the assumed probability density function (PDF) and then produce cloud fraction and liquid water content. Although it has shown promise in previous CRM and single-column model studies (e.g., Bougeault 1981; Lappen and Randall 2001; Golaz et al. 2002; Cheng and Xu 2006, 2008), there are issues to be resolved for applications in GCMs. The small time step needed in the HOC for predicting the higher-order moments and the various spurious oscillations (e.g., Moeng and Randall 1984; Cheng et al. 2004) are two issues making it difficult to apply to GCMs and MMF. Higher-order turbulence closure has recently been implemented and tested in an MMF for climate simulations. Cheng and Xu (2011, hereinafter CX11) upgraded the embedded CRM with an intermediately prognostic higher-order turbulence closure (IPHOC; Cheng et al. 2010; Cheng and Xu 2006) to an MMF, known as superparameterized Community Atmosphere Model (SPCAM). They showed a greatly improved simulation of low-level clouds over the tropical and subtropical oceans despite the very coarse horizontal resolution (at T21) used in the host GCM. Using a finite-volume 1.98 3 2.58 dynamic core for the host GCM with an increase in the vertical resolution below 700 hPa, Xu and Cheng (2013a,b), Cheng and Xu (2013a,b), and Painemal et al. (2015) examined the climatology, seasonal cycle, diurnal cycle, and cloud regime transition simulated with SPCAM-IPHOC. The SPCAM-IPHOC model can produce a globaland annual-mean low cloud amount that is within 5.3% of observations (50.3%) from the merged CloudSat,

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Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), Clouds and the Earth’s Radiant Energy System (CERES), and Moderate Resolution Imaging Spectroradiometer (MODIS) data product (C3M; Kato et al. 2011). The seasonal variations of these low-level clouds in the eastern Pacific are comparable to, and in some instances better than, those produced by the best regional highresolution climate models (Wyant et al. 2010; Wang et al. 2011). The cloud regime transition from stratocumulus and shallow cumulus to deep convective clouds and the diurnal cycle of the low-level clouds are realistic. The higher-order turbulence closure approach has recently been applied to conventional GCMs to improve the low-level clouds and turbulence. Bogenschutz et al. (2013) described climate simulations of Community Atmosphere Model, version 5 (CAM5), coupled with a higher-order turbulence closure known as Cloud Layers Unified by Binormals (CLUBB; Golaz et al. 2002). They found that CAM5– CLUBB provides a much more gradual transition of stratocumulus to trade wind cumulus regimes in the subtropical oceans that is in better agreement with observational analysis compared to CAM5. The global-mean low-level cloud fraction from CAM5– CLUBB is 41.7%. Guo et al. (2014) implemented and tested CLUBB in the Geophysical Fluid Dynamics Laboratory (GFDL) GCM. They reported that the subgrid cloud water variability in the cloud microphysics has a considerable positive impact on global cloudiness. How will IPHOC perform by bypassing the CRM in MMF? How realistic will the global distribution of low-level clouds in the CAM5-IPHOC (CAM5 implemented with a simplified IPHOC; see section 2) simulation be? How realistic will other features of climate state change with the change in the low-level clouds in CAM5-IPHOC? Furthermore, lessons learned from the implementation of IPHOC in CAM5 can benefit other similar unified schemes. The goal of this paper is threefold: 1) simplifying, improving, and implementing IPHOC in CAM5; 2) evaluating the performance of CAM5-IPHOC against available observations; and 3) comparing the performance of CAM5-IPHOC with CAM5 and HOC schemes in other GCMs. The rest of this paper is organized as follows. The simplification and improvement of IPHOC for CAM5 will be briefly described in section 2, along with the single-column model testing. The climate model results are presented in section 3. Section 4 provides the summary and discussion.

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2. IPHOC simplification and single-column testing The IPHOC used in SPCAM MMF is simplified to increase the time step and improved for a realistic coupling with CAM5. The discontinuity of temperature and moisture above the PBL top requires vertical grid-spacing as fine as a few of meters to resolve. A forecasting PBL height approach has been derived and implemented so that the discontinuity above the PBL top can be parameterized for relatively coarse vertical grid spacing. On the other hand, the main obstacle limiting the time step of IPHOC is predicting the second- and third-order moments. We chose to diagnose both the third-order moment equations and three more second-order moment equations, which are derived below and implemented in CAM5IPHOC.

a. Predicted PBL height for IPHOC The prognostic equation for the PBL height is dh E 5 1 w, dt r

(1)

where r is the density of the air, E is the entrainment rate with unit of kg m22 s21, and w is the large-scale vertical velocity, which is supplied by the host GCM. The derivation of Eq. (1) follows Lappen et al. (2010). The entrainment usually causes an increase of the PBL top, while the large-scale subsidence has an opposite effect. E is calculated as r(w0 w0 w0 )T 1 E5

(w0 w0 )T

2gDz C DR cp T r

2gDz 1 Dh cp T

,

where g is the constant of gravity, cp is the specific heat of air at constant pressure, w is the vertical velocity, and prime denotes perturbation from the grid mean. Subscript T represents the PBL top whereas the regular T is temperature, DR 5 Rh1 2 Rh is the radiative flux jump across the PBL top, and h1 and h refer to layers just above and below the PBL top. Depth scale Dz is 2

33/2

0 0 pffiffiffi 6(w w )T 7 7 Dz 5 2 3Dzm 64 em 5

,

where Dzm is the mixed layer depth and em is the integrated turbulent kinetic energy (TKE) for the mixed layer. As an example, if the vertical velocity variance at

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the PBL top is 1/16 of the vertically averaged TKE and the mixed layer depth is 1000 m, the inversion layer thickness would be approximately 13.5 m. The virtual dry static energy jump across the PBL top is Dsy, where sy 5 cpT(1 1 0.608qy 2 qc) 1 gz, where qy is the water vapor mixing ratio and qc is the cloud water mixing ratio. Note that Cr is equal to either 1 or 0 depending on whether or not a cloud is present. In this formula, the third-order moments of vertical velocity at the PBL top (w0 w0 w0 )T represent the inhomogeneity of the mixed layer, causing an increase of the entrainment. The radiative cooling [(2gDz/cp T)Cr DR] across the PBL top enhances the mixing of the dry air above the PBL top with the moist air inside the mixed layer, and so it enhances the entrainment. The second-order moment of vertical velocity (w0 w0 )T represents the strength of TKE near the PBL top, and the buoyancy effect [(2gDz/cp T)Cr Dsy ] is the main driver of the upward motion for the PBL parcels. Both of them prompt the strong upward motion and cause the decrease of entrainment rate. For stratocumulus cloud cases, the radiative jump term dominates the numerator in the expression of E, making the numerator negative. The denominator is dominated by the buoyancy term, which is also negative. So the entrainment rate is positive. The PBL top is treated as an extra layer in IPHOC. In other words, IPHOC has 33 levels in the vertical direction, one more layer than the host GCM. The treatment of the PBL layer is similar to Lappen et al. (2010), except that the rest of the layers do not change their height. We need to keep track of the indexes of the layers near the PBL top. The properties of the PBL top layer are advected and diffused the same way as the other layers unless the distance from its closest neighboring layer is less than Dz, a depth scale defined earlier. But when this happens, the advection and the diffusion between the PBL top layer and its closest neighboring layer are turned off for numerical stability. When the PBL top is overlapped with other fixed layers, the vertical coordinate needs to be reconstructed.

b. Diagnosed second- and third-order moments The host GCM provides the first-order moments of vertical velocity (w), liquid water potential temperature (ul), and total water mixing ratio (qt). The second-, third-, and fourth-order moments are determined with the IPHOC scheme, as briefly discussed below. The diagnostic third-order moment equations are obtained by assuming steady state of those moments in a GCM time step. Because the fourth- and third-order moments are not at the current time step in the new

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equations, the algebraic and explicit expressions derived following Cheng et al. (2005) are used to parameterize

the higher-order moments. So the new set of third-order moment equations become

8 0 1 < › 02 0 u0 02 ›w t ›w ›u ›w02 l 1 A2 1 A3 l A 2 3w02 w03 5 w @A1 : c8 1 p1 ›z ›z ›z ›z ›z 1 39 2 0 ›w0 u0l g ›w02 ›u0 2 ›w = 1 A2 1 A3 l A 5 1(1 2 c11 )43 w02 u0y 2 2@A1 ›z ›z ›z ›z ; u and

2 0 0 1 13 02 02 0 a0 02 t › ›a ›a ›a ›w ›a 4A w @ A 2 3w0 a0 A5 , 1 3 @A5 1 A6 a03 5 4 ›z c10 1 p2 ›z ›z ›z ›z ›z

where a is either ul or qt, t is the TKE dissipation rate, u is the potential temperature, uy is the virtual potential temperature, p1 5 4, p2 5 4, A1 5 t(a1 w02 1 a2 ltw0 u0 ), A2 5 lt 2 (a3 w02 1 a4 ltw0 u0), A3 5 l2 t3 (a5 w02 1 a6 ltw0 u0), A4 5 a7 tw0a0, A5 5 a8tw0a0, and A6 5 t(a8w02 1 a9 ltw0a0), and l 5 (1 2 c11 )g/al 5 (1 2 c11 )g/u. The constants a1 5 0.2, a2 5 0.015, a3 5 0.03, a4 5 0.005, a5 5 0.002 55, a6 5 0.000 695, a7 5 0.027, a8 5 0.17, a9 5 0.023, c8 5 2.73, c10 5 3.12, and c11 5 0.3. IPHOC still forecasts the second-order moment of vertical velocity and vertical fluxes of ul and qt. The second-order moments of ul and qt are diagnosed as follows by assuming steady state and neglecting the turbulent transport and diffusion: 2 0 3 1 0 a0 t › ›w ›a A 2 2w0 a0 5 , a02 5 4 @A7 (4) c2 ›z ›z ›z and 0 1 1 2 0 0 u0 0 q0 ›w t › ›w › t lA A 1 @A u0l q0t 5 4 @A8 9 ›z c2 ›z ›z ›z 3 ›u ›q l t 0 0 5, 2 w0 qt 2 w0 ul ›z ›z

(5)

where c 2 5 1.04, A7 5 a12 tw0 a0 , a 12 5 0.17, A8 5 0:5a12 tw0 u0l , and A9 5 0:5a12 tw0 q0t .

c. Single-column model testing An Atlantic Stratocumulus Transition Experiment (ASTEX; de Roode and Duynkerke 1997) stratocumulus case has been tested with three experiments: 1) the control experiment with the default IPHOC scheme

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(2)

(3)

(CTL), 2) the experiment with the diagnostic secondand third-order moments (DMS in Figs. 1 and 2) instead of prognostic ones, and 3) experiment with DMS and with the predicted PBL height (PBLH). The benchmark experiment uses the large-eddy simulation (LES) version of System for Atmospheric Modeling (SAM; Khairoutdinov and Randall 2003) with a horizontal domain of 6.4 km 3 6.4 km, a horizontal grid spacing of 50 m, and a homogeneous vertical grid spacing of 25 m extending from the surface to 1500 m. The time step for the LES is 2 s. The three single-column experiments use the same vertical grid spacing as the LES, but 10 s for the time step. There is no obvious degrading of results from the DMS experiment for the ASTEX case (Fig. 1). For stratocumulus clouds such as those in ASTEX, the cloud and the PBL top are at the same height. The realistic forecasting of the PBL top leads to an improved simulation of the inversion strength of liquid water potential temperature and total water (Figs. 1a,b). The liquid water content and cloud fraction are also more reasonable (Figs. 1c,d). This is closely connected with the vertical fluxes of ul and qt (Figs. 1e,f). The overestimate of ul and qt transports below the cloud top has been decreased in experiment PBLH and is more reasonable compared with LES. This improvement may come from the more realistic representation of the physical processes below the PBL top because the third-order moment of vertical velocity becomes negative from the PBLH experiment (Fig. 1h), implying that narrow downdrafts are produced from the cloud-top radiative cooling. We also performed the same three experiments (CTL, DMS, and PBLH) for the Atmospheric Radiation Measurement (ARM) shallow cumulus case (Brown

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FIG. 1. Mean profiles of (a) liquid water potential temperature, (b) total water mixing ratio, (c) cloud water content, (d) cloud fraction, and fluxes for (e) liquid water potential temperature and (f) total water, and (g) second- and (h) third-order moment of vertical velocity averaged over the last hour of from the LES and the three experiments for ASTEX.

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FIG. 2. As in Fig. 1, but for ARM averaged over hour 12.

et al. 2002). The benchmark experiment uses the SAM LES with a horizontal domain of 6.4 km 3 6.4 km and a horizontal grid spacing of 100 m. The vertical grid spacing is 40 m homogeneously extended from the

surface to 4000 m. The time step for the LES is 2 s. The vertical grid spacing of the single-column experiments is the same as that of the LES. A time step of 10 s is used.

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The differences between the mean profiles of liquid water potential temperature and total water are small from the three experiments for the ARM case (Figs. 2a,b). Experiment PBLH produces the largest vertical fluxes of ul and qt (Figs. 2e,f), but it also produces the largest liquid water content and cloud fraction (Figs. 2c,d). These variables from experiment PBLH are closer to the LES. For this case, the PBL height is below the cloud base. The representation of the discontinuity below the cloud base from experiment PBLH may result in a more reasonable decoupling between the subcloud layer and the cloud layer in shallow cumulus clouds such as those in ARM. One characteristic of the decoupling is that two maxima are produced in the second- and third-order moments of vertical velocity (Figs. 2g,h), one for the mixed layer and the other for the cloud layer, respectively. A minimum exists between the two maxima, showing the separation of the two physically different layers. The second maxima for the cloud layer of experiments CTL and DMS are not clearly seen. Further single-column testing of decreasing the vertical resolution was discussed in Xu and Cheng (2013a) and will not be repeated here.

3. Climate model results a. Model description and experiment design The CAM5 (Neale et al. 2012) that we use in this study is the standard model. Deep convection is parameterized using the Zhang–McFarlane scheme with modifications (Zhang and McFarlane 1995; Neale et al. 2008; Richter and Rasch 2008). The boundary layer scheme is based on downgradient diffusion of moist conserved variables [University of Washington moist turbulence (UWMT); Bretherton and Park 2009]. The shallow convection scheme is from Park and Bretherton (2009) [University of Washington shallow convection (UWSC)], and cloud macrophysics is computed according to the Park macrophysics as described in Neale et al. (2012). A two-moment stratiform microphysics for both liquid and ice is described in Gettelman et al. (2010). Aerosols are predicted according to Liu et al. (2012) and linked to the microphysics through the parameterization of liquid and ice activation of cloud drops and ice crystals on aerosols (Gettelman et al. 2010). The large-scale state variables are updated sequentially from each parameterization component in CAM5. CAM5-IPHOC uses a single set of equations to represent boundary layer dry and moist turbulence mixing, shallow convection, and cloud macrophysics. The UWMT, UWSC, and Park macrophysics parameterizations in the standard CAM5 are replaced by IPHOC. As in the original IPHOC, the simplified version also

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assumes a joint double-Gaussian distribution of liquid water potential temperature, total water, and vertical velocity (Cheng and Xu 2006). The distribution is inferred from the first-, second-, and third-order moments of the variables given above and is used to diagnose cloud fraction and grid-mean liquid water mixing ratio, as well as the buoyancy terms and fourth-order terms in the equations. These higher-order moments, which are not available in a low-order closure, are used to formulate subgrid-scale condensation. This scheme is applied to the liquid water clouds in this study. The experiment design is similar to those described in Xu and Cheng (2013a), including the initial conditions and the external forcings. Briefly, both the CAM5 and CAM5IPHOC models are forced by specifying climatological SSTs and sea ice with monthly-mean annual cycles (i.e., no interannual variability in SST and sea ice) while coupled with the Community Land Model at the land grid points (Oleson et al. 2004). The horizontal grid size of the GCM is 1.98 3 2.58. There are 32 layers in the vertical direction with 12 layers below 700 hPa, which facilitates a direct comparison with SPCAM-IPHOC simulations. All experiments are integrated for 10 years and 3 months. The results of the last 9 years are analyzed for model comparison and compared to the observed climatology. The utilization of DMS and PBLH approaches increases the sub-time step of IPHOC in CAM5 from 10 to 30 s, compared with 5 min used by CAM5-CLUBB and 2 min used by GFDL-CLUBB. CAM5-IPHOC simulation has an 80% increase in computational cost over CAM5 simulation, compared with a 20% increase of computational cost from CAM5 to CAM5-CLUBB. A major part of the IPHOC code is migrated directly from a 2D CRM to the single-column application in CAM5. Each variable still has three dimensions (x, z, t). This makes the optimization of the code very difficult. In the following sections, the annual means of the last 9-yr integrations for CAM5 and CAM5-IPHOC are compared for low-level clouds, surface precipitation, and cloud radiative forcing. Also summarized are comparisons of a few surface/vertically integrated quantities.

b. Low-level clouds The low-level clouds are defined as those with tops between the surface and 700 hPa in CAM5, CAM5IPHOC, and C3M observations. The maximum overlap assumption is used to calculate the low-level cloud amount from the vertical profiles of cloud fraction. Lowlevel clouds are parameterized in both models in different ways. A combination of the mass flux approach (Bretherton and Park 2009) and large-scale condensation are used to parameterize shallow cumulus and stratocumulus clouds in CAM5, respectively. The simplified

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FIG. 3. Global distribution of annual-mean low-level (below 700 hPa) cloud amounts simulated by (a) CAM5 and (b) CAM5-IPHOC and from (c) the C3M observations.

IPHOC package used in CAM5-IPHOC parameterizes turbulence by predicting the TKE and fluxes and diagnosing third-order moments and some second-order moments. The subgrid-scale condensation and partial cloudiness are diagnosed from the low- and higher-order

moments and the joint double-Gaussian PDF of liquid water potential temperature, total water mixing ratio, and vertical velocity. Figure 3 shows the global distributions of the annualmean low-cloud amounts simulated in CAM5 and

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CAM5-IPHOC and obtained from the C3M data product (Kato et al. 2011). The C3M data product merges CloudSat, CALIPSO, CERES, and MODIS observations along the CloudSat/CALIPSO track. The observations are averaged to 1.98 3 2.58 grids in space and from July 2006 to June 2010 in time. Note that optically thin clouds (optical depth , 0.3) in the C3M data are filtered out before averaging so that the observed cloud amounts are comparable to those from passive satellite sensors commonly used in model evaluation. The tropical, subtropical, and midlatitude stormtrack oceanic low clouds are simulated in both experiments. The subtropical maxima in the northeastern (NE) and southeastern (SE) Pacific, SE Indian, and NE and SE Atlantic Ocean were well reproduced and so were the midlatitudes. The major improvements in CAM5-IPHOC are that 1) the stratocumulus clouds in the narrow regions off the west coasts of continents are more abundant than in CAM5, such as the one near the west coast of Australia; 2) the stratocumulus to trade cumulus transition is also more smoothly represented with the higher-order turbulence closure, as shown below; 3) the cloud amounts in the storm track region of the Southern Hemisphere substantially increase, in better agreement with the observations, which are even more abundant than those from SPCAM-IPHOC (Xu and Cheng 2013a); 4) more low-level clouds are produced in the open oceans (e.g., Pacific and Indian basins); and 5) the global mean of low-cloud amount increases from 41.7% in CAM5 to 45.8% in CAM5IPHOC. The latter is close to the observed global mean of 50.3% (48.0% from CloudSat/CALIPSO data stored at the NCAR CAM portal, which was used in CX11). The low-level cloud distribution and the annual- and global-mean cloud amount from the CAM5-IPHOC experiment are consistent with the series of experiments performed with SPCAM-IPHOC. For example, the annual- and global-mean low-level cloud amount from Xu and Cheng (2013a) is 45.1%. The GCMs with CLUBB higher-order turbulence closure, that is, CAM5-CLUBB and GFDL-CLUBB (Bogenschutz et al. 2013; Guo et al. 2014), produce an annual-mean global low-level cloud of 41%. The low-level clouds off the west coasts of continents from these GCMs, for example, the NE and SE Pacific and Atlantic, are comparable to CAM5-IPHOC, but those in the open oceans (i.e., shallow cumulus) are more severely underestimated than CAM5-IPHOC. This is also the case when CLUBB is implemented in SPCAM5 MMF (Wang et al. 2015). IPHOC is similar to CLUBB in the sense that the double-Gaussian PDF is also used. The

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additional third-order moments may make the Gaussian more adaptable to different situations. This may contribute to a better simulation of the cumulus regime with IPHOC. The vertical cross section of annual-mean cloud fraction along 158S from the coast of South America (;808W) to 1208W is shown in Fig. 4 from the two experiments and the C3M observations. This cross section represents stratocumulus to trade wind cumulus transition. Similar cross sections were examined in other studies with regional and climate models (e.g., Wang et al. 2004a,b; Lauer et al. 2009; CX11; Xu and Cheng 2013a; Bogenschutz et al. 2013). The agreement with the C3M observations is much better for CAM5-IPHOC (Figs. 4b,c). For example, the increase in cloud fraction between 808 and 1008W (off the coast) from CAM5 to CAM5-IPHOC is ;20% (absolute) as the thin stratocumulus clouds are better parameterized there. Increases in cloud fraction between 30% and 40% (absolute) also appear west of 1008W and the cloud layers are thicker than in CAM5. Both of these features result in a closer agreement with the C3M observations. On the other hand, CAM5-IPHOC still underestimates the global-mean low-cloud amount by 4.5%, compared to 8.6% underestimated by CAM5. The regions with the largest underestimates are located at the open oceans with abundant shallow cumulus clouds (e.g., Xu et al. 2008) and over the land areas (e.g., South/ Central America). This underestimate may be connected to the global underestimate of liquid water path (LWP) in CAM5 and CAM5-IPHOC (Fig. 5). Notice that CAM5-CLUBB and GFDL-CLUBB also underestimate the annual global-mean LWP (Bogenschutz et al. 2013; Guo et al. 2014). A comprehensive and rigorous comparison between the models and observations is difficult as far as LWP is concerned because there are large uncertainties in LWP associated with satellite retrievals and liquid water inside convective clouds is not available from the models. The oceanic mean LWP is 36.7 and 55.3 g m22 from the CAM5 and CAM5-IPHOC, respectively, compared to the Special Sensor Microwave Imager (SSM/I) observed value of 97.2 g m22. The large increase in LWP mainly occurs in the subtropical regions such as the NE and SE Pacific, SE Indian Ocean, NE and SE Atlantic, and Northern and Southern Hemispheric storm tracks, and the increase can also be seen in the other parts of the three oceans as compared to CAM5, such as the deep convective region south of the equator in the western Pacific. Notice that the LWP in the Northern Hemisphere is substantially larger than the Southern Hemisphere. This is related to the precipitation pattern that will be discussed shortly.

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FIG. 4. Horizontal–vertical cross sections of annual-mean cloud fraction along 158S off the coast of South America from (a) CAM5, (b) CAM5-IPHOC, and (c) C3M observations. The unit for cloud fraction is percentage. The thick black lines in (a) and (b) represent the PBL height.

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The improved representation of low-level clouds was attributed by CX11 not only to the subgrid-scale condensation produced by IPHOC, but also closely to the large-scale variables, such as the increased surface sensible and latent heat fluxes, the increased lower tropospheric stability (LTS), and stronger longwave radiative cooling. So the relationships between low clouds and large-scale variables are very important to understand the low-cloud simulation in CAM5-IPHOC. An analysis of these relationships is performed for the five marine stratocumulus regions discussed in Klein and Hartmann (1993): Californian (208–308N, 1208–1308W), Peruvian (108–208S, 808–908W), Namibian (108–208S, 08–108E), Australian (258–358S, 958–1058E), and Canarian (158– 258N, 258–358W). The chosen large-scale variables are LTS, relative humidity (RH) at 1000 hPa (hereinafter RHs), and PBL height to facilitate a direct comparison with the relationships simulated by SPCAM-IPHOC (Xu and Cheng 2013a). As in Xu and Cheng (2013a), the observed large-scale variables are represented by European Center for Medium-Range Weather Forecasts (ECMWF) Interim Reanalysis (ERAI) data (Dee et al. 2011) and the observed low-cloud amount is from the International Satellite Cloud Climatology Project (ISCCP) data (Rossow and Schiffer 1999) in order to be conveniently compared with previous studies. The PBL heights in ERAI and CAM5 are computed as the heights at which the bulk Richardson number exceeds the critical value of 0.25 (ERAI) or 0.30 (CAM5), while the PBL height in CAM5-IPHOC is forecasted by Eq. (1). Figure 6 shows the scatter diagrams between RH and LTS with low-cloud amount color coded for the five regions. The low-level cloud amount, RHs, and LTS are positively correlated to each other in the Californian and Canarian regions from CAM5-IPHOC and CAM5. In the Peruvian region, the positive correlation between RHs and LTS from CAM5 is not as strong as CAM5IPHOC and observations, but both models underestimate the LTS upper range. That is, the cloud amount from CAM5 is more strongly correlated with LTS than with RHs. In the Namibian region, the correlation between RHs and LTS from both CAM5 and CAM5IPHOC is negative, as opposed to being positive from observations, but cloud fractions are well correlated with LTS in both models and observations. A similar result was reported in Xu and Cheng (2013a). In the Australian region, the correlations between RHs and LTS are weak or slightly negative in both the CAM5IPHOC simulation and observations, but their correlation is positive in CAM5 with significantly underestimated cloud amounts. It is likely that shallow cumulus rather stratocumulus clouds are simulated in CAM5 in this region related to the underestimate of LTS. Stratocumulus

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FIG. 5. Nearly global oceanic distribution of annual-mean LWPs (g m22) from (a) CAM5, (b) CAM5-IPHOC, and (c) SSM/I observations. LWPs at high latitudes are not plotted because of large uncertainties there in SSM/I retrieval.

clouds may be produced in CAM5-IPHOC when LTS is large, but their correlations with RHs are not as strong as in CAM5 and the observations. The relationships among the low-cloud amount, RHs, and PBL depth are shown in Fig. 7, providing evidence for boundary layer mixing, especially the relative strength of buoyancy and shear productions of TKE. As mentioned earlier, PBL depth is diagnosed via the Richardson number in CAM5, which is proportional to the ratio of buoyancy to shear. Larger PBL depth in CAM5 implies for either larger buoyancy production or less shear production. In CAM5-IPHOC, however, PBL depth is predicted using Eq. (1). PBL growth is mainly controlled by the PBL top entrainment. Despite the fact that cloud-top properties depend on the conditions

inside the PBL, an increase in the amount of entrainment of dry air from the free troposphere leads to a deeper and drier PBL. Large buoyancy and TKE are still needed to transport moisture and heat from the surface to the PBL. Otherwise, the PBL growth cannot be sustained. As seen from Fig. 7, the PBL depth and RHs are negatively correlated with small scatter in both simulations and observations for all five regions. The simulations and observations show that the higher cloud amounts are associated with the higher RHs for a given PBL depth, implying for stronger buoyancy productions at higher cloud amounts. In this sense, these relationships are similar between simulations and observations. The results are similar between this study and Xu and Cheng (2013a), which used SPCAM-IPHOC, but CAM

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FIG. 6. Monthly-mean low-level cloud amount (color coded, color bar at bottom) as a function of monthly-mean RH at 1000 hPa and LTS for (top) CAM5, (middle) CAM5-IPHOC, and (bottom) observations for the five regions described in Klein and Hartmann (1993). For observations, monthly-mean low-level cloud amount is from ISCCP, and RH and LTS are calculated from ERAI data.

version 3 (CAM3) and SPCAM results shown in DeMott et al. (2010) are different. It is noted that both CAM5-IPHOC and CAM5 have improved these relationships over CAM3 (DeMott et al. 2010). There are, however, some subtle differences between CAM5IPHOC and CAM5. For example, in the Australian and Canarian regions, CAM5 produces much smaller cloud amounts with lower RHs than CAM5-IPHOC but with comparable PBL heights, implying that clouds are less often produced in CAM5. In all regions, the lower PBL depths in CAM5 are likely linked to weaker boundary layer turbulence mixing and transport, compared to ERAI and CAM5-IPHOC.

c. Surface precipitation and cloud radiative forcing Surface precipitation is a major source and critical component of the hydrological cycle and is tightly linked to the water and energy cycles. Because surface precipitation is related to a large range of temporal and spatial scales, its simulation remains challenging. The

double intertropical convergence zone (ITCZ) problem, in which excessive precipitation is produced in the Southern Hemisphere tropics, is perhaps the most significant and most persistent bias of GCMs. The models with more positive energy sources in the Southern Hemisphere tend to have a stronger double ITCZ bias (Frierson and Hwang 2012). Hwang and Frierson (2013) found that cloud biases over the southern ocean explain most of the model-to-model differences in the amount of excessive precipitation in the Southern Hemisphere tropics. These cloud biases are suggested to be responsible for a key aspect of the double ITCZ problem in most GCMs. The annual-mean surface precipitation rates are similar between CAM5 and CAM5-IPHOC except that the precipitation at the South Pacific convergence zone (SPCZ) and the southern Indian Ocean are too weak in CAM5-IPHOC (Fig. 8). This is contrary to the double ITCZ problem in most GCMs and may be related to atmospheric energy transport and sources (Frierson and

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FIG. 7. As in Fig. 6, but as a function of PBL depth and RH at 1000 hPa.

Hwang 2012). A cross equatorial heat transport is calculated following Heaviside and Czaja (2013): HA 5

ð 2p ð P

1000

0

P100

y(cp T 1 gz 1 Lqy )r

dp dl , g

(6)

where y is the northward meridional velocity; T is the temperature; qy is the specific humidity; r is the radius of the Earth; and P1000 and P100 are the 1000- and 100-hPa pressure levels, respectively. The mass imbalance has been corrected by simply removing the column-mean (1000– 100 hPa) y from its annual-mean value. The crossequatorial atmospheric heat transports computed from Eq. (6) are 0.01, 20.25, and 20.21 PW for CAM5, CAM5IPHOC, and ERAI, respectively. The more southward energy transport from CAM5-IPHOC means that an anomalously strong Hadley circulation is induced to transport energy from the Northern Hemisphere to the Southern Hemisphere. It is likely linked to the anomalous cooling in the Southern Hemisphere that drives such transport to keep the global energy balanced. The cooling in the Southern Hemisphere also tends to weaken the eddy

activities in the Southern Hemisphere tropics, so there is less northward energy transport in CAM5-IPHOC. To investigate the sources of more cooling (negative energy sources) in the Southern Hemisphere from CAM5-IPHOC, the annual- and zonal-mean top-of-theatmosphere (TOA) shortwave cloud radiative forcing (SWCF), longwave cloud radiative forcing (LWCF), and surface energy fluxes over ocean from the two models and CERES Energy Balanced and Filled (EBAF) observations (2000–2010; Loeb et al. 2009) are presented on the left-hand-side (LHS) of Fig. 9 along with the surface precipitation. The asymmetry of these variables, represented by the difference between the Southern Hemisphere and the Northern Hemisphere, are shown on the right-hand-side (RHS) of Fig. 9 to identify which latitude bands are most important in contributing to these energy sources (Frierson and Hwang 2012). Note that x axis in the asymmetry plots is scaled as sin(u) to provide an areal integration of the meridional transport, where u is latitude. The precipitation rates at the ITCZ and between 58S and 308S from CAM5-IPHOC are slightly lower than

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FIG. 8. Global distribution of annual-mean surface precipitation rate (mm day21) from (a) CAM5, (b) CAM5-IPHOC, and (c) the GPCP observations.

those of CAM5 and compared well with Global Precipitation Climatology Project (GPCP; Adler et al. 2003) observations (Fig. 9a). As a result, the hemispheric asymmetry peak at 58 is larger in CAM5-IPHOC than in CAM5 (Fig. 9b), related to the weaker SPCZ. The strong shortwave cooling between 308S and 308N from CAM5-IPHOC (Fig. 9c) may be closely related to the abundance of low-level clouds in this region despite its underestimate of mid- and high-level clouds (Figs. 10a,c,e). As discussed later, this underestimate is compensated by higher liquid and ice contents inside clouds (Fig. 5b). On the other hand, the SWCF asymmetry from CAM5-IPHOC/CAM5 is roughly in phase with that from CERES-EBAF and there is no significant difference between the two models. Note that the SWCF asymmetry cooling peak located around 458 in CAM5

corresponds to the asymmetry peaks in low-level clouds and high-level clouds there (Figs. 10b,f). Although the differences in LWCF between the models can be easily seen in the midlatitude storm track region (Fig. 9e), the LWCF asymmetry from CAM5-IPHOC shows more cooling in the Southern Hemisphere relative to the Northern Hemisphere, except for 208–308 and 658–758 (Fig. 9f). Therefore, LWCF contributes greatly to the anomalous cooling in the Southern Hemisphere, but its asymmetry agrees less well with the observations. This result could be related to relatively fewer mid- and highlevel clouds in the Southern Hemisphere and higher cloud water contents in the Northern Hemisphere of CAM5-IPHOC (Figs. 5b and 10c–f). Finally, although the net downward surface flux is similar between CAM5-IPHOC and CAM5 (Fig. 9g), its asymmetry

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FIG. 9. Zonal mean and hemispheric asymmetry of precipitation, SWCF, LWCF, and the net downward surface flux from CAM5-IPHOC, CAM5, and the observations. The observed quantities are from GPCP, CERES-EBAF, and JRA-25, respectively. Annual zonal means are (a) precipitation, (c) SWCF, (e) LWFC, and (g) net downward surface flux; (b),(d),(f),(h) the hemispheric asymmetry defined as the difference between the Southern Hemisphere and the Northern Hemisphere of (a),(c),(e), and (g), respectively. The black dashed lines in the left panels indicate the location of the equator.

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FIG. 10. As in Fig. 9, but (a) and (b) are for low-level clouds, (c) and (d) are for midlevel clouds, and (e) and (f) for high-level clouds.

shows that it contributes more cooling (i.e., positive net downward flux) in the Southern Hemisphere in CAM5IPHOC than in CAM5 (Fig. 9h), in particular, between the equator and 458. The magnitude of the cooling is

actually larger than that of TOA LWCF at most latitudes other than the tropics (Fig. 9f). Next, we decompose the net downward surface flux into four components as F net is defined as

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SWnet 2 LWnet 2 LH 2 SH, where SWnet is surface net shortwave flux, LWnet is net longwave flux, LH is latent heat flux, and SH is sensible heat flux. These components and their asymmetries are plotted in Fig. 11 in order to explore their roles in the anomalous cooling of Fnet. Figure 11 shows that the asymmetry of SWnet is the major contributor to the anomalous cooling in Fnet. The large asymmetry in SWnet (Fig. 11b) may be related to the asymmetry of the liquid water contents (Fig. 5) and those of the mid- and high-level clouds (Figs. 10d,f). It was noted earlier that smaller mid- and high-level cloud amounts are produced in the Southern Hemisphere relative to the Northern Hemisphere in CAM5-IPHOC than in CAM5. On the other hand, the relative warming from LWnet between 308 and 508 is almost cancelled out by the relative cooling between 158 and 308 between the two models, resulting in no significant difference in the southward energy transport (Fig. 11d). There is no difference in the asymmetry between the two models from the latent and sensible heat fluxes (Figs. 11f,h). Figure 11a also shows that SWnet between 308S and 308N from CAM5-IPHOC is less than from CAM5. This is because the abundance of low-level clouds in CAM5IPHOC (Fig. 10a) prevents shortwave radiation from reaching the surface despite the fact that the high-level cloud amount is underestimated by CAM5-IPHOC. Another possible reason may be related to higher liquid water contents inside clouds (Fig. 5). Also, the smaller surface latent heat flux from CAM5-IPHOC (Fig. 11e) is due possibly to the efficient transport (mixing) from the higher-order turbulence closure, which can maintain a relatively moister boundary layer/first model layer (Figs. 6, 7). It is obvious that different clouds contribute to asymmetries in SWCF and LWCF differently. But the zonal means of SWCF and LWCF and cloud amounts cannot reveal the different contributions and the different relationships among them between the models and observations. To illustrate more precise contributions of low-, middle-, and high-level clouds on the SWCF and LWCF, the pressure vertical velocity at 500 hPa (v500) with sorted SWCF, LWCF, low-, middle-, and high-level clouds are plotted in Figs. 12 and 13, respectively, for 308S and 308N, as in Bony et al. (2004), which used this approach to compare the tropical climatology of SWCF and LWCF in three GCMs and to study their cloud radiative response to a climate perturbation. The PDFs of monthly-mean v500 for the ERAI reanalysis and the two models are very similar, with all the distributions peaking between 15 and 25 hPa day21 (Fig. 12a). The SWCF distributions in the two models can be separated into two segments of v500 regimes. In the ascent regimes, with v500 being less than

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0 hPa day21 where deep convection is favored, both CAM5 and CAM5-IPHOC systematically overestimate the negative SWCF (Fig. 12b). In CAM5-IPHOC, there are significant underestimates of high-level cloud amounts in the ascent regimes (Fig. 13c), but the SWCF and LWCF are similar to their counterparts in CAM5. This result suggests that the liquid/ice cloud contents inside clouds are much higher in CAM5-IPHOC (Fig. 5). In the subsidence segment where v500 is larger than 30 hPa day21 and low-level clouds are favored, CAM5-IPHOC produces larger SW cooling and is closer to CERES-EBAF, while that of CAM5 is opposite (Fig. 12b). This is related to the realistic low-level cloud simulation from CAM5-IPHOC in this regime (Fig. 13a). The impacts of clouds on LWCF in the two models can be separated into three segments of v500 regimes (Fig. 12c). In the strong deep convective segment with v500 between 230 and 290 hPa day21, both models overestimate the LWCF. In the ascent segment where v500 is less than 0 hPa day21 and larger than 230 hPa day21, both models compare favorably with CERES-EBAF. In the segment where v500 is between 20 and 85 hPa day21, the models slightly underestimate the LWCF. The performance of CAM5-IPHOC is only slightly better than CAM5 in the last two segments. In the subsidence regime, it is expected that the increase in low-level clouds does not impact LWCF. The reason for the similarity in the deep convective regime between the models is the same as that given for SWCF. Another comparison of SWCF and LWCF from CAM5 and CAM5-IPHOC with CERES-EBAF is shown in Fig. 14. The positive SWCF bias of more than 21 W m22 in low-level cloud prevailing regions—such as those located west of Australia (near 308S and between 808 and 1108E), west of South America (near 208S and 1008W), and the Southern Hemisphere storm track region (near 708S and between 1008 and 1408W)—has been substantially decreased. Parts of this result are shown in Fig. 12b. However, the increases in LWP in deep convective clouds, such as those located in the ITCZ region of the Pacific Ocean and northwest Pacific storm track region (Fig. 5b), increase the magnitudes of SWCF and result in overestimation of SWCF in larger areas of the tropics than in CAM5, which are not revealed in the means and standard deviations of SWCF shown in Fig. 12b. Overall, the global- and annual-mean SWCF decreases from 250.0 W m22 in CAM5 to 252.8 W m22 in CAM5-IPHOC. The root-mean-square (RMS) error increases by 0.18 W m22 but the spatial correlation increases by 0.01. For LWCF, the annual and global means increase from 23.2 to 24 W m22, compared with CERESEBAF of 26.5 W m22. RMS increases by 0.6 W m22

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FIG. 11. As in Fig. 9, but (a) and (b) are for net surface shortwave flux, (c) and (d) are for net surface longwave flux, (e) and (f) are for surface latent heat flux, and (g) and (h) are for surface sensible heat flux.

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FIG. 12. (a) Normalized PDF of annual-mean pressure velocity at 500 mb for ERAI reanalysis and for CAM5 and CAM5-IPHOC. (b) LWFC and (c) SWCF as a function of pressure velocity. The cloud radiative forcing data are from CERES-EBAF. Each vertical line represents a standard deviation for a specific vertical velocity.

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FIG. 13. (a) Low-, (b) mid-, and (c) high-level clouds as a function of pressure velocity for the C3M observations and for CAM5 and CAM5-IPHOC. Each vertical line represents a standard deviation for a specific vertical velocity.

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FIG. 14. Global distribution of annual-mean (a)–(d) SWCF and (e)–(h) LWCF simulated by CAM5 and CAM5IPHOC and their differences from CERES-EBAF (W m22): (left) CAM5 and (right) CAM5-IPHOC. (a),(b),(e),(f) The mean SWCF and LWCF. The global mean, the RMS, and the correlation with CERES-EBAF are printed at the top left of each panel. (c),(d),(g),(h) The difference in SWCF and LWCF between models and CERES-EBAF, with the global mean differences being printed at the top of each panel.

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TABLE 1. Global and annual-mean SWCF and LWCF simulated by four pairs of models with and without HOC (IPHOC/CLUBB). The three CAM5 pairs (this study; Wang et al. 2015; Bogenschutz et al. 2013) were run with different horizontal and vertical resolutions. The GFDL pair (Guo et al. 2014) was run with a higher horizontal resolution as in Bogenschutz et al. (2013). The RMS error and spatial correlation with CERES-EBAF observations are also shown if available. SWCF CAM5 (1.98 3 2.58 3 32L) CAM5-IPHOC (1.98 3 2.58 3 32L) CAM5 (1.98 3 2.58 3 30L) CAM5-CLUBB (1.98 3 2.58 3 30L) CAM5 (18 3 18 3 30L) CAM5-CLUBB (18 3 18 3 30L) GFDL (18 3 18 3 48L) GFDL-CLUBB (18 3 18 3 48L) CERES-EBAF

LWCF

Mean (W m22)

RMS (W m22)

Correlation

Mean (W m22)

RMS (W m22)

Correlation

250.0 252.8 252.3 248.5 248.8 248.9 249.0 250.2 247.1

16.80 17.07 15.88 13.86 14.15 12.15 8.66 10.31

0.84 0.85 0.81 0.82

23.2 24.0 24.1 22.4 22.5 21.8 25.2 22.9 26.5

7.00 7.60 6.75 7.45 6.90 7.61 6.00 7.20

0.91 0.89 0.88 0.87

while the spatial correlation decreases by 0.02. The slight degradation in RMS and spatial correlation is also related to the ITCZ and the weak SPCZ. The SWCF and LWCF statistics from CAM5-CLUBB and GFDL-CLUBB and their counterparts without HOC are listed in Table 1, along the pair of simulations presented in this study. The incorporation of HOC tends to increase the magnitude of global-mean SWCF except for the pair (21.8 W m22) shown in Wang et al. (2015), with 2.8 W m22 in CAM5-IPHOC, 1.2 W m22 in GFDLCLUBB (Guo et al. 2014), and 0.1 W m22 in CAM5CLUBB (Bogenschutz et al. 2013). With CLUBB, the global-mean LWCF decreases for all three simulations (21.7, 20.7, and 21.3 W m22) while it increases in CAM5-IPHOC (10.8 W m22), a trend that yields a closer agreement with CERES-EBAF observations. In general, the models without HOC are better tuned to reproduce the present-day radiative energy budget balance than those with HOC, as seen from the RMS and spatial correlation of LWCF (Table 1).

0.92 0.89

0.90 0.84

increases from 0.83 to 1.1 while the correlation coefficient increases from 0.51 to 0.74. This is the most significant improvement among all the variables. For midlevel clouds, the normalized standard deviation increases from 0.84 to 0.91. It is likely that the application of IPHOC in the middle level to resolve the subgrid-scale clouds does help the representation of those clouds. For SWCF, the normalized standard deviation decreases

d. Concise comparisons with observations and annual global-mean statistics A Taylor diagram (Taylor 2001) is used to provide an assessment of the overall performance of CAM5IPHOC compared with CAM5 (Fig. 15). The Taylor diagram provides a convenient and compact display to compare the model against observations in terms of the spatial pattern correlations and the normalized standard deviations. A better-modeled variable resides closer to the reference (REF) point. The variables chosen for comparison with observations are listed in Fig. 15. The region between 308S and 308N is chosen for this analysis. Comparing CAM5-IPHOC with CAM5, it can be seen that there are significant improvements in lowlevel clouds, midlevel clouds, and SWCF (Fig. 15). For low-level clouds, the normalized standard deviation

FIG. 15. Taylor diagrams for annual-mean surface pressure (PS), surface precipitation (PRECT), SWCF (here SWCRF), LWCF (here LWCRF), surface latent heat flux (LHFLX), surface sensible heat flux (SHFLX), low-level clouds (CLDLOW), midlevel clouds (CLDMID), and high-level clouds (CLDHGH) between 308S and 308N for CAM5 and CAM5-IPHOC. The reference data are ERAI (2000–10; Dee et al. 2011) for surface pressure, GPCP (2000–10) for surface precipitation, CERES (2000–10; Loeb et al. 2009) for SWCF and LWCF, JRA-25 (1979–2004; Onogi et al. 2007) for surface latent and sensible heat fluxes, and C3M data (2006–10) for low-, mid-, and high-level cloud amounts.

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TABLE 2. Global annual-mean climatological properties of the last 9 years from CAM5-IPHOC, CAM5, and observations. Property

CAM5-IPHOC

CAM5

Observation

22

TOA Surface All sky Clear sky All sky Clear sky LW cloud forcing (W m22) SW cloud forcing (W m22) Total Low level Middle level High level Cloud LWP (mm) Precipitable water (mm) Latent heat flux (W m22) Sensible heat flux (W m22) Precipitation (mm day21) All sky Clear sky All sky Clear sky

Annual-mean energy budgets (W m , 1downward) 1.8 6.9 5.2 4.2 TOA outgoing longwave radiation (W m22, 1upward) 233.8 234.3 257.8 257.5 TOA absorbed solar radiation (W m22, 1downward) 235.6 241.2 285.1 287.8 24.0 23.2 252.8 250.0 Cloud amount (%) 61.4 59.2 45.8 41.7 23.7 25.1 25.6 32.7 0.0553 0.0367 25.1 25.5 78.0 86.8 17.8 17.5 2.81 3.00 Net surface LW radiation (W m22, 1upward) 53.5 54.1 78.9 79.0 Net surface SW radiation (W m22, 1downward) 154.5 162.6 212.4 217.3

0.57a 1.20a,b 239.7a 265.8a 240.7a 287.8a 26.1a 247.2a 68.0c 50.3c 28.4c 30.7c 0.0972d 24.6e 87.9b 19.4e 2.67f 53.0a 81.9a 162.4a 214.4a

a

CERES-EBAF (Loeb et al. 2009). JRA-25. c C3M. d SSMI (the Special Sensor Microwave Imager). e NASA Water Vapor Project (NVAP; Randel et al. 1996). f GPCP. b

from 1.45 to 1.35 while the correlation coefficient increases from 0.74 to 0.76. The improvement of the SWCF is due to the more reasonable representation of lowlevel clouds. The degradation on the representation of the other variables is rather minor. For example, the correlation coefficients for the high-level clouds decrease slightly from 0.92 to 0.90, and the normalized standard deviations decrease from 0.76 to 0.61, because of the weak SPCZ where fewer high-level clouds are produced. Radiative balance is an important requirement for climate model simulations. In GCMs, tuning of some parameters in radiation and cloud parameterization schemes is required to achieve this balance. However, it is more difficult to tune the CAM5-IPHOC model to achieve the balance because clouds are diagnosed from the joint double-Gaussian PDF directly and there is no simple relationship that can be altered to produce a desired amount of clouds and the corresponding cloud radiative effect. Another reason for not tuning the

model is that we did not retune CAM5 either with the increased vertical resolution below 700 hPa. The TOA and surface energy balance from CAM5IPHOC is comparable to CAM5 and observations. The global imbalance at the TOA is 1.8 W m22 in CAM5IPHOC (Table 2) compared to 6.9 W m22 in CAM5. We notice that CAM5 in Bogenschutz et al. (2013) has a TOA imbalance of 4.6 W m22 and CAM5-CLUBB has an imbalance of 3.3 W m22. They used 18 3 18 horizontal grid spacing. At the surface, CAM5-IPHOC produces an imbalance of 5.2 W m22, compared to 4.2 W m22 from CAM5, and an estimate of 1.2 W m22 based on CERESEBAF version 2.6 (Loeb et al. 2009) and the Japanese 25-year Reanalysis Project (JRA-25) surface fluxes (Onogi et al. 2007). The atmospheric imbalances are 23.4 and 2.7 W m22, respectively. The smaller latent heat flux and the net shortwave radiation absorbed at the surface are the main differences between CAM5IPHOC and CAM5 (Table 3). According to Table 2, CAM5-IPHOC produces more low-level and total

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TABLE 3. Surface energy budget balance components and imbalance for 9-yr average for CAM5, CAM5-IPHOC, and observations. Surface SW and LW fluxes are from CERES-EBAF. Latent and sensible heat fluxes are from JRA-25.

CAM5-IPHOC CAM5 Observations

SW surface

LW surface

LH

SH

Imbalance

154.5 162.60 162.98

53.50 54.10 54.47

78.0 86.8 87.94

17.8 17.50 19.37

5.20 4.20 1.20

clouds, but less middle- and high-levels clouds. The smaller net shortwave radiation at the surface may be related to higher liquid water contents. The smaller surface latent heat flux may be due to the efficient transport (mixing) from the higher-order turbulence closure, which can maintain a relatively moister boundary layer/first model layer, so less latent heat flux. The result is opposite to SPCAM-IPHOC likely because of the lack of wind gustiness effect. Overall agreements of the other variables shown in Table 2 between CAM5-IPHOC, CAM5, and observations are acceptable. Compared to CAM5, there are a few improvements (e.g., low cloud amount and LWCF). On the other hand, some variables, such as precipitable water and sensible heat flux, are very close between CAM5 and CAM5-IPHOC because of the dynamic core and other parameterizations shared by the two models. The differences in TOA LW and SW, TOA LWCF and SWCF, and surface clear- and all-sky LW fluxes between the two models are 4–5 W m22. This amount is comparable to the difference between CAM5-IPHOC and observations. There is little difference in the clear-sky surface LW, but the clear-sky surface SW from CAM5IPHOC is lower than the CERES observations by 2 W m22, compared to a 3 W m22 overestimate in CAM5. The low cloud amounts from CAM5-IPHOC are larger by 8% than from CAM5, but they are still 5%–10% less than that of active-sensor C3M observations. CAM5-IPHOC underestimates the mid- and highlevel clouds by 5% and 20%, respectively. This is likely because of issues related to the coupling between the IPHOC and the deep convective parameterization in CAM5. A unified scheme might resolve the problem, which is beyond the scope of this study.

4. Summary and discussion In the present study, IPHOC is first simplified by diagnosing the third-order moments and the second-order moments of liquid water potential temperature and total water mixing ratio. A steady state in a GCM time step is assumed for these moments, so the time derivative can

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be dropped and the diagnostic formulae are derived. The diagnosing instead of predicting these variables decreases the computational cost and increases the time step for the six remaining forecasting equations because predicting the second-order and third-order moments is the main obstacle in limiting the time step for HOC. Then a PBL height (PBLH) prognostic equation is derived to forecast the PBL top height to better resolve the discontinuity of temperature and moisture above the PBL top. Single-column model tests show that the forecasting PBLH approach may produce more realistic cloud-top radiative cooling and narrow downdrafts implied by the negative third-order moment of vertical velocity for stratocumulus clouds. The forecasting PBLH approach may also produce a more reasonable cloud evolution for shallow cumulus clouds and decoupling between the subcloud layer and the cloud layer because the discontinuity near the cloud base is more reasonably represented. For both shallow cumulus and stratocumulus cases, fluxes of liquid water potential temperature and total water mixing ratio, cloud fraction, and liquid water content are improved with the forecasting PBLH approach. The simplified IPHOC package is then implemented in CAM5 to replace the boundary layer turbulence scheme, the shallow cumulus and stratocumulus parameterizations, and the liquid phase part of cloud macrophysics parameterization, so all of these subgrid-scale processes are treated in a consistent way. Both CAM5 and CAM5-IPHOC are forced with climatological SST and coupled with a land surface model. The horizontal grid size of the GCM is 1.98 3 2.58. There are 32 layers in the vertical direction with 12 layers below 700 hPa to better resolve boundary layer processes. The results of the last 9 years are analyzed for model comparison and compared to the observed climatology. Consistent with the SPCAM-IPHOC MMF (CX11; Xu and Cheng 2013a), the representation of the lowlevel clouds is substantially improved in CAM5-IPHOC relative to CAM5 and is similar to SPCAM-IPHOC. The strength and location of the low-cloud maxima in the northeastern (NE) and southeastern (SE) Pacific, SE Indian Ocean, NE and SE Atlantic Ocean, and Atlantic and Pacific midlatitudes were well reproduced. The annual global-mean low-level cloud fraction is 45.8%, close to 45.1% from SPCAM-IPHOC. There are substantial improvements on the cloud radiative forcing, especially shortwave, in the subsidence regime sorted by the pressure velocity at 500 hPa. The relationships among low cloud amount, surface relative humidity, LTS, and PBL depth agree well with observations in five stratocumulus deck regions, although the degree of agreements varies from one region to another with the

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closest agreements being in the Californian, Peruvian, and Canarian regions. In these regions, the highest cloud amounts are associated with the highest LTS, highest surface RH at 1000 hPa, and the lowest PBL height. CAM5 has difficulties to reproduce these relationships in the Peruvian region. Such preferences in either CAM5-IPHOC or observations are weaker in the Australian (observation) and Namibian (model) regions. CAM5, however, produces high correlation between surface relative humidity and LTS in the Australian region and much less cloud amount than observations and CAM5-IPHOC. CAM5-IPHOC produces a reasonable precipitation pattern, except for weak precipitation at the SPCZ and the southern Indian Ocean. This is opposite to the double ITCZ problem in most global climate models, including CAM5. It is likely related to the underestimate of the energy flux into the Southern Hemisphere atmosphere in CAM5-IPHOC. The more low-level clouds are produced in the ocean basins in the SE Pacific and the Atlantic and the storm track belt centered at 608S in the Southern Hemisphere, which contribute to less incoming TOA radiation and less net surface shortwave flux. The asymmetries in the extratropical mid- and high-level cloud amounts are linked to the net surface shortwave cooling and the TOA longwave cooling of the Southern Hemisphere relative to the Northern Hemisphere. The net surface shortwave cooling is more important than that of TOA longwave because of its larger magnitude except for the tropics. The atmospheric imbalance for the 10-yr and 3-month CAM5-IPHOC and CAM5 simulation is 2–3 W m22. There is no retuning of parameters in radiation and cloud microphysics parameterizations in the model. The global imbalance at the TOA is 1.8 W m22 in CAM5IPHOC (Table 2), which is smaller than in CAM5, but not as small as in SPCAM-IPHOC. At the surface, CAM5-IPHOC produces an imbalance of 5.2 W m22, compared to 27.51 W m22 from SPCAM-IPHOC and 4.2 W m22 from CAM5. CAM5-IPHOC produces more low-level and total clouds but less mid- and high-levels clouds. The smaller net shortwave radiation at the surface can be related to higher liquid water contents. The smaller surface latent heat flux is due possibly to the efficient transport (mixing) from the higher-order turbulence closure, which can maintain a relatively moister boundary layer/first model layer. In the future, it will be interesting to develop a unified turbulence, boundary layer clouds, and deep convection scheme under the framework of IPHOC. The intensity of subgrid-scale turbulence and the skewness of PDF can directly impact the initiation and dissipation of deep convection. This approach can allow for a smooth

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transition from shallow to deep convection because of the more consistent representation of subgrid-scale convective processes in climate models. A more reasonable diurnal cycle would be expected as a result of the new parameterization. It also does not need the ‘‘cloud macrophysics’’ module related to upper-tropospheric stratiform cloud formation/dissipation and the cloudtop detrainment source from deep convection. Therefore, it is expected that the unified approach will provide a direct, consistent linkage among subgrid-scale cloud formation/dissipation, turbulence, and cloud microphysics processes for all cloud types. Acknowledgments. This work was supported by the DOE Atmospheric System Research Program under Interagency Agreements DE-SC0005450 and DE-SC0008779. The computational resources are provided by the local Icluster and Kcluster. The C3M data and CERES-EBAF version 2.6 data were obtained from the NASA Langley Research Center CERES ordering tool (http://ceres.larc. nasa.gov/). The GPCP data are maintained by and downloaded from NOAA/OAR/ESRL PSD, Boulder, Colorado (http://www.esrl.noaa.gov/psd/). REFERENCES Adler, R. F., and Coauthors, 2003: The Version-2 Global Precipitation Climatology Project (GPCP) monthly precipitation analysis (1979–present). J. Hydrometeor., 4, 1147–1167, doi:10.1175/1525-7541(2003)004,1147:TVGPCP.2.0.CO;2. Bogenschutz, P. A., A. Gettelman, H. Morrison, V. E. Larson, C. Craig, and D. P. Schanen, 2013: Higher-order turbulence closure and its impact on climate simulations in the Community Atmosphere Model. J. Climate, 26, 9655–9676, doi:10.1175/JCLI-D-13-00075.1. Bony, S., J.-L. Dufresne, H. Le Treut, J.-J. Morcrette, and C. Senior, 2004: On dynamic and thermodynamic components of cloud changes. Climate Dyn., 22, 71–86, doi:10.1007/ s00382-003-0369-6. Boucher, O., and Coauthors, 2013: Clouds and aerosols. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 571–657. [Available online at www.climatechange2013.org/images/report/ WG1AR5_Chapter07_FINAL.pdf.] Bougeault, P., 1981: Modeling the trade-wind cumulus boundary layer. Part II: A high-order one-dimensional model. J. Atmos. Sci., 38, 2429–2439, doi:10.1175/1520-0469(1981)038,2429: MTTWCB.2.0.CO;2. Bretherton, C. S., and S. Park, 2009: A new moist turbulence parameterization in the Community Atmosphere Model. J. Climate, 22, 3422–3448, doi:10.1175/2008JCLI2556.1. Brown, A. R., and Coauthors, 2002: Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land. Quart. J. Roy. Meteor. Soc., 128, 1075–1093, doi:10.1256/003590002320373210. Cheng, A., and K.-M. Xu, 2006: Simulation of shallow cumuli and their transition to deep convective clouds by cloud-resolving models with different third-order turbulence closures. Quart. J. Roy. Meteor. Soc., 132, 359–382, doi:10.1256/qj.05.29.

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