An improved PDF cloud scheme for climate simulations



An efficient grid-scale cloud scheme for climate simulation is implemented in the atmospheric general circulation model for the Earth Simulator (AFES). The new cloud scheme uses statistical partial condensation using joint-Gaussian probability distribution functions (PDFs) of the liquid water potential temperature and total water content, with standard deviations estimated by the moist Mellor–Yamada level-2 turbulence scheme. It also adopts improved closure parameters based on large-eddy simulations and a revised mixing length that varies with the stability and turbulent kinetic energy. These changes not only enable better representation of low-level boundary layer clouds, but also improve the atmospheric boundary layer structure. Sensitivity experiments for vertical resolution suggest that O(100–200 m) intervals are adequate to represent well-mixed boundary layers with the new scheme. The new scheme performs well at relatively low horizontal resolution (about 150 km), although inversion layers near the coast become more intense at a higher horizontal resolution (about 50 km). Copyright © 2010 Royal Meteorological Society

1. Introduction

Marine boundary layer clouds are one of the most important factors affecting the radiation balance of the Earth. These clouds mainly play a role as reflectors of solar short-wave radiation. In spite of their importance, however, it has been difficult for most atmospheric general circulation models (AGCMs) to represent these low clouds accurately (Siebesma et al., 2004). One of the reasons is insufficient vertical resolution to represent thin cloud layers. Another reason is the complexity of the physical mechanisms involved (Nieuwstadt and Duynkerke, 1996). Several parametrized physical processes, such as shallow convection, turbulence, radiation and condensation, are responsible for the formation of boundary layer clouds.

Representation of boundary layer clouds is more crucial in coupled atmosphere–ocean general circulation models (CGCMs) than in AGCMs, since a lack of such clouds causes excessive incoming solar radiation into the ocean, which modifies ocean circulation and leads to an unrealistic atmospheric response in the coupled climate system. Clement et al. (2009) report that the interannual–decadal variability associated with low-level clouds by Coupled Model Intercomparison Project phase 3 (CMIP3: Meehl et al., 2007) models shows large variations among the models analysed.

Recently, some regional models have begun to produce a better distribution of low clouds. Wang et al. (2004) succeeded in reproducing low clouds over the southeastern Pacific Ocean using a regional atmospheric model, with the cloud microphysics scheme developed by Wang (2001) and the Xu and Randall (1996) cloud fraction scheme. The Xu and Randall scheme parametrizes cloud fraction as a semi-empirical function of the condensate mixing ratio and relative humidity based on results from large-eddy simulations. McCaa and Bretherton (2004) represented marine subtropical clouds over the northeast Pacific Ocean by introducing a shallow cumulus scheme coupled to a 1.5-order turbulence closure model into the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (PSU-NCAR MM5).

Similar approaches have been employed in AGCMs. Slingo (1980, 1987), Teixeira and Hogan (2002) and Mochizuki et al. (2007) parametrize cloud fraction over the boundary layer as a function of the vertical gradient of potential temperature, which represents the strength of the inversion layer. Lock et al. (2000) classify low clouds by vertical structure and vary the vertical diffusion coefficients accordingly. Although these schemes can represent low clouds effectively, additional schemes are required to deal with other cloud types. In the boundary layer, stratus near the coast gradually transitions to stratocumulus and cumulus under the trade winds (Wood and Hartmann, 2006). To capture these features, some models classify cumulus into shallow and deep convection categories and vary entrainment and overshoot rates, etc. Bélair et al. (2005) show simulation results for several kinds of clouds associated with an extratropical cyclone using the Global Environmental Multiscale (GEM) atmospheric model of the Canadian Meteorological Centre with a combination of cloud schemes. Although the multi-scheme approach can represent a number of cloud types, it is difficult to classify clouds and combine the individual cloud schemes effectively to represent smooth cloud transitions.

Another approach is to use statistical partial condensation methods using probability distribution functions (PDFs) based on turbulence closure schemes (Mellor, 1977; Sommeria and Deardorff, 1977). These methods have two important advantages: (1) a single scheme can theoretically represent all cloud types, and (2) cloud fraction, cloud water content and thermal energy are kept consistent. The schemes have usually been used in boundary layer models with high vertical resolutions, in which turbulence is represented accurately. Bechtold et al. (1996) report that such multi-layer turbulence schemes need vertical resolutions of at least 100–200 m. In addition, Smith (1990) points out that subgrid-scale fluctuations in large-scale models are influenced by mesoscale phenomena as well as small-scale turbulence. Therefore, in some AGCMs these schemes have been implemented with the addition of some assumptions to account for resolution deficiencies (Smith, 1990; Ricard and Royer, 1993). Recently, more sophisticated PDF cloud schemes have been introduced (Golaz et al., 2002; Tompkins, 2002; Larson, 2004). They treat higher-order moments of PDFs for total water content and/or thermodynamic variables and predict the PDFs. Although they are enticing approaches, the computational cost is much higher than previous schemes due to additional prognostic equations and higher resolutions with a time step as short as 20 s (Golaz et al., 2002). Since the usual time step is an order of minutes in AGCMs, the increase of computational cost is crucial in applying the scheme to AGCMs or CGCMs for climate studies.

On another front, turbulence closure schemes themselves have been improved using results from large-eddy simulations (LES) and field observations. A series of studies by Nakanishi and Niino (Nakanishi, 2001; Nakanishi and Niino, 2004, 2006, 2009) used LES results to improve the second-order turbulence model of Mellor and Yamada (1974), leading to a better representation of the planetary boundary layer (PBL) and marine fog in a mesoscale model.

The present paper describes an improved PDF cloud scheme for AGCMs. It assumes joint-Gaussian probabilities with standard deviations calculated from the turbulence scheme. The turbulence closure parameters and mixing length are also revised. All of these changes contribute to a better representation of marine boundary layer clouds. However, it is a relatively simple scheme and uses modest computational resources because it is a diagnostic second-order turbulence scheme. The description of the model and new scheme is presented in section 2. The results of simulations with the new scheme are presented in section 3 and sensitivity to vertical and horizontal resolutions in section 4. Finally, in section 5 we offer some concluding remarks, including the implications for atmosphere–ocean coupled models.

2. Model and improvements

The present study uses the Atmospheric general circulation model For the Earth Simulator version 2 (AFES2), developed at the Earth Simulator Centre, Japan Agency for Marine–Earth Science and Technology (JAMSTEC) (Ohfuchi et al., 2004; Enomoto et al., 2008). This model is based on the Centre for Climate System Research/National Institute for Environmental Studies (CCSR/NIES) AGCM (Numaguti et al., 1997) with the introduction of a new convection scheme (Emanuel, 1991; Emanuel and Živković-Rothman, 1999; Peng et al., 2004) and a new radiation scheme (MstrnX: Sekiguchi and Nakajima, 2008). AFES uses spectral discretization in the horizontal and σ coordinates in the vertical.

The original grid-scale condensation (cloud) scheme in AFES is based on a top-hat PDF for the total water content alone (Le Treut and Li, 1991) and the deviation from the grid-box mean value is a function of altitude only, as follows:

equation image(1)
equation image(2)
equation image(3)

where R is the cloud fraction, Ql the cloud water content, Qw the grid mean total water content, Qs the saturated mixing ratio, z the altitude above surface, r the deviation parameter of total water content and κ the Kármán constant (= 0.4). In this study, r0 is 0.3. This scheme cannot reflect local moisture and temperature variations created by subgrid-scale turbulence, which are found to be important in marine boundary layer clouds. Prior to this grid-scale condensation scheme, the Emanuel convection scheme is invoked in AFES to represent shallow or deep convections.

The revisions made for the present study are summarized in Table I. First, we have introduced a new partial condensation scheme, based on joint-Gaussian probability distribution functions (JPDFs) for the liquid potential temperature and total water content proposed by Sommeria and Deardorff (1977) and Mellor (1977). In the new condensation scheme, the standard deviation is estimated using the moist Mellor–Yamada Level 2 (MYL2) turbulence scheme (Mellor and Yamada, 1982, hereafter MY82). The turbulence scheme also includes condensation effects within the closure. The cloud fraction R and cloud water content Ql can be written as

equation image(4)
equation image(5)

where σs is the standard deviation of

equation image(6)
equation image(7)

which is calculated from the JPDFs and MYL2 turbulence scheme and

equation image(8)
equation image(9)
equation image(10)

where qw′ is the sub-grid scale fluctuation of total water content, θl′ the fluctuation of liquid water potential temperature, T the grid mean temperature, Tl the grid mean liquid water temperature, Θ the grid mean potential temperature, Θl the grid mean liquid water potential temperature, Qsl the saturated mixing ratio at Tl,L the mixing length, B2 one of the closure parameters of MYL2, SH the stability function of MYL2 (see Appendix B in Nakanishi, 2001), Lv the evaporative latent heat, cp the constant pressure specific heat and z the height. The derivation of these equations is described in Nakanishi and Niino (2004, hereafter NN04).

Table I. Summary of improvements of schemes.
PDFsTop-hat PDF for total water (Le Treut and Li, 1990)Joint Gaussian PDFs for liquid water potential temperature and total water (Sommeria and Deardorff, 1977 and Mellor, 1977)
Standard deviations of PDFsFunction for altitudeEstimated by moist Mellor–Yamada Level 2 scheme
Turbulence closure parametersMellor and Yamada (1982)Nakanishi and Niino (2004)
Mixing lengthBlackadar (1962)Bougeault and André (1986)
Cumulus topCAPE = 0Buoyancy = 0

Secondly, we introduced the improved closure parameters estimated from large-eddy simulations suggested in NN04. In the MYL2 scheme, SH is a function of the gradient Richardson number Ri and the closure parameters. Figure 1 shows the relationship between Ri and SH for the parameters used in MY82 and NN04. With NN04's parameters, SH changes more slowly with Ri and is smaller when Ri < 0 (unstable), while it has a wider positive region when Ri > 0. Since the diffusion coefficient is proportional to SH, the implication is that there will be more diffusion in stable layers, leading to elevated boundary layer heights.

Figure 1.

Relation between the gradient Richardson number (horizontal axis) and SH (vertical axis). The solid line is for the closure parameters of Nakanishi and Niino (2004) and the broken line for those of Mellor and Yamada (1982). The dotted line shows the minimum value of SH; 0.03.

As a trial, this scheme is applied to the sounding data of the East Pacific Investigation of Climate (EPIC) 2001 (Bretherton et al., 2004) in which the marine boundary layer and stratocumulus over the southeastern Pacific is observed by a ship and a buoy. The sounding data are provided every three hours with 10 m vertical resolution from 1400 UTC 10 October 2001 to 0200 UTC 25 October 2001. Here, we use the data between 16 and 21 October 2001, when the fixed-point observation of steady marine boundary layer clouds was conducted at 85°W, 20°S. To investigate sensitivity to vertical resolution, the data are interpolated to AFES's 48 levels (L48), which has 12 levels between the surface and σ = 0.8 with an interval of about 100–300 m. The new scheme is applied to all three-hourly sounding data for 10 m and L48 vertical resolutions during the period. Figure 2 shows vertical profiles of specific humidity, potential temperature, SH and σs averaged for the period. The L48 resolution seems to accurately capture the profiles of specific humidity and potential temperature (Figure 2(a) and (b)). However, the SH and σs show a large difference between the 10 m and L48 resolutions with the minimum of SH (SHMIN) = 0. The values of SH in the 10 m resolution are much larger than those in the L48 resolution, especially within the PBL (Figure 2(c)). The values of σs in the 10 m resolution have large peaks around the PBL top, while those in the L48 resolution are quite small (Figure 2(d)). This is caused by the high sensitivity of σs to SH around the PBL top. σs is a function of SH and the vertical gradient of the potential temperature and total water according to Eq. (7). The former has small values (<0.1) around the PBL top due to positive Ri (Figure 1), while the latter is large. The SH around the PBL top is often zero in the L48 resolution because Ri tend to be larger than those in the 10 m resolution. As a result, σs is small in the L48 resolution. Therefore, with SHMIN = 0.03, the magnitudes of SH and σs with coarse resolution become comparable with those with 10 m resolution (Figure 2(c) and (d)). These results suggest that the cut-off of SH is necessary for a coarse vertical resolution to compensate under-resolved turbulence and the strength and variation of inversion. Figure 3 shows cloud water content and cloud fraction of the new scheme with SHMIN = 0.03 and the old scheme applied to the EPIC sounding data with coarse resolution. Although the cloud fraction is not different from the old scheme, with the new scheme, not only does the cloud water content increase, but also the peak height becomes elevated. This difference is due to the σs profile (Figure 3(c)). The average liquid water path (LWP), 135.1 g m−2, is comparable to the EPIC 2001 observation result (Bretherton et al., 2004).

Figure 2.

(a) Specific humidity and (b) potential temperature of EPIC soundings and (c) SH and (d) σs (10−3) applying the new cloud scheme to EPIC soundings averaged between 16 and 21 October 2001. The solid line is 10 m resolution, the broken line with the open circle is L48 resolution with SHMIN = 0.03 and the dotted line is L48 with SHMIN = 0.

Figure 3.

(a) Cloud water content (g kg−1), (b) cloud fraction (ratio) and (c) σs (10−3) and r applying the new, with SHMIN = 0.03 (solid line), and old (broken line) cloud schemes to EPIC soundings averaged between 16 and 21 October 2001.

The other improvement is to use an alternative mixing length scheme from Bougeault and André (1986, hereafter BA86). The original scheme in AFES was that of Blackadar (1962), where mixing lengths are a function of height only and therefore independent of atmospheric conditions. Since the mixing lengths of BA86 depend on the static stability and turbulent kinetic energy (TKE), they are sensitive to the local vertical profile. The first guess of TKE for the mixing length is estimated from the dry MYL2 scheme, using the Blackadar mixing length. The mixing length of BA86 is adopted only in the lower troposphere (up to 1500 m above the surface in this study) and connected to the modified Blackadar mixing length, L, used at ECMWF (White, 2003), which decreases with height,

equation image(11)
equation image(12)

where β0 = 0.2,Hmin = 1500 m. λ is determined, as the L of BA86 equals that of Blackadar when z = Hmin. Figure 4 shows a comparison between the annual means of these mixing lengths at 15–10°S, 100°W where marine boundary layer clouds appear frequently. The mixing length of BA86 is larger below 2000 m than that of Blackadar and it decreases with height due to Eqs (11) and (12), while that of Blackadar monotonically increases with height. Note that for BA86 a minimum mixing length is applied, equal to the thickness of the thinnest layer. In this case, the thinnest layer is the one closest to the surface.

Figure 4.

Annual mean mixing length at 100°W, 15–10°S average. The solid line is T79L48 NEW and the broken line is T79L48 OLD.

In addition to the changes in the grid condensation scheme, the calculation of the cumulus top height in the Emanuel convection scheme has also been modified. In the new scheme, the cumulus top is defined by the level of neutral buoyancy, while in the original scheme it was defined by the height where convective available potential energy (CAPE) reaches zero. This modification reduces excessive overshoot of shallow convection. Deep convection also tends to be shallower, but only by a small amount.

The order of invocation of the modified schemes is:

  • (1)The Emanuel convection scheme calculates deep and shallow convection, and updates temperature, total water content and horizontal winds associated with the convection.
  • (2)The MYL2 turbulence scheme with NN04 closure parameters and BA86 mixing length estimates L,SH, vertical turbulent fluxes and σs on the updated fields.
  • (3)The JPDFs condensation scheme calculates cloud fraction and cloud water content using σs, and updates temperature, specific humidity, cloud water mixing ratio and cloud fraction.

In order to examine the new schemes, AFES was integrated for about one year from 11 February 2001 to 28 February 2002, and the data from 1 March 2001 to 28 February 2002 are used for the following examination. Two horizontal resolutions—T79 (about 150 km) and T239 (about 50 km)—and three vertical resolutions are used to test the sensitivity to horizontal and vertical resolutions. The vertical resolutions are: (1) 44 layers (L44), with 8 layers below 0.8 σ-level (about 800 hPa), (2) L48, with 12 layers below σ = 0.8, and (3) L56, with 20 layers below σ = 0.8. Initial conditions for the horizontal velocity, geopotential height, temperature and specific humidity were taken from the Japanese 25-year reanalysis (JRA25: Onogi et al., 2007), which provides 1.25 degree data on 23 levels from 1000 hPa to 0.4 hPa. Daily SST data were taken from the 0.5 degree Real-Time Global Sea Surface Temperature analysis (RTG SST: Thiébaux et al., 2003) provided by the National Centers for Environmental Prediction (NCEP). The simulated clouds are compared with the International Satellite Cloud Climatology Project (ISCCP) D2 data (Rossow and Schiffer, 1999), radiation flux data (ISCCP-FD: Zhang et al., 2004) and climatology of surface cloud observations (NDP-026E: Hahn and Warren, 2007). Also, as a reference of the planetary boundary layer height, Geoscience Laser Altimeter System (GLAS: Zwally et al., 2009) PBL height data provided by the National Snow and Ice Data Center (NSIDC) are used. While the ISCCP D2 and ISCCP-FD data are available for the simulated periods, the surface observation data of cloud fraction are climatology. The GLAS data are used only in October and November from 2003 to 2007, because the data are available from March 2003 and observed seasons are restricted. The cloud fraction in AFES is obtained via the ISCPP simulator (Klein and Jakob, 1999; Webb et al., 2001), which is built into AFES. The experiments conducted are summarized in Table II.

Table II. Summary of experiments. Bold and italic highlight differences from T79L48 NEW.
ExperimentHorizontal resolutionVertical resolutionCondensation schemeMixing length parametersTurbulence closureMinimum of SH
T79L48 NEWT79L48NewNewNew0.03
T79L48 OLDT79L48OldOldOldNone
T239L48 NEWT239L48NewNewNew0.03
T239L48 OLDT239L48OldOldOldNone
T79L44 NEWT79L44NewNewNew0.03
T79L56 NEWT79L56NewNewNew0.03

3. Results

Figure 5 shows the annual mean low-cloud fractions from ISCCP D2 data, surface cloud observations and simulations with the original (OLD) and modified (NEW) versions of AFES run at T79 (about 150 km horizontally) L48 resolutions. The T79L48 OLD run fails to represent low clouds over the eastern parts of the subtropical Pacific, Atlantic and Indian Oceans (Figure 5(c)). In particular, the cloud fraction over coastal regions is much less than that in observations. T79L48 NEW, however, is able to represent the low clouds (Figure 5(d)), and coastal clouds are significantly increased from T79L48 OLD (Figure 5(e)).

Figure 5.

Annual mean low cloud fraction (%) for (a) ISCCP, (b) surface observation climatology by Hahn and Warren (2007), (c) T79L48 OLD, (d) T79L48 NEW, and (e) NEW-OLD, respectively.

Figure 6 shows vertical–zonal cross-sections of major low-cloud regions, off California, off Peru and off Namibia in October and November 2001. The cloud water content is small and PBL heights in T79L48 OLD are lower than the GLAS climatology in each region. Inversion strengths at the PBL top are also weak. T79L48 NEW, however, shows significant increases in cloud water content around the PBL top, and the PBL has stronger inversion at the top. The PBL heights are elevated and are comparable to the GLAS observations, although they are somewhat lower near coastal regions. The heat budget analysis for the PBL clouds using temperature change rates calculated by respective physical schemes is conducted. The results suggest that the enhancement of long-wave radiation cooling from increased PBL clouds mainly contributes to the inversion intensification and vertical destabilization of the boundary layer, and the enhanced vertical mixing of convection and diffusion causes the PBL top elevation in NEW (not shown). The above results suggest that the new scheme works effectively to represent marine boundary layer clouds and thickens the PBL through the positive feedback among the improved points.

Figure 6.

October–November mean vertical cross-section of cloud water content (shaded, 10−5 kg kg−1), potential temperature (dotted line, K, contour interval is 1 K) for (left) T79L48 OLD and (right) T79L48 NEW averaged over (a) (b) 20–25°N (west of North America), (c) (d) 10–15°S (west of South America) and (e) (f) 17.5–22.5°S (west of South Africa). The bold lines show mean PBL height and the bold broken lines show maximum and minimum PBL height by GLAS averaged from 2003 and 2007.

A large difference of low-cloud fraction at higher latitudes exists between the ISCCP and surface observations (Figure 5(a) and (b)). Instead of low clouds, middle-level clouds dominate in ISCCP (not shown). Both AFES runs represent low clouds similar to surface observations, rather than middle-level clouds. Recently CloudSat radar observations (Haynes et al., 2007; Sassen and Wang, 2008) have revealed that middle clouds overlap low clouds, which are not sufficiently represented in AFES. Figure 7 shows zonal-mean cloud forcing. The short-wave cloud forcing in the high latitudes is less improved than that in subtropical to extratropical regions (Figure 7(a)). The long-wave cloud forcing in both schemes is weaker than observation (Figure 7(b)). This is partly due to horizontal resolution and will be discussed in section 4.

Figure 7.

Annual zonal mean cloud forcing (W m−2) for (a) short wave and (b) long wave. The solid lines show ISCCP-FD, the broken lines show T79L48 NEW and the dotted lines show T79L48 OLD.

The improvements reported in this paper are achieved through a combination of modifications to several physical schemes, as shown in Table I. Now, we look at their individual contributions. Figure 8(a) shows the difference of annual mean low-cloud fraction between NOBANN and T79L48 OLD to estimate the effect of the JPDFs partial condensation. The JPDF scheme makes the biggest change in simulation marine boundary layer clouds among the modifications considered. The differences of cloud water and potential temperature over the off-Peru region in October and November (Figure 9(a) and (b)) show that the modification increases cloud water contents along the PBL inversion and makes the PBL higher with strong inversion above the clouds. It suggests that cloud representation associated with turbulence around the PBL top is essentially important to simulate a realistic PBL structure.

Figure 8.

Annual mean low-cloud fraction differences (%) between (a) NOBANN and T79L48OLD, (b) T79L48 NEW and NOBA, (c) T79L48 NEW and NONN, and (d) T79L48 NEW and SHMIN = 0.02.

Figure 9.

October–November mean (left) vertical-zonal cross-sections of cloud water content (10−5 kg kg−1) and (right) potential temperature (K) differences for (a) (b) NOBANN − T79L48 OLD, (c) (d) T79L48 NEW − NOBA, (e) (f) T79L48 NEW − NONN and (g) (h) T79L48 NEW - SHMIN = 0.02 averaged over 15–10°S (off Peru).

The BA86 mixing length does not seem to act to increase low clouds globally (see the difference between T79L48 NEW and NOBA in Figure 8(b)). Rather, it acts to constrict low-cloud production over the Tropics. In marine boundary cloud regions, the use of the BA86 mixing length elevates the PBL top, while warming reduces the cloud layer (Figure 9(c) and (d)).

The use of either the closure parameters in NN04 or the setting of SHMIN = 0.03 increases low-cloud fractions globally (Figure 8(c) and (d)). The cloud water increase shown in Figure 9(e) is probably due to the larger value of the closure parameter B2 (= 15.0 in NN04, 10.1 in MY82) which is included in Eq. (7). The NN04 closure parameters and SHMIN also act to elevate the PBL height and strengthen the inversion due to cloud increase associated with the SH function change in Figure 1 (Figure 9(f) and (h)).

4. Sensitivity to vertical and horizontal resolutions

As shown in the previous section, the new cloud scheme successfully represents marine boundary layer clouds at moderate resolutions. As Bechtold et al. (1996) reported, multi-layer turbulence schemes, such as the one used in the present study, are sensitive to vertical resolution. In section 2 we pointed out that coarse vertical resolutions cause underestimation of SH. Here we examine sensitivity to vertical resolutions with a fixed value of SHMIN. Figure 10 shows EPIC 2001 sounding tests for L56 and L44 with SHMIN = 0.03. Layer thicknesses are between 200 and 300 m for L44 and between 30 and 300 m for L56 below σ = 0.8. Although SH becomes larger with higher vertical resolutions within the PBL, cloud water, cloud fraction and σs around the PBL top are insensitive to the vertical resolution because of the compensation effect by setting SHMIN = 0.03. It suggests that the new cloud scheme with SHMIN can represent marine boundary layer clouds if appropriate atmospheric conditions are given.

Figure 10.

(a) SH and (b) σs (10−3), (c) cloud water content (g kg−1) and (d) cloud fraction (ratio) applying the new cloud scheme to EPIC soundings averaged between 16 and 21 October 2001. The solid line is L56 resolution, the broken line with the open circle is L48 and the dotted line is L44. SHMIN = 0.03 for every resolution.

As shown by Hannay et al. (2009), AGCMs often go to unrealistic equilibrium states due to feedback from other dynamical and physical schemes, even if they start with adequate initial conditions and represent reasonable PBL and clouds at early time steps. Indeed, the simulation results of T79L56 NEW and T79L44 NEW runs show different behaviours in the major marine boundary cloud area (Figure 11). In T79L56 NEW run, the cloud layer is higher especially in shallow PBLs near the coast and thicker and wider than those in T79L48 NEW (Figures 6 and 11). On the other hand, T79L44 NEW shows another cloud layer within the boundary layer. This was caused by weaker vertical diffusion due to coarser vertical resolutions in the turbulence scheme. The degradation from L56 to L48 is smaller than that from L48 to L44 because the difference of layer thicknesses is small around the PBL top in the former. These results suggest that vertical resolutions fine enough to drive vertical diffusion and to resolve the PBL top are required.

Figure 11.

Same as Figure 6, but for (left) T79L56 NEW and (right) T79L44 NEW.

McCaa and Bretherton (2004) suggested that horizontal resolution is an important factor in the representation of boundary layer clouds. Although boundary layer clouds are improved significantly with a relatively low horizontal resolution of about 150 km with our new scheme, a higher horizontal resolution has a positive impact. Figure 12 shows the results from the T239L48 runs (about 50 km resolution horizontally), which is almost the same resolution as used by Wang et al. (2004) in their regional model. Compared with T79L48 NEW, T239L48 NEW represents better marine boundary layer clouds and a deeper boundary layer near the coast. Although the cloud water content in T239L48 OLD is less than in T79L48 NEW or T239L48 NEW, similar features are found in comparison between T79L48 OLD and T239L48 OLD except off California. These improvements may be caused by more fine-scale orography and/or larger wind and temperature/water vapour variations due to the higher resolution.

Figure 12.

Same as Figure 6, but for T239L48.

As a result, the distribution of zonally averaged cloud forcing in T239L48 NEW is much improved over that in T79L48 NEW (Figure 13). The short-wave cloud forcing in T239L48 NEW is closer to the ISCCP-FD data than that in T79L48 NEW. Interestingly, the long-wave cloud forcing distribution in T239L48 is quite better, in particular, at mid- and high latitudes than T79L48, irrespective of cloud schemes (OLD or NEW).

Figure 13.

Same as Figure 7, but for T239L48.

The horizontal distributions of cloud forcing are shown in Figure 14. The short-wave cloud forcing in T79L48 NEW is weaker over the maritime continent than that in ISCCP-FD and T239L48 NEW. In marine boundary layer cloud regions, the magnitudes in T79L48 NEW and T239L48 NEW are not very different, although they are weaker and the peaks are shifted westward compared with the ISCCP-FD data over the eastern Pacific in particular. One of the reasons for these westward shifts may be that the Intertropical Convergence Zone (ITCZ) is too intense over the eastern Pacific. In addition, even in T239L48, the horizontal resolution may be too coarse to represent the boundary layer structure very close to the coast, especially along the western coast of South America where the mountains are steep (Xu et al., 2004). It is interesting that the horizontal pattern of the short-wave cloud forcing over the Southern Ocean is quite similar to the ISCCP-FD data. Recently, it has been pointed out that the fine SST structures along the western boundary currents influence cloud formations and precipitation distributions (Minobe et al., 2008; Small et al., 2008). The use of high-resolution SST data (0.5 degrees) may have activated convection and extratropical cyclogenesis along the western boundary currents to produce realistic cloud forcing distribution in T239L48 NEW.

Figure 14.

Annual mean (left) short-wave and (right) long-wave cloud forcing (W m−2) for (a) (b) ISCCP-FD, (c) (d) T79L48 NEW and (e) (f) T239L48 NEW.

The long-wave cloud forcing in T79L48 NEW, which is associated with storm tracks over the northwestern Pacific, north Atlantic and Southern Oceans, as well as the tropical region, is much weaker than T239L48 NEW and the ISCCP-FD data. In T239L48 NEW, these deficits are improved, although the amplitudes are still weaker than with the ISCCP-FD data. The improvement of cloud forcing in T239L48 may suggest that high resolution for both the atmosphere and ocean, which can resolve the storm-track activity and air–sea interaction associated with oceanic fronts and eddies, is necessary to simulate the correct radiation budget as well as tropical deep convection and PBL clouds for climate studies.

5. Conclusions

The PDF cloud scheme in AFES has been modified in order to improve the representation of marine boundary layer clouds. At first, the single column examination is conducted for the EPIC sounding profiles. The examination suggests that the setting of the minimum of SH (SHMIN) is found to be a key for the joint-Gaussian PDF condensation scheme to represent boundary layer clouds with relatively coarse vertical resolutions. In the AFES examination, the JPDF partial condensation scheme with turbulence closure scheme mainly acts to improve the low-cloud distribution and intensify the inversion through the long-wave cooling from enhanced PBL clouds, while the improved turbulence closure parameters, mixing length and the value of SHMIN (>0) contribute to vertical diffusion enhancement, deeper boundary layer and an increase of low-cloud amount. These results show that the representation of PBL clouds is critically important to represent marine boundary layer structure. Because PBL clouds are formed by a combination of many physical processes, it is also important that these components are treated carefully to represent low clouds in an AGCM. As a result, the new scheme significantly improves the cloud distribution climatology and radiation budget in AFES.

Although the vertical resolution is rarely as significant to the JPDF condensation scheme as it is for the EPIC sounding application test, at least with the setting of SHMIN = 0.03, a coarser vertical resolution in AFES causes strange boundary layer structures due to the weaker vertical diffusion associated with the turbulence scheme. It means that at least 100–200 m vertical resolution is necessary to maintain boundary layer structures as suggested by Bechtold et al. (1996). A higher horizontal resolution is important, not only to represent finer marine boundary layer clouds with a deeper boundary layer near the coast, but also to improve cloud forcing distributions of tropical deep convection. Extratropical middle clouds associated with storm tracks increase with a high horizontal resolution which can resolve sharp SST fronts.

With all these improvements together, short-wave cloud forcing of marine boundary layer clouds over coastal regions is still less than observed, even at T239 or L56 resolution. Sensitivity experiments suggest that even higher horizontal and vertical resolutions are needed to represent realistic coastal low clouds, because the clouds and the PBL are affected by steep mountains and have shallower structures. In addition, the intensity of the ITCZ may be a factor in determining the circulation around marine boundary layer cloud regions and over the eastern Pacific in particular. However, the actual structure of the boundary layer in these regions has not been completely understood. Recent and future satellite observations using active sensors (A-Train and EarthCARE) and field observation campaigns (VOCALS: Wood et al., 2007) will provide more knowledge about boundary layer clouds, which will lead to improved models such as more sophisticated cloud schemes to predict PDFs (Golaz et al., 2002; Tompkins, 2002; Larson, 2004).

The deficiency of boundary layer clouds has a more serious impact in atmosphere–ocean coupled simulations. Warm biases over the eastern parts of the ocean basins in CGCMs are mainly caused by underestimation of boundary layer clouds (Gordon et al., 2000). Teixeira et al. (2008) report that improvements to the low-cloud parametrization strongly influence SST in a global ocean–atmosphere coupled model, even in a three-month integration. Komori et al. (2010) have conducted about 20 years of integration of a high-resolution CGCM with the new cloud scheme described in the present study, and they show that there are significant improvements of SST distribution and oceanic currents as well as surface winds and precipitation distributions. In the future, it is important to investigate mechanisms of diurnal variations (Teixeira et al., 2010) and interannual to decadal variations of marine boundary layer clouds (Clement et al., 2009).


AFES has been developed by numerous contributions from the AFES team. The authors thank N. Komori and B. Taguchi for beneficial comments and discussions, and A. Clayton and K. Hamilton for their help with the English language. Model integrations were performed on the Earth Simulator supported by the Japan Agency for Marine–Earth Science and Technology (JAMSTEC).