Abstract

Coincident top-of-atmosphere (TOA) radiative fluxes and cloud optical properties for portions of clouds whose tops are exposed to space within several pressure ranges are used to evaluate how a GCM realizes its all-sky radiative fluxes and vertical structure. In particular, observations of cloud properties and radiative fluxes from the Clouds and the Earth’s Radiant Energy System (CERES) Science Team are used to assess the Canadian Centre for Climate Modeling and Analysis atmospheric global climate model (CanAM4). Through comparison of CanAM4 with CERES observations it was found that, while the July-mean all-sky TOA shortwave and longwave fluxes simulated by CanAM4 agree well with those observed, this agreement rests on compensating biases in simulated cloud properties and radiative fluxes for low, middle, and high clouds. Namely, low and middle cloud albedos simulated by CanAM4 are larger than those observed by CERES attributable to CanAM4 simulating cloud optical depths via large liquid water paths that are too large but are partly compensated by too small cloud fractions. It was also found that CanAM4 produces 2D histograms of cloud fraction and cloud albedo for low, middle, and high clouds that are significantly different than generated using the CERES observations.

1. Introduction

Clouds, through their interaction with radiation and their role in the hydrological cycle, are an important component of the earth’s climate system (Solomon et al. 2007). The large ranges of temporal and spatial scales on which cloud processes occur makes them difficult to model realistically; particularly for relatively coarse-resolution global climate models (GCMs) that do not resolve most clouds (Randall et al. 2003). Modeling cloud radiative effects (CREs) (Charlock and Ramanathan 1985) in GCMs is an ongoing line of research that ultimately addresses both the structural properties of clouds, ranging from particle size distributions to cloud fraction parameterizations, and radiative transport solvers that use these properties to compute fluxes and heating rate profiles (Barker et al. 2003). Given the global nature of the problem, it is essential that GCM CREs be compared to global observations such as those provided by satellite-based instruments.

Typically, GCM top-of-atmosphere (TOA) fluxes and CREs are compared to corresponding monthly mean values derived from satellite-based passive instruments such as the Clouds and the Earth’s Radiant Energy System (CERES) radiometers (Wielicki et al. 1996). Although such comparisons are useful for identifying gross errors in GCMs, they can be ambiguous since fortuitous agreement may occur owing to cancellation of a host of errors at unresolved scales: be they spatial, temporal, or spectral. As a simple example, consider a GCM whose mean CRE shows acceptable agreement with CERES might actually have too few, but too dense, clouds at the wrong time of day. The point being that the fidelity of a GCM depends on more than getting just correct monthly mean all-sky CREs.

Rather than using just the all-sky CRE, one can use CREs for a range of cloud types in several pressure ranges (Ockert-Bell and Hartmann 1992; Hartmann et al. 1992; Chen et al. 2000), which better evaluates a GCM’s ability to simulate the presence of clouds as well as their optical properties, macrophysical structure, and resulting radiative fluxes. This sort of analysis is best done when using cloud properties and radiative fluxes that are coincident, and physically consistent, in space and time. A common approach to evaluate GCMs is to use histograms of cloud top pressure and cloud optical thickness which are then used to relate biases in cloud properties to biases in all-sky TOA CREs (Zhang et al. 2005; Wyant et al. 2006). However, this can be potentially misleading in the absence of well-defined and large cloud properties biases, for example, overly large cloud optical thicknesses, since there are multiple cloud properties that can affect CREs and inferring the integrated effect of biases in multiple cloud properties can be difficult (Barker and Räisänen 2005). In addition, calculations should be performed with a GCM radiative transfer parameterization since it is possible that biases in cloud properties will not be faithfully passed to, and through, some GCM radiative transfer schemes (Barker et al. 2003; Pincus et al. 2006). This can further confuse the connection between biases in cloud properties and cloud radiative effects.

In this paper, coincident cloud properties and TOA radiative fluxes for portions of clouds observable by satellite-based passive instruments in several layers are used to evaluate the ability of a GCM to simulate similarly defined quantities (Barker 2008). It is assumed that, if a GCM is capable of simulating vertically integrated cloud properties and resulting radiative fluxes for several layers of cloud visible to space, then it is also capable of reasonably simulating domain-mean profiles of radiative fluxes over the vertical layers. This provides some information about biases in the vertical structure of clouds in GCMs, which is useful during observational periods when there are no spaceborne active profiling instruments. It also provides a method to evaluate cloud and radiative properties that are useful to understand cloud feedbacks in GCMs (Bony et al. 2006; Zelinka and Hartmann 2010). To illustrate the utility of this diagnostic approach, cloud properties and radiative fluxes for the portions of low, middle, and high clouds observed by CERES and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments will be used to evaluate similarly defined quantities in the fourth-generation Canadian Centre for Modeling and Analysis (CCCma) atmospheric GCM (CanAM4).

The methodology and rational for the approach is further developed in section 2, satellite-based observations are discussed in section 3, methods to diagnose cloud properties and radiative fluxes within a GCM are presented in section 4, details about CanAM4 are given in section 5, and an evaluation of CanAM4 is presented in section 6.

2. Methodology and rationale

The diagnostic procedure presented here uses coincident CERES and MODIS data to define cloud properties, such as cloud optical thickness and radiative fluxes, for clouds whose tops are exposed to space in several pressure, or altitude, ranges. The rationale being that these are the clouds viewed directly by passive satellite sensors; especially for small viewing zenith angles. Inferences of cloud properties and upwelling fluxes using radiances emerging out of the cloud tops at altitude, ztop, provide information about the integrated effect of underlying cloud whose details are generally unknown. However, if the distribution of cloud properties and fluxes (i.e., integral features) for a range of ztop from a GCM resemble those inferred from satellite data, it suggests that the GCM is capable of simulating radiatively important cloud properties and their cloud radiative effect reasonably well.

This can be illustrated using the independent column approximation (ICA) (Stephens et al. 1991) for radiative transfer. In so far as the ICA can be applied to subcolumns of a GCM column, as well as collections of CERES pixels, the mean, all-sky, radiative flux over an area can be expressed as

 
formula

where p*(τ) is normalized probability distribution of cloud optical depth τ and F(τ) is flux from a 1D radiative transfer model. Separating the cloudless and cloudy portions allows Eq. (1) to be recast as

 
formula

where A is total cloud fraction, p(τ) is the normalized probability distribution of τ for clouds only, and Fclr is the mean clear-sky flux. Further expansion of Eq. (2) into M atmospheric layers gives

 
formula

where there are M layers with cloud fraction Ai and pi(τ) being the normalized probability distributions of τ for clouds with tops exposed to space in layer i. This leads to the cloud radiative effect (Charlock and Ramanathan 1985) at the top of the atmosphere as a function of clouds in layer i. Starting with the all-sky CRE,

 
formula

and substituting in Eq. (3), rearranging and noting that we get

 
formula

Since it is possible to diagnose each term in Eqs. (3) and (5) in the GCM and from observations, it is possible to better evaluate the source of model biases in TOA fluxes and CREs.

Figure 1 illustrates the usefulness, and limitations, of this method using a 500-km-long cross section of cloud occurrence from CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data (Mace et al. 2009), which is labeled CloudSat. Looking downward from a satellite much of the cloud was classified as “high,” which then obscured much of the cloud classified as “low” and “mid”; despite them having layer cloud amounts reaching 0.25 and 0.1, respectively. The adjacent images are modified version of the cloud field labeled CloudSat for which some low and middle cloud below the high cloud are removed (SIM1) and all of the middle clouds are removed (SIM2). By construction each cloud field has the same cloud fraction visible when viewed from space.

Fig. 1.

The image labeled “CloudSat” is cloud occurrence deduced from CloudSat and CALIPSO data for a 500-km-long cross section over tropical ocean; the graph (left) is its corresponding cloud fraction profile. Low clouds were taken to be below 680 hPa, high clouds were above 440 hPa, and middle clouds were between these values. Cross sections labeled “SIM1” and “SIM2” are hypothetical alterations of the CloudSat cross section and are meant to represent less than perfect simulations of the latter. In SIM1 low and middle clouds between 400 and 500 km were removed, while in SIM2 all middle clouds were removed. Values listed below the cross sections indicate cloud fraction exposed to space Ai, mean optical depth 〈τ〉, ν = (〈τ〉/στ)2 where στ2 is variance of τ, and SW albedo. The latter three quantities are for those clouds whose tops are exposed to space.

Fig. 1.

The image labeled “CloudSat” is cloud occurrence deduced from CloudSat and CALIPSO data for a 500-km-long cross section over tropical ocean; the graph (left) is its corresponding cloud fraction profile. Low clouds were taken to be below 680 hPa, high clouds were above 440 hPa, and middle clouds were between these values. Cross sections labeled “SIM1” and “SIM2” are hypothetical alterations of the CloudSat cross section and are meant to represent less than perfect simulations of the latter. In SIM1 low and middle clouds between 400 and 500 km were removed, while in SIM2 all middle clouds were removed. Values listed below the cross sections indicate cloud fraction exposed to space Ai, mean optical depth 〈τ〉, ν = (〈τ〉/στ)2 where στ2 is variance of τ, and SW albedo. The latter three quantities are for those clouds whose tops are exposed to space.

The information below the plots in Fig. 1 show that the cloud field in SIM1 has differences relative to the original in both the cloud optical thickness τ, inhomogeneity parameter ν [Eq. (9)], and albedo αp while modifications made to SIM2 change τ and ν, but produce nearly identical cloud albedos. Through examination of both cloud and radiative properties in the three layers it is possible to identify that there are differences between the cloud fields and that the differences are occurring below high clouds, but it is not possible to attribute what is causing the difference below the high clouds. Further specification of the errors requires vertical profiling capabilities like those available with active instruments.

Before applying the methodology described above to CanAM4, the method used to generate the dataset from CERES and MODIS observations is described, as is the approach used to compute the diagnostic output in CanAM4.

3. Satellite data

A 1° × 1° gridded daily mean dataset of cloud properties and TOA radiative fluxes was created from the CERES Single Scanner Footprint (SSF) data product from the Terra spacecraft (CER_SSF_Terra-FM1/FM2-MODIS_Edition2B) (Loeb et al. 2003). The Terra satellite is in a sun-synchronous, near polar orbit at an altitude of 705 km with a descending equator-crossing time of 1030 local time. The SSF product merges CERES footprint parameters including time, position, viewing geometry, radiances, and radiative fluxes with coincident information from MODIS, which is used to characterize the clear and cloudy portions of a CERES footprint. MODIS SSF parameters include radiances in five spectral bands for clear, cloudy, and total areas, cloud property retrievals (Minnis et al. 2010, manuscript submitted to IEEE Trans. Geosci. Remote Sens.), and aerosol property retrievals from the MOD04 product (Remer et al. 2005). Pixel-level radiances and cloud retrievals from MODIS are averaged over CERES footprints after weighting by the CERES point spread function (Smith 1994; Loeb et al. 2003). In addition, MODIS pixel radiance and cloud retrieval averages are determined for up to two distinct nonoverlapping cloud layers if there is a significant difference in cloud phase or effective pressure within a CERES field of view [for details see Loeb et al. (2003)].

For the purposes of illustration, data was created for each January and July between 2000 and 2005, although the dataset can be generated for the length of the observations aboard Terra or using observations collected by instruments on the Aqua satellite.

a. Radiative fluxes

CERES radiometers measure filtered broadband shortwave, total, and window channel radiances with a 20-km spatial resolution at nadir. These are first converted to unfiltered shortwave and longwave radiances (Loeb et al. 2001) and then to TOA fluxes by applying empirical angular distribution models that use scene information from MODIS cloud property retrievals (Loeb et al. 2005). As noted above, within each CERES footprint MODIS radiance and cloud property retrievals are averaged for up to two distinct cloud layers with tops exposed to space. To infer radiative fluxes for individual cloud layers within CERES footprints, we assume the all-sky broadband footprint flux inferred from CERES can be approximated as

 
formula

where Fclr is clear-sky flux and F1 and F2 are mean broadband fluxes for the two cloud tops with respective cloud fractions A1 and A2 such that A = A1 + A2 is total cloud fraction in the footprint. If either A1 or A2 is zero then it is possible to solve Eq. (6) directly since all of the remaining variables are observable. However, if there are two cloud layers, then further assumptions are made to compute the cloud-mean fluxes for each layer.

The same relationship is assumed to hold for narrrowband radiances measured by MODIS integrated over a CERES footprints giving

 
formula

where fclr is mean clear-sky radiance and f1 and f2 are mean radiances for the two cloud layers. Assuming further that broadband and narrowband measurements are related through

 
formula

F1 and F2 can be solved for using Eqs. (6), (7), and (8) since we have from the CERES and MODIS observations the cloud fractions A, A1, A2 and the radiative quantities F, Fclr, f, f1, f2, and fclr. Fluxes for each cloud layer were then averaged for each day onto a 1° × 1° grid for three cloud-top pressure ranges: greater than 680 hPa (low clouds), between 440 and 680 hPa (middle clouds), and less than 440 hPa (high clouds).

Mean longwave fluxes for each day were computed by linear averaging of instantaneous longwave fluxes. Shortwave fluxes, on the other hand, are often limited to a small range of solar zenith angles owing to Terra’s sun-synchronous orbit. Therefore, instantaneous TOA fluxes were also converted to equivalent daily average values. This was done by assuming that instantaneous cloud field and atmospheric conditions at the CERES Terra overpass time were invariant throughout the day and applying diurnal albedo models that account for albedo changes with time of day (Loeb et al. 2007). After performing this integration on all CERES footprints, footprint-level fluxes were then averaged up to a 1° × 1° grid.

b. Cloud properties

Cloud properties in the 20-km CERES footprints for up to two separate cloud layers exposed to space are computed using properties retrieved from pixel-level MODIS radiances by the CERES science team (Minnis et al. 2003). These cloud properties were averaged over each day onto a 1° × 1° grid for all, low, middle, and high clouds. Although several cloud properties are retrieved, this study focuses on cloud fraction A, logarithmic mean cloud optical thickness at ~0.63 μm, and variability of τ as defined below. These variables strongly govern the earth’s radiation budget; especially solar radiation.

The variability parameter ν (Barker et al. 1996), which describes the shape of the τ distribution assuming it follows a Γ distribution, can be computed using the maximum likelihood estimation method. This can be approximated accurately using

 
formula

where and produces results very similar to other approximations (Greenwood and Durand 1960). When computing the linear and logarithmic means of the cloud optical thickness, cloud fraction is used to weight the contributions to the mean. Smaller values of ν indicate a more inhomogeneous distribution while larger values indicate a more homogeneous distribution.

4. GCM diagnostic approach

Comparison of a GCM with the observations described above potentially requires the addition, or modification, of a new diagnostic code into a model. To provide some guidance, salient steps used to diagnose cloud properties and consistent radiative fluxes are outlined below. In the case of CanAM4, we make use of the International Satellite Cloud Climatology Project (ISCCP) simulator for cloud properties and the Monte Carlo independent column approximation (McICA) for radiative transfer, both of which are increasingly being used at climate modeling centers (Zhang et al. 2005; Barker et al. 2008).

a. Sampling

To sample the clouds and radiative fluxes in a manner similar to the observations, the Terra orbital swath was approximated using a computational model based on Keplerian orbital dynamics (Hoots and Roehrich 1980), the Terra orbital parameters, and a cross-track swath of 2400 km. One-hour-long segments of the orbit were used to sample the fields every radiative transfer time step in CanAM4 (every simulated model hour). Qualitative comparison of areas covered by the CERES swath and simulated swath showed good agreement.

b. Diagnostic cloud properties

For each GCM grid box within the simulated satellite swath, subcolumns were generated using a stochastic cloud generator (Räisänen et al. 2004) using profiles of layer cloud fractions, mean water contents and assumed cloud vertical overlap rules, and horizontal in-homogeneity assumptions consistent with those in the GCM. These subcolumns were used by a modified version of the ISCCP simulator (Klein and Jakob 1999) to diagnose cloud properties including radiative cloud-top pressure and visible cloud optical thickness for low, middle, and high clouds. Within a GCM gridbox subcolumns with an integrated cloud optical thickness greater than 0.2 and cloud tops located in either the low, middle, and high pressure ranges were grouped together for subsequent radiative transfer calculations, thereby ensuring consistency between the cloud property diagnostics and radiative transfer calculations.

c. Diagnostic radiative fluxes

Rather than use the independent column approximation (ICA) to compute radiative fluxes for cloud tops exposed to space broadband radiative fluxes were computed using the Monte Carlo ICA(McICA) (Pincus et al. 2003; Räisänen and Barker 2004). The McICA computes radiative transfer by randomly sampling distributions of cloud optical properties, that is, subcolumns, for each spectral integration point, thereby efficiently producing broadband fluxes that are unbiased relative to ICA (Räisänen and Barker 2004).

As was done for the CERES shortwave fluxes, the daily average in the GCM is computed assuming that the instantaneous cloud and atmospheric state is constant throughout the day while the solar position is varied. To do this efficiently Monte Carlo integration was used to compute the diurnal-mean shortwave fluxes (Barker et al. 1998) by randomly generating the cosine of solar zenith angle μ0 for each spectral integration point using

 
formula

where δ(J) is declination angle for day number J, λ is latitude, h is hour angle between sunrise and sunset, and R is a uniform random number between 0 and 1.

5. Application to CanAM4

To illustrate the application of the diagnostic described in section 2 and observations described in section 3, they are used to evaluate CanAM4. To aid in the analysis, aspects of CanAM4’s parameterizations and climatology are described, as are the configuration used for the simulations.

a. Description of CanAM4 and simulations

A developmental T63 35-level version of CanAM4 is used, for which most of the physical processes are described briefly in von Salzen et al. (2005). However, the cloud and radiation parameterizations in this version of CanAM4 have been changed significantly, so they are described below.

Cloud fraction is parameterized in CanAM4 using the scheme of Chaboureau and Bechtold (2002). The horizontal variability of the cloud condensate within each layer is assumed to be a Γ distribution with the variability for each layer being diagnosed from the cloud scheme and convective sources. Cloud fraction and cloud condensate vertical overlap follow the vertical decorrelation length approach (Hogan and Illingworth 2000) using decorrelation lengths of 2 km for cloud fraction and 1 km for cloud condensate (Pincus et al. 2005; Barker 2008). Radiative transfer within CanAM4 is computed using the McICA and simplified versions of the radiative transfer solvers described in Li and Barker (2002) and Li et al. (2005). Horizontal variability and cloud overlap within the radiative transfer calculations and the cloud diagnostics are handled explicitly via subcolumns generated by a stochastic cloud generator (Räisänen et al. 2004).

For interactive radiative transfer calculations (i.e., radiative fluxes and heating rates used by other processes in CanAM4) 150 subcolumns were generated, from which the McICA algorithm randomly samples one cloudy subcolumn for each integration point in the correlated k-distribution model (Li and Barker 2005). This amounts to 35 random samples in the shortwave and 46 random samples in the longwave. For diagnostic calculations along the Terra orbit the number of subcolumns was increased to 500 to reduce the stochastic sampling noise in the cloud property diagnostics, while for McICA the sampling of subcolumns was increased to 1000 for the shortwave and to 740 for the longwave to reduce the stochastic sampling noise in the radiative fluxes (Räisänen and Barker 2004). This reduction is especially important for equatorial areas, which were typically sampled only once per day.

Two simulations were performed using CanAM4, a baseline reference simulation (CONTROL) and a simulation (AUT×10) in which the autoconversion rate was increased by a factor of 10, specifically to reduce the low cloud water content. For each simulation the sea surface temperatures and sea ice were prescribed (Taylor et al. 2000) along with volcanic eruptions, greenhouse gas concentrations, solar variability, and aerosol emissions for the period 1 January 1999–31 August 2005. The first two years are considered model spin up and discarded. Diagnostic output was sampled every model hour and then averaged up to daily means for each January and July between 2001 and 2005.

As part of the CanAM4 development process, it was tuned so that its TOA radiation budget is in good agreement with the CERES Energy Balanced and Filled (EBAF) dataset (Loeb et al. 2009, i.e., the CONTROL simulation). The sampling and processing of the radiative flux observational dataset used to examine the low, middle, and high cloud (section 3) is different than that used to produce the EBAF dataset, so it cannot be expected that the TOA radiation budgets will be identical (Loeb et al. 2009). The same holds true for CanAM4 and some differences are expected in the simulated radiative fluxes owing to different sampling and processing to diagnose the fluxes.

b. CanAM4 radiation and cloud climatology

As expected the zonal mean all-sky and clear-sky albedos and outgoing longwave radiation (Fig. 2) are in generally good agreement the CERES EBAF product (Loeb et al. 2009). However, zonal mean cloud fractions and cloud optical thicknesses simulated by CanAM4 differs from the CERES cloud properties [SRBAVG2 data product, Wielicki et al. (1996)] with CanAM4 simulating less clouds equatorward of 30°S while cloud optical thicknesses are too large at all latitudes (Fig. 2).

Fig. 2.

Zonal means for July of all-sky and clear-sky TOA albedo, all-sky, and clear-sky OLR (W m−2) at the TOA, cloud fraction, and cloud optical thickness simulated by the CanAM4 (dashed black line) and from CERES observations (solid black line). The dark gray lines are monthly means reconstructed using output from CanAM4 sampled as described in section 4.

Fig. 2.

Zonal means for July of all-sky and clear-sky TOA albedo, all-sky, and clear-sky OLR (W m−2) at the TOA, cloud fraction, and cloud optical thickness simulated by the CanAM4 (dashed black line) and from CERES observations (solid black line). The dark gray lines are monthly means reconstructed using output from CanAM4 sampled as described in section 4.

Zonal means were also computed using fields sampled only along the orbit to check for systematic differences relative to uniform, global sampling throughout the day (Fig. 2). Sampling along the orbit causes the all-sky outgoing longwave fluxes between the equator and 60°N to be systematically larger; likely due to incomplete sampling of the diurnal cycle of clouds and atmospheric state. The albedo is affected by both the orbital sampling and a different sampling of the solar zenith angle, being once every model hour in the CanAM4 active radiative transfer calculations instead of the much finer time resolution for the diagnostics calculations [Eq. (10)].

6. Results: CanAM4 versus CERES

Analysis in this section is limited to the region located between 60°S and 60°N to avoid snow and ice covered regions, that is, Greenland and sea ice at northern latitudes, where the CERES cloud retrievals may be less robust. To provide context, July mean all-sky TOA albedo, OLR, and TOA cloud forcing are presented in Table 1. As one could expect, the CONTROL simulation is in good agreement with the CERES observations, while the AUT×10 simulation had the desired effect of reducing the albedo and shortwave cloud forcing.

Table 1.

July (2001–05) and global-mean top of atmosphere albedo, OLR, and CREs simulated by two CanAM4 simulations (CONTROL and AUT×10) and observations from the CERES EBAF (Loeb et al. 2009).

July (2001–05) and global-mean top of atmosphere albedo, OLR, and CREs simulated by two CanAM4 simulations (CONTROL and AUT×10) and observations from the CERES EBAF (Loeb et al. 2009).
July (2001–05) and global-mean top of atmosphere albedo, OLR, and CREs simulated by two CanAM4 simulations (CONTROL and AUT×10) and observations from the CERES EBAF (Loeb et al. 2009).

a. Near-global mean July climatology

The July means are shown in Fig. 3 for high, middle, and low clouds while the bottom row (“tot”) shows the quantities averaged over all clouds. With the exception of cloud fraction, which includes times and locations with zero cloud fraction, only grid boxes with cloud fractions greater than 5% were used to compute the cloud-fraction-weighted means to ensure that diagnostic cloud properties and radiative fluxes were computed using a reasonable number of cloudy subcolumns.

Fig. 3.

Cloud-mean solar albedo and OLR (W m−2) at the TOA, cloud optical thickness τ, inhomogeneity factor ν, and cloud fraction for high, middle, low, and all clouds (tot) cloud tops exposed to space as diagnosed from CERES observations (black horizontal line) and two CanAM4 simulations. Results between 60°S and 60°N for each July between 2001 and 2005 and only grid boxes with cloud fraction greater than 5% were used to compute the means for cloud albedo, OLR, τ, and ν, while all grid boxes with cloud fraction greater and equal to zero were used to compute the cloud fraction.

Fig. 3.

Cloud-mean solar albedo and OLR (W m−2) at the TOA, cloud optical thickness τ, inhomogeneity factor ν, and cloud fraction for high, middle, low, and all clouds (tot) cloud tops exposed to space as diagnosed from CERES observations (black horizontal line) and two CanAM4 simulations. Results between 60°S and 60°N for each July between 2001 and 2005 and only grid boxes with cloud fraction greater than 5% were used to compute the means for cloud albedo, OLR, τ, and ν, while all grid boxes with cloud fraction greater and equal to zero were used to compute the cloud fraction.

Focusing first on cloud-mean albedo (Fig. 3), we find that CanAM4 has significant positive bias for low and midlevel clouds relative to the CERES observations, which are reduced in the AUT×10 simulation. The cloud albedo biases can be linked to the cloud optical thickness biases, which are too large by almost a factor of 2 for the CONTROL simulation and in better agreement with observations for the AUT×10 simulation. The bias in the CONTROL simulation is consistent with comparisons of CanAM4 cloud liquid water path with microwave radiometers retrievals (O’Dell et al. 2008) and is consistent with biases in other GCMs (Stephens 2010). High cloud albedo for the CONTROL simulation is in surprisingly good agreement with CERES, even though the cloud optical thickness is slightly too large. The high cloud albedo and optical thickness decrease for the AUT×10 simulation, suggesting that these quantities are being affected by underlying clouds at lower altitudes, although further quantification requires more information about the underlying clouds. The OLR biases are similar for both simulations but the source of the biases are difficult to pinpoint since they can be affected by biases in the atmospheric state (temperature and water vapor) as well as the cloud properties.

The horizontal variability of cloud optical thickness, represented by the parameter ν, tends to be fairly inhomogeneous (smaller values imply more inhomogeneous clouds) for all clouds, with similar magnitudes in both the observations and CanAM4. The horizontal inhomogeneity of clouds is an important parameter affecting cloud albedo and OLR (Barker 1996; Fu et al. 2000; Barker and Räisänen 2005) and should be considered along with mean cloud optical thickness when evaluating cloud radiative effects.

The cloud-mean biases (Fig. 3) suggest that there should be significant biases in the all-sky fluxes, which is at odds with the good agreement between the CONTROL simulation and observations (Table 1). The reason for the good agreement in the all-sky fluxes are in part due to good agreement for the clear-sky fluxes and in part due to biases in the simulated cloud fraction, which controls the contribution of the cloud-mean results to the all-sky cloud fluxes, Eqs. (3) and (5). The product of cloud-mean fluxes and cloud fraction shows that it is the low and high clouds (Fig. 4) that have the largest contributions to the all-sky albedo in CanAM4 with midlevel clouds contributing least due to their small cloud fractions. The high clouds in CanAM4 contribute too much to the all-sky albedo owing to the simulation of too large high cloud fractions, while for low clouds, the contribution to the all-sky albedo in the CONTROL simulation is closer to observed owing to CanAM4 simulating too small low cloud fraction. In the AUT×10 simulation the low cloud contribution is smaller than observed due to the combination of cloud-mean albedo that is closer to observations combined with a low cloud fraction that is even smaller than observations and the CONTROL simulation.

Fig. 4.

Mean product of cloud-mean solar albedo and cloud fraction for high, middle, low, and all clouds (tot) cloud tops exposed to space as diagnosed from CERES observations (black horizontal line) and two CanAM4 simulations. Results between 60°S and 60°N for each July between 2001 and 2005 were used to compute the means.

Fig. 4.

Mean product of cloud-mean solar albedo and cloud fraction for high, middle, low, and all clouds (tot) cloud tops exposed to space as diagnosed from CERES observations (black horizontal line) and two CanAM4 simulations. Results between 60°S and 60°N for each July between 2001 and 2005 were used to compute the means.

b. July spatial and temporal climatology

Although the near-global averages presented above already show significant biases, they do not show spatial and temporal biases in clouds, so zonal (Fig. 5) and latitude–longitude plots (Fig. 6) are shown to illustrate biases in the time-mean spatial structure of CanAM4 for cloud properties in the three pressure ranges. For the most part, zonal biases in the radiative fluxes and cloud properties tend to be consistently too large or consistently too small at most latitudes in the CONTROL simulation while the magnitude and sign of differences between AUT×10 and CONTROL varies with latitude. For example, low cloud fraction is reduced between the CONTROL and AUT×10 simulations fairly consistently with latitude, but the low cloud albedo is reduced more poleward of 20°N, suggesting that changing the autoconversion rate has a larger effect at these latitudes.

Fig. 5.

Zonal means of cloud-mean solar albedo and OLR (W m−2) at the TOA, cloud optical thickness τ, inhomogeneity factor ν, and cloud fraction for high, middle, low, and all clouds (tot) cloud tops exposed to space from CERES and diagnosed from two CanAM4 simulations. Results from each July between 2001 and 2005 were used and only grid boxes with cloud fraction greater than 5% were used to compute the means for cloud albedo, while all grid boxes with cloud fraction greater and equal to zero were used to compute the cloud fraction. Observations from CERES (black lines), results from the CONTROL simulation (red lines), and results from the AUT×10 simulation (blue lines).

Fig. 5.

Zonal means of cloud-mean solar albedo and OLR (W m−2) at the TOA, cloud optical thickness τ, inhomogeneity factor ν, and cloud fraction for high, middle, low, and all clouds (tot) cloud tops exposed to space from CERES and diagnosed from two CanAM4 simulations. Results from each July between 2001 and 2005 were used and only grid boxes with cloud fraction greater than 5% were used to compute the means for cloud albedo, while all grid boxes with cloud fraction greater and equal to zero were used to compute the cloud fraction. Observations from CERES (black lines), results from the CONTROL simulation (red lines), and results from the AUT×10 simulation (blue lines).

Fig. 6.

Cloud-mean albedo and cloud fraction for high and low clouds using results from each July between 2001 and 2005. Only grid boxes with cloud fraction greater than 5% were used to compute the means for cloud albedo while all grid boxes with cloud fraction greater and equal to zero were used to compute the cloud fraction.

Fig. 6.

Cloud-mean albedo and cloud fraction for high and low clouds using results from each July between 2001 and 2005. Only grid boxes with cloud fraction greater than 5% were used to compute the means for cloud albedo while all grid boxes with cloud fraction greater and equal to zero were used to compute the cloud fraction.

July-mean high and low cloud fraction simulated by CanAM4 have a structure that is similar to the observed, as does the high cloud albedo, while the simulated low cloud albedo over oceans is notably larger than that observed, especially over oceans (Fig. 6). In regions where both high and low cloud albedo, along with low cloud fraction, are reduced between the CONTROL and AUT×10 simulations, for example, the Atlantic and eastern Pacific north of the equator, it suggests that the high cloud optical thickness and albedo is being, at least partially, controlled by low clouds. For example, for low clouds exposed to space in these regions the cloud fraction and albedo (optical thickness) are reduced between the CONTROL and AUT×10 experiments as is the high cloud albedo while the high cloud fraction is effectively unchanged. This suggests that the reduction of the low cloud fraction and optical thickness observable from space occurs, to some degree, beneath the high clouds. The reduced optical thickness of low clouds underlying high clouds reduces the optical thickness and albedo, while the high cloud albedo can be further reduced due to the reduction of underlying low cloud fraction, which exposes more of the high cloud to the dark ocean surface.

Although the time-mean distribution of cloud show spatial biases, they can hide potential biases in how time means are realized, so to further examine the near-global means in Fig. 3, 2D histograms of cloud albedo and cloud fraction are constructed using daily means (Fig. 7). These two quantities were selected since they are the most important to the all-sky radiative budget, Eq. (3), and have the largest biases in CanAM4, although histograms can be constructed using other variables. Values in each bin of the histogram is computed by summing the contributing gridbox area and then dividing it by the sum over all histogram bins.

Fig. 7.

2D histograms of daily mean all-sky and cloud-mean albedo at the TOA and cloud fraction for grid points between 60°S and 60°N for each July between 2001 and 2005.

Fig. 7.

2D histograms of daily mean all-sky and cloud-mean albedo at the TOA and cloud fraction for grid points between 60°S and 60°N for each July between 2001 and 2005.

The 2D histogram for the all-sky albedo and total cloud fraction using the CERES dataset (top-left plot in Fig. 7) is similar to that in Webb et al. (2001), which was constructed histograms using daily-mean ERBE albedo and ISCCP cloud fraction from July 1998. By using the simulated and observed cloud fractions and albedo we can see that both CanAM4 simulations tend to more frequently simulate small (<0.2) and large (>0.9) cloud fractions for low, middle, and high clouds that then contribute to the all-sky histograms. For low clouds, the cloud albedo bias in the CONTROL simulation is caused equally by clouds with smaller cloud fractions (<0.2) and larger (nearly double) the observed albedo and too frequent large cloud fractions (>0.9). The difference between the AUT×10 and CONTROL histograms show that the reduction in the near-global mean cloud albedo is due to a reduction in the cloud-mean albedo and an increased occurrence of small cloud fractions. This provides a useful indicator of the mechanisms in the model parameterizations that causes changes in the TOA radiative fluxes.

7. Conclusions

A study has been presented that evaluates GCM cloud optical properties and associated radiative fluxes using passive satellite data and inferences drawn from them. In essence, these quantities are sorted according to their associated clouds whose tops are exposed to space in predefined pressure ranges. The rationale behind this method is that cloud tops are those portions of clouds that are readily presented to satellite sensors but what lies beneath them is usually summarized integrated quantities like total optical depth. This level of information, and segregating cloud properties according to cloud-top altitude, puts a significant constraint on the nature of cloud that is not directly seen from satellites. In a GCM subgrid-scale clouds can be easily sorted and analyzed accordingly, and comparison to similarly sorted satellite data should represent a demanding assessment of the structure of GCM clouds. Agreement between a GCM and observations using this approach increases confidence that the GCM is producing accurate radiative budgets for the correct underlying vertical and horizontal distributions of cloud properties. It also increases confidence that cloud properties supplied to a GCM’s radiative transfer model are being used accurately and there are not biases in the radiative transfer model itself—an issue that would be difficult to infer solely by evaluating cloud properties.

By way of example, using observations from CERES and MODIS and diagnosed fields from a developmental version of the CCCma CanAM4, it was illustrated that this methodology has the ability to diagnose underlying biases that might go undetected if only all-sky mean values are assessed—even within a GCM that has a reasonable monthly mean TOA radiation budget. For example, it is illustrated that this version of CanAM4 reasonably well simulates the horizontal variability of cloud optical thickness and cloud fraction, in total, and for the three pressure ranges. However, the cloud albedo simulated by CanAM4 is greater than observations, with most of this being caused by overly large albedos simulated by low clouds, and to a lesser degree, middle clouds. This would be difficult to infer from all-sky albedo since it is partly compensated by cloud fractions that are too small. The bias in the low and middle cloud albedos can be attributed directly to these clouds simulating cloud optical thicknesses that are larger than observed. It is also shown that, while CanAM4 is capable of producing 2D histograms of the all-sky albedo and total cloud fraction that are similar to observed, it does not reproduce well the 2D histograms for low, middle, and high clouds. This indicates that CanAM4 realizes time-mean cloud albedos and cloud fractions in a manner different than observations, which can be used to evaluate future improvements to physical processes in the model.

Since this study only makes use of observations of clouds and radiative fluxes taken by passive instruments, it is limited to evaluating the fidelity of vertically integrated quantities that can be viewed from space. However, agreement for these quantities over M atmospheric layers also places constraints on the gridbox-mean vertical profiles of cloud properties, for both clouds exposed to space and not exposed to space, as well as the gridbox-mean vertical profile of radiative heating rates. How much of a constraint the diagnostic presented in this paper provides about the gridbox-mean cloud and radiative heating profiles is a topic for further research.

While a version of CanAM4 was used here, this methodology can be applied to any GCM capable of diagnosing subgrid-scale cloud-top radiative fluxes and cloud properties—something that can be done easily for GCMs already using McICA and satellite simulators. To aid application of this diagnostic in GCMs, a newly processed CERES product, similar to that employed in this study, will be made publicly available from the NASA Langley Atmospheric Sciences Data Center.

Acknowledgments

This study was supported by the Cloud Aerosol Feedbacks and Climate grant funded through the Canadian Foundation for Climate and Atmospheric Sciences. We thank Alejandro Bodas-Salcedo (Met Office) for providing the code for the orbit simulator and Michael Lazare and Larry Solheim (CCCma) for technical help with the CCCma CanAM4. We would also like to thank the anonymous reviewers for their constructive suggestions.

REFERENCES

REFERENCES
Barker
,
H. W.
,
1996
:
A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part I: Methodology and homogeneous biases
.
J. Atmos. Sci.
,
53
,
2289
2303
.
Barker
,
H. W.
,
2008
:
Overlap of fractional cloud for radiation calculations in GCMs: A global analysis using CloudSat and CALIPSO data
.
J. Geophys. Res.
,
113
,
D00A01
,
doi:10.1029/2007JD009677
.
Barker
,
H. W.
, and
P.
Räisänen
,
2005
:
Radiative sensitivities for cloud structural properties that are unresolved by conventional GCMs
.
Quart. J. Roy. Meteor. Soc.
,
131
,
3103
3122
,
doi:10.1256/qj.04.174
.
Barker
,
H. W.
,
B. A.
Wielicki
, and
P.
Lindsay
,
1996
:
A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part II: Validation using satellite data
.
J. Atmos. Sci.
,
53
,
2304
2316
.
Barker
,
H. W.
,
J.-J.
Morcrette
, and
G. D.
Alexander
,
1998
:
Broadband solar fluxes and heating rates for atmospheres with 3D broken clouds
.
Quart. J. Roy. Meteor. Soc.
,
124
,
1245
1271
.
Barker
,
H. W.
, and
Coauthors
,
2003
:
Assessing 1D atmospheric solar radiative transfer models: Interpretation and handling of unresolved clouds
.
J. Climate
,
16
,
2676
2699
.
Barker
,
H. W.
,
J. N. S.
Cole
,
J.-J.
Morcrette
,
R.
Pincus
,
P.
Räisänen
,
K.
von Salzen
, and
P. A.
Vaillancourt
,
2008
:
The Monte Carlo independent column approximation: An assessment using several global atmospheric models
.
Quart. J. Roy. Meteor. Soc.
,
134
,
1463
1478
.
Bony
,
S.
, and
Coauthors
,
2006
:
How well do we understand and evaluate climate change feedback processes?
J. Climate
,
19
,
3445
3482
.
Chaboureau
,
J.-P.
, and
P.
Bechtold
,
2002
:
Simple cloud parameterization derived from cloud resolving model data: Diagnostic and prognostic applications
.
J. Atmos. Sci.
,
59
,
2362
2372
.
Charlock
,
T. P.
, and
V.
Ramanathan
,
1985
:
The albedo field and cloud radiative forcing produced by a general circulation model with internally generated cloud optics
.
J. Atmos. Sci.
,
42
,
1408
1429
.
Chen
,
T.
,
W. B.
Rossow
, and
Y.
Zhang
,
2000
:
Radiative effects of cloud-type variations
.
J. Climate
,
13
,
264
286
.
Fu
,
Q.
,
B.
Carlin
, and
G.
Mace
,
2000
:
Cirrus horizontal inhomogeneity and OLR bias
.
Geophys. Res. Lett.
,
27
,
3341
3344
.
Greenwood
,
J. A.
, and
D.
Durand
,
1960
:
Aids for fitting the gamma distribution by maximum likelihood
.
Technometrics
,
2
,
55
65
.
Hartmann
,
D. L.
,
M. E.
Ockert-Bell
, and
M. L.
Michelsen
,
1992
:
The effect of cloud type on earth’s energy balance: Global analysis
.
J. Climate
,
5
,
1281
1304
.
Hogan
,
R. J.
, and
A. J.
Illingworth
,
2000
:
Deriving cloud overlap statistics from radar
.
Quart. J. Roy. Meteor. Soc.
,
126
(
569A
),
2903
2909
.
Hoots
,
F. R.
, and
R. L.
Roehrich
,
1980
:
Models for propagation of NORAD element sets
.
Tech. Rep., Defense Documentation Center, Space Track Rep. 3, 100 pp
.
Klein
,
S. A.
, and
C.
Jakob
,
1999
:
Validation and sensistivities of frontal clouds simulated by the ECMWF model
.
Mon. Wea. Rev.
,
127
,
2514
2531
.
Li
,
J.
, and
H. W.
Barker
,
2002
:
Accounting for unresolved clouds in a 1D infrared radiative transfer model. Part II: Horizontal variability of cloud water path
.
J. Atmos. Sci.
,
59
,
3321
3339
.
Li
,
J.
, and
H. W.
Barker
,
2005
:
A radiation algorigthm with correlated-k distribution. Part I: Local thermal equilibrium
.
J. Atmos. Sci.
,
62
,
286
309
.
Li
,
J.
,
P.
Dobbie
,
S.
Räisänen
, and
Q.
Min
,
2005
:
Accounting for unresolved clouds in a 1-D solar radiative-transfer model
.
Quart. J. Roy. Meteor. Soc.
,
131
,
1607
1629
,
doi:10.1256/qj.04.31
.
Loeb
,
N. G.
,
K. J.
Priestley
,
D. P.
Kratz
,
E. B.
Geier
,
R. N.
Green
,
B.
Wielicki
,
P.
Hinton
, and
S.
Nolan
,
2001
:
Determination of unfiltered radiances from the clouds and the earths radiant energy system instrument
.
J. Appl. Meteor.
,
40
,
822
835
.
Loeb
,
N. G.
,
N.
Manalo-Smith
,
S.
Kato
,
W. F.
Miller
,
S. K.
Gupta
,
P.
Minnis
, and
B. A.
Wielicki
,
2003
:
Angular distribution models for top-of-atmosphere radiative flux estimation from the Clouds and the Earth’s Radiant Energy System instrument on the Tropical Rainfall Measuring Mission satellite. Part I: Methodology
.
J. Appl. Meteor.
,
42
,
240
265
.
Loeb
,
N. G.
,
S.
Kato
,
K.
Loukachine
, and
N.
Manalo-Smith
,
2005
:
Angular distribution models for top-of-atmosphere radiative flux estimation from the Clouds and the Earth’s Radiant Energy System instrument on the Terra satellite. Part I: Methodology
.
J. Atmos. Oceanic Technol.
,
22
,
338
351
.
Loeb
,
N. G.
,
S.
Kato
,
K.
Loukachine
,
N.
Manalo-Smith
, and
D. R.
Doelling
,
2007
:
Angular distribution models for top-of-atmosphere radiative flux estimation from the Clouds and the Earth’s Radiant Energy System instrument on the Terra satellite. Part II: Validation
.
J. Atmos. Oceanic Technol.
,
24
,
564
584
.
Loeb
,
N. G.
,
B.
Wielicki
,
D.
Doelling
,
G.
Smith
,
D.
Keyes
,
S.
Kato
,
N.
Manalo-Smith
, and
T.
Wong
,
2009
:
Toward optimal closure of the earth’s top-of-atmosphere radiation budget
.
J. Climate
,
22
,
748
766
.
Mace
,
G. G.
,
Q.
Zhang
,
M.
Vaughan
,
R.
Marchand
,
G.
Stephens
,
C.
Trepte
, and
D.
Winker
,
2009
:
A description of hydrometeor layer occurrence statistics derived from the first year of merged Cloudsat and CALIPSO data
.
J. Geophys. Res.
,
114
,
D00A26
,
doi:10.1029/2007JD009755
.
Minnis
,
P.
,
D. F.
Young
,
S.
Sun-Mack
,
P. W.
Heck
,
D. R.
Doelling
, and
Q.
Trepte
,
2003
:
CERES cloud property retrievals from imagers on TRMM, Terra, and Aqua
.
Proc. SPIE 10th Int. Symp. on Remote Sensing: Conf. on Remote Sensing of Clouds and the Atmosphere VII, Barcelona, Spain, SPIE, 37–48
.
Ockert-Bell
,
M. E.
, and
D. L.
Hartmann
,
1992
:
The effect of cloud type on earth’s energy balance: Results for selected regions
.
J. Climate
,
5
,
1157
1171
.
O’Dell
,
C. W.
,
F.
Wentz
, and
R.
Bennartz
,
2008
:
Cloud liquid water path from satellite-based passive microwave observations: A new climatology over the global oceans
.
J. Climate
,
21
,
1721
1739
.
Pincus
,
R.
,
H. W.
Barker
, and
J.-J.
Morcrette
,
2003
:
A fast, flexible, approximate technique for computing radiative transfer in inhomogeneous cloud fields
.
J. Geophys. Res.
,
108
,
4376
,
doi:10.1209/2002JD003322
.
Pincus
,
R.
,
C.
Hannay
,
S. A.
Klein
,
K.-M.
Xu
, and
R.
Hemler
,
2005
:
Overlap assumptions for assumed probability distribution function cloud schemes in large-scale models
.
J. Geophys. Res.
,
110
,
D15S09
,
doi:10.1029/2004JD005100
.
Pincus
,
R.
,
R.
Hemler
, and
S. A.
Klein
,
2006
:
Using stochastically generated subcolumns to represent cloud structure in a large-scale model
.
Mon. Wea. Rev.
,
134
,
3644
3656
.
Räisänen
,
P.
, and
H. W.
Barker
,
2004
:
Evaluation and optimization of sampling errors for the Monte Carlo Independent Column Approximation
.
Quart. J. Roy. Meteor. Soc.
,
130
,
2069
2085
.
Räisänen
,
P.
,
H. W.
Barker
,
M. F.
Khairoutdinov
,
J.
Li
, and
D. A.
Randall
,
2004
:
Stochastic generation of subgrid-scale cloudy columns for large-scale models
.
Quart. J. Roy. Meteor. Soc.
,
130
,
2047
2068
.
Randall
,
D. A.
,
M. F.
Khairoutdinov
,
A.
Arakawa
, and
W. W.
Grabowski
,
2003
:
Breaking the cloud-parameterization deadlock
.
Bull. Amer. Meteor. Soc.
,
84
,
1547
1564
.
Remer
,
L. A.
, and
Coauthors
,
2005
:
The MODIS aerosol algorithm, products, and validation
.
J. Atmos. Sci.
,
62
,
947
973
.
Smith
,
G. L.
,
1994
:
Effects of time response on the point spread function of a scanning radiometer
.
Appl. Opt.
,
33
,
7031
7037
.
Solomon
,
S.
,
D.
Qin
,
M.
Manning
,
M.
Marquis
,
K.
Averyt
,
M. M. B.
Tignor
,
H. L.
Miller
Jr.
, and
Z.
Chen
,
2007
:
Climate Change 2007: The Physical Science Basis
.
Cambridge University Press, 996 pp
.
Stephens
,
G. L.
,
2010
:
Is there a missing low cloud feedback in current climate models?
GEWEX News, No. 20, International GEWEX Project Office, Silver Spring, MD, 5–7
.
Stephens
,
G. L.
,
P. M.
Gabriel
, and
S.-C.
Tsay
,
1991
:
Statistical radiative transport in one-dimensional media and its application to the terrestrial atmosphere
.
Transp. Theory Stat. Phys.
,
20
,
139
175
.
Taylor
,
K. E.
,
D.
Williamson
, and
F.
Zwiers
,
2000
:
The sea surface temperature and sea-ice concentration boundary conditions for AMIP II simulations
.
Tech. Rep., PCMDI Rep. 60, Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, Livermore, CA, 24 pp
.
von Salzen
,
K.
,
N. A.
McFarlane
, and
M.
Lazare
,
2005
:
The role of shallow convection in the water and energy cycles of the atmosphere
.
Climate Dyn.
,
25
,
671
688
,
doi:10.1007/s00382-005-0051-2
.
Webb
,
M.
,
C.
Senior
,
S.
Bony
, and
J.-J.
Morcrette
,
2001
:
Combining ERBE and ISCCP data to assess clouds in the Hadley Centre, ECMWF and LMD atmospheric climate models
.
Climate Dyn.
,
17
,
905
922
.
Wielicki
,
B. A.
,
B. R.
Barkstrom
,
E. F.
Harrison
,
R. B.
Lee
III
,
G. L.
Smith
, and
J. E.
Cooper
,
1996
:
Clouds and the Earth’s Radiant Energy System (CERES): An earth observing system experiment
.
Bull. Amer. Meteor. Soc.
,
77
,
853
868
.
Wyant
,
M. C.
,
C. S.
Bretherton
,
J. T.
Bacmeister
,
J. T.
Kiehl
,
I. M.
Held
,
M.
Zhao
,
S. A.
Klein
, and
B. J.
Soden
,
2006
:
A comparison of low-latitude cloud properties and their response to climate change in three AGCMs sorted into regimes using mid-tropospheric vertical velocity
.
Climate Dyn.
,
27
,
261
279
,
doi:10.1007/s00382-006-0138-4
.
Zelinka
,
M. D.
, and
D. L.
Hartmann
,
2010
:
Why is longwave cloud feedback positive?
J. Geophys. Res.
,
115
,
D16117
,
doi:10.1029/2010JD013817
.
Zhang
,
M. H.
, and
Coauthors
,
2005
:
Comparing clouds and their seasonal variations in 10 atmospheric general ciculation models with satellite measurements
.
J. Geophys. Res.
,
110
,
D15S02
,
doi:10.1029/2004JD005021
.