1. Introduction
For many years, the representation of clouds has been identified as one of the largest uncertainties in the simulation of climate change (e.g., Houghton et al. 2001). This fact suggests that the roles of clouds in the climate system are very complicated and we have not made rapid progress in understanding their roles. The changes in net radiation due to changes in cloud properties such as cloud fraction, cloud height, and liquid and ice water paths are collectively referred to as cloud feedbacks. To accurately represent the cloud feedbacks in the climate system, we need to improve our understanding of two elements of the feedbacks: first, the cloud properties that are associated with a given atmospheric state, and second, the divergence of radiative energy fluxes resulting from these cloud properties. This divergence in turn heats or cools the atmosphere. With improved representations of these aspects of cloud feedback, the change in net cloud radiative forcing (CRF) in a warmer climate can then be quantified. CRF is defined as the difference in radiative fluxes between the whole sky (all sky) and clear skies (Ramanathan et al. 1989).
Cloud feedback processes can be studied in several ways. Detailed reviews of these processes can be found in Curry et al. (1996), Soden et al. (2004), Stephens (2005), and Bony et al. (2006). Traditionally, cloud feedbacks have been separated into those that are due to changes in cloud physical properties, such as cloud optical thickness, and those that are due to changes in the geographic distributions of cloud occurrence resulting from changes in external forcings (see, e.g., Wetherald and Manabe 1980, 1988; Somerville and Remer 1984). Recently, cloud feedbacks have been decomposed into those due to changes in the frequency of occurrence of cloud regimes and those due to changes in cloud properties within those regimes (e.g., Lau and Crane 1995, 1997; Tselioudis et al. 2000; Jakob et al. 2005; Rossow et al. 2005; Tselioudis and Rossow 2006; Xu et al. 2005, 2007). Changes in CRF (ΔCRF) can also be separated into dynamic and thermodynamic components (Bony et al. 2004). In Bony et al. (2004), the dynamic contribution to ΔCRF results from changes in the probability density function (PDF) of monthly averaged 500-hPa isobaric vertical velocity (ω500) without any changes in how CRF varies with respect to ω500. Conversely, the thermodynamic contribution to ΔCRF results from changes in how CRF varies with respect to ω500 without changes in the PDF of ω500 itself. Bony et al. (2004) found that the regional CRF response to the sea surface temperature (SST) change correlated strongly with the dynamic response, while the change in CRF averaged over the tropics was primarily due to changes in thermodynamic effects.
Clement and Soden (2005) used general circulation models (GCMs) to examine the sensitivity of simulated CRF to an increase in the strength of the Hadley circulation. The overall CRF did not change much when averaged over the tropics. However, the increased strength of the ascending branch of the Hadley circulation caused the magnitude of the CRF to increase there. Lau et al. (1997) found that the observed sensitivity of convection to SST is greatly reduced when the dependence of convection on the divergence at 200 mb is removed. Xu et al. (2007) examined statistical characteristics of a large ensemble of tropical convective cloud systems as a function of SST for systems that were observed over the Pacific Ocean during the peak and dissipative phases of the 1997/98 El Niño. They found that cloud macrophysical properties such as effective cloud height, cloud-top temperature, and outgoing longwave radiation (OLR) are dependent upon the SST variation, but ice water path, cloud optical thickness, and the top-of-the-atmosphere albedo are not. The dependence of cloud macrophysical properties on SST is actually a manifestation of the differences in the large-scale dynamics. The observational studies by Lau et al. (1997) and Xu et al. (2007) provide motivation for this study, which attempts to isolate the dependence of cloud properties on changes in large-scale dynamics from the dependence of cloud properties on changes in SST.
GCMs resolve large-scale atmospheric motions that modulate the cloud feedback. In GCMs, subgrid-scale cloud processes are parameterized crudely, which is the main obstacle to improving the understanding of the cloud feedback problem (Randall et al. 2003; Bony et al. 2006). Cloud-resolving models (CRMs), on the other hand, can resolve cloud-scale and mesoscale dynamics within a region of one or more grid cells of a GCM (e.g., Krueger 1988; Tao and Simpson 1989). These models are useful tools for studying cloud processes. For example, CRM simulations were performed to examine the behavior of convection that reached radiative–convective equilibrium (RCE) states (e.g., Sui et al. 1994; Robe and Emanuel 1996; Tao et al. 1999; Tompkins and Craig 1999; Xu and Randall 1999; Shie et al. 2003) in the presence/absence of imposed large-scale advective forcings. The effects of changing the SST and/or advective forcings on the RCE states were also examined (Lau et al. 1994; Wu and Moncrieff 1999, hereafter WM99; Xu and Randall 1999; Shie et al. 2003). When the large-scale advective forcing is not imposed in CRMs, the resulting RCE states are somewhat analogous to the averages over both the ascending and descending branches of the Hadley circulation. However, the domain size of CRMs used in these RCE studies is only a few hundred kilometers in each horizontal direction. When a large-scale advective forcing is imposed, an analog to the ascending branch of the Hadley circulation seems rather obvious. One may also question this analog because a long-term averaged forcing profile is typically used in such CRM simulations. The cloud response to this long-term average forcing is not necessarily equivalent to the average response to individually varying forcings. This fundamental difference was not addressed at all by prior studies.
The approach adopted in this study complements the prior studies listed above, but emphasizes the importance of individually varying forcings. First, sets of simulations of observed cloud systems over many tropical locations are performed on time scales that are roughly comparable to the lifetimes of the systems. Second, individual simulations are forced with advective tendencies, but these tendencies are matched to the specific time and place that the cloud system was observed. Third, the individual simulations are initialized with thermodynamic soundings that are matched to the time and location of the cloud system. The relatively short-term nature of the simulations used in this study prevents the CRM equivalent of “climate drift” from impacting the results because imperfect physical parameterizations in CRMs may cause drifts of the equilibrium state in long-term integrations. For example, Sui et al. (1994), Grabowski et al. (1996), and Xu and Randall (1999) obtained three different equilibrium states for an identical large-scale forcing profile using three different CRMs. Thus, the short-term integrations can be a strength of the experiment design. Finally, the analyses for each set of simulations are performed in terms of the frequency distributions of cloud properties. This method provides insight into how the shape of the frequency distribution changes beyond that which can be gained by observing changes in a single mean value and standard deviation for each property.
Four sets of sensitivity experiments, in addition to the control set described above, are performed with larger/smaller magnitudes of advective cooling and moistening tendencies or with higher/lower SSTs. The experiment design bears some resemblance to that of the idealized sensitivity experiments for CRMs suggested in Bony et al. (2004), except that a large set of tropical convective systems in the ascending branch of the Hadley circulation is simulated. The goal of this study is to understand the relative roles of dynamic and thermodynamic forcings in determining the changes in the statistical distributions of cloud physical properties for a large ensemble of tropical convective systems. Separate statistical distributions will also be examined for clouds that are of the deep convective type [examined observationally by Xu et al. (2005, 2007)], as well as for other cloud types adjacent to deep convective ones, which have not yet been examined observationally. The distinction will be extensively explored in this study because there are many nonconvective and shallow convective clouds present even in the vicinity of the ascending branch of the Hadley circulation. A key question to be answered is whether the cloud properties of the overall cloud population have altered because of changes in the properties within either the deep convective or non–deep convective cloud population or because of changes in the frequency of occurrence of deep convective clouds within the overall cloud population as the thermodynamic and dynamic forcings are modified. The effects of changes in total cloud area are important only for domain-averaged mean quantities (see section 7); they are not significant for the frequency distributions of column cloud properties that will be examined extensively in this study.
The paper is organized as follows: the description of the model, the control simulations, and the sensitivity experiments are given in section 2. Subsets of the control simulations are analyzed in section 3. The results for set-averaged cloud properties are given in section 4. The PDFs of cloud properties from experiments where the forcing and SSTs are changed are described in sections 5 and 6, respectively. Domain-averaged mean CRFs are discussed in section 7. A summary and conclusions are given in section 8.
2. Numerical simulations
The CRM used in this study is the Advanced Regional Prediction System/Langley Research Center (ARPS/LaRC) model. This model is based on ARPS (Xue et al. 2000, 2001), and is identical to the “K95” version used in Eitzen and Xu (2005, hereafter EX05) except for minor changes in the formula for saturation vapor pressure. The aim of EX05 was to compare the PDFs of cloud properties produced by two versions of the CRM with different microphysics parameterizations to the corresponding PDFs that were observed. The K95 version of the model was found to produce PDFs that were more realistic than the original version. The version of the model used in this paper employs the radiative transfer parameterization of Fu and Liou (1993) and the Lin et al. (1983) microphysics parameterization with the Tao et al. (1989) saturation adjustment scheme and the Krueger et al. (1995) modifications to selected ice-phase microphysical processes.
As with EX05, we are simulating 68 deep convective cloud objects diagnosed using the Single Scanner Footprint (SSF) data product from the Clouds and the Earth’s Radiant Energy System (CERES) instrument (Wielicki et al. 1996) on board the Tropical Rainfall Measuring Mission (TRMM) Earth Observing System satellite. This product provides observations of radiative fluxes at the top of the atmosphere and retrieves data about cloud properties on the scale of footprints that have an average area of about 100 km2. Deep convection is associated with clouds that have high tops and are optically thick. Because of this, and out of convenience, deep convective cloud objects are identified for contiguous regions of footprints that meet the following selection criteria: cloud optical depth greater than 10, cloud height greater than 10 km, and 100% cloud cover within each footprint. The cloud cover is obtained from higher-resolution (2 km) imager data. More details about the SSF data product and the cloud object analysis method are contained in Xu et al. (2005). Note that the cloud objects simulated here had observed effective diameters greater than 300 km and were identified over the tropical (25°S–25°N) Pacific Ocean in March 1998.
The control set of simulations in this paper is prescribed with advective heat and moisture tendencies as in EX05 but extends to pressures below 100 hPa. The extra cooling produced slightly more very high clouds, in better agreement with observations. These tendencies were derived from European Centre for Medium-Range Weather Forecasts (ECMWF) operational analyses, which are available on a 0.5625° × 0.5625° grid every 6 h. Because the tendency data were unavailable from the ECMWF for this time period, they were actually calculated by the dynamical core of the Colorado State University (CSU) GCM, as in EX05. The dynamical core of the CSU GCM was run for a single time step. For each of the 68 cloud objects, advective tendency profiles were calculated at the ECMWF analysis time that was closest to the satellite observation of that cloud object (denoted by tl), and at t0, which is 6 h before tl. These profiles were calculated by averaging over a rectangular area that uses enough ECMWF grid cells in the zonal and meridional directions to completely cover the observed cloud object. The tendencies at t0 were used in the simulations between 0 and 6 h, and a linear interpolation of the tendencies between those at t0 and t1 were used between 6 and 12 h. Finally, the tendencies at t1 were used from 12 to 24 h. The ECMWF analyses at t0 were used to provide the initial wind, temperature, and water vapor profiles used in each simulation. These profiles were calculated by averaging over the same rectangular area described above. The SSTs used in the simulations were averaged in a similar manner and represent 68 distinct values between 298.8 and 303.5 K. Note that 50 of these 68 SSTs are within 0.5 K of the median SST of 302.44 K.
The simulations were performed in 2D. A few 3D simulations were also performed, and they produced somewhat weaker convection than the corresponding 2D simulations, particularly in the upper troposphere. However, there were not sufficient computational resources to permit robust conclusions to be made about the 3D simulations. The initial fields are horizontally uniform (with no clouds), except for random, small-amplitude (<0.5 K) perturbations to the potential temperature field throughout the domain for initiating convection. A periodic domain that is 512 km wide with a horizontal grid spacing of 2 km was used.1 A domain size of 1024 km was used by Luo et al. (2007) for simulations of the same 68 cloud objects simulated in this study. According to Y. Luo (2007, personal communication), an additional set of simulations was performed with a 512-km-wide domain, with results that were statistically similar to those of the 1024-km simulations. The vertical domain was 25 km high and had an average vertical grid spacing of 500 m. The domain was stretched between the surface and an altitude of 5 km for finer resolution in the boundary layer. Each solar zenith angle and Coriolis parameter was fixed to the value corresponding to the time and/or location of the corresponding cloud object. The top 5 km of the model domain was a sponge layer to suppress wave reflection. Each simulation was run for 24 h, with a time step of 6 s. The model output was only analyzed for the last 6 h of each simulation, as the set-averaged precipitation rates, convectively available potential energy (CAPE), column temperature, and precipitable water were relatively steady for this time period for each set of simulations, as shown in Fig. 1. The surface sensible and latent heat fluxes were also stable over the last 6 h for each set of simulations (not shown).
To test the sensitivity of the simulated cloud systems to changes in the dynamic forcing, the prescribed advective tendencies used for each of the 68 simulations were increased or decreased by 50% from their standard values for the F+50% and F−50% sets of simulations, respectively. The set-averaged tendency profiles at t1 for each of the three sets of simulations are shown in Fig. 2. The maximum in the tropospheric cooling tendencies occurs at around 350 mb (Fig. 2a), while there are two maxima in the moistening tendencies (Fig. 2b). Note that while a 50% change in the advective tendencies seems large, it is roughly comparable to the differences among the vertical velocities produced by different numerical weather prediction model analyses of the tropical western Pacific region (see Fig. 8 of Jakob et al. 2005). The change in precipitation rates with forcing is less than 50% (Fig. 1a) because of the fact that surface fluxes and radiative cooling also contribute to precipitation [see Xu and Randall (1999) for column budget analyses].
A plausible analysis approach would be to split the control simulations into high and low dynamic forcing or high and low SST subsets, and thereby diagnose the effects of dynamic forcing and SST. Such an analysis will be briefly discussed in the following section, along with the reasons that this study will instead use sensitivity experiments for this diagnosis.
To test the sensitivity of the simulated cloud objects to changes in the thermodynamic forcing, the SST used for each of the 68 simulations was raised or lowered by 2 K from its observed value for the SST+2K and SST−2K sets of simulations, respectively. When a boundary condition such as SST is changed, the model atmosphere typically takes time to adjust to that change. Since this study is interested in relatively short-duration simulations of individual cloud systems rather than RCE simulations, the initial temperature and moisture profiles were also modified2 in a manner consistent with ECMWF analyses with respect to the set-average profiles, based on 431 cloud objects observed between January and August 1998 (Xu et al. 2007). These 431 cloud objects comprise a subset with SSTs of approximately 303.25 K and a subset with SSTs of approximately 301.25 K. The resulting temperature and water vapor difference profiles are shown in Fig. 3. These profiles were added to the control water vapor and temperature profiles for each of the SST+2K simulations, and subtracted from the control profiles for the SST−2K set of simulations.
3. Control subset analysis
The 68 control simulations can be analyzed in a number of ways. One way is to compare the results from the 34 simulations with SSTs above the median to those from the 34 simulations with SSTs below the median (hereafter, the high-SST and low-SST subsets, respectively). Another is to compare results from the 34 simulations with vertically integrated values of imposed total advective cooling (a measure of the forcing abbreviated here as FRC) greater than the median to those from the 34 simulations with values of advective cooling3 smaller than the median (hereafter, the high-FRC and low-FRC subsets, respectively). In this study, model columns that have cloud optical depths τ > 1.0 are defined as cloudy, and columns with τ ≤ 1.0 are defined as clear. The domain-averaged cloud fraction to be discussed later is defined in terms of this binary quantity. The distributions of cloud properties for all columns with τ > 1.0 produced by the high-SST and low-SST subsets will be compared to one another, and a similar comparison will be made between the high-FRC and low-FRC subsets. These are termed “all cloud” distributions in this study. The retrieved properties of clouds observed by passive satellite instruments with τ < 1.0 have a large degree of uncertainty (Mace et al. 2005). The smaller CRM column width (2 km) relative to the satellite footprint size (10 km) does not impact the discussion presented in this study because its primary goal is not to compare with observations [see EX05 and Luo et al. (2007) for further discussion].
a. SST comparison
As noted earlier, although the control simulations have a fairly wide range of SSTs, most of the SSTs are clustered around the median value of 302.44 K. Thus, it is not surprising that the arithmetic mean of the 34 SSTs above the median (302.78 K) is only 1.04 K higher than the mean of the SSTs that are below the median (301.74 K).
The PDFs of albedo, effective cloud height (defined at τ = 1.0 after integrating from the top of the atmosphere), and cloud ice and snow path are shown in Figs. 4a–c, respectively, for all clouds from the high-SST, control, and low-SST simulations. The high-SST subset tends to produce clouds that have lower albedos than those of the control set (Fig. 4a), while the opposite is true of the low-SST subset, which has a PDF of albedo that is strongly peaked near 0.70. The change in albedo between the clouds produced by the high-SST and control simulations is larger than the change in albedo seen between the control and SST+2K sets of simulations shown in section 6. This may result in part from the fact that the cosines of the solar zenith angles of the high-SST subset are higher than those of the control set (resulting in lower albedos for the same optical depth), while the opposite is true of the low-SST subset. The effective cloud heights produced by the high-SST subset tend to be higher than those of the control set and the low-SST subset (Fig. 4b) for clouds with heights between 9.5 and 14 km, although the distributions of effective cloud height are similar among the three sets of simulations for clouds outside of this range. This increase in effective cloud height with SST is qualitatively similar to that seen in both Tompkins and Craig (1999) and the SST sensitivity experiments (see section 6). The PDFs of cloud ice and snow path are very similar to one another among the three sets of simulations (Fig. 4c).
b. Advective forcing comparison
In Figs. 4d–f, respectively, the PDFs of albedo, effective cloud height, and cloud ice and snow path are shown for clouds produced by the high-FRC, control, and low-FRC simulations. The albedos of the clouds produced by the high-FRC subset are higher than those of the control set and low-FRC subset (Fig. 4d), which is qualitatively similar to the results shown in section 5. The effective cloud heights (Fig. 4e) do not change much with forcing, in contrast to the results of section 5, where it is shown that effective cloud height tends to increase with the magnitude of forcing. This contrast will be discussed further in section 3c. The distributions of cloud ice and snow path (Fig. 4f) show that more columns with cloud ice and snow paths greater than 500 g m−1 are produced by the high-FRC subset than by the control set and low-FRC subset. These results are roughly similar to those shown in section 5.
c. Difficulties with this analysis
There are a number of difficulties in interpreting the comparison results shown in this section. First, the cosines of the solar zenith angles used in the simulations are different between the subsets, for example, by an average of 0.06 between the high-SST and low-SST subsets. This difference can cause some differences in the distribution of albedo even if the distribution of cloud optical depths is unchanged (Figs. 4a,c). Second, the magnitudes of the advective tendencies associated with the high-SST subset are smaller than those of the low-SST subset, particularly from the surface to 350 hPa (not shown). The resulting differences in the distributions of cloud macrophysical properties such as effective cloud height between the high-SST and low-SST subsets are smaller than those that would occur for two sets of simulations with identical advective forcings. Xu et al. (2007) also found that there were systematic changes in the distributions of observed cloud macrophysical properties and the matched vertical motion fields for deep convective cloud objects with SST. Third, the average SST of the high-FRC subset (302.2 K) is fairly close to that of the low-FRC subset (302.3 K). However, the distributions of these two sets of SSTs are quite different from one another, with the SSTs used in the high-FRC subset having a wider range than those of the low-FRC subset (Fig. 5). Therefore, it is likely that a portion of the differences between the high-FRC and low-FRC distributions of cloud properties shown in Figs. 4d–f are caused by the differences in the distributions of SSTs used in the two subsets of simulations.
Therefore, we see that some difficulties in interpreting the results can result from using two sets of forcings when changing SSTs, or from using two sets of SSTs when changing forcing. In other words, the sensitivity of cloud properties to changes in either the SST or forcings cannot be isolated. A strategy for unraveling the effects of the SST changes from the effects of the tendency changes is to fix either the SST or advective forcing while the other is allowed to vary. To accomplish this, this study uses the same set of 68 SSTs for the control, F+50%, and F−50% sets of simulations (whose results are described in section 5) and the same set of 68 forcings for the control, SST+2K, and SST−2K sets of simulations (whose results are described in section 6). In the latter case, the average cooling and moistening profiles of each of these sets correspond to those of the control lines in Figs. 2a,b.
4. Averaged cloud properties
In this section, a few set-averaged quantities are examined that are more readily compared to earlier studies than the PDFs of cloud properties presented in sections 3, 5, and 6. Cloud properties such as cloud fraction, cloud mass flux, and hydrometeor mixing ratios depend strongly on the magnitude of the advective forcings, with larger (smaller) magnitudes of these cloud properties throughout the model atmosphere for the F+50% (F−50%) set than the control set (Fig. 6). The variation of these cloud property profiles with SST is more subtle (Fig. 6). Only cloud fraction and cloud mass flux will be discussed in detail below.
The set-averaged profiles of cloud fraction are shown in Fig. 6a for all five sets of simulations. A CRM grid cell is defined as either cloudy or cloud free. The grid cell is cloudy if its visible optical depth divided by the layer thickness is greater than 0.2 × 10−3 m−1. That is, for a layer with a thickness of 500 m, any grid cell with an optical depth less than 0.1 is considered cloud free. This definition, also used by Luo et al. (2007), differs from previous ones based on condensate mixing ratios or vertical velocity (e.g., Xu and Krueger 1991) and is loosely based upon satellite passive sensor cloud detection capabilities. This new definition will be used throughout the paper.
There are three maxima in the profiles of cloud fraction. The lowest of these maxima is located at 2.5 km, corresponding to shallow cumuli. There is also a weak maximum in the profile at about 6 km, corresponding to cumulus congestus clouds. The highest cloud fraction is located between 11 and 13 km, corresponding to convective anvil clouds. These maxima are reminiscent of the trimodal distribution of tropical clouds examined by Johnson et al. (1999). The cloud fraction of the SST−2K set is higher than that of the control and SST+2K sets below an altitude of 13 km, but is lower above that level. A similar transition occurred at an altitude of about 10.5 km in RCE experiments with three different SSTs (298, 300, and 302 K) performed by Tompkins and Craig (1999, their Fig. 7), and the changes in the cloud fraction profile with SST are qualitatively similar to those seen in the Tompkins and Craig (1999) study. However, the cloud fractions simulated in these sets of simulations are much higher than those simulated by Tompkins and Craig (1999) because of the presence of large advective tendencies in these sets of simulations.
Another averaged quantity of interest is the simulated cloud mass flux (Fig. 6b), defined as the average of ρσiwi at each vertical level, where ρ is the density of air, σi is the binary cloud fraction, and wi is the vertical velocity. Since the cloud fraction is lower for the SST+2K set than the SST−2K set (Fig. 6a), the average in-cloud w must be higher for the SST+2K set to produce a higher cloud mass flux. There is a greater proportion of cloud-free grid cells with relatively strong negative vertical velocities in the SST+2K set than in the SST−2K set (not shown). The stronger subsidence in these cells may reduce the cloud fraction below 13 km in the SST+2K set by reducing the number of marginally cloudy cells. At higher altitudes, the cloud fraction is larger in the SST+2K set, perhaps because of the more intense convective updrafts, which may produce more detrainment at high altitudes. The increase in the cloud-top height in the SST+2K set may also be related to the increase in the altitude of the level of neutral buoyancy. This result also agrees with the RCE results of Tompkins and Craig (1999).
The average pseudoadiabatic and reversible CAPE were calculated for each of the five sets of simulations (Table 1). Reversible CAPE indicates that lifted parcels retain all condensed water, as in Xu and Emanuel (1989). The values in Table 1 are calculated from horizontally averaged vertical profiles at each time for each case using a starting altitude that yields the highest CAPE. Note that the values of CAPE using analyses at 2 m above the surface would be higher than those calculated here, since the first CRM level is centered at 50 m above the surface. In Table 1, it is clear that for all sets of simulations the reversible CAPE is much lower than the pseudoadiabatic CAPE, which is consistent with the findings of previous studies (Betts 1982; Xu and Emanuel 1989). The SST+2K set is associated with higher values of CAPE than the control and SST−2K sets. The F+50% set is associated with lower values of CAPE than the control and F−50% sets (see also Fig. 1b). These results suggest that a quasi-equilibrium state (Arakawa and Schubert 1974) is not reached in these short-term integrations since the values of CAPE differ significantly at the end of the integrations. Xu and Randall (1998) pointed out that the adjustment time scale to reach quasi equilibrium can be related to the magnitude of large-scale forcing.
5. Sensitivity to changes in large-scale forcing
a. Column cloud fraction
The overall column cloud fraction is 0.651 for the F−50% simulations, 0.805 for the control simulations, and 0.898 for the F+50% simulations (Table 2). These cloud fractions represent the fractions of the columns that simply fulfill the requirement that τ > 1.0. The fraction of columns that fulfill the deep convective cloud selection criteria is 0.126 for the F−50% simulations, 0.219 for the control simulations, and 0.356 for the F+50% simulations. These fractions represent 19.4%, 27.2%, and 39.6% of the cloudy columns (ADC/Aall) for the F−50%, control, and F+50% sets of simulations, respectively. The ratio of non-DC cloud fraction to DC cloud fraction decreases with forcing. This was also seen in Robe and Emanuel (1996), although their definition of convective columns differs from that used here. Thus, as the strength of the forcing increases, the overall cloud fraction increases somewhat, but this increase is largely due to DC clouds. The amount of increase in the DC and all-cloud populations may be impacted by the periodic horizontal domain because the strength of convection is affected by the lateral boundary conditions (Crook and Moncrieff 1988; Redelsperger et al. 2000).
b. Bootstrap analysis
The sensitivity of the simulated cloud properties to changes in the forcing and SST can be further examined by analyzing the PDFs of the cloud properties produced by the simulations. In EX05, the authors examined PDFs of cloud properties for those columns that fulfilled the DC selection criteria. In this study, the PDFs of these cloud properties for DC, non-DC, and all-cloud columns are examined to understand the causes of the sensitivity of these cloud properties to changes in the SST or the dynamic forcing.
The difference between two PDFs, as measured by the root-mean-square (L2) distance between two sets of simulations, can be tested for statistical significance following the bootstrap approach described in Xu et al. (2005), EX05, and Xu (2006). The bootstrap method produces a p value that quantifies the proportion of cases in which the L2 distances between randomized PDFs are greater than the L2 distances between the actual PDFs. The smaller that a p value is, the more likely it is that the PDFs are different because 1 − p is the confidence level with which we can claim that the two PDFs are from statistically different populations. The threshold value or significance level is customarily chosen to be 0.05, which corresponds to a 95% chance that the actual PDFs are statistically different. In this paper, the term “moderately significant” is used for p values between 0.05 and 0.10.
c. Albedo and snow and ice path
The distributions of top-of-the-atmosphere (TOA) albedo and snow and ice path (SIP) are shown in Fig. 7. The all-cloud distributions of albedo (Fig. 7a) have two peaks at low and high albedos that are likely associated with optically thin and thick clouds, respectively. Each of the all-cloud distributions of SIP is exponential (Fig. 7b), with the largest amount of columns having small values of SIP. Because a logarithmic y axis is used for the plots of SIP, these exponential distributions appear to be nearly linear in this figure. The increased cooling and moistening tendencies (Fig. 2) cause more widespread convection in the F+50% set of simulations, resulting in clouds that are optically thicker and more reflective than those produced by the control and F−50% sets of simulations. Because the values of albedo and SIP for DC columns (Figs. 7c,d) are generally higher than the corresponding values for non-DC columns (Figs. 7e,f), the increase in the proportion of DC columns with the magnitude of forcing (Table 2) can be said to cause the all-cloud distributions of albedo and SIP to shift toward higher values with forcing [see Eq. (2)].
The DC distributions of albedo produced by the control, F−50%, and F+50% sets are relatively Gaussian in character, although the control and F+50% distributions are skewed toward high albedos (Fig. 7c). The distributions of SIP for the DC columns all have peaks near 500 g m−2. The very lowest values of SIP are not present because of the cloud optical depth and cloud-height selection criteria for DC columns. The DC distributions of SIP are quite close to one another, although the DC columns produced by the F−50% set are more likely to have values of SIP that are less than 300 g m−2 than the control and F+50% sets (Fig. 7d). The higher frequency of DC columns that have low values of SIP and low albedo for the F−50% set of simulations is associated with the lack of convection discussed in section 4. This lack of convection is one of the reasons that several sharp peaks in the DC distributions are seen in the F−50% simulations (Figs. 7c d, 8c,d and 9c), in addition to the selection criteria used for the DC clouds.
The shapes of the non-DC distributions of albedo (Fig. 7e) are similar to those of the all-cloud distributions and are skewed toward higher values as the magnitude of the forcing increases. This is partially because the non-DC columns make up the majority of the all-cloud columns. The presence of large albedos in the non-DC distributions of albedo occurs because optically thick liquid-water clouds that are produced by the CRM are associated with high albedos but do not have an effective cloud height that fits the DC criteria. Looking at the non-DC distributions of SIP (Fig. 7f), we see that there are very few non-DC columns that have a SIP greater than 1000 g m−2. This means that the vast majority of columns in the all-cloud distributions with SIPs greater than this value are DC columns.
Statistical tests show that the F+50% and F−50% all-cloud distributions of albedo and SIP are all significantly different from the control distributions of these cloud properties (Table 3), but neither the F+50% nor the F−50% DC distribution of albedo or SIP is significantly different from the control (Table 4). The F+50% non-DC distributions of albedo and SIP are both significantly different from the corresponding control distributions (Table 5). The F−50% non-DC distribution of SIP is significantly different from the control, but the F−50% distribution of albedo is not. These results suggest that the DC distributions of these properties are not sensitive to changes in the dynamic forcing, but the all-cloud distributions are changed as the result of changes in the proportion of DC clouds and because of changes in the non-DC distributions.
d. Effective cloud height and longwave cloud radiative forcing
Longwave CRF, which is computed as the difference between clear- and all-sky OLR for all CRM columns by using the Fu–Liou radiation parameterization without and with cloud condensate respectively, is physically related to effective cloud height. As the effective cloud height increases, the amount of longwave CRF also increases, although the emissivity of clouds also plays a role in determining the magnitude of CRF. The all-cloud distributions of effective cloud height and longwave CRF are shown in Figs. 8a,b, respectively. The distributions of effective cloud height have three distinct peaks at around 3, 6.5, and over 10 km, which reflects the trimodal distribution of tropical clouds (Johnson et al. 1999). Of these three peaks, the high-altitude peak has the largest magnitude for each of the three sets of simulations, but the location of this high-altitude peak increases in altitude with increased cooling and moistening tendencies (Fig. 8a). This increase in effective cloud height with forcing reflects the increased depth of convective clouds with forcing (Fig. 6). Figure 6 shows that both cloud fraction and cloud mass flux increase with forcing, particularly above 13 km. In contrast to the distributions of effective cloud height, the all-cloud distributions of longwave CRF are relatively flat and each have a single peak, largely because high-altitude, low-emissivity clouds can have similar values of longwave CRF to high-emissivity, low-altitude clouds (Fig. 8b). Because both cloud emissivity (inferred from the SIP in Fig. 7b) and effective cloud height increase with forcing, it is expected that the amount of high longwave CRF tends to be larger in the F+50% set than the control and F−50% sets.
For DC columns, the relationship between effective cloud height and longwave CRF is even more direct than for all-cloud columns. This is because the threshold for DC columns (τ > 10) ensures that the emissivity is very close to 1. The DC distribution of effective cloud height produced by the F−50% set has a strong peak at just above 10 km, the lower threshold for DC columns, and a secondary peak at 12 km (Fig. 8c). This is probably because the convection in this set of simulations tends to be weak and the detrainment with the associated anvil clouds occurs at lower altitudes. The peaks of the control and F+50% sets are located at about 12 km, with the F+50% distribution being somewhat narrower than the control distribution. The narrowness of the F+50% distribution indicates that the overshooting (very highest) cloud tops make up a smaller fraction of the DC columns than in the control set. The shapes of the DC longwave CRF distributions are similar to the corresponding effective cloud height distributions, with another sharp peak in the distribution for the F−50% set (Fig. 8d).
The non-DC distributions of effective cloud height and longwave CRF (Figs. 8e,f) are similar to the all-cloud distributions of the same quantities. The high-altitude peaks in the non-DC distributions of effective cloud height (Fig. 8e) are not as prominent as in the corresponding all-cloud distributions (Fig. 8a), because the all-cloud distribution also includes a contribution from the DC columns, which occur exclusively above 10 km. The location of the high-altitude peak increases in height with forcing, particularly between the F−50% and control sets. The longwave CRFs produced by the F−50% set are smaller than those of the control set, reflecting the narrow depth of convection in the F−50% set (Fig. 6a).
Statistical tests show that the differences between the F+50% and control all-cloud distributions of effective cloud height and longwave CRF are significant, as are the corresponding differences between the F−50% and control distributions (Table 3). The differences between the F+50% and control sets are caused by the changes in the proportion of DC clouds rather than by changes in the DC and non-DC cloud properties (Tables 4 and 5). The differences between the F−50% and control sets are due to the changes in both the proportion of DC clouds and the non-DC (Table 5) and DC (significant for effective cloud height; see Table 4) distributions of these properties.
e. Shortwave and net cloud radiative forcings
Because each simulation is performed with a fixed, positive solar zenith angle that is associated with the instantaneous value for each observed cloud system, the unmodified, instantaneous shortwave CRFs tend to be much larger in magnitude than the longwave CRFs. The shortwave CRFs are calculated by subtracting the TOA reflected shortwave fluxes from their clear-sky values. In this section, “normalized” values of the shortwave CRF have been calculated by multiplying the shortwave CRF by the daily average value of the TOA incoming shortwave radiation at the location of each cloud object divided by the value used in the simulations. This has been done to obtain values of net CRF that are more similar to those obtained by previous investigations, which are typically based on daily or monthly mean values.
The all-cloud distributions of shortwave and net CRFs are shown in Figs. 9a,b, respectively. As one might expect, the distribution of shortwave CRF and its variation with forcing essentially mirrors that of TOA albedo (Fig. 7), except that lower (more negative) values of shortwave CRF correspond to higher values of albedo. The reasons noted earlier for the changes in the albedo distributions with forcing also apply to shortwave CRF. The all-cloud distributions of net CRF cover a similar range of values (Fig. 9b) as those of shortwave CRF, except that the distributions of net CRF have less power at large negative values and there are positive values of net CRF due to the cancellation of shortwave CRF with longwave CRF. A joint PDF between net CRF and cloud optical depth (not shown) confirms that the peaks between 0 and 50 W m−2 are due to high clouds that are too optically thin to be in the DC category and have relatively little shortwave CRF compared to their longwave CRFs.
The high, optically thick nature of DC columns ensures that the magnitudes of both longwave and shortwave CRFs are relatively high, and this causes the range of net CRF for DC columns to be narrower (−180 to 0 W m−2) than the corresponding all-cloud distributions (−250 to 100 W m−2; see Figs. 9b,d) because of cancellation between longwave and shortwave CRFs. The large proportion of clouds that are in the DC category for the F+50% set contributes to the maximum in the F+50% all-cloud distribution of net CRF near −100 W m−2 (Fig. 9b). The non-DC distributions of net CRF (Fig. 9f) are similar in shape to the all-cloud distributions, but the frequency of positive net CRFs is higher than for the all-cloud distributions, because of the lack of high, optically thick clouds, which tend to have negative net CRFs (Fig. 9d). The optically thin clouds that are associated with weakly negative shortwave CRFs and positive net CRFs are less prevalent as the forcing increases.
f. Summary
In this section, we have seen that the distributions of cloud properties are sensitive to changes in advective forcing. The increase in cooling and moistening tendencies throughout the troposphere causes more widespread convection, which skews the distributions of albedo, SIP, and the absolute value of shortwave CRF toward higher values as the magnitude of the forcing increases. The overall depth of convection and the detrainment height of anvil clouds also increase, and these changes are accompanied by increased values of longwave CRF. These changes are more significant for the all-cloud distributions (Table 3) than for the DC or non-DC distributions (Tables 4 and 5) of most variables. This is related to the fact that the proportion of DC cloudy columns increases with forcing (Table 2). However, the differences between the F−50% and control DC distributions of effective cloud height are moderately significant, and the F+50% and/or the F−50% non-DC distributions have significant differences from the control distributions for some cloud properties. Thus, the changes in the frequency of occurrence of deep convective columns, together with changes in some of the non-DC cloud properties, are primarily responsible for the changes in the all-cloud properties with advective forcing.
The sensitivity of the cloud properties to changes in advective forcing identified in this section bears some resemblance to the strong regional response of cloud properties to changes in the 500-hPa vertical velocity (Bony et al. 2004) in the absence of SST change. Similarly, the higher and brighter clouds in the F+50% simulations have analogs to the increased magnitudes of shortwave and longwave CRF in the ascending branch of the Hadley circulation seen in Clement and Soden (2005). The types of clouds that cause the increased magnitude of CRFs have also been identified here, which is not possible if only the mean cloud properties are examined.
6. Sensitivity to changes in SST
a. Column cloud fraction
The fraction of columns that fulfill the deep convective cloud selection criteria is 0.220 for the SST+2K set, 0.219 for the control set, and 0.271 for the SST−2K set (Table 2). The overall column cloud fraction for the SST+2K set is 0.787, compared to 0.805 for the control set and 0.865 for the SST−2K set. As noted earlier, most of the compensating subsidence outside the cloudy areas in the SST−2K set is relatively weak. This may be responsible for the relatively high column cloud fraction in the SST−2K set, particularly in the DC fraction. As the SST increases, the percentage of all cloudy columns that fit the DC selection criteria (ADC/Aall) changes only slightly, at 31.3% for the SST−2K set, 27.2% for the control set, and 28.0% for the SST+2K set. These differences are much smaller than those due to changes in imposed dynamic forcing as described in section 5. However, the distributions of some selected cloud properties do change with SST, particularly when the SST+2K and SST−2K sets are compared, as discussed below.
b. PDFs of cloud properties
For the all-cloud distributions of effective cloud height (Fig. 10a), the SST−2K set produces a PDF with a high-altitude peak that is skewed toward lower cloud heights than the control and SST+2K sets. Because the cloud fraction is higher for the SST−2K set, the lower cloud mass flux produced by the SST−2K set (Fig. 6b) means that the average updraft speed is lower for the SST−2K set, which prevents all types of clouds from reaching higher altitudes. The DC distributions of effective cloud height (Fig. 10c) also show increased cloud height with SST, for the same reason. The non-DC distributions of cloud height (Fig. 10e) are similar to the corresponding all-cloud distributions.
The distributions of longwave (LW) CRF (Figs. 10b,d,f) are similar to what would be expected from those of effective cloud height, with the SST−2K set producing clouds that have lower amounts of longwave CRF than the control and SST+2K sets for the high end of the longwave CRF range (longwave CRF > 140 W m−2), while the distributions are closer to one another at lower values. The distributions of LW CRF change with SST in a similar way for all three cloud categories. These results suggest that the changes in overall cloud macrophysical properties (including OLR, which is not shown) are correlated with the changes in the intensity of convection as the SST is altered. The same point can be made if one compares the shortwave (SW) and net CRFs among the three sets (Fig. 11), except that the non-DC and all-cloud distributions have larger differences between the SST−2K and control sets than between the control and SST+2K sets. This asymmetrical response to SST is less pronounced in other parameters. The changes in DC effective cloud height and in OLR with SST agree with observations presented in Xu et al. (2007). The observed changes were larger than those simulated here because the advective forcings were not identical for different values of SST for the observed cloud objects. This issue was extensively discussed in section 3 by comparing the control subsets.
In summary, we have seen that when the SST is increased or decreased by 2 K versus the control set of simulations, the distributions of most cloud properties remain relatively similar for the DC, non-DC, and all-cloud distributions (Tables 3, 4 and 5). This contrasts with the results shown in sections 4 and 5 for the sets where the advective forcing was changed, probably because the proportions of cloudy DC and non-DC clouds do not change nearly as much from the control set to the SST±2K sets as from the control to the F±50% sets. This is not to say that cloud properties are completely insensitive to SST in these simulations, as the significance tests of the SST+2K versus SST−2K distributions reveal in Tables 3, 4 and 5. The 4-K change in SST does cause at least a moderately significant difference in the all-cloud and non-DC distributions of albedo, effective cloud height, shortwave CRF, and net CRF, and the differences are moderately significant for the DC distribution of effective cloud height. The changes in the effective cloud heights and related macrophysical properties of deep convective clouds between the SST+2K and SST−2K sets are correlated to the changes in similar properties for the non-DC and all-cloud distributions of these properties. This is because changes in the intensity of deep convection also change properties of the associated thin anvil clouds.
7. Domain-averaged mean CRFs
In this section, we will examine the domain-averaged mean longwave, shortwave, and net CRFs for each set of simulations to gain a better comparison of the sensitivity of CRFs to large-scale forcings and SST through comparisons with prior RCE studies (Lau et al. 1994; Tompkins and Craig 1999; WM99). The changes in the mean CRFs due to SST and/or large-scale forcing from these sets are not readily comparable to the RCE studies mentioned above. This is partially because none of the five sets of simulations presented in this study is run until the atmosphere reaches equilibrium with the prescribed SSTs and/or large-scale forcings (Fig. 1). Keeping this caveat in mind, the 18–24-h mean longwave, shortwave, and net CRFs are shown in Table 6. The domain-averaged CRFs are listed as “total,” and the CRFs for the DC, non-DC, and τ ≤ 1 rows represent area averages for each of these categories.
The magnitudes of both the total shortwave and longwave CRFs tend to become smaller (less negative for shortwave and less positive for longwave) as SST increases. This trend agrees with that shown in WM99. [Lau et al. (1994) and Tompkins and Craig (1999) did not show the CRFs for individual experiments.] Another interesting result is that the domain-averaged longwave and shortwave CRFs change by a larger magnitude between the SST−2K and control sets than between the control and SST+2K sets. This asymmetry also appears in the three experiments performed by WM99, but with the changes in CRFs being smaller by factors of 2–3 between the 300.5- and 302.5-K experiments than between the 302.5- and 304.5-K experiments. This asymmetry is related to the asymmetry in column cloud fraction of both studies and the lack of difference in the all-cloud distributions between the control and SST+2K sets (Figs. 10b and 11a). Because Lau et al. (1994) performed only two experiments with SSTs of 301.2 and 303.2 K, such an asymmetrical response could not have been detected.
The change in CRF per degree of SST, which is regarded as the cloud feedback effect, was examined in prior RCE studies. The longwave cloud feedback is −0.83 W m−2 K−1 between the SST+2K and SST−2K sets, compared to −0.56 W m−2 K−1 in Tompkins and Craig (1999), −2.2 W m−2 K−1 in WM99, and 0.27 W m−2 K−1 in Lau et al. (1994). The agreement among these four studies is fairly good, as all of the feedbacks have a relatively small magnitude. The shortwave cloud feedback is 5.35 W m−2 K−1 between the SST+2K and SST−2K sets, compared to 4.35 W m−2 K−1 in WM99, 1.25 W m−2 K−1 in Lau et al. (1994), and 0.49 W m−2 K−1 in Tompkins and Craig (1999). The strong shortwave cloud feedback effects appear in three studies in which strong large-scale forcings were imposed in their 2D simulations: WM99, Lau et al. (1994), and this study. The small effect in Lau et al. (1994) may be due to their use of two SSTs that are 2 K apart, as mentioned earlier. For example, this effect is only 2.0 W m−2 K−1 between the experiments with SSTs of 300.5 and 302.5 K but 6.7 W m−2 K−1 between the experiment with SSTs of 302.5 and 304.5 K in WM99. The weaker convection in 3D simulations relative to 2D simulations, mentioned in section 2, and the lack of large-scale forcing in Tompkins and Craig (1999) may be the reason for the small shortwave cloud feedback effect in their study.
With the increase of the strength of imposed large-scale forcings, the magnitudes of both the total shortwave and longwave CRFs tend to become greater (Table 6). This result is primarily related to the large increase in both the overall and DC column cloud fractions (Table 2) and to the increase in the magnitude of CRF within the DC, non-DC, and τ ≤ 1 categories (Table 6). This increase in magnitude is clearly shown in the distributions of longwave, shortwave, and net CRFs (Figs. 8b,d,f and 9). The large increase in the overall and DC column cloud fraction and cloud depth (Fig. 6a) is also the primary reason why the domain-averaged longwave CRF has a sensitivity to the large-scale forcing that is 52% as strong as that of shortwave CRF, which is much larger than the corresponding ratio (15%) between the CRF sensitivities to SST discussed earlier. The changes in the domain-averaged shortwave, longwave, and net CRFs between the F+50% and F−50% sets (−66.7, 35.5, and −31.2 W m−2 for shortwave, longwave, and net) are similar in magnitude to those (−59.6, 29.3, and −30.3 W m−2) shown in WM99 between control and no forcing experiments, despite great differences in experiment design.
8. Conclusions
In this paper, the sensitivities of simulated tropical convective cloud systems to changes in the thermodynamic and dynamic forcings have been examined. The changes in the thermodynamic forcing were accomplished by changing the SST while using the control cooling and moistening tendencies, and changes in the dynamic state were accomplished by changing the cooling and moistening tendencies while using the control SSTs. An alternative method, where the control set of simulations is split between those with high or low SSTs or split between those with greater or smaller tendencies, was also examined. The main problem with this alternative method is that the control advective tendencies tended to change with SST, and vice versa, making it difficult to unravel the effects of the changes in SST and advective tendencies from one another. The separation of these two effects is extremely difficult using observations (Lau et al. 1997; Xu et al. 2007), but can be done easily with numerical simulations.
The analysis approach adopted in this study has focused on presenting the PDFs of column cloud properties instead of the conventional mean values of cloud properties. The overall cloud population was examined, together with the DC and non-DC components of the overall population. In the introduction, the following question was asked: are the cloud properties of the overall cloud population altered because of changes in the properties within either the DC or non-DC cloud population, or do they alter because of changes in the frequency of occurrence of DC clouds within the overall cloud population as the thermodynamic and dynamic forcings are modified? For the advective forcing sensitivity experiments, the answer is both; the proportion of clouds that were DC increased considerably with forcing, and the PDFs of most non-DC cloud properties also changed significantly with forcing. For the SST sensitivity experiments, the proportion of clouds that were DC did not change much with SST, but the PDFs of several of the non-DC cloud properties did change significantly between the SST−2K and SST+2K sets of simulations. For all of the sensitivity experiments, the differences among the DC distributions tended to be less significant than those among the non-DC distributions.
It is found that in the advective forcing experiments, a greater incidence of convection in response to increased cooling and moistening results in clouds that are more reflective and higher in altitude. This result indicates that the large uncertainties associated with the vertical motions produced by numerical weather prediction model analyses (Jakob et al. 2005) may be associated with large uncertainties in the cloud properties produced by the models. It also found that the similarities among the non-DC and DC PDFs produced by the F−50%, control, and F+50% sets of simulations are, relatively speaking, greater than the similarities among the all-cloud PDFs produced by these sets of simulations. This is due to large changes in the proportion of the DC population. This result can be likened to observations of boundary layer clouds over the Pacific Ocean during El Niño and La Niña (Xu et al. 2005), where the PDFs of properties of different boundary layer cloud types (defined by cloud fraction) were relatively unchanged, while the frequencies of their occurrence were quite different.
In the SST sensitivity experiments, the slightly weaker updrafts associated with the SST−2K set was associated with a smaller proportion of strong compensating subsidence and a larger cloud fraction than in the control and SST+2K sets. This effect on compensating subsidence may be an artifact of the periodic horizontal boundary conditions used in this study; in nature, some of the compensating subsidence associated with deep convective cloud systems may take place in areas that are quite far from the convection itself. It is found that the differences between the SST+2K and SST−2K non-DC and all-cloud distributions of albedo, effective cloud height, shortwave CRF, longwave CRF, and net CRF are all at least moderately significant. Though not discussed in section 6, the sensitivity of the all-cloud distributions of albedo and shortwave CRF to SST appears to be due to a decrease in snow [associated with an increase in graupel; see Tompkins and Craig (1999)] as SST increases, which has the net effect of decreasing albedo.
A major contribution of this study has been the detailed examination of the changes of column cloud properties in terms of their frequency distributions in response to changes in advective forcings and SSTs. To obtain a better comparison with prior studies, the domain-averaged mean CRFs have also been analyzed. It is found that the domain-averaged mean values of shortwave CRF are more sensitive to SST than those of the longwave CRF. However, the mean values of both longwave and shortwave CRFs are sensitive to changes in advective forcing. The sign of the changes in domain-averaged longwave and shortwave CRF with SST and forcing are the same as those in WM99 and Tompkins and Craig (1999). As the strength of advective forcing increases, cloud fraction, cloud optical depth, and effective cloud height all increase. This causes the magnitudes of the domain-averaged shortwave and longwave CRF to increase as forcing increases. This sensitivity to advective forcing is broadly consistent with the observational and GCM results reported in Bony et al. (2004) and with CRM results (Lau et al. 1994; WM99) where it was shown that the strength of both longwave and shortwave CRF increases with large-scale vertical velocity. However, the magnitudes of the forcings in this study are larger than those examined by Bony et al. (2004). This is because the forcings in Bony et al. (2004) are monthly mean values associated with a variety of weather, while the forcings in this study are in the spatial and temporal vicinity of deep convective cloud systems. The cloud feedback effects estimated from the SST−2K and SST+2K sets are comparable to prior CRM studies that used CRMs, particularly for the longwave cloud feedback effect, although the simulations are not run until the atmosphere reaches equilibrium with the prescribed SSTs.
Many of the results in this paper have shown large sensitivities in the properties of the non-DC clouds (e.g., thin anvils and shallow convection) in deep convective environments. In the future, we plan on using satellite data to determine whether non-DC clouds in the vicinity of deep convective cloud objects exhibit these same sensitivities.
Acknowledgments
The CERES data were obtained from the Atmospheric Sciences Data Center at the NASA Langley Data Center. This research has been supported by the NASA EOS interdisciplinary study program, and the Modeling, Analysis, and Prediction program managed by Drs. Don Anderson and Hal Maring. The authors thank Mark Branson at Colorado State University for providing the advective cooling and moistening tendency data, Drs. Takmeng Wong and Yali Luo for helpful discussions, and two anonymous reviewers for providing advice that improved this manuscript.
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Time series of the (a) average precipitation rate, (b) average pseudoadiabatic CAPE, (c) precipitable water, and (d) column temperature for the control, SST+2K, SST−2K, F+50%, and F−50% sets of simulations.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Set-averaged profiles of (a) prescribed advective heating tendency and (b) prescribed advective moisture tendency for the control, SST+2K, and SST−2K sets (solid), the F+50% set (dashed), and the F−50% set (dotted).
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Profiles of (a) water vapor difference and (b) temperature difference for the observed cloud objects whose set-averaged SSTs differ by 2 K. The differences were calculated by subtracting the profiles of the cooler subset from those of the warmer subset.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
All-cloud distributions of (a) albedo, (b) effective cloud height, and (c) cloud ice and snow path for the control simulations and high-SST and low-SST subsets. (d)–(f) Same as in (a), (b), and (c), but distributions are for the control simulations and high-FRC and low-FRC subsets.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Distributions of SST for the high-FRC and low-FRC simulations.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Profiles of domain-averaged (a) cloud fraction and (b) cloud mass flux for the control, SST+2K, SST−2K, F+50%, and F−50% sets of simulations.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Distributions of (left) albedo and (right) cloud ice and snow path for the control, F+50%, and F−50% sets of simulations: (a), (b) all-cloud (all); (c), (d) deep convective (DC); and (e), (f) non–deep convective (non DC) cases.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
As in Fig. 7, but for (left) effective cloud height and (right) LW CRF.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
As in Fig. 7, but for (left) SW and (right) net CRF.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Distributions of (left) effective cloud height and (right) LW CRF for the control, SST+2K, and SST−2K sets of simulations. Panels are labeled as in Fig. 7.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
As in Fig. 10, but for (left) SW and (right) net CRF.
Citation: Journal of the Atmospheric Sciences 65, 6; 10.1175/2007JAS2446.1
Pseudoadiabatic and reversible CAPE (J kg−1).
Column cloud fraction.
Bootstrap probabilities for all clouds; p values < 0.10 in bold.
Bootstrap probabilities for deep convective clouds; p values < 0.10 in bold.
Bootstrap probabilities for non–deep convective clouds; p values < 0.10 in bold.
Mean cloud radiative forcings (last 6 h).
When large-scale advective forcings are used in CRMs, periodic lateral boundary conditions have to be used because an open boundary condition produces nonzero domain-averaged vertical motion, which provides additional large-scale advective tendencies. This is why periodic boundary conditions have been used in previous CRM studies (e.g., Lau et al. 1994; WM99; Shie et al. 2003). These studies also used comparable domain sizes.
Two sets of simulations that changed the SST by +2 and −2 K without adjusting the profiles of temperature and water vapor were also performed. These sets of simulations produced similar results to those of the SST+2K and SST−2K simulations shown in this study.
The magnitude of the forcing could also be characterized by the moistening tendencies, but most of the cloud objects in this study that have large amounts of cooling also have large amounts of moistening.