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  • View in gallery

    Size distribution of supermicron absorbing aerosols from Erlick et al. (2001, case JDT178a).

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    Ambient size of supermicron absorbing in a stratocumulus updraft from Erlick et al. (2001, case JDT178a).

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    Total solar cloud forcing ratios (R) produced by the CL low cloud with added supermicron aerosol/drop bins from Figs. 1, 2. The Maxwell–Garnett mixing rule (configuration 1) and a solar zenith angle of 30° are assumed. The total solar cloud forcing ratio for the clean CL low cloud is 1.22. The corresponding dry mineral dust mass concentrations for the 16 bins are 0.15, 0.062, 0.14, 0.54, 1.4, 3.1, 4.9, 6.5, 9.3, 14, 20, 18, 5.2, 1.6, 0.0084, and 1.8 × 10−5 μg m−3, respectively, while the corresponding soot mass concentrations for the first six bins are 0.13, 0.06, 0.13, 0.49, 1.3, and 2.7 μg m−3, respectively.

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Another Look at the Influence of Absorbing Aerosols in Drops on Cloud Absorption: Large Aerosols

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  • 1 Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract

Since as early as 1969, solar absorbing aerosols inside of cloud drops have been suggested to influence cloud radiative properties. The absorbing aerosols were invoked to help explain two “anomalies”: 1) the maximum visible albedo of thick stratocumulus clouds is observed to be only 0.7–0.8, rather than close to 1.0 as would be expected from pure water clouds, and 2) the total solar cloud forcing ratio is observed to be near 1.5 for a wide range of clouds, rather than near 1.0 as would be expected from pure water clouds. While subsequent studies refuting absorbing aerosols have been limited to certain aerosol and cloud drop size ranges, in this study the authors explore the potential radiative effects of supermicron dust and soot aerosols in cloud drops, which can have especially high absorption cross sections. Because of the lack of measurements and limited microphysical simulations of such supermicron absorbing aerosols, it is not suggested that the calculations will entirely resolve the two anomalies. However, because these aerosols certainly can exist in the vicinity of clouds, the authors suggest that their potential contribution to the understanding of the anomalies should be explored. This study serves as an initial step toward that goal.

Corresponding author address: C. Erlick, Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem 91904, Israel. Email: caryn@vms.huji.ac.il

Abstract

Since as early as 1969, solar absorbing aerosols inside of cloud drops have been suggested to influence cloud radiative properties. The absorbing aerosols were invoked to help explain two “anomalies”: 1) the maximum visible albedo of thick stratocumulus clouds is observed to be only 0.7–0.8, rather than close to 1.0 as would be expected from pure water clouds, and 2) the total solar cloud forcing ratio is observed to be near 1.5 for a wide range of clouds, rather than near 1.0 as would be expected from pure water clouds. While subsequent studies refuting absorbing aerosols have been limited to certain aerosol and cloud drop size ranges, in this study the authors explore the potential radiative effects of supermicron dust and soot aerosols in cloud drops, which can have especially high absorption cross sections. Because of the lack of measurements and limited microphysical simulations of such supermicron absorbing aerosols, it is not suggested that the calculations will entirely resolve the two anomalies. However, because these aerosols certainly can exist in the vicinity of clouds, the authors suggest that their potential contribution to the understanding of the anomalies should be explored. This study serves as an initial step toward that goal.

Corresponding author address: C. Erlick, Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem 91904, Israel. Email: caryn@vms.huji.ac.il

1. Introduction

Since as early as 1969, solar absorbing aerosols inside of cloud drops have been suggested to influence cloud radiative properties. The absorbing aerosols were invoked to help explain two “anomalies”: 1) the maximum visible albedo of thick stratocumulus clouds is observed to be only 0.7–0.8, rather than close to 1.0 as would be expected from pure water clouds (see, e.g., Danielson et al. 1969), and 2) the total solar cloud forcing ratio
i1520-0469-65-2-661-eq1
where C = (FcloudyFcloudy) − (FclearFclear), F and F are the upward and downward total solar irradiances, SFC is the surface, and TOA is the top of the atmosphere, is observed to be ∼1.5 for a wide range of clouds rather than ∼1.0 as would be expected from pure water clouds (see, e.g., Cess et al. 1995; Ramanathan et al. 1995; Pilewski and Valero 1995; Chou et al. 1995; Kondratyev et al. 1995; Li et al. 1995; Li and Moreau 1996; Lubin et al. 1996; Sinha 1996; Zender et al. 1997; Harshvardhan et al. 1998; Collins 1998; Valero et al. 2000; Erlick et al. 2001; Liu et al. 2002).

Of course, absorbing aerosols were not the only explanation suggested for these two anomalies [for a more comprehensive history and analysis, see Stephens and Tsay (1990) and Wiscombe (1995)]. Other explanations that have been investigated include the presence of very large water drops (e.g., Welch et al. 1980; Wiscombe et al. 1984), cloud vertical homogeneities and cloud overlap (e.g., Welch et al. 1980; Li et al. 1994; Sinha 1996), three-dimensional cloud effects (e.g., Hayasaka et al. 1995; Li et al. 1995; Byrne et al. 1996; O’Hirok and Gautier 1998; Cairns et al. 2000), near-infrared water vapor effects, including the water vapor continuum (e.g., Harshvardhan et al. 1998), measurement errors and errors associated with inferring cloud absorption from irradiance measurements (e.g., Li et al. 1995; Arking et al. 1996), and Mie resonances in cloud drops (Zender and Talamantes 2006). Despite all of these investigations, the anomalies were never entirely resolved.

As with the other explanations for the anomalies, while a number of studies suggested that aerosols within cloud layers may contribute to enhanced absorption in clouds (Danielson et al. 1969; Grassl 1975; Chýlek et al. 1984; Li et al. 1995; Li and Moreau 1996; Sinha 1996; Erlick et al. 2001), others refuted this suggestion. The arguments against absorbing aerosols include the fact that 1) not enough absorbing aerosol mass has been measured in cloud water (Twohy et al. 1989; Chýlek et al. 1996; Liu et al. 2002); 2) the anomalies have been observed in areas with low concentrations of cloud condensation nuclei (CCN) as well as areas with high CCN concentrations (Cess et al. 1995); 3) a broadband absorber of solar radiation would dissipate stratocumulus clouds (Ackerman and Toon 1996); and 4) in the global, diurnal average, higher solar zenith angles and higher clouds cancel the enhancement in absorption found at low solar zenith angles and with low clouds, even with absorbing aerosols present (Lubin et al. 1996).

However, the previous studies of absorbing aerosols have been limited in several ways. Previous measurements of absorbing aerosols in cloud water (soot has been measured in concentrations ranging from 8 to 600 μg kg−1 water) were restricted to a certain aerosol size range (generally submicron) and a certain drop size range [generally greater than 10-μm diameter; Heintzenberg (1988); Twohy et al. (1989, Tables 2 and 3); Liu et al. (2002, Table 1)]. No measurements of supermicron size absorbing aerosols in cloud water have been reported. On the other hand, it is known that soot spherules coagulate and aggregate into larger clusters, reaching aerodynamic diameters of up to 2 μm (Berry and Percival 1986; Petzold et al. 1997; Seinfeld 2004). Likewise, dust aerosols tend to have a prominent supermicron mode. A relatively high concentration of such supermicron aerosols, which were not likely to comprise primarily sea salt, sulfate, nitrate, or desert dust, was measured in a continentally influenced air mass off the coast of California during the Monterey Area Ship Track (MAST) Experiment [Durkee et al. 2000; Russell et al. 1999; Hobbs et al. 2000; University of Washington (UW) C131-A flight 1646 on 27 June 1994 (case JDT178)]. This supermicron concentration was attributed to be primarily a mixture of soot and nondesert dust by Erlick et al. (2001). Similar observations of relatively high concentrations of supermicron soot and dust have been reported by Shi et al. (2003), Radke et al. (1995, Fig. 3), Viidanoja et al. (2002, Table 1), Garrett et al. (2003, Fig. 4), Kim et al. (2003, Figs. 2 and 3), Clarke et al. (2004), Seinfeld et al. (2004, Fig. 6), and Howell et al. (2006, Table 2) far from sources, as well as near biomass burning and pollution sources and during dust storms. Furthermore, the supermicron size is large enough for such aerosols to be efficient cloud condensation nuclei and/or scavenged by cloud drops (Rogers et al. 1991; Radke et al. 1995). The condensational growth and scavenging of such supermicron soot and dust aerosols was simulated by Erlick et al. (2001) using a size and composition resolved microphysical model (Russell and Seinfeld 1998), and by, for example, Levin et al. (1996) and Yin et al. (2000).

A second limitation of previous studies of absorbing aerosols is that in calculating the radiative effects of absorbing aerosols in clouds, a constant ratio of aerosol to drop mass or aerosol to drop volume was generally assumed. The possibility that the absorbing aerosols in internal mixtures with cloud drops are not spread evenly throughout the cloud drop size distribution was not considered. In particular, the potential radiative effect of supermicron absorbing aerosol mass in cloud water has not been evaluated.

In this study, we explore the potential radiative effects of supermicron dust and soot aerosols in cloud drops. These aerosols/aerosol clusters mixed with water drops can have especially high absorption cross sections. Even though the specific absorption (the absorption per unit aerosol mass) eventually tapers off as more water is added to the drop (Chýlek et al. 1984), the absorption cross section, which is proportional to the drop radius squared, remains high. In supermicron aerosol clusters, the absorption is even more dominant than in solid supermicron particles (Berry and Percival 1986). Because of the lack of measurements and limited microphysical simulations of such supermicron absorbing aerosols, we do not suggest that our calculations will entirely resolve the two anomalies stated earlier. However, because these aerosols certainly can exist in the vicinity of clouds, we suggest that their potential contribution to our understanding of the anomalies should be explored. This study serves as an initial step toward that goal.

2. Methods

Because of the above-stated lack of measurements and limited microphysical simulations of supermicron absorbing aerosols in clouds, we have chosen to use similar standard cloud drop distributions as used in previous studies to represent the “clean” (pure water) clouds. We start with the larger drop (CL) and smaller drop (CS) clouds from the Intercomparison of Radiation Codes in Climate Models (ICRCCM; Fouquart et al. 1991) and scale the cloud extinction optical depths roughly to 10. As in Harshvardhan et al. (1998), we assume that the clouds are 1 km thick and place them between 900 and 800 mb (low clouds) or between 200 and 180 mb (high clouds). Then we add a distribution of drops containing supermicron absorbing aerosols. The measured concentration and predicted ambient size of the supermicron absorbing aerosols (the added drops) in a moderate cloud updraft (0.3 m s−1) are taken from Erlick et al. (2001, case JDT178a), and are shown in Figs. 1 and 2. [Note that this case study may not be typical; the aerosol size distribution was categorized as “continentally influenced marine” rather than clean marine or average continental. However, it is the only case study for which we have enough information to complete such a calculation. Note also that the inclusion of high clouds is in a sense for completeness, for comparison with previous studies that examined the effect of cloud height. While soot and mineral aerosols from continental, biomass burning, and volcanic sources have been observed at high altitudes (see, e.g., Blake and Kato 1995; Bates et al. 2006, section 2.1), the extent of their microphysical interaction with clouds is not well quantified.]

To calculate the single scattering properties of the drops containing supermicron absorbing aerosols, three configurations are used: 1) the Maxwell–Garnett model, in which the distribution and size distribution of the absorbing inclusions in the drop are random (see Bohren and Huffman 1983, section 8.5; Chýlek et al. 2000; Erlick 2006); 2) the extended effective medium approximation of Sihvola and Sharma [1999, their Eq. (15)], in which the distribution of absorbing inclusions in the drop is random, but the size distribution accounts for inclusions larger than dipoles; and 3) a core plus shell model [Bohren and Huffman (1983), appendix B; checked against the program DMiLay, described in Toon and Ackerman (1981)]. The real and imaginary parts of the refractive index of water as a function of wavelength are taken from Hale and Querry (1973), while those for soot and mineral dust are taken from d’Almeida et al. (1991, Table 4.3).

To calculate the solar cloud forcing ratio, the single scattering properties of the pure water clouds and each configuration of the additional aerosol/cloud drop mixtures are input to the multiple scattering radiation algorithm of Freidenreich and Ramaswamy (1999). This algorithm is a 25-frequency solar parameterization for inhomogeneous scattering and absorbing atmospheres. The algorithm spans wavenumbers 0–57, 600 cm−1, or wavelengths 0.174 to greater than 4.0 μm. In the algorithm, the exponential sum-fit technique (Wiscombe and Evans 1977) is used to parameterize water vapor transmission in the main absorbing bands, while absorption by other gases (CO2, O2, and O3) is computed using a regular absorptivity approach. The delta-Eddington method (Joseph et al. 1976) is used to calculate the reflection and transmission of scattering layers, and the layers are combined using the adding method (Ramaswamy and Bowen 1994). The surface albedo is parameterized as a function of solar zenith angle according to the formulation of Briegleb (1992), while the atmospheric temperature, water vapor, and ozone profiles are from the midlatitude summer profile of McClatchey et al. (1972). In the cloud layers, the water vapor mixing ratio is increased to the saturated value. This multiple scattering algorithm has been shown to agree well with exact line-by-line and doubling–adding reference computations for both clear and overcast skies, particularly with respect to atmospheric absorption (Freidenreich and Ramaswamy 1999). Cloud forcing ratios are computed as an integral over the entire solar spectrum (total solar cloud forcing) at solar zenith angles 30° and 60° with all three configurations and in the diurnal average with the first configuration.

3. Results and discussion

To demonstrate the potential for supermicron absorbing aerosols in clouds to increase the total solar cloud forcing ratio, we use as a test case the CL cloud placed between 900 and 800 mb (low cloud), the Maxwell–Garnett mixing model (configuration 1), and a solar zenith angle of 30°. First we add each supermicron size bin from Figs. 1 and 2, one bin at a time, assuming that the composition of the absorbing aerosol core of that bin is either entirely mineral dust or entirely soot. The 2.008-μm bin is the largest individual bin tested for soot because even soot aggregates have not been observed at sizes larger than this. The results are shown in Fig. 3. The individual dust aerosol bins produce cloud forcing ratios between 1.22 and 1.26, with dust core diameters 6.547 and 8.290 μm producing slightly higher ratios than the other bins. While these values are certainly greater than ∼1.0, the increase over cloud forcing ratio produced by the clean CL low cloud (1.22) is not so great. As shown by Harshvardhan et al. (1998), the CL low cloud can produce a relatively high cloud forcing ratio by virtue of its large drop effective radius and its interaction with ambient water vapor. The individual soot aerosol bins, however, produce cloud forcing ratios between 1.23 and 1.49, with a strong increase in cloud forcing ratio as the soot core diameter increases beyond 0.985 μm. Note that the soot core with the largest observed diameter (∼2.0 μm) alone produces a cloud forcing ratio near the value of ∼1.5 reported by Cess et al. (1995).

Next we add the entire supermicron aerosol size distribution from Figs. 1 and 2 to the CL cloud, assuming that (i) the composition of the aerosol core of all of the bins is mineral dust, (ii) the composition of the aerosol core of all of the bins is soot up to and including diameter 1.250 μm, (iii) the composition of the aerosol core of all of the bins is soot up to and including diameter 1.584 μm, (iv) the composition of the aerosol core of all of the bins is soot up to and including diameter 2.008 μm, (v) the aerosol core of each bin is an internal mixture of 97% mineral dust/3% soot by mass, and (vi) the aerosol core of each bin is an internal mixture of 70% mineral dust/30% soot by mass. Assumptions (v) and (vi) are based on the observed fraction of soot in supermicron aerosols (3%–30%) reported by Kim et al. (2003) and Clarke et al. (2004). The effective refractive indices of the internally mixed dust/soot cores with water are calculated using a multicomponent application of the Maxwell–Garnett mixing rule.

The CL cloud single scattering parameters at 0.50 μm that correspond to each assumption are shown in the upper half of Table 1, and the 0.50-μm cloud albedo and total solar cloud forcing ratio for each assumption are shown in the upper half of Table 2. The 0.50-μm cloud albedo increases between the clean CL cloud (the row labeled No Core) and the CL clouds with the added supermicron core drops because of the added optical depth. It varies among the CL clouds with the added supermicron core drops, generally decreasing as the single scattering albedo decreases and the absorption coefficient increases, as would be expected. In accordance with observations of the first anomaly, the cloud albedo does not reach beyond 0.7–0.8, even with the added optical depth. For the CL low cloud and solar zenith angle, sza = 30°, the CL low cloud and sza = 60°, and the CL high cloud and sza = 30°, the cloud forcing ratios with the supermicron core are all significantly greater than 1.0 and significantly greater than that produced by the clean CL cloud. The cloud forcing ratio using assumption (vi) (70% dust/30% soot) is especially high, ranging from 1.41 to 2.60. For the CL high cloud and sza = 60°, however, the ratios are close to 1.0 (even less than 1.0 in some cases), except for assumption (vi). It has been shown before that high clouds do not enhance atmospheric absorption of solar radiation as efficiently as low clouds, even if significant absorption occurs within the cloud layer, because there is much less contribution of absorption by above cloud water vapor in the near-infrared; more radiation that would have been absorbed in the lower troposphere is reflected back to space (e.g., Lubin et al. 1996; Ramaswamy and Freidenreich 1998; Harshvardhan et al. 1998). Nevertheless, in the global, diurnal average, the reduction in absorption produced by the CL high cloud at high solar zenith angles is not likely to cancel the enhancement in absorption produced by the other states of the CL cloud.

The same calculations for the CS cloud are shown in the lower halves of Tables 1 and 2. The values of cloud albedo are higher than for the CL cloud but show the same general tendency. While the clean CS cloud (No Core) produces a lower initial cloud forcing ratio than the CL cloud, when it is placed at the lower altitude, the cloud forcing ratios with the supermicron core are all significantly greater than 1.0, and again the ratio produced using assumption (vi) is especially high. When the CS cloud is placed at the higher altitude, the ratios are ≲1.0, again except for assumption (vi). Here, in the global, diurnal average, some cancellation of the enhancement in absorption produced by the CS low cloud may occur if there is a large enough representation of high clouds with radiative properties similar to the CS cloud.

While the case study examined here is not readily amenable to a global cloud forcing estimate, we can get an idea of the diurnally averaged cloud forcing ratio by employing a procedure similar to that employed in the Geophysical Fluid Dynamics Laboratory (GFDL) Global Atmospheric Model (AM2; GAMDT 2004). To be consistent with the case study chosen, we average the solar irradiances at the surface and top of atmosphere over the values that the model produces every 3 h in the region of the MAST experiment (36.5° latitude, −123.50° longitude) during the summer (on, say, 1 July 1994), retaining the midlatitude summer profile of atmospheric temperature, water vapor, and ozone from McClatchey et al. (1972). The diurnally averaged midlatitude summer total solar cloud forcing ratios are shown in Table 3. The forcing ratios are generally between the values calculated at 30° and 60° solar zenith angle (cf. with Table 2). All of the ratios for the CL low cloud, the CL high cloud, and the CS low cloud are greater than 1.0, and those for the CL and CS low clouds and for all clouds with assumption (vi) are again particularly high. Therefore, in the midlatitude summer diurnal average, we find that the reduction in absorption at high solar zenith angles does not unequivocally cancel the enhancement in absorption at low solar zenith angles.

The 0.50-μm cloud albedo and total solar cloud forcing ratio calculations for the CL and CS clouds using the extended effective medium approximation (configuration 2) and the core plus shell model (configuration 3) are shown in Tables 4 and 5, respectively. In general, the same conclusions can be drawn from Tables 4 and 5 as from Tables 2 and 3. The cloud albedos do not reach beyond 0.7–0.8, even with the added optical depth of the supermicron core drops. In Table 4, the calculated cloud forcing ratios are slightly higher than those using the Maxwell–Garnett model, while in Table 5, the calculated cloud forcing ratios are slightly lower. This can be expected since the extended effective medium approximation, accounting for inclusion effects of higher order than the simple dipole, has been shown to describe greater overall absorption when absorbing inclusions are present, while the core plus shell model, with the “inclusions” effectively concentrated at the center of the drop, has been shown to describe less overall absorption for the same inclusion to drop volume ratio (see Chýlek et al. 1984; Erlick 2006).

Note that in all of these simulations, the supermicron aerosol/drops are added to the clean cloud rather than displacing similarly sized clean cloud drops. Displacing similarly sized clean cloud drops may produce an even greater effect on the cloud forcing ratio, but such a calculation is not included here because of the added level of arbitrariness it would involve in selecting which drops to replace.

4. Conclusions

Using a “continentally influenced” marine supermicron aerosol size distribution measured below clouds and an accompanying simulated drop size distribution, we showed that drops containing supermicron cores or inclusions of equivalent volume fractions to the supermicron cores, comprising dust, soot, and mixtures thereof, can significantly enhance the cloud forcing ratio of an otherwise standard clean cloud. This is true for CL (larger drop) clouds placed lower in the troposphere regardless of the solar zenith angle, for CL clouds placed higher in the troposphere with a lower solar zenith angle, and for CS (smaller drop) clouds placed lower in the troposphere regardless of the solar zenith angle. These results are fairly robust, regardless of the assumption made regarding the configuration of the absorbing aerosol mass inside of the drops, and persist even in a midlatitude summer diurnal average.

There are two obvious caveats to our results. First, for lack of additional data, we tested only one supermicron aerosol/drop size distribution. Second, our two representative clean cloud size distributions were static; that is, the absorption did not feed back on the cloud microphysics such that no “semidirect” effects (e.g., Ackerman and Toon 1996; Hansen et al. 1997, 2000; Ackerman et al. 2000) were included. Nevertheless, we have taken a first step to show that there is potential for supermicron absorbing aerosols in cloud drops to account for some of the previously observed enhancement in cloudy sky absorption, and that higher solar zenith angles and higher clouds will not unequivocally cancel such enhancement in absorption found at low solar zenith angles and with low clouds.

Acknowledgments

This work was supported by the Israel Science Foundation Grant 153/01. The authors are grateful to L. M. Russell for numerous helpful discussions on aerosol concentrations and to D. Schwarzkopf for advice on the diurnal forcing calculations, and thank three anonymous reviewers for their constructive comments.

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  • Zender, C. S., , B. Bush, , S. K. Pope, , A. Bucholtz, , W. D. Collins, , J. T. Kiehl, , F. P. J. Valero, , and J. Vitko Jr., 1997: Atmospheric absorption during the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE). J. Geophys. Res., 102 , D25. 2990129916.

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Fig. 1.
Fig. 1.

Size distribution of supermicron absorbing aerosols from Erlick et al. (2001, case JDT178a).

Citation: Journal of the Atmospheric Sciences 65, 2; 10.1175/2007JAS2381.1

Fig. 2.
Fig. 2.

Ambient size of supermicron absorbing in a stratocumulus updraft from Erlick et al. (2001, case JDT178a).

Citation: Journal of the Atmospheric Sciences 65, 2; 10.1175/2007JAS2381.1

Fig. 3.
Fig. 3.

Total solar cloud forcing ratios (R) produced by the CL low cloud with added supermicron aerosol/drop bins from Figs. 1, 2. The Maxwell–Garnett mixing rule (configuration 1) and a solar zenith angle of 30° are assumed. The total solar cloud forcing ratio for the clean CL low cloud is 1.22. The corresponding dry mineral dust mass concentrations for the 16 bins are 0.15, 0.062, 0.14, 0.54, 1.4, 3.1, 4.9, 6.5, 9.3, 14, 20, 18, 5.2, 1.6, 0.0084, and 1.8 × 10−5 μg m−3, respectively, while the corresponding soot mass concentrations for the first six bins are 0.13, 0.06, 0.13, 0.49, 1.3, and 2.7 μg m−3, respectively.

Citation: Journal of the Atmospheric Sciences 65, 2; 10.1175/2007JAS2381.1

Table 1.

Single scattering parameters for the CL and CS clouds with the added supermicron aerosol/drop size distribution from Figs. 1, 2 at 0.50-μm wavelength. The Maxwell–Garnett model (configuration 1) is used.

Table 1.
Table 2.

The 0.50-μm cloud albedo (A) and total solar cloud forcing ratio (R) produced by the CL and CS clouds with the added supermicron aerosol/drop size distribution from Figs. 1, 2. The Maxwell–Garnett model (configuration 1) is used.

Table 2.
Table 3.

Diurnally averaged midlatitude summer total solar cloud forcing ratio (R) produced by the CL and CS clouds with the added supermicron aerosol/drop size distribution from Figs. 1, 2. The Maxwell–Garnett model (configuration 1) is used.

Table 3.
Table 4.

The 0.50-μm cloud albedo (A) and total solar cloud forcing ratio (R) produced by the CL and CS clouds with the added supermicron aerosol/drop size distribution from Figs. 1, 2. The extended effective medium approximation (configuration 2) is used.

Table 4.
Table 5.

The 0.50-μm cloud albedo (A) and total solar cloud forcing ratio (R) produced by the CL and CS clouds with the added supermicron aerosol/drop size distribution from Figs. 1, 2. The core plus shell model (configuration 3) is used.

Table 5.
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