The number of cloud droplets formed from a population of aerosols depends on the aerosol number concentration, NA, the size distribution, and the chemical composition. The cloud albedo effect occurs when increasing NA causes increases to the droplet concentration, ND. We examined the effects of changing aerosol size, composition, and number on ND within the United States. We found that changing the water-soluble organic carbon (WSOC) fraction from 50% to 0.05% in the fine mode aerosol and from 50% to 95% in the coarse mode aerosol decreased ND by an average of 34%. Our results show that the changes to the aerosol composition cause over a 20% change to ND, a magnitude previously estimated to cause a 1 W m−2 change in radiative forcing. Given the realistic range of aerosol compositions used here, it is not possible for global models to correctly calculate the cloud albedo effect if composition is ignored.
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 The largest uncertainty in climate change forcing [Forster et al., 2007] is the cloud albedo effect. Global models use empirical relationships based on regional studies or mechanistic activation schemes to calculate ND [e.g., Pringle et al., 2009]. A focus of current research is to understand which microphysical variables have dominant roles, thereby eliminating the need for global models to keep unnecessary variables. For example, previous studies have shown that aerosol microphysical variables such as size, number, and small concentrations of coarse mode aerosols in a population of fine mode aerosols dominate in the prediction of ND [Chen and Penner, 2005; Dusek et al., 2006; Feingold et al., 1999; Feingold, 2003]. Other studies have shown crustal and organic aerosols also influence ND [Ervens et al., 2005; Kelly et al., 2007; Nenes et al., 2002]. Based on these studies, we changed the microphysical variables in a warm microphysics model to identify which variables changed ND by 10–20%. These limits of change in ND were chosen because a decrease in radiative forcing of −1 W m−2 has been estimated if ND is increased by 20% [Facchini et al., 1999].
2. Model Description and Input Parameters
 We used the Parcel Undergoing Thermodynamic Transitions (PUTT), a warm microphysics model [Seidl, 1989]. The initial relative humidity of the parcel was 98% and was lifted adiabatically 300 meters from an initial starting pressure of 900 mbars at a speed, w, of 10, 20, 50, 150, or 300 cm s−1. The size distribution of the aerosols was modeled as the sum of two lognormal functions each discretized into ninety bins.
 The Interagency Monitoring of Protected Visual Environments (IMPROVE) network dataset was used to create the aerosol composition (IMPROVE, IMPROVE Archived Data, 2007, available at http://vista.cira.colostate.edu/improve). The dataset includes 187 sites within the continental United States, Alaska, Hawaii, and the U.S. Virgin Islands (see Figure 1a). Particulate matter monitoring has occurred at some but not all sites from 1988 to 2004. The data was averaged into four seasons for each of the 28 regions listed by Malm et al. .
 PUTT also calculates the absorption of nitric acid gas, HNO3(g), into the aerosol particles. The parcel's initial gas-phase nitrate concentrations, 0.01 to 31.3 ppbv, were derived from the model results of Feng and Penner  for each region and season. Feng and Penner  found the model overpredicted the observations in North America. A constant value of 0.2 ppbv for each region and season, which would have given better agreement with the observations, was used in a sensitivity test.
 The predicted values for ND have different responses to internal and external aerosol mixtures [McFiggans et al., 2006], and small concentrations of large aerosols can greatly affect ND as well as the formation of precipitation [Feingold et al., 1999]. The IMPROVE dataset does not provide the coarse mode PM10.0 aerosol composition, size distribution parameters, or the mixing state of the fine and coarse mode aerosols. Measurements taken near the Owens (dry) Lake, a saline playa with large and frequent dust storms in the spring and fall [Labban et al., 2004], were used to constrain the coarse mode aerosol parameters. The composition of the fine mode was similar to the coarse mode aerosols [Labban et al., 2004]. The fine mode composition in the IMPROVE regions affected by Owens (dry) Lake dust storms was also similar to the fine mode measurements by Labban et al. . It was assumed that the fine and coarse mode compositions were equal for these regions in PUTT. Relevant measurements were not available for the composition of the coarse mode for the remainder of the regions. All regions were then assumed to have the same fine and coarse mode composition. This assumption was tested with sensitivity tests where differing fine and coarse mode compositions were used. We assumed the IMPROVE data, when averaged, was an aged background aerosol composition, so external mixtures were not used.
 A large component of the fine aerosol mass in the IMPROVE network is organic carbon (OC), but the fraction of OC that is water-soluble is not given [Malm et al., 1994, 2004]. We assumed 50% of the OC was WSOC. Measurements have found WSOC fractions in this range [Lowenthal et al., 2009; Pio et al., 2007]. Sensitivity tests also examine this assumption.
 Values for the van't Hoff factor, molecular weight, density, charge, and soluble fraction of OC were needed for the WSOC. Ervens et al.  suggested that a van't Hoff factor of one produced the lowest error in predicting ND, and Mircea et al.  showed that the average predicted ND was 20% smaller than the measured ND when the organics were assumed undissociated. Ervens et al.  also found that high molecular weight species (M > 400 g mol−1) influence droplet concentrations. For simplicity, we assumed the WSOC had a molecular weight of 50 grams mol−1, a van't Hoff factor of one, a density of 2.0 grams cm−3, and carried no charge.
 Two parameterizations of surface tension, σT, were compared in this study. Mircea et al.'s  parameterization and treating σT as the sum of the multi-component aqueous solution [e.g., Topping et al., 2007]. PUTT's treatment of σT had previously accounted for only the inorganic aerosol components [Seidl, 1989]. We included values of surface tension as a function of WSOC taken under a variety of atmospheric conditions (i.e., polluted continental, remote continental, biomass burning conditions, and wet-season) [Facchini et al., 1999, 2000; Mircea et al., 2005].
3. Description of Sensitivity Cases
Table 1 lists the base cases and test cases we considered. B, N, and NS are the base cases to which other cases are compared. The base cases use the aerosol compositions created from IMPROVE and are different in NA and σg. Any cases not marked with an S use a geometric standard deviation and mode radius fit to the size distribution of Dusek et al.  in the fine mode (σg,f = 1.5) and of Niemeyer et al.  for the coarse mode (σg,c = 1.5). Cases marked with an S use σg,f = 2.0 and σg,c = 3.5. For cases 1, 3–12, and 21, NA was calculated for each region from the measured mass concentration in IMPROVE. For cases 2 and 13–20, all regions have a fine and coarse mode number concentration of NA,f = 1000 cm−3 and NA,c = 0.75 cm−3, respectively, based on typical continental NA values [Seinfeld and Pandis, 2006]. For all cases, the fine mode and coarse mode radii are 0.03 μm and 0.3 μm, respectively.
Table 1. Base Cases N, NS, and B and Descriptions of Each Test Casea
Description of Changed Microphysical Variable of Test Case From Base Caseb
× 100%; and Mean of ND,test in cm−3
The five columns from the right list the mean of the difference of ND in the ith region of the test case from the base case normalized by mean of ND for all regions in the base case. The mean ND in cm−3 of all regions for each test case is listed after the percentage.
Test case acronym is listed in bold.
Case N: NA Calculated Regionally From IMPROVE
1. Changing size distribution to σg,f = 2.0 and σg,c = 3.5 NS
2. Changing to NA constant in every region, NA,f = 1000 cm−3, NA,c = 0.75 cm−3B
3. Changing to constant nitric acid concentration of [HNO3](g) = 0.2 ppbv NG
4. Changing to constant composition of 6% H+, 48% SO4−−, 20% WSOC, 26% Insol. NC
Case NS: NA Calculated Regionally From IMPROVE With σg,f = 2.0, σg,c = 3.5
5. Less WSOC (0.05%) in fine mode and more WSOC (95%) in coarse mode NSW2nd
6. Changing accommodation coefficient to 1.0 from 0.1 NSA
7. Not calculating surface tension from WSOC NSst
8. Less WSOC (0.05%) in coarse mode NSWin
t 0.7%, 856
9. Changing to using only the fine mode NSln1
10. Changing nitric acid equilibrium prior to uplift NSH
11. Changing to constant composition of 6% H+, 48% SO4−−, 20% WSOC, 26% Insol. NSC
12. Changing size distribution to σg,f = 1.5 and σg,c = 1.5 N
Case B: NA Constant Regionally, NA,f = 1000 cm−3, NA,c= 0.75 cm−3
13. Less WSOC (0.05%) in fine mode and more WSOC (95%) in coarse mode BW2nd
14. Changing size distribution to σg,f = 2.0 and σg,c = 3.5 BS
15. Changing to constant nitric acid concentration of [HNO3](g) = 0.2 ppbv BG
16. Changing accommodation coefficient to 1.0 from 0.1 BA
17. Changing to constant composition of 6% H+, 48% SO4−−, 20% WSOC, 26% Insol. BC
18. Changing nitric acid equilibrium prior to uplift BH
19. Less WSOC (0.05%) in coarse mode BWin
20. Changing to using only the fine mode Bln1
21. Calculating aerosol number concentration based on IMPROVE mass concentration N
 Cases marked with a G assume [HNO3](g) = 0.2 ppbv in every region, otherwise results from Feng and Penner  were used. Cases marked with a C used a simplified composition of 6% H+, 48% SO4−−, 20% WSOC, and 26% insoluble components in every region, derived from a correlation of the droplet numbers with each component of the composition over all regions and vertical velocities in cases B, BS, and BG. Surface tension was calculated using Mircea et al.'s  parameterization, but cases marked st calculate σT as the sum of the multi-component aqueous solution. Cases marked ln1 used only the fine mode mass and concentration to explore how neglecting the course mode mass would affect ND. Cases marked H assumed that a gas-aerosol nitric acid equilibrium is not achieved prior to updraft. For all simulations, the accommodation coefficient for [HNO3](g) was equal to 0.05 [Xue et al., 2005]. There is uncertainty in the value of the water vapor accommodation coefficient, α [McFiggans et al., 2006]. Cases labeled A set α to 1.0 instead of 0.1. Cases labeled Win assume 50% and 0.05% of the OC in the fine and coarse modes, respectively, is WSOC. Cases labeled W2nd assume 0.05% and 95% of the OC in the fine and coarse modes, respectively, is WSOC. Cases Win and W2nd test ranges of measured WSOC fractions [Lowenthal et al., 2009; Pio et al., 2007].
4. Case and Regional Comparisons of ND
Table 1 lists the average difference between each test case and base case normalized by the mean of the base case. Mean droplet number increases with vertical velocity. The largest differences in absolute percentage values for base case B is that with test cases N and BW2nd. The largest differences in absolute percentage values for base case NS is that with test cases N and NSW2nd. An average increase in NA in test case N creates more droplets than in base cases B and NS. In cases BW2nd and NSW2nd, the amount of soluble mass was decreased in the fine mode and increased in the coarse mode causing the larger, but fewer, more soluble aerosols to form droplets at the expense of the smaller, more numerous, less soluble fine mode aerosols. The third largest difference for ND for base case B is with test case BS. This is due to the increased width of the size distribution and higher concentration of large-radii aerosols forming droplets at the expense of the small-radii aerosols. The remainder of the sensitivity tests did not have average differences greater than 20% for ND between the base cases and test cases.
 The inter-regional variation (standard deviation divided by the mean ND) shows how the changes in composition between regions or changes in the microphysical variables affect ND. A high inter-regional variation value of ND for a case implies an empirical relationship of ND based on a region's value would not be accurate if applied to other regions. Figures 1b–1e show ND (cm−3) in every region for a subset of the test cases from Table 1. Changes in composition between regions cause an inter-regional variation in ND of 8% when all the seasons are averaged (Figure 1b), and a 15% variation of ND in the spring (Figure 1e). The mean ND is increased by 6% to 534 cm−3 in spring compared to the annual average mostly due to a factor-of-two average increase in [HNO3](g). The ND in spring is increased by 20% along the eastern U.S. in regions 2 and 16 primarily due to an average increase in [HNO3](g) from 13 to 26 ppbv. The ND in regions 8, 9, and 19 also increased by 15% due to the increase in [HNO3](g) from 7 to 14 ppbv. Changes to the composition caused changes to ND within and between regions by 10–20%.
 The annual average of ND for base case NS, shown in Figure 1c, has the same aerosol composition as the annual average of base case B (Figure 1b), and NA is also unique in every region which causes an inter-regional variation of 48%. The average ND decreased by 12% compared to case B due to an average decrease in NA in case NS. Figure 1d shows the BW2nd case which has the largest inter-regional variation of 60%. From Table 1, case BS has the third largest average difference in ND from base case B but has a negligible inter-regional variation (not shown in Figure 1). This is due to the increased width of the size distribution and higher concentration of large-radii aerosols forming droplets at the expense of the small-radii aerosols.
5. Changes to ND for Different Smax
Figure 2 shows the computed ND at the maximum supersaturation, Smax, for test cases 5–12 against base case NS separated into two Smax ranges. This was done to examine whether a parameterization of the base case that is a function of Smax and NA could be used. Slopes of best-fit lines and correlation coefficients were calculated and are reported in the caption. A test case that has a low correlation with the base case NS suggests an empirical relationship formed from the base case would not correctly predict ND.
 For both the low and high ranges of Smax, cases NSH, NSst, and NSWin have slopes and correlations of ∼1.0. This indicates that a parameterization would not need to include changes in the gas-aerosol equilibrium of nitric acid prior to updraft, the parameterization of surface tension, or a small concentration of coarse-mode aerosols with less soluble mass. In both the low and high ranges of Smax, cases NSC, N, and NSA all have correlation coefficients greater than 0.83 with slopes that range from 0.73 to 2.60. If a parameterization that is based on simplified composition or inaccurate NA and σg is applied, then the calculated average ND and cloud albedo effect will also be inaccurate. Case NSln1 shows a correlation and slope of ∼0.70 at low Smax, but a correlation and slope of 0.28 at high Smax. For the low and high ranges of Smax, NSW2nd has correlations and slopes much different from 1.0. Thus an empirical relationship that is based on aerosol parameters similar to case NS could not correctly calculate ND if applied to other regions that had a different number of modes or amount of soluble material.
 Measurements of aerosols in Europe have shown that the aerosol size distribution mostly determines the aerosol's ability to become a cloud droplet [Dusek et al., 2006]. In this study, it was found that the aerosol size distribution and composition cannot be ignored by global models when calculating the ND for the cloud albedo, which is based aerosol compositions measured in the United States from 1988 to 2004. These results are based on assumptions regarding the size-resolved and physicochemical properties of WSOC. Changing these assumptions would affect ND, and further sensitivity studies could identify which WSOC properties were most important for modeling. A global model using an empirical relationship based on regional measurements could over- or under-predict ND when applied to other regions depending on differences in composition, the number of log-normal modes, NA, and σg. Regional and seasonal differences in trace gas concentrations, organic, inorganic, and insoluble aerosol compositions cause high variability in ND, suggesting a more thorough treatment and not a simplification of aerosol composition is needed for an accurate prediction of ND.
 We thank Yang Chen for his contributions to PUTT. E.L. Roesler is funded by GREF within the DOE. The ARM Program provided partial support for this study through grant DOE-DE-FG02-97-ER62370.