Cloud condensation nuclei (CCN) are characterized by their critical supersaturation (Sc), which is a function of particle size and chemistry, namely water solubility. Measurements that relate particle size to Sc can thus be used to determine CCN solubility. A sufficiently small degree of variability of size-Sc measurements has been cited as evidence that CCN can be deduced from particle size measurements alone. Since particle size is so much easier to measure than particle chemistry or CCN this would have significant advantages for investigations of the largest climate uncertainty, the indirect aerosol effect; e.g., remote sensing of CCN. However, we present size-Sc measurements with a greater range of variability, which appears to at least limit or cast doubts on the practicality of deducing CCN from particle size measurements.
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 The size of cloud condensation nuclei (CCN) is an important atmospheric parameter that reflects the solubility or hygroscopicity of atmospheric particles. CCN size is determined by measuring the critical supersaturation (Sc) of a narrow size range of an aerosol, which can be obtained by passing the aerosol through a differential mobility analyzer (DMA) and then to a CCN spectrometer [Hudson and Da, 1996]. Various different narrow sizes can be selected by adjusting the DMA voltage to produce a size-Sc curve over the range of supersaturations (S) of significance for atmospheric clouds. This method provides a means of isolating the effects of particle composition (chemistry) on CCN activation; i.e., by removing the effect of particle size on CCN activation. Particles of the same size can have different Sc depending on their water solubility, which depends on their chemistry. It has been suggested that if the variations in particle solubility (chemistry) are small enough it might be possible to deduce particle Sc values from size measurements alone [Dusek et al., 2006]. This would be more convenient for research on the extremely important indirect aerosol effect (IAE), the largest climate uncertainty [Intergovernmental Panel on Climate Change, 2001], because particle size is easier to measure than particle chemistry or CCN. Particle size is also easier than chemistry or CCN for remote sensing. Since remote sensing of CCN would be a large step for IAE research, this is an extremely important atmospheric science issue.
 A recent report [Dusek et al., 2006] found a small enough range of variability of particle size-Sc measurements to suggest that CCN might be adequately deduced from particle size measurements. Here we present a more extensive set of size-Sc measurements that shows significantly more variability than Dusek et al. . These measurements show a size-Sc range that is similar to that reported by Hudson and Da . These measurements are also similar to Hudson and Da  in that there is a suggestion of systematic variability in the size-Sc relationship; i.e., the particles are less soluble in more polluted air masses.
 The measurement methods are the same as described by Hudson and Da . The only difference is that there were also simultaneous direct CCN measurements with a second Desert Research Institute (DRI) instantaneous CCN spectrometer. The DRI CCN spectrometers deduce spectra simultaneously from the sizes that droplets attain within a continuous flow thermal gradient diffusion cloud chamber with carefully controlled temperatures, pressure and flow rates [Hudson, 1989]. The lower Sc nuclei produce larger droplets. The instrument must be calibrated with particles of known Sc, NaCl aerosol that has passed through a DMA at various size settings (Figures 1a and 1b). The subsequent calibration curve (Figure 2) is then used to relate channel number (i.e., cloud chamber droplet size) to Sc so that a spectrum can then be deduced when ambient aerosol is sampled (Figures 1c–1f). An earlier version of the present DRI CCN spectrometers that used the same principles of operation agreed with the best CCN instruments tested in the last international CCN workshop [Hudson and Alofs, 1981; Kocmond et al., 1981].
 There is some uncertainty in ambient spectral measurements due to artificial instrument broadening and coincident pulses. However the very low concentrations that emerge from the DMA due to the small fraction of charged particles (Boltzmann equilibrium) precludes coincident pulses. The narrow size distributions from the DMA generally produce narrow droplet size distributions in the cloud chamber; at least this is the case for consistent particle compositions such as the calibrations. Mean Sc values of narrow distributions are not as vulnerable to broadening errors as are complete spectra because broadening mainly affects the wings of the distribution but has little effect on the peak or the mean.
 No correction was made for multiple charging, which has the greatest effect for the larger particles (lower Sc), because they have greater numbers of multiple charges. The maximum correction at 0.02% Sc for NaCl is 18% in Sc. This is an overestimate based on a flat input aerosol distribution to the DMA. Although we did not measure the aerosol input distribution to the DMA from either the NaCl aerosol generator or the ambient, the peak was definitely less than 100 nm (0.1% Sc). This means that for all sizes larger than 100 nm (<0.1% Sc) the larger multiply charged particles were an even smaller fraction of the singly charged particles than the flat input distribution estimate. The multiple charge correction for a flat input distribution is only 5% at 100 nm (0.1% Sc). Furthermore, any error caused by the multiply charged particles is similar for the ambient and calibration measurements. So the more negligible relative effect of such a correction had even less effect on the overall results of this study.
 The CCN spectrometer produces a simultaneous measurement of the CCN spectrum [Hudson and Yum, 2001, 2002; Yum and Hudson, 2004] over a large S range. However measurements from the DMA usually show narrow distributions in terms of concentration versus Sc (i.e., Figures 1d and 1f). A meaningful mean value of Sc can often be ascertained within a minute. Different sizes (i.e., voltages) were dialed on the DMA to produce a series of data points relating dry particle size (rd) to Sc within a few minutes (i.e., Figure 3). This was fast enough to be done on level aircraft flight legs [Hudson and Da, 1996]. The mobility provided by aircraft produced measurements in a greater variety of air masses as shown in Figure 3 and Table 1. Figure 3 also shows the theoretical relationships between dry particle size and Sc for NaCl and ammonium sulfate. These inorganic substances represent the upper limit of particle solubility; i.e., there are few substances in the atmosphere that are more soluble than NaCl. Less soluble substances (e.g., many organics) have relationships to the right and above these lines.
Table 1. Average, Standard Deviation, and Range (Maximum-Minimum) of the Solubility Parameter, B, for the13 Sets of Size-Sc Measurementsa
B (60 nm)
Average and sd of B
Ambient CN, cm−3
Ambient CCN, cm−3
Also shown are interpolated B values for a dry particle size of 60 nm and a critical supersaturation (Sc) of 0.4% for each measurement set (the missing row for these would have required extrapolations instead of interpolations). Also shown are the dates, times, altitude, and locations of each measurement set and simultaneous condensation nuclei (CN) and direct ambient CCN concentrations at approximately 0.5% S. Later rows show the average, standard deviations, and ranges of each measurement. The bottom rows show the B values for sodium chloride and ammonium sulfate.
Nov 24, 2003
0.19 ± 0.10
Nov 24, 2003
0.58 ± 0.43
Nov 25, 2003
0.38 ± 0.33
Dec 4, 2003
0.16 ± 0.04
Dec 4, 2003
0.37 ± 0.17
Dec 4, 2003
0.42 ± 0.17
Jan 19, 2005
0.97 ± 0.37
Jan 24, 2005
0.91 ± 0.24
Jan 24, 2005
1.07 ± 0.35
Jan 24, 2005
0.53 ± 0.17
July 25, 2005
off central California
0.40 ± 0.17
July 25, 2005
off central California
0.12 ± 0.03
July 25, 2005
off central California
0.36 ± 0.14
 All of the measurements shown here (Table 1) were done at geopotential altitudes less than 1.6 km, which are usually characteristic of the aerosol that is input to clouds. In fact the major concern of all of these projects was clouds and how CCN influence those clouds.
Figure 3a shows data obtained over the eastern United States and Canada during late fall 2003 as part of the Second Alliance Icing Research Study (AIRS2) [Isaac et al., 2005]. Data on Nov. 24 were obtained over an urban area (Syracuse NY) while data obtained on Nov. 25 and Dec. 4 were obtained over Lake Huron. The second set of measurements on Nov. 24 was done at a higher altitude (1550 m) above most of the pollution measured in the first Nov. 24 measurement (600 m). The much higher temperature of the aircraft cabin compared with the ambient temperatures at this season ensured drying of the aerosol below 40% R.H. before entering the DMA.
Figure 3b shows data obtained in clean maritime air masses in the eastern Caribbean near the island of Antigua, which is at the northeast corner of the Antilles. Since the predominant wind direction there in the Western Atlantic is east-northeast the fetch is generally oceanic with no islands upwind. This was the case for the two dates for which size-Sc measurements were done. These measurements were obtained as part of the Rain in Cumulus over the Ocean (RICO) experiment (R. Rauber et al., Rain in cumulus over the ocean—The RICO campaign, submitted to Bulletin of the American Meteorological Society, 2006). Drying of the aerosol was assured by heating the sample to more than 50 degrees C.
Figure 3c shows data obtained off the central California coast during the Marine Stratus Experiment (MASE) [Ghan and Schwartz, 2007]. Here measurements were obtained below and above a low stratus cloud deck on July 25. Wind direction was parallel to the coastline and concentrations were intermediate between that of maritime and continental air masses. There was a distinct difference between the below cloud and above cloud concentrations and size-Sc measurements. Here also the higher cabin temperature ensured a dry aerosol entering the DMA.
 One way to compare the various size-Sc measurements is to compare the Sc values obtained at the same rd. However it was not always possible to use exactly the same DMA voltages in all of the measurement sets, but it was usually possible to obtain interpolations at the same rd. This is how much of Figure 3d and columns 5 and 6 of Table 1 were obtained. Cases where the range of measurements did not encompass the denoted sizes or Sc values (i.e., extrapolations) are blank in Table 1 and are not counted for the extreme values in Figure 2d.
where S is supersaturation in percent, A is the Kelvin term, Brd3 is the Raoult term and r is the variable droplet size. At Sc and rc the derivative of this equation with respect to r is zero. Thus
This is then substituted back into the above Köhler equation at S = Sc
Then solving for B, with rd expressed in nanometers and typical values for the constants
Lines of constant B are parallel; B(NaCl) = 1.23 and B(ammonium sulfate) = 0.70 are shown in Figure 3 [Hudson and Da, 1996]. Lower B represents less soluble substances. Table 1 shows the average, standard deviation, and ranges (maximum-minimum) of B computed from the 13 sets of rd-Sc measurements displayed in Figure 3. Figure 4 suggests a possible relationship between B and CN concentration that is similar to the work of Hudson and Da [1996, Figure 12]. This figure for ambient CCN concentrations is similar. Figure 4 generally supports Hudson and Da  that the rd-Sc relationship usually more closely resembles that of inorganic soluble species in cleaner air masses (i.e., RICO, Figure 3b). In more polluted air masses, which generally have higher CN and CCN concentrations, dry particles with the same Sc are larger. This could be because the aerosol material is less soluble (i.e., organics) or that the same soluble material (i.e., NaCl or ammonium sulfate) is internally mixed with less soluble or insoluble material (i.e., carbon) that adds size but not nucleating ability.
Dusek et al. [2006, Figure 1] showed that 60 nm dry particles had an Sc range of 0.5 to 0.7% whereas Figure 3d here shows an average of 0.46% with a range of 0.26–0.79% Sc for 60 nm dry particles. A very similar range, 0.3–0.8% Sc, was presented in the work of Hudson and Da [1996, Figures 9 and 11] but Table 1 of Hudson and Da  showed a larger range. The present Sc range for 60 nm dry particles (0.53%) is more than twice that of Dusek et al.  (0.2%). In terms of average Sc; i.e., (0.53/0.46 = 1.15) the relative range here is more than three times that of Dusek et al.  (0.2/0.6 = 0.33). In terms of B Dusek et al.'s  range for 60 nm dry sizes is 0.15–0.29 whereas the range here extends from 0.11–0.98. Thus this 0.86 total B range is six times the B range of Dusek et al.  (0.14) for 60 nm dry particles. The entire measured B range of Dusek et al.  (0.14) for 60 nm particles is less than half of the B standard deviation in Table 1 (0.36). In terms of the relative B range (dividing the range by the average), 1.7 is three times the 0.63 relative B range of Dusek et al. . Similar relative Sc ranges were measured for other dry particle sizes (Figure 3).
Table 1 of Dusek et al.  showed a 17 nm dry particle size range for particles with 0.4% Sc (66–83 nm) but Figure 3 here shows a 49 nm range for 0.4% Sc particles (44–93 nm). In terms of the average this 74% relative range (49/66) is more than three times the 23% relative range of Dusek et al.  (17/74). Hudson and Da  found a 66% relative range of diameters at 0.4% S. Again the standard deviation here equals the entire range of Dusek et al. . In terms of B this 0.99 range is nearly six times the 0.17 B range (0.17–0.34) for 0.4% Sc particles reported by Dusek et al. . Again the relative range of 2.2 is three times the relative range of 0.68 for 0.4% Sc particles by Dusek et al. . Once again similar relative dry particle size ranges were found for other Sc values (Figure 3).
 The range of average B for the 13 measurement sets (0.95) is five times the range of all of the measurements reported by Dusek et al.  although the 1.9 relative range is only 2.3 times the 0.82 relative B range of Dusek et al. . The 0.83 total B range reported by Hudson and Da  is similar to the total average B range reported here although the full range of B measurements of 1.43 reported here is higher.
 Probably the main reason for the difference in rd-Sc variability between Dusek et al.  and the current results was the lack of cleaner air masses observed by Dusek et al. . One day of travel over the European continent is entirely sufficient to convert a maritime aerosol into a continental or polluted aerosol. Moreover, air masses over the North Sea are unlikely to be as pristine as air masses more distant from the densely populated European continent and British Isles, especially during the summer season. Most of the greater range of these measurements compared to Dusek et al.  was for higher B, or lower Sc for the same dry sizes, or smaller rd for the same Sc. The extension of the B range compared to that of Dusek et al.  was mostly for cleaner air masses that often approach the rd-Sc relationship of the soluble salts.
 Although an rd-Sc relationship approaching that of NaCl was often found in marine air masses there are frequent continental outflows (e.g., MASE, Figure 3c) that result in a large variability of the rd-Sc relationship over the ocean. Differential CCN spectra (i.e., Figures 1d and 1f) of narrow particle size ranges from the DMA might have more than one mode [Alofs et al., 1989] in mixed air masses [Hudson and Da, 1996]; i.e., externally mixed aerosol. This would render mean Sc values for such rd-Sc measurements rather meaningless. Even with a single Sc mode for the narrow size measurements, a mean Sc value would not be a sufficient characterization of size-Sc relationships if there were variability in the widths of the measured spectra [Alofs et al., 1989]. Variations in CCN spectral width of narrow particle size measurements could be due to variations in particle composition among the particles (external mixing), namely that due to variations of the soluble component of the particles. This could result in variations in the width of the spectra for rd-Sc measurements, which would also render the mean Sc values insufficient to characterize the CCN.
 The conclusion of Dusek et al.  that size measurements alone could be used to accurately estimate CCN depended on the narrow range of rd-Sc measurements that they observed at one surface location in Germany during the summer. Since they claimed to have measured this limited range in a variety of air masses this might suggest that there is the same limited range of rd-Sc in all air masses. However, we have shown that this is certainly not true. Their range seems to be characteristic of polluted air masses and not at all characteristic of cleaner air masses.
 On the other hand Dusek et al.  also said that it might be necessary to classify air masses according to their rd-Sc relationship before it is possible to deduce CCN from size measurements alone. This seems to be an admission of the greater variability of the rd-Sc relationship such as shown here and by Hudson and Da . If the air masses need to be classified according to rd-Sc this is also an admission of the importance of particle chemistry vis-a-vis particle size for determining and deducing CCN. Dusek et al.  seemed to be saying that although there may be different ranges of values of rd-Sc in different air masses, there might be small enough variability in rd-Sc within each air mass so that particle size measurements might be sufficient to estimate CCN. This would thus require measurements showing sufficiently small ranges of variability in rd-Sc and analyses similar to that presented by Dusek et al.  in a variety of air masses. The apparent systematic variability in particle solubility, B, with air mass (CN concentration) (Figure 4) suggests that the large overall rd-Sc range might give way to smaller ranges within given air masses as found by Dusek et al. . This suggests hope that size measurements might produce sufficiently accurate CCN estimates within individual air masses as long as consistent limited rd-Sc relationships can be verified. It appears that this probably has the greatest likelihood in polluted air masses, but is least likely in mixed air masses such as may be found over the ocean, especially when continental pollution is advected there. Since these are the very situations that are of most importance for understanding IAE this does not bode well for the practicality of deducing CCN from particle size measurements. Moreover, one of the advantages of deducing CCN from size measurements is the greater possibility of applying remote sensing. However, remote sensing works best over the ocean where the rd-Sc relationship is seldom within the range measured by Dusek et al.  and is often likely to exhibit a wide and variable rd-Sc range and where the mean Sc may not be sufficient to characterize the rd-Sc relationship. Any of these factors would make it difficult to deduce CCN from size measurements.
 The title of Dusek et al. , “Size matters more than chemistry for cloud-nucleating ability of aerosol particles,” is not in dispute. This was first noted by Junge and McLaren  and as Dusek et al.  point out, Sc is proportional to the third power of particle diameter and only the first power of soluble fraction. Analogously the Moon matters more for ocean tides than the Sun but neglecting the gravity of the Sun could put one into deep water. Here neglecting particle chemistry could often produce inaccurate estimates of CCN.
 Support for the AIRS2 and RICO measurements was from the US National Science Foundation grants ATM-0313899 and ATM-0342618. Support for the MASE measurements was from the Atmospheric Sciences Program of the US Department of Energy grant DE-FG02-05ER63999. The aircraft in AIRS2 and RICO was the NCAR RAF C-130 and the MASE aircraft was the Battelle G1.