Changes to the number of cloud condensation nuclei (CCN) will impact on cloud microphysical properties, with an increase in CCN resulting in more and smaller cloud droplets and in brighter clouds with longer lifetimes, higher liquid water content and increased cloud thickness . The net effect of these aerosol–cloud interactions is to cool the climate system, however significant uncertainties remain in predicting the magnitude of this impact . A better understanding of these interactions is needed to improve climate predictions.

The ability of aerosol particles to act as CCN depends upon their size and chemical composition. A number of regional and global models have been developed over recent years to predict CCN number concentrations based on these parameters e.g.. In order to verify and improve these models, measurements of CCN properties from a wide range of locations around the world are needed.

CCN properties of aerosols can be measured in the subsaturated regime with a Hygroscopicity Tandem Differential Mobility Analyser HTDMA; for a review, see and in the supersaturated regime with a cloud condensation nuclei counter CCNc;. Reconciliation studies between these two measurement techniques allows us to test our understanding of aerosol water uptake processes, and to investigate the suitability of applying simplifying assumptions to models.

Extrapolation between the sub- and supersaturation regime can be approximated through Köhler theory with hygroscopicity described by a single parameter. Several such parameters have been proposed for a review, see, such as that of . Denoted κ, this has been widely used in recent years e.g., particularly in reconciling sub-saturated particle hygroscopicity with CCN measurements. Several hygroscopicity–CCN reconciliation studies have been published over the past decade or so e.g.; however all these studies concentrated on measurements at a single site, making it impossible to generalise the conclusions. Here we present, for the first time, a meta-analysis of reconciliation studies by our group at a large number of different locations including marine, tropical, background continental and urban environments. Such a comprehensive compilation of reconciliation studies allows us to explore instrumental discrepancies and whether reconciliation is affected by the environment in which the measurements were taken.

Figure  shows all the experiments from 2006 to 2013 at which measurements were made with the HTDMA and CCNc instruments described below. The measurements that are included in this study are labelled in bold in the figure text. These include a total of eight locations, at two of which (Mace Head and London), separate summer and winter measurement campaigns were conducted. In each campaign, the measurements were conducted over three to six weeks at a time. The measurements covered a range of different ambient environments including marine (Discovery cruise, Mace Head, Weybourne), tropical (Borneo, Amazonia), continental background (Hornisgrinde, Chilbolton) and urban (London). These data sets were selected out of all those in Fig.  for the quality of the data and suitability of measurement configuration for reconciliation study. The HTDMA and/or CCNc measurement data collected in the other experiments shown in Fig.  were less suited to hygroscopicity–CCN reconciliation.

For each experiment, CCN activity was measured as a function of supersaturation and particle dry size using a Droplet Measurement Technologies cloud condensation nuclei counter CCNc;. The calibration and operation of the CCNc is described fully by and , with mostly the same methods used in all projects. Briefly, a dried (<20% RH, relative humidity) monodisperse aerosol sample was supplied by a differential mobility analyser (DMA) stepping discretely through a range of sizes (the exception being Chilbolton, where the sample was not dried). The sample was then split between the CCNc and a condensation particle counter (CPC; TSI model 3010). The ratio of the number of CCN (NCCN) to the total number concentration of aerosol particles (NCN) is the fraction of particles activated (FA(S,D0)) at a given supersaturation, S, and dry diameter, D0. The resulting activation spectra (FA(S,D0) as a function of dry diameter, D0) can be used to derive the diameter at which 50 % of the particles activate (D50) by fitting a sigmoid curve function. The hygroscopicity parameter, κ, can then be derived using the κ-Köhler model, and will be denoted by κD50.

Hygroscopic growth factor distributions were measured during each experiment using a Hygroscopicity Tandem Differential Mobility Analyser (HTDMA). Two different instruments were used: the first (HTDMA1), developed by , was used during the Discovery, Hornisgrinde, Borneo, and Amazonia experiments, while the second (HTDMA2), developed by , was used in the remaining experiments. In all cases, calibrations were conducted as discussed by , and the data were processed using the TDMAinv software described by . In the HTDMA, a dry aerosol sample is size-selected with the first DMA and then humidified to 90 % RH except at Hornisgrinde where 86 % RH was used;. The second DMA is then used to measure the size distribution of the humidified aerosol, to give the distribution of Growth Factor (defined as the ratio of wet to dry aerosol diameter) as a function of RH and dry diameter (GFRH,D0). For most of the studies, 5 to 7 dry sizes were scanned in this way, ranging from 24 to 300 nm. Values of κ can be calculated from the mean growth factor measurements as described by Eq. (): S=GF‾3-1GF‾3-(1-κ)exp⁡4σwMwRTρwD0GF‾, where S is the supersaturation (RH/ 100%), GF‾ is the mean growth factor, κ is the hygroscopicity parameter, σ is the surface tension of water, Mw is the molar mass of water, R is the universal gas constant, T is the temperature, ρw is the density of water and D0 is the dry diameter. The κ derived from the growth factor data will be denoted by κGF.

A number of approaches can be taken to calculate total NCCN as a function of supersaturation. From the CCNc data, the simplest way is to integrate NCCN(S,D0) as a function of D0 for each set supersaturation, Sset. Alternatively, the aerosol number size distribution (as measured by the CPC on the DMA) can be integrated from the largest size down to a threshold diameter (in this case, the D50 derived from the activation spectra). For the HTDMA data, a threshold diameter can be derived from the calculated κGF values for a given supersaturation, and from this, NCCN can be calculated as before. By using the Sset from the CCNc in deriving NCCN from the HTDMA, a direct comparison between the instruments can be made. In this study, NCCN from the CCNc data is derived from the aerosol size distribution and D50 and compared with NCCN derived from the HTDMA data. κ values are also compared between the instruments using the methods described above.

The calibration procedures employed in all experiments for both the CCNc and HTDMA are rigorous and described in detail by . The DMA upstream of the CCNc and the first DMA in the HTDMA were calibrated using latex spheres. The HTDMA was operated for a few hours without humidification every week or two, to calibrate for any offset between the two DMAs, and to define the instrument's transfer function. Both the HTDMA and the CCNc were generally calibrated at the start and end of each experiment using nebulised ammonium sulfate. For the HTDMA, this calibration involved running a humidogram: i.e. measuring the GF at a range of RHs at a fixed dry diameter (typically 150 nm), and comparing to theoretical GF . Corrections can then be made to the measured RH where necessary. The CCNc was calibrated by sampling nebulised and dried monodisperse ammonium sulfate from a DMA at 3–5 mobility diameters between 30 and 100 nm . At each diameter the temperature gradient in the CCNc was stepped up and an activation curve (CCN/CN) was derived. The temperature gradient at which 50 % of the particles were counted as CCN was assumed to correspond to the critical supersaturation. The temperature gradient to supersaturation relation was then derived by a linear fit to the theoretical critical supersaturation at each diameter.

The median and ranges of the aerosol size distributions for each campaign are shown in Fig. . In all cases, these were derived from the DMA and CPC attached to the CCNc. These show a wide variation in the aerosol size distributions between the different campaigns, and a similarly wide variation can be seen in the GF distributions from the HTDMA measurements, which are shown in the Supplement for each experiment, and are reported for 90 % RH at all locations (except Hornisgrinde, which is reported at 86 % RH). The aerosol size distributions observed in London are similar to previous measurements e.g., while the GF distributions show an external mixture with hydrophobic (GF ≈1) and hygroscopic modes (GF=1.5), similar to other urban measurements . At Mace Head, the winter measurements were dominated by “modified marine” air masses, while the summer experiment saw a largely “clean marine” fetch, and the measured size distributions were typical of these respective air masses . The modified marine GF distribution was dominated by a hydrophobic mode (GF ≈1.1), while the clean marine had a strong sea salt mode (GF ≈2.2). Both experiments exhibited a hygroscopic mode (GF = 1.5–1.7), which largely dominated in the summer campaign but showed significant variability along with the sea salt mode. Both the aerosol size distributions and the GF distributions measured in the Amazon were typical at that site in the dry season , but differed considerably from the other tropical measurements at the Borneo site, which, by contrast, was strongly influenced by marine air masses . In the Amazon, the GF distributions show a persistent, internally mixed aerosol with GF 1.2–1.3, while in Borneo, the dominant mode varied between GF 1.4–1.6 (depending on dry size) with an occasional hydrophobic mode. From its location, Chilbolton is regarded as a rural background site, and further analysis of other measurements taken during this campaign (unpublished data) suggests the aerosol is largely representative of regional properties, with only a small influence from local sources. The GF distributions show a persistent external mixture with modes around 1.1 and 1.5. The Discovery cruise took place off the coast of West Africa, and over the course of the campaign, three distinct air masses were seen: African, Continental (from Southern Europe) and Marine. These are not separated out for the purposes of this study, and the size distribution in Fig.  represents the whole data set. Growth factors were mostly around 1.7, and showed a largely internal mixture for most of the experiment, except for a sporadic sea salt mode at the larger sizes. A more in-depth examination of this is provided by . Hornisgrinde is a mountaintop site, which was frequently in cloud during measurements , and is described as “continental background”. The GF distribution is more variable with time and dry size that at some of the other experiments, ranging 1.1–1.4 (at 86 % RH). A bimodal GF distribution can be seen sometimes at the larger dry sizes. Finally Weybourne, while being coastal, can experience a variety of different air masses, and did so during the experiment , and frequently sees aged polluted plumes from the UK and mainland Europe. The GF distributions show a dominant hygroscopic mode (which seems to vary diurnally between 1.4 and 1.7), accompanied by a weaker hydrophobic mode. As with the other campaigns, the Weybourne data set was considered as a whole for the purpose of this study. The compilation of all these data sets therefore provides a wide range of aerosol populations, typically present in the atmosphere at different locations. From this, it should be possible to probe whether this variation has any influence on the reconciliation.

For each measurement campaign, the mean values of NCCN and κ derived from D50 and GF were found for each Sset, and the ratios of these means are plotted in Fig. . The error bars represent the standard deviation of these ratios, and hence show the variation throughout a given experiment. In some campaigns, where the HTDMA calibrations drifted between the start and end of the experiment, both were applied and the spread is illustrated in Fig.  as shaded areas. The graphs show that the level of reconciliation varied greatly between the different experiments, generally varying with supersaturation. Poorest agreement between the HTDMA and CCNc across the range of supersaturations was found in the measurements from Hornisgrinde, Borneo, Chilbolton and the Discovery cruise. The other experiments largely showed agreement within the error bars for at least some of the supersaturation range. In general, there seems to be a tendency for the HTDMA measurements to underestimate hygroscopicity compared to the CCNc, especially at lower supersaturations, resulting in a ratio greater than one. The only exception to this is the Borneo experiment, though it is not clear why this is the case.

It is also not clear why the results for the Hornisgrinde and Discovery cruise data sets stand out in the reconciliation in Fig. . Possible reasons for discrepancies between CCNc and HTDMA derived κ and NCCN for the Discovery, Hornisgrinde and Borneo data sets have been discussed at length by and , respectively, and they are likely to apply in varying degrees to the other data sets. The discrepancies are described as being due either to instrumental differences or assumptions made in the model. Previously, discrepancies between measured and modelled CCN behaviour have been attributed variously to particle surface tension at the point of activation, changes in the kinetics of uptake in the instruments, or external mixing.

When using the κ-Köhler model, the surface tension is often assumed to be that of pure water, σ = 0.072 J m-2 . In reality, surface active compounds may concentrate at the water–air interface of a deliquesced particle, suppressing surface tension and affecting the CCN activity of the particle. A number of studies have explored the effect of this assumption on reconciliation, and have found either that reducing surface tension in the calculations would not improve closure , or that unrealistic values of surface tension would be required to account for discrepancies . Moreover, more recent work has demonstrated that bulk-to-surface partitioning offsets most of the influence of any surface tension reduction .

The κ-Köhler model also does not account for changes in solution non-ideality as a function of saturation ratio. To date, it has been very difficult to probe how κ varies as RH increases towards 100 % due to the uncertainties in HTDMA instruments at high RH . Recent developments should make this possible. The presence of slightly soluble compounds can influence the reconciliation, by only contributing measurably to water uptake in supersaturated conditions. This would result in an underestimate in NCCN from the HTDMA measurements . Particle non-sphericity, and the effect this has on their classification in DMAs, can also have the effect of suppressing the calculated κ from both GF and CCN measurements. This is because of the difference between a non-spherical particle's mobility diameter and its volume equivalent diameter. In sensitivity studies, found that the κ suppression was greater in GF calculations than from measured CCN data, resulting again in an underestimate of hygroscopicity from the HTDMA measurements compared to the CCNc measurements. These effects would result in the hygroscopicity being underestimated by the GF calculations compared to the CCNc derived values , and therefore may be partly the reason why there is a tendency towards a greater than one ratio, as seen in Fig. .

Instrumental differences mainly relate to the chemical behaviour of aerosols and gases in the respective instruments. Growth factor may be underestimated in the HTDMA if the residence time following humidification is too short to reach equilibrium before sizing in the second DMA , leading to an underestimate of hygroscopicity. In addition, volatile and semi-volatile compounds can evaporate during the drying process. While the HTDMA and CCNc use the same dryer in all these measurements, the subsequent behaviour of the volatilised gases in the different conditions of each instrument can lead to further discrepancies . For example, the saturation column of the CCNc can act as a mist chamber, where droplets take on soluble material from the gas phase, potentially increasing the NCCN count. Indeed, the possible influences of semi-volatile components on droplet activation and on reconciliation between sub- and supersaturated measurements has been discussed by and the impacts of semi-volatile co-condensation expanded by .

One possible reason for the higher discrepancy in the Chilbolton reconciliation is the fact that the aerosol sample was not dried before entering the instruments (Chilbolton was the only exception). The RH was often above 50 % and as much as 70 %, and the DMAs were therefore not selecting dry sizes. To test the effect of this, the values for the dry sizes were reduced (and GF‾ increased) by a factor of 1.1, to simulate dry aerosol sizes, and the analysis repeated to get the ratios. Figure S1 in the Supplement shows that this results in a substantial improvement in the reconciliation, especially for the NCCN ratios. It should be stated here that while the factor of 1.1 represents a realistic value at the RH measured in the aerosol sample, it cannot be verified, nor does it reflect the variability in inlet RH or κ, which would cause the correction itself to vary. These new results therefore do not represent the real ratios at Chilbolton. Nevertheless, this exercise illustrates the importance of using dry aerosol samples for these measurements, however as mentioned in the previous paragraph, drying can also lead to the removal of volatile and semi-volatile compounds from the condensed phase. This is potentially a very important artefact in these measurements, which may lead to false agreement in reconciliation studies, and therefore requires further study.

The aerosol mixing state might also affect agreement, since the methods commonly used to derive hygroscopicity and NCCN with the HTDMA and CCNc do not account for externally mixed aerosol, which can have different effects in the two instruments. A number of studies have considered this, using different methods to account for external mixing. Most of these e.g. found that mixing state has no effect on measurement reconciliation, however found that it is important in obtaining agreement between between HTDMA and chemical composition derived hygroscopicity. For this study the mixing state was parameterised, using the HTDMA growth factor distribution, by the absolute value of the mean growth factor subtracted from the peak growth factor. Strong external mixing could be seen in the HTDMA measurements at Chilbolton and London (Summer and Winter), and the mixing state parameter ranged 0.12–0.20. For measurements that showed a lesser degree of external mixing (i.e. a weaker secondary mode in the growth factor distribution; e.g. Borneo, Mace Head), the mixing state parameter ranged between 0.06 and 0.12, and was less than 0.05 for measurements showing a largely internally mixed aerosol sample (e.g. Discovery cruise). accounted for external mixing in their reconciliation study by defining a critical growth factor at each dry diameter, above which particles activate at a given supersaturation. The fraction of particles above this growth factor is the activated fraction, thus providing an activation spectrum (FA(S,D0)) from which to calculate D50 and hence NCCN as described above. For the CCNc, external mixing can be taken into account by integrating NCCN(S,D0) as a function of D0 for each Sset. The ratios of the mean values of NCCN derived from each method were calculated and compared to those shown in Fig. . No improvement was seen in reconciliation in any of the data sets, suggesting that mixing state does not affect hygroscopicity–CCN reconciliation, even when the degree of external mixing is high.

As already mentioned, there is a tendency in some of the data sets shown in Fig.  for the ratios to increase with decreasing supersaturation. A similar trend has also been observed in other studies e.g., and has been explained as resulting from greater uncertainties in the instrument at lower supersaturations. The threshold diameter at these supersaturations is higher up in the tail of the particle number size distribution, and so predictions are more sensitive to the counting statistics in the size distribution.While this can explain the wide variation in the measurements (shown as large error bars) that can be seen here, it would not account for the bias (i.e. that NCCN(GF) should be consistently less than NCCN(D50)). A bias at low supersaturations due to uncertainties in the determination of the supersaturation would be eliminated by the calibration method applied to these data sets, and so would not explain it. Therefore, it is not clear what causes the larger bias at low supersaturations.

This trend is not observed in the data sets that show the poorest agreement (Discovery cruise, Hornisgrinde and Borneo), and it is noted that all these measurements were conducted with the same HTDMA (HTDMA1). However the measurements in Amazonia also employed HTDMA1 and these show relatively good reconciliation, plus the trend of higher ratios at lower supersaturations. The two HTDMAs were operated side by side, sampling ambient air in Manchester, UK, along with a CCNc, in order to compare reconciliation results. The derived NCCN and κ ratios are shown in Fig. S2. Better agreement is seen using HTDMA2, but importantly, both exhibit the trend of increased ratios at lower supersaturations that is seen in other data sets in Fig. . This information shows that differences between campaigns in the relationship between ratios of NCCN or κ and supersaturation cannot be attributed to different instruments. A detailed analysis of differences between HTDMA systems is provided by and .

The wide range of locations from which the studies presented here derive make it possible to explore whether different environments (characterised by different aerosol populations) result in different degrees of reconciliation in water uptake measurements. No common patterns could be seen in Fig.  for measurements from similar environments, distinct from others, so there appears to be no such dependency.

For each data set, NCCN was also calculated from both the HTDMA and CCNc data using campaign averages of either κ (or D50 in the case of the CCNc) or size distribution. The results are shown in the Supplement as box plots of NCCN as a function of supersaturation for each method. In most of the data sets, averaging κ does not lead to a significant change in mean NCCN(S) from either instrument, whereas NCCN(S) derived using the mean size distribution shows a much reduced variability. Taken in isolation, the data from a single instrument may imply that NCCN is rather insensitive to κ, and hence chemical composition and that, unsurprisingly, size distribution is more important for predicting NCCN, in agreement with previous studies e.g.. However, that NCCN derived from different instruments frequently differs markedly indicates a strong requirement to understand the processes leading to the discrepancies and thereafter to define a protocol for reliable NCCN quantification in line with our most informed understanding of the physical processes involved in their measurement.

This paper presents a meta-analysis of particle water uptake reconciliation studies from measurements taken at eight environmentally diverse locations, during three to six week field campaigns between 2007 to 2013. By examining such a range of data sets, it is possible to produce more general conclusions, particularly regarding instrumental discrepancies or different environments. Reconciliation between HTDMA and CCNc measurements was examined by comparing NCCN and κ as a function of supersaturation, derived from the threshold diameter seen with the CCNc and the mean growth factor measured by the HTDMA. Many of the data sets showed agreement within the variability of the measurements throughout the supersaturation range and some disagreed at all supersaturations. There did not appear to be any clear dependence of the degree of measurement reconciliation on whether the data set was collected in a marine, tropical, background continental or urban environment, and neither could differences between campaigns be attributed to the use of different instruments. There was generally poorer reconciliation at the lower supersaturations, likely resulting from greater relative uncertainties in the size distribution at the threshold diameters that are observed at these low supersaturations. Discrepancies at other supersaturations are attributed to differences in the chemical behaviour of vapours and/or particles in the different instruments. Aerosol mixing state did not appear to affect reconciliation, even when strong external mixing was observed. Calculating NCCN from any one instrument using campaign averages of either κ or size distribution would indicate relative insensitivity of NCCN to the chemical composition with more of the variability in NCCN arising from the size distribution. An improved understanding of the reasons for discrepancies in these reconciliation studies is needed, along with better knowledge of the processes underlying CCN measurements. This is vital to our ability to provide reliable quantification of CCN behaviour for use in aerosol–cloud interaction studies.