The Mace Head Atmospheric Research Station is located on the North Atlantic coast of Ireland, County Galway, at 53∘19′36′′ N, 9∘54′14′′ W (O'Connor et al., 2008). Air is sampled from the main community sampling duct that draws air from 10 m above ground level and is positioned 80–120 m from the ocean depending on the tide. Meteorological data are recorded at the station, including rainfall, solar radiation, wind speed, wind direction, temperature, RH and pressure (available at http://www.macehead.org/, last access: 26 March 2020). Measurements were conducted from 1 January to 23 March 2009 comprised 1300 h valid HTDMA and AMS data. Air masses were tracked using HYSPLIT (Rolph et al., 2017) 72 h backward trajectories with an end point of 500 m above mean sea level at Mace Head according to the Global Data Assimilation System (https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/global-data-assimilation-system-gdas, last access: 26 March 2020).

The growth factor (GF) of aerosol particles undergoing humidification was obtained using GF=DD0, where D and D0 are the electrical mobility diameters of humidified and dry aerosols, respectively.

One of the HTDMA features is the ability to reveal the aerosol mixing state by detecting the presence of more than one particle growth mode. Each growth mode represents different water uptake properties, indicating the different chemical composition of each mode. The growth factor probability distribution function (GF-PDF) was separated into four growth modes according to the GF range: a near-hydrophobic mode (NH; 1<GF<1.11), a less hygroscopic mode (LH; 1.11<GF<1.33), a more hygroscopic mode (MH; 1.33<GF<1.85) and a sea salt mode (SS; 1.85<GF). For particles in a specific GF range, for example LH, the number fraction of the mode (nf_LH) was derived from the retrieved probability density function c(GF, D) as follows: nf_LH=∫1.111.33cGF,  DogGF. It should be noted that this categorisation was not always representative. For example, in highly acidic marine aerosol, the MH mode peaked at 1.8<GF<2.0 due to a high level of highly hygroscopic H2SO4, which had a GF of up to 1.9, rather than sea salt, which has a GF of 2.1. Due to the spread of the GF-PDF, some sections of the PDF that represented non-neutralised particles could be categorised into the SS mode, which would then result in an underestimation of the averaged GF for both the MH and SS modes as well as an overestimation of the number fraction of the SS mode. The GFmean of each mode was calculated as follows: GFmean=1nfa,b∫GFcGF,DdGF.

The mass concentrations were converted to volume fractions of the individual components (organics, NH4HSO4, H2SO4, NH4NO3, (NH4)2SO4, MSA, sea salt and BC) using a simplified ion-pairing scheme (Gysel et al., 2007). The GF values of individual components are summarised in Table 1. Although the hygroscopicity of inorganic compounds is well understood and established, it is still challenging to quantify the hygroscopicity of organic matter ranging from 1 to 1.5 or from hydrocarbon to oxalic acids (Kreidenweis and Asa-Awuku, 2014); however, most of the anthropogenic organics have a GF of less than 1.2. In this study, we first used a fixed GF value of 1.18 for organics, which was the average value from several closure studies (Wang et al., 2018; Yeung et al., 2014), and a constant density of 1400 kg m-3, as used by Gysel et al. ( 2007).

Assuming constant GF and density values for organics may induce a bias in closure studies, because the hygroscopicity of organics differs according to their molecular structure, air mass history or oxidation level. The GFMSA of 1.71 was calculated using the κ value, which, in turn, was obtained using the AIOMFAC model (Fossum et al., 2018; Zuend et al., 2011) and is supported by a recent lab experiment (Tang et al., 2018). The hygroscopicity of inorganic sea salt was found to be 8 %–15 % lower than that of pure NaCl; therefore, a GF value 2.22 for inorganic sea salt (at RH 90 %) was used (Zieger et al., 2017). The closure between the measured and predicted values was characterised by a linear regression using the corresponding R2 (the variance, which is a square of the correlation coefficient) and regression slope values.

The GF estimation was based on the Zdanovskii–Stokes–Robinson (ZSR) mixing rule (Stokes and Robinson, 1966) using the measured aerosol chemical composition, which assumes that the water uptake of the mixture is equivalent to the sum of the water uptake of the individual substances. The GF calculated from the bulk chemistry of the HR-ToF-AMS (GF_AMS) can be written as follows: GF_AMS =∑iviGFi, where vi is the volume fraction of the compound in the dry particle, and GFi is the growth factor of the individual chemical components. In the above equation, any interaction between the solutes is neglected, and the volume of the dry mixture is the sum of the volumes of its dry components.

The measurement period spanned from 1 January 2009 to 23 March 2009. The data, including meteorological parameters and aerosol chemical composition, are shown in Fig 1. The average ambient temperature and RH values for the entire period were 6.5±2.5 ∘C and 85.8±8.8 %, respectively.

The measurement period was examined in terms of contrasting air mass origins, and two continental events (C1 and C2) and two marine events (M1 and M2) were selected. These contrasting events are highlighted in the time series shown in Fig. 1, and they were expected to reveal greatly different aerosol particle hygroscopic properties. The air mass backward trajectories for these four events are shown in Fig. 2. Events C1 and C2 represented air masses that originated over continental Europe 72 h prior to being transported across the UK and Ireland towards Mace Head. Events M1 and M2, in comparison, were considered to represent clean marine air that originated over the northeastern Atlantic Ocean and was transported to the west coast of Ireland. The start and end time of each event is summarised in Table S1. The mass concentrations of the chemical composition, including non-sea-salt sulfate, nitrate, ammonium, organic matter, MSA, sea salt and BC, of each event are summarised in Table S2. It is important to emphasise that marine air masses are not always pristinely clean despite their advection over oceanic waters. Therefore, only data with a BC concentration of less than 15 ng m-3 and a wind direction within the 190 to 300∘ sector were included in the data analysis of marine events; these data are summarised in Table S2. The mean BC concentrations during the M1 and M2 events were 10.1 and 9.9 ng m-3, respectively, demonstrating the value of the conservative approach to qualifying pristine marine air masses; the corresponding data capture is presented in Fig. S3 for the M1 event. A strict and conservative BC criterion has been used to filter the cleanest maritime air masses. An analysis of the representativeness of clean maritime air masses has been extensively discussed by O'Dowd et al. (2014), where no correlation was found between organic matter (OM) and BC for the different BC concentration ranges of 0–15 and 15–50 ng m-3 (R2 values of 0.006 and 0.046, respectively). Figure S8 shows the non-refractory organics and non-sea-salt sulfate concentration from AMS versus the BC concentration in this study, which once again demonstrate no relationship with clean marine air masses derived using the conservative BC criterion. However, a relationship was found between the above-mentioned species in continental air masses, as one would expect in air masses where pollutants are typically internally mixed and advected by long-range transport to the site.

The size-resolved GFs measured by the HTDMA (denoted as GF_HTDMA) were plotted against GFs estimated with the ZSR mixing rule using AMS chemical composition data (denoted as GF_AMS). A linear regression was used to fit the GF_AMS and GF_HTDMA, with the slope of a nonzero intercept linear regression fit reflecting how well the estimation agrees with the measurements. As shown in Fig. 6, the regression slopes were 0.91 and 1 for 35 and 165 nm, respectively, and the variance increased from 0.61 to 0.84 with the increase in D0, suggesting that the closure agreement improves for larger particle sizes. For example, the GF_AMS of 35 nm D0 aerosols showed an overestimation with over 93 % of the data points located outside of the 10 % deviation from the 1:1 line. The comparison of 165 nm aerosols with bulk chemistry was very good with over 95 % of data points lying within 10 % deviation of the 1:1 line. The slope of the linear regression was 1.02, suggesting that there was no systematic error in the GF estimation. The results of the comparison suggests that (1) the chemical composition that was used to derive the GF was bulk PM1 data, which may differ significantly from Aitken-mode particles but approximate accumulation-mode particles quite well – thereby affecting a poorer comparison of Aitken-mode particles; and (2) that the Kelvin effect, which would become significant at small sizes, was neglected in the calculation. Contrary to the study of Hong et al. (2018), the correlations between GF_AMS and GF_HTDMA in this study, even those of small particles, showed much better correlations than the total lack of a correlation found by the former work. As described in Sect. 2, the chemical compositions measured by AMS in this study were bulk PM1 chemical composition, where the contribution of sub-50 nm particles was negligible. Consequently, it is expected that the calculated GF values deviate considerably from the measured GF for particles smaller than 50 nm. Given the that the best agreement was obtained for the larger sizes and considering the relevance of this for cloud condensation nuclei, we now focus on the closure results of 75, 110 and 165 nm particles to assess event results. As shown in Fig. 6, although the general closure agreement was good, a large number of data points were still scattered around the regression line. The comparison between GF_AMS and GF_HTDMA was plotted for continental and marine events, as shown in Fig. 7.

The regression lines approached the 1:1 line with increasing size. For example, the R2 values were 0.47 and 0.18 for 75 nm particles during continental and marine events, respectively. For aerosol with a D0 of 165 nm, the regression coefficients were 0.72 and 0.54, and the slopes were 1.1 and 0.85 for continental and marine events, respectively.

The regression results were reasonable, even for 75 nm particles, but they certainly improved with increasing size for the continental events; however, the improvement was not as significant for marine events (Fig. 7). Although a few data points were outside of the 10 % deviation range for 75 nm, the R2 for 75 nm was as low as 0.18 due to the lack of dynamic range in GF_AMS; nevertheless, over 95 % of the data points were well within the 10 % deviation, and all of the marine event data points were well within 10 % of the 1:1 line for 110 and 165 nm. Despite the fact that the above regressions suggested that a reasonable closure was achieved for continental and marine events, the closure results for each individual event were different. For 75 nm particles in C1, over 60 % of the estimated GFs were outside of the 10 % deviation range, whereas in C2 very few GFs fell outside of the 10 % deviation range. In contrast, for 165 nm particles, C1 GFs were typically overestimated, whereas C2 GFs were underestimated. The above results clearly demonstrated an increasing impact of the hydrophobic mode in smaller particles (Fig. 4) which was poorly captured by the bulk PM1 mass. Marine event GF_HTDMA and GF_AMS values were in good agreement, with 95 % of the data points lying within the ±10%. During individual marine events, over 80 % of the M1 GF values were underestimated, whereas M2 GFs were mostly overestimated. The regression slope of all of the data was 1, indicating that the GF_HTDMA of marine aerosol could be estimated fairly well based on AMS bulk PM1 measurements using the ZSR rule with the sea-salt concentration measured by AMS.

The overall very good agreement was a result of utilising sea-salt mass concentrations derived by AMS (Ovadnevaite et al., 2012). The result verifies AMS as an good technique for near-real-time sea-salt measurements. During the selected marine events, the PM1 aerosol volume fraction of sea salt ranged from 2 % to 95 %. In our study, the use of high time and mass resolution AMS data and the subsequent inclusion of sea-salt mass improved the closure greatly. As far as we are aware, this current chemical composition and hygroscopicity closure study is the first of its kind conducted on sea-salt-containing aerosol.

Although general agreement between the measured and estimated GF values was found in both continental and marine aerosol, the closure results for each event were slightly different. This motivated us to explore the cause of the closure errors by focusing on three metrics: (1) the O : C ratio, (2) the volume fraction of ammonium nitrate (vi(NH4NO3)) and (3) the aerosol mixing state.

The introduction of a constant GForg was considered to be the cause of a systematic error. The relationship between GForg and the organic oxidisation level is under intensive debate. In some studies, the GForg has been found to increase with an increasing O : C ratio in both chamber and ambient studies (Jimenez et al., 2009; Lambe et al., 2011; Massoli et al., 2010; Wong et al., 2011; Wu et al., 2016), and theoretical calculations have also demonstrated that GForg exhibits a linear dependence on the O : C ratio (Nakao, 2017). However, the correlation between GForg and the O : C ratio varies among aerosol sources, and some studies have reported no significant relationship (Chang et al., 2010; Suda et al., 2014).

Figure 8a shows the relationship between the O : C ratio and the GF deviation by plotting a normalised error |(GF_HTDMA - GF_AMS) / GF_HTDMA)|. When the O : C ratio was below 0.5, a slight overestimation was observed, but the deviation was less than 10 %; however, when the O : C ratio was between 0.5 and 1.25, no obvious pattern could be discerned. Freshly emitted hydrocarbon compounds have a relatively low O : C ratio and lower hygroscopicity; therefore, a GForg value of 1.1 is likely to cause an overestimation. When the O : C ratio increases to 0.6, the reported GForg value ranges from 1.15 to 1.4, depending on the air mass (Hong et al., 2018).

The introduction of a constant density and constant GForg may not be valid for every event, and is likely to cause slight overestimation, but this cannot explain deviations above 10 %, at least for the aerosol observed at Mace Head.

Another reason for the apparent overestimation of GF_AMS was considered to be the evaporation of NH4NO3 in the HTDMA instrument, which has been implicated in causing closure failure during nitrate-enriched periods in previous closure studies (Gysel et al., 2007; 2001; Swietlicki et al., 1999). Gysel et al. (2007) reported that 50 %–60 % of the volume of NH4NO3 evaporated within the HTDMA for particle diameters ranging from 50 to 60 nm. Despite this possible cause of the underestimation of GF in the HTDMA, the presence of nitrate is unlikely to be the main cause of the discrepancy in our study for several reasons. First, the residence time of aerosols in our HTDMA system is about 10 s, which is significantly shorter than other systems such as the HTDMA in Gysel et al. (2007), which has a residence time of approximately 60 s and resulted in significant NH4NO3 evaporation. Second, no obvious correlation was found between the GF deviation and the volume fraction (vi) of NH4NO3 (R=0.07; Fig. 8b). Therefore, as far as our study is concerned, there is no evidence that ammonium nitrate evaporation is responsible for the closure discrepancy.

The mixing state of aerosol can influence the hygroscopicity closure in two ways. First, the accuracy of AMS measurements is determined by the collection efficiency: for internally mixed aerosols the efficiency is constant for all particles, whereas in external mixtures the application of a constant collection efficiency may produce differences between the real and measured chemical species concentration. Second, externally mixed aerosol has a size-dependent chemical composition where the bulk chemistry tends to be more representative of larger particles (165 nm) that carry the bulk of mass over smaller particles (35 nm) that contribute negligibly to mass. For external mixture, the bulk chemical measurement of PM1 mass may induce errors at smaller sizes, whereas for internal mixture, the error tends to be smaller.

Two metrics were adapted to represent the mixing state: (1) the GF spread factor and (2) the number fraction of the NH and LH modes, nf(NH + LH), both of which were derived from the GF-PDF of 165 nm aerosols. The GF spread factor was defined as the standard deviation of the GF-PDF divided by an arithmetic mean GF (Stolzenburg and McMurry, 1988). As the MH mode was present during every event at every particle size, the number fraction of the NH and LH (nf(NH + LH)) modes could be used as a metric of the external mixing (Ching et al., 2017; Su et al., 2010). As shown in Fig. 8c and d, the GF spread factor and the nf(NH + LH) factor have the largest regression coefficient with GF deviation (R of 0.51 and 0.57, respectively).

As shown in Fig. 8c, when the GF spread factor is less than 0.2, most of the GF deviations remain within 10 %. When the GF spread factor increases over 0.2, the range of GF deviation increases to 30 %. A similar relationship is found between nf(NH + LH) and the GF deviation, but the tendency is constrained within 10 %, and many outliers cannot be captured by increasing nf(NH + LH). This is because the relationship between nf(NH + LH) and the GF spread factor is not linear. Certain aerosol populations, such as an external mixture of inorganics and sea salt, that do not contain the NH and LH modes could exhibit a larger GF spread factor. It is also possible that aerosol with a small spread factor value could contain a significant number of particles in the NH and LH modes. Above all, we conclude that, although the scatter is larger, aerosol with a larger GF spread factor tends to be associated with high GF deviation. Two examples of GF-PDFs with a GF spread factor larger than 0.2 are shown in Fig. S6. These examples suggest the existence of a multi-modal distribution. Comparing their chemical composition during C and M events, the presence of sea salt and elevated BC-containing particles was found, as shown in Fig. S7, suggesting that the externally mixed and anthropogenically impacted aerosol and/or sea-salt-containing polluted aerosol are responsible for the discrepancy. Therefore, we suggest that great care must be exercised in estimating hygroscopicity using the bulk PM1 chemical composition when the BC concentration exceeds 0.1 µg m-3 and the sea salt concentration is below 0.5 µg m-3. It has to be noted that the frequency of occurrence of a GF spread factor greater than 0.2 is as low as 1 % at Mace Head, suggesting that the sea-salt-containing bulk PM1 chemical composition can generally be used to achieve closure with aerosol hygroscopic properties.