Figure S1. Trajectory analysis for the May 2011 campaign (1 to 9 May). The bottom figure
shows the time series of the modal growth factors for 150 nm dry diameter aerosols measured
over the period. Blue circles represent the more-hygroscopic mode while black circles
represent the non-hygroscopic mode. The size of the circles is scaled to the number fraction of
the peak modes (see the size scale given in the right of the time series figure). Two periods
with the influence of maritime air masses (blue boxes in the time series plot) were identified
during the campaign. The two graphs above the time series plot show the trajectories and
vertical profiles (in meters above ground level) of each period.
Figure S2. Trajectory analysis for the Sep 2011 campaign. The middle figure shows the
time series of the modal growth factors for 150 nm dry diameter aerosols measured over the
period. Blue circles represent the more-hygroscopic mode, red circles represent the
less-hygroscopic mode and black circles represent the non-hygroscopic mode. The size of the
circles is scaled to the number fraction of the peak modes (see the size scale given in the right
of the time series figure). Three different air masses, maritime (blue boxes in the times series
plot), coastal (green boxes) and continental (red boxes), were identified during the campaign.
The graphs in the top and bottom panels show the trajectories and vertical profiles (in meters
above ground level) of each period during the campaign classified based on the air mass
origin.
Figure S3. Trajectory analysis for the Nov 2011 campaign. The middle figure shows the
time series of the modal growth factors for 150 nm dry diameter aerosols measured over the
period. Blue circles represent the more-hygroscopic mode, red circles denote the
less-hygroscopic mode and black circles indicate the non-hygroscopic mode. The size of the
circles is scaled to the number fraction of the peak modes (see the size scale given in the right
of the time series figure). Two different air masses, coastal (green boxes in the times series
plot) and continental (red boxes), were identified during the campaign. The graphs in the top
and bottom panels show the trajectories and vertical profiles (in meters above ground level) of
each period during the campaign classified based on the air mass origin.
Size resolution of measurement data for closure study
For the hygroscopicity-composition closure, the size resolution of the HR-ToF-AMS
data should be comparable to that of the HTDMA data. From the HR-ToF-AMS-measured
mass-size distributions, the size-segregated composition can be obtained by integrating the
spectra over any given size range. However, increasing the size resolution by integrating over
a narrower size range, especially for small particles of low mass concentrations, may lead to
insufficient signal statistics. These highly size-resolved mass concentrations would have very
low signal-to-noise ratios. Hence, a compromise between the size resolution and signal
statistics has to be made for a good size-resolved closure analysis.
In order to evaluate the optimal size resolution of the data for the best closure, closures
using various size resolutions were compared. The HR-ToF-AMS size range (100 – 345 nm
in Dva) was divided into four or two bins. Scatter plots for the GF* based on HTDMA
measurements against the predicted GFmix are presented in Figure S4 for four size resolutions.
The closures were performed for acidic aerosols measured in the May, Sep and Nov
campaigns. Some of the detected aerosols had excess NH4+ and were excluded. The GFmix
values were calculated using the ion pairing scheme for GFinorg and constant GForg values
(1.16 to 1.2, depending on particle size). In the highest size resolution four-bin closure, the
GF* of each size obtained with the HTDMA was compared to the size-resolved GFmix
calculated using the four individual HR-ToF-AMS bin concentrations. They are called “4 size
bins” in Figure S4. For the two-bin analysis, the average GF* values for particles of 75 and
100 nm in Dem and of 150 and 200 nm in Dem were calculated and compared with the GFmix
based on the corresponding HR-ToF-AMS two-bin composition datasets (“2-bin sum”). In
addition, the 4-size average GF* was compared with the GFmix calculated using the mass
concentration integrated over the four selected HR-ToF-AMS size ranges (“4-bin sum”) and
the PM1 concentration.
As can be seen from Figure S4, the R2 values increase with decreasing size resolution.
Note that in the linear fit without an intercept, the R2 has a definition different from that in the
simple linear regression. The R2 here was obtained from its computational definition (1 – sum
square error/sum square total) and can be negative if the data points are sufficiently scattered.
In Figure S4, the R2 is negative when the GFmix values are spread over a larger range than the
measurements are. Low correlations may be due to the uncertainty related to the low
HR-ToF-AMS bin concentrations in the highly size-resolved datasets. For all size bins, the
mass concentration for each ion was usually lower than 1 μg/m3. In fact, the bin
concentrations for small particles (dry Dem = 75 and 100 nm) were usually lower than 0.2
μg/m3. Closure using the sum of the concentrations over two neighboring size bins to
comparing with the two-size averaged GF* values only slightly improves the correlation for
the May and Sep data (2-bin sums in Figure S4). Significant improvement is seen in the 4-bin
sum closure. The R2 values for the closure with the 4-bin sum GF* and HR-ToF-AMS PM1
predictions in the May and Nov campaigns are highest among all four resolution settings.
However, the PM1 data generally overpredicted the GF, with the slope smaller than one in all
cases, especially in the May and Sep campaigns. This may be related to the size difference
between the two data sets. The HR-ToF-AMS PM1 data covered the larger particles. PM1
particles usually had higher sulfate-to-organic ratios than did the smaller particles (data not
shown) and hence did not yield good closure results.
In summary, the overall mass concentration measured in this study was relatively low
(the average non-refractory PM1 concentration was about 15±10 μg/m3). Averaging the
HR-ToF-AMS composition over a size range was found to provide reliable signal statistics
for good closure analysis. Based on the evaluation of the size resolution for this study, using
the 4-bin sum composition over the range from 100 to 345 nm in Dva, corresponding to 67 to
216 nm in Dem, yields the best closure. To facilitate the evaluation for using various models in
closure, this “4-bin sum” analysis is adopted for the subsequent closure analyses, except for
the GForg approximations using the O:C ratios and PMF organic factors (see main article
section 3.3.1) which rely on PM1 composition data.
Figure S4. Scatter plots of the HTDMA-measured GF* against the GFmix predicted from the
HR-ToF-AMS-measured composition in three individual field campaigns (May, Sep and Nov
2011). The GFinorg was calculated using the ion pairing scheme assuming a constant GForg
value between 1.16 and 1.2 (depending on particle size) and an organic density of 1250 kg/m3.
The first (from left) column compares GF* of each size obtained with the HTDMA (75, 100,
50 and 200 nm in Dem) and the size-resolved GFmix calculated using the four individual
HR-ToF-AMS bin concentrations (see the text for the HR-ToF-AMS data integration); the
second column is for two combined size bins; the third one is for the average GF* among the
four sizes against the GFmix predicted from the total mass concentration over the four size bins;
and the fourth column compares the average GF* among the four sizes with the
HR-ToF-AMS PM1 data. The size resolution decreases from left to right. The red solid lines
are the 1:1 lines; the two red dotted lines represent +/-10% deviation; and the black solid lines
are the best-fit lines for the data through the origin.
Table S1.
HTDMA results under the influences of maritime airstreams in May 2011a
GF*
κ*
75
1.05±0.04 0.02±0.02 0.15±0.11
46%
1.59±0.05 0.40±0.05
1.56±0.06 0.37±0.06
100
1.03±0.05 0.02±0.02 0.15±0.12
54%
1.58±0.05 0.37±0.05
1.55±0.06 0.35±0.05
150
1.01±0.05 0.01±0.01 0.15±0.11
56%
1.59±0.05 0.37±0.04
1.56±0.06 0.34±0.05
200
0.99±0.02
49%
1.61±0.05 0.38±0.05
1.58±0.07 0.34±0.05
0.15±0.13
GF2
κ2
Maritime
0±0.01
nf 1
%occur1b
D0 (nm)
a
GF1
κ1
Period
Data are the average values (±standard deviation) of growth factor (GF), number
fraction (nf) of the lower GF mode (either the non-hygroscopic or the less-hygroscopic mode,
i = 1) and the more-hygroscopic mode (i = 2) for four dry diameters (D0) over the study
periods. The ensemble mean growth factor GF* and the mean kappa value translated from
GF* (κ*) for each diameter are also shown.
b
The mean values of the percentage frequency of occurrence of the lower GF mode.
Table S2. HTDMA results under the influences of maritime, coastal and continental
airstreams in Sep 2011 (see the footnote for Table S1 for the definition of each symbol)
%occur1
GF2
GF*
κ*
Maritime
75
1.13±0.08 0.06±0.04 0.31±0.24
71%
1.60±0.08 0.44±0.04
1.51±0.10 0.33±0.09
100
1.07±0.07 0.03±0.03 0.11±0.09
61%
1.58±0.06 0.37±0.06
1.55±0.07 0.35±0.06
150
1.06±0.08 0.03±0.03 0.16±0.15
60%
1.59±0.08 0.37±0.07
1.55±0.09 0.33±0.08
200
1.04±0.08 0.02±0.03 0.14±0.15
45%
1.61±0.06 0.38±0.05
1.59±0.08 0.36±0.07
75
1.09±0.06 0.04±0.03 0.30±0.30
51%
1.56±0.09 0.37±0.08
1.51±0.14 0.33±0.12
100
1.07±0.05 0.03±0.02 0.11±0.08
48%
1.55±0.10 0.35±0.09
1.54±0.11 0.34±0.10
150
1.05±0.05 0.02±0.02 0.10±0.10
49%
1.56±0.13 0.34±0.11
1.54±0.13 0.33±0.11
200
1.05±0.05 0.02±0.02 0.12±0.08
54%
1.60±0.11 0.37±0.10
1.58±0.12 0.35±0.11
75
1.12±0.07 0.06±0.04 0.49±0.26
71%
1.49±0.11 0.31±0.09
1.36±0.09 0.21±0.06
100
1.03±0.04
0.01±0
0.16±0.07
74%
1.45±0.06 0.26±0.05
1.41±0.06 0.23±0.04
150
1.01±0.05
0.01±0
0.17±0.11
56%
1.43±0.07 0.24±0.05
1.39±0.07 0.21±0.05
200
1.03±0.05 0.01±0.01 0.17±0.11
71%
1.48±0.06 0.27±0.05
1.43±0.06 0.23±0.04
Continental
nf 1
κ2
D0 (nm)
Coastal
GF1
κ1
Period
Table S3. HTDMA results under the influences of coastal and continental airstreams in Nov
2011 (see the footnote for Table S1 for the definition of each symbol)
nf 1
%occur1
GF2
κ2
GF*
κ*
D0 (nm)
Coastal
75
1.05±0.06 0.02±0.02 0.12±0.06
39%
1.50±0.08 0.32±0.07
1.48±0.07 0.30±0.06
100
1.05±0.07 0.02±0.03 0.13±.0.09
43%
1.51±0.07 0.31±0.06
1.49±0.07 0.29±0.06
150
1.05±0.06 0.02±0.02 0.14±0.10
61%
1.52±0.06 0.31±0.05
1.49±0.06 0.28±0.05
200
1.06±0.06 0.03±0.03 0.17±0.10
71%
1.55±0.07 0.33±0.06
1.51±0.07 0.29±0.06
75
1.06±0.06 0.03±0.03 0.13±0.09
55%
1.53±0.06 0.34±0.05
1.51±0.05 0.32±0.04
100
1.05±0.06 0.02±0.03 0.12±0.08
57%
1.53±0.06 0.33±0.05
1.50±0.05 0.30±0.04
150
1.03±0.05 0.01±0.02 0.11±0.07
68%
1.53±0.06 0.31±0.05
1.50±0.05 0.29±0.04
200
1.04±0.05 0.02±0.02 0.12±0.08
72%
1.55±0.06 0.32±0.05
1.51±0.06 0.29±0.05
Continental
GF1
κ1
Period
Figure S5. Temporal evolution of GF at 90% RH, total mass concentration (each of the
second panel) and mass fractions of major ions (each of the third panel), and organic mass
fractions of three organic ions (each bottom panel) measured by HR-ToF-AMS for D0 = 75
nm (top panel), 100 nm (middle panel) and 200 nm (bottom panel) aerosols in the May 2011
campaign. Two measurement periods influenced by maritime air masses were identified (blue
boxes in the figure).
Figure S6. Temporal evolution of GF at 90% RH, total mass concentration (each of the
second panel) and mass fractions of major ions (each of the third panel), and organic mass
fractions of three organic ions (each bottom panel) measured by HR-ToF-AMS for D0 = 75
nm (top panel), 100 nm (middle panel) and 200 nm (bottom panel) aerosols in the Sep 2011
campaign. The measurement period is classified into three air mass groups: maritime (blue
boxes), coastal (green boxes) and continental (red boxes).
Figure S7. Temporal evolution of GF at 90% RH, total mass concentration (each of the
second panel) and mass fractions of major ions (each of the third panel), and organic mass
fractions of three organic ions (each bottom panel) measured by HR-ToF-AMS for D0 = 75
nm (top panel), 100 nm (middle panel) and 200 nm (bottom panel) aerosols in the Nov 2011
campaign. The measurement period is classified into two air mass groups: coastal (green
boxes) and continental (red boxes).
Comparison between the simplified ion pairing scheme and E-AIM
The amounts of four inorganic components, including ammonium sulfate (AS),
ammonium bisulfate (ABS), sulfuric acid (SA) and ammonium nitrate (AN) in the aerosol
samples were calculated based on the mass concentrations of three major inorganic ions
(sulfate, nitrate and ammonium) measured with the HR-ToF-AMS using the simplified ion
pairing scheme [Reilly and Wood, 1969; Gysel et al., 2007]:
(S1)
where n(i) is the number of moles of each species.
GFinorg was calculated using the following equation based on the ZSR mixing rule:
(S2)
The volume fractions of the four major species were calculated from their mass fractions and
dry densities. We used the individual GF values of each pure component obtained from
E-AIM [Clegg et al., 1992; Wexler and Clegg, 2002] to calculate GFinorg. Reduction in the GF
values due to the Kelvin effect on smaller particles was also considered. All physical
parameters and GF values of pure inorganic species used in the GFinorg calculations are given
in Table S4. On the other hand, GFinorg can be directly predicted from Inorganic Model II of
E-AIM. Details of the E-AIM calculations are available in section 2.4.1 of the main article.
In this section, we compare the performances of simplified ion pairing scheme and E-AIM
in predicting GFinorg of the mixed particles using a constant GForg value of 1.18. Figure S8
shows the closure results applying the ion pairing scheme and E-AIM. Overall, the two
inorganic models gave very similar results. Underpredictions were seen for the Nov campaign
probably due to the smaller GForg value used (the best-fit GForg is 1.28, see discussion in
section 3.3.2). Predictions from the ion pairing scheme gave slightly smaller slopes and higher
GFinorg than E-AIM did. The small difference may be related to the presence of SA, a
non-deliquescent species which retains water even under dry conditions. For example, the GF
of pure SA droplets at 5% RH is about 1.2 based on E-AIM. The presence of SA would cause
water to be retained in aerosols classified by the first DMA in the HTDMA system at 5% RH.
This results in a lower GF derived from the ratios of the diameters at 90% RH to those at 5%
RH measured with the HTDMA. In contrast, the ion pairing scheme predicted the GFinorg
based on the GF values of each inorganic species at 90% RH, assuming no hygroscopic
uptake (i.e., GF = 1) under dry conditions.
To further evaluate the role of SA in the closure analysis, the performances of the two
models when the aerosols contained SA and when they did not are compared in Figure S9.
The presence of SA in the aerosol samples was identified based on the ion pairing calculation.
The results for May campaign are not presented because of insufficient data. For the aerosols
without SA (the first and the third columns in Figure S9), both models with a constant GForg
of 1.18 produced good closure for the Sep campaign (slope > 0.98 and R2 of about 0.6). There
was no significant difference in the predictions between the ion pair scheme and E-AIM for
both campaigns. The percentage differences in the slope and R2 between the two models were
smaller than 1% and 5%, respectively. For the cases with SA, E-AIM gave similar results to
those for aerosols without SA. However, the ion pairing scheme predicted slightly higher
GFmix values than those for aerosols without SA. Although the slope of the Nov closure using
the ion pairing scheme was close to 1, the closure was probably biased since the GForg value
was underestimated. If a higher GForg of 1.28 (instead of 1.18) is used, a better closure will be
obtained with E-AIM while the ion pairing scheme will again produce a higher GFmix than the
GF* from HTDMA measurements. In general, the ion pairing scheme and E-AIM gave very
close GFinorg values. However, for the SA-containing aerosols, E-AIM was able to predict a
small water content under dry conditions while the ion pairing scheme was not. Hence, better
closure was achieved with E-AIM when the aerosols contained SA.
Table S4.
Physical parameters and growth factors of pure inorganic species.
Inorganic
Molecular
Dry density
GF (90% RH)
GF (90% RH)
GF (90% RH)
GF (90% RH)
species
weight (g/mol)
(ρ, kg/m3)
D0 = 75 nm
D0 = 100 nm
D0 = 150 nm
D0 = 200 nm
(NH4)2SO4
132.14
1769
1.68
1.70
1.71
1.72
NH4HSO4
115.11
1780
1.75
1.77
1.78
1.80
H2SO4
98.08
1830
2.04
2.05
2.06
2.07
NH4NO3
80.04
1720
1.77
1.79
1.80
1.82
Figure S8. Scatter plots of the HTDMA-measured GF* against the GFmix predicted from the
HR-ToF-AMS-measured composition for acidic aerosols in three individual field campaigns
(May (top row), Sep (middle row) and Nov 2011 (bottom row)). A constant GForg value of
1.18 and organic density of 1250 kg/m3 were assumed. The left column presents the closure
using the ion pairing scheme to predict the GFinorg while the results from E-AIM are shown in
the right column. See Figure S4 for descriptions of the lines in each plot.
Figure S9. Comparison of the GF values of acidic aerosols with or without sulfuric acid (SA)
in Sep and Nov 2011 predicted by the ion pairing scheme and E-AIM. A constant GForg value
of 1.18 and organic density of 1250 kg/m3 were assumed. The upper panel represents the
closure using the ion pairing scheme while the lower panel shows the results from E-AIM.
The first and third (from left) columns show the closures without SA in Sep and Nov 2011,
respectively. The second and fourth columns are for the closures when SA was present. See
Figure S4 for descriptions of the lines in each plot.
Figure S10. More-hygroscopic mode GF (top panel), total mass concentration (middle
panel) and wind direction (middle panel) measured between 13 and 16 Sep 2011.
Figure S11. Average aerosol mass concentration vs κ* for particles with a dry diameter
between 75 and 200 nm with the influences of various air masses.
Figure S12. Time series of the HTDMA-measured GF*, the predicted GFmix (E-AIM for
GFinorg and GForg = 1.18) based on the HR-ToF-AMS composition, volume fraction of total
organics (the top panel for each month) and the prediction bias (= (GFmix – GF*)/(average of
GFmix and GF*) x 100%); pink markers in the bottom panels) in the May, Sep and Nov
campaigns. The blue markers represent GF* and the green markers are for GForg. The black
triangles represent the organic volume fraction εorg.
Table S5. Summary of the results (slope and R2 of the linear fit passing through the origin)
of all closures in this study
Size resolution, ion pairing scheme for GFinorg and GForg = 1.16 – 1.20 (Figure S4)
May 2011 (up to 9th)
Sep 2011
2
Nov 2011
2
Slope
R
Slope
R
Slope
R2
4 size bins
0.972
-0.705
0.956
0.288
0.992
-0.548
2-bin sum
0.979
-0.244
0.965
0.332
1.002
-0.651
4-bin sum
0.991
0.239
0.977
0.588
1.017
0.313
PM1
0.953
0.318
0.939
0.538
0.993
0.402
Ion pairing scheme vs E-AIM, GForg = 1.18 (Figures S8-S9)
May 2011 (up to 9th)
Ion pairing, all acidic
Ion pairing, w/out SA
Ion pairing, SA only
E-AIM, all acidic
E-AIM, w/out SA
E-AIM, SA only
Sep 2011
Nov 2011
Slope
R2
Slope
R2
Slope
R2
0.992
0.235
0.978
0.590
1.018
0.309
0.984
0.608
1.022
0.456
0.958
0.613
1.004
0.106
0.991
0.588
1.028
0.437
0.992
0.594
1.029
0.468
0.987
0.568
1.026
0.344
No closurea
1.002
0.286
No closurea
Closures using approximated GForg and E-AIM for GFinorg (Figure 6)
May 2011 (up to 9th)
Sep 2011 (1st half / 2nd half)b
Nov 2011
Slope
R2
Slope
R2
Slope
R2
GForg = 1.18
1.002
0.286
1.028 / 0.954
0.627 / 0.424
1.028
0.437
f44 (4-bin sum)
1.000
-0.559
0.963 / 0.954
-1.448 / -2.014
1.000
-0.350
O:C (PM1)
0.962
0.233
0.991 / 0.915
0.785 / 0.349
1.001
0.468
PMF (PM1)
0.968
0.258
0.987 / 0.899
0.764 / 0.325
0.988
0.547
a
No closure was performed because of insufficient data.
b
Closure results for the first half and second half of Sep 2011 are shown separately.
References
Gysel, M., J. Crosier, D. O. Topping, J. D. Whitehead, K. N. Bower, M. J. Cubison, P. I.
Williams, M. J. Flynn, G. B. McFiggans, and H. Coe (2007), Closure study between
chemical composition and hygroscopic growth of aerosol particles during TORCH2,
Atmos. Chem. Phys., 7, 6,131–6,144, doi:10.5194/acp-7-6131-2007.
Reilly, P. J., and R. H. Wood (1969), Prediction of properties of mixed electrolytes from
measurements on common ion mixtures, J. Phys. Chem., 73, 4292–4297.
Clegg, S. L., K. S. Pitzer, and P. Brimblecombe (1992), Thermodynamics of multicomponent,
miscible, ionic solutions. II. Mixtures including unsymmetrical electrolytes, J. Phys.
Chem., 96, 9,470–9,479.
Wexler, A. S., and S. L. Clegg (2002), Atmospheric aerosol models for systems including the
ions H+, NH4+, Na+, SO42−, NO3−, Cl−, Br− and H2O, J. Geophys. Res., 107(D14),
doi:10.1029/2001JD000451.