Introduction
Ice-nucleating particles (INPs) are a unique class of aerosol particles that
catalyze ice formation under atmospheric conditions. A variety of particle
types have been identified as INPs, including mineral dust, black carbon,
volcanic ash, glassy aerosols, and primary biological particles such as
bacteria, fungal spores, and pollen (see reviews by Szyrmer and Zawadzki,
1997; Möhler et al., 2007; Ariya et al., 2009; Després et al., 2012;
Hoose and Möhler, 2012; Murray et al., 2012; Yakobi-Hancock et al.,
2013). Although only a small fraction of aerosol particles nucleate ice
(e.g., Rogers et al., 1998), INPs are important since they can lead to
changes in the properties and lifetimes of mixed-phase and ice clouds,
ultimately affecting climate and precipitation (Baker, 1997; Lohmann and
Feichter, 2005; Baker and Peter, 2008; DeMott et al., 2010; Creamean et al.,
2013).
Vali et al. (2015) describes four modes of heterogeneous ice nucleation:
deposition nucleation, where ice forms on the INP directly from the gas
phase; condensation freezing, where ice nucleates during the condensing of
water onto the INP; immersion freezing, where crystallization is initiated
by an INP within a supercooled liquid droplet; and contact freezing, where
the freezing of a supercooled liquid droplet is due to impaction by an INP.
In this study we focus on freezing via the immersion mode in dilute solution
droplets, which is relevant to mixed-phase cloud conditions.
Due to the importance of INPs for climate and precipitation, there has been
a renewed interest in measuring the concentrations of INPs in the atmosphere
(DeMott et al., 2011). While much of this work has focused on measurements
of the total number concentration of INPs, there has been less emphasis on
determining their size distributions in the atmosphere. Information on
airborne INP size distributions may be particularly helpful in identifying
the predominant INP sources. For example, information on the size
distribution of INPs may help rule out or support the role of fungal spores
in atmospheric ice nucleation since they are often in the supermicron range
(Graham et al., 2003; Elbert et al., 2007; Sesartic and Dallafior, 2011;
Després et al., 2012; Huffman et al., 2012). A similar approach can be
used with black carbon particles, since they are mainly in the submicron
range (Clarke et al., 2004; Schwarz et al., 2008, 2013).
Previous modeling studies have shown that the transport and distribution of
INPs, and aerosol particles in general, are sensitive to the size of the
particles assumed in the models (Burrows et al., 2009; Wilkinson et al.,
2011). Information on the size distributions of INPs are thus needed for
accurate modeling of their transport and distributions in the atmosphere
(Morris et al., 2004; Hoose et al., 2010a, b; Sesartic et al., 2013;
Haga et al., 2014; Spracklen and Heald, 2014).
The seven locations used in this study and conditions
during sampling.
Location
Environment
Coordinates
Elevation
Sampling
Number
Average sampling
Average
Average relative
Particle size
(m)
period
of samples
time (h)
temperature (∘C)
humidity (%)
range (µm)a
Alert, NU,
Arctic
82.45∘ N
12 a.g.l.
Mar. 29–Jul. 23,
9
18
-17.4
77
0.10–10
Canada
62.51∘ W
200 a.s.l.
2014
Whistler Mountain,
Alpine
50.06∘ N
2 a.g.l.
Mar. 30–Apr. 23,
4
6.7
-0.8
83
0.18–10
BC, Canada
122.96∘ W
2182 a.s.l.
2014
Amphitrite Point,
Coastal
48.92∘ N
5.5 a.g.l.
Aug. 6–27,
34
7.8
13.8
97
0.18–10
BC, Canada
125.54∘ W
25 a.s.l.
2013
The Labrador Sea,
Marine
54.50∘ N
2 a.g.l.
Jul. 11,
1
6.2
10.9
75
0.10–10
Canada
55.37∘ W
15 a.s.l.
2014
CEA, Saclay,
Suburban
48.70∘ N
10 a.g.l.
Jul. 15–Aug. 4,
15
7.2
20.6
69
0.10–10
France
2.14∘ E
168 a.s.l.
2014
UBC campus,
Suburban
49.26∘ N
24 a.g.l.
May 12–16,
4
6.3
15.2
70
0.10–10
BC, Canada
123.25∘ W
120 a.s.l.
2014
Colby,
Agricultural
39.39∘ N
2 a.g.l.
Oct. 14–15,
3
4.5
17.0
48
0.10–10
KS, USA
101.06∘ W
968 a.s.l.
2014
and 39.39∘ N
101.08∘ W
a Aerodynamic diameter based on the 50 % cutoff of the MOUDI (Marple
et al., 1991).
Sampling locations used in this study: (1) Alert,
Nunavut, Canada; (2) Whistler Mountain, British Columbia, Canada; (3)
Amphitrite Point, British Columbia, Canada; (4) the Labrador Sea, Canada;
(5) CEA in Saclay, France; (6) the University of British Columbia campus,
British Columbia, Canada; and (7) Colby, Kansas, USA. Site coordinates are
given in Table 1 with details in Sect. 2.1. The image was modified from Bing
Maps, 2014 (http://bing.com/maps).
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Information on the size distribution of INPs is also needed to determine whether
techniques used to measure atmospheric INP concentrations capture the entire
INP population. For example, the continuous flow diffusion chamber (Rogers
et al., 2001b) is often used for measuring INPs (e.g., DeMott et al., 1998;
Rogers et al., 2001a; Richardson et al., 2007; Pratt et al., 2009; Prenni et
al., 2009; Eidhammer et al., 2010; Chou et al., 2011; Friedman et al., 2011;
Hoyle et al., 2011; Corbin et al., 2012; Garcia et al., 2012; Tobo et al.,
2013; McCluskey et al., 2014). This type of instrument has the advantage of
providing real-time measurements of INPs with the ability to detect very
large INP number concentrations, but the aerodynamic diameter of particles
measured with it is limited, from d50≤ 2.4 µm in some studies
(e.g., Garcia et al., 2012) to d50≤ 0.75 µm in others (e.g.,
DeMott et al., 2003). Such techniques may miss supermicron or coarse-mode
(i.e., larger than 2.5 µm) INPs. The exact proportion of INPs missed
may depend on temperature. Such online instruments have typically focused on
measurements below approximately -20 ∘C as sample volume
considerations limit effective sampling of lower INP number concentrations
at warmer temperatures. The exact proportion of INPs missed may also depend
on altitude since the removal of atmospheric particles by wet and dry
deposition in the atmosphere is expected to be size dependent. As an
example, supermicron particles have larger dry deposition loss rates than
submicron particles.
Previous studies of INPs as a function of size have been carried out in the
field (e.g., Vali, 1966; Rosinski et al., 1986; Mertes et al., 2007;
Santachiara et al., 2010) and in the laboratory (e.g., Welti et al., 2009;
O'Sullivan et al., 2015). These and additional studies are further discussed
in Sect. 3.2. In the current study, we add to the existing body of
size-resolved INP measurements by reporting ground-level INP size
distributions from six locations in North America and one in Europe,
covering a diverse set of environments and investigating immersion freezing
at -15, -20, and -25 ∘C.
Results and discussion
INP number concentrations
The total number concentration of INPs active at -15, -20, and -25 ∘C are shown for each site in Fig. 2. Freezing events were rare
at temperatures warmer than -15 ∘C, accounting for only 1.3 %
of all cases, and are therefore not reported. Some of the DFT experiments
proceeded such that all droplets froze at temperatures slightly below -25 ∘C. Since this scenario prohibits calculation of INP number
concentrations, -25 ∘C is the lowest temperature reported. As
expected, INP number concentrations were found to increase with decreasing
freezing temperature with the average concentration at -25 ∘C
(3.8 ± 2.9 L-1) being more than an order of magnitude larger than
at -15 ∘C (0.25 ± 0.15 L-1).
INP number concentrations were relatively low at the Alert and Whistler
Mountain sites with values of 0.05 and 0.10 L-1 at -15 ∘C,
0.22 and 0.16 L-1 at -20 ∘C, and 0.99 and 1.1 L-1 at -25 ∘C, respectively. These findings are consistent with
previous measurements at similar locations. For example, Arctic measurements
of Bigg (1996) for particles < 10 µm and Fountain and Ohtake (1985) using filter samples found mean INP concentrations of 0.01 L-1 at -15 ∘C and 0.13 L-1 at -20 ∘C,
respectively, with both deposition and condensation modes likely possible,
and Prenni et al. (2007) measured an average INP number concentration for
particles with and aerodynamic diameter < 1.5 µm of
approximately 0.33 L-1 between -8 and -28 ∘C with
deposition, condensation, and immersion modes likely possible. At high-elevation sites, Bowers et al. (2009) at Mt. Werner in Colorado and Conen et al. (2012) at the research station Jungfraujoch in Switzerland measured mean
immersion-mode INP number concentrations of approximately 0.02 L-1 at -10 and -12 ∘C, respectively, using filter samples of
0.2–0.3 µm pore size. High-elevation sites can receive large
quantities of dust, which can act as efficient INPs at lower temperatures
(Chou et al., 2011), but this was unlikely during our measurement period
based on the low INP number concentrations.
INP number concentrations at Amphitrite Point were 0.23, 0.94, and 2.15 L-1 at droplet freezing
temperatures of -15, -20, and -25 ∘C, respectively. Despite the predominance of marine air masses being
sampled, the major source of INPs at Amphitrite Point during the study
period was likely biological particles from local vegetation (Mason et al.,
2015b). Similar values were measured in the Labrador Sea, where INP number
concentrations at -15, -20, and -25 ∘C were 0.38, 1.3, and
2.8 L-1, respectively. These concentrations are consistent with previous
measurements within the marine boundary layer in regions influenced by air
flow off of nearby coasts, for instance those of Schnell (1977) in the
immersion freezing mode for sizes > 0.45 µm off the coast
of Nova Scotia, roughly 1100–1500 km southwest of our sampling site in the
Labrador Sea, and Rosinski et al. (1995) over the East China Sea in the
deposition and condensation modes for sizes > 0.2 µm.
However, INP number concentrations found during marine studies can vary by
several orders of magnitude with changing location as summarized by Burrows
et al. (2013).
The mean fraction of INPs larger than (a) 1 µm and
(b) 2.5 µm. Uncertainty is the standard error of the mean, assuming a
normal distribution. Shading in the histogram corresponds to INP activation
temperature: -15 ∘C is dark gray, -20 ∘C is an
intermediate gray, and -25 ∘C is light gray. As 2.5 µm
does not align with the size cut of a MOUDI stage, the fraction of INPs
larger than 2.5 µm was found by assuming that number concentration of
INPs 1.8–3.2 µm in size was uniformly distributed over that size
range. As only one sample was available from the Labrador Sea, no
uncertainty is reported.
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The highest concentrations of INPs at a freezing temperature of -25 ∘C were found at the Colby sites, where the average number
concentration was 8.9 L-1. Aerosol sampling was conducted adjacent to
soya and sorghum fields during and following periods of combine operation.
This high concentration of INPs is consistent with previous work of Garcia
et al. (2012) that showed elevated concentrations of INPs downwind of corn
fields during combine harvesting, and Bowers et al. (2011) who found greater
INP concentrations in air above cropland than above suburban or forest
sites.
The suburban sites of Saclay and the UBC campus also showed high INP
concentrations, being 4.4 and 6.1 L-1, respectively, at a
freezing temperature of -25 ∘C. Both sites were likely influenced
by multiple sources of INPs. For example, both are in close proximity to
major metropolitan centers and forest vegetation, which are potential
sources of anthropogenic INPs (e.g., Hobbs and Locatelli, 1970; Al-Naimi and
Saunders, 1985; Knopf et al., 2010, 2014; Ebert et al., 2011; Corbin et al.,
2012; Cziczo et al., 2013; Brooks et al., 2014) and biological INPs (e.g.,
Vali et al., 1976; Kieft and Ruscetti, 1990; Richard et al., 1996; Hirano
and Upper, 2000; Diehl et al., 2002; Prenni et al., 2009; Iannone et al.,
2011; Pummer et al., 2012; Huffman et al., 2013; Tobo et al., 2013; Haga et
al., 2014; Wright et al., 2014), respectively. The sampling site at Saclay
was also within 1 km of agricultural fields, an additional source of
biological aerosols that may act as INPs (e.g., Lindow et al., 1982; Hirano
et al., 1985; Georgakopoulos and Sands, 1992; Möhler et al., 2008;
Bowers et al., 2011; Garcia et al., 2012; Haga et al., 2013; Morris et al.,
2013; Hiranuma et al., 2015).
INP size distributions
Figure 3a shows the relative contribution of supermicron aerosol particles
to the total measured INP population. Note that the same particle size range
was not investigated at all locations with particles in the range of
0.10–0.18 µm not being measured at Whistler Mountain or Amphitrite
Point, and no uncertainty is reported for the Labrador Sea measurement as
only a single sample was available. Averaging over all sampling locations
with a 1 SD uncertainty, 91 ± 9, 79 ± 17, and 63 ± 21 %
of INPs had an aerodynamic diameter > 1 µm at ice
activation temperatures of -15, -20, and -25 ∘C, respectively. At
-15 ∘C, the percentage of supermicron INPs ranged from 78 % at
Whistler Mountain up to 100 % at the Labrador Sea and Colby sites. At
lower temperatures, there was more variation between samples: at -20 ∘C the percentage of supermicron INPs ranged from 52 %
at Whistler Mountain to 100 % over the Labrador Sea, and at -25 ∘C the percentage of supermicron INPs ranged from 39 %
at Whistler Mountain to 95 % over the Labrador Sea.
Figure 3b shows the fraction of INPs that are in the coarse mode, calculated
by assuming that half of the INPs found in the 1.8–3.2 µm MOUDI size
cut were larger than 2.5 µm (i.e., INPs are uniformly distributed over
this size range). Measurements of the total particle size distribution were
not available at all locations to test this assumption. Furthermore, it is
not known whether the INP size distribution follows the total particle size
distribution a priori. Averaging over all sampling locations, the percentage of INPs
in the coarse mode was 62 ± 20, 55 ± 18, and 42 ± 17 %
(1 SD) at ice activation temperatures of -15, -20, and -25 ∘C,
respectively. The percentage of INPs in the coarse mode was found to range
from 38 % at Saclay to 91 % in Colby at -15 ∘C, from 26 % at Whistler Mountain to 73 % in Colby at -20 ∘C, and from
20 % at Alert to 64 % at the Labrador Sea at -25 ∘C.
Despite great diversity in the studied locations, each had a significant
contribution from coarse-mode particles to the measured INP population.
Previous size-resolved INP measurements.
Study
Location
Geographical
Altitude
Particle sizes
Mode of ice
Ice nucleation
Result
description
investigated (µm)
nucleation
temperature (∘C)a
Rucklidge (1965)
West Plains,
Forest and
4 m a.g.l.
TSP
Condensation and/or
-12 to -25
≤14 % of INPs
Missouri
pasture
deposition
> 1 µm
Vali (1966)
Alberta,
Western
Hail melt
TSPb
Immersion
-12.8
16 % of INPs
Canada
Canada
water
> 1.2 µmc
Rosinski et al. (1986)
Central and western
Marine
Near sea
0.5 to > 8
Immersion
-10.8
100 % of INPs
South Pacific Ocean
level
> 1 µm
< 0.5 to > 8
Condensation
-5 to -6
1 % of INPs
> 1 µm
Rosinski et al. (1988)
Gulf of
Marine
Near sea
0.1 to > 4.5
Condensation
-15 to -16
45 % of INPs
Mexico
level
> 1 µm
Berezinski et al. (1988)
European territory of
Eastern
100–500 m a.g.l.
0.1 to > 100
Condensation
-15 to -20
37 % of INPs
the former Soviet Union
Europe
> 1 µm
Mertes et al. (2007)
Jungfraujoch,
Alpine
3580 m a.s.l.
0.02 to 5
Unknown
-17.4
< 1 % of ice
Switzerland
(ice residual)
residuals > 1 µmc
Santachiara et al. (2010)
S. Pietro
Rural Italy
3 m a.g.l.
TSP
Condensation
-17 to -19
47 and 30 % of INPs
Capofiume, Italy
> 1 and 2.5 µm, respectively
Huffman et al. (2013)
Manitou Experimental
Forest during/
4 m a.g.l.
0.32 to > 18
Immersion
-15 to -20
89 % of INPs
Forest, CO, USA
after rainfall
and deposition
> 1 µm
Forest during
4 m a.g.l.
0.32 to > 18
Immersion and
-15 to -20
46 % of INPs
dry periods
deposition
> 1 µm
a We used data at the temperatures of this study (-15, -20, and -25 ∘C) when available, otherwise the next closest temperature was
used.
b TSP = total suspended particulate.
c Particle size reported for Vali (1966) is based on filter pore size,
and particle size reported in Mertes et al. (2007) is based on electrical
mobility and optical measurements. In all other studies, particle size is
given as the aerodynamic diameter.
The median size of INPs at ice-activation temperatures of
-15 ∘C (green), -20 ∘C (blue), and -25 ∘C
(red) when averaged over all analyzed samples. Upper and lower uncertainties
are the 75th and 25th percentiles, respectively.
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The median sizes of INPs at ice activation temperatures of -15, -20, and -25 ∘C are shown in Fig. 4 with the 25th and 75th
percentile values. At -15 ∘C, the median INP size is relatively
large at all locations, varying from 2.1 µm at Saclay to 4.7 µm at Colby with an average of 3.2 ± 0.9 µm (1 SD). As droplet
freezing temperature decreased, the median INP size also decreased, with the
exception of samples from the Labrador Sea and the UBC campus. At -25 ∘C, the median size of INPs varied from 0.83 µm at Alert
to 3.1 µm at the Labrador Sea site with an average of 1.9 ± 1.0 µm. The median
size of the INPs was > 1 µm in all
cases with the exception of the Alert and Whistler Mountain sites at a
freezing temperature of -25 ∘C. Alert, in the polar tundra at
high latitude, and Whistler Mountain, at high elevation and periodically in
the free troposphere, are remote with fewer local sources of aerosols.
In Fig. 4, the difference between the 75th and 25th percentile
sizes is relatively small at all locations at -15 ∘C. A narrow
INP size distribution at -15 ∘C is consistent with a single type
or class of particles dominating freezing at this temperature. With
decreasing temperature, the interquartile range significantly increased: the
75th and 25th percentile INP sizes decreased by an average factor
of 1.2 and 3.7, respectively, between -15 and -25 ∘C,
corresponding to a 63 % increase in the average interquartile range.
INP size distributions are further explored in Fig. 5, where the fraction of
the measured INP number concentration found in each MOUDI size bin is shown.
Colors on the red end of the scale illustrate that a large fraction of the
INPs measured at a particular location belong to that particle size bin.
Total INP number concentrations as a function of temperature are given in
Fig. S1 and histograms of the INP size distributions are given in Figs. S2–S8. Figure 5a shows that most INPs active at -15 ∘C
were 1–10 µm in size. In particular, when averaged
over all locations, 72 % of the INPs active at -15 ∘C were
between 1.8 and 5.6 µm. Furthermore, the major mode (i.e., the global
maximum in a size distribution) was always larger than 1.8 µm. At
lower freezing temperatures the INP size distributions broadened with
increased contributions from smaller aerosol particles, evident by the more
uniform intensity of Fig. 5b and c. By -25 ∘C, six of the seven
locations had a submicron INP mode, and at Alert and Whistler Mountain this
was the major mode. A general broadening of the INP size distribution with
decreasing temperature would be expected if there were an increase in the
number of particle types exhibiting ice activity with decreasing activation
temperature.
Fractional INP concentrations as a function of aerosol
particle size, location, and activation temperature: (a) -15 ∘C;
(b) -20 ∘C; and (c)-25 ∘C. The color bar indicates
the fraction of INPs measured in each particle size bin. Aerosol particle
sizes correspond to the 50 % cutoff aerodynamic diameters of the MOUDI
stages (Marple et al., 1991). Missing sizes for the Whistler Mountain and
Amphitrite Point sites are uncolored.
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Several previous studies have conducted size-resolved INP measurements. In
most of these studies, the fraction of INPs larger than a given particle
size was not reported, and in some cases the temperatures studied were
different than in the current study. To better compare our data with these
previous studies, we have used the literature data to calculate the fraction
of INPs larger than either 1, 1.2, or 2.5 µm at temperatures as close
as possible to the freezing temperatures we used. Details of the
calculations are presented in the Supplement, and the results of the
calculations are summarized in Table 2.
Table 2 shows that in six out of the nine previous studies, a large fraction
(16–100 %) of the INPs was found to be supermicron in size, consistent
with the current study. Here the work of Rosinski et al. (1986) is
considered as two separate studies given the change in the investigated mode
of ice nucleation. Although the condensation and immersion freezing
measurements reported in Rosinski et al. (1986) appear contradictory, it is
important to note that the two freezing results for Rosinski et al. (1986) shown in Table 2 correspond to different temperature ranges (compare
-5 to -6 ∘C for condensation and -10.8 ∘C for immersion freezing). One possibility is that small particles dominated
the INP population at the warmest temperatures while larger particles
dominated the INP population at the colder temperatures investigated by
Rosinski et al. (1986).
The ice nucleation efficiency of particles as a function of size have also
been investigated in laboratory experiments (e.g., Lüönd et al., 2010; Archuleta et al., 2005; Welti et al., 2009). In general this work
has shown that ice nucleation efficiency increases as particle size
increases. Furthermore, several studies have investigated correlations
between the concentrations of INPs and aerosol particles above a certain
size (Richardson et al., 2007; DeMott et al., 2010; Chou et al., 2011; Field
et al., 2012; Huffman et al., 2013; Prenni et al., 2013; Tobo et al., 2013;
Ardon-Dryer and Levin, 2014; Jiang et al., 2014, 2015). For example, using
data from a variety of field measurements DeMott et al. (2010) observed a
correlation between INP concentrations and the concentration of aerosol
particles > 0.5 µm, and Ardon-Dryer and Levin (2014) found
that INP concentrations in Israel were better correlated to the
concentration of aerosol particles 2.5–10 µm in size than those
< 2.5 µm. These results are also consistent with INPs being
relatively large in size.
Summary and conclusions
INP number concentrations in the immersion mode as a function of size and
droplet freezing temperature were determined at six locations across North
America and one in Europe. INP number concentrations varied by as much as an
order of magnitude between locations, and were generally found to be lowest
at the remote sites of Alert and Whistler Mountain and highest at the
agricultural sites of Colby and the suburban sites of Saclay and the UBC
campus, consistent with previous studies. Several key findings indicate the
potential importance of large INPs at ground level: (1) 91 ± 9 and 62 ± 20 % of INPs measured at -15 ∘C across all locations
are supermicron or in the coarse mode, respectively; (2) at the lowest
temperature analyzed, -25 ∘C, 63 ± 21 and 42 ± 17 % of INPs across all locations remained in the supermicron regime and
coarse mode, respectively; (3) at -15 ∘C, the median INP size was
relatively large at all locations, varying from 2.1 µm at Saclay to
4.7 µm at Colby with an average of 3.2 ± 0.9 µm; and (4)
at -25 ∘C, the median size INP varied from 0.83 µm at
Alert to 3.1 µm above the Labrador Sea with an average of 1.9 ± 1.0 µm.
Our measurements indicate that, when averaged over all studied locations and
temperatures, 78 ± 19 and 53 ± 20 % of immersion-mode INPs
may be missed if either supermicron particles or coarse-mode particles are
not sampled at ground sites. As noted in Sect. 1, some instrumentation for
measuring ambient INP number concentrations restricts the upper range of
sampled aerosol particles. The data presented may be useful for estimating
the fraction of INPs not measured with these instruments at ground sites and
in different environments.
All measurements used in this study were conducted at ground level and,
apart from those at Whistler Mountain, were also close to sea level. As the
large contribution of supermicron and coarse-mode INPs to the overall INP
population noted here may not necessarily hold for higher altitudes,
additional size-resolved INP measurements as a function of altitude are
needed. In obtaining such data, careful consideration will be needed toward
sampling issues with aerosol inlets and transfer through sample lines on
aircraft platforms. It can be anticipated that supermicron particle transfer
will be strongly restricted without special inlets or care, and this may
especially impact INP sampling.
A caveat to this study is that our measurements were confined to aerosol
particle sizes greater than either 0.10 or 0.18 µm. If there were a
significant contribution from INPs of smaller sizes (Vali, 1966; Schnell and
Vali, 1973; Pummer et al., 2012; Augustin et al., 2013;
Fröhlich-Nowoisky et al., 2015; O'Sullivan et al., 2015; Tong et al.,
2015; Wilson et al., 2015), and these smaller sizes did not coagulate or get
scavenged by larger particles, the values presented here would represent
upper limits to the contribution of supermicron and coarse-mode particles to
the total INP population. Additional studies exploring the relative
atmospheric abundance of INPs < 0.10 µm are necessary (Hader
et al., 2014). Future studies of the size distribution of INPs should also
include measurements of particle mixing state to determine whether particles are
internally or externally mixed at the locations where the size distribution
of INPs are being measured.