ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-18-4831-2018On the functional form of particle number size distributions: influence of particle source and meteorological variablesAerosol number size distribution functional formCugeroneKatiakatia.cugerone@polimi.ithttps://orcid.org/0000-0003-1834-0815De MicheleCarlohttps://orcid.org/0000-0002-7098-4725GhezziAntonioGianelleVorneGilardoniStefaniaPolitecnico di Milano, Department of Civil and Environmental
Engineering, Milan, ItalyRegional Agency for Environmental Protection Lombardia, Milan,
ItalyNational Research Council, Institute of Atmospheric Science
and Climate, Bologna, ItalyKatia Cugerone (katia.cugerone@polimi.it)10April20181874831484226November201624March201721February201821February2018This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/18/4831/2018/acp-18-4831-2018.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/18/4831/2018/acp-18-4831-2018.pdf
Particle number size distributions (PNSDs) have been collected periodically
in the urban area of Milan, Italy, during 2011 and 2012 in winter and summer
months. Moreover, comparable PNSD measurements were carried out in the rural
mountain site of Oga–San Colombano (2250 m a.s.l.), Italy, during
February 2005 and August 2011. The aerosol data have been measured through
the use of optical particle counters in the size range 0.3–25 µm,
with a time resolution of 1 min. The comparison of the PNSDs collected in the
two sites has been done in terms of total number concentration, showing
higher numbers in Milan (often exceeding 103 cm-3 in winter
season) compared to Oga–San Colombano (not greater than 2×102 cm-3), as expected. The skewness–kurtosis
plane has been used in order to provide a synoptic view, and select the best
distribution family describing the empirical PNSD pattern. The four-parameter
Johnson system-bounded distribution (called Johnson SB or JSB) has been tested for this
aim, due to its great flexibility and ability to assume different shapes. The
PNSD pattern has been found to be generally invariant under site and season
changes. Nevertheless, several PNSDs belonging to the Milan winter season
(generally more than 30 %) clearly deviate from the standard empirical
pattern. The seasonal increase in the concentration of primary aerosols due
to combustion processes in winter and the influence of weather variables
throughout the year, such as precipitation and wind speed, could be
considered plausible explanations of PNSD dynamics.
Introduction
High concentrations of suspended aerosol in the lower atmosphere cause short-term
health effects and increase the possibility of contracting serious chronic
respiratory and cardiovascular diseases .
In addition, two environmental issues are that atmospheric aerosols reduce the visibility
and alter the Earth's radiation balance . In particular, aerosol size distribution is
a climate-relevant variable that affects the optical properties of
particles and their cloud forming potential as well .
Number concentrations of aerosol particles are generally very high in urban
and kerbside environments, compared to rural and pristine areas, due to the
proximity to pollution sources . Urban particle
number concentrations (in the range 10–800 nm) are usually above
104 cm-3 during the cold season, while at a regional background site
they do not exceed 103 cm-3. In
urban environments, the most important sources of atmospheric aerosols are
combustion processes (mainly related to traffic, residential heating and
energy production), road dust re-suspension, and formation of secondary
aerosols from gas and particulate-phase precursors. While combustion
emissions and secondary aerosol contribute mainly to fine particles (below
1 µm), road re-suspension and part of the traffic emissions
contribute to the coarse particle mode . In
pristine areas, aerosols are mainly composed of secondary aerosol (fine
particles) and re-suspended soil dust (coarse particles). Source and removal
processes determine season and spatial variability in particle size
distributions.
Models can describe particle number size distributions (PNSDs) by two different
approaches. In the sectional approach, particles are distributed into size
bins, or sections. Such an approach is computationally expensive but does not
require any assumptions about the functional form of the particle size
distribution. More computationally efficient models represent aerosols with a
limited number of modes, described by mathematical equations. This scheme
requires knowledge of the mathematical function that best describes the
multimodal distribution of ambient aerosol. In the literature, different
probability distribution functions have been used to represent particulate
size distributions. The first one is the classic normal distribution that
was soon discarded because of its symmetry . Other
distributions have been used in limited specific applications:
proposed the modified-gamma
distribution for describing the particulate size distribution of marine or
coastal particles for studying the light scattering phenomena;
employed the Weibull distribution to fit the aerosols
generated from fragmented rocks; introduced a new
mathematical form, derived from the Weibull distribution, the so called
Rosin–Rammler, to model the evolution of atmospheric aerosol. Later,
introduced firstly the hyperbolic and
secondly the generalized hyperbolic distribution to represent the statistical
variability in sand grading. Other authors
proposed the power-law
distribution to model atmospheric aerosol number size distributions. This is
mathematically simple to compute, compared to other functional forms,
but it is only accurate over a limited size range, beyond which significant
errors can arise . Above all, the most used distribution
to describe PNSDs is the lognormal (,
among others). This functional form is mathematically simple, easy to apply
and allows for a good match with a wide variety of empirical data; even if a
theoretical justification for its widespread use does not exist and no one demonstrated it
as superior to the other distribution in a general sense
.
Here, the four-parameter Johnson system-bounded distribution (hereafter called Johnson SB or JSB) is presented for modelling
PNSD data, in addition to the classical mixture of (two) lognormals widely
used in the literature . The
great flexibility and versatility of this distribution, together with its
boundedness (which matches the physical limitations of the analysed aerosol
particles) make the Johnson SB a good candidate for this purpose. The use of
this distribution has also been inspired by
; and , where the authors
have recently demonstrated the accuracy of this probability function in
modelling the number size distribution of drops at the ground, a
particular case of PNSD. Furthermore, the outcomes of this study are in
accordance with the works of and , in which JSB
was firstly proposed for this aim. In order to statistically prove the
adequacy of this distribution, we use the skewness–kurtosis moment ratio
diagram (S-K plane), the locus of the couples skewness (β3) and
kurtosis (β4) as a diagnostic tool . The availability
of a great number of PNSD data makes it possible to plot a large amount of
empirical couples (β3, β4) on the S–K plane. In this way, the
general PNSD empirical pattern and in parallel a consistent theoretical
distribution family can be individuated.
In the next sections, we present the results of the
analysis of a large amount of PNSD data, collected with optical particle
counters at two different sites: the urban site of Milan and the rural mountain
site of Oga–San Colombano. For these cases, the PNSD pattern (i.e. the
domain where the sample points are in the skewness–kurtosis plane) is well
represented by the JSB domain, except for the urban winter data. In
other words, the PNSD pattern does not change, even if we change the site or
the season with the exception mentioned above. In winter, the pattern seems
to be altered, probably by the influence of the aerosols point sources,
which cause an increase in the total particle counts. In order to give our
interpretation of these trends, we used the S–K plane to summarize, from the
statistical point of view, the aerosol dynamics due to anthropogenic and also
meteorological forcings.
Datasets and instrumentation
The data have been collected from two sites: the urban site located in Milan
at Pascal Città Studi (45∘28′42′′ N,
9∘13′54′′ E; 120 m a.s.l.) and the rural high-altitude
site at Oga–San Colombano (46∘27′40′′ N,
10∘18′07′′ E; 2290 m a.s.l.). The urban site is representative
of “urban background” conditions and is not directly affected by local
traffic emissions (), while the latter was a temporary
experimental high-altitude site. Table provides details about the
period of observation considered in this analysis and the number of minutes.
We would like to point out that the analysed time ranges have been selected
also according to the availability of the aerosol PNSD datasets, which were
kindly provided by ARPA Lombardia.
List of sites with indication of season, date of measurement and number of minutes.
Aerosol particle number concentrations were measured using an optical
particle counter (OPC; Grimm 107 Environcheck model) with a time resolution
of 1 min. The measured size distributions range from 0.3 to 25 µm
subdivided into 26 size bins for all of the analysed months and sites. The only
exception is the winter dataset of Oga–San Colombano collected in February
2005 (SC1), characterized by size distributions between 0.3 and 25 µm,
subdivided in 15 size bins. The OPC measurements allow for the quantification of
a portion of fine mode particles (between 300 nm and 1 µm) and the coarse
mode particles (above 1 µm). The instrument is based on the
quantification of the 90∘ scattering of light by aerosol particles.
The two sites present very different characteristics regarding the
magnitude, the distribution and the composition of the aerosol fraction and
the climatic characteristics. In particular, Oga San Colombano shows a higher
relative contribution of organic aerosol, likely of secondary origin, as
suggested by a higher organic to elemental carbon ratio .
Milan shows a higher nitrate to sulfate ratio, in agreement with a stronger
impact from combustion sources such as traffic and industrial emissions
. Milan has a humid subtropical climate (Cfa), according
to the Köppen climate classification . Milan's
climate (as in all of the Valpadana valley, northern Italy's inland plain) is
influenced by the natural barrier of the mountains (the Alps in the north and
the Apennines in the south), which obstruct and prevent inflows from the north,
south and west. Winters and summers are usually dominated by high pressure,
while autumns and springs are characterized by an alternation between high and
low pressure. These conditions usually cause high moisture levels in the lower atmosphere
and air stagnation, especially during high pressure seasons.
Furthermore, Milan's climatic conditions can be considered a typical example
of an urban climate: urbanization has evidently changed the form of the
landscape, and has also produced changes in the area's air. According to the
European directive 2008/50/CE, all of the European countries must respect the
standard limits related to air quality . In
particular, the maximum daily levels of PM10 should not exceed
50 µg m-3 (for more than 35 days per year), while the annual
limit is 40 µg m-3 (which should not be exceeded on a yearly
average). During 2011 (2012), the maximum daily limit in Milan was passed
122 (97) times, during the winter period, and the average yearly level was
47 (43) µg m-3.
On the contrary, Oga – San Colombano is a mountainous rural site, characterized by
the typical Alpine climate (Dfb, according to the Köppen climate
classification) with warm summers and long, cold and snowy winters. Specifically,
the analysis site is located far away from higher mountains, and
for this reason is not often shaded. Typically, San Colombano presents free
air circulation and stagnation of cold air during winters. These
characteristics allow low aerosol levels (the average annual value of
PM10 is 6 µg m-3 with standard deviation of
5 µg m-3), mostly consisting of particles produced far away
and transported locally by the wind and thus good air quality all over the
year.
The influence of primary aerosol sources
and meteorology on PNSD has been investigated for the site of Milan. To study
the effect of pollutant concentration here, we use nitrogen dioxide
(NO2) and nitrogen oxide (NO) measurements, collected with a
chemiluminescence technique following the requirements of the European standard
EN 14211:2005: ambient air quality. Meteorological variables, namely
precipitation and wind speed, have been measured respectively with a
tipping-bucket rain gauge and by an anemometer located at the Regional Agency for Environmental Protection (ARPA) station of
Lambrate (45∘29′46′′ N, 9∘15′28′′ E;
120 m a.s.l.), which is around 3 km away from Pascal Città Studi.
Median (solid lines) and mean (dashed lines) number size
distributions for two selected winter and summer datasets of Pascal Città Studi
(MI3, MI8) and the two datasets of Oga–San Colombano (SC1, SC2). The
coloured blue and red areas are limited below and above by the 5th and the
95th percentiles of the corresponding dataset.
Data analyses
The different characteristics of the aerosol number size distributions at
Milan (urban site) and Oga–San Colombano (rural site) are shown in
Fig. . Here, median (solid lines) and mean (dashed lines) number
size distributions for the two datasets of Oga–San Colombano (SC1, SC2 in the
left panel) and two selected winter and summer datasets of Milan (MI3, MI8 in
the right panel) are shown, together with the 95th confidence intervals
(coloured areas). Similar results can be obtained considering the other
datasets of Milan. Median and mean number size distributions of all of the
datasets present a common decreasing trend inside the analysed size range,
0.3–25 µm, but also evident discrepancies. In particular, the
coloured areas depicted in the plots denote a greater PNSD variability for
SC1 and SC2 compared to MI3 and MI8. The distance between the 5th and the
95th percentiles of the latter is very small in the diameter range
0.3–3 µm, accumulation mode particles and smaller coarse mode
particles, and is characterized by higher number concentrations (especially
in winter) compared to Oga–San Colombano.
Looking at these plots, it is difficult to understand if a unique functional
form is able to describe the variety of PNSDs. In order to clarify this
issue, we propose the use of the skewness–kurtosis moment ratio diagram as a
diagnostic tool. This plane was introduced by and then
updated by various authors, e.g. and
. The skewness–kurtosis (β3-β4) plane
presents the skewness (Eq. ) in abscissa, and the kurtosis
(Eq. ) in ordinate,
β3=EX-μXσX3,β4=EX-μXσX4,
where X is the variable, E[…] is the expected value, and μX and
σX are respectively the mean and the standard deviation of X. The
Pearson limit curve β4-β32-1≥0 divides
the theoretically impossible and possible areas, in which a couple
(β3, β4) can be found. In this diagram, each theoretical
probability distribution is represented by a domain, which can be a point, a
line or an area, depending on the number of shape parameters involved.
Therefore, this plane can be used as a diagnostic tool for the identification
of distributions able to model given datasets, comparing the theoretical
domain of the distributions and the sample variability in data. In
Fig. , following , we have
reported the domain of some families of distributions including normal,
exponential, gamma, lognormal, Johnson SB and Johnson SU, and in addition,
for the first time, a mixture of two lognormals. From Fig. , it is
possible to identify the following features:
normal and exponential are represented by a single point. In particular, the square (0,3) represents the normal and the triangle (2,9) the exponential;
gamma (long-dashed line) and lognormal (dotted-dashed line) are distributions represented by a line;
the Johnson SB is the upper and lower bounded family and occupies the area (medium grey region) limited below by the Pearson
limit curve and above by the lognormal line. The Johnson SU is the unlimited family; it covers all of the rest of the plane (light grey region)
and is limited below by the lognormal curve
the domain of a mixture of two lognormals (red dots area) is represented by an area embracing the lognormal line. The domain has
been determined numerically by Monte Carlo simulations as reported in
Supplement A.
Given this, we use the skewness–kurtosis plane to search the best functional
forms able to describe the sample PNSDs of Milan and Oga–San Colombano
datasets and to analyse the effects of primary pollutants and weather
variables, in order to clarify the dynamics of PNSD variations.
(β3, β4) domain of some families of distributions
including normal (square), exponential (triangle), gamma (dashed line),
lognormal (dotted-dashed line), Johnson SB (medium grey area) and Johnson SU
(light grey area), and a mixture of two lognormals (red dotted area).
Location of the sample couples (β3, β4) from SC1
(a), SC2 (b), MI3 (c), and MI8 (d) datasets
in the skewness–kurtosis plane with theoretical distribution reference
domains. Cyan dots represent PNSDs with TP < 25 000, blue dots
25 000 < TP < 62 500, purple dots 62 500 < TP < 100 000
and magenta dots TP > 100 000. The dotted-dashed line is the lognormal
distribution, the dotted line is the Weibull distribution and the dashed
line is the gamma distribution.
Results and discussionsUrban vs. rural sites
In order to analyse and compare PNSDs characterized by different ambient
conditions and different seasons, we calculate the skewness and the kurtosis
of each minute of the four datasets previously considered, SC1 (a), SC2 (b),
MI3 (c), MI8 (d), and we report the sample couples (β3,β4) in the
skewness–kurtosis plane, see Fig. . In this plane, the limit curve
represented by the thick black solid line divides the statistically
unfeasible area (dashed area) by the portion of the plain that can be
occupied by the pairs (β3, β4). The theoretical domains of some
selected distributions are also reported: normal (black square), exponential
(black triangle), lognormal (black dotted-dashed line), Weibull (black dotted
line), gamma (black dashed line), Johnson SB, (JSB – dark grey area) and
Johnson SU (light grey area). The domain of the mixture of two lognormals (not
reported here), being characterized by a greater shape variability with respect to
the simple lognormal distribution, is represented by an area embracing the
lognormal line (see Supplement A for more details). The sample couples
(β3,β4) are divided into four classes and coloured as a function of
the total particle count (TP) of the related minute: cyan dots represent
PNSDs with TP < 25 000, blue dots 25 000 < TP < 62 500, purple
dots 62 500 < TP < 100 000 and magenta dots TP > 100 000.
Firstly, by analysing Fig. , we see that the majority of the couples are located inside the JSB
theoretical domain (see Table ). This is a four-parameter
distribution characterized by a bounded domain, which is suitable for the
particles diameter, being a finite variable. MI3, the Pascal Città Studi
dataset collected on February in midwinter, represents the only evident
exception with 29.6 % of the data points outside of the JSB domain.
Figure also indicates the existence of a relation between the
position of the dots and their colour, and thus between the functional form
and the total particle count. In particular, the sample skewness–kurtosis
couples tend to move left and to exit from the JSB domain with the increase
in TP. This is again especially true for MI3, which is characterized by
96 % of the data points belonging to the fourth class, with
TP > 100 000, while for SC1, SC2 and MI3 the percentages are
respectively 18, 2 and 14 %. To stress this point, let's consider only the
data outside the JSB domain. The percentage of data outside JSB with
TP > 100 000 is 73.2, 33.3, 99.5 and 95.5 %, respectively for SC1,
SC2, MI3 and MI8. The smaller percentage observed for SC2 is likely due to
the limited number of data points characterized by large TP, and thus not
statistically significant. We can conclude that, in the case of a very high
number of aerosol particles, the Johnson SB cannot be considered anymore as
the most accurate distribution in describing PNSDs. From Fig. , it
is possible to see that the data points outside the JSB domain are located
within the domain of Johnson SU (light grey) and in some cases in the domain
of the mixture of two lognormals, which seem good candidates to represent
them, even if these distributions are not upper bounded, like the variable
under investigation. Similar results have been obtained for other Milan
datasets (see Supplement B).
As proof of this, we have fitted the JSB distribution to the measured PNSDs
using the maximum likelihood method (see Supplement C for more details).
Figure shows the size distribution of particle number at the urban
site MI3 in winter (red), at the urban site in summer MI8 (blue) and at the
rural site SC2 (green), together with their corresponding position in the
(β3, β4) space. The three PNSDs are representative of their own
datasets. In particular, the MI3 PNSD collected at 21:57 UTC counts
1 155 778 particles, the MI8 PNSD collected at 16:34 UTC counts
9465 particles and the SC2 PNSD collected at 20:41 UTC counts
2755 particles. The JSB accurately fits PNSD data in the last two cases,
characterized by a lower total number of particles. The figure clearly
illustrates that when the size distribution is efficiently described by the
JSB parameterization, the corresponding distribution falls in the grey area,
the JSB domain. The mixed lognormal distribution, represented in the
skewness–kurtosis plane with dark grey dots, is not able to represent the
PNSDs in none of the three cases.
Comparison of empirical PNSDs (dots) and JSB fittings (lines) from
MI3 (red), MI8 (blue) and SC2 (green), first column. Correspondent location
of the (β3,β4) couples in the (S–K) plane, second column.
Location of the sample couples (β3, β4), black
dots, from MI1 (upper panel) and MI2 (lower panel) in the skewness–kurtosis
plane with theoretical distribution reference domains. Red dots represent
PNSDs with ratio NOx/ NO2 between 1 and 1.1, orange dots
1.1 < NOx/ NO2< 1.5, yellow dots
1.5 < NOx/ NO2< 3 and green dots
NOx/ NO2> 3.
Primary pollutants influence
The analysis of the skewness–kurtosis plane shows the existence of a PNSD
pattern, which is generally under site and season changes, with the exception
of the winter datasets. During winter seasons in urban environments, a
significant change in the general PNSD pattern, consisting of a shift toward
the centre of the S–K plane, has indeed been observed. A plausible explanation of
PNSD dynamics can be found in the recurrent winter increase in aerosol
emissions (much more evident in urban sites), due to heating ignition and
high traffic levels.
In order to clarify this point, measurements of two common atmospheric
components, in particular nitrogen dioxide (NO2) and nitrogen oxide
(NO) collected at Pascal Città Studi, have been considered. Nitrogen
oxides (NOx= NO + NO2) can form naturally in the
atmosphere by lightning and some is produced by plants, soil and water, but
their major source in urban areas is the burning of fossil fuels like coal,
oil and gas . NOx are mainly produced by combustion
processes. Nevertheless primary combustion emissions are dominated by NO over
NO2. NO2 can then be formed through the oxidation of NO in the
atmosphere. It follows that the NO2 to NOx ratio can provide a
measure of the oxidative capacity of the atmosphere
and it is a measure of the temporal
proximity to emission sources. In addition, measurements performed in Milan
during different field experiments show that the ratio of NO2 to
NOx anti-correlates with the ratio of black carbon to PM1,
suggesting that the NO2/ NOx in these urban areas is an
indicator for secondary pollutant formation relative to primary traffic
emissions. In Fig. we have again reported the skewness–kurtosis
plane, where we have plotted in black the data points of MI1 (upper panel)
and MI2 (lower panel). Then, we have selected the data points belonging to
minutes characterized by values of the ratio NOx/ NO2 between
1 and 1.1 (red dots – strong prevalence of secondary aerosols), 1.1 and 1.5
(orange dots – light prevalence of secondary aerosols), 1.5 and 3 (yellow –
light prevalence of primary aerosols), greater than 3 (green – strong
prevalence of primary aerosols). Both of the two datasets are characterized by
high aerosol numbers and high percentages of data points outside the JSB domain
(74 and 65 %, respectively). The percentages of data points characterized
by a ratio NOx/ NO2 greater than 3 are around 50 %,
indicating a prevalence of the primary aerosol contribution. Most of such
data points fall in the region characterized by a size distribution dominated
by submicron particles as depicted in Fig. . If we only select the
data points outside the JSB domain, the percentage of data points with ratios
greater than 3 (strong prevalence of primary aerosols) is 56 % for MI1
and 50 % for MI2, while the percentage of data points with ratio greater
than 1.5 (light or strong prevalence of primary aerosols) is 88 % for MI1
and 67 % for MI2. These findings support our hypothesis that in urban
sites during winter season, the increase in primary aerosols emission by local
sources causes an evident increase in primary aerosol compound
concentration. This can be considered as one of the causes of the location shifts
of (β3, β4) couples in the skewness–kurtosis plane.
Location of the sample couples (β3, β4) in the
skewness–kurtosis plane for the days 19, 20 and 21 February 2012. The dots
are coloured according to the time slot as explained in the legend. Between
09:00 and 17:00 UTC of 20 February a precipitation event with a maximum
intensity of 1 mm h-1 and average intensity of 0.6 mm h-1
occurred.
Median (solid lines) and mean (dashed lines) number size
distributions for the minutes before (blue), during(green) and after (red)
the rain event on 20 February 2012. The coloured blue, green and red areas
are limited below and above by the 5th and the 95th percentiles of the
correspondent dataset.
Location of the sample couples (β3, β4) in the
skewness–kurtosis plane for the days 14, 15, 16 and 17 February 2012. The
dots are coloured according to the time slot as explained in the legend.
Between 15 and 16 February, relatively high wind speed with maximum of
3.8 m s-1 (recorded on 15 February at 15:00 UTC) occurred.
Weather variables influence
The aerosol concentration variation due to the increase in particle
emissions in the atmosphere is not the only cause of PNSD shape changes. The
occurrence of weather events, such as precipitation or high wind speed,
indirectly causes a modification of the particle concentration, which often
results in a decrease in number and mass of aerosol particles suspended in
the lower atmosphere . In particular, the aerosol wet
removal during rain events, known as the scavenging process, is caused by the
vertical movement of the falling raindrops, which intercept the suspended
aerosol particles and bring them to the ground . Also,
the blowing of high wind speeds in urban areas far away from the sea, like
Milan, cleans the atmosphere by dispersing and diluting the aerosol particles
and preventing local accumulations . The visible effect
of these phenomena in the skewness–kurtosis plane is described again by a
shift in the position of the couples (β3, β4), but in the
opposite direction (toward the right-side of the S–K plane) with respect to the one
(toward the centre of the S–K plane) caused by the influence of the high
concentration of primary aerosol compounds. In other words, the couples
(β3, β4) are forced to stay in the JSB theoretical domain.
Therefore, looking at the skewness–kurtosis plane, the influence of the
weather variables is only visible if the occurrence of high wind speed or
significant precipitation events are foregone by particle size concentrations
characterized by couples (β3, β4) outside the JSB domain. These
conditions generally occur in winter seasons in urban areas, as we have seen
in the previous paragraph.
Two practical examples are taken from the dataset MI3 (February 2012). The
first is related to precipitation (Fig. ), the second to wind
(Fig. ). In both cases, we represent the skewness–kurtosis
plane and we track the movement of the couples (β3, β4)
before, during and after the respective weather event. The dots are coloured
according to the time window in which the PNSDs have been collected.
Figure shows the location of the sample couples (β3,
β4) in the skewness–kurtosis plane during the days 19, 20 and
21 February 2012; each day is represented in a specific panel to visualize
the movements of the couples precisely. On 19 February the couples are stably
located outside the JSB domain, as normal for an urban site in midwinter, no
precipitation occurs. In 20 February between 09:00 and 17:00 UTC a
rainfall event with a maximum intensity of 1 mm h-1 and average
intensity of 0.6 mm h-1 occurred. The influence of meteorological
change is clearly reflected in the skewness–kurtosis plane: the dots related
to PNSDs collected between midnight and 08:00 UTC (blue and cyan) on this day
are still outside the JSB area, but starting from 08:00 UTC until around
20:00 UTC the dots (green, yellow and orange) move right and enter inside JSB
domain, then after 20:00 UTC they start to exit (red dots) and remain outside
also during 21 February. In Fig. , median (solid lines) and mean
(dashed lines) number size distributions measured in the minutes before
(blue), during (green) and after (red) the rain event are shown, together
with the 95th confidence intervals (coloured areas). The distributions during and
after the rain event are characterized by lower aerosol concentration levels
with respect to the distribution before the rain. This phenomenon is a clear
consequence of the scavenging effect of precipitation. Furthermore, in the
distribution before the rain event, the high particle concentration in the
smaller diameter classes and the existence of outliers with diameters bigger
than 4–5 µm can be considered the reason for the position outside
the JSB domain in the skewness–kurtosis plane. Distributions having such
strong peaks in the first diameter classes, but with the presence of particles
in big diameter classes, can be generally represented by theoretical
distributions having a “long” right tail, characteristic of unbounded
distributions.
Similarly, the effect of high wind speed is reported in Fig. ,
where the location of the sample couples (β3, β4) in the
skewness–kurtosis plane during the days 14, 15, 16 and 17 February 2012 is
shown. During these days, and in particular between 15 and 16 February,
relatively high wind speed with a maximum of 3.8 m s-1 (recorded on
15 February at 15:00 UTC) occurred. The increase in wind speed causes a
movement to the right (inside JSB area) of the couples (β3,
β4), but when the wind speed decreases the couples returns to outside
of the JSB domain fairly quickly.
In other words, the modifications of PNSD shape (caused by an increase or
decrease in aerosol concentration by new emissions or weather events) result
in movements of the sample (β3, β4) couples in the moment
ratio diagram, and consequently in changes in the pool of distributions
potentially able to describe the PNSDs. Inside this pool, the Johnson SB
distribution seems the best, in the case of low polluted conditions – achievable
also after significant weather events, such as precipitation or high wind
speed. Gamma, lognormal and Weibull can be considered accurate too, but for a
limited number of times. Conversely, in the case of high concentration, none of
these distributions should be inserted into the pool: the PNSD shape changes
because of the elevated increment of the fine particles, which shift the
sample mode to the left and cause an increase in the number of outliers.
(β3, β4) couples are shifted into an area of the
skewness–kurtosis plane belonging to unlimited distributions, such as the
Johnson SU or the generalized hyperbolic. These distributions become the best
suitable for PNSDs characterized by this kind of shape, despite the limited
(above and below) nature of the variable under examination, the aerosol diameter.
Conclusions
In this work, OPC data, collected at two sites (one urban, Milan at
Pascal Città Studi, and one rural, Oga–San Colombano) have been analysed.
The aerosol particle number concentrations present very different
characteristics: the magnitude, the composition of the aerosol fractions and
also the empirical distribution shape vary a lot within the dataset. These
variations are caused both by the different nature of the measurement sites
(urban and polluted Pascal Città Studi, rural Oga–San Colombano) and by
the season of measurement. This likely suggests that a unique statistical
distribution cannot cover all of the PNSD forms.
In order to statistically identify the best distribution describing the
empirical PNSD pattern, the skewness–kurtosis plane has been used as a
synoptic tool. Our analyses show that the four-parameter Johnson SB, thanks
to its flexibility, could be considered as the most accurate distribution for
representing the empirical PNSD forms, being able to describe the
majority of the PNSDs analysed, under conditions of low pollution levels.
Other distributions, such as gamma, Weibull, lognormal and mixture of two
lognormals, could be considered adequate too, but for a much more limited
portion of the datasets. Further work is needed to quantitatively describe
the goodness of the JSB distribution, and the link between the fit parameters
and aerosol sources and processes. Such analyses will be the subject of a
future study.
The urban datasets, collected in January and February in midwinter, represent
the only evident exceptions, since their PNSDs clearly deviate from the
pattern generally found for the other datasets. The combined analysis of the
skewness–kurtosis plane and the ratio between NOx and NO2 suggested
that the increase in the concentration of primary aerosol compounds, due to
the seasonal winter increase in combustion processes from a countless number
of point sources, can be considered a plausible explanation of PNSD
empirical pattern dynamics. In particular, the increment of the fine
particle shifts the sample mode to the left and causes an increase in the
number of outliers. In these cases, distributions like the Johnson SU and the
mixture of two lognormals can be good candidates. This important issue will
be investigated in future works.
Nevertheless, also the occurrence of weather events, such as precipitation
and high wind speed, by indirectly decreasing the aerosol concentrations, can
have considerable influence on PNSD dynamics. The influence of these events
is particularly evident in winter months, when the aerosol concentration is
normally high and the PNSDs deviate from the general empirical pattern.
Precipitation or high wind speed decrease the aerosol concentration, making
the empirical PNSDs again following the general empirical pattern, even if
only for a limited time (more or less corresponding to the duration of the event
itself).
A subset of the dataset analysed during
the current study is available in the
http://ecohys.blogspot.it/p/data.html (Cugerone et al., 2016)
repository. The complete dataset is available from the corresponding author
on request.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-18-4831-2018-supplement.
The authors declare that they have no conflict of
interest.
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