Growth of aerosol particles to sizes at which they can act as cloud
condensation nuclei (CCN) is a crucial factor in estimating the current and
future impacts of aerosol–cloud–climate interactions. Growth rates (GRs) are
typically determined for particles with diameters (

The role of aerosol particles in global climate is one of the largest
uncertainties in our current knowledge of the climate system (Boucher et
al., 2013). Aerosol particles that are large enough, having diameters
(

The condensable biogenic vapours typically originate from emissions of
volatile organic compounds (VOCs) from plants (e.g. Kulmala et al., 1998;
Riipinen et al., 2011). In the atmosphere, VOCs are oxidized mainly by ozone
(

The growth rate of atmospheric particles can be determined after a period
during which formation of particles with roughly similar size has occurred
on a regional scale. Typically, the growth rates are determined after
atmospheric NPF events, during which new particles are simultaneously formed
from vapour molecules in a large area (Kulmala et al., 2012). After a NPF
event, the growth of the formed particle mode can be typically followed up
to 15 nm or sometimes up to 50 nm, but very rarely up to 100 nm. In order to
observe the growth until 100 nm at the measurement station under typical
conditions, simultaneous NPF should happen in a very large area (e.g. with
wind speed 5 m s

The growth rate has been shown to increase with increasing particle diameter
in nucleation mode (

Here, we first present an easy-to-use automatic method to determine the
particle growth rates from particle number size distribution data by
analysing growing particle modes that do not need to immediately follow the
NPF event. The growth rates can be calculated for different particle size
ranges: nucleation mode (

An example of the evolution of particle size distribution and the determined growth periods over five consecutive days in June 2016. White circles show the found peaks in particle size distribution and the black lines show the determined monotonic growth periods.

The automatic determination of growth rates, described in more detail in
Sect. 2.2., was developed using the particle size distribution (PSD) data
recorded at the SMEAR II station (Hari and Kulmala, 2005) with a
differential mobility particle sizer (DMPS, Aalto et al., 2001) system,
which has a time resolution of 10 min. The applied data set is 20 years
long, from January 1996 to August 2016, and presents the PSD for particles
in diameter range from 3 to 1000 nm. The measurement station is situated in
a boreal forest area with the dominant tree species being Scots pine (

The determined growth rates were compared with meteorological variables and
gaseous compounds, such as ozone, sulphur dioxide and nitrogen oxides,
recorded at SMEAR II. The temperature was measured with PT-100 sensor at
16.8 m height and the ozone concentration with an ozone analyser (TEI 49C,
Thermo Fisher Scientific, Waltham, MA, USA). These data (as well as the data
for several other parameters, which were investigated in terms of their
connection to growth rates but which we do not present in this paper)
together with a more-detailed explanation of their measurements can be found
in the AVAA database (

Next, the growth rates were compared with monoterpene concentrations ([MT])
and related parameters determined using proxies developed by Kontkanen et
al. (2016). The applied proxy for monoterpene concentrations is given in Eq. (12)
in Kontkanen et al. (2016). They showed that the correlation
coefficient between this proxy and measured concentration was 0.74 and that
for 80 % of the data points the proxy had a bias smaller than a factor of
5.8, which is rather small considering that the monoterpene concentration
varies over almost 3 orders of magnitude. In addition to [MT], we
inspected the correlation of GR with the proxy of monoterpene oxidation
products

Finally, we compared the GRs with the source rate of monoterpene oxidation
products, i.e. the oxidation rate of monoterpenes (OxRate), which is the
numerator on the right-hand side of Eq. (

The DMPS data, described in Sect. 2.1, is first smoothed over five time
steps with a median filter. Peak diameters (marked as white circles in Fig. 1)
are determined from the smoothed data for each size distribution by
fitting a parabola to logarithmic particle concentrations in size bins around
local concentration maxima. The growth rates are determined by making linear
least-squares fits to these peak diameters as a function of time if they
fulfil the criteria described below. In the following description the PSDs
are marked with PSD

The peaks of PSD

When all the peaks within the PSD data file (typically for 1 day) have been assigned to a group (which in some cases can consist of only six points), the groups are inspected one by one in order to find periods with monotonic growth of the peak diameter within the groups. The monotonicity is determined with three conditions: (i) temporal and diameter differences between consecutive peaks; (ii) similarity of the growth rates, retrieved from linear least-squares fits to the peaks, along the growth period; and (iii) a combination of these two parameters. When these monotonicity conditions (described in more detail below) are violated for the third time, the growth period is ended. The peaks that cause the two first violations are excluded from the growth period before continuing to the next PSD.

The maximum allowed temporal and diameter differences between consecutive
peaks (condition i above) are 0.5 h and 20 nm, respectively, which are
stricter limitations than when the grouping of the peaks is done. The
condition for monotonicity (ii) above the fitted growth rate is not
fulfilled if both (a) the addition of a new peak changes the growth rate by a
factor larger than 1.5 in comparison to the growth rate during the first
hour of the growth period and (b) the slope of the fit to the peaks in the
latest three PSDs differs by a factor larger than 2 from the growth rate during
the first hour. The combined condition (iii) uses the original growth rate
GR

Finally, when the original growth periods of a minimum of 1 h have been determined using the monotonicity conditions described above, each growth period is inspected to find out whether it can be combined with a previous or following growth period. This is done because growth periods shorter than 2 h are not considered long enough for determining the growth rate. Two growth periods are combined if their growth rates do not differ by more than a factor of 1.5 and if the growth rate of the combined growth period (retrieved from the linear least-squares fit to the peaks included in both initial periods) does not differ by more than a factor of 1.5 from the former initial period. Additionally, the latter initial period needs to start within a timeframe of at most half of the sum of the initial growth period durations, but not more than 2 h, before and after the end of the former growth period.

In the analysis, the combined and non-combined growth periods are not separated. The minimum duration applied is 2 h, but in many parts of Sect. 3 the results are also presented separately for periods with duration over 5 h. It should be noted that our method simply searches for monotonic increases in particle-mode diameters, and hence it does not differentiate the condensational growth from growth due to coagulation or other possible phenomena that may cause apparent growth of a particle mode. Such phenomena, e.g. the faster coagulation scavenging of the smallest particles within a mode in comparison to the largest particles within the same mode, are typically considered more significant for particle growth in diameter ranges below 10 nm and in more polluted environments. Thus, we assume that the results in this article are not significantly impacted by them.

We made a comparison between GRs determined with our automatic method and manually determined GRs for nucleation-mode particles (Nieminen et al., 2014). For the comparison, we received start and end times of 153 growth periods during the years 2003–2013. It is notable that the manual growth rates were determined only for the time until the mode reaches 25 nm in diameter, because the initial purpose for their determination had been in calculating new particle formation rates, whereas the compared automatic GRs were for the growth periods that had initial diameters below 25 nm. In order to prevent the possibility of comparing different parts of a growth period, between which the particle growth rate might have changed drastically, we chose for comparison only the growth periods for which the automatic and manual growth periods overlapped for at least 2 h. Another note to be made on the manual GR data is that these 153 events represent only a small fraction of the manual GR values for the years 2003–2013, but for the rest of the manual GRs the start and end times were not readily available.

Values of the variables in the model runs for the base case run.
Variables marked with asterisk (

In order to investigate how the diameter of the particle, vapour
concentration and particle-phase chemistry affect the growth rate, we
applied a simple one-particle process model. The model included a particle,
which consists of extremely low-volatility molecules (ELVOC), semi-volatile
molecules (SVOC) and non-volatile dimers formed from SVOCs in the particle
phase (SVOC

Diurnal variation of all the determined growth rates in
different size ranges. Red horizontal line represents the median value and
the blue box the 25th and 75th
percentile values. The whiskers reach approximately

Number of determined growth periods segregated by time of year (rows), times of day (columns) and aerosol size modes (top: nucleation mode, middle: Aitken mode, bottom: accumulation mode). Note that the segregation to modes is made based on the starting size of the observed growth period.

The change in the diameter of the particle is calculated as

The initial values for all the variables are given in Table 1.

The number of determined growth rates in different size ranges during different times of the year and day are presented in Table 2. The number is the largest for the Aitken mode in summer and the smallest for the nucleation mode in summer.

The observed growth rates did not show a clear diurnal cycle (Fig. 2). This is rather surprising, since the strong diurnal cycles of oxidant concentrations, in terms of OH and nitrate radicals, would be expected to affect the concentrations of condensable vapours and the growth rates. The possibility of the opposite diurnal cycles of these factors partly cancelling out their impact and further analysis on their effect is presented in Sect. 3.2.1.

In the nucleation and Aitken mode, the growth rates showed a seasonal cycle with a maximum in summer (Fig. 3). This is in agreement with previous analyses made for this site (Dal Maso et al., 2007; Yli-Juuti et al., 2011; Nieminen et al., 2014). In contrast to smaller sizes, in accumulation mode the median GRs had a minimum during summer.

Monthly variation of all the determined growth rates in different size ranges. See caption for Fig. 2 for details of the markers.

The month-specific median growth rates were very similar in the nucleation
and Aitken modes, varying between 1.8 and 4.1 nm h

Observed particle growth rate as a function of the initial
size of the growing mode, in panel

The comparison of nucleation-mode GRs with manually determined GRs from
Nieminen et al. (2014) showed a strong correlation (

Particle growth rate as a function of mean temperature during the growth period, binned with respect to the start size of the observed growth. The blue points depict all the determined growth periods, red ones the long (> 5 h) growth periods and the black lines are log-linear least-squares fittings for all the growth periods (blue points).

The coupling of the observed growth rates and the particle size is shown in
Fig. 4. Especially the highest observed growth rates increase when the mean
diameter of the growing particle-mode increases, but a similar increase is
observed also for the lowest growth rate values for diameters larger than 30 nm.
These features are evident for all the determined growth rates and for
the long growth periods with duration more than 5 h (Fig. 4a), as well as for both
winter and summer (Fig. 4b). At diameters smaller than 30 nm, very few growth
rates lower than 1 nm h

Particle growth rate (April–September, growth starts at

Parameters of linear least-squares fits for growth rates starting
from

We chose the initial diameter of the growing mode, instead of, for example, the mean diameter, for describing the impact of particle diameter on GR, because applying the mean diameter of the growing mode would cause an artificial bias to the results (if two growth periods with similar duration and different GRs started at same diameter, the one with higher GR would have a larger mean diameter than the one with lower GR; this would result in a positive correlation between GR and mean diameter, even though the diameters were the same in the beginning and thus the reason for different growth rates should not be the diameter). We will further inspect the impact of particle diameter on the growth rate later (Sect. 3.3). However, because in Fig. 4 the growth rate seems to be very different in different size ranges, in the following section we inspect the impacts of other parameters on growth rate in 10 nm size bins.

Growth rates with duration > 2 h during April–September as a function of condensation sink in size bins.

The first source-related parameter that we inspected was temperature. It has
been shown that during the vegetation growing season in Hyytiälä
the condensational growth of particles is driven by biogenic vapours, such
as monoterpenes (Paasonen et al., 2013), and their emissions depend strongly
on temperature (Guenther et al., 1993). In Fig. 5 GR is depicted as a
function of the mean temperature during the observed growth period in 10 nm
size bins from below 10 to 200 nm in April–September. The growth rates
clearly increased as a function of temperature in bins with diameters below
100 nm. In diameter bins of 100–130 nm the effect of temperature was not
observed, but for bins with diameters > 130 nm a weak negative
correlation between GR and temperature was found. It should be noted that
the uncertainties in the determined values of growth rates increase with an
increasing diameter, because the relative change in diameter is larger for
smaller particles. Another factor contributing to higher uncertainties for
larger GRs is that the width of the DMPS size channels is roughly directly
proportional to the diameter. Thus, the growth rates at larger diameters are
determined with coarser particle size distributions relative to the growth
rates, which increase at most by a factor of 3 when the diameter increases
by a factor of 10 (in Fig. 4, the higher end of GRs increases from

We used linear least-squares fits in a log-linear space to examine the temperature dependence. Interestingly, the fitted functions, shown in each panel of Fig. 5 with fitting parameters and correlation coefficients tabulated in Appendix A, were not very different for the diameter bins having the mean diameters lower than 100 nm. Instead of showing consistently higher growth rates for larger (or closer to 100 nm) particles at certain temperature, Fig. 5 shows that growth periods starting from larger sizes are observed on average with higher temperatures than those starting from smaller sizes. This could, in principle, suggest that the association between the particle diameter and growth rate depicted in Fig. 4 is not directly causal. The dependence of GR on diameter could also appear because the particles with the same age under different growing conditions would be observed at the measurement station at different sizes: at warmer air masses and concentrations of condensable vapours the particles would arrive at the station with larger sizes. We will examine this in more detail in Sect. 3.3.

Because of the relatively similar temperature dependences in size bins below
100 nm, all the growth rates in these bins together show a reasonably clear
connection with the temperature (Fig. 6a). The Pearson correlation
coefficients for log(GR) and temperature in April–September had

Next, we repeated the analysis by substituting the temperature with the
monoterpene concentration proxy. Surprisingly, the correlation between GR
and monoterpene concentrations was weaker (log–log correlation for
April–September:

Finally, we varied the weighting factors for OH and

A higher condensation sink is expected to decrease particle growth rates by
consuming the condensable vapours faster. Thus, it is surprising that the
observed particle growth rates correlated clearly better with the
approximated oxidation rate of monoterpenes alone than with the same rate
divided by CS, which would be the logical solution based on steady state
approximation of the condensable vapour concentration. However, there is a
strong coupling between the temperature, monoterpene emissions and
concentration of accumulation-mode particles in many vegetated regions,
including the forests around SMEAR II (Paasonen et al., 2013). This coupling
stems from the enhanced growth of particles due to the higher temperatures
and monoterpene emissions in the air mass history, which naturally leads to
higher concentration of larger particles and thus higher CS (Liao et al.,
2014). Due to this causality, the dependence between the observed growth
rate and condensation sink, or rather its logarithm, is very similar to that
between GR and temperature (Fig. 7): the negative relation between CS and GR
is evident only in particle size ranges 110 nm <

Growth rate of growth periods with duration > 2 h and starting size 50 nm <

The positive relation between GR and CS would indicate that the source of
condensable vapours is closely connected to CS, which can result from the
strong contribution of the (semi-)condensable vapours to the build-up of CS
prior to the observation. Based on our data, this relation seems very
strong. We were not able to find negative correlations between GR at

Growth rate as a function of particle diameter for growth periods with duration > 2 in April–September, presented in temperature bins.

Since all the variables that were shown to correlate with the growth rate above are strongly interlinked, we tested which of them explains the variation of GR best in the case where the variation in the other parameters was limited. In Fig. 8 the relations of GR in the size range from 50 to 60 nm with temperature, monoterpene concentration, monoterpene oxidation rate and condensation sink are presented by limiting the variation of one of these variables at a time to lie between its 30th and 70th percentile. The highest correlation coefficients were found for GR as a function of monoterpene oxidation rate (third column from left) regardless of which of the other parameters was limited. Additionally, the lowest correlation coefficients in each column were encountered when the variation in the monoterpene oxidation range was limited (third row from the top). Similar features were observed for different subsets of GRs in terms of the growth period duration, size range and time of the year, although not always as clearly as in the presented case. This finding confirms that the oxidation rate of monoterpenes is the strongest of the inspected variables in determining particle growth rates.

It should be noted that we also made an extensive number of tests with other variables recorded at the SMEAR II station (meteorological variables, gaseous- and aerosol-phase concentrations, ratios between different variables, etc.) with similar methodologies as in Paasonen et al. (2010) and Kontkanen et al. (2016), but significant alternative or additional correlations were not found.

Difference in growth rate as a function of difference in diameter for growth periods that overlap temporally for at least an hour. Data are presented in different condensation sink ranges for April–September.

The similarity of the functions fitted to GR vs. temperature data in
different size ranges below 100 nm (Fig. 5 and Appendix A) could be
interpreted so that the apparent relation between the diameter and GR (Fig. 4a) is caused by a link between temperature and the size in which the growth
rate is observed. In order to investigate this further, we depict in Fig. 9
the growth rates as functions of the starting size of the observed growth
period in different temperature ranges. The high end of the GRs grows
steadily with

We inspected the temporally overlapping growth periods, which are determined
to take place simultaneously for at least 1 h. In Fig. 10 the
difference in the growth rates (

Modelled growth rate of an aerosol particle with
indication of factors causing the changes in GR as a function of diameter
(panel

However, when CS was higher than

The diameter growth rate under a constant concentration of vapour should remain relatively constant with particle size at diameters larger than a few tens of nanometres (at which sizes the Kelvin effect does not affect the growth significantly) if the condensation is limited only by the condensation and evaporation of the vapour without any changes in the volatility of the vapour. The increase in GR with particle diameter suggests that the maximum uptake of semi-volatile vapours is influenced by aerosol-phase reactions, e.g. dimer formation, during which the volatility decreases. This has been proposed earlier based on modelling, for example, by Apsokardu and Johnston (2018).

Our one-particle process model, described in Sect. 2.3 with atmospherically
relevant input values for the base case (tabulated in Table 1), shows a
clear increase in the diameter growth rate with an increasing particle
diameter (blue solid line in Fig. 11) in roughly the same diameter range
(10–300 nm) as the observations. This increase is caused by the
aerosol-phase formation of non-volatile SVOC

Figures 11b–d illustrate the sensitivity of the growth rate to gas-phase concentrations of ELVOC and SVOC (Fig. 11b), SVOC saturation vapour concentration and dimerization rate coefficient (Fig. 11c), and the molar masses of ELVOC and SVOC (Fig. 11d). This sensitivity analysis gives us some suggestions for the parameters determining the particle growth rate in Hyytiälä:

The diameter corresponding to maximum GR decreases with decreasing

The growth rate at diameters below 10 nm is directly proportional to molar
mass and concentration of ELVOC (assuming constant density). At larger
diameters, the growth rate is directly proportional to SVOC concentration
and inversely proportional to

We generated an automatic method that seeks for growing particle modes from
particle number size distribution data and determines the growth rate (GR)
for these growth periods. This method finds growth periods from the
nucleation mode (

The growth rates in the nucleation mode showed a clear annual cycle, with the highest rates being recorded in July and the lowest in December and January. A similar but less pronounced cycle was observed in the Aitken mode, but in the accumulation mode the annual cycle was opposite, having a minimum in July and August. Clear diurnal cycles were not observed.

We investigated the particle growth rates from April to September in more detail, since during this period the biogenic emissions are expected to dominate the aerosol growth. We found that the behaviour of the growth rates for particles smaller and larger than 100 nm were very different: in the nucleation- and Aitken-mode GR increased with an increasing temperature, while in the accumulation mode this relation was opposite. We showed that the temperature dependence of GR was likely caused by the formation of condensable vapours as GR correlated with the oxidation rate of monoterpenes more strongly than with the temperature.

The growth rates were found to correlate in a similar way with the
condensation sink (CS) as with the temperature and monoterpene oxidation
rate, i.e. showing a positive correlation for GRs of particles with

Finally, we found that the maximum observed growth rate increased with an
increasing particle diameter. While the highest observed growth rates at

Our study suggests that the aerosol growth to cloud condensation nuclei sizes in the boreal forest is dominated by the condensational growth caused by semi-volatile oxidation products of biogenic volatile organic compounds. The observed increase in the particle growth rate as a function of particle size has a significant effect on the climate impacts of aerosol particles formed either during NPF events or emitted into the Aitken mode sizes from traffic or other sources. The increasing growth rate increases the fraction of the nucleation- and Aitken-mode particles surviving to CCN sizes and being able to form cloud droplets. This effect, or the processes leading to it, i.e. the semi-volatile vapours forming non-volatile dimers in the aerosol phase, needs to be included in climate model simulations when aerosol–cloud and aerosol–radiation interactions are estimated. Additionally, the observation that the condensation sink appears not to limit the growth of particles in the sub-CCN size range is in contrast with various estimates of the aerosol dynamics. Our findings suggest that the formation of CCN-sized particles is not as strongly self-limiting a process as previous studies have suggested.

The data recorded at SMEAR II site are available at

Fitting parameters resulting from linear least-squares fits for
parameterizations of growth rates with growth period starting sizes in 10 nm
bins and the related correlation coefficient

PP had the original idea for the method, planned the analysis, designed the model and wrote most of the article. MP, HJ, PP and JK developed the automated method. MP, PP and JK conducted the data analysis. VMK and MK helped in planning the analysis and interpreting the data. All authors contributed to writing the manuscript.

The authors declare that they have no conflict of interest.

This study was funded by the Academy of Finland (project no. 307331), European Commission (project ID: 742206), the Doctoral Programme in Atmospheric Sciences (ATM-DP, University of Helsinki, Jenni Kontkanen), and the European Regional Development Fund and the Mobilitas Pluss programme (project MOBTT42). The authors would like to thank Tuomo Nieminen from the University of Eastern Finland for providing the manually determined growth rate data for comparison, as well as Santtu Mikkonen and Ville Leinonen from the University of Eastern Finland for fruitful discussion. Edited by: Kari Lehtinen Reviewed by: two anonymous referees