ACCURACY OF ‘APPARENT’ PARTICLE FORMATION RATES CALCULATED FORWARD AND
BACKWARD USING THE KERMINEN AND KULMALA EQUATION
L. DADA1, P. PAASONEN1, J. KONTKANEN1, T. NIEMINEN2, V.M. KERMINEN1 AND M. KULMALA1
1
Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki, Finland
Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, FI-70211 Kuopio, Finland
2
Keywords: LONG-TERM ANALYSIS, BOREAL FOREST, GROWTH RATE
Presenting author email: [email protected]
INTRODUCTION
Atmospheric aerosol particles span a range of diameters between less than one nanometer to few hundred
micrometers. These particles are the result of primary emissions, such as sea spray, desert dust and combustion
particles, or secondary formation in the atmosphere through gas-to-particle formation. After their formation,
particles are susceptible to either growth by condensation or loss to available sinks (Kulmala et al., 2013).
In this study we focus here lies on the nanometer-sized particles formed via secondary gas-to-particle
transformation. This phenomenon is known as new particle formation (NPF), and it has been observed in many
locations around the globe (Kulmala et al., 2004 and 2012). The importance behind NPF rests in its ability to
contribute to cloud condensation nuclei (CCN) concentrations, which in turn alter cloud characteristics (Merikanto
et al., 2009; Kerminen et al., 2012). Accordingly, NPF may influence climate by changing various cloud properties
and is found to result in global cooling (IPCC, 2013).
In order to understand deeply the NPF phenomenon and its accompanying effects, it is important to dig into the
properties of particles, starting with their concentrations in different size ranges and formation rates at different
diameters. In clean environments, where no major fluctuations in sink or precursor vapor concentrations are
observed, Kerminen and Kulmala (2002) derived an analytical formulae to determine the ‘apparent’ formation rate
of particles at small sizes based on the observed formation rates from measurements of particles at a larger sizes.
Therefore, the formula can be used to estimate the formation rates of particles, which are smaller than those
detected with most of the commonly used particle counters. In this work, our aim is to study the accuracy of this
method by using long-term data sets in a clean background environment in Southern Finland. With the
development of new instruments able to detect particles and ions down to less than 1 nm in diameter, we are able
to study the precision of the Kerminen and Kulmala equation for the derivation of ‘apparent’ formation rates.
METHODS
Data for our study were collected from the SMEAR II (Station for Measurement of Ecosystem –Atmosphere
Relations, Hari and Kulmala, 2005), from where there is a long term comprehensive data set of particle number
size distributions, gas concentrations, meteorological parameters, etc. The SMEAR II station is located in Hyytiälä,
southern Finland, and is within a pine forest away from human activities and major anthropogenic pollution. Those
features make the station suitable for NPF analysis, as it can be considered a semi-clean background location,
which somewhat represents the northern hemisphere boreal forests.
Our analysis was based on the particle number size distributions measured by a twin DMPS (Differential Mobility
Particle Sizer) system (Aalto et al., 2001) for the diameter ranges 3-500 nm until 2004 and 3-1000 nm starting
from 2005. These data were used for classifying days into NPF event and non-event days using the method by Dal
Maso et al. (2005). The DMPS measurements were also applied for calculating the condensation sink (CS, e.g.
following Kulmala et al., (2012) used also in the analysis).
For our analysis, we used the data set covering the period from March 1996 to December 2014. Our focus was on
Class I events (Dal Maso et al. 2005), which are NPF events homogenous enough for determining their growth
rates. The nucleation mode growth rates (GR) were calculated following the method presented by Hussein et al.
(2005), for the Class I events between 1996 and -2014.
While the main aim of our study is to study the accuracy of backward calculation (Using bigger particle sized
particles’ ‘real’ formation rates to calculate ‘apparent’ formation rates of smaller ones) using the Kerminen and
Kulmala (2002) equation, we are also interested in understanding the accuracy of the forward calculation in order
to for example, estimate missing data.
Accordingly, let us assume that we want to do a comparison between the formation rate of 5 nm particles and
above (J5) i) determined from measurements (J5,Measured) using DMPS number size distributions and ii) obtained
from forward calculation starting from using the J3 measured value of J3 (J5,Calculated). It is important to note that J5
is delayed by a value of GR x (|dp2 – dp1|).
Measured values of formation rates were obtained according to the formula presented by Kulmala et al. (2012):
𝐽𝑑𝑝 =
𝑑𝑁𝑑𝑝
𝑑𝑡
𝐺𝑅
+ 𝐶𝑜𝑎𝑔𝑆𝑑𝑝 . 𝑁𝑑𝑝 + 𝛥𝑑 . 𝑁𝑑𝑝 ,
(1)
𝑝
where the coagulation sink (CoagS) is calculated based on Kulmala et al. (2012) and it describes sink for the
formed particles due to their coagulation in larger particles, analogously to CS for vapours.
For example, J3 which is the formation rate of particles in the size range 3 - 25 nm:
𝐽3,𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 =
𝑑𝑁3−25
𝑑𝑡
𝐺𝑅
+ 𝐶𝑜𝑎𝑔𝑆. 𝑁3−25 + 𝛥𝑑 . 𝑁3−25
𝑝
(2)
According to Kerminen and Kulmala (2002)
𝐶𝑆 ′
𝐽𝑑𝑝 ,2 = 𝐽𝑑𝑝 ,1 𝑒𝑥𝑝 (−𝛾 𝐺𝑅 (𝑑
1
𝑝 ,1
−𝑑
1
𝑝 ,2
)) ,
(3)
where dp,2 > dp,1, and CS’(m-2) = CS/4πDi , where CS (here determining the CoagS for the particles in size range
dp,1 – dp,2) is the condensation sink and Di is the diffusion coefficient. γ is calculated following the equation
provided by Kerminen and Kulmala (2002).
Thus, we calculate formation rate at J5 forward from J3 (calculated using equation (2)) as follows:
𝐶𝑆 ′ 1
1
𝐽5,𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 = 𝐽3,𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑒𝑥𝑝 (−𝛾 𝐺𝑅 (3 − 5))
(4)
RESULTS, DISCUSSION AND CONCLUDING REMARKS
Figure 1. Correlation between J5,Measured and J5,Calculated.from J3,Measured (10 min averages from 690 days). The linear
regression and correlation coefficient are added to the plot. Results show quite a good correlation.
Our preliminary results show that a good agreement lies between J5,Measured and J5,Calculated , resulting in a correlation
coefficient of R = 0.81 (Figure 1). Similar analyses were applied for formation rates at different particle sizes
calculated from measurements from different ‘real’ formation rate sizes. For example, J 7 was measured and
compared to J7 calculated from J3 and J5 individually. Also, measured J10 was compared to J10 calculated from J3,
J5 and J7, and so on. Our results show the good agreement between the measured and calculated values. Based on
our analyses of the long term data set, we present the accuracy and precision of the Kerminen and Kulmala equation
in different size ranges. Similarly, we will use the same method to compare observed formation rates in sub-3 nm
sizes from PSM (Particle Size Magnifier; Vanhanen et al., 2011) and NAIS (Neutral and Air Ion Spectrometer;
Manninen et al., 2009; Mirme and Mirme, 2013) to ‘apparent’ formation rates calculated backward using DMPS
(3 nm and above) formation rates, and vice versa (forward from PSM sub-3 nm formation rates to ‘apparent’ rates
at diameters larger than 3 nm). To form a complete picture, we will present results from multiple instruments in
forward and backward pathways. We will apply the same method for different seasons in order to understand the
prevailing factors. Our results will determine the applicability of the Kerminen and Kulmala equation in SMEARII
station and give indications of its use in other locations. This will be useful for future analyses of data sets for
which sub-3 nm measuring instruments are not available and where missing data needs to be estimated.
ACKNOWLEDGEMENTS
This work was funded by the Doctoral Programme in Atmospheric Sciences (ATM-DP, University of Helsinki).
Part of this work was supported by the Academy of Finland Centre of Excellence program (grant no. 272041).
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