Atmospheric aerosol microphysical processes are a
significant source of uncertainty in predicting climate change.
Specifically, aerosol nucleation, emissions, and growth rates, which are
simulated in chemical transport models to predict the particle size
distribution, are not understood well. However, long-term size distribution
measurements made at several ground-based sites across Europe implicitly
contain information about the processes that created those size
distributions. This work aims to extract that information by developing and
applying an inverse technique to constrain aerosol emissions as well as
nucleation and growth rates based on hourly size distribution measurements.
We developed an inverse method based upon process control theory into an
online estimation technique to scale aerosol nucleation, emissions, and
growth so that the model–measurement bias in three measured aerosol
properties exponentially decays. The properties, which are calculated from
the measured and predicted size distributions, used to constrain aerosol
nucleation, emission, and growth rates are the number of particles with
a diameter between 3 and 6 nm, the number with a diameter greater than 10 nm,
and the total dry volume of aerosol (

Atmospheric aerosols scatter and absorb incoming solar radiation (Cubasch et al., 2013). They also provide sites for cloud droplet formation, known as cloud condensation nuclei (CCN) (Twomey, 1974). Through the latter process, they contribute to the aerosol indirect effect in which aerosols perturb the CCN concentrations, affecting the Earth's energy balance by altering cloud properties such as cloud coverage, reflectivity, and lifetime (Lohmann and Feichter, 2005). The indirect effect is the most uncertain mechanism of global radiative forcing (Stocker et al., 2013). Given the importance of aerosol indirect radiative forcing, considerable effort has been devoted to developing chemical transport models (CTMs) that predict CCN concentration fields (Adams and Seinfeld, 2002; Easter, 2004; Kajino and Kondo, 2011; von Salzen et al., 2000; Spracklen et al., 2005, 2010; Wilson et al., 2001; Yu and Luo, 2009; Zhang et al., 2004). CTMs simulate atmospheric processes and aerosol microphysics driven by meteorological fields.

The major sources of uncertainty in using a CTM to predict CCN include uncertainties in the rates of the following processes: particle formation, emissions, and growth (Carslaw et al., 2013; Pierce and Adams, 2009b; Spracklen et al., 2008, 2011; Westervelt et al., 2014). New particle formation, or nucleation, is the formation of thermodynamically stable clusters near 1 nm in diameter from condensable vapors. The general understanding of nucleation is still an open challenge (Adams et al., 2013). Particle emissions can be estimated from data such as emission factors and activity levels of each emission source for different classes of sources. However, these data are less commonly tabulated for number concentration emitted as opposed to mass emitted, and measurements of the emitted particle size distributions are sparse. Particles grow partially due to the condensation of sulfuric acid and oxidized volatile organic compounds (VOCs). An uncertain quantity of VOCs is emitted from biomass burning, anthropogenic sources, and the biosphere (Folberth et al., 2006). After their emission, sulfuric acid and VOCs form secondary organic aerosol (SOA) (e.g., Kerminen et al., 2018; Kulmala et al., 2014; Shrivastava et al., 2017), and the SOA yield from VOCs is also uncertain.

Predicted CCN concentrations can be improved either by nudging the concentration fields themselves or by estimating the particle formation, emissions, and growth rates that largely control CCN concentrations. Estimating the key uncertain aerosol processes is preferred to directly estimating CCN concentrations because it provides insight into the underlying model biases (Benedetti et al., 2018). A systematic way to estimate uncertain atmospheric processes is to use data assimilation or inverse modeling techniques that employ a combination of CTMs and field measurements.

Long-term observations of particle size distributions are available from
large measurement networks such as the European Supersites for Atmospheric
Aerosol Research (EUSAAR) (Asmi
et al., 2011), the German Aerosol Ultrafine Network (GUAN) (Birmili et al., 2015),
and the Global Atmosphere Watch World Data Centre for Aerosols (GAW-WDCA)
(

Previous studies used size distribution measurements from smog chamber experiments with 0D (“box”) models simulating the aerosol general dynamic equation (GDE) to estimate uncertain terms in the GDE (Pierce et al., 2008; Verheggen and Mozurkewich, 2006). These inverse models estimate processes such as nucleation, growth, and chamber wall loss by minimizing the model–measurement bias. The minimization procedure involves iteratively fitting the model to the measurements and requires knowledge of the sensitivity of the size distribution to the uncertain processes for each iteration. However, this method does not guarantee that the optimal process rates will be discovered within a low number of iterations, making the inverse model potentially computationally expensive when applied in the context of a three-dimensional model.

Furthermore, previous inverse modeling studies with 3D CTMs have focused on estimating emission rates of gases, such as methane, ammonia, sulfur oxides, and nitrogen oxides (Bergamaschi et al., 2010; Gilliland et al., 2003; Hein et al., 1997; Henze et al., 2009; Houweling et al., 1999) from in situ measurements. Other investigations have estimated aerosol emissions from remote aerosol optical depth measurements (Chen et al., 2019; Dubovik et al., 2008; Escribano et al., 2016, 2017; Huneeus et al., 2012, 2013; Wang et al., 2012; Xu et al., 2013; Zhang et al., 2015, 2005) or from in situ observations (Viskari et al., 2012b, a). These previous researchers used various inverse modeling techniques to solve their proposed problem, including a Kalman filter and a four-dimensional variational (4D-Var) method with an adjoint model. These techniques are not ideal to estimate aerosol microphysical processes for three reasons: (1) complexity in the relationship between ambient size distribution and the emissions as well as aerosol formation and growth, (2) significant computational cost in optimizing multiple (potentially spatially distributed) parameters, and (3) the adjoint model used with 4D-Var becoming obsolete when the 3D CTM is updated.

In this study, we utilize estimation techniques from the field of nonlinear process control to address disadvantages in the current inverse modeling techniques. Understanding a complex process is vital when controlling it to a set point or goal, so adaptive controllers utilize online estimation algorithms to improve the controller's internal model with data. We apply ideas from inventory control and passive systems theory (Farschman et al., 1998; Ydstie, 2002) to formulate an estimation algorithm for aerosol microphysics. Inventory control uses a set of variables, called inventories, to define the overall performance of the inverse model. These ideas have been used to control the float-glass process (Ydstie and Jiao, 2006), a pressure tank (Li et al., 2010), and production of solar-grade silicon (Balaji et al., 2010). The same theories have been used to estimate chemical kinetics and the heat of reaction (Zhao and Ydstie, 2018). An estimation technique based on inventory control is attractive because it is developed for complex and nonlinear systems, does not require significant computational cost, and is flexible to model updates because of the algorithm's high-level perspective. By this, we mean that the algorithm needs to know the net rates of certain processes but is insensitive to the details of how those rates are calculated. In coding terms, the process rates can be estimated by looking at changes before and after the corresponding subroutine is called and is robust to changes in the subroutine itself, setting it apart from adjoint methods.

In this work, we aim to design an inverse modeling technique from nonlinear process control theory that can incorporate size distribution measurements with a 3D CTM; however, as a first development step, we limit the estimation algorithm to a box model. Our objective is to input size distribution measurements to the inverse model in order to estimate uncertain aerosol processes simulated in a box model: particle formation, emissions, and SOA production rates. We will first describe the inverse model and how it is designed to estimate particle formation, emissions, and growth. Then, we will validate the method on sets of synthetic measurements relevant to conditions in a 3D CTM. Next, we will assess the effect of instrument noise on the estimates by corrupting the synthetic measurements with a realistic noise signal. Finally, we will test the inverse model on realistic field data by estimating time-varying particle formation, emissions, and growth at three measurement sites: San Pietro Capofiume, Italy; Melpitz, Germany; and Hyytiälä, Finland. While the ultimate goal of this work is to deploy the inverse method in a 3D CTM, all of the steps presented here are proof-of-concept work in a zero-dimensional atmospheric box model.

Inverse models use the observed model output to estimate a set of control variables such that the predicted model output matches the observations as closely as possible. Common control variables estimated in the atmospheric inverse modeling and data assimilation fields include emission fluxes and mixing ratios. A disadvantage of using mixing ratios as control variables is that it does not address underlying errors in processes that are responsible for the mismatch between the model and observations. While model-predicted mixing ratios are improved, little insight is gathered into the causes of the errors. In this work, we consider control variables that are scaling factors applied to three highly uncertain but important aerosol processes: particle nucleation, emissions, and growth. Since these processes significantly affect the evolution of the measured properties, we anticipate greater understanding in these uncertain process rates over mixing ratio control variables.

The TwO-Moment Aerosol Sectional (TOMAS) algorithm simulates both
discretized mass and number size distributions. In this work, we utilize a
zero-dimensional version of TOMAS as our box model. The algorithm was
originally described by Adams and Seinfeld (2002) based on numerical methods for simulating cloud droplet microphysics originally proposed by Tzivion et al. (1987, 1989). The code has been updated several times since the original release (Pierce and Adams, 2009a; Trivitayanurak et al., 2008; Westervelt et al., 2013). The TOMAS box model used here simulates sulfuric acid, ammonia, and sulfur dioxide vapors as well as five particle species: sulfate, ammonium, sea salt, organic carbon, and water. The discretized size distribution includes
43 size sections, defined by particle mass, that are logarithmically spaced
by a factor of 2. The smallest particle is

In this work we utilize a simplified version of TOMAS v1.0.0 (McGuffin, 2020) that was described by Westervelt et al. (2013). The simulated microphysics include nucleation, coagulation, condensation, wet deposition, size-resolved dry deposition, and emissions. The model incorporates a combination of binary and ternary nucleation mechanisms (Napari et al., 2002; Vehkamäki et al., 2002) in which the ternary parameterization allows calculation of the rate of formation of new particles 3 nm in diameter if the concentration of ammonia gas exceeds 0.1 ppt. Condensation of sulfuric acid vapor and VOCs follow a kinetic scheme in which the vapor condenses to Fuchs-corrected surface area (Riipinen et al., 2011). The rate of aerosol mass accumulation due to condensation of VOCs is defined here as the production rate of secondary organic aerosol (SOA), in which the combined processes of VOC emissions, chemistry, and condensation result in a total SOA production rate. Sulfuric acid vapor is assumed to be in pseudo-steady state between aerosol nucleation, growth, and its photochemical production from sulfur dioxide (Pierce and Adams, 2009a). Organic carbon aerosol, sulfur dioxide, and ammonia are emitted at a constant flux in which the primary organic aerosol (POA) emissions are based on measured size distributions of particles emitted from heavy- and light-duty vehicles (Ban-Weiss et al., 2010). Sea spray emissions are not considered here since we are simulating a continental measurement station. Therefore, sea salt does not contribute to the simulated aerosol composition. POA emission, SOA production, and particle nucleation rates will be adjusted based on the measurements, so the a priori rates are not significant here.

Particle sinks, such as wet deposition and transport, are simplified as a single first-order loss of particles with a time constant of 12 h, which is much faster than a time constant for depositional losses only. This high loss rate is important for our application of the box model to simulate field measurements. A weakness of any application of a box model to ambient data is that advection, convection, and dilution are not simulated explicitly. The microphysical processes constrained here are all aerosol sources, so a large sink will allow the box model to match measurements that are rapidly decreasing, e.g., due to an inflow of cleaner air. Dry deposition is calculated with a resistance-in-series approach (Zhang et al., 2001).

Schematic of the TOMAS box model with the online estimation technique. The
measured size distribution is projected to the inventory variables
(

To perform the inverse modeling technique, we adjust the TOMAS box model by
introducing three time-varying scaling factors as the control variables that
we want to estimate. Then, we estimate the control variables from
moments of the size distribution that are sensitive to the uncertain
processes. The estimation method used here requires us to define “inventory
variables”, which are measurable quantities that are additive, positive,
and continuously differentiable (McGuffin et al., 2019b). The observed and predicted size distributions are projected to the inventory variables (

The parameter estimation technique was described in detail by McGuffin et
al. (2019b); it was previously used to estimate
sea spray emissions in a 3D CTM (McGuffin et
al., 2019a). We will give a brief summary of the parameter estimation
technique here. Instead of using a least-squares regression or the analytical
maximum a posteriori solution, as other parameter estimates are generated
(i.e., variational data assimilation or Bayesian inference techniques), we
update the parameter estimate so that the model–measurement error
exponentially decays, as shown in Eq. (2). In this case, the error is
defined based on the chosen inventory variables (

The left-hand side of Eq. (2) represents the rate of change of the
model–measurement error, which is invertible for the scaling factors

There are two main drawbacks to the parameter estimation technique utilized
here. First, we require knowledge of the derivative of the observations,
which may include noise from differentiation. Unlike noise in the
observations, noise in the derivatives cannot be dampened by adjusting the
tuning parameter

We determine if the system is ill-conditioned based on the condition number
(

Another drawback of this estimation method, which is shared with most
inverse techniques, is the effect of uncertainty in model errors not
corrected by the estimator (

Since the scaling factors are allowed to vary temporally, the estimated scaling factors are specific to the model and its a priori particle formation, emission, and growth rates. The scaling factors do not have any inherent physical meaning. Additionally, the estimated process rates cannot simply be reconstructed from the a priori rate and the estimated scaling factor since aerosol processes can be dependent on the state of the atmosphere; e.g., particle formation and growth depend on aerosol surface area. For all these reasons, instead of analyzing the estimated scaling factors, we will look at the estimated aerosol process rates.

The particle size distribution was observed from May 2006 through June 2007
at three rural locations: San Pietro Capofiume, Italy (SPC); Melpitz,
Germany (MPZ); and the Station for Measuring Ecosystem–Atmosphere Relations
II (Hari and Kulmala, 2005) site in
Hyytiälä, Finland (HYY). All three measurement sites use
twin-differential mobility particle sizer (DMPS) instruments to observe the
ambient size distribution with particle diameters ranging from 3 nm to
various upper size limits. The largest particle diameter measured is 0.6, 0.8, and 1

Random noise in the measured inventory variables could corrupt the estimated scaling factors. Instead of directly inputting the observed inventory variables, we smooth the observations and calculate their derivatives with a Savitzky–Golay filter (Savitzky and Golay, 1964). The filter fits a polynomial of a predetermined degree to the dataset over a time horizon that is also predetermined. The filtered value is then taken as the value of the polynomial at the midpoint of the time horizon. Additionally, the rate of change of a dataset is determined by differentiating the fitted polynomial at the midpoint. The method is computationally efficient since the there is an analytical solution to the best-fit polynomial coefficients (Savitzky and Golay, 1964).

Estimated, measured, and a priori inventory variables are in the left panels, and
estimated, true, and a priori process rates are in the right panels for scenario no. 26 of the
proof-of-concept scenarios. The measurements are

In this work, we use the Savitzky–Golay filter of degree 1 so that we perform a moving-horizon average over a 3 h window on the raw measured inventory variables. A small averaging window is used for the field measurements to make sure the nucleation events are not filtered out. Then, we use finite differences on the filtered data to calculate the derivative of the measurements. The measurement derivatives and hourly filtered measurements are used to linearly interpolate the measurements to a frequency of 5 min, which is the model time step.

To evaluate the inverse modeling technique, we estimate particle formation,
emissions, and growth rates based on simulated inventory variables, or
“synthetic measurements”. The synthetic measurements are from the TOMAS
box model itself with scaling factor inputs (

Figure 2 shows how the inverse modeling approach
performs for a week-long simulation in which the original model
underpredicted aerosol mass (via dry aerosol volume

Scatter plots of time-averaged

Scatter plots of time-averaged nucleation rate

Since the objective is to design an inverse technique that is robust enough
to apply in a global 3D CTM, we repeat the above method for a set of 27
scenarios that span a range of process rates typically encountered in the
atmosphere. We explore different particle formation, emissions, and SOA
production rates that span approximately 0.001–300 cm

Similarly, Fig. 4 shows that the estimated
nucleation, emissions, and growth rates are accurately estimated if the
synthetic measurements are well-conditioned. Particle formation only
directly affects

Although the inverse modeling technique in general estimates the correct inventory variables and aerosol process rates, we also wish to investigate whether the estimated size distribution will match the true size distribution. Accurately simulating the size distribution is very important to correctly predict the effect that aerosols have on climate. Figure 5 shows that the average estimated size distribution based on the inventory variables matches the average size distribution of the synthetic measurements generated from an intermediate set of particle formation, emissions, and SOA production rates. For the 23 well-conditioned scenarios with low bias in the estimated aerosol process rates, the estimated size distribution similarly closely matches the true size distribution.

Average particle size distributions in scenario no. 14 (nucleation,
SOA production, POA emission rates: 2.7 cm

Box plot showing the standard deviation of “noisy synthetic
measurements” relative to their average value in all 27 scenarios for the
inventory variables originally (

The estimation technique performs very well when utilizing “perfect
measurements” (

We calculated the uncertainty in the size distribution from an instrument model described in Appendix A using the operating parameters of the DMPS operated at San Pietro Capofiume. The true size distribution is input to the instrument model to determine the size distribution uncertainty, which assumes Poisson counting statistics for each size bin from the counts by the condensation particle counter (Kangasluoma and Kontkanen, 2017). The inventory variables considered here are observed by combining several size bins observed by the DMPS. Inventory variable uncertainty is the uncertainty of the size distribution's corresponding size bins added in quadrature, which leads to inventory variables that are not as noisy as the individually measured particle sizes. Since the inventory variables are defined as the total concentration across a size range, the method intrinsically dampens instrument noise as random errors across multiple channels tend to cancel each other out.

Beeswarm plots showing

The normalized standard deviation in the noisy

Figure 7 shows the mean bias and variance in the estimated process rates for each of the 23 scenarios as blue crosses and red circles when synthetic measurements without and with noise are used, respectively. In Fig. 7a, we find that the normalized mean bias across the 23 scenarios does not significantly change, with median values without and with noise of 0.03 and 0.03, 0.005 and 0.007, and 0.004 and 0.006 for nucleation, emissions, and growth, respectively. Figure 7b shows a statistically significant difference in the normalized variance of estimated SOA production and POA emission rates between the cases using measurements with and without noise. The estimated process rates using noisy measurements have a somewhat higher variance compared to the estimates with perfect measurements. The high variance in estimated process rates is due to the estimator tracking synthetic measurement noise, which is translated to noise in the process rates. In the future, the gain should be adjusted to a lower value so the measurement noise is filtered and the estimated process rates are smoother.

This section evaluates the inverse method by utilizing field measurements of
particle size distribution from SPC, MPZ, and HYY instead of synthetic
measurements to estimate particle formation, emissions, and SOA production.
Since we previously found that an ill-conditioned sensitivity matrix results
in inaccurately estimated process rates when using synthetic measurements, we
avoid solving an ill-conditioned system by reducing the system of equations.
If the condition number of

The purpose of this section is to test the inverse method on real data, including size distributions not generated by the TOMAS model itself (the synthetic measurements above). A challenge here arises from the processes that are not well-captured in a box modeling framework, namely long-range transport of aerosol to the measurement site, including abrupt changes in air mass. Recognizing that our long-term goal is to deploy the estimation framework in a three-dimensional model that will include an improved and more detailed representation of long-range transport, we mitigate them here with several simple approaches.

Frequency scatter plots comparing hourly estimates to hourly
measurements of

First, we filter the measurements to select time periods when meteorology is
relatively stable. We classify whether a time is stagnant from the three
conditions determined by Garrido-Perez et al. (2018) in
addition to a condition on the sea level pressure. A time period is
considered stagnant if (1) the reanalysis wind speed at 10 m of altitude is less
than 3.2 m s

Second, we choose a first-order removal timescale that is faster than
aerosol removal processes (i.e., deposition) to allow the box model to
adjust to air mass changes. Finally, we use this largely as a
proof of concept, taking caution in interpreting the process rates. We
expect that, in a box modeling framework, the

The inverse modeling method assumes that all simulated processes in the box model are correct except for the processes scaled by the control variables. Thus, the primary emitted size distribution must have the correct shape in order to estimate emissions correctly. The aerosol size distribution we emit into the TOMAS box model in this section reflects primary organic aerosol emissions from a 3D CTM (GEOS-Chem). Here, the particle emissions are from fossil fuel and biomass burning emission inventories averaged over western Europe (Bond et al., 2007).

Average particle size distributions measured, originally predicted
with a priori rates in TOMAS, and estimated with the inverse model are shown in the
solid red, dotted black, and dashed blue profiles, respectively. Results are
shown using measurements at

Additionally, we remove condensation of sulfuric acid from the box model
simulation so that we are estimating overall particle growth while
perturbing SOA production with the growth scaling factor. Using only this
box model and measurements of particle size distribution, we cannot
distinguish between sulfate and VOC condensation since both similarly
affect the size distribution in the model. Since we have removed sulfuric
acid from the box model, the default nucleation parameterization will not
produce new particles. Instead, we replace the nucleation scheme with a
constant new particle formation rate of 0.2 cm

At each measurement site, the estimated inventory variables are close to the hourly measurement of those same parameters, as shown in Fig. 8. At SPC, MPZ, and HYY the normalized absolute errors across the three inventory variables are 0.10, 0.14, and 0.13, respectively, which is improved with respect to the predictions with a priori process rates, as shown in Fig. S1 in the Supplement. Each row in Fig. 8 shows frequency scatter plots of the hourly estimated versus observed inventory variable; the color represents the count of data points in that respective grid cell.

Figure 9 shows the average estimated, measured, and
original model-predicted size distributions at each measurement site.
Although the inventory variables are close to the observations, the
estimated size distributions do not match as well as with the
synthetic measurements. We expect that the estimated size distribution does
not match the field measurements because the mass and number of particles larger
than 100 nm indicate long-range species that are influenced by processes not
included in the version of TOMAS used here, i.e., various primary aerosol
emission sources, transport, aerosol aging. Several factors contribute to
the bias between the estimated and observed size distribution between 4
and 20 nm. First, TOMAS nucleates 3 nm particles based on the

Estimated diurnal nucleation rate during stagnant events for each
measurement site:

We find that the estimated nucleation rates are reasonable as shown in
Fig. 10, which shows the average diurnal profile
estimated for each site. The average estimated nucleation rate at all of the
sites has a realistic magnitude near 1 cm

This work has explored a way to assimilate particle size distribution data
with an aerosol microphysics algorithm used in 3D CTMs by designing a novel
estimation algorithm borrowed from the field of nonlinear process control.
The estimation framework is robust, computationally inexpensive, and
flexible to model updates. It has been tested with synthetic measurements,
noisy synthetic measurements, and European field measurements. We show that
the particle size distribution inverse modeling technique estimates
particle formation, emissions, and SOA production accurately when there is
no measurement error and all other processes are known accurately.

We applied the inverse technique to field data from San Pietro Capofiume,
Melpitz, and Hyytiälä between May 2006 and June 2007. Error in the
estimated

Although there is reason to believe that the estimated emissions and SOA production rates are not correct when applying the box model to field measurements, these rates are estimated correctly in the synthetic measurement case. The key differences between field and synthetic measurements are the model–measurement biases outside of particle formation, emissions, and growth. The zero-dimensional version of TOMAS used here does not incorporate sufficient detail about meteorology or emission sources to give successful inverse modeling results. However, a 3D CTM that includes processes such as transport, photochemistry, and diverse emission sources could be more successful in an inverse modeling study. If the method applied here is integrated into a 3D CTM, there is potential to estimate key uncertain parameters that control aerosol dynamics and thereby improve the predicted size distribution field.

The DMPS takes aerosol samples and reports the particle count of a specific size
bin during a time interval, as represented by the following equation:

We assume that the uncertainty of the measurement only comes from the counting,
which follows Poisson counting statistics, since the information about the
uncertainty of the working conditions is unknown. Thus, the uncertainty from
measurement is

The code used in this work is available online (McGuffin, 2020). Data on particle size distribution measurements were provided through the EBAS (Aalto and Kulmala, 2012; Sonntag et al., 2008) for the MPZ and HYY stations. Stefano Decesari provided size distribution measurements for the SPC station. Precipitation data were downloaded from the European Climate Assessment & Dataset (Cornes et al., 2018). Sea level pressure and wind speed data were downloaded from the NASA Goddard Earth Sciences Data and Information Center (GMAO, 2015a, b).

The supplement related to this article is available online at:

PJA, BEY, and DLM conceptualized the simulations and estimation technique. DLM adapted the model code with the estimation algorithm and performed all simulations. RF and YH conceptualized the measurement uncertainty. YH created the uncertainty code. DLM authored the text with contributions from all co-authors. YH wrote Appendix A.

The authors declare that they have no conflict of interest.

The authors acknowledge Thomas Tuch, Pasi Aalto, Stefano Decesari, and Jorma Joutsensaari for providing descriptions and technical specifications of their measurement setup. This work was performed partially under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344 with IM release number LLNL-JRNL-813683.

We acknowledge the E-OBS dataset from the EU-FP6 project UERRA (

This research was supported by the Carnegie Mellon University Department of Chemical Engineering and the Mahmood I. Bhutta Fellowship in Chemical Engineering. Tuukka Petäjä acknowledges financial support through the Academy of Finland (304347), the Center of Excellence in Atmospheric Sciences, and the European Commission through the Horizon 2020 research and innovation program under grant agreement no. 689443 via project iCUPE (Integrative and Comprehensive Understanding on Polar Environments).

This paper was edited by Christina McCluskey and reviewed by three anonymous referees.