Atmospheric new particle formation and growth: review of field observations

In the macroscopic view of NPF, the particle formation rate is defined as the flux of growing nanoparticles through a certain particle size barrier, described usually by the particle diameter, dp. This flux is denoted as J_dp , and a widely-used unit for it is cm⁻³ s⁻¹ (or particles cm⁻³ s⁻¹). Two other quantities related to the particle formation rate are the clustering rate and nucleation rate. The clustering rate refers to the net formation rate of small clusters consisting of a small number of cluster building blocks, usually molecules, being an essential quantity in the microscopic description of NPF. In case there is a well-defined energy barrier that the clusters need to overcome in order to produce growing nanoparticles, the formation rate of clusters passing this barrier is called the nucleation rate. In the scientific literature, the terms particle formation rate and nucleation rate are used sometimes synonymously, even though it should be kept in mind they are two separate theoretical concepts that should not be mixed with each other.

When analyzing particle GRs, it is important to distinguish between the growth of an individual aerosol particle and the growth of a particle population (figure 2). The conservation of mass defines directly the GR of an individual aerosol particle, GR_ind = ddp/dt, as:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{d{m}_{{\rm{p}}}}{dt}=\displaystyle \frac{d({\rho }_{{\rm{p}}}{V}_{{\rm{p}}})}{dt}={V}_{{\rm{p}}}\displaystyle \frac{d{\rho }_{{\rm{p}}}}{dt}+\displaystyle \frac{1}{2}\pi \,{\rho }_{p}{{\rm{dp}}}^{2}\\ \,\,\,\times \,\displaystyle \frac{d{\rm{dp}}}{dt}\approx \displaystyle \frac{1}{2}\pi \,{\rho }_{{\rm{p}}}{{\rm{dp}}}^{2}{{\rm{GR}}}_{{\rm{ind}}}.\end{array}\end{eqnarray} \tag{ 1 }$$

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Here m_p, V_p and ρ_p are the particle mass, volume and density, respectively, t is the time, and the term dm_p/dt represents the net mass flux of new material into the particle. The last form of the equation includes the approximation that the addition of new mass into the particle changes little the particle density. The net mass flux into the particle can be caused by condensation of low-volatile (LVOC) vapors into the particle, by heterogeneous formation of low-volatility substances on the surface or inside the particle from more volatile vapors, or by coagulation of small clusters with the particle (Seinfeld and Pandis 1998, Riipinen et al 2012, Lehtipalo et al 2016).

By a growing particle population we mean a reasonably well-separated mode of particles undergoing a growth into larger sizes, typically nucleation or Aitken mode particles formed during the past few hours by NPF. The mean size of such a mode increases not only by the growth of individual aerosol particles (GR_ind), but also by self-coagulation (GR_scoag) and coagulation scavenging (GR_scav). In self-coagulation, some of the particles inside the growing mode collide with each other (figure 2), which increases the mean size of the mode and simultaneously decreases the total particle number concentration of this mode. In coagulation scavenging, some of the particles in the growing mode collide with larger particles, i.e. with particles clearly outside the growing mode (figure 2). Since such collisions are most efficient for the smallest particles in the growing mode (see section 2.2.2), this process increases the mean size of the mode although no real particle growth is taking place inside the mode. The overall GR of the mode is roughly the sum of the three contributions mentioned above

$$\begin{eqnarray}&&{\rm{GR}}\approx {{\rm{GR}}}_{{\rm{ind}}}+{{\rm{GR}}}_{{\rm{scoag}}}+{{\rm{GR}}}_{{\rm{scav}}}.\end{eqnarray} \tag{ 2 }$$

Determining the value of each term in in equation (2), and especially separating the contribution of GR_scoag from those of GR_ind and GR_scav, requires knowledge about the lower and upper borders of the growing particle mode. Determining this information can be very difficult for atmospheric particle number size distributions. The contribution of GR_scoag to GR is only important at very high concentrations (>10⁵ cm⁻³) of particles in the growing mode (Kerminen et al 2004, Anttila et al 2010). The most practical unit of GR in atmospheric applications is nm h⁻¹.

Two additional concepts that are commonly used in analyzing atmospheric NPF are condensation sink (CS) and coagulation sink (CoagS) defined by Kulmala et al (2001):

$$\begin{eqnarray}&&{\rm{CS}}=2\pi {D}\displaystyle {\int }_{0}^{\infty }\beta ({\rm{dp}})\times {\rm{dp}}\,n({\rm{dp}})d{\rm{dp}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\rm{CoagS}}({\rm{dp}})=\displaystyle {\int }_{0}^{\infty }K({\rm{dp}},{\rm{dp}}^{\prime} )n({\rm{dp}}^{\prime} )d{\rm{dp}}^{\prime} .\end{eqnarray} \tag{ 4 }$$

Here β(dp) is the transition-regime correction factor for condensation onto a particle with a diameter of dp (Fuchs and Sutugin 1971), D is the vapor diffusion coefficient, n(dp) is the continuous particle number size distribution function, and K(dp, dp') is the Brownian coagulation coefficient between particles of diameters dp and dp'. The CS represents the average rate at which a non-volatile gaseous compound condenses into the entirely aerosol particle population, so the inverse of CS is equal to the average lifetime of a non-volatile compound in the gas phase. Similarly, CoagS(dp) can be viewed as the average rate at which particles of a diameter dp coagulate with the whole particle population, and its inverse represents the average particle lifetime against coagulation scavenging. It should be noted that, due to limitations in atmospheric particle number size distribution measurements, the integration over particle diameters in equations (3) and (4) is always cut from both lower and upper ends of the particle size spectrum. Leaving out the particles smaller than a few nm in diameter is usually well justified because such particles rarely make important contributions to either CS or CoagS. Contrary to this, in environments influenced heavily by dust, sea salt or primary biogenic particles, particles larger than a few hundred nm in diameter could substantially increase both CS and CoagS.

When investigating the role of gas-phase chemistry in the particle formation and growth, useful concepts are the total concentration of non-volatile gaseous compounds, C, and their production rate in the gas phase, Q (e.g. Kulmala et al 2001). These two quantities are highly idealized descriptions of a real atmosphere, where a large number of compounds of different volatility is simultaneously present. In order to deal with this issue, Donahue et al (2011) suggested to group organic compounds into a few volatility classes to describe their gas-particle partitioning: extremely low-volatile (ELVOC), LVOC, semi-volatile, intermediate-volatile and volatile (VOC) organic compounds. In many applications, C can be approximated as the sum of gaseous sulfuric acid and ELVOC concentration, even though it should be kept in mind that none of the gaseous compounds present in the atmosphere is strictly non-volatile. Likewise, it has been shown that the growth of atmospheric aerosol particles is affected not only by the least volatile compounds, but also by low- and semi-volatile compounds (e.g. Tröstl et al 2016).

The formation of new atmospheric aerosol particles and their growth to larger sizes are coupled closely to each other, as well as to the concentrations of aerosol precursor compounds and properties of a pre-existing particle population. Understanding these couplings is essential when analyzing NPF using atmospheric observations. In the following we will summarize some of the most important couplings between the relevant variables (J, GR, CS, CoagS, C, Q, particle number size distribution function), keeping in mind that the derived equations become increasingly inaccurate when approaching the cluster regime as discussed in the previous sub-section.

Mathematically, the particle formation and GRs are connected to each other via the continuous particle number size distribution function, n(dp):

$$\begin{eqnarray}&&{J}_{{\rm{dp}}}=n({\rm{dp}})\times {\rm{GR}}({\rm{dp}}).\end{eqnarray} \tag{ 5 }$$

The GR defined by equation (5) was recently named as the flux-equivalent GR, since the GR of a particle population can be determined in different ways (Kontkanen et al 2016b; see also section 2.3.2). It should be noted that equation (5) is strictly valid only when the particle number concentration around the size dp is conserved, i.e. when n(dp) is affected solely by the growth of individual aerosol particles. In its present form, equation (5) should not be applied for cases in which either self-coagulation or coagulation scavenging give a large contribution to the growth of a particle population.

Condensation and coagulation sinks describe essentially the same phenomenon, the only difference being that in CS one of the colliding parties is a gas molecule while in CoagS it is a molecular cluster or small aerosol particle, the other colliding party being the pre-existing particle population in both cases. Lehtinen et al (2007) showed that the CoagSs of particles with diameters dp₁ and dp₂ can be related to each other via the following approximate formulae:

$$\begin{eqnarray}&&{\rm{CoagS}}({{\rm{dp}}}_{{\rm{2}}})\approx {\rm{CoagS}}({{\rm{dp}}}_{1})\times {\left(\displaystyle \frac{{{\rm{dp}}}_{1}}{{{\rm{dp}}}_{2}}\right)}^{m},\end{eqnarray} \tag{ 6 }$$

where the exponent m (typically in the range 1.6−1.8) depends on the shape of the pre-existing particle population. A direct consequence of equation (6), together with the similarity between the condensation loss of a gas molecule and coagulation scavenging of a small aerosol particle, is that also CS and CoagS are connected with each other:

$$\begin{eqnarray}&&{\rm{CoagS}}({\rm{dp}})\approx {\rm{CS}}\times {\left(\displaystyle \frac{{\rm{dg}}}{{\rm{dp}}}\right)}^{m},\end{eqnarray} \tag{ 7 }$$

where dg is the diameter of the condensing gas molecule. In practical applications, CS is often calculated by assuming the condensing vapor to be sulfuric acid, in which case dg should be the diameter of a sulfuric acid hydrate (dg ≈ 0.71 nm, see Lehtinen et al 2007).

Equation (6) indicates that the probability by which an aerosol particle is lost by coagulation decreases relatively rapidly with an increasing particle size, so the survival probability of a growing particle is determined by the competition between its GR and its scavenging rate by coagulation with larger particles. For a growing particle population, the formation rates of different-size particles can be related to each other via (Lehtinen et al 2007):

$$\begin{eqnarray}&&\begin{array}{l}{J}_{{{\rm{dp}}}_{{\rm{2}}}}={J}_{{{\rm{dp}}}_{{\rm{1}}}}\exp \left(\displaystyle \frac{{{\rm{dp}}}_{1}}{m+1}\left[1-{\left(\displaystyle \frac{{{\rm{dp}}}_{2}}{{{\rm{dp}}}_{1}}\right)}^{m+1}\right]\right.\\ \left.\,\,\,\,\times \,\displaystyle \frac{{\rm{CoagS}}({{\rm{dp}}}_{1})}{{\rm{GR}}}\right),\end{array}\end{eqnarray} \tag{ 8 }$$

where the competition between the particle growth and coagulation scavenging appears as the ratio CoagS/GR. Equation (8) assumes implicitly that the particle GR is constant over the diameter range [dp₁, dp₂], and that GR is not affected by self-coagulation. The first of these assumptions is usually not valid (see section 5.1). Korhonen et al (2014) derived a modified version of equation (8), in which the particle GR is allowed to change linearly with an increasing particle size. Self-coagulation does not affect the accuracy of equation (8), except at high formation rates of new particles, and an iterative procedure that takes this into account the effect of self-coagulation was introduced by Anttila et al (2010). Based on equation (7), Kerminen and Kulmala (2002) showed that the relation between J_dp1 and J_dp2 can also be written using CS instead of CoagS. Finally, a generalized numerical method for relating J_dp1 and J_dp2 from experimental data was recently introduced by Kürten et al (2015).

The concentration of any non-volatile compound in the gas phase (C) is determined by the balance between its production rate and its loss rate by condensation into pre-existing particles:

$$\begin{eqnarray}&&\displaystyle \frac{dC}{dt}=Q-{\rm{CS}}\times C.\end{eqnarray} \tag{ 9 }$$

In the atmosphere, C evolves towards a pseudo-steady state given by:

$$\begin{eqnarray}&&C=\displaystyle \frac{Q}{{\rm{CS}}}.\end{eqnarray} \tag{ 10 }$$

The accuracy of equation (10) depends on the magnitude of CS and the rate at which Q is changing over time (Kerminen et al 2004). Excluding very clean environments (small CS) and environments with exceptionally rapid changes in Q (e.g. fresh pollution plumes), equation (10) can be considered as a good approximation to the value of C. Equation (10) offers a simple means to estimate C when this quantity cannot be measured directly. The application of this concept had led to the derivation of the widely-used proxy for the gas-phase sulfuric acid concentration (Petäjä et al 2009), and the recent proxy for the concentration of oxidized organic compounds in the gas phase (Kontkanen et al 2016c).

The GR of individual aerosol particles can be written as

$$\begin{eqnarray}&&{{\rm{GR}}}_{{\rm{ind}}}=\displaystyle \sum {{\rm{GR}}}_{{\rm{cond}},{i}}+\displaystyle \sum {{\rm{GR}}}_{{\rm{het}},{i}}+{{\rm{GR}}}_{{\rm{oth}}},\end{eqnarray} \tag{ 11 }$$

where GR_cond,i is the GR due to net condensation of vapor i into the particle, GR_het,i is the GR due to some heterogeneous reaction of vapor i on the surface or inside the particle, and GR_oth represents other growth processes such as collisions of molecular clusters with the particle. The condensational growth term can further be written into the following form:

$$\begin{eqnarray}&&{{\rm{GR}}}_{{\rm{cond}},{i}}=A\times [{C}_{{i}}\,\mbox{--}\,{C}_{{i},0}\times {\rm{Ke}}({\rm{dp}})],\end{eqnarray} \tag{ 12 }$$

where C_i and C_i,0 are concentration of vapor i in the gas phase over a flat surface having the same composition as the particle, A takes into account the collision rate between vapor molecules and the particle, and Ke is the Kelvin term which increases rapidly with the decreasing particle size for particles smaller than a few nm in diameter (e.g. Wang et al 2013). For a non-volatile compound, C_i,0 = 0 and A is relatively constant over the particle diameter range of 3−10 nm (Nieminen et al 2010), such that GR_cond,i is directly proportional to both C_i and Q_i (see equations (10) and (12)).This means that the contribution of any non-volatile compound to the particle GR can be estimated relatively easily once either its gas-phase concentration or its production rate in the gas-phase is known. In practical applications, sulfuric acid and ELVOCs can usually be treated as if they were non-volatile, whereas for more volatile vapors the term C_i,0 × Ke(dp) needs to be taken into account when estimating the value of GR_cond,i.

Let us consider a measurement device that provides data on particle number concentrations, N_i, in several size bins i over the diameter range [dp_min, dp_max] and with a temporal resolution of ∆t. From such measurements, one can determine the particle formation rate at the lower boundary of any of the size bin i, dp_i, that belongs to the diameter range [dp_min, dp_max]. This is in practice done by looking at the temporal behavior of the total particle number concentration over some number (n) of size bins starting from the bin i: N = N_i + N_i+1 + ... N_i+n−1, where dp_i+n ≤ dp_max (figure 3). The time evolution of N can be related to the particle formation rate at dp_i via the following balance equation:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{{\rm{\Delta }}N}{{\rm{\Delta }}t}\approx {J}_{{{\rm{dp}}}_{{i}}}-{J}_{{\rm{d}}{{\rm{p}}}_{{i}+{n}}}-\displaystyle \frac{1}{2}\displaystyle \sum _{j={i}}^{{i}+{n}-{\rm{1}}}{K}({{\rm{dp}}}_{j},{{\rm{dp}}}_{j}){N}_{j}^{2}\\ \,-\,\displaystyle \sum _{j={i}}^{{i}+{n}-{\rm{1}}}{\rm{CoagS}}{({{\rm{dp}}}_{{j}})}_{\gt {\rm{d}}{{\rm{p}}}_{j+1}}{N}_{j}+\displaystyle \sum _{j={i}}^{{i}+{n}-{\rm{1}}}{P}_{j}-\displaystyle \sum _{j={i}}^{{i}+{n}-{\rm{1}}}{v}_{j}{N}_{j}.\end{array}\end{eqnarray} \tag{ 13 }$$

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Here P_j is the rate of primary particle emissions into the size bin j, v_j is the loss rate of particles in this size bin by deposition, and the subscript j + 1 in CoagS means that only particles in the size bins j + 1, j + 2 +... are considered when calculating the CoagS. The third term in equation (13) takes into account coagulation between the particle in the diameter range [dp_i, dp_i+n], called self-coagulation. Equation (13) does not include the flux of particles into, nor the flux of particles out from, the size range [dp_i, dp_i+n] due to particle self-coagulation. Another, rather minor approximation made in equation (13) is that the coagulation terms are calculated at the lower boundary of each size bin.

For sizes at which atmospheric particle formation rates are usually determined (<10−20 nm diameter), dry deposition of particles is usually negligible compared with the particle removal rate by coagulation scavenging (Kerminen et al 2004). By neglecting the last term in equation (13) and rearranging, we obtain:

$$\begin{eqnarray}&&\begin{array}{l}{J}_{{{\rm{dp}}}_{{i}}}\approx \displaystyle \frac{{\rm{\Delta }}N}{{\rm{\Delta }}t}+\displaystyle \frac{1}{2}\displaystyle \sum _{j=i}^{{i}+{n}-{\rm{1}}}{K}({{\rm{dp}}}_{j},{{\rm{dp}}}_{j}){N}_{j}^{2}+\displaystyle \sum _{j=i}^{{i}+{n}-{\rm{1}}}{\rm{CoagS}}\\ \,\times \,{({{\rm{dp}}}_{{j}})}_{\gt {\rm{d}}{{\rm{p}}}_{i+1}}{N}_{j}+{J}_{{\rm{d}}{{\rm{p}}}_{i+n}}-\displaystyle \sum _{j=i}^{{i}+{n}-{\rm{1}}}{P}_{j}.\end{array}\end{eqnarray} \tag{ 14 }$$

While the approximations made above are not always valid, equation (14) can be considered as a general expression for the particle formation rate at the diameter dp_i in the atmosphere. Of the five terms on the right hand side of equation (14), the first one is obtained directly from the size distribution measurements, the second term can be calculated from the same measurements, and so can the third term when dp_max is large enough so that the measured size range includes the dominant fraction of the CoagS (see equation (4)). The fourth and last terms are the trickiest ones and require a special attention in data analyses. Below we discuss shortly how equation (14) has commonly been used, and how it should be used, when analyzing atmospheric NPF events.

One way to use equation (14) is to consider a relatively narrow size range [dp_i, dp_i+n], with dp_i+n well below 10 nm. The main advantage of this approach is that the last term of equation (14) representing primary particle emissions can usually be considered to be negligible. The drawback is that the flux of particles growing out of the size range [dp_i, dp_i+n], i.e. the fourth term on the right hand side of equation (14), needs to be taken into account. Determining this flux requires making approximations on the particle number size distribution and GR at dp_i+n (see equation (5)), which causes potentially large errors in the calculated particle formation rate at dp_i (Vuollekoski et al 2012). Another way to use equation (14) is to consider a broader size range [dp_i, dp_i+n], with dp_i+n being in the range 20−30 nm. In this case, neglecting the fourth term on the right hand side of equation (14) is usually a reasonable approximation. A potential problem, however, are primary particle emissions: especially in urban environments, vehicular exhaust may be a substantial source of sub-20–30 nm particles (Ban-Weiss et al 2010, Brines et al 2015, Paasonen et al 2016), and these particles should be included in the fourth term of equation (14).

An issue worth noting is how the second and third terms on the right hand side of equation (14), representing coagulation losses, should be treated. Firstly, it is important to make a difference between these two terms, since for self-coagulation (the second term) the resulting aggregate will usually remain in the size range [dp_i, dp_i+n] while for coagulation with larger particles (the third term) it will not. Secondly, due to the relatively strong dependence of the CoagS on the particle size (see equation (6)), the third term on the right-hand side of equation (14) should be calculated separately for all the size bins belonging to the size range [dp_i, dp_i+n], rather than using a single 'representative' diameter in this size range. Accurate determination of the coagulation terms in equation (14) is especially important in highly-polluted environments where these terms may give a significant contribution to ∆N/∆t (Cai and Jiang 2017).

The particle GR can be determined from particle number size distribution measurements either with (e.g. Kuang et al 2012, Pichelstorfer et al 2018) or without (e.g. Kulmala et al 2012) considering the general dynamic equation for the growing particle population. The latter approach relies on two fundamentally different methods. In the first of these, termed the mode-fitting method (Dal Maso et al 2005, Kulmala et al 2012), a log-normal distribution function is fitted to a growing particle population, and some particle diameter characterizing this mode (number median diameter, mode peak diameter) is then determined. This procedure is repeated for successive time steps determined by the temporal resolution of the measurements, resulting in a series of particle diameter-time pairs (d_i, t_i; i = 1 ... n). In the second method, termed the appearance time method (Lehtipalo et al 2014), a series of particle diameter-time pairs is determined as well, but with a different logic: d_i is chosen to be some characteristic diameter of each measured size bin, while t_i is the time when the measured particle number concentration in this size bin reaches some pre-defined limit, typically its overall maximum or some fraction of that maximum.

In both the mode-fitting and appearance time method, the particle growth rate, GR, is obtained from the slope of a curve fitted to the obtained series of the particle diameter-time pairs (d_i, t_i; i = 1 ... n). This procedure provides typically a single value, and at most a few values, of GR for each NPF event. The resulting GR can therefore be interpreted as NPF event-average particle GR over a given particle diameter range. It should be noted that the size range, of which the obtained values of GR are representative, may vary considerably between different studies as well as between individual NPF events in a single study.

Estimating how the particle GR varies with time and particle size during a single NPF event involves large uncertainties, and is usually not possible without solving the general dynamic equation in combination with measurement data. The general principles of such approach, along with some examples on its application for measurement data, have been discussed in detail by Verheggen and Mozurkewich (2006), Kuang et al (2012), Yu et al (2016) and Pichelstorfer et al (2018), and thus will not be repeated here.

There is no method for the treatment of measurement data that can accurately reproduce the flux-equivalent particle GR defined by equation (5). For example, it has been shown using numerical simulations that the appearance time method discussed above systematically gives values of GR that exceed the corresponding flux-equivalent particle GR, and that this difference increases rapidly when going to sub-3 nm particle sizes (Olenius et al 2014, Kontkanen et al 2016b).

There are several field measurement sites, for which no total particle number size distribution data are available, yet corresponding data for the charged fraction of the particle population exist. From such data, one can determine the formation rate of charged particles by using an equation that is otherwise similar to equation (14) but has two additional terms: a term that takes into account the loss of charged particles by ion–ion recombination, and a term that takes into account the attachment of small ions to neutral (uncharged) aerosol particles (see Manninen et al 2010, Kulmala et al 2012). Because of these two additional processes, the formation rate of charge particles is sensitive not only to the formation rate of charged clusters but also to the ambient ion concentration, the particle GR, and the size at which the formation rate is being determined (Kerminen et al 2007). As a result, one should be extremely careful in interpreting measurement data on the formation rate of charged particles, especially for sizes larger than about 2−3 nm in particle diameter, and in comparing such data between different environmental conditions.

Determining particle GRs from measured size distributions of charged particles can be done using the same procedures as outlined in section 2.3.2 for measured size distributions of total particle populations. When doing this, however, one needs to remember that the growth of a charged particle population differs somewhat from that of the total particle population. First, the condensation growth of charged aerosol particles is expected to be enhanced compared with similar-size neutral particles (Yu and Turco 2000, Nadykto and Yu 2003, Lushnikov and Kulmala 2004). Existing evidence suggest, however, that this effect is important only to the very smallest aerosol particles, being probably negligible for particles larger than 3 nm in diameter (e.g. Lehtipalo et al 2016). Second, coagulation losses of charged particles may be up to a factor of two higher than corresponding losses of neutral particles (Leppä et al 2011). This feature may affect calculated particle GRs in cases where coagulation losses give a significant contribution to the apparent particle GR (see equation (2)). Finally, the GR of charged particles might be affected by ion–ion recombination and ion-aerosol attachment (Gonser et al 2014). Only few field studies have compared the observed GRs of charged particles to those of the total particle population (Yli-Juuti et al 2009, Vakkari et al 2011, Yli-Juuti et al 2011, Hirsikko et al 2012, Gonser et al 2014). The overall message from these studies is that these two GRs typically compare relatively well with each other for particles larger than a few nm in diameter, while larger differences are occasionally seen for smaller particles. It is unclear to which extent these differences reflect real aerosol dynamical differences between the charged and neutral particles, and to which extent they arise from possible biases associated with different measurements or GR analysis methods.

The intensity of solar radiation reaching the Earth's surface is perhaps the most important factor in determining whether atmospheric NPF takes place or not. In practically all the measurement sites from where at least a few months of measurement data are available, the average solar radiation intensity was found to be higher during the NPF event days compared with non-event days (Birmili and Wiedensohler 2000, Vehkamäki et al 2004, Hamed et al 2007, Kristensson et al 2008, Jeong et al 2010, Guo et al 2012, Hirsikko et al 2012, Jun et al 2014, Kanawade et al 2014, Pierce et al 2014, Qi et al 2015, Wonaschütz et al 2015). No clear radiation threshold needed to initiate a regional NPF event has been identified, except at one study site (Lee et al 2008). The presence of clouds, by attenuating the solar radiation intensity below the cloud layer, decreases the probability of NPF to occur (Baranizadeh et al 2014, Dada et al 2017). An ongoing NPF event can be interrupted by the appearance of clouds (Hirsikko et al 2013), or by the occurrence of a solar eclipse (Jokinen et al 2017).

By acting as a sink for LVOC vapors and small clusters, a higher pre-existing aerosol loading is expected to hinder the occurrence of NPF. Existing observations confirm this expectation, since at most measurement sites the average value of CS was found to be lower on NPF event days compared with non-event days (Birmili et al 2003, Dal Maso et al 2007, Wu et al 2007, Asmi et al 2011, Pikridas et al 2012, Wang et al 2013, Young et al 2013, Kanawade et al 2014, Qi et al 2015, Salma et al 2016a, Dada et al 2017, Dai et al 2017). An exception to this pattern was the study by Birmili and Wiedensohler (2000) made in Melpitz, Germany, where the average pre-existing particle surface areas was somewhat higher on NPF event days compared with all the other days. In a couple urban locations, a threshold for CS, or aerosol surface area, above which NPF is very unlikely, was identified (e.g. Salma et al 2016a, Cai et al 2017). However, occurrences of NPF at very high values of CS have been observed (Nie et al 2014, Xiao et al 2015, Kulmala et al 2017).

The average ambient relative humidity (RH) tends to be lower on NPF event days than on non-event days in both clean and polluted environments (Birmili and Wiedensohler 2000, Birmili et al 2003, Vehkamäki et al 2004, Hamed et al 2007, Wu et al 2007, Lee et al 2008, Suni et al 2009, Guo et al 2012, Jun et al 2014, Kanawade et al 2014, Pierce et al 2014, Qi et al 2015, Zhao et al 2015, Salma et al 2016a, Dada et al 2017). Several possible reasons for this apparently close connection between the ambient RH and occurrence of NPF have been proposed, including the typically negative feedback of high RH on the solar radiation intensity, photochemical reactions and atmospheric lifetime of aerosol precursor vapors (e.g. Hamed et al 2011). In reality the situation is likely to be more complicated than this, since in many locations also air masses originating from very different source areas tend to be characterized by different levels of RH (e.g. Birmili et al 2003, O'Halloran et al 2009, Suni et al 2009, Dada et al 2017).

The effect of the ambient temperature (T) on NPF is ambiguous, showing very different responses between different studies. This feature is probably related to the simultaneous presence of several temperature-dependent processes that may either enhance or suppress NPF. Such processes include biogenic emissions of aerosol precursor vapors into the atmosphere and their oxidation to low-volatility vapors (e.g. Grote and Niinemets 2008), accumulation of aerosol particles which increases CS (e.g. Paasonen et al 2013), formation of molecular clusters and nanoparticles from various precursor vapors (e.g. Dunne et al 2016, Kürten et al 2016), and the diurnal evolution of the BL. Further complications arise from the strong seasonal cycle of the ambient temperature in many continental locations. For example, Dada et al (2017) found that in Hyytiälä, Finland, NPF is more frequent at higher values of T during the cold part of the year, while the opposite is true during the warm part of the year.

A close connection between the formation rate of new atmospheric aerosol particles and gas-phase sulfuric acid (H₂SO₄) concentration has been reported for a number of measurement sites (Weber et al 1995, 1996, 1997, Birmili et al 2003, Kulmala et al 2006a, Sihto et al 2006, Riipinen et al 2007, Kuang et al 2008, Nieminen et al 2009, Petäjä et al 2009, Paasonen et al 2010, Wang et al 2011, Yao et al 2018). Much less information is, however, available on how H₂SO₄ affects the occurrence of NPF, and even fewer studies have reported higher measured H₂SO₄ concentrations on NPF event days than on non-event days (Birmili et al 2003, Boy et al 2008, Wang et al 2011). Several studies have attempted to look at the relation between NPF and H₂SO₄ concentration by using some proxy variable for the gas phase H₂SO₄ concentration. Such analyses are subject to large uncertainties due to the scarcity of studies investigating the validity of these proxies in different environments (Petäjä et al 2009, Mikkonen et al 2011), and therefore will not be discussed here in more detail.

The main gaseous precursor for H₂SO₄ is sulfur dioxide (SO₂). Being also a major atmospheric pollutant that has undergone strict air quality regulations over the years, the potential connection between atmospheric NPF and SO₂ concentration has been of great interest. Observations in this regard are inconclusive: NPF event days have been reported to have both higher (Birmili and Wiedensohler 2000, Woo et al 2001, Dunn et al 2004, Boy et al 2008, Young et al 2013, Zhao et al 2015) and lower (Wu et al 2007, Dai et al 2017) ambient SO₂ concentrations, as compared with SO₂ concentrations measured during the non-event days or outside the periods of active NPF. In one study, the relation between the occurrence NPF and SO₂ concentration was found to be inconsistent between different seasons (Qi et al 2015). These contrasting observations can be understood by the delicate balance between the factors that favor (a higher gas-phase H₂SO₄ production rate) and disfavor (a larger sink for LVOC vapor and molecular clusters) NPF downwind major SO₂ sources. The potential influence of SO₂ emission reductions, driven mostly by past air quality regulations in United States and Europe, on the NPF event frequency will be discussed shortly in section 3.1.2.

Organic vapors, especially highly-oxygenated and extremely low-volatility organic compounds (ELVOC), have been speculated to participate actively into atmospheric NPF (e.g. Kulmala et al 1998, 2013, 2014, Ehn et al 2014, Jokinen et al 2015, Bianchi et al 2016). Since long-term ELVOC measurements are lacking at the moment, little can be said about how these compounds influence the occurrence of atmospheric NPF events. Dada et al (2017) showed, using 20 years of measurement data from Hyytiälä, Finland, that a proxy for the concentration of oxidized organic compounds in the gas phase (see section 2.2.2) was, on average, higher on NPF event than on non-event days in every month of the year. This observation gives some confidence that the ELVOC concentration might be among the most important variables affecting occurrence of NPF in the continental atmosphere.

In a number of studies, the probability by which NPF events occur has been found to depend strongly on the wind direction or, more specifically, on the origin of measured air masses (e.g. Hamed et al 2007, Sogacheva et al 2007, Suni et al 2009, Asmi et al 2011, Shen et al 2011, Vakkari et al 2011, Nieminen et al 2014, Qi et al 2015, Mordas et al 2016, Kolesar et al 2017). Such dependency is quite expected, since in most locations air masses coming from different directions tend to be affected by different levels of biogenic emissions and anthropogenic pollutants, and exposed to different meteorological conditions prior to their arrival at the measurement site.

The above discussion summarizes our current understanding on how different atmospheric variables are related to the occurrence of NPF. Over the years, people have also searched for more general criteria to predict whether NPF takes place or not under given atmospheric conditions. Based on the pioneering theoretical work by McMurry and Friedlander (1979) and McMurry (1983), McMurry et al (2005) developed a parameter 'L' to distinguish the days with NPF from those without NPF in a sulfur-rich environment. Kuang et al (2010) extended this work to more diverse environments with a parameter 'L_Γ' and demonstrated the value of this parameter to be a good predictor for the occurrence of NPF. Kulmala et al (2017) introduced a dimensionless survival parameter 'P', a variable closely related to L_Γ, and pointed out that we are still lacking a general understanding on why NPF occurs under extremely-polluted conditions. The main problem in applying L, L_Γ or P to predicting the occurrence of NPF is that determining their values requires knowing either the cluster GR or gas-phase concentration of vapors causing this growth. Such information is rarely available from atmospheric measurements. By relying on some combination of variables known to either favor or disfavor NPF, people have developed such NPF predictors that can relatively easily be derived from routine measurement data (e.g. Clement et al 2001, Boy and Kulmala 2002, Hyvönen et al 2005, Mikkonen et al 2006, Jayaratne et al 2015, Nieminen et al 2015). While many of these NPF predictors seem to work well for limited data sets, or constrained atmospheric conditions, none of them has been shown to have a universal predictive power in the continental troposphere.

Regional NPF is typically a daytime phenomenon. The studies covering at least two full years of measurements have reported that the starting times of NPF formation events are confined almost exclusively between the sunrise and sunset (Vehkamäki et al 2004, Hamed et al 2007, Wu et al 2007, Asmi et al 2011, Qi et al 2015). Furthermore, the active period of NPF tends to end before sunset (Hamed et al 2007, Wu et al 2007, Qi et al 2015). Nighttime NPF have been reported in a few locations, including a boreal forest and its surroundings (Vehkamäki et al 2004, Junninen et al 2008, Svenningsson et al 2008, Buenrostro Mazon et al 2016, Rose et al 2018), a pine forest in France (Kammer et al 2018), an Eucalypt forest in Australia (Suni et al 2008), a Mediterranean Island (Kalivitis et al 2012), a rural site affected by orographic cloud processing (Wiedensohler et al 1997), an industrial complex in South Africa (Hirsikko et al 2012), and an urban site in Australia (Salimi et al 2017, Pushpawela et al 2018). In some of these locations the particle growth following nighttime NPF was very limited (e.g. Kalivitis et al 2012, Buenrostro Mazon et al 2016, Rose et al 2018), while in some locations such growth could be very intense, producing particles of several tens of nm in diameter (Suni et al 2008, Svenningsson et al 2008). Two aircraft studies have reported indications of nighttime NPF in the free troposphere (FT) (Lee et al 2008, Rose et al 2015a). All these features, together with findings related to the solar radiation intensity (see section 3.1.1), tend to imply a very crucial role of atmospheric photochemistry in maintaining regional NPF and growth.

The duration of a NPF event refers to the length of the period during which active NPF is taking place or, in a more practical sense, the length of the period during which very small particles enter the measured particle size range. Very few publications report the duration of the observed NPF events, even though such information is essential when determining the event-average NPF rates.

A typical feature of regional NPF events is that the newly-formed particles grow gradually into larger sizes. In theory, this growth continues until the particles are removed from the atmosphere by deposition or coagulation processes. In practice, however, one can track the growth of newly-formed particles from a few hours up to a day or two when using measurements conducted at a fixed location. Several factors contribute to our inability to follow the particle growth further in time, including the diurnal evolution of the continental BL and associated mixing, limited spatial extent of NPF (see section 2.3.3), and general difficulties in separating 'aged' particles of different origin using routine measurements. In a vast majority of cases, the growth of newly-formed particles appears to be irreversible. However, there are a few locations where the newly-formed particles first grow in size for a few hours and then, occasionally, appear to shrink to various extents (Yao et al 2010, Cusack et al 2013, Young et al 2013, Skrabalova et al 2015, Lihavainen et al 2016, Salma et al 2016b, Zhang et al 2016, Alonso-Blanco et al 2017). For a more detailed discussion on this phenomenon, we refer to a recent paper by Alonso-Blanco et al (2017).

In a few locations, the occurrence of two or more NPF events during the same day have been reported (Suni et al 2008, Svenningsson et al 2008, Hirsikko et al 2013, Kyrö et al 2013, Rose et al 2015b, Salma et al 2016a). Such phenomenon, while rather rare, has several possible causes. First, the presence of clouds can interrupt an ongoing NPF event for a while, after which either the same event will continue or a new event will begin (e.g. Hirsikko et al 2013). Second, it is possible that due to changing air masses or evolving chemical composition in the same air mass being measured, two different types of regional NPF events are being initiated at different times of the same day (e.g. Salma et al 2016a). Finally, sometimes a 'local' NPF event may emerge on top of a regional NPF event (e.g. Kyrö et al 2013).

The frequency of NPF occurrence varies over the course of a year, since most of the variables influencing NPF have a pronounced seasonal variation. In a vast majority of the sites, NPF is more frequent in summer compared with winter (Qian et al 2007, Dall'Osto et al 2018, Nieminen et al 2018). The season with the highest NPF event frequency tends to change from summer in polar and many high-latitude regions (Heintzenberg et al 2017, Nieminen et al 2018) toward the spring or autumn in most other regions (e.g. Jeong et al 2004, Stanier et al 2004, Dal Maso et al 2005, Hussein et al 2008, Pryor et al 2010, Asmi et al 2011, Kyrö et al 2014, Asmi et al 2016, Mahish and Collins 2017, Wang et al 2017b, Nieminen et al 2018). This pattern is, however, by no means universal, and the overall ranking order of the seasons in terms of their NPF frequency shows a substantial variability between individual measurements sites (e.g Wu et al 2007, Meija and Morawska 2009, Manninen et al 2010, Shen et al 2011, Vakkari et al 2011, Hirsikko et al 2012, Qi et al 2015, Wonaschütz et al 2015, Dall'Osto et al 2018). Very few studies have found NPF to be most frequent during the wintertime (Lee et al 2008, Pikridas et al 2012). Although the NPF frequency has varying seasonal characteristics at different sites, the GRs of newly-formed particle display almost exclusive a summer maximum (e.g. Nieminen et al 2018). This feature originates from higher biogenic emissions and typically stronger atmospheric photochemistry during the summertime, both of them enhancing the production of LVOC vapors responsible for the particle growth, while there is practically nothing during summer (except perhaps extreme temperatures) that would be expected to suppress the particle growth.

Changes in anthropogenic emissions, along with climate change, are expected to affect the probability of occurrence of atmospheric NPF. Unfortunately, very few observational data on long-term changes in the NPF event frequency exist. Hamed et al (2010) showed that both the intensity and frequency of NPF decreased considerably between two time periods (1996−1997; 2003−2006) at a rural site in Melpitz, Germany, and hypothesized that this decrease was mainly due to the major decline in gas-phase SO₂ concentrations over the same time period. Wang et al (2017b) demonstrated a further decline in NPF and SO₂ concentrations from 2003 to 2011, so that that annual NPF event frequency decreased from 40%−50% in 1996−1997 down to <20% during 2007−2011 in Melpitz. Saha et al (2018) reported that the regional NPF event frequency decreased from about 30% during 2001−2002 to about 10% during 2016−2017 In Pittsburg, Pensylvania, in United States, accompanied by a strong decline in the SO₂ concentration of about 90% between these two time periods. Kyrö et al (2014) observed a strong decline (−3.7% yr⁻¹) in the NPF event frequency at Värriö in Northern Finland over the time period of 1998−2011, and attributed this decline to decreasing sulfur emissions from the nearby industrial sources in the Kola Peninsula. Pallas, a site about 300 km west from Värriö, however, displayed no trend in the NPF event frequency during 2000−2010 (Asmi et al 2011). The study by Asmi et al (2011) did not report the temporal behavior of the SO₂ concentration in Pallas, but it is known that compared with Värriö, Pallas is considerably less affected by SO₂ emissions from the Kola Peninsula. In Hyytiälä, Finland, particle formation and GRs show a slight positive trend (0.2%−0.5% yr⁻¹) since 1996 (Nieminen et al 2014), whereas no clear trend but a prominent inter-annual variability can be seen for the NPF event frequency (Nieminen et al 2014, Dada et al 2017). Finally, Kalivitis et al (2018) reported a slight increase in the NPF event frequency over the period 2008–2015 at Crete, Greece, in the eastern Mediterranean.

Several studies have attempted to estimate the spatial extent of regional NPF. For this purpose, various methods based on single-site measurements have been developed (e.g. Birmili et al 2003, Hussein et al 2009, Crippa and Pryor 2013, Kristensson et al 2014, Nemeth and Salma 2014). A more detailed view on the spatial extent and variability of NPF can be obtained by using simultaneous measurements from two or more stations, and such analyses have been performed for Northern (Tunved et al 2003, Vana et al 2004, Komppula et al 2006, Hussein et al 2009) and Central Europe (Wehner et al 2007), the Carpathian Basin (Salma et al 2016a), the Mediterranean atmosphere (Berland et al 2017), Eastern North America (Crippa and Pryor 2013), Ontario, Canada (Jeong et al 2010, Jun et al 2014), the Korean Peninsula (Kim et al 2016), North China Plain (Wang et al 2013) and Eastern China (Shen et al 2018). The general conclusion from these studies is that the spatial extent of regional NPF is typically a few hundreds of km, and possibly exceeding 1000 km in some environments.

Despite the usually relatively large spatial extent of regional NPF, most of the studies mentioned above observed a notable variability in the timing, duration and intensity of NPF events across the study region. This spatial variability appears to be larger for particle formation rates compared with particle GRs. Paired urban and rural locations display interesting features in this regard: in comparison with rural sites, NPF in the nearby urban sites tend to be less frequent (Yue et al 2013, Jun et al 2014, Salma et al 2016a), yet more intense in terms of observed particle formation and GRs (Wang et al 2013, Salma et al 2016a). Furthermore, when occurring, regional NPF may start, on average, either later (Wehner et al 2007, Salma et al 2016a) or earlier (Jung et al 2013, Yue et al 2013) at the urban site than at the nearby rural site. Observations indicate that the spatial variability of regional NPF is apparent not only between the urban and rural locations, but also within an urban area (e.g. Siakavaras et al 2016) and over a rural or sea areas (e.g Crumeyrolle et al 2010, Crippa and Pryor 2013, Berland et al 2017). Challenges in distinguishing between regional and local NPF events at sub-regional scales makes it difficult to perform detailed analyses of small-scale variabilities in regional NPF.

The vertical extent of regional NPF has been investigated in rather few studies. Airborne observations suggest that in some regions NPF and subsequent particle growth seem to be confined into the BL (O'Dowd et al 2009, Crumeyrolle et al 2010), while in other regions this phenomenon may also take place in the FT (Rose et al 2015a, Bianchi et al 2016, Berland et al 2017) or at the interface between the BL and FT (Siebert et al 2004, Dadashazar et al 2018). In Beijing, China, the height in the atmosphere having the strongest NPF was observed to move from within the BL at low aerosol loadings to the top of the BL or to the lower FT at high aerosol loadings (Quan et al 2017). Observations in several mountain-top locations indicate a relatively frequent occurrence of seemingly regional NPF events at high altitudes (see section 3.2.5). It is unclear how big fraction of these NPF events is truly of free tropospheric origin, and whether they are related to a recent transport of aerosol precursors from the BL.

It would be tempting to conclude that the spatial extent and variability of regional NPF is affected solely by spatial inhomogeneities in the sources of aerosol precursor compounds. However, the delicate balance between the factors that favor atmospheric NPF on one hand, and the factors that suppress it on the other hand, changes this picture. Tunved et al (2006) showed that in originally clear air entering a boreal forest zone, atmospheric NPF is first initiated after the air mass have traveled some time over the forested area, and then maintained until the increasing pre-existing aerosol loading kills it. In this case, the spatial extent of NPF as well as its temporal characteristics at any fixed location are dictated by the rate at which the transported air masses accumulate aerosol precursor compounds. Another example of the dynamic nature of regional NPF comes from Beijing, China, where the occurrence of NPF was found to be tied to a multi-day cycle of air pollutant accumulation (Guo et al 2014). These examples demonstrate the complex interplay between the spatial extent and temporal characteristics of regional NPF—a feature that is rarely taken into account when analyzing NPF observations made at fixed locations.

Published analyses of regional NPF events in rural and remote continental areas cover a wide range of environments, including boreal and other forested areas, agricultural regions, grasslands and various types of environments located at different distances from major urban centers. In the following we consider boreal forest sites separately from other types of sites, mainly because the boreal forests are the only environment having long-term measurements of atmospheric NPF from several different sites. Arctic and polar continental environments, as well as mountains sites, will be considered separately in sections 3.2.3 and 3.2.5.

The SMEAR II station (Hari and Kulmala 2005), located in a boreal forest environment in Hyytiälä, Finland, was the first field site from where regional NPF events were reported in a scientific literature (Mäkelä et al 1997), and the same site has so far the longest published times series of such events (Nieminen et al 2014). The observed particle formation and GRs span roughly an order of magnitude between the different boreal forest sites, the median values being 0.4 cm⁻³ s⁻¹ and 2.7 nm h⁻¹, respectively (table 1). The annual frequency of NPF event varies between about 10% and 30%, with lowest frequencies corresponding to the northern edge of the boreal forest zone and the Siberian part of this region. The NPF event frequency has often a maximum in spring, possibly another maximum in late summer or autumn, and is typically very low during the wintertime (Dal Maso et al 2007, 2008, Kristensson et al 2008, Asmi et al 2011, Nieminen et al 2014, Kyrö et al 2014).

Particle formation rates in rural and remote locations other than boreal forest sites span over a relatively large range of values (table 1), as one might expect due to the variable characteristics of these environments. The median value of J from these environments is about ten times higher than that from the boreal forest sites, and the same concerns the high- and low-end values of this quantity between the rural China and boreal forest environment. Compared with J, smaller differences exist in GR between the rural and remote locations, and the median value of this quantity outside China is only slightly higher than that in boreal forests. Typical particle GRs in Chinese rural sites are about twice those in rural sites elsewhere in the world.

The frequency of regional NPF in rural and remote locations varies a lot. At one extreme, NPF event frequencies between about 70% and 90% were reported in South Africa (Vakkari et al 2011, Hirsikko et al 2012, Vakkari et al 2015). At the other extreme, NPF was found to be quite rare around a forested location in Siberia (Heintzenberg et al 2011), and almost non-existent in the Amazonian rainforest (Martin et al 2010, Wimmer et al 2018, Andreae et al 2018, Rizzo et al 2018).

Since the last review that concentrated on observed atmospheric NPF (Kulmala et al 2004), a large number of studies have investigated NPF in various types of urban environments. The median particle formation rates are the lowest in Antarctica, followed Arctic and boreal forest sites, and still higher in other remote and rural environments as well as in urban areas (table 1). In China, high particle formation rates tend to be observed in almost all the sites.

The median particle GR from the urban sites is 1.5–2 times that from the non-Chinese rural and remote locations (table 1). Somewhat larger differences can be seen at the low-end values of this quantity, mainly because observed particle GRs smaller than about 1 nm h⁻¹ are rare in urban environments. It could be mentioned that particle GRs >10 nm h⁻¹ are common in many urban locations, especially in China, but seemingly also in some other polluted environments (Mönkkönen et al 2005, Wu et al 2007, Iida et al 2008, Kalafut-Pettibone et al 2011, Peng et al 2014, Qi et al 2015, Xiao et al 2015, Zhao et al 2015).

Typical frequencies of regional NPF events in urban environments are in the range of 10%–30% (Stanier et al 2004, Qian et al 2007, Dall'Osto et al 2013, Brines et al 2015, Wonaschütz et al 2015, Hofman et al 2016, Salma et al 2016a). Higher NPF event frequencies were observed in Po Valley, Italy (36%, Hamed et al 2007), London, United Kingdom (36%, Hofman et al 2016), Beijing, China (40%, Wu et al 2007), and Nanjing, China (44%, Qi et al 2015). NPF event frequencies as low as 5% were reported in Birmingham, United Kingdom (Alam et al 2003) and in Helsinki, Finland (Hussein et al 2008). No consistent pattern in the seasonal variability of the NPF event frequency in urban areas can be identified.

Particle number concentration and size distribution measurements conducted in the Arctic suggest that this region is an active area of NPF during the summertime (Leaitch et al 2013, Tunved et al 2013, Freud et al 2017). This view is supported by the few published regional NPF event frequencies, reaching values between about 30% and 40% in Tiksi, northern Russia, and in Station Nord, northeast Greenland (Asmi et al 2016, Nguyen et al 2016). Summertime NPF was found to be frequent also in air masses measured at the Zeppelin station, Svalbard (Dall'Osto et al 2017, Heintzenberg et al 2017), as well as in Canadian Arctic marine and coastal environments (Collings et al 2017). Interestingly, the summertime NPF event frequencies in the Arctic seem to be clearly higher than those reported at a few sub-Arctic sites at the edge of the boreal forest zone at the same time of the year. The frequency of NPF during the winter is very low in most Arctic locations. Dall'Osto et al (2017) reported an anti-correlation between the NPF event frequency in Svalbard and both monthly and annual extent of Arctic sea ice area, suggesting that future reductions in the Arctic sea ice extent might lead to enhanced NPF over the Arctic.

Although cases of regional NPF have been observed throughout the Arctic, data on NPF and GRs are available from few sites only (table 1). Based on these rather limited data, particle formation and GRs in the Arctic atmosphere appear to be comparable to those observed in boreal forest environments.

It should be noted that in addition to NPF taking place inside the Arctic BL, sources of nucleation and small Aitken mode particles might also be the entrainment from the FT (e.g. Tunved et al 2013, Croft et al 2016, Igel et al 2017, see also section 3.2.4), or primary particles emitted from the Arctic Ocean (Leck and Bigg 1999, 2005, Orellana et al 2011, Karl et al 2013). Heintzenberg et al (2017) applied three different types of search algorithms for NPF and particle growth events in the Svalbard region over a 10 year measurement period, partly reflecting the different sub-60 nm particle sources, and found evidence on varying and relatively complex marine biological source processes for these particles.

Over Antarctica, a prominent feature of the aerosol system is the very pronounced annual cycle of the total particle number concentration, being up to 20–100 times higher during the austral summer than during the winter (Shaw 1988, Gras 1993, Ito 1993, Hara et al 2011, Weller et al 2011, Järvinen et al 2013, Fiebig et al 2014, Kim et al 2017). The magnitude of this seasonal cycle appears to be higher on the upper plateau of Antarctica than at the coastal Antarctic sites, whereas overall particle number concentration levels are clearly higher at the coastal Antarctica. Particle number size distribution measurements suggest that the summer maximum in particle concentrations can, to a large extend, be explained by NPF taking place in the Antarctic atmosphere. The vertical location of Antarctic NPF has not been well quantified, even though there are some indications that NPF takes more preferably place in the Antarctic FT than in the BL (Koponen et al 2002, Hara et al 2011, Humphries et al 2016).

Regional NPF has been investigated mainly during the summertime in Antarctica, and there are too few data to estimate the frequency of occurrence of this phenomenon. The available information suggests, however, that regional NPF events observed at the surface level are probably less common in the summer Antarctica than they are in the summer Arctic atmosphere (Koponen et al 2003, Park et al 2004, Pant et al 2011, Järvinen et al 2013, Kyrö et al 2013, Weller et al 2015). A study conducted on the upper plateau of Antarctica demonstrates that also wintertime regional NPF is possible in this environment (Järvinen et al 2013). Typical particle formation rates associated with regional NPF in Antarctica are about an order of magnitude lower than those in the Arctic or boreal forest environments, whereas the corresponding particle GRs are comparable to those in other environments (see table 1). In the Antarctic atmosphere, also cases displaying very low particle GRs between about 0.1 and 1 nm h⁻¹ were reported (e.g. Park et al 2004, Weller et al 2015).

When discussing NPF in marine areas, it is important to distinguish between remote marine areas with minimal anthropogenic influence, continental outflow regions with potentially large anthropogenic effects on NPF (e.g. McNaughton et al 2004), and coastal regions which may have their own NPF mechanisms (see section 4.2). Below we discuss shortly NPF taking place in the remote marine areas, with an emphasis on the marine boundary layer (MBL). This region has been of great research interest after the proposed feedback mechanisms between marine sulfur emissions and climate (Charlson et al 1987), in which increased ocean temperatures in a warming climate would cause larger dimethyl sulfide (DMS) emissions to the atmosphere and subsequently increased CCN production due to more efficient NPF and particle growth. Higher CCN concentrations would then result in higher albedos of MBL clouds, causing a cooling effect that would partly compensate for the initial climate warming. The various steps and overall importance of this climate feedback mechanism have been investigated, and debated, a lot during the past three decades (e.g. Ayers and Cainey 2007, Woodhouse et al 2010, Quinn and Bates 2011, Thomas et al 2011, Mahajan et al 2015).

Indications on NPF inside the MBL have been reported from several marine locations (e.g. Covert et al 1992, Hegg et al 1993, Clarke et al 1998a, Weber et al 1999, Petters et al 2006). However, excluding high-latitude marine areas (see section 3.2.3), this phenomenon appears to be sporadic in nature (Covert et al 1996, Heintzenberg et al 2004), requiring quite specific conditions to occur like a very low pre-existing aerosol loading. Regional NPF with subsequent particle growth to larger sizes have been observed only outside tropical MBL, and the reported particle GRs are relatively low, of the order of 1 nm h⁻¹ (O'Dowd et al 2010, Ueda et al 2016).

Following the observations by Bigg et al (1984) and Clarke (1993), Raes (1995) suggested that, instead of NPF inside the MBL, entrainment of particles formed initially in the FT would be the main source of secondary aerosol particles in the remote MBL. Strong support for this hypothesis was later obtained from compilations of ship cruises and aircraft missions (Covert et al 1996, Clarke and Kapustin 2002), as well as from field campaigns combining different types of measurements (Raes et al 1997, Kamra et al 2003, Clarke et al 2013, Quinn et al 2017). The view that regional NPF does not commonly occur in mid- and low-latitude remote MBLs, and that both ultrafine particle and CCN populations in these regions are maintained by a combination of sea-spray emissions from the ocean surface and entrainment from the FT, is further supported by models simulating processes determining the MBL aerosol particle budget (Capaldo et al 1999, Katosheveski et al 1999, Pirjola et al 2000), as well as by large-scale model simulations (e.g. Korhonen et al 2008, Woodhouse et al 2010).

The near absence of primary particle sources and longer aerosol particle lifetimes in the FT compared with the BL make this environment an interesting location from the atmospheric NPF point of view. Furthermore, as discussed is section 3.2.4, FT has been identified as a potentially important source of newly-formed particles into the BL. The characteristics of NPF in different regions and heights of the FT have been investigated with airborne measurements and by conducting measurements at fixed locations on mountains. Below we discuss shortly our current understanding on NPF in the FT based on these two experimental approaches.

By relying on high-altitude aircraft measurements in the FT, Clarke (1993) found an inverse relation between the sub-15 nm particle concentration and aerosol surface area, and concluded that the upper part of the FT provides conditions favorable for NPF. Later measurements confirmed the upper FT as an active area of NPF, especially in the tropics but also in the northern-hemispheric mid-latitudes (Zaizen et al 1996, de Reus et al 2001, Clarke and Kapustin 2002, Singh et al 2002, Heintzenberg et al 2003, Hermann et al 2003, Weigelt et al 2009, Takegawa et al 2014). Several studies reported associations between NPF in the upper FT and convective uplifting, possibly accompanied with emissions from continental surface sources (e.g. Wang et al 2000, Heintzenberg et al 2003, Benson et al 2008, Köppe et al 2009). In many studies, the outflow regions of convective clouds were identified as an active location of NPF (see section 4.3), but there is no proof that the presence of clouds would be a necessary condition for free-tropospheric NPF. In addition to convection, tropopause folds were observed to initiate NPF in the upper FT (Young et al 2007).

Measurements at mountain stations make it possible to investigate regional NPF in the FT, and its connection with FT-BL interactions. Continuous measurements at mountain sites reveal variable frequencies of NPF event days: 64% with a maximum close to 100% during the dry season at Chacaltaya (5240 m a.s.l) in Bolivia (Rose et al 2015b), >35% with a maximum close to 50% during the monsoon and post-monsoon seasons at Pyramid station (5079 m a.s.l) in Nepal (Venzac et al 2008), 15% with moderate spring and late summer maxima at Jungfraujoch (3580 m a.s.l) in Switzerland (Herrmann et al 2015), 52% with a spring maximum and summer minimum at Storm Peak Laboratory (3210 m a.s.l) in Colorado, United States (Hallar et al 2011, 2016), 30% with a summer maximum of about 50% at Izana (2373 m a.s.l) in Tenerife island (Garcia et al 2014), 65% with an autumn maximum of about 90% at Maido observatory (2150 m a.s.l) on Reunion Island (Foucart et al 2018), 11% with a spring maximum of about 20% at Mukteshwar (2180 m a.s.l) in India (Neitola et al 2011), 32% with a spring maximum of 75% at Mount Tai (1534 m a.s.l) in China (Shen et al 2016a), and 23% with no clear seasonal prefence at Puy de Dome (1465 m a.s.l) in central France (Rose et al 2013). Signs of frequent NPF were also reported from three other high-altitude sites: Mount Saraswati (4520 m a.s.l) in the Trans-Himalayan region (Krishna Moorthy et al 2011), Mount Waliguan (3816 m a.s.l) in China (Kivekäs et al 2009) and Mount Lemmon (2790 m a.s.l) in Arizona, United States (Shaw 2007).

In several mountain sites, NPF was found to be strongly associated with upslope valley winds bringing air from lower altitudes, plausibly from the BL (Weber et al 1995, Shaw 2007, Nishita et al 2008, Venzac et al 2008, Rodriqez et al 2009, Shen et al 2016a). In Mukteshwar, a low-altitude mountain site in India, NPF was common only during the spring months when the site was located within the BL (Neitola et al 2011). In Jungfraujoch, Switzerland, NPF was found to be restricted to air masses that had been in contact with the BL within the last couple of days (Bianchi et al 2016). These observations give further support for the important role of surface emissions in causing NPF in the FT.

Reported particle formation rates from different mountain sites span over a relatively large range of values, with the median value being slightly larger than that in the boreal forest environment yet considerably lower than that in other remote or rural environments (table 1). Reported particle GRs at mountain sites are relatively high, comparable to those in many of the sites in the continental BL.

Observations of aerosol particle chemical composition combined with simultaneous measurements of aerosol particle size distributions have been used to identify the chemical composition of the compounds responsible for particle growth in NPF events. Direct observations of nucleation-mode particle chemical composition have been made with thermal desorption chemical ionization mass spectrometer (TDCIMS) (Smith et al 2004) and with nano aerosol mass spectrometer (NAMS) (Wang et al 2006). Of these two instruments, NAMS, measures the atomic composition of the particles, while TDCIMS utilizes a softer ionization method and can identify the chemical composition of the particles in more detail (e.g. Smith et al 2010). However, as most studies do not report detailed composition of the condensable vapors, we will group the identified growth channels into growth by condensation of organic compounds (organic aerosol, OA), sulfate (SO₄), ammonium (NH₄) and nitrate (NO₃).

In addition to chemical composition measurements of the nucleation mode, also size-resolved chemical composition measurements for >30 nm with aerosol mass spectrometer (AMS) (Jayne et al 2000) and non-size resolved submicron aerosol chemical composition measurements with aerosol chemical speciation monitor (ACSM) (Ng et al 2011) have been utilized. In the AMS-based studies two approaches have been used to infer the chemical composition of the growth. If concentrations of the measured compounds are high enough to have good signal levels, the composition of <60 nm particles can be considered to represent the chemical composition once the newly-formed particles have grown above the AMS detection limit (e.g. Zhang et al 2004). On the other hand, the time evolution of the chemical composition of the bulk submicron aerosol can be used to infer the source rate for different chemical compounds if it can be assumed that changes in the submicron aerosol composition are dominated by condensation during the NPF event (e.g. Pierce et al 2011). In most cases, if the size time evolution of the number size distribution is smooth enough to derive formation and GRs during NPF event, also the source rates of OA, SO₄, NH₄ and NO₃ can be derived from the time derivative of the respective AMS mass concentrations (e.g. Vakkari et al 2015).

When comparing chemical composition measurements between the nucleation mode and larger sizes, the effect of volatility needs to be taken into account. This means that as particles grow into larger sizes, (organic) compounds with higher saturation vapor pressure are able condense onto them (Donahue et al 2011). A direct consequence of this is that estimating the growth of nucleation mode particles based on chemical composition measurements of Aitken and accumulation mode particles with an AMS causes an overestimation on the contribution of organic compounds to this growth (e.g. Ehn et al 2014). However, measuring Aitken and accumulation mode particles can be interpreted to represent the composition responsible for the particle growth to CCN-sizes.

Measurements of the composition of compounds contributing to growth have been carried out in diverse environments ranging from urban to remote continental areas. At urban locations, studies have been carried out at Pittsburgh, US (Zhang et al 2004), Beijing, China (Wiedensohler et al 2009, Zhang et al 2011), Bakersfield, US (Ahlm et al 2012), Wilmington, US (Bzdek et al 2012) and Brisbane, Australia (Crilley et al 2014). Additionally, Setyan et al (2014) reported observations made in the urban outflow of Sacramento, US, and Vakkari et al (2015) reported observations made in the urban outflow of Johannesburg, South Africa. All urban studies utilized AMS measurements combined with number size distribution measurements, except Bzdek et al (2012) where a combination of NAMS and number size distributions was used, and Vakkari et al (2015) where a combination of ACSM and number size distributions was used. An overview of the chemical composition of the growth at urban locations is given in figure 5. Two of the above-mentioned urban studies (Wiedensohler et al 2009, Crilley et al 2014) did not report quantitative composition, and are therefore not included in figure 5, nevertheless both these studies concluded that the growth was dominated by inorganic species.

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Observations at regional background locations, representing typically a mixture of anthropogenic and biogenic sources, include Tecamac, Mexico (Smith et al 2008), Lewes, US (Bzdek et al 2012, 2013, 2014) and Welgegund, South Africa (Vakkari et al 2015). The study at Tecamac is based on TDCIMS measurements, the studies at Lewes on NAMS measurements and the study at Welgegund on ACSM measurements. Similar to urban locations, the two main constituents of particle growth at regional sites are OA and SO₄ (figure 5). Likewise, a study utilizing AMS measurements at Melpitz, Germany (Wu et al 2015) identified SO₄, NH₄ and OA as the main compounds responsible for the particle growth, but the fractional contribution of each compound was not estimated. A recent study with TDCIMS at Southern Great Plains, US (Hodshire et al 2016) determined the contributions of OA, SO₄, NH₄ and amines to the particle growth.

In contrast with urban and regional studies, measurements in the environments with least anthropogenic influence indicate the growth dominated by OA ('rural' in figure 4). In this category, we consider observations from Hyytiälä, Finland (Allan et al 2006, Pierce et al 2011, Riipinen et al 2012, Pennington et al 2013), Egbert, Canada (Pierce et al 2011), Whistler Mountain, Canada (Pierce et al 2012) as well as the clean sectors at Cool, US (Setyan et al 2014) and at Welgegund, South Africa (Vakkari et al 2015). Also Han et al (2014) report OA-dominated growth from Wakayama, Japan. Except for Pennington et al (2013) all studies from the rural locations are based on AMS or ACSM measurements.

In summary, the chemical composition of the growing particles depends on the mixture of precursor compounds present at the time of the NPF event. Consequently, as more and more pristine environments are considered, the fraction of OA increases. This is seen clearly at sites that have distinct clean sectors: at a single location the growth can vary from fully OA to SO₄-dominated depending on the air mass origin (Setyan et al 2014, Vakkari et al 2015, Hodshire et al 2016). Finally, it is worth noting that amines have been observed in nucleation and Aitken mode particles at several locations, even though their fractional contribution to the particle growth has not been quantified (Mäkelä et al 2001, Smith et al 2010, Hodshire et al 2016).

The two most widely used indirect approaches to get information on the compounds responsible for the particle growth during atmospheric NPF are to measure the particle hygroscopicity or volatility, or some combination of these two. Hygroscopicity measurements reveal the particle mixing state with respect to their water uptake and are useful in distinguishing between totally water-insoluble material, highly-hygroscopic substances like sulfuric acid or ammonium sulfate, and less-hygroscopic material like a big fraction of secondary organic compounds. Volatility measurements provide additional insight into this chemistry, as compounds with different vapor pressures are expected to be evaporated from particles at different temperatures. Both hygroscopicity and volatility measurements can be conducted with a good time resolution and for several pre-selected particle sizes (e.g. Swietlicki et al 2008, Villani et al 2008).

Hygroscopicity and volatility measurements made in forested environments indicate that both highly-and less-hygroscopic material condense onto particles formed by atmospheric NPF, and that the contribution of highly-hygroscopic material is more important for smaller particles and during the photo-chemically active time of the day (Hämeri et al 2001, Petäjä et al 2005, Ehn et al 2007a, Ristovski et al 2010, Wu et al 2013, Jung and Kawamura 2014). In urban environments, the relative contributions of highly- and less-hygroscopic material to the particle growth seem to vary, in addition to which nucleation mode particles show occasionally an external mixture indicative of two very different sources for these particles (Väkevä et al 2002b, Sakurai et al 2005, Petäjä et al 2007, Park et al 2009). The few measurements made in coastal environments show a relatively high contribution of highly-hygroscopic material in nucleation mode particles and indications of almost insoluble material in the smallest particles (Väkevä et al 2002a, Johnson et al 2005, Park et al 2009). Finally, an investigation conducted at a high-latitude Arctic site, Svalbard, suggests a very large fraction of ammonium sulfate in particles originating from atmospheric NPF (Giamarelou et al 2016).

In a couple of locations, particle volatility measurements have revealed the presence of a practically non-volatile core in growing nanoparticles (Wehner et al 2005, Ehn et al 2007b, Wang et al 2017b). This core was found to occupy about 20%−40% of the particle volume, with no apparent size dependency for this fraction. The origin of the non-volatile core is somewhat unclear but was hypothesized to result from either photochemical or heterogeneous processes that produce extremely non-volatile material into the growing particles (Wang et al 2017b).

In addition to particle hygroscopicity and volatility measurements, a few other experimental techniques have been developed and applied over the years to get information about the chemical composition of nucleation mode particles in the atmosphere. Such techniques include the transition electron microscopy which provides morphological information of particles (e.g. Mäkelä et al 2002, Leck and Bigg 2005, Karl et al 2013), pulse height analyzer ultrafine condensation particle counter used in parallel with mobility size distribution measurements (O'Dowd et al 2003), ultrafine organic tandem differential mobility analyzer which provides an estimate on the organic fraction of particles of pre-selected sizes (Vaattovaara et al 2005, Laaksonen et al 2008), and condensation particle counter battery which reveals the water-affinity of sub-20 nm particles (Kulmala et al 2007, Riipinen et al 2009). While providing some new insight into this topic, the information obtained using these approaches has, in most cases, remained rather qualitative.

A few studies have measured gas-phase concentrations of one or more LVOC compounds and, by assuming their irreversible condensation onto aerosol particles, then estimated how big fraction of the observed particle growth can be explained by these compounds. In case of gaseous sulfuric acid, this fraction was found to be below 10%, on average, at two forested European sites with very different levels of exposure to anthropogenic pollutants (Boy et al 2005, Fiedler et al 2005). A much higher contribution by sulfuric acid, between about 30% and 60%, was reported for the particle growth in Beijing, China (Yue et al 2010). Since the pioneering studies by Ehn et al (2012, 2014), people have gradually started to measure gas-phase concentrations of a subset of highly oxygenated (organic) molecules (HOMs), or their clusters, under field conditions (Mutzel et al 2015, Jokinen et al 2016, Bianchi et al 2017, Frege et al 2017, Mohr et al 2017). HOMs include both ELVOCs and LVOCs (Tröstl et al 2016), so they are very good candidates for the organic compounds that give a major contribution to the growth of newly-formed particles in the atmosphere. Quantitative estimates on how big fraction of the observed particle growth can be explained by different HOMs, or groups of HOMs, do not yet exist for real atmospheric aerosol systems. Finally, it should be noted that a number of studies have estimated the gas-phase concentration of sulfuric acid or (extremely)LVOC organic compounds from direct measurements of their precursor compounds in the gas phase using either available proxies for this purpose (e.g. Petäjä et al 2009, Mikkonen et al 2011, Kontkanen et al 2016c) or by simulating explicitly the precursor gas-phase chemistry, and then used these values to further estimate the particle GR. Most of these studies agree in a broad sense with the results presented above but, because of the inherently large uncertainties associated with these analyses, will not be reviewed here.