Consequences of dynamic and timing properties of 1 new aerosol particle formation and consecutive growth events 2

Dynamic properties, i.e. particle formation rate J6 and particle diameter growth rate 6 GR10, and timing properties, i.e. starting time (t1) and duration time interval (t) of 247 7 quantifiable (class 1A) atmospheric new particle formation (NPF) and consecutive particle 8 diameter growth events identified in the city centre and near-city background of Budapest over 9 6 full measurement years together with related gas-phase H2SO4 proxy, condensation sink (CS) 10 of vapours, basic meteorological data and concentrations of criteria pollutant gases were 11 derived, evaluated, discussed and interpreted. In the city centre, nucleation ordinarily starts at 12 09:15 UTC+1, and it is maintained for approximately 3 h. The NPF and growth events produce 13 4.6 aerosol particles with a diameter of 6 nm in 1 cm of air in 1 s, and cause the particles with 14 a diameter of 10 nm to grow with a typical rate of 7.3 nm h. Nucleation starts approximately 15 1 h earlier in the near-city background, it shows substantially smaller J6 (with a median of 2.0 16 cm s) and GR10 values (with a median of 5.0 nm h ), while the duration of nucleation is 17 similar to that in the centre. Monthly distributions of the dynamic properties and daily 18 maximum H2SO4 proxy do not follow the mean monthly pattern of the event occurrence 19 frequency. The factors that control the event occurrence and that govern the intensity of particle 20 formation and growth are not directly linked. Condensing atmospheric chemical species and/or 21 their processes in the city centre seem to contribute equally to new particle formation and 22 particle growth. In the near-city background, however, chemical compounds available and their 23 processes power particle growth more than particle formation. There is a minimum growth rate 24 of approximately 1.8 nm h that is required for nucleated particles to reach the lower end of 25 the diameter interval measured (6 nm) under the actual/local conditions. Monthly distributions 26 and relationships among the properties mentioned provided several indirect evidence that 27 chemical species other than H2SO4 largely influence the particle growth and possibly 28 atmospheric NPF process as well. The J6, GR10 and t can be described by log-normal 29 distribution. Most of the extreme dynamic properties could not be explained by H2SO4 proxy, 30 CS, meteorological data or pollutant gas concentrations. Approximately 40% of the NPF and 31 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-918 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 1 October 2018 c © Author(s) 2018. CC BY 4.0 License.

growth events exhibited broad beginning, which can be an urban feature.For 9% of all cases, it was feasible to calculate 2 separate sets of dynamic properties.The later onset frequently shows more intensive particle formation and growth than the first onset by a typical factor of approximately 1.4.The first event is of regional type, while the second event, superimposed on the first, is often associated with sub-regional, thus urban NPF and growth process.

Introduction
Molecules and molecular fragments in the air collide randomly, and can form electrically neutral or charged clusters.Most clusters decompose shortly.Chemical stabilising interactions among certain components within a cluster can enhance its lifetime, during which it can grow further by additional molecular collisions through some distinguishable size regimes (Kulmala et al., 2014).If the diameter of these clusters reaches a critical value of 1.5±0.3nm (Kulmala et al., 2013), they become thermodynamically stable, and their further growth turns into a spontaneous process.Supersaturation is a necessary atmospheric condition for this principal conversion.It is virtually a phase transition, which takes place in a dispersed manner in the atmosphere, so it generates an aerosol system.The newly formed particles grow further by condensation to larger particles in most cases due to the existing supersaturation.Photochemical oxidation products such as H2SO4 (Sipilä et al., 2010), extremely low-volatile organic compounds (ELVOCs, Ehn et al., 2014;Jokinen et al., 2015) and highly oxygenated molecules (HOMs, Bianchi et al., 2016;Kirkby et al., 2016;Tröstl et al., 2016) together with H2O vapour, NH3 (Kirkby et al., 2011), amines (Almeida et al., 2013), other oxidation products of volatile organic compounds (VOCs; Metzger et al., 2010;Schobesberger et al., 2013;Riccobono et al., 2014) and NO2 can play an important role in both the formation and growth.The VOCs include compounds of anthropogenic and biogenic origin mainly isoprenoids such as -pinene (Kirkby et al., 2016).In some specific coastal regions, iodine oxides produced from marine biota are involved (O'Dowd et al., 2002).Atmospheric concentration of these key compounds at a level that is smaller typically by 12-14 orders of magnitude than the concentration of air molecules is already sufficient for the phenomenon (Kulmala et al., 2014).Relative importance of the organics increases with particle size (Riipinen et al., 2011;Ehn et al., 2014), and their supersaturation is maintained by fast gas-phase autooxidation chemical reactions of VOCs (Crounse et al., 2013).The overall phenomenon is ordinarily confined in time for 1 day or so, and, therefore, it can be regarded as an event in time, and is referred as new aerosol particle formation (NPF) and consecutive particle growth event.
Such events appear to take place almost everywhere in the world and anytime (Kulmala et al., 2004;Nieminen et al., 2018).Their occurrence frequency and, more importantly, their contribution to particle number concentrations were found to be substantial or determinant in the global troposphere (Spracklen et al., 2006;Kulmala et al., 2014).Moreover, their contribution to the number of cloud condensation nuclei (CCN) can be 50% or even more (Makkonen et al., 2009;Merikanto et al, 2009;Sihto et al., 2011), which links the events to climate system, and emphasizes their global relevance (Kerminen et al., 2012;Carslaw et al., 2013;Makkonen et al., 2012;Gordon et al., 2016).New particle formation and growth events were proved to be common in polluted air of large cities as well with a typical relative occurrence frequency between 10% and 30% (Woo et al., 2001;Baltensperger et al., 2002;Alam, et al., 2003;Wehner et al., 2004;Salma et al., 2011;Dall'Osto et al., 2013;Xiao et al., 2015;Zhang et al., 2015;Kulmala et al., 2017, Nieminen et al., 2018).The coupling and relationships between regional and urban (sub-regional) NPF was demonstrated at least under favourable orographic conditions (Salma et al., 2016b).New particle formation can increase the existing particle number concentrations in city centres by a factor of approximately 2 on nucleation days, while it can produce approximately 28% of ultrafine (UF) particles on a longer (e.g.annual) time scale (Salma et al., 2017).Particle concentrations from NPF are also important when compared to the (primary) particles emitted by their dominant source in cities, namely by road vehicles with internal combustion engines (Paasonen et al., 2016).These jointly imply that particles from NPF and growth events in cities can influence not only the urban climate but can contribute to the public's excess health risk from particle number exposures (Oberdörster et al., 2005;Braakhuis et al., 2014;Salma et al., 2015), and, furthermore, could be linked to the role of human actions in all these effects.
In spite of these potentials, conclusive interpretation of the data obtained and results derived specifically for cities remained hindered so far.Several-year long semi-continuous critically evaluated and coherent data sets are require for this purpose, which have been generated gradually.As part of this international progress, investigations dedicated to urban NPF and growth events in Budapest have been going on since November 2008.Measurements for 5 full years were realised in the city centre at a fixed location, 1 full year was devoted to measurements in a near-city background environment, and some other measurements were accomplished in different urban microenvironments for time intervals of a few months.The main objectives of this study are to determine, present and analyse the dynamic properties, i.e. particle formation rate and particle diameter growth rate, timing properties, i.e. starting time and duration time interval of nucleation process of NPF and growth events together with the major sources and sink of condensing vapours, basic meteorological data and criteria pollutant gases for 6 years, to investigate and interpret their relationships, to discuss their monthly distributions, to evaluate and detect some of their features specific for urban atmospheric environments, and to demonstrate some specific urban influence on the determination of these properties.These quantities and relationships are of basic importance in many atmospheric processes for several reasons, and some of them are also discussed.

Experimental methods
The measurements took place at two urban locations in Budapest, Hungary.Most measurements were realised at the Budapest platform for Aerosol Research and Training (BpART) facility (N 47 28' 29.9'', E 19 3' 44.6'', 115 m above mean see level (a.s.l.; Salma et al., 2016a).This site represents a well-mixed, average atmospheric environment for the city centre.The other location was situated at the NW border of Budapest in a wooded area of the Konkoly Astronomical Observatory of the Hungarian Academy of Sciences (N 47° 30' 00.0 '', E 18° 57' 46.8'', 478 m a.s.l.).This site characterises the air masses entering the city since the prevailing wind direction in the area is NW.The measurements were accomplished for 6 full-year long time intervals, i.e. from 03-11-2008 to 02-11-2009, from 19-01-2012 to 18-01-2013, from 13-11-2013 to 12-11-2014, from 13-11-2014 to 12-11-2015, from 13-11-2015 to 12-11-2016 and from 28-01-2017 to 27-01-2018.In the measurement year 2012-2013, the instruments were set up in the near-city background, while in all other years, they were installed in the city centre.Local time (LT=UTC+1 or daylight saving time, UTC+2) was chosen as the time base of the data unless otherwise indicated because the daily activity time pattern of inhabitants substantially influences the atmospheric processes in cities (Salma et al., 2014).The main measuring system was a flow-switching type differential mobility particle sizer (DMPS).It consists of a radioactive ( 60 Ni) bipolar charger, a Nafion semi-permeable membrane dryer, a 28-cm long Vienna-type differential mobility analyser and a butanol-based condensation particle counter (TSI, model CPC3775).The sample flow was 2.0 L min -1 in the high-flow mode, and 0.31 L min -1 in the low-flow mode with sheath air flow rates 10 times larger than for the sample flows.The DMPS measures particle number concentrations in an electrical mobility diameter range from 6 to 1000 nm in the dry state of particles (with a relative humidity of RH<30%) in 30 channels, which finally yields 27 channels after averaging 3 overlapping channels when joining the data for the 2 flow modes.The time resolution of the measurements was approximately 10 min till 18-01-2013, and 8 min from 13-11-2013 (after a planned update of the DMPS system).There was no upper size cut-off inlet applied to the sampling line, and a weather shield and insect net were only attached.The sampling inlet was installed at a height of 12.5 m above the street level in the city centre, and of approximately 1.7 m in the near-city background.The measurements were performed according to the international technical standard (Wiedensohler et al., 2012).The availability of the DMPS data over 1-year long time intervals are summarised in Table 1.Synoptic meteorological data for air temperature (T), RH, wind speed (WS) and wind direction (WD) were obtained from a measurement station of the Hungarian Meteorological Service (HMS, no.12843) by standardised methods with a time resolution of 1 h.Global solar radiation (GRad) data were measured by the HMS at a distance of 10 km in E direction with a time resolution of 1 h.Meteorological data were available in >90% of the possible cases in each year.Concentrations of SO2, O3, NOx and CO were obtained from measurement stations of the National Air Quality Network in Budapest (in a distance of 4.5 km from the urban site, and of 6.9 km from the nearcity background site) located in the upwind prevailing direction from the measurement sites.
They are measured by UV fluorescence (Ysselbach 43C), UV absorption (Ysselbach 49C), chemiluminescence (Thermo 42C) and IR absorption methods (Thermo 48i), respectively with a time resolution of 1 h.The concentration data were available in >85% of the yearly time intervals.It is worth mentioning that concentration of SO2 in the Budapest area is ordinarily distributed without larger spatial (and temporal) differences (Salma et al., 2011).For the present study, this was actually proved by evaluating the concentration ratios from two different municipal station which were located in 2 different directions with an angle between them of 60 in the closest distance from the BpART.The mean SO2 concentration ratio and standard deviation (SD) for the 2 stations were 81±20% over the 5-year long measurement time interval, which appears to lay within the experimental uncertainty.The assumption can be justified indirectly by a conclusion on the monthly distribution of SO2 concentration in Sect.4.2.

Data treatment
The measured DMPS data were evaluated according to the procedure protocol recommended by Kulmala et al. (2012) with some refinements that are related mainly to urban features (see Sect. 3.1).Particle number concentrations in the diameter ranges from 6 to 1000 nm (N), from showing jointly the variation in particle diameter and particle number concentration density in time were also generated.Identification and classification of NPF and growth events was accomplished on these surface plots (Dal Maso et al., 2005;refined in Németh et al., 2018 for urban sites) on a daily basis into the following main classes: NPF event days, non-event days, days with undefined character, and days with missing data (for more than 4 h during the midday).Relative occurrence frequency of events was determined for each month and year as the ratio of the number of event days to the total number of relevant (i.e.allmissing) days.A subset of events with uninterrupted evolution in time, which are called quantifiable (class 1A) events, were further distinguished because the time evolution of their size distribution functions were utilised to determine the dynamic and timing properties with good accuracy and reliability.

Dynamic and timing properties
Growth rate (GR) of nucleation-mode particles was calculated by mode-fitting method (Kulmala et al., 2012).Particle number median mobility diameter (NMMD) of the nucleation mode were obtained from fitting the individual size distributions by DoFit algorithm (Hussein et al., 2004).The growth rate was determined as the slope of the linear line fitted to the time series of the NMMD data within a time interval around a diameter d, where the dependence could be satisfactorily approximated by linear fit.Since the nucleation mode was mostly estimated by N6-25 in the calculations of the formation rate (see below), and since the median of the related diameter interval (from 6 to 25 nm) is close to d=10 nm, GRs for particles with a diameter of 10 nm were determined (GR10).This type of GR can be interpreted as an average GR as far as the given particle diameter range is concerned, but it actually expresses the beginning of the growth process only, which may have considerable effects on the formation rate calculations in specific cases (see later).Time evolution of an aerosol population is described by the general dynamic equation which was rearranged, simplified and approximated by several quantities (Kulmala et al., 2001;Dal Maso et al., 2002;Kulmala et al., 2012;Cai and Jiang, 2017) to express the formation rate J6 of particles with the smallest detected diameter of dmin=6 nm in a form actually utilised in the present evaluation as The first term on the right side of Eq. 1 expresses the concentration increment.The particle number concentration in the size range from 6 to 25 nm (N6-25) was selected to approximate the nucleation-mode particles NnucN6-25.This is a usual and reasonable choice because it was proved to be advantageous and effective way in handling fluctuating data sets since N6-25 often exhibits less sensitivity and smaller scatter in time than the fitted area of the nucleation mode.
It is implicitly assumed that the intensity of the NPF is constant for a certain time interval, and, therefore, dN6-25/dt can be determined as the slope of the linear function of N6-25 versus time t within an interval where the dependence could be satisfactorily approximated by linear fit.A limitation of the relatively wide size range (6-25 nm) selected can be manifested by disturbances from primary particles in particular in urban environments.This is taken into account by the last term of Eq. 1, and is discussed later.The second term on the right side of Eq. 1 expresses the loss of particles due to coagulation scavenging (due to pre-existing larger particles).The coagulation scavenging efficiency for particles with a diameter of 10 nm (CoagS10) was selected to approximate the mean coagulation efficiency of nucleation-mode particles (CoagSnuc).This diameter was chosen by considering the median of the related diameter range, which was discussed above for GR.The coagulation efficiency was calculated from classical aerosol mechanics with adopting a mass accommodation coefficient of 1 and utilizing the Fuchs' transition-regime correction factor separately for all the size channels belonging to the selected size range (Kulmala et al., 2001;Dal Maso et al., 2005;Kulmala et al., 2013) by using the computation scripts of the University of Helsinki.Self-coagulation within the nucleation mode was neglected due to its limited concentration.Hygroscopic growth of particles was not considered since this depends on chemical composition of particles, which is unknown but expected to change substantially in time.The third term on the right side of Eq. 1 expresses the particle growth out of the considered size range by condensation of vapours.
The GR10 was selected to approximate a representative value at the median of the particle diameter range considered (Vuollekoski et al., 2012).It is implicitly assumed that GR10 can be regarded to be constant over the time interval of interest.Nevertheless, the diameter growth of nucleation-mode particles in time is occasionally strongly limited (Fig. S1a).In these specific cases, the mean relative area of the nucleation mode below 25 nm was determined by fitting the individual size distributions around the time of the maximum nucleation-mode NMMD, and the ratios were averaged.The correction in form of the mean relative area was adopted as a multiplication factor for the growth out term in Eq. 1.On a very few days, the particle growth was followed by a decrease in nucleation-mode NMMD (Salma et al., 2016a).In these cases, the shrinkage rate (with a formal GR10<0) was derived and adopted.The fourth term on the right side of Eq. 1 expresses the contribution of (high-temperature) emission sources, usually vehicular road traffic (Paasonen et al., 2016;Salma et al., 2017) to the N6-25, which can provisionally disturb the assumption of NnucN6-25.A typical example of such a situation is shown in Fig. S1b from 10:09 to 12:23 LT.In these specific cases, the contribution of primary emissions was estimated from the slope of the time series of the fitted peak area of the Aitken mode below d<25 nm (NAi,<25) in the time region of interest.Reliable separation of the nucleation and Aitken modes from each other was hindered or was not possible for a few individual size distributions due to overlapping modes and scatter in the concentration data, and these individual Aitken-mode areas were excluded from or skipped in the time series.Relative contributions of the concentration increment, coagulation loss and growth out from the diameter intervalwhich were significant in all calculationsto J6 are decreasing in this order with mean values of 71%, 17% and 12%, respectively (Table S1).
The formation and growth rates for the measurement years of 2008-2009 and 2012-2013 were obtained earlier by a slightly different way and neglecting the urban features (Salma et al., 2011(Salma et al., , 2016b)).To obtain consistent data sets, the dynamic properties for these 2 years were reevaluated now by adopting the refinements described above and implementing the experience gained over the years.The mean new-to-old rate ratios with SDs for the GR10 and J6 were 1.06±0.32and 1.23±0.37,respectively in the city centre (2008)(2009) and 1.04±0.21and 1.20±0.35,respectively in the near-city background (2012)(2013).The re-calculation yielded non-negligible improvements for the mean formation rates.Some individual formation and growth rates, in particular the smaller values, were substantially impacted.
The assumption and estimations above usually represent a reasonable approximation to reality.
The N6-25 is derived from the experimental data in a straightforward way, the GR10 and the corrections for primary particles and limited particle growth depend on the quality of the size distribution fitting program as well, while the CoagS10 is determined by using a theoretical model.The resulting accuracies of the dynamic properties, in particular of J6, look rather complicated, and depend on the spatial heterogeneity in the air masses measured particularly for the observations performed at a fixed site, size and time resolution of the concentrations measured, diameter range of the size distributions, fluctuations in the experimental data, selection of the particle diameter channels (interval), choice of the time interval of interest (for linear fits), sensitivity of the models to the uncertainties (Vuollekoski et al., 2012), and also on the extent of the validity of the assumptions appliedparticularly under highly polluted conditions (Cai and Jiang, 2017).The situation is further complicated with the fact that the dynamic (and also the timing) properties are connected to each other.Finally, it is important to recognise that some NPF and growth curves on the surface plots have rather broad starting time interval (Fig. S1a and S1c).They occur in a considerable abundance in cities, e.g. in 40% of all quantifiable events in Budapest (Sect.4.4).This may yield badly defined or composite dynamic properties, whose uncertainty can have principle limitations overwhelming the experimental and model uncertainties.
Timing properties of NPF and growth events are increasingly recognised, and they can provide very valuable information even if they are estimated indirectly from the observed diameter interval >1.5 nm (Sect.1).The earliest estimated time of the beginning of a nucleation (t1) and the latest estimated time of the beginning of a nucleation (t2) were derived by a comparative method (Németh and Salma, 2014) based on the variation in the content of the first size channel of the DMPS system.Both time parameters includes a time shift that accounts for the particle growth from the stable neutral cluster mode at approximately 2 nm to the smallest detectable diameter limit of the DMPS systems (6 nm in our case) by adopting the GR value in the size window nearest to it in size space.The difference t=t2-t1 was considered as the duration time interval of the nucleation process.It represents the time interval during which new aerosol particles are generated in the air.The uncertainty of the timing parameters is regarded to be around 30 min under ordinary NPF and growth situations.

Sources and sink
Gas-phase H2SO4 was not measured in the campaigns, and its relative effect was estimated by its proximity measure (proxy) containing both the major source and sink terms under steadystate conditions according to Petäjä et al. (2009).It was calculated for radiations >10 W m -2 .In principle, it is possible to convert the H2SO4 proxy values to H2SO4 concentrations by an empirical scaling factor of k=1.4×10 -7 ×GRad -0.70 , where GRad is expressed in a unit of W m -2 (Petäjä et al., 2009).The factor was, however, derived for a remote boreal site, and, therefore, we usually prefer not to perform the conversion since urban areas are expected to differ from the boreal regions, and adopting the factor could distort the dynamic relationships or time trends Condensation sink for vapour molecules onto the surface of existing aerosol particles was computed for discrete size distributions as described in earlier papers (Kulmala et al., 2001;Dal Maso et al., 2002, 2005) and summarised by Kulmala et al. (2013).The equilibrium vapour pressure of the condensing species was assumed implicitly to be negligible at the surface of the particles, so similar to sulfuric acid.Dry particle diameters were considered in the calculations.

Results and discussion
Annual median particle number concentrations based on the individual data in the near-city background in 2012-2013, and in the city centre for the separate measurement years of 2008-2009, 2013-2014, 2014-2015, 2015-2016 and 2017-2018 were 3.4×10 3 , and 11.5×10 3 , 9.7×10 3 , 9.3×10 3 , 7.5×10 3 and 10.6×10 3 cm -3 , respectively, which indicate some overall decreasing trend in the city centre.There was no obvious pattern in the distribution of monthly median particle number concentrations.The mean UF/N ratio with SD for the same measurement time intervals were 67±14%, and 79±6%, 75±10%, 75±11%, 76±11% and 80±10%, respectively.The values correspond to ordinary urban atmospheric environments in Europe (Putaud et al., 2010).An overview on the number of classified days separately for the 1-year long measurement time intervals is given in Table 1.The availability of the daily size distribution surface plots with respect to all days ensures that the data are representative on yearly and monthly time scales, except for 08 and 09-2015, when there were missing days in larger ratios.The number of quantifiable event days (248 cases) is also considerable, which establishes to arrive at firm conclusion on the NPF and growth events as well.event days, non-event days, undefined days, missing days and the coverage of relevant days with respect to all days in the near-city background and city centre separately for the 1-year long measurement time intervals.

Environment
Background Centre It was previously shown that the NPF and growth events observed in the city centre and its background ordinarily happen above a larger territory or region (Salma et al., 2011;Németh and Salma, 2014), and they are linked to each other (Salma et al., 2016b).From the point of the occurrence frequency distribution, they could, therefore, be evaluated jointly in the first approximation.An overall monthly mean relative occurrence frequency of nucleation days derived for all 6 measurement years is shown in Fig. 1.The annual mean frequency with SD was 22±5%, which is considerable and is in line with other urban sites (Sect.1).The monthly mean frequency has a temporal variation, which can be characterised by a noteworthy pattern.
The mean monthly dependency exhibits an absolute and a local minimum in January (5.6%) and August (21%), respectively, and an absolute and a local maximum in April (40%), and September (31%), respectively.Nevertheless, the SDs of the monthly (and annual) means indicate prominent variability from year to year.The pattern can be related to multivariate relationships and complex interplay among the influencing factors, which include the air temperature (January is the coldest month, while August is the warmest month in the Carpathian Basin) and enhanced emission of biogenic VOCs in springtime (March-April) and early autumn (September) as well (Salma et al., 2016b).The properties and variables studied were derived in full time resolution.They were averaged in several ways for different conditions and for various purposes to obtain typical average descriptive characteristics.In 1 case (31-08-2016), the NPF and growth event could reliable be identified, while the measured absolute particle number concentrations could not be validated due to some experimental troubles, and, therefore, it was left out from the further calculations.Similarly, there were 1 and 4 NPF and growth events with unusually/extraordinarily large dynamic properties in the measurement years 2014-2015 and 2017-2018, respectively.More specifically, 5 individual J6 data when expressed in a unit of cm -3 s -1 and 1 individual GR10 data when given in nm h -1 were >20 (Table 3).These extremes were left out from the overview statistics to maintain the representativity (they could be influenced by some unknown extra or very local sources) and to fulfil better the basic requirements of correlation analysis.If an event showed a double beginning then the dynamic properties for the first onset were considered in the basic overview since this onset is of regional relevance (Salma et al., 2016b).The extreme dynamic properties and the characteristics for the second onsets were, however, evaluated separately and are discussed in detail and interpreted in Sect.4.4.

Ranges and averages
Ranges and averages with SDs of formation rate J6, growth rate GR10, starting time of nucleation (t1) and duration time interval of nucleation (t) are summarised in Table 2 for separate measurement years and for the joint 5-year long city centre data set.In the city centre, nucleation generally starts at 09:15 UTC+1, and it is typically maintained for approximately 3 h.The NPF and growth events ordinarily produce 5.6 new aerosol particles with a diameter of 6 nm in 1 cm 3 of air in 1 s, and cause the particles with a diameter of 10 nm to grow with a typical rate of 7.6 nm h -1 .The statistics for J6 and GR10 are based on 199 and 203 events, respectively.The corresponding data for the separate years show considerable variability without obvious trends or tendencies.The differences between the years can likely be related to changes in actual atmospheric chemical and physical situations and conditions, and to the resulting modifications in the sensitive balance and delicate coupling among them from a year to year.Spread of the individual data for GR10 is smaller than for J6; the relative SDs for the joint 5-year long city centre data set were 38% and 68%, respectively, while the (external) relative SDs calculated from the annual mean values were 4.2% and 14.0%, respectively.The dynamic properties and t1 data tend to be smaller in the near-city background than in the city centre.In general, nucleation starts 1 h earlier in the background, and the events typically show significantly smaller J6 (with a median of 2.0 cm -3 s -1 ) and GR10 (with a median of 5.0 nm h - 1 ).Duration of the nucleation is very similar to that in the city centre.All starting times of nucleation were larger than (in a few cases, very close to) the time of the sunrise.This implies that no nocturnal NPF and growth event has been identified in Budapest so far.The particle growth process (the so-called banana curve) could be traced usually for a longer time interval (up to 1.5 d) in the background than in the centre.These conclusions are in line with the ideas on atmospheric nucleation and consecutive particle growth process (e.g.Kulmala et al., 2014;Zhang et al., 2015), and they also confirm some our earlier findings with respect to Budapest and its regional background within the Carpathian Basin achieved with shorter, 2-year long data sets (Salma et al., 2016b).Ranges and averages with SDs of some related atmospheric properties, namely of mean CS averaged for the time interval from t1 to t2, daily maximum gas-phase H2SO4 proxy, daily mean T and RH (Table S2), and of daily median concentrations of SO2 (as the major precursor of gasphase H2SO4), O3 (as an indicator of photochemical activity), NOx and CO gases (as indicators of anthropogenic combustion activities and road vehicle emissions) (Table S3) were also derived for quantifiable NPF and growth event days, and are further evaluated.The annual mean CS values exhibited decreasing tendency in the city centre over the years (as can be expected from the particle number concentrations as well).The individual values remained below approximately 20×10 -3 s -1 , which agrees well with the results of our earlier study (Salma et al., 2016b) according to which the CS suppresses NPF above this level in the Carpathian Basin.Maximum H2SO4 proxy values reached substantially higher levels (by a factor of approximately 2) in the near-city background than in the city centre due mainly to the differences in the CS and also [SO2].The differences between the 2 sets of proxy data (between the 2 sites) are particularly evident when considering their smallest values.The largest variability in the annual average values were observed for the proxy.A maximum concentration of H2SO4 molecules of 10 6 -10 7 cm -3 were estimated by adopting the scaling factor (Sect. 3.2).
The dynamic properties seem to be not very sensitive to air T; which displayed quite similar and comparable values over the years and at both sites.This conclusion is likely linked to several temperature-dependent environmental processes simultaneously present in the area which balance the effect of T. Some events happened at daily mean temperatures below zero.
The daily mean RH and its SD for the city centre and near-city background were 54±11% and 64±12%, respectively.There were events that occurred at RHs as high as 90%.Relationships of the dynamic properties with T and RH are also obscured with strong seasonal cycle of these meteorological data and with the fact that air masses arriving to the receptor site in different trajectories are often characterised by the distinct levels of meteorological data.As far as the pollutant gases are concerned, SO2 showed somewhat smaller daily median values, and O3 exhibited substantially smaller levels on event days in the city centre than in the near-city background, while concentrations of NOx and CO were obviously larger in the city than in its close background.The differences can primarily be explained by the intensity and spatial distribution of their major sources and atmospheric chemical reactions, and the joined concentration data resembles typical situations without photochemical smog episodes in cities.
There was no obvious decrease in SO2 concentration during these years in contrast with an earlier decreasing trend from mid-1980s till about 2000.No evident or sensitive effect of atmospheric gases on the dynamic or timing properties could be deduced from the averaged data.This can probably be explained by a dedicated balance between the intensifying and suppressing effects, which were averaged out on a yearly time scale.Relationships on shorter scales are further investigated and discussed in more detail in the following sections.

Monthly distributions
Distributions of the monthly mean J6, GR10, daily maximum gas-phase H2SO4 proxy, mean CS, daily mean air T and RH, and daily median SO2, O3, NOx and CO concentrations for quantifiable NPF and growth events for the joint 5-year long city centre data sets are shown in Fig. 2. The distributionseminently for J6, GR10, H2SO4 proxy and SO2do not follow the monthly pattern of the event occurrence frequency at all (cf.Fig. 1).Instead, the J6, GR10 and H2SO4 proxy tend to exhibit larger values in summer months, and they temporal changes over the other months are smooth and do not show distinctive features.The elevations are substantial; the estimated maximum level was larger than the baseline by a factor of 2.1 for the J6, and by a factor of approximately 1.4 for the GR10 and H2SO4 proxy.The result is in line with other observations according to which the GR exhibits almost exclusively a summer maximum (Nieminen et al., 2018).The intensity of solar radiation at the surface, its seasonal cycling, concentration of atmospheric condensing vapours in different months, biogenic processes and the fact that rate coefficient of many thermal chemical/physicochemical processes in the nature (including GR, Paasonen et al., 2018) increases with T could play an important role in explained the distributions of the dynamic properties, although a more comprehensive study involving chemicals and their photochemistry is required for more detailed explanation.The properties are biased and influenced jointly by the intensity of the solar electromagnetic radiation.
Nevertheless, the misalignment between the monthly distributions of occurrence frequency and all the other properties indicates that 1) the event occurrence or its basic causes are not linked with the dynamic properties in a straightforward or linear manner, and 2) gas-phase H2SO4 does not seem to be the controlling factor of NPF occurrence in the Carpathian Basin including Budapest.The mean J6, GR10 and H2SO4 proxy data still have considerable uncertainty, which makes their interpretation not yet completely conclusive.The uncertainties are influenced by the inherent fluctuations in the data sets, number of the individual data available for different properties and months, variations in other or unknown relevant environmental conditions, and by their variability from a year to year.The resulting uncertainties are expected to decrease with the length of the available data sets, which emphasized the need for continuation of the measurements.The monthly distributions of CS, and SO2 and NOx concentrations could be represented by constant values of the overall means and SDs of (9.4±4.3)×10 - s -1 , 4.7±2.1 µg m -3 and 81±38 µg m -3 , respectively with an acceptable accuracy.This suggests that CS, SO2 and NOx in Budapest do not critically or substantially affect either the dynamic properties (or the event occurrence).Monthly distributions of air T and O3 concentration showed a maximum over summer months, while RH reflected the T tendency.Distribution of CO was more changing and less certain than for the other gases, and, therefore, its interpretation is encumbered so far.However, it doesn't seem to obviously affect the dynamic properties.

Relationships
Pearson's coefficients of correlation (R) between J6 and GR10 revealed significant linear relationship between them for all annual data sets (the mean R and SD were 0.768±0.099,number of data pairs n=243).It has to be noted that J6 and GR10 are not completely independent variables (see Eq. 1 and Table S1).Scatter plots between J6 and GR10 for the separate 1-year long measurement time intervals are shown in Fig. 3.For the city centre, the regression lines follow the line of equality in all 5 years.The mean slope (b) with SD for the joint 5-year long city centre data set was b=0.94±0.07expressed formally in a unit of cm -3 s -1 nm -1 h.At the same time, the regression line for the near-city background deviated significantly from the J6=GR10 line, with a b=0.67±0.10cm -3 s -1 nm -1 h.This implies that the relevant chemical species and/or their processes in the air of the city centre contribute equally to the formation of 6-nm particles and to their growth process.In the near-city background, however, the chemical compounds available and their processes power particle growth more than new particle formation.This may be related to the differences between the city and its close environments as far as the atmospheric composition, chemistry and physics, and other delicate conditions are concerned (Paasonen et al., 2018).The narrower range and smaller number of individual dynamic properties available in the near-city background relative to those in the city centre may represent some weakness in the explanation.The intercepts (a) of the regression lines were, however, identical for all data sets within their uncertainty interval.The mean intercept and SD were estimated to be -1.7±0.8 cm -3 s -1 .This finding is interpreted as the existence of a minimum GR or more exactly of a minimally required GR that corresponds to J6=0.Particles that exhibit at least this level of GR can escape coagulation mainly with larger particles, and reach the diameter of 6 nm detectable in the present study by condensational growth.The minimal GR was derived as GRmin= -a/b, and its mean and SD are 1.8±1.0nm h -1 for the conditions ordinarily present in the Budapest air.Nucleation processes which are initiated under circumstances that cause the newly formed particle with a diameter of 10 nm to grow with a rate <GRmin are normally not observed.Anyway, these are expected to be weak phenomena due to the relationship between GR10 and J6, while the events close to it can also be masked by fluctuating experimental data.Their identification and evaluation can be made feasible by decreasing the lower measurement diameter limit of DMPS systems down to 3 nm, or by different instruments such as particle size magnifier or neutral cluster and air ions spectrometer.

Extreme and multiple events
The joint 6-year long data sets of J6, GR10 and t containing all, 247 individual data each could be characterised by lognormal distribution function.This is demonstrated by log-probability graph for J6 in Fig. S2 as example.The coefficient of determination, median and geometric standard deviation for J6, GR10 and t data sets were 0.990, 4.0 cm -3 and 2.3; 0.993, 6.8 nm h - 1 and 1.46; and 0.998, 02:57 (0.123 d) and 1.74, respectively.One of the major properties of this distribution type is that it contains relatively large individual data with considerably high abundances.There were 5 individual J6 and 5 individual GR10 data above the 98% percentile of the data sets, which belonged to 9 separate NPF and growth events (days).Their specifications, properties and parameters are summarised in Table 3.All these events occurred in the city centre from April to September.Their number in the separate consecutive measurement years (Sect.2) were 1, 0, 1, 2, 0 and 5, respectively.The medians of J6, GR10, CS and air T for the subsets of these 9 extreme event days were larger by factors of 5.2, 2.4, 1.5 and 1.4, respectively than for the city centre data, while the medians of the other properties and concentrations in these 2 respective data sets agreed within approximately 10%.There was a single event associated with an extreme H2SO4 proxy (of 23×10 -5 g m −5 W s) and relatively low NOx concentration (44 µg m -3 ), which indicate exceptionally favourable conditions for NPF and growth.In addition to this case, there were only a few (1-2) days that were characterised by an unusually large CS (23×10 -3 s -1 )which could in turn be linked to higher dynamic rates (Sect.4.3)or by somewhat larger SO2 (8.1 µg m -3 ) or lower NOx concentration (34 µg m -3 ).For all the other events, however, no simple or compound property of the investigated variables could explain the extreme rates.Instead, they may be related to some other chemical species and/or atmospheric processes, which were not including in the present study.Since the extreme NPF and growth events usually resembled the time evolution for regional events (well developed banana curves)sometimes with multiple onsets -, the missing atmospheric players in increased concentrations or their relevant processes are expected to appear on a larger horizontal spatial scale.
Table 3. Date (in a format of dd-MM-yyyy), new particle formation rate J6 (in a unit of cm -3 s -1 ), particle diameter growth rate GR10 (nm h -1 ), starting time t1 of nucleation (HH:mm UTC+1), duration time interval t=t2-t1 of nucleation (HH:mm), mean condensation sink CS during the nucleation process (10 -3 s -1 ), daily maximum gas-phase H2SO4 proxy (10 4 g m −5 W s), daily mean air temperature T (C), daily mean relative humidity RH (%), daily median concentrations of SO2, O3, NOx (µg m -3 ) and CO (mg m -3 ) gases, and the type of the onset for extreme quantifiable (class 1A) new particle formation and growth events.Each quantifiable NPF and growth event was labelled as ordinary or broad by visual inspection of its beginning part.If the width of the beginning was smaller than approximately 2 h or there was a determinant single growth curve (rib) on the size distribution surface plot then the onset was labelled as ordinary, otherwise as broad (Fig. S1a and S1c for broad onsets).Broad onsets can be generated by 1) long-lasting nucleation process, 2) disrupted and started over nucleation due to changing atmospheric and meteorological conditions or 3) multiple nucleation processes close to each other in time (Salma et al., 2016b).The broad onsets were specified as doublets if the nucleation mode could be separated into 2 submodes by size distribution fitting.
Approximately 40% of all quantifiable events had a broad onset.This indicates that NPF and growth events with broad/multiple onsets are abundant in the urban environment.This could be an important difference from remote or clean atmospheres.For 9% of all cases, it was feasible to calculate 2 sets of dynamic properties for onsets 1 and 2, respectively with a reasonable accuracy.In the near-city background, the medians of J6 and GR10 for the onset 1 were similar or somewhat smaller than the corresponding medians for the whole near-city background data set, while for the onset 2, they were substantially larger, namely 4.1 cm -3 s -1 and 10.0 nm h -1 , respectively (cf.Table 2).Actually, the latter values were closer to the medians of the city centre than for the near-city background.The dynamic properties for the city centre for both the onset 1 and onset 2 were somewhat larger than for the whole the city centre data set.Approximately 75% of the doublets resulted in individual onset2/onset1 ratios larger than unity.Their overall median ratios for J6 and GR10 were similar and approximately 1.4, while for the near-city background, they were about 2. The results are in line with and confirm our earlier conclusion according to which the second onsets (if it is a new formation process and not just a started over event) often generate new particles more intensively than the first onsets (Salma et al., 2016b).
These particles also grow faster.This can be explained by the fact that the first event is often or likely of regional scale since its dynamic properties resemble those of the regional background process (Yli-Juuti et al., 2009), while the later event can be characterised by values typical for the city centre (Salma et al., 2016b).The later event (or events) are mainly caused and governed by sub-regional processes.These findings are also coherent with a previous observation of NPF and growth events with multiple onsets in semi-clean savannah and industrial environments (Hirsikko et al., 2013), and they also fit well into the existing ideas on mixing regional and urban air parcels that exhibit different properties such as precursor concentrations, T and RH (Kulmala et al., 2017).

Conclusions
Dynamic and timing properties of 247 NPF and growth events were studied together with supporting aerosol properties, meteorological data and pollutant gas concentrations in near-city background and city centre of Budapest for 6 years.The results and conclusions derived here can form in important component that is based on atmospheric observations, and is to be combine with results from laboratory experiments and finally, with theoretical models to further improve our understanding on the NPF potentials to increase UF and CCN concentrations on various spatial and temporal scales.Magnitude of the particle number concentration level produced solely by NPF and growth (strength of the events) can roughly be estimated by considering the median J6, median duration of the nucleation process (Table 2) and the typical coagulation loss of these particles (0.17; Sect.3.1 and Table S1).In central Budapest, it yields a concentration of 10 4 cm -3 , which is comparable to the annual median concentrations (Sect. 4).This simple example indicates that the phenomenon is not only relevant for aerosol load and climate issues on larger/regional or global spatial scales (which were first recognised) but it can affect the urban climate and the health risk of inhabitants of cities as well.This recognition lead to emergence of the urban studies.At present, there is an evident and strong need for continuous urban NPF and growth studies on long term at fixed locations including relevant precursors and potential chemical participants of the phenomenon.They can also contribute to our general understanding of the nucleation phenomenon when their specialities and peculiarities are resolved and taken into account when dealing with its various implications.
The present research based on ambient atmospheric measurements provided several evidence that some important chemical players in the NPF and growth events are still missing.
Considering the results and conclusions of cloud chamber experiments, these factors are expected to be related mainly to oxidation products of VOCs and/or their processes.Further dedicated research including sophisticated measurements, data evaluations and modelling studies is required to find and identify these species and their processes, and to account their multifactorial role in more detail.Such measurement campaign focusing on chemical composition of molecular clusters, precursors and nucleating vapours by applying recent expedient instruments in Budapest over the months of the highest expected event occurrence has been just realised within a frame of an international cooperation.Its perspective results can hopefully provide additional and valuable information for some of the conclusion base on indirect evidence so far, and can further clarify the overall picture on urban multicomponent nucleation and growth phenomenon.
Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-918Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 1 October 2018 c Author(s) 2018.CC BY 4.0 License.investigated.The conversion was applied only to estimate the order of average H2SO4 atmospheric concentration levels.The results derived by utilising the proxy are subject to larger uncertainties than in other cases because of these limitations, but they may indicated gross tendencies.

Figure 1 .
Figure 1.Monthly mean relative occurrence frequency of new aerosol particle formation and consecutive particle diameter growth events with respect to the number of relevant days for the joint 6year long data set.The error bars show ±1 standard deviation, the horizontal line in cyan indicates the overall annual mean frequency, the yellow bands represent ±1 standard deviation of the annual mean, and the smooth curve in red serves to guide the eye.

Figure 2 .
Figure 2. Distribution of monthly mean aerosol particle formation rate J6 in a unit of cm -3 s -1 and particle diameter growth rate GR10 in a unit of nm h -1 (a), mean condensation sink for vapours (CS) in a unit of s -1 averaged over the nucleation time interval (t1, t2) and daily maximum gas-phase H2SO4 proxy in a unit of µg m −5 W s (b), daily mean air temperature (T) in a unit of C and daily mean relative humidity (RH) in % (c), and daily median concentrations of SO2, O3, NOx and CO for quantifiable (class 1A) new particle formation and growth events in the city centre for the joint 5-year long time interval.The error bars are shown for one side for clarity, and indicate 1 standard deviation.Number of the individual data averaged in each month is displayed next to the symbols.The horizontal lines indicate the overall mean.The nonlinear curves assist to guide the eye.

Figure 3 .
Figure 3. Scatter plots for aerosol particle formation rate J6 and consecutive particle diameter growth rate GR10 in city centre (a and c-f) and near-city background (b) separately for the 1-year long measurement time intervals.Number of data point (n), their coefficient of correlation (R) and the intercept (a) and slope (b) of the regression line with standard deviations are also indicated.The lines in black represent the line of equality J6=GR10, the solid lines in red show the regression lines, while the dashed parts in red are extrapolated from the regression line.

Figure 4 .
Figure 4. Dependence of the growth rate GR10 (in a unit of nm h -1 ) of new particle formation and growth events normalised to the daily maximum gas-phase H2SO4 proxy (µg m −5 W s) on the reciprocal proxy value in the city centre and near-city background.The linear line in red represents the line fitted to the joint data set.Number of individual data considered (n), their coefficient of determination (R 2 ) and the intercept (a) and slope (b) of the fitted regression line with standard deviations are also shown.

Table 1 .
Number of days with new aerosol particle formation and growth event, quantifiable (class 1A)

Table 2 .
Ranges , averages and standard deviations of aerosol particle formation rate J6, particle diameter growth rate GR10, starting time (t1) and duration time interval (t=t2-t1) of nucleation process of quantifiable (class 1A) new particle formation and growth events in the near-city background and city The cells in yellow indicate the values which are above the 98% percentile of the corresponding data sets.N.a.: not available.Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-918Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 1 October 2018 c Author(s) 2018.CC BY 4.0 License.