MALTE is a one-dimensional model comprised of boundary layer meteorology, biogenic emission of volatile organic compounds, gas-phase chemistry and aerosol dynamics in order to predict particle formation and growth processes under atmospheric conditions (Boy et al., 2006). Here, we apply the zero-dimensional version, namely the MALTE-BOX model, to simulate NPF events at the SORPES station. In the MALTE-BOX model, boundary layer meteorology and biogenic emission modules are switched off; instead, the biogenic and anthropogenic VOC emissions and their following transport and dispersion are calculated by the regional chemical transport model WRF-Chem. Concentration of various organic compounds at the SORPES station predicted by WRF-Chem model are input into MALTE-BOX model every 10 min (Table 1 provides the compounds calculated by WRF-Chem as input to MALTE-BOX). Likewise, measured concentrations of trace gases including CO, SO2, NO, NO2 and O3, with the same temporal resolution, are also included as input fields. In addition to gas phase precursors, the inputs also include an initial particle number size distribution at 00:00 LT on each day, ambient temperature, relative humidity and the condensation sink of sulfuric acid (as defined in Sect. 2.3).

In the MALTE-BOX model, particles are assumed to be spherical. A fixed sectional approach with 40 size bins ranging from 1.4 to 2000 nm in diameter is used in the present study. The aerosol dynamics has all basic aerosol processes, including nucleation, condensation, coagulation and deposition. The new particle formation rates of newly formed clusters are estimated by the kinetic nucleation theory of sulfuric acid (Sihto et al., 2006), which is related to the sulfuric acid concentration as follows: J=k1×[H2SO4]2, where k1 is the kinetic coefficient that includes both the collision frequency and the probability of forming a stable cluster after the collision. Kinetic nucleation theory has been shown to have good performance in simulating cluster formation in various environments including both clean continental area and polluted urban site (Wang et al., 2013b; Zhou et al., 2014). The nucleated particles were added to the first size bin in the model.

We conducted a set of sensitivity simulations to establish a suitable value for the nucleation coefficient k1. After comparing the simulations and DMPS measurements, k1 was set to 6.0 × 10-13 cm3/# for 10 July and 22 August, and 2.2 × 10-10 cm3/# for 22 June. These values were similar to those we commonly used in the simulations for NPF at other stations (Boy et al., 2008a; Paasonen et al., 2010; Zhou et al., 2015). The high value on 22 June might imply that other low-volatility vapours – most probably from anthropogenic origin – are involved and play a crucial role in the particle formation process at this site. Moreover, being limited by the detectable size of the DMPS (we can monitor particles larger than 6 nm in diameter), means that the observed formation process could be steered by the condensational growth of the smallest clusters to the detection limit.

We included relevant chemical reactions of the MCM (Master Chemical Mechanism) in this model, as described in Boy et al. (2013). The chemistry scheme included the full MCM chemical paths for the following parent molecules: methane, methanol, formaldehyde, acetone, acetaldehyde, 2-methyl-3-buten-2-ol (MBO), isoprene, alpha-pinene, beta-pinene, limonene and beta-caryophyllene. The Kinetic PreProcessor (KPP) was applied to numerical solving for the concentrations of each individual compound (Damian et al., 2002), except for those species whose concentrations were manually input from direct measurements and the WRF-Chem model. Apart from sulfuric acid, about 20 low-volatility organic compounds (ELVOCs) and seven selected semi-volatile organic compounds (SVOCs) are regarded as condensing vapours, following the simplified chemical mechanism presented by Ehn et al. (2014). Specifically, seven representative SVOCs (MCM-nomenclature: C719OOH, LIMALOOH, C924OOH, NORLIMOOH, C811OOH, C818OOH and C819OOH) with vapour pressures estimated to range from 104 to 106 molecules cm-3 (using the group contribution method described by Nannoolal et al., 2008) and recently detected ELVOCs (C10O5-12Hx, C10NO5-13Hx and C20O8-16Hx) with vapour pressures between 10 and 103 molecules cm-3 are included as condensing vapours in the model.

The WRF-Chem version 3.6 was used here to estimate concentrations of various organic vapours from anthropogenic and biogenic emissions as there was no VOC measurement at the SORPES site during the study period. WRF-Chem is an online three-dimensional, Eulerian chemical transport model that considers the complex physical and chemical processes, such as emission and deposition of pollutants, advection and diffusion, gaseous and aqueous chemical transformation, aerosol chemistry and dynamics (Grell et al., 2005). It is capable of simulating atmospheric chemistry on a regional scale and has been successfully applied in several of our previous studies (Huang et al., 2014, 2015). In this study, the model domain covered East China and its surrounding area, centred at 32.0∘ N, 119.0∘ E with a 20 × 20 km grid resolution, as demonstrated in Fig. 1. There are 24 vertical layers from the ground level to the top pressure of 50 hPa, in which 10 layers are placed under 1 km to better resolve the boundary layer processes. The 6-hourly final operational global analysis (FNL) data with a 1∘ × 1∘ spatial resolution produced by the National Centres for Environmental Prediction (NCEP) was used as initial and boundary conditions of meteorological fields. The simulations were conducted for June to August 2013 when NPF events were frequently detected (Qi et al., 2015). During the simulation period, each run covered 60 h, in which the first 12 h were just for model spin-up and the last 48 h results were adopted for following analysis and box modelling. The outputs of compound concentrations from the preceding run were treated as the initial conditions for the next run. Key physical parameterization options for the WRF-Chem modelling are the Noah land surface scheme to describe the land–atmosphere interactions (Ek et al., 2003), the Lin microphysics scheme (Lin et al., 1983) with the Grell cumulus parametrization to reproduce the cloud and precipitation processes (Grell and Devenyi, 2002), the YSU boundary layer scheme (Hong, 2010), and the RRTMG short- and long-wave radiation scheme (Mlawer et al., 1997).

Anthropogenic emissions from power plants, residential combustion, industrial processes, on-road mobile sources and agricultural activities were derived from the MEIC database (Multi-resolution Emission Inventory for China, see www.meicmodel.org). Emissions of major pollutants, such as carbon monoxide, sulfur dioxide, nitrogen oxides, ammonia and speciated VOCs are all included in this emission inventory database. The MEGAN (Model of Emissions of Gases and Aerosols from Nature, version 2) module embedded in WRF-Chem is used to calculate biogenic emissions online (Guenther et al., 2006). It estimates the net emission rates of isoprene, monoterpene and other biogenic VOCs from terrestrial ecosystems into the above-canopy atmosphere. Gas-phase chemistry is explicitly represented by the model through the SAPRC photochemistry scheme (Carter, 1999), which includes 225 gas-phase reactions among 81 chemical species in the model. We mapped some predicted organic species in WRF-Chem to the MALTE-BOX following the correspondence denoted in Table 1. Regarding the monoterpenes (alpha-pinene, beta-pinene, camphene, myrcene, carene and limonene) used in MALTE-BOX chemistry (details in Boy et al., 2013), the distribution was performed equally because no VOC-measurement were available at the SORPES station during the study period.

Meteorological conditions play an important role in transport, diffusion and chemical reactions in the atmosphere. Simulated hourly 2 m temperature and 10 m wind speed were evaluated using hourly temperature and relative humidity observations at the SORPES station. Statistical analysis of model performance for the three NPF days are listed in Table 3, including mean bias (MB) and root mean square error (RMSE). Generally, the model reproduced the observed 2 m temperature and 10 m wind. As mentioned, modelled VOC concentrations, which are vital for NPF simulation, are included as an input field in the MALTE-BOX model. Although there was no VOC measurement during the summer of 2013, the SORPES site and the Environmental Monitoring Centre of Jiangsu Province (118∘47′ E, 32∘4′ N) were equipped with GC/MS (gas chromatography/mass spectrometry) in the summer of 2014. In order to evaluate the model's performance in simulating VOC concentrations, we conducted another WRF-Chem run for the August of 2014 and then compared the model results with corresponding observations. The comparison of alkene, aromatic and isoprene concentrations in Fig. 4a–c illustrates that WRF-Chem is capable of reproducing the magnitude and temporal variations of VOC concentration originating from both anthropogenic and biogenic sources. Specifically, modelled results tend to underestimate alkene concentration but overpredict aromatic level with normalized mean bias of -11 and 20 %, similar to previous simulations for Shanghai (Tie et al., 2013). There still exist substantial uncertainties in China's anthropogenic VOC emission inventory, particularly speciated estimations, which was ascribed to uncertainties in the activity data, limited direct experiments on emission factors and source profiles (Wei et al., 2008; Zheng et al., 2009). Large biases in model-predicted aromatic level are expectable since it is mainly emitted from petrochemical plants, gasoline vehicle and biomass burning with greater uncertainties in activity level estimation (Liu et al., 2008). In terms of biogenic VOCs, simplification in vegetation classification and numerical descriptions, limited understanding of controlling factors could introduce biases in modelled levels of BVOCs (Guenther, 2013). Given these uncertainties, the gaps between simulation and observations in Fig. 4a–c are acceptable. As for simulated biogenic terpenes, whose oxidation products have low vapour pressures similar to sulfuric acid and condense onto aerosol surfaces, the spatial patterns in the morning of the aforementioned three NPF days showed great differences (Fig. 4d–f). During the first and third NPF cases, prevailing easterly winds did not bring much biogenic VOCs since biogenic emissions are most intensive in the southern part of China. By contrast, on 10 July when the air temperature was getting higher and southwesterly winds dominated, enhanced biogenic emissions and the shift in wind direction led to the fact that the modelled terpene concentrations at the SORPES station were almost two times those in the other two NPF days.

Figure 5 shows the variations of modelled particle number size distributions during the three NPF days. The model system does reproduce the occurrence of these three NPF events although they were under distinct meteorological conditions and affected by entirely different potential source regions. On 22 June when measured air masses originated from the urbanized YRD region, the calculated onset of activation of freshly formed cluster to grow above the 6 nm line appeared around 08:30 LT. According to the diurnal pattern of simulated concentrations of gaseous compounds illustrated in Fig. 6, the OH radical level increased rapidly from 1 × 105 to 3 × 106 cm-3 just after sunrise, promoting the gaseous oxidation of SO2 in the atmosphere and subsequent accumulation of sulfuric acid from nearly zero to around 5 × 106 cm-3. Simultaneously, the pre-existing particle concentration dropped due to the boundary layer evolution (Fig. 3). The continuously growing sulfuric acid concentration and decreasing condensation sink jointly led to this fast NPF event. Simulated J6 was 9.3 cm-3 s-1, slightly higher than the observed value of 7.6 cm-3 s-1. Among different kinds of condensing vapours, sulfuric acid contributed most to the growth of newly formed particles. As demonstrated in Fig. 7, while considering the growth of particles less than 10 nm in diameter, sulfuric acid's contribution accounted for more than 50 %. The reason is that, influenced by air mass from the emission-intensive YRD region, SO2 was reaching up to 20 ppb and the contribution of sulfuric acid on this day was much higher compared with the other 2 days and those published in earlier studies (Boy et al., 2003, 2008b). GR6-30 was simulated to be 6.9 nm h-1, about half of that derived from measurements. Overestimated newly formed clusters might be one reason for smaller simulated GR6-30. Another, as described before, is that condensing vapours in the box model only included biogenic low-volatility compounds. However, aromatic-related oxidation products have been suspected of contributing to particle growth, especially in polluted area like China (Zhang et al., 2004; Yue et al., 2010). Failing to characterize condensing vapour originating from anthropogenic organic compounds might be another cause of the underpredicted growth rate.

During the second NPF case, the OH radical concentration was mostly less than 1 × 106 cm-3. The production of sulfuric acid was expected to be relatively slow due to the simultaneous lower concentrations of both SO2 and OH radical. As demonstrated in Fig. 6, the concentration of sulfuric acid was approximately 3 × 105 cm-3 just when the NPF started, about one-tenth and one-seventh of the corresponding values on 22 June and 22 August, respectively. Nonetheless, prevailing southwesterly winds brought along terpene-rich air masses. Some of the terpenes, such as alpha-pinene and limonene, feature significantly high yields of ELVOCs as well as SVOCs while reacting with ozone or OH radicals (Ehn et al., 2014; Jokinen et al., 2015). Such dense low-volatility oxidation products substantially enhanced the condensational growth of newly formed particles. The individual contributions from sulfuric acid, SVOCs and ELVOCs to growth of newly formed particles were quantified in Fig. 7, which indicated that biogenic low-volatility compounds overwhelmingly dominated in the very initial stage of cluster growth with contribution as high as 95 %, demonstrating a vital role of ELVOCs and SVOCs in this NPF event (Ehn et al., 2014). During this event, SVOC-induced condensational growth of small clusters was especially higher, which might be attributed to the fact that modelled SVOC concentrations increased dramatically shortly after the nucleation started and was almost ten times higher than those during the other two events.

Unlike during the first two NPF cases, the level of pre-existing particles was unusually low during the third event because a strong wind from the ocean swept over East China. The clean air mass reduced the condensation sink (see Table 2), much lower than the values typically observed at the SORPES site before (Herrmann et al., 2014). Even though SO2 concentrations were pretty low, sulfuric acid accumulated remarkably and probably initiated this NPF event. As listed in Table 2, during Case 3 when the air mass originated partly over the Shanghai and surrounding city clusters, the model underpredicted the growth rate by nearly a factor of 7 and overestimated the particle formation rate by a factor of 3. This means that most probably anthropogenic low-volatility compounds not included in the model were contributing to the growth and decreased the surviving probability of the newly formed clusters in the model. It is completely opposite for Case 2 when the air mass did not originate from strongly anthropogenic-influenced areas and the model outcome was in good agreement with the measurements.

Though the model succeeded in the prediction of DMPS-measured NPF occurrence, the simulated activation of NPF was about 1 hour later than the observations. Considering the number concentration in the size range 6–10 nm (N6-10) as the newly formed particles, the model shows a distinct underestimation at the beginning of the NPF events (Fig. 5). As mentioned in Sect. 2, we assumed the kinetic mechanism in the MALTE-BOX. Nonetheless, chamber and in situ experiments suggested that monoterpene oxidation products could cluster directly with a single sulfuric acid molecule under ambient conditions and that the interaction between organic and sulfuric acids likely leads to a reduced nucleation barrier (R. Y. Zhang et al., 2004; Schobesberger et al., 2013). Furthermore, according to the simulation, the production of ELVOCs and SVOCs was mainly initialized by the reactions between monoterpene and ozone. It has been recognized that NPF events tend to be strongly associated with the monoterpene oxidation products by ozone in both remote and urban environments (Laaksonen et al., 2008; Guo et al., 2012). Thus, there was a good chance that the ELVOCs played an important part in the NPF processes considered here. As presented in Fig. 6, a considerable amount of ELVOCs accumulated before the modelled NPF occurred and during the observed NPF events. The time shifts of the starting times is consistent with the hypothesis that organic vapours may play a key role in the particle formation process (Paasonen et al., 2009; Metzger et al., 2010). Figure 8a shows the dependence of measurement-derived J6 on modelled gaseous sulfuric acid and ELVOC concentrations; 6 nm NPF rates, even under the same sulfuric acid concentration, were substantially enhanced by the presence of ELVOCs. It is noteworthy that formation rates of 6 nm particles, not nucleation rates, are available here due to the limitation of instruments. It is hard to identify which process is most promoted by ELVOCs, the particle formation or the early condensational growth. Metzger et al. (2010) attempted to disentangle the influence of organic oxidation products in particle formation and suggested an overall dependency on the formation rate of H2SO4 and organic oxidation products with the lowest volatility (NucOrg) as follows: J1.5=k×[H2SO4]1.0[NucORG]0.8, where J1.5 is new particle formation rate of 1.5 nm cluster; k represents a pre-factor which is recommended to be 7.2 ± 1.4 × 10-13 cm3 s-1 in Metzger et al. (2010); [H2SO4] and [NucOrg] refer to the concentration of sulfuric acid and low-volatility organic oxidation products that can participate in the particle formation process, respectively. By assuming that NucOrg is part of the ELVOCs in the present work, we examined the relationships between measured particle formation rate with [H2SO4]1.0[ELVOCs]0.8 and compared it with [H2SO4]2 in Fig. 8b–c. The better representation and correlation of the latter provides further evidence for an involvement of ELVOCs in the formation and condensational growth of particles up to 6 nm.

In terms of the condensational growth of freshly formed particles, ambient low-volatility compounds are predominant contributors – in particular, with semi-volatile and possibly non-volatile organic matters generating from a complex series of photochemical reactions (Kroll and Seinfeld, 2008). In the present work, the model notably underestimates the nuclei condensational growth (GR6-30) for Case 1 and Case 3 compared with the corresponding observations, whereas the observation and simulation were comparable for Case 2 (Table 2). These differences could partly be due to the fact that here we only took oxidation products for certain selected organic compounds into account as sources of condensable vapours. When the experimental site was substantially influenced by intensive industrial activities and vehicle emissions from the YRD region in Case 1 and Case 3, reactive uptake and condensable secondary organic products from anthropogenic VOCs, which can accelerate particle growth (R. Y. Zhang et al., 2004b; Kroll et al., 2005; Volkamer et al., 2006), were partly missing in the present model. Regarding the impacts of biogenic VOCs, we found that ELVOCs and SVOCs remarkably contributed to particle condensational growth. Modelled contributions from ELVOCs, SVOCs and sulfuric acid demonstrated that, during these three NPF days, condensation of ELVOCs and SVOCs played an important role in the initial growth of particles less than 10 nm. In particular, the contribution increased to over 90 % on 10 July when the terpenes-rich air mass influenced the SORPES site.

The comprehensive modelling study on the observed NPF makes it possible to better understand NPF processes at the SORPES station. However, there remain many uncertainties in this modelling system, which need to be addressed in future work. Given the expensive computational cost, reactions of VOCs are represented by the lumped mechanism in the regional-scale WRF-Chem model. Relevant parameters cannot be precisely determined for one lumped class, while the MALTE-BOX model provides accurate information for each specific organic compound. The gaps between the two models concerning VOC classification would introduce uncertainties. Moreover, in the MALTE-BOX model, sulfuric acid tends to be underpredicted, which was demonstrated in both polluted urban environment and clean rural environment (Wang et al., 2013a; Zhou et al., 2014; Zhou et al., 2015). There are multiple reasons behind the systematic underestimation. It has been shown by field measurements, laboratory experiments and numeric simulation that Crigee Intermediates (CIs) or other derivatives are capable of accelerating the oxidation of SO2 into SO3 (Hatakeyama and Akimoto, 1994; Kurten et al., 2011; Boy et al., 2013). These reactions have been incorporated in the MALTE-BOX model but would need further investigations concerning the reactions rates and other important reaction parameters (e.g. thermal lifetimes of CIs, pressure dependency). In addition, owing to the significantly incomplete knowledge of HONO sources, in particular during daytime, it has not yet been possible to simulate realistic HONO levels using current models (Elshorbany et al., 2014; Czader et al., 2015). The lack of HONO measurement input to the model might also result in an underestimation of sulfuric acid, especially with dramatically increasing traffic emissions during the rush hours (Wang et al., 2013b). For instance, in the first case, the air masses were carrying on more anthropogenic pollutants from the emissions-intensive YRD region, and the sulfuric acid concentrations and particle formation rates are more likely to be underpredicted. Last but not least, we adopted a mandatory value for the kinetic coefficient, which includes the probability that a collision of two molecules results in the formation of a stable critical cluster, as well as all other important details concerning the particle formation process such as temperature and humidity. This condition-dependent coefficient needs to be resolved in further modelling work on the basis of more in situ and laboratory experiments.