Forecasts for concentrations of trace gases SO2, O3, NOx, CO, and OH as well as particulate matter (PM10, comprising the total mass concentration of particles smaller than 10 µm in diameter), and relative humidity were obtained from the Finnish Meteorological Institute's SILAM (System for Integrated modeLling of Atmospheric coMposition) air quality model (Sofiev et al., 2006). This model provides predictions for the above-mentioned variables for the next 5 days at several heights above the ground. Input information for SILAM includes anthropogenic emissions from the TNO-MACC data set, IS4FIRES information on wild fires, as well as emission calculations for sea salt, pollen, wind-blown dust, and natural volatile organic compounds. The weather forecast input data are obtained from the FMI HIRLAM model. The horizontal resolution of SILAM in the Scandinavian area is 6–7 km. All SILAM forecast data are freely accessible via the internet (http://silam.fmi.fi/), and the forecast for the northern Europe area is updated once per day. For the purpose of the current NPF event forecasts, we used predictions for the ground level (15 m above ground) during next 3 days from the model grid point nearest to Hyytiälä SMEAR II station with the time resolution of 1 h.

As supporting data, we also used several “traditional” weather forecasts available on the internet (including forecasts by the Finnish Meteorological Institute, Foreca, and Norwegian Meteorological Institute), mainly to evaluate the probabilities of cloudiness and rain. During the campaign time, the weather was rather variable and the forecasts were changing rapidly (even several times a day) from clear skies to partly cloudy and possibly rainy. All these conditions are known to affect directly the probability of NPF.

Air mass arrival directions and source areas were forecast for 96 h prior to the arrival of air at Hyytiälä using the HYSPLIT single particle Lagrangian transport model developed by NOAA and freely available on the internet (http://www.arl.noaa.gov/HYSPLIT.php). As input meteorological data for the model, we used the US National Weather Service's Global Forecasting System (GFS) weather forecast data which extend 192 h forwards in time. The horizontal location accuracy of the air mass trajectory calculations using HYSPLIT has been estimated to be on the order of 10–30 % of the total distance the air parcel has travelled (Stunder, 1996; Stohl, 1998; Draxler and Hess, 1998, 2010). We considered trajectories arriving each hour to Hyytiälä at 250 m height above ground calculated 96 h backwards in time. Typically air masses travelled less than 1000 km during this time, meaning that the air mass source area predictions based on the back trajectory calculations could be considered accurate within 100–300 km or better. Also, since we did not consider just individual air-mass back trajectories but rather took into account all the air masses that were to arrive during the morning and early afternoon (which is the typical time of NPF occurrence in Hyytiälä), the effect of uncertainties in the position of individual trajectories was diminished.

Typical conditions on NPF and non-NPF days in Hyytiälä are shown in Table 1 for May and June during years 1996–2012. The conditions are shown for the time window 08:00-11:00, which is the time when NPF typically starts in Hyytiälä. In a data-mining study of the SMEAR II station long time-series records of aerosol size distributions and meteorological parameters, Hyvönen et al. (2005) found that the condensation sink (describing the pre-existing aerosol surface area) and relative humidity were the two parameters most effectively separating NPF days from non-NPF days. Particle formation was occurring only on days with a low CS and low RH. On the other hand, photochemical production of vapours participating in nucleation and growth, namely sulfuric acid and oxidation products of organics, is more efficient in clear-sky conditions with high UV radiation intensity compared to cloudy conditions. Thus, our main criteria in forecasting NPF to occur were clear sky conditions, low condensation sink (in practice low PM10 concentration, which was obtained from SILAM) and from low relative humidity in the early morning to noon-time, as this is the time when regional NPF events start in Hyytiälä (Kulmala et al., 2013). Note that in spring and summertime, days with low relative humidity are typically also warm and sunny, so these conditions are not necessarily independent of each other. However, the difference between NPF days and non-NPF days is also seen in the absolute humidity (water vapour concentration, see Table 1).

The air mass source area and transport route to Hyytiälä were considered when making the NPF forecasts. In the long time-series analysis by Dal Maso et al. (2007), the occurrence of NPF in Hyytiälä was observed to be highly favourable in air masses originating from the Arctic and North Atlantic oceans, and on the other hand suppressed in southern air masses. This is typically connected to clean air arriving from the west and more polluted air originating from central and eastern Europe, directly influencing the sink for newly formed particles. However, in air masses originating from the south and south-east to Hyytiälä, SO2 concentrations are typically higher than in westerly air masses, which would favour NPF due to a higher production rate of sulfuric acid (Riuttanen et al., 2013). Table 2 summarizes the criteria used for making the NPF forecasts. The flowchart representing the main decision making process for the NPF forecasts is shown in Fig. 1. The threshold values for SO2 and PM10 shown in the flowchart are based on the observed range of these variables on NPF and non-NPF days (Table 1).

We also developed several “nucleation parameters” to forecast the intensity of NPF. The parameters that worked best were either related to only the proxy concentration of sulfuric acid, or were related to proxies for both sulfuric acid and oxidation products of volatile organic compounds (such as monoterpenes). Paasonen et al. (2010) studied several different parameterizations for the formation rate of 2 nm particles, and found that at the Hyytiälä site nucleation rate could be mainly explained by the sulfuric acid concentration to the power of 1 or 2.

The simplest nucleation parameter is described by the following equation: NP1=SO2⋅OHPM10⋅RH, where the sulfur dioxide concentration (SO2), hydroxyl radical concentration (OH), particulate mass concentration (PM10) and relative humidity (RH) are taken from the SILAM air quality forecasts for the grid point closest to Hyytiälä. The particulate mass concentration is available from the SILAM forecasts. In Hyytiälä, the PM10 concentrations correlate well with the condensation sink CS which describes the total sink of the newly formed particles due to the pre-existing aerosol population. The PM10 concentrations (in units µg m-3) can be scaled to CS (in units s-1) using the linear relationship CS = 4.59 × 10-4 × PM10 (linear regression based on measurement data from Hyytiälä in 1996–2012 with correlation coefficient r=0.81). The relative humidity is included as RH-1 in Eq. (1) in order to take into account the observed anti-correlation between the relative humidity and particle formation intensity, mainly due to the fact that the highest sulfuric acid concentrations are limited to times of low ambient relative humidity (Hamed et al., 2011).

A nucleation parameter taking into account the oxidation products of monoterpenes, in addition to sulfuric acid, is described by the following equation: NP2=SO2⋅OHPM10⋅RH⋅expaT⋅kOHOH+kO3O3BLH⋅PM10. Here, the concentrations of sulfur dioxide SO2, hydroxyl radicals OH and ozone O3 (in units of cm-3), particulate mass PM10 (in units µg m-3), as well as relative humidity RH (in percentages), and temperature T (in units ∘C) were obtained from the SILAM forecasts. The concentrations of monoterpenes were predicted based on the ambient temperature, as their concentrations have been shown to follow an exponential temperature dependence in Hyytiälä with the scaling coefficient a=0.078 ∘C-1 (Lappalainen et al., 2009). The OH and O3 concentrations were used to calculate the proxy concentrations of the monoterpene oxidation products, and the reaction coefficients kOH=7.5 × 10-11 and kO3=1.4 × 10-17 cm3 s-1 are the averages of the reaction coefficients for individual monoterpene species weighted according to their typical concentrations observed in Hyytiälä (Hakola et al., 2003; Yli-Juuti et al., 2011). The modelled boundary layer height BLH is included in Eq. (2) to take into account the dilution of monoterpene emissions into the developing boundary layer.

The PEGASOS–Zeppelin Northern mission was a 40-day-long measurement campaign between 3 May and 11 June 2013. An overview of the meteorological conditions as well as trace gas and particle concentrations observed at the SMEAR II station during the campaign is shown in Fig. 2. Most of the days were sunny with either clear or partly clear skies. Rain occurred on 13 days during the campaign. The air was rather clean from anthropogenic pollution, especially in the first and last week of the campaign. Occasionally, there were pollution episodes seen e.g from a 10-fold rise of the SO2 concentration from its typical level of about 0.1 ppb. At the end of May, a longer period occurred during which more polluted continental air was transported from central Europe to Hyytiälä.

Figure 3 shows the arrival routes of air masses to Hyytiälä during the period of our measurement campaign. These trajectories were calculated for the 250 m arrival height above ground, and 96 h backwards in time. From the beginning of the campaign until middle of May, approximately 17 May, the air masses originated mainly from over the Atlantic, and arrived at Hyytiälä either directly from the west over Scandinavia or from the south-west, making a turn over the Baltic Sea. Air in Hyytiälä was relatively clean during this time, characterized by low particulate mass and trace gas concentrations. Especially SO2 had very low concentrations during this time, with the exception of one pollution-related peak on 9 May. After mid-May, air masses turned to arrive mainly from east at Hyytiälä, originating either from over the Arctic Ocean or from the continental north-west Russia. During this time until early June, the condensation sink and PM10 concentrations were higher than in early May, indicating more polluted air. Also high concentration peaks in the trace gases SO2 and CO were more frequent during this time. During the last weeks of the campaign in the beginning of June, air masses turned again to arrive at Hyytiälä from the west over Scandinavia, resulting in cleaner air with low particulate matter and trace gas concentrations.

Figure 4 shows the particle number size-distributions along with the forecasted NPF occurrence and the time series of the nucleation parameters NP1 and NP2. In the beginning of the campaign, several strong NPF bursts occurred (high nucleation mode particle concentrations on 3, 6, and 8 of May), and our forecasts were able to capture these as well as the days with no new particle formation. Both of the nucleation parameters peaked on these 3 NPF event days, and were clearly lower on the days between NPF events, except NP1, which had a relatively high value also on 4 May. During the beginning of the campaign time, air masses originated mainly from over the Atlantic Ocean and arrived at Hyytiälä after passing over Scandinavia. On some of these days, the air was remarkably clean, characterized by very low SO2 concentrations (below 0.1 ppb), resulting in low sulfuric acid concentrations and weak or no NPF event on clear-sky conditions. The daytime peak value of 104 or higher for nucleation parameter NP1 was typically associated with the occurrence of NPF.

After mid-May until early June, the air masses arrived at Hyytiälä mainly from the east, either spending several days over continental Russia or, in some cases, coming more directly from over the Arctic Ocean via north-west Russia. The air mass circulation was driven by a persistent high-pressure system residing over central Finland. This resulted in a rather unusual air mass transport pattern to Hyytiälä, and also made the NPF forecasting more challenging. During this time, there were situations when the polluted air masses resulted in a high condensation sink, preventing the occurrence of NPF. Also the SILAM forecasts for the SO2 and PM10 concentrations were less accurate during the easterly air masses compared with air masses coming from the west or the south. This might be related to less accurate emission data for these species over the Russian area.

The nucleation parameter NP2 started to have high values more frequently after the middle of May. One factor influencing this was the higher air temperatures during this time compared to the beginning of the campaign, as the emissions of monoterpenes are highly influenced by the ambient temperature. NPF events, however, were not as frequent during this time. On one hand, this period was influenced by the more polluted air masses arriving at Hyytiälä from the east. On the other hand this period included quite a few days (13 out of 22 days after 20 May) when a growing particle mode was observed to appear in Hyytiälä starting from sizes above 10–20 nm. These types of NPF events are typically observed during the summertime in Hyytiälä, and they might be connected to higher particle growth rates during the summer, leading to the observation of the newly formed particles after they have already grown for several hours (Buenrostro Mazon et al., 2009). Days on which the maximum value of the nucleation parameter NP2 exceeded 0.02 started to be more likely an NPF event day rather than a non-event day.

The nucleation parameters NP1 and NP2 have a clear connection to the NPF: they represent the ratios between the source and sink terms for the newly formed particles. However, the numerical values for NP1 and NP2 and especially their uncertainty depend greatly on the weather forecast and air-quality forecast data taken from the SILAM model. As it is out of the scope of this work to evaluate the accuracy of the SILAM predictions for the various parameters used, the values of NP1 and NP2 presented in this study should be regarded as qualitative. When comparing the different days during the campaign, they did however provide useful information to support the NPF forecasting.

The particle number size distributions measured by the differential mobility particle sizer (DMPS) during the whole campaign are shown in the upper panel of Fig. 4. Using the criteria developed by Dal Maso et al. (2005), each day was classified as either an NPF event, non-event, or undefined day. On NPF event days a new mode of particles smaller than 25 nm is observed and these particles can be observed growing to larger sizes during several hours. NPF event days are further classified according to the possibility to reliably derive particle formation and growth rates (Class I) or not (Class II). The days when no new sub-25 nm particles appeared were classified as non-NPF days. Undefined days are those days for which it was not possible to unambiguously determine whether NPF occurred or not. Table 3 shows the forecast and the corresponding event classification for each day. During the 40-day campaign, clear regional NPF events lasting for several hours were observed on 11 days in Hyytiälä. Six of these days were also forecast to be NPF days, and four to have a possibility of NPF to occur. The NPF day which we forecast to be a non-NPF day (9 June) was cloudy and had a possibility of rain according to weather forecasts, and the air masses were forecast to originate from the west, which is not the direction from where air masses typically arrive to Hyytiälä on NPF event days (Dal Maso et al., 2007). On 10 days of the campaign there was no particle formation occurring in Hyytiälä, and these were also forecast to be non-NPF days, except for 2 days (17 and 28 May) for which a possible NPF event was forecast. This was most probably caused by the very low SO2 concentration. On only one of the days forecast to be non-NPF day was there appearance and growth of new nucleation mode particles.

Comparison of the event classification and the event forecasts is shown in Table 4. We follow the method of Hyvönen et al. (2005) for calculating the score indices for the performance of the event forecasts on the 21 days classified as either NPF or non-NPF days (undefined days are removed from this comparison). Out of these 21 days our forecasts had two false NPF event days (non-event day forecast to be either event or to have a possibility for event) giving a 10 % false-event fraction, and one NPF event day forecast to be a non-event day giving a 5 % missed-event fraction. The total error of the NPF forecasts (false and missed events) during the 21 classified days of the 40-day campaign was (2+1)/21=14 %, which is comparable to the performance of the classification methods presented in the study by Hyvönen et al. (2005).