The Gaussian plume model is a solution to an advection–diffusion equation that describes the changes in the pollutant concentrations due to advection of wind and turbulent mixing with the surrounding air (Stockie, 2011). Accordingly, the concentration of a pollutant i, Ci, emitted from a point-like source, can be expressed as follows: Ci(x,y,z)=Qi2πUσyσzexp⁡-y2σy2exp⁡-(z-H)2σz2+exp⁡-(z+H)2σz2. Here x, y and z are the spatial coordinates, aligned so that the x axis corresponds to the wind direction and H is the height at which i is emitted (stack height). Also, Qi is the emission rate of i at the source, U is the mean wind speed and σz as well as σy are the so-called dispersion coefficients which reflect the spatial extent of the plume as a function of the downwind distance x. The dispersion coefficients were calculated using the parameterization of Klug (1969) and the atmospheric stability class, which is needed to calculate the dispersion coefficients. Atmospheric stability classes were estimated based on the measurements of the wind speed and solar radiative flux at the surface. Moreover, the pollutant concentrations were calculated along the centre line of the plume, the value of U was set to constant and was equal to the average wind speed during the flights. Finally the value of z was set equal to the stack height (150 m).

It is worth noting that the background concentration of i is zero according to Eq. (1): Ci→0 when z→∞ or y→±∞. However, the flue gas emitted from the stack was actually cleaner in terms of particle number concentration than the background air when the flue gas was cleaned properly. In order to account for such cases, the following equation was used instead of Eq. (): C^=C∞+C0-C∞C0×Ci, where C∞ is the background concentration of i, and C0 is its concentration at the source. It can be readily shown that Eq. () is a solution to the advection–diffusion equation underlying Eq. (). Also, it is easily verified that C^→C∞ when z→∞ or y→±∞. Finally, the value of Qi in Eq. () was chosen so that C^→C0 when z→H and x,y→0.

An important output of the model is the dilution ratio of the flue-gas plume, DR, which is calculated based on Eq. (). DR(t)=[CO2(t)]-[CO2,∞][CO2,stack]-[CO2,∞] In Eq. () [CO2(t)] and [CO2,∞] are the modelled CO2 concentration at time t and the CO2 concentration measured in the stack, respectively.

The SO2 and particle emissions of the power plant were strongly dependent on the flue-gas cleaning system. This can be seen in Table 1, which shows flue-gas concentrations for CO2, SO2, NOx, O2, particle number (Ntot), dust as well as flow rate in the duct in both flue-gas cleaning conditions. In the shift from FGD + FF off to FGD + FF on, the SO2 concentration decreased to nearly a fifth, the concentration of dust decreased by a factor of 50 and the Ntot decreased by a factor of 4000. For other parameters the effect of FGD + FF was insignificant.

Figure 2 shows the particle number size distributions of flue gas in the stack in both cleaning conditions. These were measured using an electrical low pressure impactor (ELPI) and a scanning mobility particle sizer (SMPS) in both FGD + FF on/off cases. In the FGD + FF on case, the SMPS measurement is a median value over a few hours of operation due to low particle number concentrations in the stack. Based on the SMPS measurement the particle geometric mean electrical mobility equivalent diameter was 80 nm and the width of particle number size distribution (geometric standard deviation, GSD) was 1.45 for FGD + FF off. In comparison, the geometric mean electrical mobility equivalent diameter was 31 nm for FGD + FF on and the width of particle number size distribution was 2.15. Based on the measurements using the ELPI geometric mean aerodynamic equivalent diameter was 141 nm and GSD was 1.41 for FGD + FF off. The difference in mean diameter measured using the ELPI and the SMPS comes from the difference in size classification principles of these instruments and enables the determination of effective density of measured particles. The effective density calculation is based on the relation between the electrical mobility equivalent diameter and the aerodynamic equivalent diameter of the particle (see Ristimäki et al., 2002). In this study case the difference in equivalent diameter indicates effective density larger than unit density for emitted particles (approximately 3.1 g cm-3). In comparison, Saarnio et al. (2014) used an effective density of 2.5 g cm-3 to convert the electrical mobility diameter measured using a SMPS to an aerodynamic diameter. When studying FGD + FF on, the particle concentrations were so low and thus accurate determination of mean particle size was not possible from the particle size distribution measured by the ELPI.

Flue-gas samples from the stack were diluted with hot dilution air before the particle instruments and thus the particle number concentrations (Table 1) and particle size distributions (Fig. 2) are for non-volatile particles. In combustion studies the hot dilution air is typically used to prevent the formation of liquid nucleation particles and to minimize the effects of condensation of semi-volatile compounds on particles. However, to ensure the measured particles were non-volatile and not affected by the dilution method itself, a thermodenuder (Rönkkö et al., 2011) was used periodically after the sampling and dilution. The thermodenuder did not affect the particle number size distribution, which confirms the non-volatile nature of the measured particles. Due to this non-volatility of the particles, the lifetime of the primarily emitted particles in the atmosphere can be longer than that of volatile particles, e.g. nucleation mode particles observed in vehicle exhaust (Lähde et al., 2009).

Figure 3 shows the measured flue-gas plume concentrations as a function of plume age. Diffusion losses for the particles in the sampling lines were calculated based on the measurement set-up (see Fig. S4). The data were recorded based on GPS coordinates, which were used to calculate distances from the stack, and the distances were changed to correspond plume age using wind speeds of 6.5 and 4.0 m s-1 (lidar, Fig. S2). The calculation showed that nearly 70 % of the 2.5 nm particles in diameter was lost in the sampling lines and thus the total concentration shown in Fig. 3 can be higher than shown here. The vertical lines denote the 2 km distance from the stack. Figure 3 shows the dilution timescale of the flue gas in terms of CO2 and SO2 in both operation conditions. The same trend in SO2 and Ntot concentrations as observed in Table 1 was measured by instruments installed in the helicopter; in FGD + FF off the particle and SO2 concentrations were higher than the FGD + FF on situation. It should be kept in mind that in FGD + FF off only one of the two flue-gas cleaning systems was bypassed.

Plume dilution can be evaluated by the CO2 concentrations (in Fig. 3a and b), which show that the FGD + FF off case dilutes to approximately background levels in 200 s (0.74 km) and the FGD + FF on case in 300 s (1.5 km). The peak values for CO2, SO2 and Ntot were 3195 ppm, 2193 ppb, 3.3×104 cm-3 in the FGD + FF off and 3254 ppm, 585 ppb, 0.4×104 cm-3 for the FGD + FF on. However, dilution decreases the CO2, SO2 and Ntot concentrations in the atmosphere to 422 ppm, 52 ppb in FGD + FF off, and 473 ppm, 89 ppb in FGD + FF on. The Ntot reached near background concentrations after 200 s and 300 s. The background gaseous concentrations for each measured gaseous component were 403 ppm and 2–8 ppb for CO2 and SO2, respectively. The boundary layer mixing started during the FGD + FF on measurements and thus the background values measured from the upwind side flight loops from the stack were averaged and subtracted from both FGD + FF on/off. It can be noted that very near (first 10–50 s) the stack the helicopter was not in the plume. This can be seen from CO2 and SO2 concentration values presented in Fig. 3a and b when approaching plume age zero. Thus, the dilution process is discussed below, mainly from the maximum concentrations onward.

An increase in total particle concentration can be seen in Fig. 3 after 400 s aged the flue-gas plume. This tendency can be seen in both flue-gas cleaning situations. Based on Fig. 3a, for the FGD + FF off situation, the background particle concentration was 1430 cm-3, after 200 s the concentration was at the background level and after 400 s it increased significantly, even up to an average level of 5000 cm-3. Based on CO2 measurements, the dilution of flue gas was practically complete at 200 s. Similarly, in the FGD + FF on situation after 500 s the particle concentration was slightly above background, after which it increased even up to 5000 cm-3 after 700 s. Thus, the concentrations in the diluted and aged flue-gas plume were higher than the background and significantly higher than could be expected based on the primary particle concentrations and observed dilution profiles. In general, taking into account the fact that there is no comprehensive measurement of the primary precursor matrix (only [SO2] is measured), the primary precursor matrix might include low-volatile organics and SO3, which can increase the probability of new particle formation. Due to the increasing trend in particle concentration, some estimation about formation rates can be calculated. Depending on the plume age, the mean formation rates calculated from the data shown in Fig. 3 depended on the plume age being for FGD + FF off 0–81 cm-3 s-1 and for FGD + FF on, 0 to 18 cm-3 s-1 (mean slope of increasing total particle number concentration at 400–482 and 500–692 s).

Particle size distributions, shown in Fig. S5, were calculated from the EEPS data measured from the helicopter in both FGD + FF on/off situations as a 10 s moving median method. The particle size distribution in the FGD + FF off case had a mode around 80 nm, which refers to the solid particle median diameter measured with the SMPS from the flue gas in the stack. The particle size distribution measurement made using the EEPS (Fig. S5) supports the results for total particle number measurement made by the CPC (Fig. 3), i.e. in terms of particles the flue gas dilutes in 0–300 s in FGD + FF off. In addition, the particle size distributions measured by the EEPS indicates a slight increase of nanoparticle concentrations during the dilution and dispersion of the flue gas in the atmosphere. Although EEPS total particle number concentration cannot be compared to total concentration of CPC because Levin et al. (2015) showed that EEPS total particle number concentration is not comparable with a CPC. Further, Fig. S5 shows that the EEPS particle size distribution data are noisy and, based on Awasthi et al. (2013), can show maximum of 67 % error compared to SMPS.

The validity of the Gaussian plume model was tested against CO2 measurements from the plume. Median CO2 concentrations were calculated using the measurement data at a 5 s interval separately for the FGD + FF on/off cases and the locations of the peak CO2 concentration (tmax⁡, [CO2,max⁡]) were identified from the resulting time series. The value C0 was chosen for Eq. () so that the modelled CO2 concentration, C^CO2, was around [CO2,max⁡] when t=tmax⁡. The choice of C0 was made in this manner rather than initializing the model to use the stack concentrations due to the following two reasons. First, the Gaussian plume model does not yield reliable results close to the source, i.e. within a few tens of metres (Arya, 1995). Second, the comparison of the results near (first 10–50 s) the source is problematic because the helicopter was not located at the plume centre line during the initial stages of the measurements.

Comparison of the measured and modelled CO2 concentrations is shown in Fig. 4 and in Table . The chosen stability classes were b and c for FGD + FF on and c and d for FGD + FF off, corresponding to the stability conditions ranging from unstable to neutral (Pasquill, 1961). As can be seen, the model reproduces the observed trends rather well, in particular for FGD + FF off, while the model tends to slightly overestimate the observed concentrations for FGD + FF on. The modelled and measured concentrations were within one standard deviation in general. Mean relative error (MRE) and correlation coefficients (R2) were calculated between the measured and modelled concentrations for CO2. In order to further investigate the performance of the model, a comparison was made between measured SO2 and Gaussian-model-diluted SO2 concentrations, shown in Fig. S6 and Table 2. The results showed that the model consistently overestimates the SO2 concentration in the plume, typically by a factor between 3 and 4, compared to the measured values. This difference could be partly explained by the oxidation of SO2 because it is not taken into account by the model. However, this discrepancy between MREs and R2 does not affect the model performance as the measured SO2 concentrations, instead of being modelled, were used in the plume model simulations.

Modelled and measured CO2 concentrations showed that the model reproduced the observed dispersion of the plume relatively accurately. Thus the model was applied to calculate [NOx], [OH] and [H2SO4], which were needed to investigate the possibility of new particle formation in the plume. These results are summarized in Fig. 5. It is seen that sulfuric acid concentrations exponentially increase during the initial stages of the simulation and then reach constant concentration around 1×106 and 1×107 cm-3, a range which is also comparable to the atmospheric observations of [H2SO4] (Mikkonen et al., 2011) formation. Mikkonen et al. (2011) reported that H2SO4 concentrations varied between 1.86×105–2.94×106 molec cm-3 and Sarnela et al. (2015) reported [H2SO4] concentrations 4.4×106–11.5×106 molec cm-3 for Finnish industrial and non-industrial area. More H2SO4 is formed in the FGD + FF off case because of higher primary SO2 emission compared to the FGD + FF on case.

Initially, OH concentrations are lowered by large concentrations of NOx which subsequently decrease during plume ageing. NOx reduction leads to increases in [OH] and [H2SO4]. While the [OH] increased consistently during the simulations, [SO2] decreased because of dilution. Due to these opposed trends, the production term for the sulfuric acid in Eq. (), did not change greatly during the later stages of the simulations. Moreover, the condensation sink (CS) diluted rapidly to its background value, which was around 1×10-2 s-1. These facts explain why the modelled sulfuric acid concentrations, calculated with Eq. (), did not change notably after the initial rapid increase.

The modelled nucleation rate Jnuc is directly proportional to the sulfuric acid concentration and hence the trends in [H2SO4] are directly reflected in Jnuc (Fig. 5). Furthermore, in our measurements the particles were detected at the lowest CPC detection limit which was 2.5 nm, J2.5. According to the scheme applied here (see Eqs.  and ), the fraction of freshly nucleated particles that survive into detectable sizes depends mainly on their growth rate (GR) and condensation sink (CS). The average given by the model GRs were 0.34 or 0.19 nm h-1 in the FGD + FF off case, and 0.07 or 0.04 nm h-1 in the FGD + FF on case for the two stability class scenarios. These values are clearly smaller than atmospheric GR observations in urban areas (e.g. Stoltzenburg et al., 2005). As a lower GR leads to a lower surviving fraction, we conclude that the modelling results do not explain the observed particle formation in the flue-gas plume.

A series of additional calculations were performed in order to investigate the sensitivity of the results to the values of the key input parameters. First, Jnuc is proportional to the constant A, the exact value of which is not accurately known, and this uncertainly translates directly into the calculated nucleation rates. A sensitivity analysis was made for the nucleation model in order to evaluate the sensitivity of nucleation rates to the value of A (shown in Table ). In these calculations, a value of 1×10-6 was chosen for A, which is an order of magnitude higher than in base case simulations. The choice of the value was based on the study of Sihto et al. (2006) who investigated NPF (new particle formation) events occurring in boreal forest. As can be seen, an increased value of A alone is not sufficient to explain observed new particle formation. A second source of uncertainty is the sulfuric acid concentration, which was calculated using a rather simple scheme (see Sect. 2.1.1). Increases in [H2SO4] leads to both increased Jnuc and GR and ultimately to larger J2.5. Results displayed in Table  show that J2.5 is more consistent with observations when [H2SO4] is increased 5 or 10-fold and when A is set equal to 1×10-6 like in Sihto et al. (2006). Therefore, underestimation of [H2SO4] may explain the discrepancy between the observations and base case model results. This might be caused by underestimation of [OH] or overestimation of CS. Regarding the modelled OH concentrations, it can be noted that they are relatively low, reaching values of around 1×105 cm-3 by the end of the flights. In comparison, concentrations of around 1×106 cm-3 have been reported during the daytime around noon in various atmospheric environments (Hofzumahaus et al., 2009; Petäjä et al., 2009), 0.26×106 molec cm-3 in Mace Head (Berresheim et al., 2002), and 1×106–2×107 molec cm-3 in Atlanta (Kuang et al., 2008). Relatively low modelled OH concentrations can be explained by high NOx concentrations which were calculated to decrease consistently from several tens of ppm down to around 200 ppb during the flights (not illustrated here). Such high concentrations of NOx are consistent with low [OH] (see Fig. 1 in Lonsdale et al., 2012). It could thus be speculated that the model underestimates [H2SO4] and consequently the rate of new particle formation due to overestimation of [NOx]. Moreover, it should be noted that neither SO3 nor low-volatile organic vapours that might have been present in the measured flue gas were not accounted for in the modelling study. Previous studies suggest that these exhaust compounds may also increase the formation rate of nucleation particles (Pirjola et al., 2015; Ehn et al., 2012; Arnold et al., 2012), which may explain the discrepancy between measurements and model calculations. Regarding the estimation of the value of CS, it should be noted that its values were taken from the field site measurements located nearby rather than from in situ measurements. Therefore it can be speculated that actual CS values were lower than those used as input to the model, which causes additional uncertainties.

Each power plant (over 50 MW) in the EU has emission limits for SO2, NO2 and particle mass concentrations. For the studied power plant the limits are 600 mg Nm-3 (210 ppm), 600 mg Nm-3 (290 ppm) and 50 mg Nm-3. A comparison of the results in Table 1 with these emission limits shows that the emissions were clearly below these limits when the power plant operation was normal (FGD + FF on). It was observed that these low emissions can be achieved through properly working flue-gas cleaning systems. In addition to primary emissions, flue-gas cleaning systems also seemingly affect the compounds, which can act as precursors for new particles, e.g. SO2 tends to oxidize in the atmosphere to form SO3 and further forms H2SO4, which can nucleate or condensate to particle phase. This study clearly shows the importance of flue-gas cleaning technologies and underlines the proper usage of the technologies when the atmospheric pollution is discussed in terms of coal combustion. For example, according to Huang et al. (2014) in Xi'an and Beijing 37 % of the sulfate in atmospheric particles is emitted from coal burning.

In this study the power plant plume diluted to background levels in 2 km (200–400 s), which is faster than in other in-flight measurements (Stevens et al., 2012; Junkermann et al., 2011). This difference may be because the dilution of plume and other processes are affected by source strength, background concentrations and meteorology (Stevens et al., 2012). We observed that while SO2 and CO2 were already diluted to background levels, the effect of the source to aerosol concentration was still clearly distinguishable after 2 km. In our study, we collected high time-resolution data close to the power plant stack, which enabled us to model the plume dilution on a detailed scale. From this, we were able to observe that while SO2 and CO2 were already diluted to background levels at a distance of 2 km – in agreement with the dilution modelling – the effect of the source on the aerosol number concentration was distinguished at distances > 2 km. We attribute this to nucleation taking place in the ageing plume.

According to the modelling results from Stevens et al. (2012), atmospheric new particle formation via nucleation of sulfuric acid begins in the flue-gas plume at 1 km distance from the coal-fired power plant, whereas the sulfuric acid formation begins right after emission. Our study therefore supports this previous modelling work by showing that nucleation may take place in the aged plume and is most effective after 400 s, corresponding to a distance of approximately 2 km from the emission source in the atmosphere.

In light of the new results authors would like to distinguish the primary particle emission from the newly formed particle emission because those particles have different effects on the atmosphere and different formation mechanisms. By comparing primary particle emission with newly formed particle emission, the effects of different particles in the atmosphere could be taken into account more precisely in aerosol models or air quality assessments.

For instance, rough estimates for particle number emission factors can be calculated by comparing the measured particle number concentration with the simultaneously measured CO2 concentration of the flue-gas plume (see e.g. Saari et al., 2016). By utilizing this method for particles existing in the flue-gas plume between the ages of 25–55 s, the emission factor with respect to CO2 was 2.0×1010 (g CO2)-1, as well as from ages over 400 s 8×1010 (g CO2)-1 in the FGD + FF off case. Similarly, in the FGD + FF on case, the emission factors were 4×109 (g CO2)-1 (for aerosol dispersed 55–85 s in the atmosphere) and 3.74×1010 (g CO2)-1 (for aerosol dispersed more than 500 s in the atmosphere). In comparison, the primary emissions were 1.75×1010 (g CO2)-1 for FGD + FF off and 8.0×106 (g CO2)-1 for FGD + FF on. Thus, new particle formation can increase the real atmospheric particle number emissions even by several orders of magnitude. It should be noted that particle formation depends strongly on the plume age [SO2] and primary particle concentrations, and it is possible that there are some low-volatile organics or SO3 present in the plume, affecting the nucleation.

Our observations show that the number of secondary particles formed in the flue-gas plume can be several orders of magnitude higher than the primary particles directly emitted from the flue-gas duct. The formation can already be observed at a distance of ca. 2 km from the stack; this distance is significantly lower than the grid size used in many atmospheric models, which demonstrates the need for subgrid parameterizations for power-plant-originating secondary particles. Such a parameterization does already exist (Stevens and Pierce, 2013), but it does not account for different types of sulfur removal technologies such as semi-dry desulfurization and wet desulfurization. Determining the effect of different removal technologies on power plant secondary aerosol production would increase the accuracy of particle-loading predictions for regional air quality and global models.