The scattering and backscattering coefficients (σsp and σbsp, respectively) were measured at three wavelengths (λ=450, 525, and 635 nm) using an integrating nephelometer (Aurora 3000, Ecotech). The sample air was taken through a 2 m stainless steel tube, the top of which is 1 m above the roof. The inlet has a rain cap and an external heater to prevent condensation. The zero of the nephelometer was checked by filtered air every day and the span by Tetrafluoroethane (R134a) every 2 weeks. The monthly average relative humidity (RH) at SORPES varies from 65 to 80 % (Ding et al., 2013b) and the aerosol hygroscopic growth is usually significant when RH increases above 50 % (Baltensberger et al., 2003; Zhang et al. 2015; WMO, 2016). We use an internal heater to reduce the RH of the sample air below 50 % for most of the time. Since the internal heater of the nephelometer often malfunctioned, ∼ 25–30 % of data suffered from high RH. The respective data were corrected as will be discussed below. Light absorption was measured using a 7-wavelength Aethalometer (AE-31, Magee Scientific) at λ=370, 470, 520, 590, 660, 880, and 950 nm. The Aethalometer is a filter-based instrument that measures light attenuation from which light absorption can be calculated. The detailed calculation will be discussed below. The Aethalometer shares the same PM2.5 cyclone inlet with several trace gas analyzers. The sample air is taken through a stainless steel tube to the instruments. The flow rate for the Aethalometer was set to 5.0 L min-1 for the whole period. An internal flowmeter records the real-time flow rate continuously, and flow checks were conducted twice a year using a bubble flowmeter (Gilibrator system, Gilian). The time resolution of the Aethalometer data was set to 5 min and it was set to change the sampling spot when the maximum attenuation was 125. These settings were used for the whole period.

Supporting measurements were conducted for the same period (Ding et al., 2013b, 2016b). Particle number size distributions were measured using a custom-made differential mobility particle sizer (DMPS) in the size range of 6–800 nm (mobility diameter) and an aerodynamic particle sizer (APS, TSI model 3321) in the size range of 0.52–20 µm (aerodynamic diameter). More details can be seen in Qi et al. (2015). The number size distributions were used here for modeling scattering coefficients, for calculating effective diameters, and for estimating particle mass concentrations as will be discussed below.

Mass concentrations of particles smaller than 2.5 µm (PM2.5) were measured with an online analyzer based on the light scattering and beta ray absorption (Thermo Scientific, 5030 SHARP, USA). The trace gas measurements (NOx and NOy) used in this work were conducted with a NO-NO2-NOx Analyzer (model 42i, Thermo Scientific, USA) and a NO-DIF-NOy Analyzer (model 42i-Y, Thermo Scientific, USA). These data were used for estimating the photochemical age of air masses. More details for PM2.5, trace gases, water soluble ions, and meteorological parameters can be found in Ding et al. (2013b, 2016b) and Xie et al. (2015).

First the truncation error of the scattering measurements was corrected according to Müller et al. (2011). In addition, since 28.6 % of total data were measured when the sample air relative humidity RHsample>50 %, due to an intermittent fault of the internal heater of the nephelometer, the scattering coefficients were corrected for hygroscopic growth in order to maximize the data availability when the internal heater of the nephelometer was malfunctioning. Hygroscopic aerosols take up water as humidity increases thus increasing σsp. The impact of relative humidity on σsp is defined as the scattering enhancement factor f (RH, λ): f(RH,λ)=σsp(RH,λ)/σsp(dry,λ), where σsp (dry, λ) and σsp (RH, λ) represent scattering coefficients at wavelength λ in dry and humid conditions, respectively. We used the parameterization with the equation f(RH)=c⋅(1-RH)-g in this study. The constants c and g for total scattering (backscattering) coefficient were set to 0.72(0.87) and 0.65(0.34), respectively, according to Carrico et al. (2003) who derived them from measurements during ACE-Asia, a well-recognized aerosol experiment in Asia. Here we choose the value for “polluted” condition in their study. All total scattering coefficients and backscattering coefficients measured with sample relative humidity RHsample>50 % were corrected according to Eq. (2) to RH = 50 %. By considering that the RH sensor inside the nephelometer may not be as accurate as the one at the meteorological station, we recalculated the sample RH using the Clausius–Clapeyron equation. It was assumed that the absolute humidity of the sample air and at the RH sensor 20 m away from the inlet are the same. The pressure and temperature of the nephelometer were used for correcting the scattering coefficients to standard temperature and pressure (STP) conditions (T=273.15 K, p=1013 hPa). All aerosol optical properties discussed in this paper use STP condition unless otherwise specified. A brief comparison between non-corrected scattering coefficients and data corrected with the two parameterizations is presented in the Supplement Sect. S1.

The Aethalometer does not measure absorption coefficient directly, instead it measures the light attenuation (ATN) of aerosol-loaded spots on quartz filters. The attenuation coefficient σatn at wavelength λ is calculated from σatn(λ)=AΔATN(λ)QΔt, where Q is the flow rate, A is the spot size, and ΔATN is the change of attenuation during the time step Δt. The Aethalometer firmware converts σatn to equivalent black carbon (BCe; Petzold et al., 2013) mass concentration by dividing it with a wavelength-dependent mass attenuation coefficient of 14 625 m2 g-1λ(nm)-1. However, it is not as straightforward to calculate the absorption coefficient σap. Several algorithms for calculating σap from Aethalometer data have been presented, e.g., Weingartner et al. (2003), Arnott et al. (2005), Schmid et al. (2006), Virkkula et al. (2007), and Collaud Coen et al. (2010). In principle they can all be presented in the form of σap=fσatn-sσspCref or σap=σatn-s′σspCrefR, where f and R are functions that correct for the loading, s and s′ are the fraction of scattering coefficient that results in a change of ATN and would be interpreted as absorption and BCe if not taken into account, and Cref is the multiple-scattering correction factor. There are no unambiguous forms for f, R, s, s′, and Cref. A recent analysis suggested that f is influenced by the aerosol backscatter fraction (Virkkula et al., 2015). Arnott et al. (2005) and Schmid et al. (2006) suggest that Cref is wavelength-dependent, whereas Collaud Coen et al. (2010) used a non-wavelength-dependent Cref. In this study, we used the Collaud Coen et al. (2010) algorithm with Cref=4.26, the value obtained from measurements in a flat region near populated and industrialized areas at Cabauw, the Netherlands (Collaud Coen et al., 2010).

Light absorption and scattering depend on wavelength λ approximately as λ-AAE and λ-SAE, where AAE and SAE are the Ångström exponents of absorption and scattering, respectively. SAE can be calculated from σsp measured at two wavelengths λ1 and λ2 from SAE=-log⁡(σsp,λ1)-log⁡(σsp,λ2)log⁡λ1-log⁡(λ2). For multiple wavelengths, SAE can also be calculated by taking the logarithm of scattering coefficients and the respective wavelengths and SAE is the slope obtained from their linear regression as was done by Virkkula et al. (2011). SAE is typically considered to be associated with the dominating particle size so that large values (SAE > 2) indicate a large contribution of small particles and small values (SAE < 1) a large contribution of large particles. However, this relationship is not quite unambiguous, as discussed by, for example, Schuster et al. (2006) and Virkkula et al. (2011). In this study, unless otherwise specified, we use σsp at λ=635 and 450 nm to calculate SAE; For the tables, other wavelength pairs were also used. To calculate absorption coefficient according to Eg. (4), σsp measured at the nephelometer wavelengths were interpolated and extrapolated to the Aethalometer wavelengths according to σsp,λx=σsp,λ1 (λ1/λx)SAE .

AAE can be calculated from Eq. (6) by using σap instead of σsp. AAE is an indicator of the dominant light absorber so that values around 1 indicate absorption by BC (e.g., Bond and Bergstrom, 2006; Bond et al., 2013) and clearly larger values by other absorbers. For example, light absorbing organics may yield AAE in the range 3–7 (e.g., Kirchstetter and Thatcher, 2012). The interpretation is ambiguous since AAE not only depends on the dominant absorber but also on the size and internal structure of the particles. For instance, for pure BC particles, AAE variation may have AAE < 1 and BC particles coated with non-absorbing material may have AAE in the range from < 1 to almost 2 (e.g., Gyawali et al., 2009; Lack and Cappa, 2010). In this study, unless otherwise specified, we use σap at λ=370 and 950 nm to estimate AAE; For the tables, other wavelength pairs were also used.

The ratio of scattering to extinction is the single scattering albedo (SSA) SSA=σsp,λσext,λ=σsp,λσsp,λ+σap,λ It is a measure of the darkness of aerosols. At low SSA aerosols heat the atmosphere and at high values they cool it, depending also on other parameters (e.g., Haywood and Shine, 1995). SSA is ∼ 0.3 for pure BC particles (e.g., Schnaiter et al., 2003) and 1 for purely scattering aerosols. SSA was calculated for the Aethalometer wavelengths. The backscatter fraction, b=σbspσsp, was calculated at λ=450, 525, and 635 nm. It is a measure related to the angular distribution of light scattered by aerosol particles. For very small particles, b approaches the value 0.5 (e.g., Wiscombe and Grams, 1976; Horvath et al., 2016) and decreases with increasing particle size. From b, it is possible to estimate the average up-scatter fraction β, one of the properties controlling the aerosol direct radiative forcing (e.g., Andrews et al., 2006). The larger b is, the more aerosols scatter light to space and cool the atmosphere or heat it less if the aerosol is so dark that it heats the atmosphere as shown in the formula for the top of the atmosphere aerosol radiative forcing efficiency (RFE = ΔF/τ), i.e., aerosol forcing per unit optical depth (τ): ΔFτ=-DS0Tat21-Acω0β1-Rs2-2Rsβ1ω0-1, where D is the fractional day length, So is the solar constant, Tat is the atmospheric transmission, Ac is the fractional cloud amount, Rs is the surface reflectance, and β is the average up-scatter fraction calculated from b. If the non-aerosol-related factors are kept constant and if it is assumed that β has no zenith angle dependence, this formula can be used for assessing the intrinsic radiative forcing efficiency by aerosols (e.g., Sheridan and Ogren, 1999; Delene and Ogren, 2002). The constants used were D=0.5, So=1370 W m-2, Tat=0.76, Ac=0.6, and Rs=0.15 as suggested by Haywood and Shine (1995), and β was calculated from β = 0.0817 + 1.8495b-2.9682b2 (Delene and Ogren, 2002).

The size distributions measured with the DMPS were used to calculate three weighted mean diameters, the geometric mean diameter (GMD), GMD=exp⁡∑Niln⁡Dp,iNtot, the surface mean diameter (SMD), SMD=∑Dp,iSiStot=∑Dp,i3Ni∑Dp,i2Ni, and volume mean diameter (VMD), VMD=∑Dp,iViVtot, where i is number of size bin, Dp,i is mobility diameter, and Ni is number concentration. The mass concentration of particles smaller than 0.8 µm was calculated from m0.8=ρpVtot=ρp∑Niπ6Dp,i3, where the density of particles ρp was assumed to be 1.7 g cm-3. The DMPS measures the mobility diameter which for spherical particles equals the physical diameter Dp. The aerodynamic diameter of spherical particles with density ρp is Da=ρpρpρ0ρ0Dp, where ρ0 is the density of water. For Dp=0.8 µm and ρp=1.7 g cm-3, this yields Da=1.0 µm. In the results, therefore, the mass concentration calculated from the number size distributions will be denoted as PM1. The reasoning for the use of a density of 1.7 g cm-3 was presented by Wang et al. (2017). The PM1 concentrations were calculated by using the density of 1.7 g cm-3 even though it was not determined with any physical measurements so an explanation is needed. The density of the major inorganic aerosol compounds ammonium sulfate and ammonium nitrate are 1.76 and 1.725 g cm-3, respectively (e.g., Tang, 1996). The density of sulfuric-acid-coated soot has been estimated to be 1.7 g cm-3 (Zhang et al., 2008). Ambient aerosol particles also contain many unknown compounds such as organics and also some water even at RH < 50 %. Densities of real atmospheric aerosols have been published from several regions. Just to name some, the mean apparent particle density of 1.6 ± 0.5 g cm-3 was determined for urban aerosol by Pitz et al. (2003) and at a boreal forest site the average density was 1.66 ± 0.13 g cm-3 (Saarikoski et al., 2005). Based on the above, it is reasonable to use the density of 1.7 g cm-3 for the estimation of aerosol mass concentration from the number size distributions. It is clear, however, that this value is uncertain and also that in reality it is not constant as the chemical composition of aerosols varies.

The DMPS measurements were continuous throughout the whole study period, while the APS for a few months only. We estimated the contribution of particles smaller than 800 nm to scattering by using the DMPS and APS data measured during one month in July–August 2014. Scattering coefficients were calculated from σsp(λ)=∫Qsp(λ,Dp,m)π4Dp2n(Dp)dDp, where Qsp is the scattering efficiency that depends on particle size (Dp), wavelength (λ) and refractive index (m) of the particles. The results showed that the contribution of particles in the DMPS size range was ∼ 91 % of the whole integrated σsp. Since the APS data were short we did not model scattering for the whole period, but only discuss the weighted mean diameters from DMPS data.

Figures 6a and b present the scattering and absorption coefficients and Fig. 6c the photochemical age as -log(NOx / NOy) observed at the different wind directions and speeds by using polar coordinates. Figure 6d presents a standard wind rose for the 2 year measurement period. The prevailing wind direction is E and NE. Only a small fraction of wind blew from the SW and NW. There was no big difference in wind speed from the different directions: the largest and lowest average wind speed (WS) was 3.9 and 2.0 m s-1 from the directions 100–105 and 160–165∘, respectively.

Generally, both σsp and σap decreased with increasing wind speed when WS > 1 m s-1 in all directions (Figs. 6a, b, S7). This suggests that at strong winds, air was generally more diluted with cleaner air from upper altitudes by turbulent mixing. The effect of horizontal transport, increased dispersion, and shorter residence time within emission areas may also contribute to the decrease in σsp and σap. We do not make further analyses on the possible explanations, it would require extensive modeling that is out of the scope of the present paper. An exception was the west-northwesterly (WNW) wind direction (WD ≈ 285 ± 15∘) sector since σsp did not decrease much with increasing wind. In this sector the above-mentioned dilution effect required stronger winds: the highest σsp was observed at WS ≈ 2.5 ± 0.5 m s-1 but almost as high values were still observed at WS ∼ 7 m s-1, above which σsp started decreasing. However, the frequency of winds from this sector WD was very low, only 1.3 % of whole period so it does not change the general picture of decreasing scattering with increasing wind.

High σsp (>480 Mm-1) was also observed at weak (WS < 2 m s-1) southwesterly (SW, WD ≈ 215 ± 10∘) winds. This is probably a mixture of large-scale, regional, and local emissions. The center of the city is in that direction and at low wind speeds pollutants are easily transported to SORPES without a strong dilution. However, the center of Nanjing is still too close to be the most important contributor to light-scattering particles, especially in case particles are formed by NPF and growth by condensation. A rough estimate of the transport distance needed to grow particles to sizes that scatter light efficiently can be calculated by using the information on the particle growth rate and wind speed. The time evolution of the average diurnal particle size distribution (Fig. 5) shows that new particles with Dp≈10 nm formed before noon grew to sizes that scatter light significantly, i.e., Dp>∼ 100 nm in about 10 ± 1 h yielding an approximate growth rate (GR) of ≈ 9 ± 1 nm h-1, which agrees with the analysis of Qi et al. (2015). In 10 h at WS = 0.5 m s-1 the air mass would have drifted a distance of 18 km which is just the distance to the city center. At the weakest winds from the SW the contribution of the city to the amount of scattering particles may thus have been observed even if particles were formed by NPF. However, in a city a large fraction of aerosols are primary particles, especially BC emitted from vehicles in the size range of ∼ 60 ± 20 nm (e.g., Bond et al., 2013; Kulmala et al., 2016). At a GR of ≈ 9 nm h-1 it would take ∼ 5 ± 2 h for them to grow to sizes >100 nm. In these cases particles emitted from within Nanjing will also affect scattering but their SSA would be lower than the observed SSA. This was estimated by a core-shell Mie code (Wu and Wang, 1991) that yields SSA < 0.6 at λ=520 nm for BC particles with a core of 60 ± 20 nm coated with 40 nm of scattering material, for instance ammonium sulfate. At the weakest winds from the SW sector the observed SSA at λ=520 nm was > 0.9, clearly higher than it would be if particles were emitted as BC particles within Nanjing and coated by condensation, supporting the interpretation that sources of the high σsp during weak winds are not only within Nanjing.

When wind speed is higher, regional transport of pollutants plays an even more important role. The highest σsp in Fig. 6a is in the WNW sector at WD ≈ 285 ± 15∘ and WS ≈ 2.5 ± 0.5 m s-1. At this speed the air masses drift 90 ± 18 km in 10 h that was estimated to be the time to reach optically significant particle sizes since the formation by NPF. This is outside the urban area of Nanjing. In an urban environment, significant amounts of particles are also emitted as primary particles, mainly BC, so it should be estimated whether they could explain the observation. At WS = 2.5 m s-1 it would take approximately 2 h for air masses to be transported the 18 km from the center of the city so at the observed high growth rate of 9–10 nm h-1 particles would grow 18–20 nm. Fresh BC particles are typically in the size range of ∼ 60 ± 20 nm (Bond et al., 2013) so they would reach the size range of ∼ 80 ± 20 nm. This is still much too low to explain the high σsp in the WNW sector. Further, 60 ± 20 nm BC particles coated with 20 nm of scattering material would have a very low SSA: the core-shell Mie code (Wu and Wang, 1991) yields SSA < 0.3 at λ=520 nm, whereas the SSA at WD ≈ 285 ± 15∘ and WS ≈ 2.5 ± 0.5 m s-1 was high, > 0.95. These analyses suggest that the aerosol responsible for these highest values originated from outside the urban area of Nanjing regardless of whether they were formed by NPF or emitted as primary particles. An additional analysis (Supplement Sect. S7.2) shows that K+ concentration was slightly elevated in this sector suggesting biomass burning may have contributed some to the high σsp.

At low and moderate winds (WS < ∼ 3 m s-1) from east and southeast (WD range ∼ 75–165∘), σsp was also high, > 480 Mm-1, suggesting that the air masses from the YRD have a higher σsp than the average value. The SSA in this sector was also high, > 0.92, indicating aged aerosol which was in agreement with the high photochemical age of air masses, i.e., -log(NOx / NOy) > 0.28 (Fig. 5c).

The absorption coefficient had a different dependence on wind. The relationship between σap and WS is very clear: at weak wind, σap was obviously high and it decreased significantly as WS increased in all wind directions (Fig. 6a, b, S7). It was the highest at weak southwesterly winds (SW, WD ≈ 225 ± 15∘ and WS ≈ 0.8 ± 0.2 m s-1) but high σap values were observed especially at winds from the southern sector WD = 180 ± 30∘ at WS < 2.5 m s-1. The high σap values in the SSW sector (WD ≈ 200 ± 10∘) were observed approximately from the same direction as the above-mentioned σsp SW peak direction and can be attributed to emissions from the urban areas of Nanjing. This is also supported by the comparison with the polar contour plot of the photochemical age of air masses, i.e., -log(NOx / NOy) (Fig. 5c). It shows that photochemically fresh air with -log(NOx / NOy)≤0.12 was observed at SORPES with winds from this same direction. Also σap≥42 Mm-1 from the SSE sector (WD ≈ 165 ± 15∘) follows approximately the contour of -log(NOx / NOy)≤0.12 suggesting that the high σap from this sector was associated with photochemically fresh traffic emissions. An analysis using aerosol chemical composition and wind data (Supplement S2.3) suggests that the main cause for the high σap during winds from the SSE sector is the nighttime heavy traffic on country dirt roads to several small factories and mines located within about 3–10 km to the SE of SORPES

A careful inspection of the contour polar plots for σsp and σap (Fig. 5a, b) shows that in the WNW sector actually both of them have local maxima at the same WS–WD combinations. In these local maxima SSA is high, ∼ 0.95 or higher, suggesting that the aerosol is aged. On the other hand, photochemically fresh air with -log(NOx / NOy)≤0.2 was also observed with winds from the same WNW sector as the highly scattering aerosol. These are apparently controversial results since to grow particles to the size range that scatters light at high efficiency requires time. Wind blows from this direction mostly in winter (Fig. 5d). The high σsp was observed in winter pollution episodes during which SSA grew during the evolution of the episodes, as will be discussed below. There is a highway located to the west of SORPES so the lower-than-expected photochemical age can be explained by the flow of the aged and grown particles over the highway and mixing with fresh NOx emissions.

Another interesting wind direction is the NE sector (WD ≈ 45 ± 15∘). At all wind speeds from that sector the photochemical age is relatively low and the lowest (-log(NOx / NOy)≤0.12) at high wind speeds (WS ≈ 6 ± 1 m s-1). With this WS–WD combination both σsp and σap were low. This suggests that in this direction there is a NOx emitter that does not emit significant amounts of BC and that it is relatively close since particles have not grown to size ranges large enough to affect σsp significantly.

The 72 h retroplumes were calculated every 3 h, so there were eight retroplumes per day. To assess the source areas of high (low) σsp and σap the retroplumes of the 3 days with the highest (lowest) daily-averaged σsp and σap of each month were averaged, altogether 576 retroplumes. Since there are approximately 30 days per month, the three lowest daily averages represent approximately the lowest 10 % and the three highest daily averages the highest 10 % of the daily averages. The reasoning for this approach is that (1) diurnal cycles are dominated by cycles of PBLH and photochemistry and (2) seasonal variation hides obvious pollution episodes in cleaner months. The results are shown in Fig. 7. It shows that the potential source region of the highest 10 % of both σsp and σap are within a large area from eastern China, with the highest retroplume around Nanjing spread between the longitudes 115–123∘ E (∼ 700 km) and the latitudes 28–35∘ N (∼ 800 km) (Fig. 7a, b). The color represents the product of integrated particle concentration and residence time of the particles within a certain grid cell, as explained in Section 2.5. It can be interpreted that pollutants emitted in a grid cell with the value of 10-12 can affect the extensive AOPs at SORPES 100 times more than a grid cell with the value of 10-14 if the emission rate is the same and chemical reactions, removal, and other processes during the transport are ignored. For the lowest 10 % of both σsp and σap daily-average air masses mainly originated from the ocean in the east with a fast transport pathway (Fig. 7c, d). A comparison of Fig. 7a, b suggests a slightly different transport pattern for the highest 10 % of σsp and σap daily averages. For both σsp and σap, sub-regional air masses from the southeast contribute clearly to the highest 10 %, i.e., from the city cluster in the YRD region (Ding et al., 2013b), as well as air masses transported from various directions, indicating more local emissions for Nanjing and the adjacent cities. The most obvious difference is that high σsp is more clearly associated with air mass transport from the northwest, especially from regions north of 35∘ N, i.e., from the NCP and Shandong province. These are regions where the high emission of SO2 could have a large regional impact on scattering coefficient in the south as a high concentration of sulfate is formed.

The results from the retroplume calculation (Fig. 7) apparently seem inconsistent with the results from the wind rose analysis (Fig. 6). One of the explanations is that the wind rose analysis was based on hourly data but the retroplume calculations on daily averages. In other words, the wind rose results show more details about the change of aerosol coefficients according to changes in wind direction of local wind at high temporal resolution, but the latter shows more information about the history of air masses when they get transported long distances.

It is possible to count approximately 14–16 distinguishable pollution episodes by using either the PM concentration or the scattering coefficient time series. The analyzed period was 120 days long so, on average, there was a pollution episode about every 8 ± 1 days. The definition of the start and end of a pollution episode is not unambiguous, so the above number should be treated cautiously. The concentrations of PM2.5 and PM1 tracked each other very closely suggesting that, within the uncertainties, most of the aerosol mass is secondary, pollution-related compounds, and that soil dust which in general is in the super-micron size range contributed very little to aerosol mass and scattering at SORPES.

The trajectory cluster time series, color coded on the top of Fig. 9, shows that when air masses were associated with the West or the YRD clusters, there were no big differences in concentrations. The Coastal trajectory cluster was often but not always associated with lower concentrations. Most of the episodes ended with trajectories associated with the North cluster (see Supplement Fig. S11). Meteorological analyses show that the trajectories associated with the North cluster brought air from the north, high above Beijing during cold fronts. There were also episodes during which there were trajectories belonging to many different clusters, YRD, West, and Coastal but there were no clear differences in concentrations until the clearing phase associated with the cluster North. During these episodes, polluted air arrived from all directions in line with wind roses that showed there was no strong dependence on wind direction. Instead, the concentrations kept rising.

Most episodes followed a similar pattern: during the evolution phase the PM concentrations grew day after day during several days at a rate of some tens of µg m-3 day-1 but the end of the episode was usually abrupt, air cleared within hours. The largest drop in the period occurred on 2–3 February when PM concentrations, σsp, and σap decreased by more than an order of magnitude within hours. The same cycle applied to all extensive parameters: PM and BCe concentrations, σsp and σap clearly increased more slowly during the growth phase of the episodes than decreased in the end (Fig. 9b, e). At the same time the daily maximum PBLH (Fig. 9a) decreased during most of the episodes from more than ∼ 1500 m to less than ∼ 700 m. This PBLH decrease is in agreement with the analysis of Petäjä et al. (2016) and Ding et al. (2016a) who showed that high PM and especially BC concentrations enhance the stability of a polluted boundary layer, which in turn decreases the boundary layer height and consequently cause a further increase in PM concentrations.

Even during the growing phase of the episodes there were obvious diurnal cycles of the AOPs. For instance, low PM concentrations, σsp, and σap during daytime and higher at night combined with a growing trend can be explained with the formation of a residual layer: when the PBLH decreases at night part of the aerosol remains above the PBL. The following day new pollutants get mixed with the pollutants remaining in the residual layer. This leads to a continuous accumulation of aerosols in the PBL and a slower, non-symmetric cycle. Part of the accumulation is due to BC, as is seen in the increasing BCe concentration even though the mass fraction of BCe (fm(BCe)=BCe/PM2.5) decreased from ∼ 10 to ∼ 3 % during the growth phase of the episodes (Fig. 9c). The particle number size distribution time series (Fig. 9d) shows that there are indications of NPF also during the polluted period. Even though these new particles grow quickly, it is shown above that their contribution to total scattering remains low during the day of NPF.

The intensive aerosol properties, i.e., those that do not depend on the amount of particles, clearly evolved during the pollution episode cycle. First, the effective particle size grew, which is depicted as the time series of the geometric mean diameter (GMD; Fig. 9d). There was an obvious diurnal cycle with the GMD as well. The growth leads to many changes in the intensive AOPs. The mass scattering efficiency MSE = σsp m-1 (Fig. 9f) grew during the extended pollution episodes from about 4 to ∼ 6 m2 g-1, which is in the range presented by Hand and Malm (2007). In other words, the unit mass of aerosol scattered light more efficiently at the end of the episode than at the beginning. An obvious explanation is that this is due to the growth of both particle diameter and the scattering efficiency (Qs) even though the changing refractive index also plays a role in this. The Ångström exponents of scattering and absorption (SAE and AAE, respectively; Fig. 9g) as well as the backscatter fraction b (Fig. 9i) decreased as the particles grew. The decrease in AAE during the growing phase of the episodes are explainable by a growing shell on a BC core as has been modeled by Gyawali et al. (2009) and Lack and Cappa (2010). At the same time, SSA (Fig. 9h) increased, which can be explained by condensation of light-scattering material and thus increasing the thickness of a shell surrounding a BC core.

Contrary to the strong evolution of the other AOPs during the growth phase of the pollution episodes, the radiative forcing efficiency (RFE = ΔF/τ; Fig. 9j) did not vary strongly. This is interesting since intuitively it could be thought that the higher SSA grows the lower is the RFE, in other words the more the particles cool the atmosphere. That RFE remained fairly stable is due to the growth of the particles: larger particles scatter light upwards less efficiently than small ones, which to some extent compensates the higher SSA as will be shown below. A similar phenomenon was observed by Garland et al. (2008) during an intensive campaign in Guangzhou in southeastern China in July 2006.

The scatter plots (Fig. 10) show that all the analyzed AOPs clearly depend on SMD and VMD but not so obviously on GMD. σsp was generally higher the larger the weighted diameters were (Fig. 10a). This is the intuitively most logical relationship of all those presented in Fig. 10 since σsp of a size distribution is calculated from Eq. (13) that includes the surface area of a spherical particle. When particles grow their surface area grows and they scatter more light.

The observed darkest aerosol had SSA < 0.85, which is not even close to that of pure fresh BC. Then GMD was in the range of 30–80 nm, SMD at 250 nm, and VMD at 300–350 nm. These can be compared with BC size distributions observed elsewhere. Schwarz et al. (2008) measured BC size distributions with a single-particle soot photometer (SP2) and found that the mass median diameter (MMD) and geometric standard deviation of these distributions were 170 and 1.71 nm, respectively, in an urban air, and 210 nm and 1.55, respectively, in continental background air. These values yield number mean BC diameters of 72 and 118 nm for urban and continental background air, respectively. Our GMD was in the same range but VMD was clearly larger. It can therefore be deduced that even the darkest aerosol we observed was not fresh BC. The cases with very high SSA and GMD < 40 were very probably associated with NPF events. The SSA growing with growing weighted mean diameters is plausibly explainable by a larger scattering shell on an absorbing core.

SAE is a parameter that is often used as a qualitative indicator of dominating particle size so that large values indicate a large contribution of small particles and small values a large contribution of large particles. For SMD and VMD this is indeed so in our data (Fig. 10c). GMD, on the other hand, cannot be predicted at any uncertainty with SAE. All these are consistent with the relationships observed in a completely different environment, the boreal forest at SMEAR II, Finland (Virkkula et al., 2011). All the same conclusions apply to the relationship between the weighted mean diameters and backscatter fraction, b, which is an even better indicator of the dominating particle size (Fig. 10d). This is logical since it is well known that forward scattering increases with growing particle size. Both b and SAE provide information on the particle size distribution but they are sensitive to somewhat different particle size ranges (e.g., Andrews et al., 2011; Collaud Coen et al., 2007). Collaud Coen et al. (2007) presented a detailed model analysis of both of these AOPs and showed that b is most sensitive to small accumulation mode particles, i.e., particles in the size range < 400 nm whereas SAE is more sensitive to particles in the size range 500–800 nm. Delene and Ogren (2002) showed the importance of fine-to-coarse scattering ratio (ratio of scattering in the PM1 and PM10 size ranges).

The relationships of SSA are analyzed further with the scatter plots in Fig. 11. SSA was in general higher than σsp was but the range of SSA was very large, ∼ 0.82–0.98 when σsp was in the range < 400 Mm-1 (Fig. 11a). SSA was always high, > 0.94 in the most polluted air masses when σsp was > 1000 Mm-1. The color coding with the photochemical age further shows that the most polluted air masses were mainly aged with PA > 0.4. There are, however, some data points with PA < 0.2 indicating relatively fresh air even at σsp≈1000 Mm-1. These points have a lower SSA, down to ∼ 0.90. It is very unlikely that scattering coefficients as high as 1000 Mm-1 are due to nearby emissions so the data suggests that in these cases the aerosol consists of an external mixture of long-range-transported strongly scattering particles and fresh, possibly traffic-related, BC particles that have not yet been coated with a thick shell. The comparison of SSA with the backscatter fraction b (Fig. 11b) shows that the lowest SSA was mainly observed when b was in the range ∼ 0.12–0.16 and the highest SSA at b < 0.10, which indicates large particles as discussed above. The highest backscatter fractions were observed in fresh air masses (PA < 0.2) and lowest in the most aged air masses. However, there were again some points with both a low PA and b suggesting that there was an external mixture of long-range-transported and fresh aerosols. The scatter plot of SSA vs. PA (Fig. 11c) shows very clearly that the darkest aerosol (SSA < 0.9) was in the freshest air masses. But it also shows that in some of the fresh air masses with PA < 0.1, SSA was very high, > 0.96, suggesting that there were also such NOx emissions that were not associated with BC emissions. This is in line with the analysis presented above in Sect. 3.4.1.

The comparison of SSA with AAE (Fig. 11d) shows that AAE was in the range ∼ 0.9–1.2 which is approximately that estimated from traffic emissions (e.g., Zotter et al., 2017). Lower AAE was observed with high SSA and low backscatter fractions, i.e., when particle size distributions were dominated by large particles. In the analysis of the polluted winter period it was stated that the decrease in AAE during the growing phase of the episodes could be explained by a growing shell on a BC core (e.g., Gyawali et al., 2009; Lack and Cappa, 2010). A similar relationship is observed in the scatter plot of the whole data set.

The aerosol-related parameters affecting the radiative forcing efficiency RFE = ΔF/τ, Eq. (9), are the single-scattering albedo and backscatter fraction. In this study, RFE is always negative, in other words aerosols cool the atmosphere. To avoid confusion, we define “increase” as “the magnitude of the effect is increasing; the sign of the effect is negative” throughout the text. A simple intuitive assumption is that the darker the aerosol, i.e., the lower the SSA is, the less it cools the atmosphere, which means the magnitude of RFE should be lower (the sign of the effect is negative). However, the scatter plot of the real data shows there was a very weak relationship between RFE and SSA alone (Fig. 12a). The relationship between RFE and b is somewhat clearer: the magnitude of RFE increases with increasing b (Fig. 12b). But the data are really scattered in a wide range, which is due to the fact that RFE depends on both SSA and b.

The relationships between RFE, SSA, and b become clearer in a scatter plot of SSA vs. b, where the isolines of constant RFE as a function of both parameters are plotted (Fig. 13). Most data are between the RFE isolines -22 and -28 W m-2. The data do not exactly get clustered around any single RFE isoline. This was studied by classifying SSA into backscatter fraction bins with a width of Δb=0.01, calculating the percentiles of the cumulative distributions in each bin and presenting them in the box plots in Fig. 13. Interestingly, the highest b bin (b=0.17-0.18) has the lowest median SSA but also the most negative RFE, ∼ -28 W m-2, but the lowest b bin (b=0.09-0.10) has the highest SSA but the most negative RFE, ∼ -24 W m-2. This is systematic: decreasing b, i.e., growing particles resulted in a higher SSA and less negative RFE. This means that actually the magnitude of RFE was larger for the darker aerosol, which suggests they would cool the atmosphere more efficiently than the aerosol with the higher SSA. This is due to the size of the particles: small particles scatter light upwards more efficiently than the large ones, which to some extent compensates the darkness of them.

The probability distribution of RFE is presented in Fig. 13 and the percentiles of the cumulative distribution of RFE in Table 1. The median RFE = -25.0 W m-2 and the 10 to 90th percentile range from -27.2 to -22.7 W m-2. Again the values are compared with those calculated for the boreal forest site in Finland (Virkkula et al., 2011). At SMEAR II the median RFE = -23.4 W m-2, close but the magnitude is smaller than at SORPES and the 10 to 90th percentile range was from -28.8 to -16.9 W m-2, which is a clearly larger range of values. The main differences between these two sites are (i) that as the magnitude of RFE at SORPES is higher, i.e., the aerosol cools the atmosphere more efficiently and (ii) that the distribution of RFEs are more narrow than at the clean site. This may be due to the above-described relatively constant RFE during the evolution of the pollution episodes, which occurred frequently. This is also in line with the climatology shown by Andrews et al. (2011) according to which the cleanest sites had the widest RFE range.