Figure  provides an overview of the particle extinction conditions at Leipzig. Shown is the frequency distribution of measured 550 nm ambient extinction coefficients (top panel) and, for comparison, the extinction frequency distribution after normalization of all values to 0 % relative humidity (bottom panel) by using Eq. () and an appropriate input parameter γ discussed below. The 2009–2012 mean values and standard deviations (SDs) are 0.21±0.17 for ambient conditions and 0.11±0.08 km-1 for dry aerosol conditions. Thus the particle water content is responsible for roughly 50 % of particle extinction in the lowermost part of the troposphere at this urban site. analyzed the Leipzig EARLINET Raman lidar observations conducted from 2000 to 2003, and found a mean extinction coefficient for 532 nm wavelength and ambient humidity conditions of 0.094±0.05 km-1 in the upper part of the planetary boundary layer (PBL; above 1000 m height). The surface extinction values found in this study are a factor of 2 larger than the ones found from EARLINET. Most likely, the EARLINET lidar statistic is biased by drier cloud-free days while the SÆMS data are taken at all ambient conditions. Also the present statistic is based on all measurement cases including cases with near-surface capped inversions and not only based on well-mixed conditions. So it is reasonable that the surface mean extinction values shown here are larger than the EARLINET data.

Days with a strong decrease in relative humidity during the morning hours or a strong increase in the evening served as the basis for our specific investigation of the influence of water uptake by particles on their optical properties. We sampled 143 days during the 4-year period with a pronounced diurnal cycle in terms of relative humidity. For the parameterization we only used cases with a diurnal cycle of the relative humidity from max 75 % in minimum to min 80 % in maximum with > 20% difference from minimum to maximum without any changes in air-mass origin or precipitation during the measurement. Figure  presents two examples. Besides the influence of the relative humidity, changing air flow direction (long-range transport) and the daily evolution of the PBL can have a sensitive impact on the near-surface particle extinction coefficient. The backward trajectories (HYbrid Single-Particle Lagrangian Integrated Trajectory Model, HYSPLIT; http://www.arl.noaa.gov/HYSPLIT.php) indicate almost constant long-range aerosol transport conditions during the shown measurement periods. The 96 h back trajectories from 20 August (Fig. a) all originated at 3500 m height and indicate an almost identical descend linearly in height until their arrival in Leipzig with a maximum height separation between the individual trajectories of <500m (trajectory heights not shown in the plot). The three back trajectories from 27 August revealed that the air masses remained at a constant height of 500–1000 m for 96 h. The aerosol optical depth at 500 nm as observed with the AERONET photometer was around 0.1± 0.04 over the whole day until 16:00 UTC on 20 August, and thus confirmed the almost constant aerosol conditions during the time period shown in Fig. b.

According to the lidar observation on 20 August 2009, the PBL development (growth of the PBL height with time) was found to influence the aerosol extinction properties close to the surface not before about 11:30 UTC. As a general result of the 2009–2012 lidar observations, we found that the diurnal PBL evolution only affects the near-surface aerosol concentration to a significant amount when the growing PBL grasps into the clean free troposphere so that any further increase in PBL depth reduces the aerosol concentration in the entire PBL by downward mixing of clean free-tropospheric air. As long as the convectively active PBL is developing into the polluted residual layer on top of the growing, but shallow PBL, the impact of the PBL development on the measured near-surface extinction coefficient was usually found to be low. The steady decrease of the extinction coefficient from 11:30 to 15:00 UTC on 20 August 2009 in Fig. b is the result of the growing PBL and corresponding downward mixing of clean air from the free troposphere. The PBL depth increased from 1300 to 1900 m (30 % increase). This is directly reflected in the decrease of the extinction coefficient from values around 0.2 to values around 0.14, while the relative humidity decreased from 53 to 48 % only.

On 27 August 2009, cloudy weather prevailed. The trajectories in Fig. d show a constant air flow from southwest. The lidar detected a deep, aged aerosol layer (residual layer) up to 2 km height in the morning. The depth of this stable stratified layer increased only slightly up to 2.5 km height until the evening probably driven by shallow PBL convection as detected from ceilometer measurements near Leipzig. The AERONET photometer recorded an aerosol optical depth of 0.2±0.05 for 500 nm throughout the day, indicating a polluted, aged European air mass. Thus, the average PBL extinction coefficient remained constant within a relative uncertainty of 20 % throughout the day, which indicates that the precondition of a constant aerosol load (i.e., a constant dry aerosol extinction) is valid. Finally, only the near-surface extinction decreased significantly with decreasing relative humidity, which itself was caused by a near-surface temperature increase after sunrise. It should be noted that because of the present 2 km deep aerosol layer the decrease of the extinction coefficient in the shallow surface layer did not affect the column aerosol optical depth (AOD) significantly. The humidity was close to 100 % in the early morning around 03:30 UTC and decreased to almost 35 % in the afternoon around 13:30 UTC. The correlation between the simultaneously measured relative humidity and particle extinction coefficient for the 2 different days is shown in Fig. c and f. Curve fitting (assuming a relative-humidity dependence according to Eq. ) reveals the value for γ as given in Fig. c and f. For the pronounced relative-humidity dependence on 27 August 2009, the parameter is quite similar to the one for urban haze according to . For 27 August 2009, we obtain the exponent γ=0.50 according to Eq. (); found γ=0.44.

The calculation of the extinction enhancement factors relies on the assumption that the initial air mass, and more specifically the dry aerosol extinction, is constant throughout the measurement while the relative humidity changes. For the calculation we excluded all days with precipitation to exclude wet depositional loss or days with a distinct change of the air-mass origin during a measurement. We also had to exclude all measurements with visibilities less than the optical path length and days with no significant aerosol load (clean days, bp,e < 0.05 km-1). Secondary aerosol production, advection of aerosol from local sources to the site or an air mass with lower aerosol concentration, temperature-driven partitioning of ammonium nitrate (e.g. Morgan et al., 2010) and of semi-volatile material (e.g. Donahue et al., 2006), and boundary-layer dilution can force this assumption to fail. Accompanying in situ measurements of the extinction coefficient by the dried aerosol would be one choice to provide a dry reference. However, in Leipzig such data were not available for the long-term period investigated here. Therefore, in a first step we have analyzed the backward trajectories to ensure a constant air-mass origin during the measurement. Secondly, the time periods we used to quantify the dominant optical-enhancement process where usually no longer than 4 h. For the effect of boundary-layer dilution it was often found from lidar measurements that the residual layer from the previous day is still present in the morning above the nocturnal inversion layer. The turbulent PBL growth process then mixes the residual layer downwards while the surface aerosol is mixed upwards. Hence, statistically the net dilution effect is smaller than expected from PBL growth alone so that in a lower extreme considering a negligible nocturnal aerosol production at the surface and no deposition of aerosol from the residual layer the dilution effect could even be nonexistent. On average, the possible uncertainties given by the reasons above are still small (on the order of 33 % throughout a measurement; see Sect. 3.7) compared to extinction enhancement by relative humidity (on the order of 200–300 %). With the given preconditions we were able to select 143 days out of our 4-year data set in order to derive the extinction enhancement factor on a statistical basis. The main results of the analysis are summarized in Fig. . For each of the 143 days, the optimum curve after Eq. () and the corresponding value for γ were determined. From these data sets, the mean value γ‾ and the corresponding δγ, as presented in Fig. , were calculated. The curve for the mean enhancement factor (blue curve in Fig. ) is obtained with Eq. () and the mean value γ‾. The upper and lower boundaries of the gray-shaded area in Fig.  are obtained by using γ‾+δγ (upper boundary) and γ‾-δγ (lower boundary) in Eq. (). We found a close agreement of the blue curve with the green curve for urban haze according to in Fig. . More case studies and more details to the parameterization efforts can be found in . In Fig. of our study (mean enhancement factor), we find the extinction enhancement to be 2.41 at 85 % RH, which is very close to the previous finding of 2.78 in Melpitz, the rural background measurement site of TROPOS .

In order to investigate to what extend regional and long-range transport of aerosols influenced our measurements, we performed an extended cluster analysis based on 4-day HYSPLIT backward trajectories for all selected observations. We considered 18 000 individual SÆMS observations performed in the years 2009–2012 in this study. The cluster analysis revealed eight significant air flow regimes for which different optical properties were obtained. The ambient RH for our measurements was found to be 65 % on average for each cluster with a standard deviation of 15 % RH within each cluster. The mean differences between the clusters RH were found to be low (max. 5 %) with the maximum of 70 % RH for cluster 3 and the minimum of 63 % RH for cluster 4. Figure  presents an overview of the near-surface particle extinction conditions over Leipzig for different airflow directions. In Fig. a, the mean value and SD of the particle extinction coefficient for ambient conditions are given. Note the clusters originating west of Leipzig (for strong westerly winds and for slow air-mass transport from the west). Figure b shows the cluster mean extinction values after normalization of the individual data points to 0 % relative humidity by using the derived cluster mean values for γ (Fig. c) and the respective RH of each data point. Figure c presents the cluster mean γ values, which were calculated by Eq. () for individual days. In Fig. c, γ values reaching almost 0.6 and indicating more hygroscopic particles were found for the north and east clusters, whereas the lowest values around 0.4 were observed when the air was advected from the west or northeast. γ is closely correlated with the 80–40 % extinction growth factor and takes values of around 0.4, 0.5 and 0.6 for growth factors around 1.55, 1.7 and 1.85, respectively. In Fig. d, the dry particle extinction coefficients are given for the individual years from 2009 to 2012.

The main findings can be summarized as follows: after removal of the humidity effect on light extinction, the extinction coefficients are generally a factor of 2 lower than that for ambient conditions, disregarding specific airflow conditions. The largest extinction coefficients with a mean value of 0.23 km-1 (0.11 km-1 for dry particles) were observed when the air masses were advected from easterly directions, i.e., from the eastern parts of Leipzig (with the highway A14), from the most eastern parts of Germany, Poland, Ukraine and polluted southeastern European regions. The lowest extinction coefficients (about a factor of 2 lower than the east-cluster values) were observed during situations with fast westerly air-mass transport. Pronounced contributions to particle extinction by the Leipzig city center (clusters 5–7 in Fig. c) were not found. On average, the near-surface extinction coefficients are about 0.17 km-1 (0.08 km-1 for dry particles) with an only weak dependence on the airflow conditions. Particle extinction conditions at our SÆMS measurement site were seemingly widely controlled by local and regional aerosol sources and, only to a second order, by long-range aerosol advection.

The year-by-year statistics of dry particle extinction coefficients in Fig. d support this impression. Air masses advected from the east show the highest extinction values in each of the 4 years and the variations of the individual cluster-mean extinction values around the overall mean are in the 10–20 % range (except for the east cluster). However, year-by-year differences are also obvious. The comparably large 2010 extinction values are caused by strong construction activities in the eastern parts of the Leipzig greater area. Highway construction took place over the entire year in order to extend the highway (A14) from four to six lanes. In contrast, on 1 March 2011 the Environmental Green Zone restrictions were brought into effect in Leipzig to meet the European Union's regulation on particulate matter, which bans vehicles that do not meet certain emission requirements for the city. This implementation may have caused the overall low particle extinction values observed in 2012. There is almost no difference in the precipitation amount for the years 2011 and 2012 that could explain a potentially stronger washout effect in 2012 and frequent cleaning of the streets (and reduced road dust effects). Figure  provides an overview of the mean particle enhancement factor (and corresponding SD) for the different airflow clusters. The shown mean values and SD of the ratio of particle extinction at 80 or 95 % relative humidity to the one at 40 % relative humidity were directly calculated from the available individual days with strong humidity variability (either from 40 to 80 or from 40 to 95 % RH, respectively) for each of the eight air flow regimes separately. Because of the larger required RH span in ambient conditions, Fig 8a includes additional observational cases with respect to Fig 8b. As can be seen in Fig. , large differences between the clusters were not found. The 80–40 % extinction enhancement factor was 1.75±0.4, on average with variations between the clusters mean values on the order of 0.1. Stronger differences between the clusters were found for the 95–40 % extinction enhancement factors. The largest value of 3.5 was observed for northerly air flows with the comparably largest influence of marine particles (at comparably low levels of pollution advection from the Baltic Sea and Scandinavia). The lowest enhancement factor of 2.3 was found for the south-wind cluster with a high amount of anthropogenic less-hygroscopic pollution particles. On average, the 95–40 % extinction enhancement factors were 2.8±0.6.

Table 1 provides literature values of the extinction enhancement factors for comparison. Values between 1.1 and 3.3 have been published for the 530–550 nm wavelength range. For biomass burning aerosol or background (rural) particles extinction enhancement factors as low as 1.0–1.2 were found. For polluted continental areas, the enhancement factors accumulate from 1.6 to 2.0, and for marine particles values above 3.0 are observed. Our observations fit well into the larger frame of observed enhancement factors and adds new values for the high-humidity range (95–40 % enhancement factors).

In Fig. , we compare our SÆMS measurements for a time period of 5 days in September 2009 with particle extinction coefficients at 550 nm derived from ground-based in situ measurements of the dry particle size distribution . Such a comparison was already successfully performed for a 10-day period in March 2000 , with a similar apparatus as SÆMS but by using a very short optical path in the vicinity of the in situ measurement stations. A successful comparison between in situ aerosol observations on the roof of the TROPOS building and the SÆMS observations along the 2.8 km path was also shown in Fig. 8 in for 3 May 2009.

The in situ extinction coefficients are computed from the measured size distributions of dried particles, i.e., for particle size distribution measured at relative humidities around 30 %. A so-called PM10 inlet is used so that very coarse particles with diameters larger than about 10 µm are not measured. The particle size distributions were measured with a tandem differential-mobility particles sizer (TDMPS; 3–800 nm in diameter) and with an aerodynamic particle sizer (APS; 0.8–10 µm in diameter). The in situ data we used for this study are 1 h averages. The particle extinction coefficient was calculated by means of a Mie scattering code based on as described in . The real part of the refractive index n was set to a constant value of 1.53 (typical value for urban haze). Absorption by particles was considered by assuming an imaginary part of 0.01i.

As can be seen, a good overall agreement between the in situ and SÆMS dry extinction time series (black and red curves) is obtained. The 2009 mean (±SD) and median dry particle extinction coefficients are 0.061±0.055 and 0.046 km-1 (in situ), respectively, and 0.073±0.036 and 0.065 km-1 (SÆMS, dry), respectively. The humidity-corrected SÆMS extinction coefficients in Fig.  are calculated from the ambient SÆMS extinction values by using the extinction enhancement parameterization shown in Fig. . The good agreement between the black and red curves indicates the usefulness of the developed parameterization. The correlation coefficient is found to be 0.71.

The strong impact of relative humidity on particle extinction (SÆMS, ambient) is illustrated in Fig. . During the gray-shaded time periods from 13:00 to 17:00 UTC, when the PBL is well mixed on sunny days (days 267–269 in Fig. ), the relative humidity and particle extinction are at their daily minimum. During the afternoon hours, the PBL has the largest vertical extent, which contributes to the observed low extinction values around 15:00 UTC. The systematically lower in situ extinction coefficients on these sunny days compared to the SÆMS (dry) values may be partly caused by the used constant refractive index, which is probably not appropriate for all aerosol conditions throughout the day, especially not when aged particles (after long-range transport) are mixed down from higher altitudes and partly substitute the less aged urban haze close to the ground. The humidity correction may also not be valid at all for the aerosol conditions found during the convectively active period. Furthermore, we compare point measurements with long-path measurements 300–3140 m apart from the PM10 inlet. TROPOS is part of an area with complex urban building structure, whereas the optical path of SÆMS crosses areas with much fewer buildings, even areas without any building, is parallel to several large motorways and crosses the A14 highway.

In Fig. , extinction distributions derived from year-2009 AERONET sun photometer and SÆMS (ambient) measurements are compared. The shown distribution curves are optimum fits to the respective frequency-of-occurrence distributions of measured and derived extinction coefficients. As before, we considered only data measured in the afternoon from 13:00 to 17:00 UTC, when the probability is highest that the PBL is well mixed. In the case of the AERONET observations, the extinction distribution curve shows PBL mean extinction values (vertical column mean values). First, we converted the measured 500 nm particle extinction with the Ångström exponent (500–870 nm) to 550nm wavelength by Eq. (1). Then, all calculated 550 nm aerosol particle optical thickness (AOT) values were divided by the respective PBL height, obtained from numerical weather prediction data (GDAS1: global assimilation system; http://www.arl.noaa.gov/gdas1.php) , before the calculation of the frequency-of-occurrence distribution. At well-mixed conditions the PBL mean particle extinction coefficient is closest to the extinction value measured with SÆMS during the day.

As can be seen in Fig. , a rather good agreement between the SÆMS (ambient) and the AERONET observations is found. The mean extinction coefficients and SDs for 550 nm has been 0.12 ± 0.09 (AERONET) and 0.11 ± 0.06 km-1 (SÆMS). A systematic overestimation of the PBL mean extinction value must be kept in consideration in the interpretation of the AERONET observations, because, on average, 20 % of the AOT is caused by particles in the free troposphere .

For comparison, also the distribution of dry extinction coefficients as obtained from the SÆMS observations after humidity correction and the extinction distribution calculated from the in situ-measured dry particle size distributions are shown for the specific 13:00–17:00 UTC time period. The possible reasons for the deviations found between the two dry extinction frequency-of-occurrence distributions were discussed above.

Finally, we briefly summarize the influence of a relative-humidity increase on the spectral slope of the particle extinction coefficient for the wavelength range from 390 to 881 nm. Figure  shows a steady increase of the Ångström exponent (see Eq. ) with increasing relative humidity for the entire spectrum from 390 to 881 nm and a decrease for the short wavelength range (390–440 nm). The figure is based on all measurements from 2009 to 2010. The reason for the increase of the 390–881 nm Ångström exponent and the decrease of the 390–440 nm Ångström exponent is shown in Fig. . A strong increase of the 390nm particle extinction coefficient was observed with increasing relative humidity; an even stronger increase was observed at 440 nm, whereas no trend or even a decreasing trend of the extinction strength was observed with increasing relative humidity at 881 nm. A strong water-uptake effect for fine-mode particles with a radius <100 nm can explain the strong increase of the extinction coefficient at the shorter wavelengths as our Mie scattering calculations indicate. Furthermore, the impact of fine-mode particles on the extinction coefficient at 881 nm is low. At this wavelength the extinction coefficient is primarily determined by larger particles. Although coarse-mode sea-spray particles cannot be fully ignored in Leipzig, most of the time the coarse mode consists of road and soil dust particles, which do not grow significantly with water uptake. As a consequence, the extinction coefficient at 881 nm might remain constant for all ambient humidity conditions (cf. Fig. 2) while the 390 nm extinction coefficient increases by fine-mode particle hygroscopic growth. Consequently, the overall 390–881 nm Ångström exponent might also increase with relative humidity. Significantly different Ångström exponents for the eight air-flow classes were not observed pointing again to the dominating influence of local and regional pollution on the aerosol conditions at our field site. It is finally worthwhile to mention that the mean value and SD for the 440–881 nm Ångström exponent for the years of 2009 and 2010 are 1.55±0.42 in the case of the AERONET column measurements. In contrast, the 390–881nm SÆMS Ångström exponents show a mean value of 0.91±0.68 for the 2009–2010 period, a clear indication of the strong impact of coarse particles on the SÆMS observations.

The fitting parameter (Eq. ) depends on the knowledge of the initial dry particle extinction coefficient. Unfortunately, this value is not easily available for our measurement technique. Although various measures were taken to ensure constant dry conditions (see Sect. 3.3) certain errors can arise from the assumption of a constant dry particle extinction. Not only dilution effects within the PBL but also changes in local emissions, gas-to-particle partitioning effects, new particle formation and other photo-oxidation processes could contribute to the error.

For our data set of 2009, corresponding in situ data (TDMPS + APS, hourly averaged, measured at approximately 30 % RH), which coincide with the cases used for the calculation of γ, were available at TROPOS. These in situ size spectra were used to determine the dry extinction coefficient in a simplistic manner (Mie scattering, λ=550nm, n=1.53+0.01i, cf. Fig. 9). In order to estimate an error that occurred from our assumption of a constant dry extinction coefficient, we calculated the relative change of the dry extinction coefficient from the moment of highest and lowest RH, respectively, within our fit periods. Based on 54 cases from 2009, the average dry extinction was found to be lower by 33.5 % (with a SD of 35.7 %) during low RH conditions (usually later during the day) with respect to the time of high RH (usually in the morning). This systematic underestimation suggests that effects other than hygroscopicity also played a role and should be considered in more detail for future studies. For this study it means, that the mean γ is possibly overestimated.

Rearranging Eq. () towards γ leads to γ=ln⁡bp,e(λ,ϕ0=0)-ln⁡bp,e(λ,ϕ1)ln⁡(1-ϕ1). The error propagation of Eq. () with respect to the uncertainty of the dry particle extinction Δbp,e(λ,ϕ0=0) results in Δγ=∂γ∂bp,e(λ,ϕ0=0)Δbp,e(λ,ϕ0=0)=1ln⁡(1-ϕ1)Δbp,e(λ,ϕ0=0)bp,e(λ,ϕ0=0), where the number of data points used for a fit were typically on the order of 15. All slope fits were derived in the RH range of ϕ1>40 %. The number of cases used for the parameterization is N= 143, and the error of γ is Δγ⋅N-1. Following these considerations, an error of γ of 0.05 due to the unknown dry particle extinction coefficient seems realistic.