The Polar Nephelometer (PN) (Gayet et al., 1997) measures the angular-scattering intensities (ASIs) of an ensemble of particles ranging from less than 1 µm to about 1 mm diameter, which intersect a collimated laser beam (λ= 804 nm) near the focal point of a parabolic mirror. Observations are usually limited to 32 scattering angles θ near-uniformly positioned from 15∘to 162∘. Measurements at nearly forward and backward directions (θ<15∘ and θ>162∘) are not reliable due to the diffracted light pollution caused by the edges of holes drilled on the paraboloidal mirror (see, e.g., Jourdan et al., 2010). The sampling volume is defined by the cross-sectional area of the beam (10 mm long and 5 mm diameter) multiplied by a linear speed of air populated with particles passing through the instrument. Direct measurement of the ASIs allows particle types (droplets or nonspherical particles) to be distinguished and calculation of the optical parameters to be performed (extinction coefficient Ext and asymmetry parameter g, see Gayet et al., 2002). Generally, the g value decreases with increasing nonsphericity of the particles, all other parameters being the same (Gayet et al., 2002, 2012). The accuracies of the extinction coefficient and asymmetry parameter are 25 and 4 % (Jourdan et al., 2010; Gayet et al., 2012).

The FSSP-300 and FSSP-100 forward-scattering spectrometer probes (Baumgardner et al., 1992; Petzold et al., 1997; Frey et al., 2011) measure the intensity of light scattered by single particles in a forward direction at angles from 6 to 15∘ (Jeßberger et al., 2013), which is governed mainly by diffraction and therefore depends on (i) the refractive index of the particles, and (ii) the projected area of the particle which itself depends on the particle shape. Indeed, the size calibration for nonspherical particles is expressed in terms of equivalent surface diameter, i.e., the diameter of a sphere that has the same projected area (Mishchenko et al., 1997). The FSSP-300 signal is resolved into an array of 31 channels in the size range of 0.35 to 38.6 µm. The signal is then converted into a corresponding particle size using water droplet response (the refractive index of 1.33). Because of the ambiguities in the Mie scattering curve, the FSSP-100 size distributions have been rebinned to 14 size bins in the diameter range from 1.02 to 47.05 µm (water droplet).

The trace gases SO2, HCl, and HNO3 were measured by the Airborne chemical Ionization Mass Spectrometer (AIMS) (Voigt et al., 2014a; Jurkat et al., 2016) equipped with an inlet system and a custom-made ion source generating SF5- reagent ions (Jurkat et al., 2010). Air is drawn into the backward-facing perfluoroalkoxy (PFA) inlet using a pumping system. In the high-voltage gas discharge ion source SF5- ions are produced from a flow of SCF8 in N2 at pressures controlled to 40 hPa. The SF5- ions react selectively with trace species to form product ions via a fluoride transfer reaction (Jurkat et al., 2011). The ions pass three differentially pumped vacuum chambers of the mass spectrometer system, before they are detected with a channeltron detector. An in-flight calibration is performed by adding a permanent flux of isotopically labeled 34SO2 to the inlet line. Further, HNO3 and HCl were calibrated in the laboratory after the flights. Accuracies of 17–36 % were achieved for SO2, 33–35 % for HCl, and 18–36 % for HNO3, mainly depending on dilution of the inlet flow (Voigt et al., 2014a, b).

Water vapor was measured with the tunable diode laser system WARAN (WAter vapoR ANalyzer), which primarily consists of a commercial WVSS-II water vapor sensor (SpectraSensors Inc.) (Kaufmann et al., 2014) with a measurement range from 30 to 40 000 ppmv. In the measurement cell, a laser is tuned over the water vapor absorption line at 1.37 µm and the water vapor mixing ratio is determined from the absorption signal. The passive sample flow through the system is realized using a Rosemount inlet. The water vapor mixing ratio is measured with a relative uncertainty < 6 % at 2.4 s time resolution and for water vapor mixing ratios above 500 ppmv relevant for the low-altitude flight legs shown here. The instrument is calibrated before and after the campaign using a frost point hygrometer (MBW373LX) as the reference. The uncertainty of 0.5 K in the static air temperature measurement translates to a relative uncertainty of around 4 % in the saturation pressure over water. Adding both contributions, the relative humidity with respect to water (RHw) can be determined with a relative uncertainty of a RHw value generally less than 10 %.

Degassing plumes from the volcanoes Mt. Stromboli and Mt. Etna were probed on 30 September 2011 (from 06:50 to 08:40 UTC). Visual observations from the cockpit of the Falcon showed that there was a single plume degassing from Mt. Stromboli, whereas there were two distinct degassing plumes from Mt. Etna, see Fig. 1a. The Etna plumes were spreading at two different altitudes and they originated from at least two craters, namely Northeast Crater (upper plume) and Bocca Nuova Crater (lower plume) (Voigt et al., 2014a). From the four main craters at Mt. Etna, these two craters were identified as the major emitters on that day. The Falcon flight track over Sicily is shown in Fig. 1b. It was set up to probe the two Etna plumes and the Stromboli plume.

Figure 2 shows time series of trace gases measurements, flight altitude, extinction coefficient, and asymmetry parameter derived from the Polar Nephelometer measurements. The very low relative humidity has to be particularly emphasized. The values of RHw are lower than the crystallization humidity of most sulfates, nitrates, and chlorides (see, e.g., Tang and Munkelwitz, 1991). In other words, the plumes were spreading in the dry troposphere. In addition, the air temperatures within the plumes were always above the freezing point, i.e., > 273.15 K. The extinction coefficient series reveals several peaks that correspond to the time intervals when the research aircraft was probing the degassing plumes (see shaded areas in Fig. 2). The close correspondence between the extinction coefficient and the time series of the trace gases HNO3, SO2, HCl is evident in Fig. 2. The trace gas composition of the volcanic plumes has been investigated by Voigt et al. (2014a). Different trace gas mixing ratios of CO2 / SO2 and SO2 / HCl have been identified in the volcanic plumes from the Northeast and Bocca Nuova craters. Specifically, it is shown that neither SO2 conversion to sulfate nor HCl uptake in sulfate aerosol play a major role in the aging plume under dry tropospheric conditions.

We employed the PCA to carry out the cluster analysis (see, e.g., Jolliffe, 2002, chap. 9; Jourdan et al., 2010), that is, to separate the recorded angular-scattering intensities (ASIs) into clusters. The advantage of the PCA consists of the fact that it is self-sufficient; in other words, no a priori hypotheses are needed, because the clustering is only based on internal properties of a data set. In brief, the PCA is an unsupervised method used to explore the intrinsic variability of the data.

The PCA is particularly fruitful when one deals with high-dimensional data. The PCA provides the possibility of capturing much of the total data variation in a few dimensions and organizing observed data into meaningful clusters. That is, with the PCA technique, each vector of the data can be represented adequately by a few coefficients, usually three, which correspond to eigenvectors of a covariation matrix. This is especially true when a limited number of primary physical parameters have a major impact on the measured functions (in our case, angular-scattering intensities). The obtained coefficients can be used in visualization of the data by scatter plots.

Algebraically, principal components could be defined as particular linear combinations of a set of variables. These linear combinations represent the selection of a new coordinate system obtained by rotating the original system of coordinates. The new axes correspond to the directions with maximum variability and provide a simpler description of the covariance structure of the original set of variables (Johnson and Wichern, 1998).

The peculiarity of our approach is that the log transformation is applied to the angular-scattering intensities before the PCA is carried out (see details in Jourdan et al., 2003; Shcherbakov et al., 2005). The reason for such a preprocessing is the following. In contrast to phase functions, ASIs are not normalized, e.g., they are proportional to the particle concentration. In addition, the ASIs values, as well as the variances at the forward angles, as a rule, are of orders of magnitude higher than that ones at the sideward and backward angles. In such conditions, the conventional PCA yields the first principal components that only follow the variance at the forward angles; they do not reproduce all the ASIs variability. The preprocessing, that is, the logarithm of ASIs values, makes the variances comparable at all angles. In the strict sense, the log transformation leads to the multiplicative model of the variance analysis, in contrast to the conventional PCA, which is based on the additive model. At the same time, the variance can be discussed in terms of the additive model when ASIs are plotted in the log scale.

Expressed mathematically, our approach leads to the following representation of measured angular-scattering intensities σj(θi) in terms of the principal components ξl(θi), that is, the first k eigenvectors of the correlation matrix of the log-transformed data set: lnσjθi≈〈ln⁡[σ(θi)]〉+∑l=1kCj,lξlθi, where θi is the scattering angle, the index i designates the ith scattering angle and takes values from 1 to 32, the index j refers to the jth observation of the analyzed flight sequences, 〈…〉 denotes averaging over the total data set (i.e., 1803 PN measurements). When vector expressions are employed, σj has the components σj(θi); ξl, ln⁡σj, and ln⁡σ have the components ξl(θi), lnσjθi, and 〈lnσjθi〉, respectively. The coefficients Cj,l are computed as Cj,l=ln⁡σj-〈ln⁡σ〉T⋅ξl, where T denotes a transposed matrix. Each vector (i.e., ln⁡σj at each j) is represented by a few coefficients Cj,l with quite good accuracy.

The PCA results were obtained using the CONCERT data recorded during the flights on 16 September 2011 (from 14:40 to 17:50 UTC) (Kaufmann et al., 2014) and on 30 September 2011 (from 06:50 to 08:40 UTC) (Voigt et al., 2014a). The data set contains the ASIs measured in degassing plumes, cirrus and contrails. Such a large set was chosen to point out that the scattering pattern of degassing plumes is clearly distinctive (see below).

When the PCA is applied to ASIs, the principal components can have a clear physical meaning. Figure 3a shows the first three principal components along with the corresponding eigenvalues λl normalized as a percentage of the total variance. The first vector ξ1 almost does not depend on the scattering angle, it accounts for 96.8 % of the data variability. This means that it is closely linked to the extinction coefficient and about 97 % of the ASIs variation is mostly due to fluctuations of the particle concentration.

It is well known that effects of size distribution, refractive index, particle shape, and surface roughness are better represented using phase functions, i.e., normalized ASIs. Thus, not only the other principal components are of importance, their contribution to the remaining variability has to be evaluated.

The second vector ξ2 represents 70.4 % of the remaining variability; it has negative values at sideward angles. Generally, high negative values of the corresponding coefficients Cj,2 of such a vector take into account the irregular shape and/or the deep surface roughness of large particles. All of this leads to lower values of the asymmetry parameter (see, e.g., Jourdan et al., 2010).

The third vector ξ3 represents 15.6 % of the remaining variability. Its shape reveals that ξ3 is related to the forward-/backward-hemisphere partitioning of the scattering. The high negative values of the corresponding coefficients Cj,3 imply that less energy is scattered in the forward hemisphere and, thus, more energy is scattered in the backward hemisphere.

Figure 3b shows the scatter plot of the Cj,3 expansion coefficient vs. the Cj,2 coefficient. Therefore, such a presentation describes the features of the PN data set in one of the clearest and most informative ways. Each point is directly associated with one of the measured ASCs. Three main distinctive clusters of points can be identified in Fig. 3b. Additional analysis of the total CONCERT-2011 data set provided the possibility of associating the clusters with the measurements performed within cirrus clouds, contrails, and the degassing volcanic plumes (see the notations in Fig. 3b).

The negative Cj,2 values of the cirrus cluster are typical of irregular large ice particles (see, e.g., Jourdan et al., 2010). The contrail cluster is characterized by high positive values of Cj,2. This feature means that the corresponding phase functions are quite similar to those of ensembles of large spherical particles. The fraction of spherical particles increases with increasing Cj,2. This is especially true for the young contrail subcluster. A detailed discussion can be found in Gayet et al. (2012).

The peculiarity of the degassing plume cluster is that the coefficients Cj,2 are close to zero. Thus, the properties of the degassing plume ASIs can be discussed just in terms of the vector ξ3. That fact results in the following. The effective diameter and the asymmetry parameter of the degassing plume particles have to be smaller, if not much smaller, compared to those of other clusters in the data set, among them the young contrails. Another property of the degassing plume cluster is that it falls into subclusters. Figure 3c repeats Fig. 3b but with the focus of attention on the degassing plumes. It is seen that the ASIs of the NECa and NECb plumes are close to each other; they form one cluster. The BNa and BNb clusters are a little bit separated with the third coefficients, but belong to the same range of the second coefficient that accounts for 70.4 % of the ASIs shape variability. Other properties of the degassing plume subclusters will be discussed in detail below.

Our retrievals were performed with the software and the pre-calculated kernels developed by Dubovik et al. (2006). We recall that the software is employed in the operational processing of AERONET (AErosol RObotic NETwork) for retrieving detailed properties from observations of ground-based sun/sky radiometers (Eck et al., 2008). We will briefly describe the main features of the retrieval algorithm and its implementation on our specific data set.

The pre-calculated kernels contain optical characteristics of spheroids mixtures. The surface of particles can be smooth or severely rough (Yang et al., 2013). A mixture of spheroids of different aspect ratios, sizes and surface texture (smooth or severely rough) is employed as a generalized aerosol model (representing spherical, nonspherical, and mixed aerosols). The aspect ratio values belong to the range (0.3–3.0); the surface-roughness parameter can take only two values 0.0 or 0.2.

The code offers the possibility of retrieving a complete set of aerosol parameters, including the complex refractive index and the size distribution. The aerosol size distribution is presented using size bins; and the size bins are formed with discrete logarithmically equidistant size values. As for size distribution retrievals, the undoubted advantage of the Dubovik code consists in the fact that solutions are constrained to be nonnegative, which significantly improves the quality of retrievals. The constraint is imposed through an elegant and well-founded approach, more specifically, the assumption of the log-normal distribution of measurement errors (see, e.g., Dubovik et al., 2011).

The code includes a quite large set of input parameters that is very advantageous for an experienced user. For example, for different hypotheses of aerosol composition, among others, effects of the ultrafine fraction can be tested. On the one hand, supervised retrievals are time consuming; on the other, one has the possibility to assure a high quality of retrievals. We list some criteria of the retrieval quality in the following. Final results are scarcely affected by small variations of input parameters. When the regularization-parameter value is chosen according to the “L-curve” method (see, e.g., Hansen, 1992), the retrieval residuals correspond to the measurement errors. In a generally nonlinear case, particular attention must be given to the verification if the obtained solution corresponds to the global minimum of an objective function. As for aerosol characteristic retrievals, different starting values of the refractive index may be randomly tried.

Summarized, we modeled the degassing plumes as a mixture of two main particle fractions; one consists of spherical and one of nonspherical particles. Although aerosol particles were not ellipsoidal, we consider randomly oriented spheroids as a reasonable approximation of an ensemble of quite small nonspherical aerosols. In addition, we recall that we considered smooth and severely rough particles (Yang et al., 2013).

Details of the software package used in this works, as well as the code application are described in the supplementary material. To summarize briefly, different initial guesses for the inversion code were performed on a multidimensional grid of the input parameters using a number of input files. The minimum and the maximum sizes of particles as well as the spherical/nonspherical partitioning ratio belong to the set of assessed parameters in addition to the refractive index and the size distribution.

Three representative examples of retrievals are shown in Fig. 4. The corresponding time sequences SV, BNa and NECb are identified in the time series in Fig. 2 by shadowed areas. In Fig. 4a–c, the left panels display the particle size distributions measured with the FSSP-300 and FSSP-100 (solid lines) and the retrieved one (solid black circles). It should be pointed out that the FSSP measurements in Fig. 4 represent particle size distributions considering the size response to water droplets. Due to size response uncertainties linked to different refractive indexes and/or particle shape in plume aerosols (Pinnick and Auvermann, 1979; Dye and Baumgardner, 1984; Jaenicke and Hanusch, 1993; Febvre et al., 2012), the comparison with retrieved size distributions should only be considered qualitative in Fig. 4. Despite these limitations, the FSSP data and the retrieved distributions reveal very similar features of the degassing plume aerosols, in particular the absence of large particles. The calibrated probe response of the specific FSSP adjusted to different refractive indexes is beyond the scope of this paper.

The size distribution was retrieved along with the refractive index m=n+iχ and the spherical/nonspherical partitioning ratio (SNR) of aerosol particles (see Table 1). In the following, the SNR defines the percentage in number of spherical particles relative to the total number of particles. Furthermore, the refractive index and the partitioning ratio are assumed to be constant over the full size range of the retrieved particle size distribution. We emphasize that the information content of the PN data is inadequate for retrieving size-dependent values of such parameters. In other words, variations of the shape and/or the refractive index of small particles lead to variations of the phase function that are lower than the PN measurement errors. Therefore, the refractive index and the partitioning ratio are assumed to be constant over the full size range.

The following results are especially noteworthy. The real part n of the refractive index belongs to the interval from 1.35 to 1.38; the aerosol particles were either nonabsorbing or weakly absorbing; the SNR values are equal to 100 %, i.e., the best fits of the Polar Nephelometer data were obtained with the model of spherical particles (Table 1).

The assessed value of the maximal particle diameter is about 15 µm for the all degassing-plume penetrations (Fig. 4). That is, the size parameter of the probed aerosols is rather small (lower than 60 for the wavelength of 0.8 µm). This feature can explain the fact that all our retrieval results were very close for both values of the surface-roughness parameter. The PN measurements are not sensitive enough to distinguish whether small particles have smooth or rough surface. In view of this result and the SNR values, the degassing-plume aerosols are assumed to be smooth spheres.

The right panels of Fig. 4a–c represent the following data. The average scattering phase function (without normalization) measured by the Polar Nephelometer is shown by solid red circles (see the averaging time intervals in Table 1). The retrieved phase function, shown by solid black circles, was computed from the retrieved size distribution. The main result of Fig. 4 is that the retrieved phase functions agree well with the observations. It should be underscored that there is no systematic bias between them. In other words, the measured ASIs are well fitted by the retrieved phase functions. The residuals (Res) were computed with the formula Res=100⋅1N∑i=1NIθiret-IθimeasIθimeas2, where Iθi is the light intensity at the scattering angle θi, and the subscripts “meas” and “ret” refer to the measured and retrieved values, respectively. The low values of the residuals are noteworthy as well, see Table 1.

Table 1 summarizes the measured and retrieved characteristics. As mentioned above, the relative humidity RHw was low, i.e., about 36 % within the Stromboli plume and near 10 % during the Etna plume samplings. The air temperature was positive, including at the Etna upper-plume altitude (0.3 ∘C). The number concentration (Conc) of aerosols with the diameter d>0.9 µm is estimated within the range of 25–51 cm-3. The effective diameter (Deff) was low, between 1.5 and 2.8 µm, where both parameters Conc and Deff were deduced from the FSSP data. The retrieved values of the refractive index belong to the interval from 1.35 to 1.38. Low values [0.65–0.70] of the asymmetry parameter g correspond to ensembles of small particles, which is in agreement with the Deff values. The extinction coefficients Ext were computed from the retrieval data and the values are quite small, confirming that the ASIs were recorded in single-scattering conditions. We recall that the optical characteristics correspond to the wavelength of 0.8 µm and that the all parameters were recorded at distances of more than 6 km from the plume sources.

As mentioned above, the ASIs of the degassing plumes are partitioned into subclusters (see Fig. 3c). The ASIs of the NECa and NECb plumes are spread within a cluster that is well distinguished from other ones. The second coefficients Cj,2 of the BNa and BNb data are within the same range of values. (We recall that the second vector ξ2 represents 70.4 % of the ASIs shape variability.) Consequently, the asymmetry-parameter values of the Bocca Nuova plumes (BNa and BNb) are a little bit higher compared to those of the Northeast Crater (NECa1, NECa2, NECb), see Table 1. The histograms in Fig. 5 show probability distribution functions of the asymmetry-parameter values computed from the measured ASIs of the BNa and NECb plumes. These two distributions were selected only by using larger data sets, i.e., higher statistical significance. Generally speaking, the BNb and NECa distributions are close to histograms of the BNa and NECb, respectively. As seen in Fig. 5, the distributions are narrow, suggesting quite homogeneous aerosol plume properties. The distinction between optical characteristics of the BN and NEC plumes could result from the difference in chemical composition of aerosols (Voigt et al., 2014a). Though completely independent, this classification of the individual volcanic plumes is similar to results from trace gas composition measurements of Voigt et al. (2014a) for plumes SV, BNb, NECa, and NECb. In addition, the difference in the BN and NEC aerosol emissions was underscored earlier by Allen et al. (2006), who studied aerosol particles at the summit of Mt. Etna downwind from the degassing vents, and by Scollo et al. (2012), who reported observations of the Multiangle Imaging SpectroRadiometer. Martin et al. (2008) evidenced persistent differences in the size distributions of sulfate aerosols between the two main Etna summit plumes.