2.1 Aerosols and sulfur dioxide observations

The ground-based sites selected for the analysis of the transport and the optical characteristics of the volcanic plume include nine AERONET sites in South America and southern Africa: São Paulo (23.3^∘ S, 46.4^∘ W), Gobabeb (23.3^∘ S, 15.0^∘ E), Pretoria (25.4^∘ S, 28.1^∘ E), Durban (29.5^∘ S, 31.0^∘ E), Buenos Aires (34.4^∘ S, 58.2^∘ W), Neuquén (38.5^∘ S, 68 ^∘ W), Bariloche (41.0^∘ S, 71.2^∘ W), Comodoro (45.5^∘ S, 67.2^∘ W), and Rio Gallegos (51.3^∘ S, 69.1^∘ W). The location of these sites in the Southern Hemisphere allows for a large-scale view of the transport of the volcanic aerosol plume. Measurements are obtained at 15 min intervals under cloud-free and daytime conditions. The direct solar extinction and diffuse sky radiance measurements are used to compute the AOD and to the retrieve the aerosol size distribution, using the methodology of Dubovik and King (2000). The estimated uncertainty in the AOD measurements under cloud-free conditions ranges from 0.01 to 0.02 (Dubovik et al., 2000, 2006; Eck et al., 2003, 2005). A detailed description of the CIMEL sun photometer, the AERONET network, and the associated data retrieval is given by Holben et al. (1998). The AOD values presented in this work are selected at Level 2.0 (cloud-screened and quality assured) and were downloaded from http://aeronet.gsfc.nasa.gov/ (last access: 5 March 2020). All of the available observations performed before the Calbuco eruption until 2016 are also used for this work. The available daily observations and the associated period for each site are reported in Table 1. The number of available daily observations range from 242 to 3495 (Durban and Neuquén respectively) (Table 1). The difference between these sites is mainly due to their activity period. It is worthwhile mentioning that measurements were made quasi-continuously at each site during the period selected for this study.

Table 1Number of available and background daily observations at each site for both the sun photometer and MODIS.

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During the eruption, lidar measurements were also performed at the Bariloche site, which is the closest site to the Calbuco volcano (less than 90 km). The lidar installed at the San Carlos de Bariloche Airport uses a Nd : YAG laser emission system based on a Quantel Brilliant B 20 Hz laser, with 366 mJ at 1064 nm (Ristori et al., 2018). The collection of the backscattered photons is carried out with a 20 cm Cassegrain telescope connected to a spectrometric box via an optical fibre. The system can detect three elastics lines (355, 532, and 1064 nm), two Raman lines (387 and 607 nm), and water vapour (at 408 nm). In this study, elastic lidar signals from 532 nm were processed to retrieve the extinction profile (Fernald, 1984). The Klett–Fernald–Sassano (KFS) method was applied as the inversion algorithm. The analytical solution obtained using the KFS method assumes a constant relation between the extinction-to-backscattering profiles – referred to as the lidar ratio (LR) – which is a key point of this method. The LR value is obtained from the values reported in the literature (Trickl et al., 2013; Ridley et al., 2014; Sakai et al., 2016), which are associated with the nature of the aerosols, or iteratively using a reference AOD given by the sun photometer. In this study, we used the AOD given by the sun photometer deployed at the Bariloche site. Another parameter that we need to retrieve the optical properties is the altitude reference, which corresponds to the altitude without an aerosol load. The statistical uncertainties of the optical products are calculated based on the Monte Carlo method (D'Amico et al., 2016), which is widely used in EARLINET (the European Aerosol Research LIdar NETwork). The systematic errors related to the inversion method mainly stem from the input parameters: the LR and the altitude reference values. On average, the error related to the altitude reference is 15 %, and the error related to the LR is around 20 %.

The Moderate Resolution Imaging Spectroradiometer (MODIS) is an instrument aboard the Earth observation system (EOS) Terra (EOS AM) and Aqua (EOS PM) satellites. The orbit of Terra is timed so that it passes over the Equator from north to south in the morning. The orbit of Aqua is timed so that it passes over the Equator from north to south in the afternoon. MODIS provides radiance measurements in 36 spectral bands between 0.44 and 15 µm, with different spatial resolutions: 250 m (bands 1 and 2), 500 m (bands 3–7), and 1 km (bands 8–36) (Bennouna et al., 2013). MODIS aerosols retrievals are carried out separately over land and ocean using two independent algorithms (Bennouna et al., 2013). Numerous works such as Kharol et al. (2011), El-Metwally et al. (2010), and Baddock et al. (2009) have presented a comprehensive description of the Terra MODIS and have also outlined its operation. In this study, the MODIS data aboard the Terra (EOS AM) satellite were used: https://giovanni.gsfc.nasa.gov/giovanni/ (last access: 10 January 2020). The MODIS AOD data utilized in this work were collected for the 2002–2016 period over an $\mathrm{0.5}{}^{\circ }\times \mathrm{0.5}{}^{\circ }$ (latitude and longitude) area centred on each site in order to analyse local and regional aerosol loadings. We only used high-resolution MODIS retrievals with very good quality flags to generate AOD statistics over these regions. Taking the previously mentioned conditions into account, the number of available daily observations ranged from 1204 to 3731 (at Rio Gallegos and Durban respectively; Table 1).

The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument onboard the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite was used to study the transport of the Calbuco plume. CALIPSO has flown in a sun-synchronous polar orbit since 2006 with a cycle of 16 d (Winker et al., 2009). In addition to CALIOP, CALIPSO is composed of two other instruments: (i) the Imaging Infrared Radiometer (IIR) and (ii) the Wide Field Camera (WFC). CALIOP is an elastically backscattered lidar operating at 532 and 1064 nm, equipped with a depolarization channel at 532 nm. Moreover, CALIOP can be categorized into two product levels: level 1 and level 2. The level 1 products are made up of calibrated and geolocated profiles of the attenuated backscatter returned signal. Level 2 products, in comparison, are derived from level 1 products and are classified in three types: profile, vertical feature mask, and layer products (Lopes et al., 2012). Layer products provide layer-averaged properties of detected aerosol and cloud. Profile products provide retrieved extinction and backscatter profiles within these layers. The data products are provided at various spatial resolutions. A detailed description of CALIPSO is given in Winker et al. (2009, 2010, 2013). In this work, the analysis of the 532 nm aerosol extinction coefficient data product for the period from 23 April to 3 May 2015 was used for the identification of volcanic plumes on the respective days of observation.

The Ozone Monitoring Instrument (OMI) data product OMSO2G is also used to analyse the transport of the SO₂ plume from the source region to South Africa. OMI is a nadir-viewing spectrometer that has been operating aboard the National Aeronautics and Space Administration (NASA) EOS AURA satellite since July 2004. The AURA satellite occupies a near polar sun-synchronous orbit at an altitude of 705 km (Krotov et al., 2016). A full technical description of the OMI data product is given in the OMI Algorithm Theoretical Basis Documents (Barthia et al., 2002). The OMSO2G products used in this work are selected at Level 2.0, version 3, and are accessible from http://disc.sci.gsfc.nasa.gov/Aura/data-holdings/OMI/ (last access: 15 January 2020). The OMSO2G products are obtained from reflected solar radiation measured in spectral range from 310 to 340 nm. The data used in this work are reprocessed with the new algorithm based on principal component analysis (PCA; Li et al., 2013), which reduces the retrieval noise by 50 % compared with the previous version. The OMSO2G products are available for four vertical distributions in a sampling grid of $\mathrm{0.125}{}^{\circ }\times \mathrm{0.125}{}^{\circ }$ with respect to latitude and longitude (Krotov et al., 2016). The stratospheric layer (STL) data set is used for this investigation. Earlier works have reported that this data set is suitable for studying volcanic eruptions (Sangeetha et al., 2018; Li et al., 2013; Krotov et al., 2016). The estimated uncertainty in SO₂ values under cloud-free conditions for the four vertical distributions ranges from 0.1 to 0.4 DU and from 0.7 to 0.9 DU at equatorial and high latitudes respectively.

2.2 Back-trajectory model: HYSPLIT

The HYSPLIT model was used to calculate backward and forward trajectories in order to derive information on the transport of the volcanic aerosol plume. The National Oceanic and Atmospheric Administration (NOAA) Air Resource Laboratory (ARL) developed the HYSPLIT model that is currently used for computing simple and complex air parcel trajectories (Draxler and Rolph, 2003; Stein et al., 2015). The model can also provide information regarding the dispersion, chemical transformation, and deposition simulations of pollutants. The ability of HYSPLIT to derive information on the atmospheric transport, dispersion, and deposition of pollutants and volcanic ash has been highlighted in several studies (Stunder et al., 2007; Chen et al., 2012; Kumar et al., 2017; Sangeetha et al., 2018; Lopes et al., 2019; Shikwambana and Sivakumar, 2019). A detailed description and the historical evolution of the model is given by Stein et al. (2015) and is briefly presented here. The calculation of the trajectories is based on a hybrid method between the Lagrangian and Eulerian approaches (Stein et al., 2015). In order to reduce the uncertainties induced by the meteorological fields and the numerical methods employed, HYSPLIT can be run in the trajectory clustering mode. The concept of clustering is a multivariate statistical method that consists of merging the trajectories that are closer to each other and classifying them into distinct groups. In the present work, the back-trajectory calculations were helpful to determine if the measured AOD values over the selected sites were associated with air masses that originated from the Calbuco volcano. The back-trajectories of air masses were calculated every 6 h over the selected sites using the Global Data Assimilation System (GDAS) database for altitudes ranging from 16 to 19 km. The back-trajectory calculations were performed using the vertical motion calculation method.

2.3 Methodology

The characteristics of the optical properties of the volcanic plume were analysed using AOD measurements. The AOD measurements are comprised of the volcanic plume AOD_P and the background values. Thus, the aerosols optical depth of the volcanic plume at a given wavelength AOD_P (λ) can be obtained by subtracting the background aerosol optical depth AOD_B (λ) from the AOD (λ) measurements. In previous studies, this methodology has been applied to the Microtops II portable sun photometer measurements taken close to volcano site (Watson and Oppenheimer, 2001; Porter et al., 2002; Mather et al., 2004; Martin et al., 2009; Sellitto et al., 2017, 2018). In this paper, this approach was applied and adapted to CIMEL sun photometer measurements taken at nine sites. To investigate the properties of the volcanic plume, it is important to make background measurements when the atmosphere is clear of volcanic aerosols as well as measurements during an eruption. Given that CIMEL sun photometers are fixed instruments, this requirement is implicitly respected and allows for the definition of a statistically significant background situation. In the present work, the background period is defined as the period before January 2015 and after January 2016. Except for the Durban site, the AOD_B (λ) calculation is based on an average of 6 years of daily observations (Table 1). The anomalies were filtered out in order to obtain the daily optical depth of the “clear” atmospheric layer. Thus, the calculated daily AOD_B (λ) means from April to December were assumed to be within the standard deviation of the hourly recorded data. Moreover, the perturbation induced by the Puyehue–Cordón Caulle eruption (40.3^∘ S, 72.1^∘ W; Chile) (Diaz et al., 2014) on the calculation of the background values was taken into account. As a consequence, the measurements performed during the period from June to October 2011 were discarded from the calculation of the AOD_B (λ). Taking the above-mentioned conditions into account, the number of observations used for the calculation of the daily AOD_B (λ) means ranged from 89 to 2489 (Table 1). The uncertainty of the plume AOD (σ_AODp) is derived using the standard deviation of the AOD (λ) measurement and the standard deviation of the AOD_B (${\mathit{\sigma }}_{{\text{AOD}}_{\text{B}}}$), as shown by Sellitto et al. (2017). This uncertainty is given by Eq. (1):

where n is the number of individual background measurements (AOD_B) made to compute the average background.

The spectral variability of the volcanic plume was analysed using the Angström exponent α_P and the atmospheric turbidity β_P (Angström, 1964). The Angström exponent α_P is a well-known optical proxy for the aerosol size distribution (Shaw, 1983; Tomasi et al., 1997). The Angström exponent α_P is generally close to zero or negative for aerosols whose extinction properties are governed by large particles (a mean radius distribution greater than 1 µm). Conversely, α_P values greater than 1 are typical of small particles (a mean radius distribution less than 1 µm). The Angström turbidity β_P is the best-fit value of AOD_P (λ) at 1 µm, which depends on the total number and refractive index of aerosol particles. In this work, the optical properties of the volcanic plume were analysed at three selected wavelength bands that correspond to ultraviolet (UV, 380 nm), visible (Vis, 500 nm), and near-infrared (NIR, 1020 nm). Previous works revealed that observations at UV wavelengths are helpful for the characterization of the optical and microphysical properties of the volcanic plume (Porter et al., 2002; Mather et al., 2004; Sellitto et al., 2017). The Angström exponent α_P and turbidity β_P of the volcanic plume are calculated at a specific wavelength pair, 380–1020 nm, given by Eqs. (2) and (3).

As reported by Sellitto et al. (2017), the use of a spectral interval that is as large as possible leads to a decrease in the uncertainties of α_P and β_P. According to this research, the uncertainties of the derived α_P and β_P values are calculated as follows:

The spatio-temporal data analysis carried out between MODIS and sun photometer instruments helps both to detect the passage of the volcanic plume and its contribution to the total aerosol column variation over the selected sites. The previously described methodology was applied to the MODIS observations in order to determine the AOD of the volcanic plume AOD_P-MODIS and the background values AOD_B-MODIS at 550 nm. MODIS observations are helpful for obtaining a good description of the background behaviour over sites where sampling is not sufficient, such as the Durban site. Table 1 reveals that the MODIS observations used to build the background situation are homogenous between the different sites and range between 689 and 3216 observations. It is necessary to convert the AOD values from MODIS and sun photometer observations to a common wavelength in order to compare them. The AOD values obtained from sun photometer at 500 nm were converted to the MODIS wavelength following Eq. (4), which has been used in previous works (Prasad and Singh, 2007; Alam et al., 2011):

where α is the Angström parameter obtained from sun photometer between 440 and 870 nm.

Figure 1(a) A time-averaged map of the SO₂ column in the lower stratosphere observed by OMI during the 22 April–1 May period. (b) Forward-trajectory analysis of air masses from the HYSPLIT model starting at the Calbuco volcano coordinates at 16 km (blue line with grey dots), 18 km (green line with grey diamonds), and 20 km (red line with grey triangles). (c) A time-averaged map of MODIS AOD (550 nm) during the 22 April–1 May period. The locations of the selected sites are indicated by black boxes and the site abbreviations: Bariloche (B), Neuquén (N), Buenos Aires (BA), São Paulo (SP), Comodoro (C), Rio Gallegos (R), Gobabeb (G), Durban (D), and Pretoria (P).

4.1 Statistical detection of the volcanic plume

Figures 4 and 5 depict the daily mean evolution of the AOD at 550 nm obtained from sun photometer and MODIS observations at six South American sites between 15 April and 1 December. The selected sites allow for an overview of the latitudinal distribution of AOD over the South American region. These sites are located in urban and semiurban areas dominated by industrial activities and local air pollution (e.g. vehicle emissions and air traffic). Thus, a north–south gradient appears in the background AOD values obtained from sun photometer and satellite observations over South America (Figs. 4, 5): background AOD values and their variability decrease with increasing latitude. The annual mean AOD background values range from $\mathrm{0.11}\pm {\mathrm{4.10}}^{-\mathrm{3}}$ in São Paulo to $\mathrm{0.03}\pm {\mathrm{1.10}}^{-\mathrm{3}}$ in Rio Gallegos. The highest AOD values (with an annual mean of greater than or equal to 0.10) and the largest variability are observed at São Paulo and Buenos Aires respectively (Fig. 4a, b, c, d). These regions are the most industrialized of the selected South American sites (Gassman et al., 2000; Lopes et al., 2019). The AOD values over the Neuquén site, which is located 4^∘ south of Buenos Aires, are half of those observed at Buenos Aires on average (Fig. 5a, b). In addition to urban and industrial activities, the evolution of the background values over São Paulo and Buenos Aires is influenced by biomass burning activities, which explain the increase in AOD values during the austral winter (June–August) (Andreae et al., 2004; Freitas et al., 2009; Torres et al., 2010). Based on sun photometer observations over South America, Hoelzemann et al. (2009) showed a clear difference in the AOD behaviour between sites influenced by fires and those influenced by urban emissions. This explains the contrast between the northern and southern parts of South America.

The South American region is influenced by the regional and long-range transport of air masses from several potential sources of aerosols, which induce seasonal variability in the optical properties of aerosols over the country. For instance, the transport of dust from the Patagonian region impacts the seasonal variability of the optical properties of aerosols at neighbouring sites such as Comodoro (Li et al., 2010; Otero et al., 2015). Moreover, the southern parts of Argentina are frequently impacted by air masses from the Antarctic, which could influence the variability of AOD over Rio Gallegos (Kirchhoff et al., 1997; Otero et al., 2015). We can also not exclude the hypothesis that the increase in the AOD values observed from sun photometer and MODIS measurements performed at Rio Gallegos during the austral winter could be explained by the transport of air masses from the Antarctic region (Fig. 5e, f). Figure 6a reveals that the background AOD values and their variability over São Paulo and Buenos Aires compare fairly well with the observed values over the Gobabeb site ($\mathrm{0.10}\pm \mathrm{6}\times {\mathrm{10}}^{-\mathrm{3}}$ on average). The background AOD values observed at Gobabeb are slightly lower than those observed at Durban ($\mathrm{0.16}\pm \mathrm{8}\times {\mathrm{10}}^{-\mathrm{3}}$ on average) and Pretoria ($\mathrm{0.17}\pm \mathrm{8}\times {\mathrm{10}}^{-\mathrm{3}}$ on average) from both the sun photometer and MODIS (Fig. 6). The Gobabeb site, in the Namib Desert, is far less sensitive to the effect of urban pollution than the Durban and Pretoria sites. It can be observed that all of these African sites exhibit an increase in the AOD values during the austral spring season, which is well known to be the biomass burning season (Eck et al., 2003; Garstang et al., 1996; Das et al., 2015; Piketh et al., 1999; Kumar et al., 2017).

The daily AOD measurements performed between 15 April and 1 December 2015 were compared with background values in order to highlight the passage of the volcanic plume. Furthermore, back-trajectory analysis of daily AOD measurements from 2015 with higher than background values were carried out in order to link these observations to the Calbuco plume. Thus, it is possible to determine the residence time of the plume over a specific site. This duration is defined as the period during which AOD measurements from 2015 fall outside of the standard deviation of the daily background means. The residence time of the Calbuco plume detected from total columnar aerosols measurements is reported in Table 2 and is depicted by the grey shaded areas in Figs. 4, 5, and 6. The estimation of the residence time of the plume mainly depends on the availability of daily observations. This condition results in discrepancies in the residence time between the MODIS and sun photometer observations. Given its good temporal resolution, the daily comparison of the observed AOD from MODIS during the background period and during the Calbuco event is possible over a long period of time. Measurements collected by these two instruments are complementary and allow for the improvement of the estimation of the residence time over the selected sites. This is clearly illustrated by the Bariloche site, as no measurements were recorded at this site by the sun photometer from 26 April to 10 May during the background period (Fig. 4e, f); however, the use of MODIS observations has allowed for the estimation of the residence time to be improved, with the conclusion that the plume passed over this site from 23 April to 10 May 2015. In spite of the large variability in the background values over the São Paulo and Buenos Aires sites, the passage of the volcanic plume is clearly visible from the sun photometer and MODIS observations (Fig. 4a, b, c, d). This previous comment is also true for the African sites (Fig. 6). It is worthwhile mentioning that the residence times obtained for these sites are in agreement with the chronology reported in the previous subsection from CALIOP and OMI observations. It can be observed that the passage of the volcanic plume is not clearly visible over the southern parts of the South American region. Figure 4e reveals that the passage of the Calbuco plume over the Rio Gallegos site is not visible from AOD measurements recorded by the sun photometer. This could be explained by the low daily sampling interval during 2015. Conversely, the AOD measurements recorded by MODIS from 12 to 25 May 2015 are higher than daily background values (Fig. 5f). The air mass back-trajectory calculations confirm the link between these observations and the Calbuco eruption, which is in agreement with the results reported by Zuev et al. (2018). They analysed the trajectory of air masses associated with the Calbuco volcano from 22 April until the end of August between 15 and 19 km using the NOAA HYSPLIT model. Zuev et al. (2018) showed that the air masses were within the limits of the subtropical stream and the polar vortex, impacting the southern parts of South America. However, the aforementioned MODIS observations are within the standard deviation of the daily background mean. As a consequence, it is impossible to determine the residence time over the Rio Gallegos site following the previously defined statistical criteria. Figure 5e and f do not call the passage of the volcanic plume over the Rio Gallegos site into question but rather suggest that the AOD measurements are not statistically significant. A possible explanation for this is that the amount of aerosols transported toward Rio Gallegos is lower than the amount transported toward the northern parts of South America, which then reaches South Africa a few days later. Thus, this lower concentration of volcanic aerosols gets lost in the variability of the background values. In the following subsection, the contribution of the volcanic plume to the total columnar aerosols will be discussed in more detail.

Figure 7Daily mean AOD anomaly (%) at (a, b) São Paulo, (c, d) Bariloche, and (e, f) Gobabeb calculated from sun photometer (a, c, e) and MODIS (d, d, f) observations between 19 April and 31 May.

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4.2 Statistical variations of the total columnar aerosols

The daily AOD anomalies induced by the transport of the volcanic plume are estimated and calculated as a relative difference by considering the daily background as a reference value. The Bariloche site is clearly the most exposed to the volcanic plume, which is illustrated by the significant difference (a factor of 2.5 on average) between the daily AOD measurements from 2015 and the background values (Fig. 4e). During the first few days following the eruption, the AOD values obtained from lidar and sun photometer observations range from 0.18 to 0.24 (Fig. 4e). This validates that these high values are not the result of technical artefacts but are rather attributed to the passage of the Calbuco plume detected by two independent ground-based instruments. The maximum values of the relative difference are observed over the Bariloche site (Fig. 7c, d). Figures 7c and d reveal that the AOD anomalies calculated from the sun photometer and MODIS observations during the first few days after the eruption range from 35 % to 85 %. Moreover, despite its geographical distance from the Calbuco volcano site and its significant background variability, the passage of the plume over the São Paulo site induced significant daily AOD anomalies ranging from 20 % to 55 % (Fig. 7a, b). The African sites situated in the west, such as Gobabeb, were the first impacted by the volcanic plume, and AOD anomalies induced by its spread are significant. Over the Gobabeb site, the daily AOD anomalies ranged from 10 % to 55 % (Fig. 7e, f). Table 2 contains the mean AOD anomaly values calculated during the plume's residence over all of the selected sites. Overall, the AOD anomalies induced by the passage of the plume over the South American sites are higher on average than those obtained over the South African sites (Table 2). This is consistent with the contrast in the extinction coefficients obtained by CALIOP between South America and South Africa that were reported in the previous subsection. Table 2 reveals that the highest AOD anomalies (greater than 35 %) are observed over the northeastern parts of South America, enclosing the Bariloche, Neuquén, Buenos Aires, and São Paulo sites. The AOD anomalies for the Comodoro site, which is south of the Calbuco site, are estimated to be 26.4±1.5  % and 14.5±2.5 % from the sun photometer and MODIS respectively. There seems to be a difference between the sites located to the north and south of the Calbuco volcano with regards to the AOD anomalies induced by the passage of the plume. It is worthwhile mentioning that the latitudinal distribution of AOD anomalies over South America is consistent with the geographical spread of the volcanic plume obtained from satellite observations. Both the satellite and ground-based observations reveal that the majority of the volcanic plume was transported over the northeastern part of South America during the first few days following the eruption. Conversely, the AOD anomalies induced by the spread of the plume from west to east over South Africa have a homogeneous distribution. On average, the AOD anomalies for Gobabeb and Durban from sun photometer observations are estimated to be 22.5±13.0 % and 24.8±11.1 % respectively, whereas the values from MODIS observations are estimated to be 20.1±11.2 % and 27.5±10.8 % respectively (Table 2). On average, the difference between the AOD anomalies obtained from MODIS and sun photometer observations is less than 7 % with the exception of the Comodoro site, where the difference is estimated to be 11.9 %. The discrepancies in term of AOD anomalies between MODIS and sun photometer observations may be primarily attributed to the estimation of the residence times, as previously mentioned. It is important to note that the discrepancies between background measurements from MODIS and sun photometer observations should not be excluded.

Table 3Statistical parameters for the comparison between sun photometer (Phot) and MODIS (MOD) observations for each site.

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Figure 8Correlation of AOD daily mean observations (550 nm) between sun photometer and MODIS observations during the entire period of available data at (a, b) São Paulo, (c, d) Pretoria, and (e, f) Comodoro. The histograms show the mean bias error (MBE) of the two data sets against the number of observations for each site.

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The correlation coefficient and mean bias error (MBE) values between sun photometer and MODIS AOD observations are depicted in Fig. 8 and reported in Table 3. The correlation coefficient values range from 0.51 to 0.76 with the highest correlation observed over the Pretoria site (Fig. 8c, d). This is in agreement with previous studies which have revealed that MODIS and sun photometer observations are significantly correlated over land instead of over the ocean and coastal sites due to the low surface reflectivity over land (Chu et al., 2002; Vermote et al., 1997; Hoelzemann et al., 2009; Bréon et al., 2011). It is worth noting that the correlation between the sun photometer and MODIS observations over the São Paulo site is similar to those observed over Durban and Pretoria (Fig. 8a, b). In addition, the root-mean-square error (RMSE) was calculated and is reported in Table 3. The RMSE and MBE values range from 4.2 % to 13.2 % and from −9.7 % ±3.2 % to 8.2 % ± 0.9 % respectively. The highest discrepancies between the sun photometer and MODIS measurements (a correlation coefficient lower than 0.60 and a RMSE greater than 9 %) are observed in the southern parts of South America, close to the Comodoro and Rio Gallegos sites. In particular, the Comodoro site has the weakest correlation (0.51) and the lowest MBE value of −9.7 % ± 3.2 % (Fig. 8e, f). Previous studies have already pointed out the bias in the AOD data sets collected by MODIS and ground-based instruments in the Southern Hemisphere between 45 and 65^∘ S (Zhang and Reid, 2006; Shi et al., 2011; Lehahn et al., 2010; Madry et al., 2011; Toth et al., 2013). Madry et al. (2011) suggested that this bias could be due to the production of sea salt particles from the near-surface high winds occurring along this zonal band. Toth et al. (2013) investigated the quality of MODIS data sets in this zonal band by comparing them with CALIOP and sun photometer observations. They showed that about 30 %–40 % of the observed bias with the ground-based observations could be attributed to cloud contamination. Table 3, reveals that MODIS overestimates the AOD when compared with sun photometer observations for most of the selected sites, which is consistent with previous studies (Ichoku et al., 2005; Abdou et al., 2005; Hauser et al., 2005; Hoelzemann et al., 2009). This bias may be explained by the fact that sun photometer measurements are made under cloud-free conditions, whereas MODIS is able to detect aerosols under cloudy conditions. However, sub-pixel cloud can be targeted as aerosols, which erroneously raises the retrieved AOD (Hoelzemann et al., 2009). Conversely, we note that MODIS underestimates the AOD when compared with sun photometer observations over the São Paulo and the South African sites (Table 3). For the latter, this was found to be consistent with results obtained by Hao et al. (2005) during the Southern African Regional Science Initiative(SAFARI 2000) campaign which showed that AOD values from MODIS are systematically lower at 470, 550, and 660 nm compared with ground-based measurements by automated and handheld sun photometers in the regions of intense biomass burning. They suggested that this bias may be due to errors in the assumed aerosol scattering phase function or surface directional properties. Thus, several potential causes (surface reflectance, cloud contamination, and retrieval bias) could contribute to the discrepancies between MODIS and sun photometer observations (Tripathi et al., 2005; More et al., 2013; Kumar et al., 2015). The previously mentioned statistical results indicate that the daily AOD values obtained from sun photometer and MODIS observations are in fairly good agreement. Overall, the anomalies induced by the transport of the Calbuco plume can be statistically detected and evaluated using AOD measurements at mid-visible wavelengths. In order to improve the discussion, the observed AOD from the UV to the NIR spectral ranges will be analysed in the following section.