The POLIPHON method can be used to obtain particle microphysical property profiles (i.e., particle number, surface area, and volume concentration) and then particle mass, CCN, and INP concentration profiles for several aerosol types using a combination of polarization lidar and sun photometer (Mamouri and Ansmann, 2014, 2015, 2016; Marinou et al., 2019). This method has been widely used in the estimations of CCN- and INP-relevant aerosol parameters for multiple aerosol types including dust (Ansmann et al., 2019a; Hofer et al., 2020; He et al., 2021b, 2022a, b), marine aerosol (Mamouri and Ansmann, 2016, 2017; Haarig et al., 2019), continental aerosol (Mamouri and Ansmann, 2016, 2017), and smoke (Ansmann et al., 2021; Haarig et al., 2019). In this study, we focus on the dust-related CCN and INP properties.

The calculation is given in Table 1. First, the dust backscatter coefficient βd and extinction coefficient αd can be derived by polarization lidar observations based on the inversion method from Fernald (1984) and the dust-component separation method from Tesche et al. (2009), as shown by the following equation: 1βdz=βpzδpz-δnd1+δdδd-δnd1+δpz, where δd=0.31 and δnd=0.05 are dust (subscript “d”) and non-dust (subscript “nd”) particle depolarization ratios (Burton et al., 2013), respectively, and δp and βp are the lidar-derived particle depolarization ratio and backscatter coefficient, respectively. The lidar ratio (LR) for dust usually ranges from 30 to 60 sr depending on the different dust sources (Müller et al., 2007; Mamouri et al., 2013; Hu et al., 2020; Peng et al., 2021). Then, the dust extinction coefficient can be converted into particle mass concentration Md, particle number concentration n250,d (r > 250 nm), and particle surface area concentration sd and s100,d (r > 100 nm) by multiplying their corresponding conversion factors, i.e., cv,d, c250,d, cs,d, and cs,100,d. Finally, the dust-related INP concentration nINP,d can be retrieved by inputting n250,d and sd into different INP parameterization schemes (DeMott et al., 2010, 2015; Niemand et al., 2012; Steinke et al., 2015; Ullrich et al., 2017). In addition, particle number concentration n100,d (r > 100 nm) is considered a good proxy for dust-related CCN concentration nCCN,ss,d as discussed by Mamouri and Ansmann (2016). Here, the subscript ss denotes the water supersaturation. Thus, nCCN,ss,d can be obtained by multiplying n100,d by a water-supersaturation-dependent factor fss,d, which is 1.0 for a typical liquid water supersaturation value of 0.2 %.

In the POLIPHON method, as introduced above, a series of conversion factors are essential to the conversion from the dust extinction coefficient to dust microphysical parameters regarding CCN and INP concentrations. The conversion factors are pre-calculated from the historical database of sun photometer observations (denoted as j for each data point, counting from 1 to Jd). The calculation processes are shown below (Ansmann et al., 2019b): 2cv,d=1Jd∑j=1JdVd,j/Dτj/D=1Jd∑j=1Jdvd,jαd,j,3c250,d=1Jd∑j=1JdN250,d,j/Dτj/D=1Jd∑j=1Jdn250,d,jαd,j,4cs,d=1Jd∑j=1JdSd,j/Dτj/D=1Jd∑j=1Jdsd,jαd,j,5cs,100,d=1Jd∑j=1JdS100,d,j/Dτj/D=1Jd∑j=1Jds100,d,jαd,j, where D is an introduced thickness for a given aerosol layer, and τ is the AOD at 532 nm calculated from the sun-photometer-measured AOD at 500 nm together with the Ångström exponent (for 440–870 nm). Vd and N250,d are the column particle volume concentration and column large particle (radius > 250 nm) number concentration, respectively; Sd and S100,d (radius > 100 nm) are the column particle surface area concentrations. Vd, N250,d, Sd, and S100,d are derived from the particle size distribution data in AERONET aerosol inversion products, which are introduced in detail in Sect. 2.2. αd is the layer-mean aerosol extinction coefficient at 532 nm; vd and n250,d are the layer-mean volume concentration and large particle (radius > 250 nm) number concentration, respectively; and sd and s100,d (radius > 100 nm) are the layer-mean particle surface area concentrations. The subscript “d” denotes “dust”, which is considered the major contribution in column aerosol loading for the selected sun photometer data.

In addition, it is challenging to estimate the CCN concentration because the ability of aerosol particles to serve as CCN has a complex relationship with the particle hygroscopicity (associated with particle size and chemical composition) and water supersaturation level (Wang et al., 2010; Moore et al., 2012). As suggested by Shinozuka et al. (2015), a log–log regression analysis was performed to retrieve the CCN-relevant conversion factor c100,d and regression coefficient χd with the following equation: 6log⁡n100,d=log⁡c100,d+χdlog⁡αd. In general, dust-related conversion factors have a regional-dependent characteristic associated with the origin of dust regions as well as the specific local anthropogenic dust emissions (Philip et al., 2017). To extend the POLIPHON method toward global dust applications, Ansmann et al. (2019b) provided dust-related conversion factors at 20 AERONET sites in/near the typical desert regions, where other types of aerosols have less or even negligible contributions to the aerosol properties of the atmospheric column. Therefore, the obtained conversion factors can be considered the representatives of pure or quasi-pure dust situations. To select the dust-occurring datasets for calculation, they adopted the constraints of the column-integrated Ångström exponent (for 440–870 nm) < 0.3 and aerosol optical depth (at 532 nm) > 0.1. Due to the influence of anthropogenic aerosols, the available dust-occurring data points are insufficient for calculating the conversion factors. To solve this issue, He et al. (2021b) applied simultaneous polarization lidar observations to assist in the filtration of dust-occurring datasets in Wuhan (30.5∘ N, 114.4∘ E), a central Chinese megacity impacted by both local anthropogenic aerosol emissions and long-range-transported dust (He and Yi, 2015; He et al., 2022c; Liu et al., 2022).

Dust plumes can also realize transoceanic transport in the Northern Hemisphere; there are two well-known pathways, i.e., the transatlantic route from the Saharan desert to America (Yu et al., 2021; Dai et al., 2022) and the transpacific route from Asian dust sources (Taklimakan and Gobi deserts) to America (Guo et al., 2017; Hu et al., 2019). However, dust-related conversion factors over the ocean are rarely reported. Sea spray aerosols usually have a large size, presenting a similarly small Ångström exponent as dust particles (Haarig et al., 2017). To avoid the interference of sea spray aerosols, we use another scheme to identify the dust-occurring datasets, taking advantage of the particle linear depolarization ratio (PLDR) in AERONET aerosol inversion products (Shin et al., 2019). Therefore, sufficient available dust data points can be selected even at remote oceanic sites.

AERONET is a global ground-based aerosol monitoring network and has provided more than 25 years of aerosol column property observations. CE318 sun–sky photometers are used to measure direct solar irradiance (generally at 340, 380, 440, 500, 675, 870, 1020, and 1640 nm) and directional sky radiance to retrieve the spectral-resolved AODs and, in turn, the additional aerosol inversion products. Moreover, the latest-applied CE318-T can also perform nighttime measurements of the spectral lunar irradiance. In this study, the AERONET database (Holben et al., 1998; Dubovik et al., 2000; Dubovik and King, 2000) was employed to retrieve the dust-related conversion factors at 9 sites near/in deserts (to compare with the values given in Ansmann et al., 2019b, as a validation of the newly proposed dust selection scheme) and at 20 oceanic and coastal sites influenced by long-range-transported dust (see Fig. 1). The oceanic and coastal sites can be classified into five regional clusters, i.e., the Pacific, Pacific coast, Atlantic, Indian Ocean, and Arctic Ocean, representing dust characteristics in different regions.

We used the quality-assured level-2.0 AOD in AERONET Version 3 aerosol optical depth solar products (Giles et al., 2019). Moreover, the particle volume size distribution with 22 size bins (radius) ranging from 50 nm to 15 µm and PLDR in AERONET Version 3 aerosol inversion products are also used for calculating Vd, N250,d, Sd, and S100,d as described in Sect. 2.1 (Sinyuk et al., 2020). The specific calculation processes can be found in Mamouri and Ansmann (2014, 2015) and Ansmann et al. (2019b). For the near-/in-desert sites, level-2.0 (quality-assured) aerosol inversion products are applied, while for the oceanic and coastal sites, level-1.5 (cloud-screened and quality-controlled) aerosol inversion products are applied, since the level-2.0 PLDR data are unavailable. The basic information of the selected sites is shown in Table 2, including period, longitude, latitude, and the number of data points for total, dust-dominated mixture, and pure dust (PD) observations.

In AERONET retrieval, based on the aerosol spheroid model, the combination of the particle size distribution and complex refractive index can be used to further compute the two elements of the Müller scattering matrix, i.e., F11(λ) and F22(λ) (Bohren and Huffman, 1983; Dubovik et al., 2006; Shin et al., 2018), which can then be used to derive the backscattering PLDR with the following formula: 7δλp=1-F22λ,180∘/F11λ,180∘1+F22λ,180∘/F11λ,180∘. AERONET PLDR data are a good indicator of dust occurrence and have been verified to be well correlated with lidar-derived values (Noh et al., 2017). Shin et al. (2018) found that PLDR values at 870 and 1020 nm are more reliable according to the comparison with those from lidar observations for pure dust particles. Therefore, we use PLDR at 1020 nm δ1020p (only denoted as PLDR hereafter) to select the dust-occurring data points for the POLIPHON conversion factor calculation (Shin et al., 2019). Note that the overestimation of near-infrared PLDR is reported by comparison with concurrent polarization lidar observations (Toledano et al., 2019; Haarig et al., 2022), possibly due to the assumption of the spheroid particle in AERONET inversion. Nevertheless, δ1020p values are only used to qualitatively identify the dust presence with the presupposed threshold values. Its validity will be verified by comparing the derived conversion factors with those from Ansmann et al. (2019b) in Sect. 3.1.

The column-integrated dust ratio (Rd,1020), representing the contribution proportion of dust backscatter to the total particle backscatter in the atmospheric column, is defined as follows: 8Rd,1020=δ1020p-δndp1+δdpδdp-δndp1+δ1020p. It should be noted that the dust (δdp) and non-dust (δndp) particle depolarization ratios are set to 0.30 and 0.02, respectively, to be consistent with the value proposed by Shin et al. (2019). These two values are slightly different from those used in the POLIPHON method in Eq. (1). According to the scheme from Shin et al. (2019), we classify data points with Rd,1020 values of > 0.89 as pure dust (PD) and 0.53–0.89 as dust-dominated mixture (DDM, which can also be considered “mixed dust”, as in He et al., 2021b). Note that in this study, the DDM includes the combination of sectors B (fine-mode fraction (FMF) = 0–0.4), C (FMF = 0.4–0.6), and E (FMF = 0.6–1.0) in Shin et al. (2019). A flow chart for dust-occurring data point selection and dust-related conversion factor retrieval is shown in Fig. 2. For the near-/in-desert sites, we presented the results from the PD cluster, which is adequate for calculating the conversion factors. For the oceanic and coastal sites, the results from both the PD and PD+DDM clusters are provided for comparison.

To validate the performance of the newly proposed dust dataset selection scheme, we chose 9 out of 20 AERONET sites used in Ansmann et al. (2019b) to compare the obtained conversion factors. They are mainly from three typical regions, including North Africa, the Middle East, and Asia (see Fig. 1). It should be mentioned that c100,d values tend to be divergent when the aerosol extinction coefficient is larger than 600 Mm-1. Hence, the validations were only performed for cv,d, c250,d, cs,d, and cs,100,d. Figure 3 shows the scatters regarding the relationships between 532 nm aerosol extinction and n250,d, vd, sd, and s100,d for pure data situations at Cape Verde, Dushanbe, and Mezaira'a. The conversion factor values are also given accordingly. Here, level-2.0 AOD and aerosol inversion product data were employed. PD datasets selected with the method from Shin et al. (2019) perform well, as a highly linear correlation can be found, with linear Pearson correlation coefficients exceeding 0.9.

In addition to the three sites in Fig. 3, the conversion factors for the remaining six sites are shown in Table 3 as well. The results for both PD and PD+DDM clusters are provided here. Generally, regional differences in dust characteristics can be found in different dust sources. cv,d, c250,d, and cs,d calculated from the PD and PD+DDM datasets are almost consistent with each other, suggesting the absolute dominance of dust particles at these near-/in-desert sites. Interestingly, there are larger differences in cs,d and cs,100,d between the PD and DDM clusters at two Middle East sites, i.e., Eilat and Mezaira'a. After a careful check, it is noted that the DDM datasets have aerosol extinction coefficient values of 300–600 Mm-1 and show significantly larger sd and s100,d than those for PD datasets (see Fig. A1). The special pattern reflects the involvement of a specific type of local aerosol in the dust-dominated mixture. Moreover, the PD–DDM differences are even larger for cs,100,d at both sites, indicating that the additional involved aerosols may play a vital role in the particle size spectral of > 100 nm. According to further examination, this special pattern can generally be found at partial sites from the Middle East, Africa, and polluted European cities, which, however, are rarely present at sites from east Asia, Australia, South America, and North America. Thus, it should be noted that more care should be taken when employing DDM data to retrieve dust-related conversion factors at terrestrial sites in the Middle East, Africa, and polluted European cities in future work.

For comparison, we also plot the conversion factors in Fig. 4 together with those given by Ansmann et al. (2019b) (hereafter denoted as “A-19”). cv,d and c250,d calculated from three dust datasets (PD, DDM+PD, and A-19) coincide with each other very well. The relative differences between either A-19 and PD or A-19 and DDM+PD are generally as small as < 8.5 % for c250,d (except for 19.2 % at the DA site) and < 12.5 % for cv,d (except for 20.0 % at the DA site). Compared with A-19, cs,d values calculated from PD datasets generally show relative differences of < 16.5 % (except for 23.2 % at the CV site); in contrast, cs,d differences between DDM+PD datasets and A-19 are much larger (up to < 36.2 %). For cs,100,d, compared with the results from A-19, values calculated from PD datasets show relative differences as high as < 36.2 %, while values from PD+DDM datasets show relatively larger relative differences up to < 42.5 %. Using either the FMF (Lee et al., 2010) or Ångström exponent (Ansmann et al., 2019b) in the AERONET data as the dust criterion implies an assumption that dust is constrained to the coarse mode. However, the proportion between fine- and coarse-mode dust may be altered during transport due to the quicker removal of dust particles with larger sizes (Yu et al., 2021); hence, the dust criterion AE < 0.3 may exclude a portion of fine-mode dust-dominated (with a radius < 100 nm) cases, resulting in a general underestimation of cs,d. Furthermore, region-featured emissions of non-dust small particles are also possibly responsible for this discrepancy.

In this study, we chose 20 ocean and coast AERONET sites, which were classified into five region categories including the Pacific, Pacific coast (both east and west coasts), Atlantic, Indian Ocean, and Arctic Ocean (Huang et al., 2015; Zhao et al., 2022). Figure 5 shows the relationships between 532 nm aerosol extinction and n250,d, vd, sd, and s100,d for both the PD and PD+DDM cases at Mauna Loa (middle Pacific), Shirahama (west Pacific coast), Tudor Hill (west Atlantic), and Amsterdam Island (south Indian Ocean). The conversion factor values are also given accordingly. To eliminate abnormal values and retain the available dust data as much as possible, the data points with an aerosol extinction of > 20 Mm-1 are considered in the calculation. PD data points generally show a good linear correlation. For the PD+DDM cluster, three island sites show a similar good correlation except for Shirahama, which is due to the small contribution of marine aerosols to total column aerosol loading (usually with a global mean AOD of ∼ 0.05, Smirnov et al., 2009). At the Shirahama site, it is conjectured that anthropogenic aerosols considerably contribute to the column aerosol loading and lead to the spread of scatters, which reflect variations in the characteristics (size distribution, complex refractive index, and so on) of other aerosol components in the dust-dominated mixture.

The conversion factors cv,d, c250,d, cs,d, and cs,100,d at the other oceanic and coastal sites are also provided in Table 4. The results for only the PD cluster and combined PD and DDM clusters are listed. We consider the conversion factors with ≥ 12 available PD data points valid (provided in Table 4). Moreover, to guarantee robustness, only the retrieved conversion factors with the linear Pearson correlation coefficient R exceeding 0.70 are considered valid, except for PD-derived c250,d values at NR (R = 0.32) and AS (R = 0.50), which should especially be handled with care in scientific applications. We also plot these dust-related conversion factors in Fig. 6 for comparison. According to the estimation in Sect. 3.1, it is suggested to preferentially use the PD datasets in the calculation to avoid the potential contribution of specific local aerosols, e.g., the special pattern in cs,d and cs,100,d at Eilat and Mezaira'a (see Sect. 3.1). Nevertheless, PD+DDM datasets may take part in the calculation as a suboptimal option if the sole use of PD datasets cannot guarantee the validity of conversion factors (10 out of 20 sites).

As seen in Fig. 6, c250,d mainly ranges from 0.17 to 0.28 Mm cm-3; the c250,d values calculated from the PD and PD+DDM datasets agree with each other very well, except for the Midway Island and Nauru sites, indicating that few non-dust aerosols contribute to the particle size spectra of > 250 nm and that c250,d is a relatively stable factor from region to region. For cs,d and cs,100,d, their values from the DDM+PD datasets mainly have a systematically positive deviation (< 25 %) compared with those from the PD datasets, which may be affected by marine aerosols. In addition, cs,d and cs,100,d values at coastal sites (especially at Shirahama, Osaka, and Hokkaido University) are considerably larger than those at remote ocean sites, revealing their higher sensitivity (compared with c250,d) to the involvement of other aerosols. However, large differences in cv,d values are found not only between the PD and PD+DDM datasets but also from region to region. He et al. (2021b) also reported that mixed dust in Wuhan has a smaller cv,d than pure dust near the source region of Asian dust. Another interesting finding for cv,d is that the values in the Arctic are only half of those in other regions. PD data points are rarely identified in the Arctic, and conversion factors are all calculated from the DDM datasets here; abundant other aerosol types in the Arctic, e.g., smoke, anthropogenic aerosol, and marine aerosol (Engelmann et al., 2021; Zhao et al., 2022), may account for the low cv,d values. Nevertheless, cv,d can be beneficial to the validation of the mass extinction efficiency, a variable combining cv,d and dust density, in the 3-D global dust model (Adebiyi et al., 2020; Kok et al., 2021b; Wang et al., 2021, 2022).

The region-to-region variations in the conversion factors (i.e., cv,d, cs,d, and cs,100,d) can be clearly found, as shown in Fig. 6. Although it is difficult to quantitatively study the reasons behind this region-dependent feature, one can first attribute this to the diverse contributions from different dust sources. Excluding some occasional extreme events (Uno et al., 2009), a given oceanic region is generally influenced by specific dust sources via typical dust transport pathways. In the middle- and low-latitude Atlantic, the primary dust transport pathway is from the Saharan desert in North Africa to the eastern coastal regions of North America (Rittmeister et al., 2017; Yu et al., 2021). In the North Atlantic, Baddock et al. (2017) reported that dust aerosols are mainly from Iceland. Dust aerosols in the Arctic are more complicated, coming from high-latitude dust sources in the Northern Hemisphere (e.g., Alaska, Canada, northern Europe, and Russia) (Bullard et al., 2016; Meinander et al., 2022), local Arctic sources (Shi et al., 2022), Asia (Zhao et al., 2022), and North Africa (Shi et al., 2022). For the Pacific, dust aerosols mainly originate from the central and east Asian dust sources and transport to North America (Guo et al., 2017; Hu et al., 2019). At the remaining oceanic sites in the Southern Hemisphere, dust aerosols can be related to Australia, New Zealand, Patagonia, and southern Africa (Bullard et al., 2016; Struve et al., 2020; Kok et al., 2021a; Meinander et al., 2022). In addition, at the downstream areas, the possible aging and mixing of dust with other aerosol types during long-range transport may also be responsible for the region-to-region variations in conversion factors (Kim and Park, 2012; Goel et al., 2020).

In addition to the INP-relevant conversion factors, the relationship between 532 nm aerosol extinction and CCN-relevant parameters n100,d is also studied in this section. The analysis is based on the relationship between log⁡(n100,d) and log⁡(αd) as reported by Shinozuka et al. (2015). Figure 7 shows the relationship between the aerosol extinction coefficient at 532 nm and particle number concentration (radius > 100 nm) n100,d at nine oceanic and coastal sites. The data points representing PD (in blue) and DDM+PD (in orange) are both plotted. Ansmann et al. (2019b) found that log⁡(n100,d) and log⁡(αd) are strongly correlated when taking data points with αd in the range of 100–600 Mm-1 into consideration, while the correlation strength significantly decreases and the data points tend to be dispersive once αd values exceed 600 Mm-1. The AERONET sites selected here generally show a clear atmospheric environment with limited pollution aerosols and can generally fulfill the constraint of αd<600 Mm-1, except for these coast sites, e.g., Shirahama and Osaka. To retain sufficient data points, we adopted data points with αd values ranging from 20 to 600 Mm-1 in our calculation.

Table 5 lists the values of c100,d and χd for both the PD and DDM+PD datasets. Considering the regression coefficient χd>0.50 as valid analysis, attention should be given when using the results at the coast sites Osaka, American Samoa, and Amsterdam Island. The PD and DDM+PD datasets generally show a similar slope (corresponding to χd) in regression analysis, except for the Osaka site, for which an evident intersection between two fitted lines appears, attributed to the sparse PD data points available for fitting. Moreover, it should be mentioned that using the newly proposed dust dataset selection scheme to retrieve the CCN-relevant conversion factors seems not to be robust on the continent. Thus, more care should be taken when retrieving c100,d and χd for those polluted city regions in future work.

The dust-related conversion factors may significantly vary along the way of dust transport due to the potential modifications of dust microphysical properties caused by particle sedimentation, aging processes, external mixing with other aerosols, and so on. There are two main transoceanic paths of dust transport, i.e., the transatlantic path from the Saharan desert to America (Rittmeister et al., 2017; Yu et al., 2021; Dai et al., 2022) and the transpacific path from Asian dust sources (Taklimakan and Gobi deserts) to America (Guo et al., 2017; Hu et al., 2019). Here we selected several sites along these two paths to evaluate the variations in conversion factors. For the transpacific transport, six sites from Asian dust sources to America were selected, including Dushanbe, SACOL in Lanzhou, Shirahama, Midway Island, Mauna Loa, and Trinidad Head. For the transatlantic transport, four sites from North Africa to America were selected, including Dakar, Cape Verde, ARM Graciosa, and Tudor Hill.

Figure 8 shows the conversion factors cv,d, c250,d, cs,d, and cs,100,d at the selected sites along the two dust transport paths. These conversion factors are calculated from the PD+DDM cluster. It is noted that the microphysical properties of dust particles originating from the Saharan desert and Asian dust sources are very different. Moreover, with the increase in transport distances, an evident variation tendency is observed for all the conversion factors at both transoceanic paths. cv,d values show a significant decline along with transport, indicating that the proportion of dust particles in the atmospheric column tends to be smaller due to sedimentation. He et al. (2021b) also observed a relatively smaller cv,d of 0.52 × 10-12 Mm m3 m-3 in the downstream area in central China compared with the value obtained near the sources of Asian dust. c250,d values show a gradual increase trend along with transport, suggesting the increased contribution of large-sized sea spray aerosols in the atmospheric column. For cs,d, a general decline is observed between the values before and after transoceanic transport. A plunge of cs,d is prominent for the transpacific path. In contrast, cs,100,d values only show an apparent enhancement for the transatlantic path, while the variation trend for the transpacific path is generally inapparent. This suggests that particles with radii < 100 nm should be responsible for the decrease in cs,d after transoceanic transport.