The POLIPHON data analysis consists of five steps. An overview of the main retrieval packages is shown in Table . In the first step, the dust and non-dust contributions to the particle backscatter coefficient are separated by using the measured profile of the particle linear depolarization ratio . However, this is only possible if a polarization-sensitive lidar or ceilometer is operated. Besides non-spherical dust particles, volcanic ash, wildfire smoke in the upper troposphere and lower stratosphere (UTLS) and dry marine particles in the shallow marine boundary layer can cause enhanced light depolarization . However, by using backward trajectory analysis these contributions to the measured depolarization ratio can be easily identified so that a clear quantification of the dust backscatter coefficient is possible. Step 1 is important because mineral dust belongs to the key aerosol types in the atmosphere and influences cloud processes in a very specific way as will be discussed below. If a polarization-sensitive lidar instrument is not available, one may use available modeled aerosol profile information to estimate the dust backscatter fraction, as described in the next section.

Aerosol-type and aerosol source information for detected aerosol layers can be generally obtained, e.g., via height-resolved air mass source attribution , backward trajectory analysis , or from large-scale atmospheric simulations with the CAMS (Copernicus Atmosphere Monitoring Service) model. CAMS is a global atmospheric composition forecast production system . Furthermore, simultaneously measured extinction and backscatter profiles observed with Raman lidar or High Spectral Resolution Lidar (HSRL) can be used to identify the non-dust aerosol types in the observed layers when using a polarization lidar.

Complex mixtures of aerosols, as they may frequently occur in coastal polluted areas near deserts as for example in the Eastern Mediterranean , are probably the most difficult scenarios regarding a proper identification of all contributing aerosol types. However, in the majority of aerosol scenarios, the aerosol conditions are much more simple, as numerous lidar observations of well-defined lofted desert dust plumes, pronounced wildfire smoke layers, marine aerosols over the remote oceans, or of the anthropogenically polluted boundary layer over the industrial continents show.

Note that conversion factors for volcanic ash are not included in Table . The volcanic ash conversion factors are very similar to the ones for mineral dust as observations showed .

In the third step, the aerosol-type-dependent components βi(λ) of the observed particle backscatter coefficient must be converted into respective particle extinction coefficients σi(λ) by using published data sets of aerosol-type-dependent extinction-to-backscatter ratios or lidar ratios Si(λ) (; ). Meanwhile, many publications for lidar ratios at λ = 355 and 532 nm, and a few reports for the wavelength of 1064 nm are available in the literature . The new generation of space lidars (355 and 532 nm HSRLs), measuring both the backscatter and the extinction coefficient of a given aerosol mixture, is able to produce its own aerosol-type-dependent lidar-ratio climatology by analyzing the observations, e.g., in pure dust or pure marine regions, in dense wildfire smoke plumes , or highly polluted urban areas.

In the fourth step, the POLIPHON extinction-to-number conversion factors c50,i(λ), c100,i(λ), and c250,i(λ), the extinction-to-surface-area conversion factors cs,i(λ), and the extinction-to-volume conversion factors cv,i(λ) are applied to convert the lidar-derived aerosol-type-dependent extinction coefficients σi(λ) into particle number concentration n50,i (considering all particles with dry-particle radius > 50 nm), n100,i (considering all particles with dry-particle radius > 100 nm), and n250,i (considering all particles with dry-particle radius > 250 nm), and into surface area (si) and volume concentrations (vi). Table  (primary retrieval products) provides an overview of these conversions. The dry-aerosol products (index: dry) are required as input in the estimation of particle mass, CCN, and INP concentrations. The dry-aerosol properties are, however, derived from extinction coefficients σi,amb(λ) measured at ambient humidity conditions (Index: amb). The impact of water uptake by aerosol particles is small and thus the uncertainty introduced by unknown water uptake effects as long as the relative humidity (RH) is < 70 %. Aerosol particles can be regarded as dry at RH < 50 %. At RH > 75 % significant water uptake occurs in the case of hygroscopic particles such as anthropogenic sulfate particles . Atmospheric conditions with RH > 75 % are particularly relevant for aerosol observations in the vicinity of clouds, where retrieving aerosol microphysical characteristics accurately is key to properly studying aerosol–cloud interaction. The water-uptake impact must thus be considered in the POLIPHON data analysis. This aspect is further discussed in Sect. .

According to Table , the conversion factors are designed in such a way that the required dry-particle microphysical products can be directly obtained from the observations (conducted at ambient conditions). Besides the number, surface, and volume concentrations in Table  further products are computed in the case of dust, such as n60,d,dry, s100,d,dry, vdc,dry, and vdf,dry. The quantities will be explained in Sect. .

In the fifth and final step of the POLIPHON data analysis, the aerosol products, which are of importance for environmental monitoring and studies of aerosol–cloud interaction, are calculated. The dry-particle mass concentration Mi,dry is obtained from the derived volume concentration vi,dry in combination with particle density information. The particle densities ρd, ρc, ρm, and ρbb for dust, continental aerosol pollution, dry marine particles, and wildfire smoke particles are set to 2.6, 1.5, 2.16, and 1.15 gcm-3, respectively . The particle density for stratospheric sulfate particles ρvs is a strong function of temperature . The H2SO4 concentration of the sulfuric acid-water solution droplets can be calculated by using model-based temperatures and by assuming a typical water vapor concentrations, e.g. of 5 ppm in the dry lower stratosphere.

An important POLIPHON application is the estimation of CCN and INP concentrations in the vertical profile up to tropopause level. Dust particles play a special role in aerosol–cloud-interaction processes. They are omnipresent in the atmosphere . On the one hand, pure dust particles are hydrophobic in contrast to other relevant aerosol types, such as marine or anthropogenic pollution particles. Thus, dust particles seem to be quite inefficient CCN as long as they are not internally mixed with soluble, hygroscopic material. For hydrophobic dust particles, the dust particle number concentration n250,d may be regarded as an appropriate proxy for the dust CCN reservoir .

During long-range transport, chemical aging and cloud processing lead to a coating of dust particles by soluble material . This aspect was already discussed by . Contaminated dust particles are very efficient CCN, because they are comparably large and hygroscopic. For these particles n100,d is a good CCN proxy. Even smaller dust particles may serve as CCN after accumulation of hygroscopic substances so that n60,d may be regraded as an overall proxy for the dust CCN reservoir.

It should be emphasized in this context, that the light depolarization characteristics of the contaminated, irregularly shaped dust particles is not affected (compared to the ones of pure dust particles showing no contamination) as long as RH indicates dry conditions (RH < 60 % to 70 %). This is the clear conclusion of our field-campaign and long-term studies in highly polluted environments such as Cabo Verde during the winter season and at Dushanbe in Tajikistan . An accurate separation of dust and non-dust fractions is possible even in cases with aged and internally mixed dust particles. This conclusion is supported by accompanying sun photometer observations, i.e., by the good agreement between sun-photometer-derived fine- and coarse-mode AOTs and the lidar-derived dust and non-dust AOTs. Complex mixtures of dust and anthropogenic pollution can be regarded as an external mixture of contaminated dust and haze particles.

The number concentrations n50,i,dry and n100,d,dry in Table  (primary POLIPHON products) are used as CCN proxies nCCN,0.2%,i for hygroscopic (i = c, m, bb) and hydrophobic (dust, i = d) particles, respectively, for a typical water supersaturation of 0.2 % (relative humidity over water of 100.2 %). Such a supersaturation is reached during updraft conditions with low vertical velocities of clearly below 1 ms-1. At stronger updraft speeds and correspondingly higher supersaturation values of 0.4 % to 0.7 %, the nCCN values may be a factor of 5–10 higher than the ones for 0.2 % as we pointed out in .

Mineral dust is the most important INP type . Two different INP parameterization concepts are discussed in the literature and used in simulation models, the time-independent (diagnostic) approach and the time-dependent (prognostic) approach . The time-independent approach includes a time-independent particle-number- and surface-area-based descriptions of ice nucleation , denoted as D10, D15, and U17, respectively, in Table . The particle number concentration n250,c,dry (considering continental, insoluble particles with radius > 250 nm) is used as aerosol input in the D10,IF parameterization scheme to estimate the INP concentration in the case of immersion freezing (IF). Immersion freezing means that nucleation occurs on an insoluble particle which is immersed in a cloud water droplet . The dust particle number concentration n250,d,dry is used as aerosol input in the D15,IF parameterization scheme used to estimate the dust INP concentration . provides a deposition ice nucleation (DIN) parameterization for dust particles. DIN (ice nucleation initiated by water vapor deposition on INPs) typically occurs at cirrus level and temperatures < -40 °C. The dust surface area concentration sd,dry is the aerosol input. Further diagnostic INP parameterization for marine particles , biological aerosol components , and organic particles are available, but not listed in Table . Aerosol input is always the surface area concentration.

The time-dependent approach to immersion freezing is following the classical nucleation theory (CNT) (; ). In the time-dependent approach, all particles can be activated at a random base and belong to the reservoir of INPs within a given cloud layer. Aerosol-type-dependent nucleation rates control the nucleation of ice crystals per second . According to and the large particles with radius > 250 nm are the most favorable INPs. We may thus introduce the number concentration n250,i,dry as INP reservoir proxy. In (KA13, ABIFM: water-activity based immersion freezing model) and (W12, DIN), time-dependent INP parameterizations for immersion freezing and deposition ice nucleation, respectively, are described.

Finally, an INP parameterization for homogeneous freezing is listed (K00, HOM). This ice nucleation mode describes freezing of liquid sulfate particles (background aerosol particles or volcanic sulfate particles in the upper troposphere) at temperatures below -40 °C. Here, the volume concentration vvs is the aerosol input parameter. Note, that all ice nucleation processes are strong functions of temperature, relative humidity, and vertical wind conditions (creating the ice supersaturation conditions required to start ice crystal nucleation). More discussion on INP retrieval and estimation with focus on lidar INP profiling are given in and .

Main goal of the article is to present an updated set of POLIPHON conversion factors c50,i(λ), c100,i(λ), c250,i(λ), cs,i(λ), and cv,i(λ) for five different aerosol types, defined in Table , and four lidar/ceilometer laser wavelengths. The POLIPHON conversion factors required in Table  are obtained from statistical analyses (explained in the Appendix ) of the correlation between two data records xi,j(λ) and yi,j. For simplicity, we assume dry-aerosol conditions in this introductory section. In Sect. , we explain the procedure for the general case of AERONET observations at ambient humidity conditions. The data set xi,j(λ) contains all individual observations (from j=1 to Nobs) of the aerosol optical thickness AOTi,j for wavelength λ and aerosol type i measured at one of the selected AERONET sites. The data set yi,j contains the column-integrated values of one of the microphysical retrieval products such as ∫n50,i,j(z)dz, ∫n250,i,j(z)dz, ∫si,j(z)dz, or ∫vi,j(z)dz with height z above the AERONET station.

The AERONET data base stores all individual observations of the AOT from 340 to 1640 nm and the related column-integrated particle size distribution for all AERONET sites . The size distributions are obtained by applying a well-designed and validated comprehensive inversion scheme to the spectrally resolved AOT observations and the measured spectral sky radiances. From the particle size distributions, the column-integrated properties ∫n50,i(z)dz, ∫n250,i(z)dz, ∫si(z)dz, and ∫vi(z)dz, are calculated in the first step of the data analysis to obtain the POLPIHON conversion factors. Details are given in . As will be presented in the next section, we selected preferably AERONET sites with long-term observation over more than 10 years and thus having data records of the order 1000–100000 individual observations of optical and corresponding microphysical properties.

In the next step, a linear regression is applied for a well-defined subgroup of AERONET observations, e.g., for all dust-dominated observations (aerosol type index i = d) collected at a given near-desert station. The statistical analysis is repeated for all selected AERONET stations within or close to a desert. The applied least-squares estimation (LSE) method , described in the Appendix , considers all individual dust observational data sets AOTd,j(λ), ∫n100,d,j(z)dz, ∫n250,d,j(z)dz, ∫sd,j(z)dz, and ∫vd,j(z)dz), collected at one station. For each data set consisting of pairs of a given AOTi,j(λ) and one of the defined microphysical products, e.g., of the dust particle volume concentration vd,j, the linear regression analysis is performed and yields the conversion factor, e.g., the dust extinction-to-volume conversion factor cv,d(λ) as needed in Table . For dust, the linear regression analysis is performed with 8 different microphysicial properties (∫n60,d,j(z)dz, ∫n100,d,j(z)dz, ∫n250,d,j(z)dz, ∫sd,j(z)dz, ∫s100,d,j(z)dz, ∫vd,j(z)dz, ∫vdf,j(z)dz, and ∫vdc,j(z)dz). In all other cases (marine and continental aerosol, wildfire smoke, and volcanic sulfate), four regression studies are conducted per wavelength with AOTi,j(λ) and with one of the four defined microphysical products ∫n50,i,j(z)dz, ∫n250,i,j(z)dz, ∫si,j(z)dz, and ∫vi,j(z)dz.

The long list of 8 dust conversion factors is related to specific role of dust in cloud processes. Freshly emitted hydrophobic dust particles may be rather inefficient CCN. Only particles with radius > 100 nm or even larger ones, partly > 200 nm in radius, may be able to serve as CCN. However, dust particles coated with hygroscopic substances may act as CCN already at radius sizes of > 50–60 nm. With n60,d,dry, we introduce a new CCN proxy for contaminated dust, e.g., dust particles with sulfate coating.

In the case of ice nucleation, the surface area concentration sd is usually the input parameter in INP parameterization. However, in immersion freezing processes with hydrophobic dust INPs, only the surface area concentration of the activated CCN (n100,d) inside the droplets is then relevant in heterogeneous ice nucleation processes, i.e., the surface area s100,d considering only the dust particles with radius > 100 nm should be used as aerosol input pararmeter in the INP parameterizations.

For a number of reasons summarized by , especially when illuminating the life cycle of dust in the atmosphere, lidar-derived profiles of fine-mode and coarse-mode dust mass concentrations are useful to improve parameterizations of dust emission, long-range transport and deposition in atmospheric models. Lidar-model comparisons regarding fine-mode and coarse-mode fractions during long-range transport were discussed in . Therefore, we include extinction-to-volume conversion factors for fine mode cv,df and coarse mode cv,dc.

For a given station (assigned to one of the five aerosol types), the regression analysis is repeated for each of the different 4–8 microphyscial products to obtain the respective set of 4–8 conversion factors. This procedure is repeated for each of the four wavelengths. In the final step, we averaged all station-by-station conversion factors (for a given aerosol type, wavelength, and microphysical product) to obtain the mean conversion factors for all defined aerosol types and wavelengths. In the next two sections, we introduce the selected 62 AERONET stations and how we filtered the AERONET data sets to obtain the aerosol-type-dependent AERONET data sets required as input in the regression analyses.

Table  and Fig.  provide an overview of all selected 62 AERONET stations used in our statistical data analysis. We selected 12 AERONET stations in or close to desert regions to be able to determine conversion factors for pure desert dust conditions (i = d). Similarly, we selected 8 stations on islands in the Pacific, Indian, and Atlantic Ocean with long-term observations of more than 10 years in order to derive representative marine-aerosol conversion factors (i = m). In the case of continental anthropogenic pollution (i = c), we selected 25 AERONET stations to cover remote (background), rural, and urban conditions on different continents.

In the case of wildfire smoke observations (i = bb), we used the stations, data sets, and data filtering options in this POLIPHON update effort as selected in . However, this time, we excluded the observations at the Table Mountain station in California. The impact of urban haze from the Los Angeles region is always high and does not allow a trustworthy retrieval of pure smoke conversion factors. In , conversion factors for 532 nm were presented, only. Now we repeated all computations for all four wavelengths, i.e., for 355, 532, 911, and 1064 nm, and applied, for the first time, also a weighted linear regressions analysis to the wildfire smoke observations.

In the case of the stratospheric sulfate conversion factors for fresh volcanic aerosol (from the Hunga Tonga-Hunga Ha'apai volcanic eruption in mid-January 2022, in the following simply denoted as Hunga Tonga eruption), we used the same observations (stations, measurement days, observation times) as presented in Figs. 3 and 4 in . These stations are Maïdo on La Reunion, France, Windpoort and Gobabeb in Namibia, Metsi in South Africa, SP-EACH at São Paulo, Brazil, and PSDA, Chile, located in the Antofagasta region in northern Chile. The observations in late-January 2022 are characteristic for fresh sulfate (effective radius around 300 to 500 nm) with a low impact of sedimentation and removal of large particles. The volcanic sulfate particles formed a well defined accumulation mode (similar to the one of UTLS wildfire smoke).

To obtain conversion factors for aged Hunga Tonga sulfate aerosol, one year after the eruption, we used the observations at the Antarctic AERONET site of Utsteinen (72° S, 23.3° E, 1400 m above sea level, 160 km away from the Southern Ocean). The 500 nm AOT is close to 0.02 at unperturbed atmospheric conditions over the Antarctic stations so that any further AOT contribution, e.g., from the stratosphere, is visible in the data. The effective radius was 160 nm for these unperturbed aerosol conditions in January 2022. One year later, in January 2023, under the full influence of Hunga Tonga aerosol, the AOT increased to 0.04–0.05 and the effective radius of the pronounced accumulation mode caused by the volcanic sulfate aerosol was around 250 nm. These Utsteinen AOT observations were found to be in good agreement with our lidar observations at the German Antarctic Neumayer station (about 500 km west of the Utsteinen site) during the first months of 2023. The profile data showed 532 nm AOTs of 0.02–0.025 for the height range from the tropopause up to 20 km. According to the AERONET observations discussed by , the 500 nm AOT caused by the volcanic aerosol was of the order of 0.3–0.5 and the effective radius of the well-defined accumulation mode was close to 400 nm in January 2022.

We used the opportunity to analyze volcanic sulfate layers in the lower troposphere. Respective observations could be recently realized after the eruptions of the Cumbre Vieja volcano on La Palma in the autumn of 2021 . We included observations at Leipzig after the eruption of the Icelandic Eyjafjallajökull volcano in April 2010 in this study .

The data downloaded from the AERONET data base for each station in Table  are listed in Table . The version-3-inversion data files contain AOT values for 440, 675, 870 and 1020 nm, separately for fine-mode and coarse-mode aerosol, and the corresponding particle size distribution for each individual observational data set. Furthermore, the volume and surface-area concentrations, separately for fine-mode and coarse-mode fractions, are available. These products are sufficient to calculate all conversion factors for 532 and 911 nm. From interpolations between neighboring AOT values by using respective Ångström exponents, we obtained the 532 and 911 nm total (fine-mode and coarse-mode), fine-mode, and coarse-mode AOTs. In, principle, the version-3-inversion data files with all the AOT information for 440, 675, 870 and 1020 nm can also be used to extrapolate to 355 and 1064 nm in order to create fine-mode, coarse-mode and total AOT data sets for 355 and 1064 nm.

However, the specific absorbing and scattering features of mineral dust and wildfire smoke in the 355–532 nm wavelength range cannot be accurately reproduced by simple extrapolation of the 355 nm AOT from the version-3-inversion AOTs for the 440–1020 nm wavelength spectrum. Therefore, we used the directly observed 380 and 440 nm AOTs (Version 3, AOT data in Table ) to obtain the 355 nm (total) AOT by extrapolation. Afterwards, we selected those 355 nm AOT values that were temporally close to the observations used to retrieve the version-3 inversion products. Analogously, we determined and selected the respective 1064 nm AOT values from directly measured 870 and 1020 nm AOTs. In the next step, we computed the coarse-mode AOTs at 355 and 1064 nm via extrapolation by using the coarse-mode AOT information in the version-3-inversion data files (covering the wavelength range from 440 to 1020 nm). Finally, we calculated the difference between the total and the coarse-mode AOTs to obtain the fine mode AOTs at 355 and 1064 nm. Internal checks and comparison between the total, fine-mode, and coarse-mode AOTs from 355 to 1064 nm indicated the consistency between all optical data.

Most conversion factors were computed by using total AOT and respective total (fine + coarse-mode) size distribution data. However, the wildfire smoke and volcanic sulfate conversion factors were determined by using the fine-mode AOTs and the respective microphysical properties computed from the fine-mode part of the size distribution, only. More details to this aspect can be found in . The fine-mode data in the AERONET data base cover the full size distributions (well-formed, monomodal accumulation mode) of wildfire smoke and volcanic sulfate particles.

It should be emphasized that the fine-mode AOT is almost equal to the total AOT in the case of wildfire and volcanic-sulfate-dominated observations. This means that the computation of the 355 and 1064 nm coarse-mode AOTs and subsequent subtraction from the total AOTs do not introduce a significant bias in the fine-mode AOT data required to derive the wildfire smoke and volcanic sulfate conversion factors.

Note that in the case of all AERONET observations with a strong impact of UTLS aerosols on the measured AOT, only level 1.5 AERONET data are available. These UTLS-aerosol-dominated observations are completely removed and are not part of the level 2.0 data base. Similarly, many of the level 1.5 data are removed in the case of lower tropospheric volcanic sulfate layers. Level 1.5 data are cloud-screened but not further checked for instrumental biases. Level-2.0 data are available after regular inspection and calibration of the photometers at AERONET topical centers and recalculation of the level 1.5 data by using, e.g., updated filter transmission functions. Thus, we decided to use level 1.5 data in all analyses of tropospheric and stratospheric volcanic sulfate layers and in the analysis of UTLS smoke layers. Level 2.0 data were used in the case of lower tropospheric smoke data, only.

After setting up proper data fields of the total, fine-mode, and coarse-mode AOT and related microphysical inversion products, we can step forward towards the regression analyses. Well defined data sets for pure marine, pure dust, and pure continental haze conditions are needed in the correlation studies to obtain the aerosol-type-dependent conversion factors. We applied the filter options as defined in Table  to identify and select all pure marine observations conducted at the 8 marine AERONET stations, the pure dust cases over the 12 desert AERONET stations, and the continental-haze-dominated measurements over the 25 urban and rural continental AERONET sites defined in Table . For the sake of completness, the regression analysis considers dust fine-mode AOTs and the respective dust fine-mode column volume concentrations and, respectively, dust coarse-mode AOTs and dust coarse-mode column volume concentrations to obtain the dust fine-mode and coarse-mode volume conversion factors cv,df and cv,dc.

Note that we considered 532 nm AOT < 0.5, only, in the dust-related analysis to avoid any bias introduced by potentially incorrect AERONET observations that may occur in rather dense aerosols along the sunphotometer observational path. Such conditions may especially be given during measurements shortly after sunrise and shortly before sun set . Fortunately, there are several AERONET stations that showed low bias at greater AOTs > 0.5, and in these cases we did not find a strong hint that we have a bias when we ignore all dust situations with AOT > 0.5. On the other hand, the majority of dust events around the globe show AOTs < 0.5 at 500–550 nm so that our conversion factors, presented here, are applicable to all these dust scenarios. In more than 80 % of cases out of all observations at AERONET stations close to dust source regions, 500 nm AOT < 0.5 was found.

The Ångström exponent AE for the 440–870 nm wavelength range was used to distinguish the different basic aerosol types. High AE values of 1.6–2.0 indicate urban haze with a large fraction of freshly produced small particles. Lower AE values of 1.1–1.5 indicate aged aerosol ensembles, in most cases a mixture of anthropogenic pollution and soil, road, and industrial dust. Very low and low AE values of < 0.3 (mineral dust) and from 0.2–0.6 (marine aerosol) are caused by coarse-mode dominated particle ensembles. Because AE values of 0.2–0.6 can also occur during dust events, we used the 532 nm AOT to distinguish dust from marine observations. Only dust cases with a 532 nm AOT exceeding 0.1 were considered in the statistical regression analyses. Marine AOTs are usually well below 0.07. A clear discrimination option to distinguish dust-dominated and marine-aerosol-dominated observations is important for AERONET stations on the islands of Tenerife (Izaña), Cabo Verde, and Barbados (Ragged Point). The filtering conditions for wildfire smoke were discussed in and in the foregoing section for volcanic sulfate aerosol.

One of the most important aspects to be considered in the regression analyses is the need for dry-aerosol conversion factors in Table . However, the AERONET observations are conducted at ambient humidity conditions. As a result of water uptake, hygroscopic particles in the air are larger at RH of 80 % than at RH of 40 % when they are dry or almost dry. This increase in particle size must be taken into account in the statistical analyses. The strategy to obtain the dry-aerosol conversion factors from AERONET aerosol data observed at ambient RH conditions is explained in Table . In order to be in line with the notation in Table  and the general lidar nomenclature (particle extinction coefficient instead of AOT, number, surface, volume, and mass concentration instead of column values of these quantities), we divided all AERONET AOTs and column microphyscial products by a typical vertical atmospheric length scale (aerosol layer depth) of 1000 m, and proceed with these data sets within the linear regression studies. This change is considered in Table .

The goal is to derive those conversion factors (in column 2 in Table ) from the regression analysis with xi,j(λ) and yi,j data sets for swollen aerosol particles (in columns 3 and 4) that can be interpreted as conversion factors (in column 1) needed to solve the equations in Table 2. More details to this topic can be found in .

We may explain our basic data analysis concept by the following examples for continental haze: c60,c,amb is the obtained conversion factor when applying the linear regression analysis to all data pairs σc,amb,j and n60,c,amb,j (with observational running index j from 1 to Nobs). n60,c,amb,j considers all particles with radius > 60 nm. We assume a typical RH of 60 % during the AERONET observations. The continental pollution particles shrink by about 15 %–20 % when the relative humidity decreases to 40 % (dry conditions). This means that n60,c,amb,j is approximately equal to n50,c,dry,j and represents the particle number concentrations considering all dry particles with radius > 50 nm.

As indicated in Table , over polluted continents with a strong fraction of hygroscopic sulfate particles, a small water uptake effects has to be generally considered. Even when the photometer observations over rural and urban AERONET sites are conducted at sunny conditions, an RH of 60 % as an RH average value for entire continental planetary boundary layer PBL must be considered. Most of the aerosol (usually more than 80 %–90 % of the tropospheric aerosol content) resides in the boundary layer over the polluted continents. As mentioned, at these slightly enhanced humidity conditions the particle radius is about a factor of 1.15 ± 0.05 larger than the dry-particle radius at RH < 40 % .

We assume an even higher marine PBL RH value of 80 % over the island stations during the observations of marine aerosols so that we expect a particle radius increase by roughly a factor of 2.0 according to an extinction enhancement factor of 3.7 at 532 nm as observed by when RH increased from dry conditions with RH = 40 % to humid conditions with RH = 80 %. Such very high enhancement factors close to 4 could be measured in pure marine air over Barbados during the winter season in the absence of any continental influence from Africa, South and Central America.

Water vapor effects are neglected in the case of desert dust observations, RH < 50 % is assumed during the sunny AERONET observations at the AERONET stations close to or in deserts. As in the case of desert dust, we also assume dry conditions (RH < 50 %) during wildfire smoke and volcanic sulfate observations. Dry conditions generally prevailed in the upper troposphere and lower stratosphere and were probably also given in most cases of AERONET observations of smoke in the lowest 5 km of the troposphere over the AERONET stations in or close to fire regions. In the case of the few observations of lower tropospheric volcanic sulfate layers, we also assumed dry conditions in the regression analysis for a better comparison of all determined tropospheric and stratospheric sulfate conversion factors.

As described in detail in , the respective dry-aerosol surface area concentrations and volume concentrations for continental aerosol pollution (at RH = 40 %) are a factor of 1.33 and 1.5, respectively, lower than the ambient-condition (RH=60 %) surface area and volume concentrations in the case that the particle radius decreases by a factor of 1.15. Similarly, the dry aerosol surface area and volume values are smaller by a factor of 4 and 8 than the observed ones, respectively, when the particle radius shrinks by a factor of 2. These factors are considered in Table  (columns 2, 3, and 4).

In the case of the conversion factor, used to obtain particle number concentrations, we used a different way to consider the water uptake effect. As shown in Table , we simply interpret the computed values of n60,c,amb,j and n290,c,amb,j as n50,c,dry,j and n250,c,dry,j, respectively, when assuming a particle radius reduction by a factor of 1.15. Similarly for marine aerosol, we assume that the observed values n100,m,amb,j and n500,m,amb,j are representative for the respective dry-aerosol values n50,m,dry,j and n250,m,dry,j, respectively, when the particle radius is reduced by a factor of 2.

If nearby radiosonde observations are available so that a precise knowledge of the RH profile is given one can, in principle, transfers the continental extinction coefficient measured with lidar at a given RH level to extinction coefficients at 60 % in the retrieval of urban and rural continental aerosol microphysical properties, to the extinction coefficient at 80 % in the retrieval of the microphysical properties of marine particles, and to extinction values for 40 % in the retrieval of dust, smoke and volcanic sulfate microphysical properties before applying the POLIPHON conversion factors as given in Table 6 (column 1). The RH-related transfer of the extinction coefficient can be done following the Hänel parameterization (; ). If radiosonde observations are not available one may use modeled RH profiles. However, these profiles have to be generally handled with caution. Especially during conditions with cloud developments, modeled RH fields may not reflect properly the true RH conditions during the lidar observations. In such complicated cases, we recommend to leave out any humidity correction.

As a further remark, we recommend to avoid the application of the POLIPHON method in cases of lidar observations just below the base of cloud layer, i.e., where RH is of the order > 90 % so that strong water uptake by the particles causes large backscatter and extinction coefficients. The use of these large backscatter and extinction coefficients in the POLIPHON computations may lead strong biases (overestimation) in the estimates of the microphysical properties because of the large and not well known RH-controlled impact of water uptake effects. We recommend to use only POLIPHON products in aerosol–cloud-interaction studies for heights at least 500 m below the observed cloud base heights .

It is also worth noting that spaceborne lidar applications rely on trustworthy aerosol observations in the lateral vicinity of clouds layers in aerosol–cloud interaction studies. However, enhanced hygroscopic growth at high relative humidity can increase aerosol scattering by up to 80 % near these cloud boundaries . Therefore, studies considering POLIPHON applications to spaceborne lidar data should exclude aerosol profiles in direct contact with a cloudy column, i.e., aerosol profiles measured within an area of approximately 5 km around the cloud field of interest.

Table  shows the results of the regression analysis applied to four contrasting AERONET data sets. Desert dust observations (IZA, Izana, Tenerife), a marine case (AMS, Amsterdam Islands) and observations at two urban AERONET stations (BEI, Beijing, China; PRE, Pretoria, South Africa) were used in the correlation studies. As outlined in Appendix , the applied least-squares estimation method of fitting the best straight line to data points xi,j and yi,j delivers the slope bi and the intercept ai. In our AERONET-based statistical data analysis, slope bi is a good proxy for the conversion factor ci, describing the relationship between the extinction coefficient (xi) and the microphyscial product (yi). Physically, the most reasonable solution for bi is given when ai≈0, so that the microphysical values are close to zero when the particle extinction coefficient is close to zero. However, due to the scatter in the yi,j values, mostly caused by AERONET retrieval uncertainties, the intercept ai is larger or lower than 0. Table  shows a few examples of solution sets for the intercept ai±δai and slope bi±δbi in the case of the linear regression analysis with xd,j=σd,amb,j at 532 nm and yd,j=n100,d,amb,j (IZA, dust observations, c100,d retrieval). The Amsterdam Island example uses xm,j=σm,amb,j at 532 nm and ym,j=n100,m,amb,j (Amsterdam Island, AMS, marine conditions, c50,m retrieval). The urban examples are based on the regression analysis with xc,j=σc,amb,j at 532 nm and yc,j=n60,c,amb,j (BEI, urban haze, AE range: 1.1–1.5, PRE, urban haze, AE range: 1.6–2.0, c50,c retrieval).

As can be seen, the intercept value ai can have a noticeable impact on the solution for bi. According to Eq. (), the slope bi is equal to yi‾/xi‾ when the intercept is ai=0. We see that bi is smaller than this ideal bi (for ai=0) when ai is positive, and vice versa, bi is larger than the ideal bi when ai is negative. In most cases, it was found that ai had only a minor impact on the determination of bi, so that bi was close to yi‾/xi‾ (within about 5 % around yi‾/xi‾) as is the case in Table  for the Beijing and Pretoria data.

In Fig. , the available data and obtained regression products are shown. The different, but similar regression lines corroborate that the use of the yi‾/xi‾ values as conversion factors is fully justified. Note, that the shown c50,i and c100,d retrievals are the most critical ones compared to retrievals of the conversion factors used to estimate n250, surface area and volume concentrations. In Fig. , the statistical analysis is based on strongly scattered data with a considerable fraction of unwanted outliers. The data are less noisy in the case of the other conversion factors .

In the following tables in Sects.  and , we use the values for yi‾/xi‾ with the weighted mean values xi‾ and yi‾ according to Eqs. () and (), respectively, as the conversion factors and interpret them as the dry-aerosol conversion factors that are needed in the main POLIPHON Table  to obtain the microphysical properties n50,i,dry, n100,i,dry, n250,i,dry, si,dry, and vi,dry.

Tables – show the products of the regression analyses for all AERONET stations. The 532 nm conversion factors are listed. Table  contains the dust conversion factors obtained from the analysis of the selected 12 dust AERONET stations. The marine conversion factors in Table  are obtained from the regression studies with the observations at the 8 selected marine stations. Tables  and show all conversion factors for anthropogenic haze derived from the selected 25 selected continental rural and urban AERONET stations. As already mentioned, Nobs in the four tables is the number of used xi,j and yi,j data pairs in the correlation studies and R2 is the coefficient of determination and indicates the uncertainty in the obtained results. The lowest R2 values are usually obtained in the c50,i and c60,d regression studies. The highest R2 values are usually obtained for cs,i and cv,i.

The station-by-station results in the four tables provide an impression of the variability in the obtained conversion factors for the three main aerosol types. The reasons for the variability are varying ambient humidity conditions during the observations, varying aerosol conditions, especially regarding the size distributions of the observed aerosol mixtures over the polluted continents, and uncertainties in the AERONET inversion products (yi,j values).

Fairly similar conversion factor sets were obtained for the different stations in the case of pure dust (Table ) and pure marine observations (Table ). A less homogeneous picture was obtained from the AERONET observations of anthropogenic pollution (Tables  and ). As a new aspect, we distinguish between continental anthropogenic pollution for the two different AE ranges to better cover conditions with aged and fresh anthropogenic pollution and situations with urban haze and pollution conditions preferably occurring in rural regions. AE of 1.6–2.0 indicates the dominance of freshly produced, relatively small anthropogenic particles whereas AE from 1.1–1.5 suggests a considerable impact of larger particles, i.e., of aged anthropogenic particles including mixtures of fine-mode pollution and coarse-mode particles such as road, soil, and industrial dust. In winter, residential heating including wood burning contributes to the haze over the continents while during other seasons, bioaerosol (pollen, spores) and biological material from agricultural and harvesting activities may dominate the coarse-mode fraction. In the original study , we only considered the conversion factors for the AE 1.6–2.0 range, but especially at rural sites, the conversion factors for the 1.1–1.5 AE range may be more appropriate to estimate CCN concentrations. The comparison of the conversion factors in Tables  and reveals that the conversion factors are typically different by 10 %–20 %. The conversion factors c50,c and cs are lower, and thus n50,c and sc are lower for a given extinction coefficient, in the case of aerosols mixtures showing AE from 1.1–1.5 compared to the respective values for AE from 1.6–2.0. The opposite is the case for the c250,c and cv,c conversion factors.

Regional differences in the dust conversion factors as discussed in may exist, but seem to be small. The most robust AERONET inversion product is the surface area concentration for dust particles with radius > 100 nm, and thus the most trustworthy conversion factor is cs,100,d in Table . stated that the uncertainty in the particle size distribution is large for the particles with radius < 100 nm and > 7 µm (> 50 %) and small (10 %) for particles with radius from 100 nm to 7 µm. As can be seen, all values of cs,100,d for different desert stations (WHI, TAM, TRE, BIR, GOB) are in the range from 1.58 and 1.60 Mmµm2cm-3. Regional differences are not visible. The variability of the other conversion factors in Table , e.g., of cv,d of 0.65 Mmµm3cm-3 (TAM), 1.06 Mmµm3cm-3 (WHI), 0.88 Mmµm3cm-3 (TRE), 0.88 Mmµm3cm-3 (BIR), and 0.61 Mmµm3cm-3 (GOB) may be the result of a combination of uncertainties in the inversion products and local aerosol characteristics. Regional aspects cannot be fully excluded when discussing conversion factors for AERONET stations close to deserts in Australia, South and North America, Africa, and Asia, but the regional impact is weak.

Figures  and  show the impact of the conversion factor variability on the retrieval of the CCN and dry-aerosol mass concentrations in the case of marine, dusty, and haze conditions. The particle extinction coefficient at 532 nm is set to 100 Mm-1 and converted into the shown CCN and dry-mass concentration values. As can be seen, a rather low variability in the POLIPHON results and thus in the respective conversion factors is observed in the case of marine particles. Rather homogeneous conditions obviously prevail over the AERONET island stations during pure marine conditions as defined in Table . A similar conclusion can be drawn in the case of desert dust. A stronger variability is observed for anthropogenic haze conditions. One needs to take a 50 % uncertainty always into account in CCN estimations.

One aspect is left to be discussed here. compared balloon-borne in situ observations of dust volume concentrations and dust extinction coefficients with respective products from AERONET observations at Cabo Verde in September 2022 and concluded that AERONET-based volume conversion factors may be up to 50 % lower than the true conversion factors in the case of dust events with a strong fraction of very large to giant dust particles (with particle radius exceeding 15 µm). The AERONET inversion algorithm only considers dust particles with radius < 15 µm so that the derived volume concentrations are wrong if a significant amount of large to giant particles are present. However, these special cases that may occur after strong dust storms over desert regions or during dust devil events seem to be rare. Except the lidar observation during the dust devils events in southeastern Morocco, close to Saharan dust sources in the summer of 2006, we never observed cases in which large to giant particles dominated the lidar observations. Only a few lidar observations are reported in the literature , that indicated the occurrence of a strong fraction of large to giant dust particles so that the use of the AERONET conversion factors presented here may lead to an underestimation of the dust mass concentration as suggest.

Mean values for all conversion factors, for the five aerosol types, and the four wavelengths are presented in Tables –. All station-by-station values, listed in Tables – were averaged, separately for each conversion factor and aerosol type, to obtain the mean 532 nm conversion factors for the three fundamental aerosol types (marine, dust, continental pollution). In the same way, the data sets of conversion factors for 355, 911, and 1064 nm were processed. The results are shown in Tables  and . The statistical analyses applied to the wildfire smoke and volcanic sulfate observations lead to the conversion factors given in Tables  and .