First of all, the types of fires, e.g., flaming versus smoldering combustion, the fuel type (burning material), and the combustion efficiency at given environmental and soil moisture conditions determine the initial chemical composition and size distribution of the smoke particles injected into the atmosphere. Burning of biomass at higher temperatures, during flaming fires, generates smaller particles than smoldering fires . In forest fires, the flaming stage is usually followed by a longer period of smoldering fires.

Smoke particles from forest fires are largely composed of organic material (organic carbon, OC) and, to a minor degree, of black carbon (BC). The BC mass fraction is typically <5 % but may reach values of 10 %–15 % in cases of complex mixtures of anthropogenic haze with domestic, forest, and agricultural fire smoke . Biomass burning aerosol also consists of humic-like substances (HULIS), which represent large macromolecules . The particles and released vapors within biomass burning plumes undergo chemical and physical aging processes during long-range transport. There is strong evidence from lidar observations that smoke particles grow in size during the aging phase . Processes that lead to the increase in particle size are hygroscopic growth of the particles, gas-to-particle conversion of inorganic and organic vapors during transport, condensation of large organic molecules from the gas phase in the first few hours of aging, coagulation, and photochemical and cloud-processing mechanisms. The lidar observations are in agreement with modeling studies of , who used the theory of particle aging processes described by . Condensational growth dominates the increase in particle size in the first 2 d after emission of a plume. Thereafter coagulation in the increasingly diluted plumes becomes the dominating process. A significant shift of the particle size distribution indicated by an increase in the number median radius from about 0.2 µm shortly after emission to about 0.35 µm after 6 d of travel was found in several cases of Canadian smoke by . The aging effect has to be considered in the retrieval of smoke conversion factors. We distinguish fresh and aged smoke observations in Sect. .

analyzed aircraft in situ measurements of a smoke layer advected from North America and observed over Germany at 10–12 km height in September 2011 and found, in agreement with many other airborne in situ observations, an almost monomodal size distribution of smoke particles with a pronounced accumulation mode (particles with diameters from roughly 200 to about 1400 to 1800 nm). A distinct coarse mode was absent.

The black-carbon-containing smoke particles showed coating thicknesses of roughly 50–220 nm and shell-to-core diameter ratios of typically 2–3. assumed a concentric-spheres core–shell morphology for the strongly-light-absorbing BC core and further assumed purely-light-scattering coating material (i.e., no absorption by the shell) in their analysis of the airborne in situ observations. The authors emphasized that their core–shell model is an idealized scenario because the BC cores of combustion particles are fractal-like or compact aggregates and BC can be mixed with light-scattering material in different ways, including, e.g., surface contact of BC with the light-scattering components, full immersion of BC in the light-scattering component, or immersion of the light-scattering components in the BC aggregate. A process that can produce near-surface BC morphology is coagulation of almost bare BC aggregates with BC-free particles. Condensation of secondary organic or inorganic aerosol components on BC particles can result in particles either with core–shell morphology (concentric or eccentric) or with near-surface BC morphology. All these possible morphology features must be considered in the discussion and estimation of the smoke optical properties and of the potential of smoke particles to serve as INP (Sects.  and ).

Changes in the morphology (size, shape, and internal structure) of smoke particles and their internal mixing state (e.g., soot particle coating) are ongoing during long-range transport. As pointed out, freshly emitted soot particles, i.e., BC particles, are typically hydrophobic, lacy fractal-like aggregates of carbonaceous monomers and become hydrophilic as a result of coating and other aging processes. Lace soot undergoes compaction upon humidification. All these effects lead to an increased ability of smoke particles to serve as CCN with increasing long-range travel time.

Soot compaction (and collapse of the core structures) changes also the scattering and absorption cross sections depending on the refractive index, the monomer diameter, and the structural details. Many publications dealing with the optical properties became available in recent years . mentioned that their model considers 11 different model morphologies ranging from bare soot to completely embedded soot–sulfate and soot–brown carbon mixtures. In agreement with earlier studies, they found that for the same amount of absorbing material, the absorption cross section of internally mixed soot can be more than twice that of bare soot. Thus absorption increases as soot accumulates more coating material during long-range transport. As a general finding of the modeling studies, the absorption enhancement is a complex function of many factors such as the size and shape of the soot aerosols, the mixing state, the location of soot within the host, and the amount and composition of the coating material. All these facts make it necessary to distinguish between fresh smoke (<2.5 d after injection) and aged wildfire smoke (>2.5 d of long-range transport) in our attempt to determine smoke conversion parameters.

As already mentioned, smoke particles after long-range transport seem to be favorable CCN because they become increasingly hydrophilic during aging. In contrast to the impact of smoke on cloud droplet formation, the characterization of their influence on ice nucleation is rather difficult. The link between ice nucleation efficiency and particle chemical and morphological properties and the ongoing modifications of the properties during long-range transport is largely unresolved . However, it is widely assumed that the ability of smoke particles to serve as INP mainly depends on the organic material (OM) in the shell of the coated smoke particles . BC is not considered to be an important contributor to immersion freezing , which is assumed to be the preferred heterogeneous ice nucleation mode.

present a review on the role of organic aerosol (OA) and OM in atmospheric ice nucleation. A unique feature of OA particles is that they can be amorphous and can exist in different phases, including liquid, semisolid, and solid (or glassy) states, in response to changes in temperature (T) and relative humidity (RH) . At low temperatures, e.g., in the UTLS region, where the atmospheric temperature can be as low as 180 K, it is conceivable to assume that the particles are in a glassy state. Most of the secondary organic aerosol particles are solid above 500 hPa (about 5 km) according to modeling studies and for temperatures <240 K .

It has been shown that humic and fulvic matter can act as deposition nucleation and immersion freezing INPs . Furthermore, these macromolecules can undergo amorphous phase transition under typical tropospheric conditions similar to the processes we assume the organic coating of the smoke particles experience.

Aerosol particles serving as INPs usually provide an insoluble, solid surface that can facilitate the freezing of water . Deposition ice nucleation is defined as ice formation occurring on the INP surface by water vapor deposition from the supersaturated gas phase. Although, recent studies suggest that deposition ice nucleation can be the result of pore condensation freezing, where homogeneous ice nucleation occurs at lower supersaturation in nanometer-sized pores . When the supercooled smoke particle takes up water or its shell deliquesces, immersion freezing can proceed, where the INP immersed in an aqueous solution can initiate freezing . Finally, if the smoke particle becomes completely liquid (and no insoluble part within the particle is left), homogeneous freezing will take place at temperatures below 235 K .

However, in reality, at given air mass lifting conditions, the ice nucleation process can be very complex. The time that solid OM needs for transition to a more liquid state, termed as humidity-induced amorphous deliquescence, can range from several minutes to days at temperatures low enough for ice formation . Thus the phase change (as function of T and RH) can be longer than typical cloud activation time periods (governed by the updraft velocity), potentially inhibiting full deliquescence and allowing the OA or the organic coating to serve as INP. When amorphous OA or OM are involved in ice nucleation, the condensed-phase diffusion processes within OA particles will most probably govern the ice nucleation pathway .

The following potential scenarios of atmospheric ice nucleation are uniquely attributable to the presence of amorphous OM. (1) Ice formation in the glassy region may be due to ice nucleation on the solid organic particle, i.e., deposition ice nucleation. (2) During partial deliquescence, a residual solid core is coated by an aqueous shell, and immersion freezing may proceed. (3) At full deliquescence RH, where the particles are completely liquid (and contain no solid soot fragments), homogeneous freezing will occur at temperatures below about 238 K. (4) The presence of a glassy phase in disequilibrium with surrounding water vapor (e.g., cloud activation at fast updrafts as discussed below) may suppress or initiate ice nucleation beyond the homogeneous ice nucleation limit . A slower updraft velocity allows for more time for deliquescence to proceed, potentially resulting in full deliquescence of the OA particle at warmer and drier conditions compared to when a faster updraft is active. Therefore, the same OM can be present in different phase states under the same atmospheric thermodynamic conditions (i.e., T and relative humidity over ice RHi), resulting in different ice nucleation pathways and corresponding ice nucleation rates. OA particle size or coating thickness can also impact the rate and atmospheric altitude of the organic phase change, as larger particles or thicker coatings require more time to reach full deliquescence . There are many more peculiarities of amorphous OM that make INP parameterization and prediction efforts very complicated as discussed in detail by .

Since amorphous smoke OA may take up water and partially deliquesce, resulting in an aqueous solution at possibly subsaturated conditions, we apply the water-activity-based immersion freezing (ABIFM) parameterization and homogeneous ice nucleation parameterization by Koop et al. (2000). ABIFM derives the number of INPs per volume of air for a given time period, when T, RH, and particle surface area s are known (see Sect. 3.1.1). A deposition ice nucleation scheme based on classical nucleation theory is outlined in addition (Sect. 3.1.3) to cover the potential pathway of glassy smoke particles to serve as INPs. Again, T, RH, and s are input in the INP estimation.

To demonstrate the prediction or retrieval of smoke INP profiles from lidar observations in Sect. , we apply two example OA model systems serving as surrogates of amorphous organic smoke particles. One is based on a macromolecular humic or fulvic acid that undergoes amorphous phase transitions in response to changes in RH and T and free-troposphere long-range-transported particles that possess an organic coating acting as INPs .

As discussed in Sect. , the estimation of INP concentrations is challenging due to the chemical complexity of the smoke aerosol. The parameterizations introduced in this section cover the OM-related ice nucleation for the temperature range in the upper troposphere (<-40∘C). Only for these low temperatures, organic smoke particles may be able to influence ice nucleation in the atmosphere. In the following, we present procedures to compute INP concentrations for immersion freezing, deposition ice nucleation, and homogeneous freezing.

The smoke conversion parameters cv, cs, c50, c250, and x, required to solve Eqs. ()–(), were determined from sun photometer observations at nine AERONET stations, distributed over several continents. Figure  shows the considered AERONET stations. The observations at these sites cover the full range of smoke scenarios, from fresh to aged plumes, for different fire types and burning material, and smoke occurrence in the troposphere and stratosphere.

Yellowknife (AERONET site: Yellowknife Aurora) and Churchill in Canada were selected because these AERONET sites were located in the outflow region of major smoke plumes which originated from the record-breaking wildfires in British Columbia , Canada, in August 2017. Strong pyrocumulonimbus (pyroCb) towers developed and lifted enormous amounts of wildfire smoke into the upper troposphere and lower stratosphere (UTLS) from 21:00 UTC on 12 August to 00:30 UTC on 13 August 2017 . The smoke observation at Yellowknife and Churchill could be thus well assigned to the time after injection and allowed us to study the change in the smoke conversion parameters as a function of time from 12–18 h to about 5 d after injection.

The AERONET stations at Rio Gallegos (CEILAP-RG), Argentina; Punta Arenas (Punta-Arenas-UMAG), Chile, at the southernmost tip of South America; and Marambio in Antarctica were selected because well-aged smoke layers crossed these stations in January and February 2020 . The smoke originated from strong fires in southeastern Australia and traveled the 10 000 km distance within 8–12 d. Strong pyroCb activity lifted the smoke layers up to UTLS heights, and self-lifting processes caused further ascent to heights 10–20 km above the tropopause . The background AOT levels are clearly below 0.05 at 532 nm at these high northern and southern mid-latitudinal stations, far away from industrialized centers, so that the smoke layers could be clearly identified and dominated the sun photometer observations over many days (Yellowknife, Churchill) and weeks (Punta Arenas, Rio Gallegos, Marambio).

In order to consider several centers of biomass burning of global importance we selected six further AERONET stations. Smoke from exceptionally strong forest fires in the western United States and western Canada was observed over Reno (University of Nevada, Reno), Nevada, and Table Mountain (Table Mountain, CA), California, from the end of August to mid-October 2020 (in close distance to the fire sources) and allowed the determination of conversion parameters for very fresh and mixtures of fresh and aged North American tropospheric smoke layers.

We downloaded long-term observations performed at the AERONET stations Alta Floresta, Brazil (Amazonian forest fires); Mongu, Zambia, in southern Africa; Mukdahan, Thailand; and Singapore in Southeast Asia to consider observations in key fire areas of global importance. The Mongu data sets consists of sun photometer observations at the Mongu site from 1997–2009 and at the Mongu Inn site from 2013–2019. Fairly constant burning conditions are given at Mongu from July to November of each year. The long-term observations in the Amazon region, southern Africa, and Southeast Asia cover smoldering and flaming fires, fresh and aged smoke layers, and agricultural, grassland, savannah, peat, forest, and bush fires. The selection of these AERONET stations in key burning areas was guided by the smoke study of .

The AERONET smoke studies are supplemented by multiwavelength lidar observations of smoke conversion parameters. These vertically resolved observations were performed at Punta Arenas, Chile ; Manaus, Brazil ; near Washington, DC ; at Cabo Verde; in the outflow regime of central western African smoke , at Leipzig and Lindenberg, Germany ; and on the German icebreaker Polarstern drifting through the high Arctic close to the North Pole during the winter half year of 2019–2020 . The lidar results are shown in Sect. . The retrieval of the microphysical properties was based on backscatter coefficients measured at 355, 532, and 1064 nm and extinction values at 355 and 532 nm , except for the smoke observations over Lindenberg in the summer of 1998. Here, particle backscatter coefficients at six wavelength (355, 400, 532, 710, 800, 1064 nm) and extinction coefficients at 355 and 532 nm were available .

We used the version-3 level-2.0 inversion AERONET products in the case of the long-term observations in the Amazon region, southern Africa, and Southeast Asia and level-1.5 data in the case of the remaining stations. The reason for using level-1.5 data was to significantly increase the number of available observations in our smoke-related studies. Many observations showing high to very high smoke AOTs could not pass the strict criteria of the AERONET data quality checks and were thus removed from the level-2.0 data set. We compared the level-2.0 AERONET products with the corresponding (reduced) level-1.5 products to guarantee that the used level-1.5 data set was of high quality.

In agreement with the AERONET data analysis of , we used the fine-mode AOTs stored in the AERONET database. Smoke particles form a well-developed accumulation mode (with sizes up to about 1 µm in radius) and the related optical properties are assigned as fine-mode AERONET products . However, as will be discussed in Sect. , a bimodal distribution (accumulation plus coarse mode) was often retrieved from the AERONET sun and sky observations. This was also pointed out by . The second mode is probably related to soil, road, and desert dust or marine aerosol in the planetary boundary layer. The comparison with respective lidar observations clearly indicates that smoke produces a pronounced accumulation mode only. A coarse mode is absent. Thus, we computed the smoke-related values of s, v, n50, and n250 from the downloaded size distributions by considering the size classes 1–11 only (covering the accumulation mode and thus the radius range up to 0.9–0.95 µm) and correlated these calculated microphysical values with the fine-mode AOT at 532 nm as stored in the AERONET database to finally obtain the conversion parameters. Details of the computation of s, v, n50, and n250 from the AERONET size distributions can be found in .

We begin the discussion of the AERONET results with an overview of the smoke measurements at Yellowknife and Churchill (stratospheric smoke), Reno and Table Mountain (tropospheric smoke), and at Punta Arenas, Rio Gallegos, and Marambio (stratospheric smoke) in Fig. . The downloaded AOT data sets contain values of fine-mode, coarse-mode, and total AOT for 440, 675, 870, and 1020 nm. The AOT τ for 532 nm is obtained from the 440 nm AOT τ440 and the Ångström exponent a by 16τ=τ440(440/532)a. The Ångström exponent a is defined as a=ln⁡(τ440/τ675)/ln⁡(675/440) with wavelengths λ of 440 and 675 nm. We separately computed 532 nm AOT for fine-mode, coarse-mode, and total aerosol size distributions by using respective fine, coarse, and total aerosol Ångström exponents. In Fig. , the total, i.e., fine-mode plus coarse-mode, AOT is shown. In all other figures below, we exclusively used the fine-mode AOT at 532 nm. In cases with a strong smoke occurrence, the fine-mode fraction is usually >0.9.

The measurements at Yellowknife and Churchill in Fig. a were performed 0.5–2.5 d and 2–5 d after injection of smoke into the UTLS height range over British Columbia, Canada, respectively. The injection took place between 21:00 UTC on 12 August 2017 and 00:30 UTC on 13 August 2017 . As can be seen, the first smoke plumes arrived over Yellowknife, Canada, already 12–18 h after injection. The 532 nm AOT reached values of almost 2.5. The smoke plumes traveled southeastward and crossed Churchill about 1.5–4 d later. A maximum AOT of 2.7 was measured over Churchill. At clean background conditions the AOT is about 0.025 to 0.05 at these Canadian AERONET stations. To consider all smoke observations over Yellowknife from 13–15 August 2017 (days 225–227) we set the AOT threshold level to 0.45; i.e., we considered cases with total 532 nm AOT of ≥0.45, only, in our conversion study.

Rather strong fires occurred in California during the late summer and early autumn of 2020 (Fig. b). Mixtures of fresh and aged smoke were observed over Reno and Table Mountain. We increased the 532 nm total AOT threshold level to 0.6 to avoid a significant impact of urban haze on the wildfire smoke observations and derivation of smoke conversion parameters. The haze-related AOT was about 0.1–0.25. The exclusive use of the AERONET fine-mode products further eliminated the potential impact of non-smoke aerosol such as coarse dust and marine particles on the correlation studies.

Figure c shows the observations of aged Australian wildfire smoke in southern South America and northern Antarctica. The smoke traveled more than 10 000 km within 8–12 d before reaching our combined lidar and AERONET station at Punta Arenas . The diluted smoke caused 532 nm AOTs mostly between 0.05 and 0.3. Maximum values were close to 0.5. At clean background conditions, the AOT is in the range from 0.025–0.035. In our smoke-related AERONET data analysis, we considered all observations with AOT > 0.05 and again carefully checked that all used cases, even those with low AOT, showed clear and dominating smoke signatures (i.e., a pronounced accumulation mode). We selected the low AOT threshold of 0.05 to have sufficient cases in our conversion study for well-defined aged smoke. For each of the shown AOT observation in Fig.  we downloaded the required size distributions and computed the respective column-integrated values of scol, vcol, n50,col, and n250,col (by considering the size classes 1–11).

To obtain the smoke extinction-to-volume conversion factor cv, 17cv=vcolτ, required to derive volume and mass concentrations with Eqs. () and (), the ratio of the vertically integrated (column) particle volume concentration vcol to the fine-mode 532 nm AOT τ was formed for each individual smoke observation. To facilitate the lidar-related discussion we divided the column values by an arbitrary layer depth D (length of the vertical column) and obtain 18cv=vcol/Dτ/D=vσ, with the layer mean volume concentration v and the layer mean particle extinction coefficient σ. The introduced layer depth D has no impact on the retrieval of the conversion factors and is only introduced to move from column-integrated values and AOT to more lidar-relevant quantities like concentrations and extinction coefficients. In this study, we set D=1000 m as in the studies before .

For each smoke observation j (from number j=1 to J), available in the AERONET database, we computed cv,j and then determined the mean value, which we interpret as a representative smoke conversion factor, 19cv=1J∑j=1Jvjσj. In the same way, the conversion factors c250, needed to estimate the large-particle number concentration with Eq. (), and cs, required in the surface area retrieval with Eq. (), were computed: 20c250=1J∑j=1Jn250,jσj,21cs=1J∑j=1Jsjσj.

It is noteworthy to emphasize again that only the accumulation-mode size range (radius classes 1–11) was considered in the computation of n250 and s.

In the retrieval of the conversion parameters required to obtain n50 (Eq. ), we used a different approach . Following the procedure suggested by , we applied a log–log regression analysis to the log(n50,j)–log(σj) data field and determined in this way representative values for c50 and x that fulfill best the relationship, 22log⁡(n50)=log⁡(c50)+xlog⁡(σ).

As emphasized in Sect. , the particle size distribution of smoke particles changes with time during the first days after injection into the atmosphere as a result of particle aging processes (chemical processing, particle collisions, and coagulation). The changing size distribution has a strong influence on the microphysical and optical properties as well as the correlation between v, s, n50, and n250 and the smoke extinction coefficient σ.

Figure  provides insight into the full range of size distributions of atmospheric smoke particles. The smallest particles found at Alta Floresta indicate rather fresh smoke, probably just a few hours after emission. The size distributions for Yellowknife (measured on 13 August 2017, 23:18 UTC) and Churchill were observed about 20 h and 3.5 d after injection of smoke into the UTLS height region, respectively. Aged smoke after long-range transport over more than 1 week was observed at Punta Arenas (8 d after emission) and Lindenberg (10.5 d after emission). It is obvious that the size distribution is shifted towards larger particles with increasing residence time in the atmosphere. All size distributions are normalized so that the integral over each shown size distribution is one. Lidar observation conducted at Leipzig, 180 km to the southwest of Lindenberg , and over Punta Arenas agree well with the respective AERONET size distributions. The lidar observations corroborate that the smoke size distribution is unimodal.

Figure  shows unimodal as well as bimodal size distribution in cases clearly dominated by smoke. Similar bimodal size distributions were presented in the smoke study of . The weak coarse mode may result from aerosols in the boundary layer (marine particles, soil, and road dust). The lidar observations do not show this coarse mode.

To consider the changing smoke size distributions shown in Fig.  in the smoke data analysis, it would be desirable to have conversion parameter sets for fresh, weakly aged, and aged smoke particles. However, in all likelihood such an approach would be impractical and/or unreasonably difficult. As will be discussed below in detail, the majority of AERONET smoke observations close to the fire regions indicate that fresh smoke was usually mixed with enhanced levels of background aerosol which, to a large extent, consists of aged smoke. This regional background aerosol obviously builds up over the fire regions during the long-lasting fire seasons. Therefore, we decided to distinguish just between two different measurement scenarios: (a) aged smoke observations (smoke observed after long-range transport over 5 d and more) and (b) measurements of mixtures of fresh and aged smoke (in the near-range to large fire areas). For these two scenarios we developed conversion parameterizations.

Figure  shows the relationship between (a) the smoke volume concentration v and the smoke-related extinction coefficient σ, (b) particle surface area concentration s and σ, and (c) the particle number concentration of larger smoke particles n250 and σ for aged Australian smoke. The correlation between the number concentration n50 and σ is discussed in Sect. . As a general impression, a clear relationship between v, s, and n250 and σ is found, at least up to extinction coefficients of 300 Mm-1 (or 0.3 in terms of the fine-mode AOT at 532 nm). The spread in the data reflects variations in the smoke properties (size distribution, refractive index). However, the relatively low scatter in the data is a sign for large similarities in the smoke properties (observed over several weeks). This may be related to the fact that the flaming-fire type prevailed, eucalyptus trees were the main burning material, smoke lifting was always linked to strong pyroCb activity and thus similar lifting features, and the size distributions of aged smoke particles after 8–12 d long-range transport are at all very similar.

The mean relationships between v, s, and n250 and σ are visualized by straight blue lines. The respective mean conversion factors cv, cs, and c250 are given as numbers in the different panels and also summarized in Table . These mean conversion factors were computed from the data in Fig. a, b, and c by using the Eqs. (), (), and (), respectively.

Figure  presents the correlations between the smoke volume concentration v and the smoke extinction coefficient σ (Fig. a) and between the smoke surface area concentration s and the smoke extinction coefficient (Fig. b) for North American forest fires. The forests in the western United States and Canada mainly consist of pine, fir, aspen, and cedar trees. The flaming-fire type probably prevailed in August 2017 and August–October 2020. The observations in Fig.  cover fresh and aged smoke plumes as well as mixtures of both. Strong variations in the size distribution are reflected in the comparably large scatter in the data. The upper part of the data fields shows cases dominated by fresh smoke (smaller particles) and the lower part, around the blue regression line for aged smoke (from Fig. ), is dominated by aged smoke (larger particles). Nevertheless, a clear relationship between the computed volume and surface area concentrations and the measured smoke extinction coefficient is given.

We used the observations at Yellowknife (1–2 d old stratospheric smoke) and Reno (tropospheric smoke, observed a few hours to several days after injection) to compute the conversion parameters and mean relationships visualized by red solid lines in Fig. . The mean values of cv and cs, as given in the figures, were calculated with Eqs. () and (). Only the Yellowknife and Reno data in Fig.  were considered in this computation. All mean conversion factors are summarized in Table .

The Yellowknife data points (fresh smoke) are close the red lines. This may indicate that the respective conversion factors (given as numbers in Fig. ) describe predominately fresh and weakly aged North American smoke properties. The blue straight lines (for aged Australian smoke) seem to define the lower limit of the range of values in Fig. . Many observations taken at Table Mountain, east of Los Angeles (tropospheric smoke), and at Churchill (2–5 d old stratospheric smoke) are close to the blue lines for aged smoke.

In this section, we switch from short-term observations of record-breaking and major fire episodes to long-term observations (partly over decades) in key burning areas of global importance. We assume that these long-term observations cover the full range of smoke-property-influencing aspects (smoldering and flaming fires, very different fuel types, short- to long-range smoke transport, and related smoke aging effects). Figure  presents the correlations between the computed smoke values of the volume concentration v and surface area concentration s and the smoke-related fine-mode extinction coefficient σ at 532 nm for all four selected subtropical and tropical stations. A relatively strong variability is found for the relationship between the surface area concentration and extinction coefficient in Fig. b, and even significant differences between the different data sets (Southeast Asian vs. African and Amazonian observations) are visible. In contrast, a quite narrow distribution of all observations is given for the volume-to-extinction relationship in Fig. a.

The spread in the data is again widely a function of the size distribution and thus of the age of the smoke layers. As in Fig. , the upper part of the data fields is strongly influenced by smaller particles and thus fresh smoke, whereas the lower part is controlled by larger particles and thus aged smoke.

The green straight lines show the mean regression lines for the Mongu, Zambia, data set. The computation of the mean conversion factors is performed in the same way as described in the forgoing sections. We included again the mean regression lines for aged Australian smoke (blue lines) and also for comparably fresh North American smoke (red lines) in Fig. . It is obvious that the blue lines for aged smoke indicate the lower boundary of the data range in Fig. a and b well. On the other hand, the upper boundary of the data field seems to be less well defined. Obviously many of the observed plumes of tropical and subtropical fires, especially over Zambia and the Amazon region, are just a few hours old, and thus the smoke particles were very small. The smoke particles of the Amazon region, southern Africa, and Southeast Asia are frequently considerably smaller than North American smoke particles (represented by the red lines in Fig. ).

It is noteworthy to mention that analyzed the relationship between the column smoke volume concentrations vcol and the 550 nm fine-mode AOT τ550 for a large number of AERONET stations around the world with strong impact of wildfire smoke and found similar mean values for the ratio vcol/τ550 as given for the extinction-to-volume conversion factor cv in our figures and in the summarizing Table . The study of includes also Russian stations (Moscow, Tomsk, Yakutsk). We may thus conclude that our conversion parameter set well covers main aspects and characteristics of wildfire smoke layers around the world.

Lidar provides an independent approach to derive microphysical parameters of smoke and thus to determine the link between the retrieved microphysical and measured optical properties of smoke particles . This option provides the favorable opportunity to check the quality and robustness of our results obtained by analyzing the AERONET data. One of the main problems of sun photometer observations is that the entire vertical column is observed so that, e.g., boundary-layer aerosols can be a disturbing factor in the study of lofted tropospheric and stratospheric smoke plumes. These problems are absent in the case of profiling techniques such as lidar. In the case of active remote sensing methods, the optical and microphysical properties are exclusively determined for the smoke layers. However, the uncertainties in the lidar retrievals can be large, and thus the obtained data products can scatter over a wide range just as a function of these uncertainties.

In Fig. , lidar data sets of smoke observations from 53∘ S (Punta Arenas) to 86∘ N (North Pole range) are considered. Correlation between v and s values and σ for fresh and aged smoke plumes originating from fires in western Canada, eastern Siberia, southeastern Australia, eastern United States, the Amazon Basin, and central western Africa are shown. The AERONET-derived mean relationship between v, s, and n250 and σ for aged, fresh, and the long-term African observations as discussed in the foregoing sections are shown again as blue, red, and green lines.

A large scatter in the lidar-based smoke correlation values is visible in Fig.  with data points even below the blue lines and above the green lines. This large scatter is partly related to the specific retrieval methodology and data analysis strategy as well as to varying assumptions in the analysis of the different lidar data packages. The most robust results (less sensitive to input errors) are obtained in terms of surface area concentrations when using the inversion algorithm of . This method was applied to the lidar observations at Praia, Cabo Verde; Manaus, Brazil; and Lindenberg, Germany. The other observations taken at Leipzig, Punta Arenas, and the North Pole region were analyzed by applying the analysis scheme of .

In Fig. b, it can be seen that most of the smoke layers observed over Praia (smoke from central western Africa) contain aged smoke particles (the data points are close to the blue line), and only a minor part of the observations indicate fresh smoke plumes (these data points are close to the green line). Many smoke layers contained a mixture of fresh and aged smoke. All the lidar data, representing smoke after long-range transport (Lindenberg, Leipzig, North Pole, Punta Arenas), are close to the blue line for aged smoke or even below this line and thus in good agreement with the AERONET-based correlation studies. From the consistency found in the correlations shown, based on AERONET and lidar observations, we can conclude that the AERONET smoke conversion parameters presented here allow trustworthy retrieval of smoke microphysical properties from backscatter lidar observations.

Figure  shows the correlation between the CCN-relevant particle number concentration n50 and the extinction coefficient σ for two contrasting smoke data sets, i.e., for the observations of aged Australian smoke and, on the other hand, for the observations of fresh smoke (Yellowstone) and mixtures of fresh and aged smoke (Reno). According to the applied regression analysis, fresh smoke plumes contain much more CCN-relevant small particles (roughly a factor of 3 more) than aged plumes. For a given extinction coefficient of σ=100 Mm-1, n50 is 635 cm-3 (for aged Australian smoke over Punta Arenas), 1900 cm-3 (for North American smoke), and 3200 cm-3 (for Mongu, Zambia). The numbers for n50 and the extinction exponent x (see Eq. ) in Fig.  and Table  are obtained by considering the respective data sets shown in the figure or mentioned in the table in the linear regression analysis described in Sect. .

In the framework of a multiyear measurement campaign, we monitored the stratospheric perturbation caused by the record-breaking Australian bushfires with a polarization Raman lidar Polly over a full year, starting in January 2020 . A measurement example is shown in Fig. . The results obtained by applying the conversions scheme in Sect.  are presented in Figs. –. In the first step, we calculated the extinction coefficients from the 532 nm backscatter coefficients by using a smoke lidar ratio of L=95 sr as measured with the Raman lidar Polly . Then we applied the conversion factor cv in Table  for aged smoke to obtain the volume concentration v. By assuming a particle density of ρ=1.15 g cm-3 for the smoke particles, we obtain the mass concentration m shown in Fig. .

Such a high aerosol pollution level of 15 µg m-3 at heights from 20–26 km height has never been observed in the stratosphere before, not even after major volcanic eruptions . Stratospheric background levels are of the order of 0.01 µg m-3 . As shown in Fig. , the particle depolarization ratio was significantly enhanced as a result of fast lifting by pyroCb clouds over the Australian fire regions . The aging process was obviously not fully completed and the particles were probably glassy. This may explain the deviation from the perfect spherical shape of the particles and the enhanced depolarization ratios .

Figure  shows the derived surface area concentration s and the particle number concentration n50. Information on number concentrations and surface area at stratospheric heights is of interest, e.g., in PSC and ozone research. A record-breaking ozone depletion was observed in the stratosphere over Antarctica starting in September 2020 . PSC particles play a strong role in this context because they permit the activation of chlorine components (on the surfaces of the PSC particles) which subsequently destroy ozone molecules. Even if we assume a strong decay of the stratospheric smoke perturbation by a factor of 10 or 100 in the Southern Hemisphere (at mid- to high latitudes) from January 2020 to September 2020, and thus a reduction in the smoke number concentration from about 500 cm-3 in Fig.  (in the height range from 21 to 25.5 km height) to 50 or even 5 cm-3, such number concentrations are still high and are in the range of particle concentrations typically observed in PSCs (0.01–10 cm-3) . Smoke particles may be able to serve as nuclei in processes of heterogeneous nucleation of PSC particles and thus may influence PSC microphysical properties. On the other hand, smoke surface area concentrations of around 120-130 µm2 cm-3 in the stratospheric layer in Fig.  are extremely high, and even if the smoke concentration was reduced by a factor of 10 to 100 until September 2020, surface area concentrations of around 10 or around 1 µm2 cm-3 are still high and partly in the same range of typical surface area concentrations in PSC clouds so that at least a weak influence on ozone depletion by providing surface areas for chlorine activation cannot be excluded.

The surface area concentration is also an essential aerosol input parameter in the INP parameterization and thus an important quantity in the research field of aerosol–cloud interaction with focus on mixed-phase-cloud and cirrus formation in the troposphere. INP estimates are shown in Fig. . We use the aerosol type parameters for leonardite as given in Table  in the calculation of immersion freezing INP (nINP,I, Sect. 3.1.1). The calculations start with the computation of the water activation criterion Δaw (Eq. ). Ice nucleation is a strong function of the vertical velocity (lifting of moist air parcels), which leads to ice supersaturation and thus determines Δaw. In the case study here, we assume realistic upper-tropospheric cirrus formation conditions and ignore in this demonstration of INP number estimation that we observed the smoke layer in the dry stratosphere 10–15 km above the local tropopause. We assumed RHw=79.85 % and 82.35 % and a temperature T of -50∘C. The corresponding RHi values are around 125 % and 130 %. Homogeneous freezing proceeds in significant numbers at about RHi=150 % at -50∘C. Thus, for slow air lifting, smoke particles potentially acting as INPs have a good chance to sensitively influence cirrus formation. With these input values for RHw and T, we obtain Δaw=0.175 and 0.2. The value for the ice melting point aw,i (Eq. ) is 0.6235 at -50∘C. Afterwards, we calculated the ice nucleation rate Jhet,I (Eq. ) and the INP concentration nINP,I (Eq. ) by assuming a lifting period of 600 s during which ice supersaturation conditions according to Δaw of 0.175 and 0.2 are given. We also computed deposition nucleation INP solutions (nINP,D, Sect. 3.1.3) by assuming the same T, RHi, RHw, and Si input parameters together with an overall lifting period of 600 s.

Figure  shows the results of the nINP,I and nINP,D estimations. A strong dependence on relative humidity and ice supersaturation is visible. Obviously a threshold value of ice supersaturation Si has to be reached and exceeded before efficient immersion freezing in the case of leonardite starts. The estimated deposition nucleation INP concentration is much higher than the immersion-freezing INP values for the assumed atmospheric conditions. The obtained high INP numbers are directly correlated to the large amount of smoke particles. The obtained INP number concentrations are not too uncommon. For example, INP number concentrations reached about 10–100 L-1 in a Saharan dust plume . Neglecting any radiative heating effects of the smoke layer and microphysical processes such as sedimentation and competition for water vapor, these results clearly indicate that organic smoke particles can impact ice formation processes in the upper troposphere during favorable moisture conditions and gravity wave activity with updraft phases lasting longer than several minutes.

In Fig. , also values for n250 (large particle fraction) are shown. It is usually assumed that particles with diameters >500 nm can be regarded as the overall reservoir for INPs . Number concentrations of 10–100 cm-3 or 10 000–100 000 L-1 indicate that this reservoir of large smoke particles cannot be depleted when nINP is in the range of 0.1 to 100 L-1, not even during extended cirrus formation processes lasting several hours.

The competitive process to heterogeneous ice nucleation is homogeneous freezing. If ice supersaturation Si reaches sufficient levels, corresponding to Δaw of 0.29–0.31, nINP,hom (Eq. ) would be of the order of 600–700 L-1 for v≈10-8 cm3 L-1 (mean value of the 20–26 km layer).

As mentioned, the uncertainty in the INP retrieval is large and is widely related to the current status of our knowledge about smoke INP type characteristics. The lidar input parameters s and v could be obtained with low relative errors of 25 %–35 %. The research on the role of wildfire smoke particles in cirrus and PSC formation is one of the key topics in atmospheric research with focus on aerosol–cloud interaction .

Strong fires occurred in the western United States and western Canada during the late summer of 2020. The smoke even reached Europe . Figure  shows an overflight of CALIPSO from North Dakota down to Texas. Two smoke layer complexes were detected between 5 and 10 km height: one over North and South Dakota and another one over Texas. According to the backward trajectory analysis, the plumes over North and South Dakota originated from fires in western Canada and were observed after 1 d of travel from the main fire area to North and South Dakota. The plumes over Texas originated from heavy Californian fires and were observed after 3–5 d of travel time from the Californian smoke sources. Cirrus formed in the neighborhood of the smoke layers.

Figure  presents the height profiles of smoke extinction coefficient, mass concentration, surface area concentration, and estimated INP concentration for the smoke layers detected over eastern North and South Dakota. We used a lidar ratio of 70 sr to convert the measured smoke backscatter coefficients into extinction values and applied the conversion parameter set for fresh smoke as recommended in Table . A potential influence of multiple scattering was ignored. For dense aerosol layers, multiple scattering can introduce substantial unquantified errors into the CALIPSO lidar retrievals of particle backscatter and extinction coefficients . However, multiple scattering effects may be of the order of about 5 %–10 % (underestimation of the true extinction coefficient by 5 %–10 %) in cases with smoke layer optical thickness ≤0.5 at 532 nm . The particle depolarization ratio was >0.1 and thus indicated the presence of nonspherical smoke particles.

According to Table  (fifth column), the uncertainties in the lidar products are higher now compared to measurements with ground-based Raman lidar at Punta Arenas. Relative uncertainties of 40 %–45 % in the extinction coefficient are mainly caused by the lidar ratio assumption. The uncertainties in the mass and surface area concentrations are around 50 %.

In the computation of the immersion-freezing INP concentrations in Fig. b, we highlight the impact of the selected organic aerosol type (leonardite, LEO, vs. free-tropospheric aerosol, FTA, Table ). We assumed a water activity criterion of Δaw=0.2 or RHi=130 % at T=-40∘C and again set the period during which ice nucleation was possible at these thermodynamic conditions to Δt=600 s. As can be seen, the assumed organic substance can have a very sensitive impact on the estimated INP values. The third organic substance in Table  (Pahokee peat) leads to similar INP values as obtained for leonardite. In cirrus research, it is thus essential to know the origin of the smoke and a good knowledge of the burning material to be able to properly characterize the aerosol type involved in the cloud formation studies.