The September monthly mean meteorological situation is shown in Fig. 1 from Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA2) reanalysis (Buchard et al., 2017; Randles et al., 2017) along with locations of relevant sites. A thorough meteorological analysis for all ORACLES deployments is provided in Ryoo et al. (2021). For the period under consideration here, they found that the African Easterly Jet-South (AEJ-S), fast-moving zonal easterlies centered on 650 hPa around 5–15∘ S, was active and corresponded closely to the long-term climatology. Figure 2 shows 650 hPa winds from MERRA2 reanalysis at the beginning, at the end, and on 2 intermediate days during which HSRL-2 measurements were made. ER-2 flight tracks during the September 2016 IOP are shown in Fig. 3. Note that flights were primarily confined to within roughly 1000 km of the African coast with only the 22 September flight venturing further. Flights such as executed during the IOP are unable to follow air parcels in a Lagrangian fashion to examine the evolution of smoke plumes. Here, we provide an alternate framework by which to study evolving aerosol properties in an average sense. In order to establish average characteristics of the BB smoke plume as it travels over the ocean, we have chosen five grid boxes of 2∘ latitude and longitude on a side at various distances from the source and aggregated observations. The choice of grid boxes was based on the availability of data from the flights (Fig. 3) and the general direction of transport of the smoke as evidenced by the wind fields in Fig. 2. The grid boxes so chosen are marked on Figs. 2 and 3, and the rationale for the choice is explained below.

Figure 4 shows 48 h backward trajectory frequency analyses at 3.5 km, roughly the central altitude of the plume using NOAA Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) trajectory calculations (https://www.ready.noaa.gov/HYSPLIT_traj.php, last access: 18 September 2021) which were carried out using archived Global Data Assimilation System (GDAS) 0.5∘ meteorology (Stein et al., 2015). The frequency distribution is a 48 h history of the paths taken by air parcels arriving at the grid boxes marked A and C at 3500 m altitude. The time period of the frequency analyses covers the entire period during which HSRL-2 measurements were made, 12–24 September 2016. The selected grid box pairs indicate that Box A receives aerosol that has earlier crossed Box B, and Box C is downwind of Box D; boxes B and D receive aerosol directly from BB sources on land. The grid box pairs A/B and C/D can therefore provide information on the evolution of the microphysics and vertical distribution of BB aerosol plumes after leaving the continent. This strategy is similar to that used in comparisons of models with observations for this campaign by Shinozuka et al. (2020), who also showed that observations made on the sampled days were representative of monthly means. In addition to the four boxes strongly influenced by smoke, a southern box, E, has been chosen to provide a control contrast to the other areas in that it is influenced primarily by maritime air as seen from Figs. 1 and 2.

The days during the campaign that were included in the averaging procedure are shown in Table 1. Also included is the typical time of the day when the measurements were made, which is a function of the flight pattern of the ER-2. The number of lidar return profiles averaged for each grid box and statistics related to the backward trajectories are also listed. These grid boxes contained aircraft tracks on multiple days during which trajectory analysis showed near-uniform wind direction between 2.5 and 4.5 km altitude throughout the IOP. With the exception of the grid box centered at 22∘ S, 9∘ E, all indicate flow from the source region of BB aerosol. Table 1 also lists the mean and standard deviation of time duration in hours spent over water of air parcels arriving at 3500 m altitude at the grid box during the averaging period. There is no entry for Box E since arriving air had a maritime source and did not originate from land. It must be stressed that the duration is not calculated from the source region on land which is distributed over a large area of central Africa (e.g., Fig. 9 of Redemann et al., 2021) and cannot be uniquely identified with specific observations made over the ocean. The plume has already been airborne over land for several hours (see Fig. 4) and aerosol would have undergone transformations that occur at short timescales (Cappa et al., 2020). The duration was calculated by running HYSPLIT backward trajectories of air parcels arriving every six hours starting at 06:00 UTC on the days of the first flight and ending at 18:00 UTC on the days of the last flight of the averaging period, and is shown in some detail in Fig. 5 which essentially reflects the profile of the prevailing wind speeds. The inference is that BB smoke at 3500 m altitude arrives at A on average about 30 h after passing B and arrives at C 35 h after passing D. The change in selected aerosol properties as measured by the HSRL-2 during this travel in the marine environment provides information on the evolution of the plume during this time period.

Vertical profiles averaged over the times of overflight in 2∘ × 2∘ latitude/longitude boxes shown in Fig. 3 on the days given in Table 1 are for the following properties:

Aerosol extinction at 532 nm, αa, determined by aerosol number concentration, microphysical properties, and relative humidity;

The northern plume is a column of aerosol of relatively constant extinction from just above 2.5 to 5 km while the southern plume has a profile of extinction that increases nearly linearly with height from a minimum near the cloud top to a maximum at 5 km (Fig. 6). The vertical structure of the aerosol profiles measured by HSRL-2 was compared to water vapor profiles represented by the MERRA2 model. Pistone et al. (2021) explored the relationship between aerosols, CO, and water vapor as measured by ORACLES airborne in situ measurements and represented by models including MERRA2. They found the MERRA2 water vapor profiles, like the measured water vapor profiles, exhibited a linear relationship with CO and biomass burning plume strength; they also found that smoky, humid air produced by daytime convection over the continent advected over the ocean and into the ORACLES study region. MERRA2 water vapor profiles produced at 3 h increments and 72 pressure levels were interpolated to the times and locations of the HSRL-2 profiles. Water vapor mixing ratio generally decreased significantly just above the PBL then increased for altitudes around 2 to 3 km before decreasing again. This behavior is generally consistent with the relationship between water vapor and aerosol scattering reported by Pistone et al. (2021).

Figure 10 shows the median, 25th, and 75th percentile relative humidity (RH) profiles computed by interpolating the MERRA2 0.5∘ 3 h humidity profiles to the locations and times of the HSRL-2 measurements. The profiles typically show a more pronounced increase in RH with altitude that more closely follows the HSRL-2 measurements of aerosol extinction profiles, although the MERRA2 profiles typically begin decreasing above 4 km whereas the airborne in situ RH measurements and HSRL-2 aerosol extinction profiles begin decreasing above 5 km. Interestingly, during three of the dates (12, 16, 22 September), considerable portions of the smoke layers correspond to MERRA2 relative humidity above 60 %–70 %. This increase in RH with altitude could help explain at least some of the increase in aerosol extinction with height observed in the HSRL-2 profiles of the C/D Box pair. Aerosol humidification often amplified the increase in aerosol extinction by factors of 1.5 or more (Doherty et al., 2022).

The Ångström exponent (Fig. 7) and depolarization (Fig. 8) indicate the presence of fine spherical particles at the top of the plume and increasing sizes towards the bottom. The lidar ratio (Fig. 9) above 3 km for the two pairs is between 70 and 80 sr, suggesting strong absorption (Müller et al., 2019), but is considerably less and highly variable in Box E and in the lower layers of the aerosol plume in Box D where the smoke plume most likely has components of continental aerosol such as dust and pollution typical of the nearby Namibian coast (Klopper et al., 2020). The most striking feature of the results is the very small profile-to-profile variability of the intensive lidar parameters in the upper 2 km of the plume over the course of several days as evident from the range of values in the 25–75 percentile shaded grey in Figs. 7–9. This suggests strongly that the particles maintain their size, shape, and absorbing properties over the first few days of transport over the ocean. This result is of some importance for climate studies in which the radiative properties of BB aerosol are input to the calculation of radiative forcing. Complex chain aggregates as found near the source of fires (Pósfai et al., 2003; China et al., 2013) are typically not represented in climate models. However, if the aerosol is already spherical and maintains its size over the time period of radiative interactions being studied, then core–shell models of varying degrees of complexity could perhaps suffice (Zhang et al., 2020). The lower portion of the plume containing larger BB aerosol particles is subject to mixing with marine and continental particles from regions not affected by biomass burning and is highly variable in nature. This would be more difficult to model, but Fig. 6 shows that the aerosol extinction coefficient decreases rapidly at lower levels so errors in representation may be acceptable.

The lidar measurements are inverted to obtain information regarding particle size. The inversion is performed on 1 min averages of six independent 10 s backscatter profiles and 1 min average extinction profiles. Details of the inversion process are in Müller et al. (2019) and references therein. The particle size distribution is represented using a series of eight triangular basis functions that can represent both monomodal and bimodal size distributions (Müller et al., 2019). Points to note are that the procedure makes the following assumptions: the particles are spherical and homogeneous having wavelength-independent complex index of refraction. The low (< 5 %) values of depolarization through most of the plume, shown in Fig. 8, suggest that the spherical assumption is justified. There is most likely structure and inhomogeneity in the core of the particles but current particle optical models are unable to incorporate these complexities. Results from this inversion procedure have been compared to coincident airborne in situ particle measurements. Müller et al. (2014) present results from a campaign off the northeast coast of the US showing that the inversion results agree with in situ measurements of effective radius and also number, surface area, and volume concentration within error bars. Sawamura et al. (2017) report on campaigns in the wintertime San Joaquin Valley of California and summertime near Houston, TX. They found high correlation and low bias in surface and volume concentration in situ measurements relative to HSRL with the best agreement for submicron fine-mode aerosol which is most relevant to the current study. Müller et al. (2019) report retrievals and their uncertainty for 1 d in the ORACLES campaign, 22 September 2016. Considering only optical data with strong signal–to–noise ratio, they estimate retrieval errors are 25 % for number concentration. The relative uncertainty in effective radius for parts of the flight track where particle size was nearly constant was below 20 %.

In order to help separate particles that have BB source from coarser particles of continental or marine origin, we specify a submicron fraction (SMF) as the contribution to the extinction at 532 nm of particles in the radius range 0.05–0.50 µm (Anderson et al., 2005). Figure 11 shows the profiles of SMF for the five grid boxes and, not surprisingly, the bulk of the smoke plume especially between 3 and 5 km contains aerosol almost entirely in the submicron range. Below 3 km, at locations both near and further way from the coast, there is a marked increase in the fraction of larger particles. The increase in depolarization (Fig. 8) at these lower levels and a decrease in the lidar ratio (Fig. 9) suggest mixing with the aforementioned non-BB aerosol particles. However, the sharp decrease in extinction below 3 km (Fig. 6) indicates that their contribution to direct radiative effects would be minimal. Finally, Fig. 12 shows the vertical profile of the effective radius of the SMF aerosol population. The effective radius is 0.16 µm with little variation between 3 and 5 km. Of greater significance is that it remains very similar between the pairs of grid boxes along the transport trajectory of the smoke. The retrieved effective radius is similar to the results presented by Müller et al. (2014) for a mixture of urban aerosol and smoke. Their comparison with in situ measurements showed a slight overestimate but within a standard deviation. The retrieved and in situ results also show that the particle size is uniform with altitude even when the number concentration drops by a factor of 3. Another set of prior comparisons of HSRL-2 and in situ measurements is provided in Sawamura et al. (2017). Here again the effective radius of the submicron fraction of particles, 0.15 µm, is uniform with altitude and comparable though biased slightly low compared to in situ observations.

The effective radii of the SMF aerosol which typically vary between 0.15 to 0.20 µm, are generally consistent with the sizes reported previously for smoke aerosol in the ORACLES region. Haywood et al. (2021) provide a composite of the aerosol sizes for biomass burning aerosol off the South African coast. These size distributions, which were derived from airborne in situ measurements (Haywood et al., 2003; Peers et al., 2019; Wu et al., 2020), typically correspond to SMF aerosol effective radii between 0.14–0.17 µm and were for the dry aerosol. Shinozuka et al. (2020) reported on airborne aerosol sizes measured during ORACLES by an Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) deployed on the NASA P-3 aircraft. The UHSAS measured particles with dry diameters between 60 and 1000 nm. SMF aerosol effective radii derived from the UHSAS measurements of volume mean diameter were generally around 0.09–0.10 µm for the dry aerosol. Shinozuka et al. (2020) noted that the UHSAS measurements were somewhat undersized and so were adjusted to account for this effect; this adjustment improved scattering closure with coincident nephelometer measurements. As discussed in Sect. 4.1, the RH on some days was above 60 %–70 % so that effective radii under ambient conditions could be expected to be somewhat higher than for the dry aerosol. Using measurements from an airborne Differential Aerosol Sizing and Hygroscopicity Spectrometer Probe (DASH-SP), Shingler et al. (2016) quantified the size-resolved growth factors for several aerosol types; they found that at RH ∼ 70 %–80 %, particle diameters for biomass burning aerosols were about 15 %–20 % larger than for the dry aerosol. Xu et al. (2021) derived aerosol properties during the 2016 ORACLES mission using an inversion algorithm that combined HSRL-2 and Research Scanning Polarimeter (RSP) remote sensing measurements. These retrieved aerosol properties were then compared with those derived from the UHSAS measurements described by Shinozuka et al. (2020). For measurements acquired on 12 September 2016, the SMF aerosol effective radius derived from the remote sensing measurements was generally between 0.12–0.15 µm and was only slightly (0.012 µm) higher than the effective radii for the (dry) SMF aerosol derived from the UHSAS measurements. This suggests that some of this difference is associated with differences in RH between the remote sensing retrievals and the in situ measurements.