Figure 1 demonstrates the spatial coverage that was observed during the first two deployments of ACTIVATE. The ACTIVATE study region is characterized as predominately a marine environment impacted by anthropogenic continental outflow (Corral et al., 2021; Painemal et al., 2021). In most marine conditions the coarse-mode aerosol concentrations are composed primarily of sea salt, which accounts for a small percentage of the N _a in the troposphere (Murphy et al., 2019). This is especially true when the marine background is influenced by anthropogenic continental outflow where total N _a can be on the order of 1,000 cm⁻³.

A list of instruments and corresponding measurements utilized from each of the ACTIVATE aircraft is provided in Table 2. The RSP aerosol product is based on an optimal estimate using the research scanning polarimeter–microphysical aerosol properties from polarimetery (RSP-MAPP) algorithm (Stamnes et al., 2018). Fine- and coarse-mode aerosol optical and microphysical properties are directly retrieved using seven channels that measure the total and polarized radiance across the visible–shortwave spectrum (wavelength = 410–2,260 nm) with over 100 viewing angles between ±55°. The RSP has a field of view of 14 mrad, which results in a ∼126 m footprint for an aircraft at 9 km altitude. This RSP retrieval uses a coupled atmosphere–ocean radiative transfer model to improve the accuracy of the retrieved aerosol properties.

The RSP-MAPP retrieval algorithm (v1.48) inverts RSP data under the assumption that the aerosols are bimodal, split into a fine-mode and coarse-mode aerosol, with each mode defined by a lognormal size distribution. This version of RSP-MAPP assumes that the aerosol size distribution has one fine-mode and one coarse-mode comprising non-absorbing sea salt particles. Such a bimodal aerosol model works well over the ocean because the RSP visible to shortwave-infrared channels are not sensitive to particles D ≲ 100 nm. The fine-mode aerosol properties including aerosol absorption are fully retrieved, namely, fine-mode AOD, size distribution parameters of effective radius and effective variance, and complex refractive index. The coarse-mode AOD, effective radius, and effective variance are also retrieved under the assumption that the coarse-mode consists of non-absorbing sea salt particles with a real refractive index close to water. The coarse-mode sea salt aerosol is assumed to be located from the ocean surface to 1 km, while the fine-mode aerosol is assumed to be mixed homogeneously from the ocean surface to the aerosol top height, which is also retrieved. From the aerosol optical and microphysical properties, RSP-MAPP implicitly retrieves the column-averaged fine- and coarse-mode σ _ext (σ _ext,f and σ _ext,c , respectively). The RSP-MAPP algorithm also provides an estimate of fine- and coarse-mode column-averaged N _a (N _a,f and N _a,c , respectively). In cloud-free conditions, RSP and HSRL-2 column AODs have been shown to agree to within 0.02 at 532 nm (Stamnes et al., 2018). The column-averaged aerosol particle number concentration derived from the RSP data (N _RSP) is defined as the following: N RSP = N ̄ a = A O D σ ̄ ext × A T H , (1) where we explicitly use a bar to represent the column-averaged polarimeter-retrieved aerosol cross section and number concentration. The AOD and σ _ext are referenced at 532 nm. Both AOD and N _RSP are, in part, governed by a retrieval of the aerosol top height (ATH, Wu et al., 2016). RSP-MAPP retrieves the ATH under the assumption that the fine-mode size and composition are uniform throughout the column, and as a result the fine-mode σ _ext is implicitly retrieved as a uniform value.

The HSRL-2 products include ambient vertically resolved lidar backscattering and extinction coefficients and ambient linear depolarization ratio (LDR) at wavelengths of 355, 532, and 1,064 nm (Fernald, 1984; Hair et al., 2008; Burton et al., 2018). The HSRL-2 field of view is 1 mrad, which corresponds to a ∼9 m footprint for an aircraft at 9 km altitude. Similar to the RSP, the HSRL-2 is not very sensitive to particles that fall in or below the Aitken size range (Burton et al., 2016). The HSRL-2 can also provide AOD by using the difference in the molecular channel signals at the top and bottom of the layer. Finally, the HSRL-2 retrieves the MLH (Scarino et al., 2014). To limit the scope of this analysis to spherical particles, LDR is used to filter out non-spherical from the data set (Burton et al., 2013). A LDR threshold of > 13% was used to filter out non-spherical particles from the analysis. This LDR threshold was chosen because the ACTIVATE study region is characterized as predominately a marine environment impacted by anthropogenic continental outflow (Corral et al., 2021; Painemal et al., 2021).

The measured in situ N _a values are used for the validation of the N _a product presented in this work. These data are taken from the laser aerosol spectrometer (LAS, Model 3,340, TSI, Inc.), which measures concentrations of particles with dry D ranging in sizes from 94 to 7,500 nm at a 1 Hz temporal resolution. The N _a measurements provided by the LAS are provided at standard temperature and pressures (273.15 K and 1,013 mb). While the LAS has a measurement range up to 7,500 nm, the maximum cutoff D of the sample inlet prevents the measurement of particles with ambient D greater than 5,000 nm (McNaughton et al., 2007; Chen et al., 2011). To take into account potential hygroscopic effects, we only include particles with dry optical D up to 3,488 nm in this analysis. The total N _a measured by the LAS is referred to from this point forward as N _LAS. The lower dry D cutoff of 94 nm is similar to the lower cutoff of the remotely-sensed N _a values but the N _LAS unavoidably misses some of the coarse-mode N _a due to the aforementioned inlet limitations.

The LAS has a low counting efficiency at three low size bins: 94–106 nm, 106–119 nm, and 119–133 nm, which we compensate for by multiplying the number concentration measured in those size ranges by correction factors of 1.90, 1.45, and 1.20, respectively. Losses for the LAS are calculated at nominal cabin temperature (20 °C) and pressure for low-altitude flight segments (900 mb). These correction factors are calculated using the product of losses by impaction, gravitational settling, and diffusion (Baron and Willeke, 2011). All tubing is conductive silicone and flows are laminar from the inlet manifold to both the LAS optical block. In addition to N _LAS, the aerosol particle size distribution effective radius (r _e ) of the fine-mode is derived from the corrected LAS and defined as effective radius of the particles that have dry optical diameters between 94 and 1,130 nm (r _e,94–1130). The r _e,94–1130 is used primarily to assess the homogeneity of the fine-mode aerosol particles that is assumed to be true for the RSP-MAPP–derived fine-mode σ _ext.

Ambient liquid water content (LWC) and N _d are used to classify in situ data as cloud-free, ambiguous, or cloud. Ambient LWC and N _d are both derived from ambient particle size distribution measured by using a cloud droplet probe (CDP, Droplet Measurement Technologies, Sinclair et al., 2019). The CDP can measure particles in the ambient D size range of 2,000–50,000 nm, and the N _d -CDP derived by the CDP is noted by N _CDP. An important limitation with deriving LWC from the CDP is an integration of the particle size distribution assuming unit density and constrained to the real refractive index of water. If the particles are anything other than spherical, with unit density and with real refractive index of 1.33, this LWC number has no meaning. Previous studies of aerosol–cloud interactions in marine environments have used a LWC threshold of < 0.02 g m⁻³ to classify data as cloud-free (Wang et al., 2014; Dadashazar et al., 2017; MacDonald et al., 2018). While this LWC threshold generally works well, the LWC of stratiform clouds has been shown to be as low as 0.0012 g m⁻³ (Yin et al., 2014). To ensure the avoidance of cloud edges, measurements where LWC was between 0.001 and 0.02 g m⁻³ and where N _d was between 5 and 50 cm⁻³ are classified as ambiguous. Only measurements where LWC and N _d were less than 0.001 g m⁻³ and 5 cm⁻³, respectively, are classified as cloud-free.

To further illustrate the three cloud classifications (cloud-free, ambiguous, and cloud) used in this study, Figure 2 provides a heat map (with marginal histograms) of all available 1 Hz LWC and N _CDP measurements taken during ACTIVATE 2020. In addition to the LWC and N _d thresholds, a sampling inlet flag is used to verify the Falcon aircraft’s sampling inlet was sampling air via the isokinetic inlet or via the counterflow virtual impactor (BMI Inc.; Shingler et al., 2012). The former is used to sample aerosol particles, while the latter is used to sample cloud droplets. Finally, ambient relative humidity (RH) is derived from measurements of the water vapor mixing ratio, which is measured by using a diode laser hygrometer (DLH, Diskin et al., 2002), and of temperature, which is measured by using the turbulent air motion measurement system (TAMMS, Thornhill et al., 2003). Ambient RH is used for an indication of the impacts of water vapor on r _e,94–1130.

In this section, we describe the mathematical formulation used to derive N _a from standard HSRL-2 and RSP products. The formulation to derive N _a described in this study has its foundation in the spherical particle Mie theory (Bohren and Huffman, 1983). Using the Mie theory and the environmental setup established in Section 2.1, we describe how column-averaged σ _ext,f (from RSP-MAPP) and vertically resolved α _ext (from HSRL-2) can be used to calculate vertically resolved N _a . We limit this analysis to the 532 nm wavelength for simplicity. While the RSP-derived σ _ext is a column average and is separated into fine- and coarse-modes, we assume the fine- and coarse-mode aerosols are externally mixed as two distinct aerosol types. This assumption allows us to calculate a mixed σ _ext using number concentration weighted averaging as follows: σ ext ≡ σ ext z = N a , f z × σ ext , f z + N a , c z × σ ext , c z N a , f z + N a , c z , (2) where we show explicitly the vertically resolved dependence on altitude z. Aerosol particle extinction cross section is related to N _a at every altitude layer by α _ext using the following: N a ≡ N a z = N a , f z + N a , c z = α ext z σ ext z ≡ α ext σ ext . (3) However, we choose cases based on the HSRL-2 and in situ measurements where the coarse-mode α _ext has a minimal impact, and accordingly simplify the equation to remove the coarse-mode terms. By setting the N _a,c and σ _ext,c terms to zero we obtain the following relationship for the aerosol number concentration from Eqs (2), (3), resulting in the method proposed in this study: N a ≡ N a z = N a , f z ≊ α ext z σ ̄ ext , f ≡ α ext σ ext , f , (4) where Equation (4) is applied to every altitude bin of the vertically resolved α _ext measured by the lidar (HSRL-2), while σ _ext,f is set equal to the column-averaged value retrieved by the polarimeter (RSP). The σ _ext,f is dependent on only the fine-mode aerosol size and composition. That the fine-mode aerosol cross section is kept constant is an assumption that the fine-mode aerosol properties do not significantly differ from the column-averaged value in such a way that it significantly biases the retrieval of N _a . Another limitation related to this assumption is that both extinction cross section and extinction coefficient are expected to increase with increasing RH. Using an average cross section could cause N _HSRL+RSP to biased high/low with an increase/decrease of ambient size.

This section describes how remote sensing and in situ data are processed to apply the N _a derivation outlined in Section 2.3. First, we limit the application of the method to observations of spherical aerosol particles using the LDR threshold of ≤ 13 % to filter out non-spherical data points from the smoothed α _ext data. Next, the α _ext and LDR data are smoothed into temporal-altitude grids of 0.0167 Hz and 150 m. The HSRL-2–derived AOD are also smoothed to a temporal resolution of 0.0167 Hz. Once the HSRL-2–derived α _ext and AOD data are smoothed, they are then collocated with the RSP by comparing the timestamps and selecting the nearest HSRL-2 data point (in time) to each of the RSP data points. A total of 7,727 RSP data points are collocated with HSRL-2–derived AOD and vertically resolved profiles of α _ext. Once the remote sensing data are placed in the native RSP temporal resolution, any scenes where the HSRL-2- and RSP-derived AOD deviate from each other are discarded. Points are discarded when deviation between the two AOD measurements exceeds whichever is greater 0.05 or 50% of the HSRL-2–derived AOD. As an additional constraint the fine-mode AOD derived from the RSP must be within 0.10 of the HSRL-2 AOD. The HSRL-2- and RSP-derived AOD can deviate from each other when there are cirrus clouds above the King Air, when there is at least one aerosol layer above the King Air, or when there are one or more detached troposphere aerosol layers. As a result of this filtering step, there are 774 collocated data points removed from the total set of 7,727. This empirical method of cloud and multiple aerosol layer influence does not guarantee the removal of all such contamination. In the future, the N _a derivation can be upgraded to be applied to conditions where aerosols are present in one or more detached troposphere layer(s) and in the presence of significant amounts of non-spherical aerosol particles.

After the remote sensing data are aligned and filtered, the aerosol particle number concentration of particles with dry optical diameters between 94 and 3,488 nm (N _LAS) data are filtered for clouds and adjusted to ambient temperature and pressure for direct comparison with the remote sensing observations. From the cloud filtered ambient N _LAS data, all available in situ vertical profiles (e.g., spirals, in-line descents, and in-line ascents) are organized for collocation with the remote sensing data. For this collocation stage the remote sensing profiles are collocated with the in situ profiles. The nearest remote sensing profile within 6 min and 15 km to the start or end of the in situ profile is selected for comparison. After collocation, N _LAS from each in situ profile is averaged to the same altitude grid as the HSRL-2 data (i.e., altitude bins that are 150 m in depth and extend from 0 to 9 km).

With collocation performed, the HSRL-2 + RSP-derived N _a (i.e., N _HSRL+RSP) can be equivalently compared to the N _LAS at each altitude grid point of each collocated vertical profile. In order to validate the column-averaged N _a that is derived from the RSP (i.e., N _RSP), the column-averaged N _LAS is calculated by taking an arithmetic mean of the entire N _LAS profile. With this final step, both N _HSRL+RSP and N _RSP can be equivalently quantitatively validated using vertically resolved N _LAS or column-averaged N _LAS, respectively. This study makes use of correlation coefficient (r), range-normalized root-mean-square deviation (NRMSD), range-normalized mean absolute deviation (NMAD), and relative bias, which have been previously used for quantitative validation of aerosol microphysical properties (Sawamura et al., 2017; Stamnes et al., 2018). Each of these statistical metrics has the following formulations: r = ∑ j = 1 n p [ ( X ( j ) − X ̄ ) × ( Y ( j ) − Y ̄ ) ] ∑ j = 1 n p [ X ( j ) − X ̄ ] 2 × ∑ j = 1 n p [ Y ( j ) − Y ̄ ] 2 , (5) N R M S D = 100 % m a x ( X ) − m i n ( X ) × ∑ j = 1 n p [ Y ( j ) − X ( j ) ] 2 n p , (6) N M A D = 100 % m a x ( X ) − m i n ( X ) × ∑ j = 1 n p | Y ( j ) − X ( j ) | n p , (7) relative  bias = Y ( j ) − X ( j ) Y ( j ) + X ( j ) × 2 × 100 % , (8) where X and Y are the set of in situ–derived N _a and remote sensing–derived N _a , respectively; n _p is the total number of points for each set; and X ̄ and Y ̄ are the mean of sets X and Y, respectively. This study also makes use of the p-value corresponding to each r.

In this section, we examine the two optimal aerosol profiles from the first deployment of ACTIVATE 2020 (Figures 3, 4). For these two profiles, each corresponding research flight took place in a generally cloud-free conditions (both low level and cirrus), that allow for the use of the novel N _HSRL+RSP product to create altitude vs. longitude color maps of N _a to provide some spatial context to each profile (Figure 3A, Figure 4A). The N _HSRL+RSP is gridded into 0.01° longitude bins (maintaining the 150 m altitude bins), but the in situ sampling flight track is displayed in the native 1 Hz resolution for qualitative, observational comparison of N _LAS and the N _HSRL+RSP. From this qualitative comparison, it is evident that the N _LAS and N _HSRL+RSP reasonably agree for these two flights that include the optimal profiles. In addition to the qualitative comparison between N _LAS and N _HSRL+RSP, these vertically resolved profiles illustrate the significant differences in the two profiles.

The first optimal profile’s research flight occurred from 13:52:27 to 17:08:12 on 26 August 2020 (Figure 3). This first optimal flight appears to have had two aerosol layers, one below 1 km and one between 1 and 2 km (e.g., smoke aerosol), as well as N _LAS and N _HSRL+RSP ranges that reached as high as 2,508 and 9,103 cm⁻³, respectively. The second optimal flight occurred from 16:45:10 to 20:01:40 on 28 August 2020 (Figure 4) and had lower maximum N _LAS and N _HSRL+RSP (1,031 and 4,209 cm⁻³, respectively), relative to the first optimal flight. The second optimal profile’s research flight had possibly more than one aerosol layer between 1 and 4 km, in addition to a homogeneous aerosol layer up to 1 km. Both of these profiles were observed to have detached aerosol layers above the PBL (e.g., smoke aerosol). Smoke aerosol was found to be present in this region on 26 August (Mardi et al., 2021) and on 28 August (Sorooshian et al., 2021).

Another contrast between the two optimal flight study regions was the MLH, which had the ranges of 0:00–0:88 km and 0:00–0:67 km for the first and second optimal flights, respectively. Both flights had similar RSP-ATH ranges that were 1:14–4:83 km and 1:83–4:85 km for the first and second optimal flights, respectively. In order to better analyze the closure between N _LAS and N _HSRL+RSP, we examine the closure statistics that result from the optimal profiles (Figure 3B, Figure 4B) where the aircraft horizontal-temporal separation is constrained (see Section 2.4).

The horizontal spatial and temporal aircraft separation of the first and second optimal profiles is 1.94 km–3.79 min and 11.99 km–5.97 min, respectively. The MLH of the first and second optimal profiles are at 0.59 and 0.35 km, respectively. The ATH of the first and second optimal profiles are at 4.15 and 4.00 km, respectively. The median relative bias, NMAD, and NRMSD observed in the first case study were generally worse (median relative bias = 64%, NMAD = 29%, and NRMSD = 33%), relative to the second case study (median relative bias = 42%, NMAD = 21%, and NRMSD = 28%). The r between N _HSRL+RSP and N _LAS for the first and second optimal flights are 0.92 and 0.81, respectively, and both profiles are among those that have the most statistically significant correlations in the set of collocated profiles (i.e., r > 0.80 and p-value ≤ 1 0 − 9 ). In addition to these statistics Figure 5 also provides a visual illustration of the vertically resolved N _LAS-N _HSRL+RSP and column-averaged N _LAS-N _HSRL+RSP closure.

To provide insight into the reasons for differences in the N _LAS-N _HSRL+RSP closure, we examine the differences in the vertical profiles of RH, r _e,94–1130, α _ext, and LDR that correspond to the optimal profile that occurred on 26 August 2020 (Figures 3C–F) and the optimal profile that occurred on 28 August 2020 (Figures 4C–F). The RH sampled in the first optimal profile overall decreases with increasing altitude up the ATH at ∼ 4 km, while the RH sampled in the second optimal profile remains relatively constant until the ATH, also at ∼ 4 km. In both optimal profiles, the RH decreases sharply right above the MLH. Then, in the first optimal profile, both the α _ext and RH increase with altitude above the MLH to 1.5 km. In the second optimal profile, α _ext and RH and α _ext and RH are relatively constant except for a sharp increase about 1.5 km. We found that the RH is negatively correlated with r _e,94–1130 between 1 and 2 km in the first optimal profile. This behavior is in contrast to the second optimal profile, where the r _e,94–1130 increases around the spike in RH at 2 km altitude. The increase in α _ext might otherwise seem to indicate multiple aerosol layers sampled in both optimal profiles, but the profiles of RH and r _e,94–1130 suggest that the changes are a result of increases in RH rather than a separate unmixed layer, except in the second optimal profile around 1.5 km. At this location it is observed that LDR is elevated in the second optimal profile, and indicates the presence of non-spherical coarse-mode dust particles in the second optimal profile associated with the sharp increase in α _ext at 1.5 km. The dust is likely coarse-mode since there is little change in r _e,94–1130. Despite the presence of coarse-mode dust, the retrieval of the vertically resolved N _HSRL+RSP, which is driven σ _ext in addition to α _ext, does not seem to be generally impacted except at 1.5 km where the coarse-mode dust loading peaks.

In addition to examining the profiles to identify multiple aerosol layers, the α _ext profile, in combination with r _e,94–1130 and RH profiles, allow us to examine the assumption of using a single fine-mode σ _ext to derive vertically resolved N _HSRL+RSP. The narrow r _e,94–1130 range observed in the second profile suggests that there is no significant change in the fine-mode aerosol composition and size distribution. Because r _e,94–1130 can be dependent on N _LAS, and RH can indicate the mixing state of the atmosphere, the positive correlation between both N _LAS and RH with r _e,94–1130 near the surface (≤200 km altitude) seen in each profile may indicate that changes in r _e,94–1130 for near the surface are partly related to atmospheric mixing rather than composition change.

These findings from the analysis of the first optimal profile suggest that method is robust in that the correlation for N _HSRL+RSP is high despite a ∼60% bias at elevated N _a and despite the separate smoke aerosol observed in the first profile. The analysis of the LDR profile suggests that non-spherical particles are not impacting the retrieval of N _HSRL+RSP significantly. In the next section, we combine data from these optimal profiles with the remaining cloud-free collocated profiles of N _HSRL+RSP and N _LAS to further support these findings and strengthen the validation of the N _HSRL+RSP product.

Following the initial validation with the optimal case studies, we use all collocated vertically resolved N _LAS data to perform a more statistically weighted validation of N _HSRL+RSP product using Figure 6A. Furthermore, we show that this error is generally similar to the error observed in the validation of N _RSP with column-averaged N _LAS (Figure 6B). Finally we examine Figures 6C,D and Table 3 to demonstrate the improvements gained in validation of both vertically resolved and column-averaged N _a by removing profiles where cloud presence is detected in the column.

As noted above, there are 32 cloud-free profiles, two ambiguous profiles, and eight cloud profiles, which contain 322, 13, and 47, respectively, vertically resolved points for the comparison validation of N _HSRL+RSP and N _LAS. The r, median relative bias, NMAD, and NRMSD that result from the comparison of the points contained in the cloud-free profiles are 0.76, 33%, 16%, and 24%, respectively. Additionally, this cloud-free data set resulted in a P ₉₀ of 106% in absolute relative bias. Data from both the ambiguous profiles and the cloud profiles resulted in worse, i.e., increases in NMAD (28% and 26%, respectively) and NRMSD (34% and 33%, respectively), relative to the NMAD and NMAD that resulted from the data cloud-free profiles. Relative to the cloud-free profile dataset, the r (0.71) and P ₉₀ in absolute relative bias (107%) did not change much for the ambiguous profile data set but r decreases to 0.50 and P ₉₀ in absolute relative bias increases to 145% for the cloud profile dataset.

Due to the limited number of column-averaged N _a points (n _p = 2) that are classified as ambiguous, the validation statistics for this set is not meaningful and will be omitted here. The validation statistics resulting from the comparison of the column-averaged N _a points classified as cloud-free and cloud are similar to that resulting from the vertically resolved N _a closure, with the exception of relative bias. The NMAD improves, i.e., decreases, from 42% to 21% and the NRMSD decreases from 47% to 28%. In contrast to the vertically resolved N _a , the median relative bias resulting from the column-averaged N _a comparison of the eight collocated points is −0.76, which improves to −0.53 for the 32 profiles from the column-averaged cloud-free dataset. In addition, the P ₉₀ in absolute relative bias of the column-averaged cloud data set is larger (131%), relative to the column-averaged cloud-free data set (121%). These findings suggest that the significantly improved performance of one set over the other, which is likely due to the fact that the retrieval of column-averaged N _a is more sensitive to deviations from ideal cloud-free conditions than the vertically resolved N _a . It is also possible that the retrieval of column-averaged N _a is more sensitive to separated aerosol layers that are possibly present. However, due to the relatively limited number of collocated points and profiles, wider application is needed to definitively conclude the main reason for the difference.