Evaluation of aerosol number concentrations from CALIPSO with ATom airborne in-situ measurements

. The present study aims to evaluate the available aerosol number concentration (ANC) retrieval algorithms for spaceborne lidar CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) aboard CALIPSO (Cloud-Aerosol Lidar and Infrared Pathﬁnder Satellite Observations) satellite with the airborne in-situ measurements from ATom (Atmospheric Tomography Mission) campaign. We used HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory model) to match both the measurements in space and identiﬁed 53 cases that were suitable for comparison. Since the ATom data include dry aerosol 5 extinction coefﬁcient, we used kappa parameterization to adjust the ambient measurements from CALIOP to dry conditions. As both the datasets have a different vertical resolution, we re-grid them to uniform height bins of 240 m from the surface to a height of 5 km . On comparing the dry extinction coefﬁcients, we found a reasonable agreement between the CALIOP and ATom measurements with Spearman’s correlation coefﬁcient of 0.715. Disagreement was found mostly for retrievals above 3 km altitude. Thus, to compare the ANC which may vary orders of magnitude in space and time, we further limit the datasets 10 and only select those height bins for which the CALIOP derived dry extinction coefﬁcient is within ± 50 % of the ATom measurements. This additional ﬁlter further increases the probability of comparing the same air parcel. The altitude bins which qualify the extinction coefﬁcient constraint are used to estimate ANC with dry radius >50 nm ( n 50 , dry ) and >250 nm ( n 250 , dry ). The POLIPHON (Polarization Lidar Photometer Networking) and OMCAM (Optical Modelling of CALIPSO Aerosol Microphysics) algorithms were used to estimate the n 50 , dry and n 250 , we found the estimated n 50 , dry an order less than the in-situ measurements for marine dominated cases. We propose a modiﬁcation to the 20 OMCAM algorithm by using an AERONET-based marine model. With the updated OMCAM algorithm, the n 50 , dry agree with the ATom measurements. Such concurrence between the satellite-derived ANC and the independent ATom in-situ measurements the use of CALIOP in studying the aerosol-cloud interactions.

The information on aerosol-type specific extinction coefficient, aerosol type, and relative humidity are used to compute the ANC.

POLIPHON
The Polarization Lidar Photometer Networking (POLIPHON, Mamouri andAnsmann (2015, 2016)) method combines lidar-130 derived type-specific aerosol optical properties with concurrent long-term AERONET measurements of aerosol optical depth (AOD) and retrieved column size distributions (Dubovik et al., 2000(Dubovik et al., , 2006 to estimate the ANC. A regression analysis of the AERONET-derived column extinction coefficients and number concentrations (integral of the aerosol size distribution) yields the conversion equation to derive ANC from lidar-derived extinction coefficients. The regression analysis was based on AERONET observations at sites with pure marine or pure mineral dust conditions as well as observations in environments 135 dominated by urban haze or wildfire smoke. The complex analysis resulted in aerosol type-specific conversion equations of the form n j,dry = C · α x , where n j,dry is the aerosol number concentration with dry radius >j nm, α is the extinction coefficient, C is the conversion factor, and x is the extinction exponent. In this study, we use the regression parameters for marine and continental aerosols 140 given in Mamouri and Ansmann (2016). The one for desert dust is taken from Ansmann et al. (2019) and represent a global average. For smoke aerosols, we use the averaged value for aged smoke given in Ansmann et al. (2021) as most of the ATom measurements were performed over oceans away from smoke sources. The values of the regression constants along with their sources are listed in Table 2. A typical RH of 80 % and 60 % were assumed while calculating the conversion factors for marine and continental (including smoke) aerosol types. Note that for dust aerosols, POLIPHON provides the ANC for dry radius dV (r) d ln r = α α n · 2 i=1 ν i √ 2π ln σ i exp ( −(ln r − ln µ i ) 2 2 ln σ i 2 ).

170
Choudhury and Tesche (2022) show a large discrepancy in their comparison of theoretically possible ANC for marine aerosols as estimated by POLIPHON and OMCAM. This can be attributed to the difference in the temporal extent and geographical location of the measurements, and different instruments employed in measuring of the marine size distributions used in the two algorithms. The regression constants for marine aerosols used in POLIPHON are estimated from 7.5 years of AERONET measurements from 2007 to 2015 at Barbados (Mamouri and Ansmann, 2016). However, the marine model

Hygroscopicity correction
To compare the CALIOP-derived ambient extinction coefficients with the results of the dry measurements conducted during ATom, we need to correct the former for the effect of hygroscopic growth. Furthermore, the extinction-coefficient-to-ANC conversion discussed in Section 2.3.2 holds only for dry conditions. The POLIPHON method assumes a constant RH of 80 190 % for marine and 60 % for continental aerosols and may result in errors for higher RH conditions. MOPSMAP includes an in-built functionality to address hygroscopic growth based on the kappa parametrization (Petters and Kreidenweis, 2007) :::::::::::::::::::::::::: (Petters and Kreidenweis, 2007) in the RH range from 0 % to 99 %. We use the normalized aerosol size distributions and refractive indices of different aerosol types from CALIPSO aerosol model to calculate the extinction coefficient for different values of relative humidity. Figure 1 shows the variation of the hygroscopic growth factor, i.e. the ratio between the ambient 195 and dry extinction coefficient, with relative humidity for continental (polluted continental, clean continental, elevated smoke) and marine CALIPSO aerosol types with kappa values of 0.3 and 0.7, respectively. The kappa values are global averages and are suggested by Andreae and Rosenfeld (2008) for use in satellite retrievals. Nevertheless, studies have found that the kappa values may vary with the aerosol composition and age (Pringle et al., 2010;Cheung et al., 2020). Thus considering a fixed kappa value for a particular aerosol type defined in CALIPSO may incur additional uncertainties in the ANC retrieval.

200
Moreover, the RH values included in the CALIPSO level 2 data product are estimated from global model simulations which may incorporate additional uncertainties. Having said that, we still use the parametrization with globally averaged kappa values, which were found to provide reasonable results in the case study presented in Choudhury and Tesche (2022) and the example cases presented later in Section 3.1. Mineral dust is considered to be hydrophobic in our analysis. For every CALIOP data bin, the extinction coefficient is corrected based on the aerosol type and relative humidity value by dividing it with the hygroscopic 205 growth factor that corresponds to the ambient relative humidity. Note that this methodology is different from the one used in Choudhury and Tesche (2022), where the hygroscopicity correction is applied to the particle size distribution before the computation of the ANC. In the present study, the application of the hygroscopicity correction to the extinction coefficient is necessary so that the dry extinction coefficient from the CALIOP measurements can be compared directly with the ATom data set. The hygroscopicity corrected extinction coefficient is then used to compute the CALIOP-based ANC using the OMCAM 210 and POLIPHON algorithms. Note that in the case of POLIPHON, we only apply the hygroscopicity correction when RH is greater than 80 % and 60 % for marine and continental aerosols, respectively, and modify the corresponding ambient extinction coefficient to RH values of 80 % and 60 %. This is because the extinction to ANC conversion equations (Eq. 1) was formulated assuming such RH values which are representative of typical marine and continental environments.

215
The ATom data consists of continuous airborne in-situ measurements from altitudes of 200 m to 12 km. The measurement tracks for the first ATom campaign are shown in Figure 2. For a comparison between the ANC derived from CALIOP observations and airborne in-situ measurements conducted during ATom, we need to find those cases for which the two data sets are closest in time and space. In our first attempt at finding intercepts between the tracks from CALIPSO and ATom, we did not consider the aircraft flight level and matched only the 2d latitude and longitude coordinates. As a result, we found that most of the intercepts were found at altitudes above 5 km within the free troposphere. At such altitudes, CALIOP rarely detects aerosol structures except for elevated layers from long-range transport. Hence, we limit the ATom data in the present study to altitudes below 5 km before finding intercepts with the CALIPSO ground track. This slicing results in a collection of discontinuous measurements during either ascent or descent, or both (v-shaped). Such segments have a latitudinal extent of about 1 to 2 degrees which facilitates the incorporation of the HYSPLIT air-parcel trajectory model (Draxler and Rolph, 2010) for finding 225 the intercepts.
Major parts of the ATom measurements were conducted over the Pacific and Atlantic oceans. Compared to over land, the aerosol composition over the oceans is rather homogenous and we can expect a good correlation between ground-based and satellite measurement (Kovacs, 2006;Liu et al., 2008;Tesche et al., 2013). Therefore, we include the CALIPSO tracks that are within 500 km from an ATom measurement in our comparison. Also, for smaller distances, the airborne measurements 230 should be appropriately connected to the nearby CALIPSO overpass. We use HYSPLIT air-parcel trajectories to first determine the section of the CALIPSO overpass that is most appropriate for comparison with the ATom measurements and to second estimate the correct temporal difference between the measurements. This approach is also used in (Tesche et al., 2013(Tesche et al., , 2014 for validating CALIPSO measurements against ground-based lidar and in-situ measurements. For running HYSPLIT, we use Global Data Assimilation System (GDAS) meteorological files with a spatial and temporal resolution of 1 degree and 3 hours,

235
respectively. The overall track selection methodology is illustrated in Figure 3 for an ATom1 flight segment on 8 May 2016.
Since the flight measurements are three dimensional, each of the HYSPLIT initialization coordinates has a unique combination of latitude, longitude, and altitude. To reduce the complexity of the analysis, we limit the initial trajectory starting points by selecting one out of every 20 points in the segment of the aircraft track. Figure 3a shows the forward and backward trajectories starting and ending at different altitudes of the ATom track segment, respectively, and the segment of CALIPSO measurements 240 that is most suitable for the comparison. The vertical displacement of the air parcels along the trajectories is shown in Figure   3b. For most of the found intercepts, the vertical displacement of the air parcels along the trajectories is negligible and, hence, not considered in our comparison study. As seen in Figure 3a, the trajectories intercept the CALIPSO track at different times.
In such situations, we compute the net time difference by averaging the time differences at different height levels. For the example shown in Figure 3a, the air parcels take 9 h (between 1 and 3 km) to 13 h (below 1 km) to reach the CALIPSO track, 245 which leads us to apply an average time delay of 11 h. Including the pre-existing time delay of approx. 9 h between the two observations, the average effective time difference for this case is 2 hours. The average distance between the two tracks as calculated using the Haversine formula is found to be 457 km. Following this approach, we identified a total of 53 intercepts for which the measurements of CALIOP and ATom are considered as appropriate for comparison. A detailed overview of these cases is given in Table A1 along with the aerosol-type specific extinction coefficient contribution and the average distance and 250 time delay between the observations. The average distance between the tracks is less than 500 km for all the intercepts. The time delay between the measurements varies from 0 to 20 hours with 11 cases exceeding 10 hours. Marine aerosols are found to be the dominant aerosol type in 44 cases (83 %), followed by polluted continental (4 cases), elevated smoke (3 cases), and dust (2 cases). Such conditions are not unexpected as most of the observations are over oceans. Note that there were many further intercepts where factors like signal attenuation due to the presence of clouds, low signal-to-noise ratio due to low aerosol concentrations or an absence of aerosols lead to CALIOP data that were not suitable for comparison with the ATom measurements. Most of these intercepts were found close to the poles and the equator.
The atmospheric parameters included in the ATom data are at standard temperature (273.15 k) and pressure (1013.25 hPa) and need to be converted to ambient conditions. The temporal resolution of ATom data used in this work is 10 seconds and the corresponding altitudinal resolution varies between 0 and 110 m depending on the speed of the aircraft. However, the vertical 260 resolution of CALIOP data is 60 m in the troposphere. Also, there can be more than one measurement for a certain altitude range in an ATom segment as it can include both ascending and descending measurements. To compare the two data sets, we thus re-grid them to a uniform vertical resolution of 240 m (4 CALIOP height bins) between 0 and 5 km altitude by averaging both data sets within these height bins. This approach also compensates for the potential vertical displacement of air parcels along the trajectory between the locations of the measurements of CALIOP and the ATom aircraft. However, a limitation to 265 this methodology is the velocity shear at different height levels. It is worthwhile to note that the main motive of this study is to validate the ANC as retrieved from CALIOP data rather than the extinction coefficient. Even after considering all the complex screening constraints aimed at identifying the best match between CALIOP and ATom measurements by compensating the temporal and spatial differences between them, disagreement may still arise because of different (i) measuring instruments with dissimilar sensitivities used in ATom and CALIPSO, (ii) measurement techniques, and (iii) spatial and temporal resolutions 270 of the datasets (Tesche et al., 2014). The extinction coefficient from ATom is obtained by applying the Mie theory to the dry aerosol size distributions for radius <2.4 µm. This may be inaccurate for coarse mode non-spherical aerosol particles. The CALIPSO retrievals on the other hand have to go through a complex feature detection algorithm to identify aerosol layers and may fail to detect optically thin layers with inadequate signal to noise ratio. While the airborne in-situ data from ATom are point measurements, the along-swath width of the CALIPSO level 2 data bin is 5 km. Moreover, the HYSPLIT trajectories 275 used to find the intercepts use model outputs and may have associated errors. Even so, it is necessary to perform a closure study utilizing these concurrent measurements for validating the recently developed lidar-based ANC retrieval algorithms. In order to somewhat compensate for such unquantifiable effects in the comparison of ANC, we only use those data bins for which the difference between the dry extinction coefficient from CALIOP is within ±50 % of that in the ATom data. This additional filter further increases the probability that we are comparing the ANC within the same air parcel.

Example cases
We start the presentation of results in Figure 4 with four comparison examples that present the profiles of extinction coefficient and ANC as derived from ATom and CALIOP measurements. The first three cases represent different prevailing aerosol types while the fourth shows a combination of all four types. The majority of cases includes airborne measurements during both 285 ascent and descent and, hence, there can be two ATom measurements at one level. All CALIPSO overpasses except for the marine dominated case shown in the examples occurred during nighttime. for altitudes higher than 300 m, we found a reasonable agreement between the humidity corrected extinction coefficient from CALIOP and the ATom measurements ( Figure 4a). This illustrates the ability of the kappa parametrization to account for aerosol hygroscopicity for highly humid marine environments. The n 50,dry profiles derived from CALIOP data using the POLIPHON technique is at par with that measured during ATom. However, the OMCAM estimates are relatively noisy, perhaps because of highly variable RH, and are lower than the ATom measurements for most altitudes. This is also evident in other 295 marine-dominated cases e.g., near-surface measurements in Figure 4h. However, in the case of n 250,dry , both the OMCAM and POLIPHON estimates for marine-dominated CALIPSO retrievals are in much better agreement with the ATom data.
The second example of the intercept on 17 August 2016 is dominated by a mixture of marine and smoke aerosols at altitudes below 1.5 km and only smoke at higher altitudes. Figure 4b shows that the extinction coefficients from CALIOP and ATom are at par below 2 km altitude. At higher altitudes, where elevated smoke is the dominant aerosol type, CALIOP gives much 300 higher extinction coefficients than found from the ATom measurements. A plausible reason behind the larger values is perhaps the temporal (11 h) and spatial (205 km) difference between the observations. The properties of an elevated smoke layer may change drastically with the travelled distance and age of the air parcel. Though the CALIOP-derived n 50,dry and n 250,dry profiles using POLIPHON and OMCAM accurately capture the altitudinal variation revealed in the ATom measurements, they are far more variable with altitude and differ from the in-situ measurements at altitudes between 2 km and 4 km.

305
In the third example of 1 October 2017, the aerosol types detected by the CALIPSO retrieval are polluted continental and mineral dust, with the former dominating. The CALIOP extinction coefficient and n 50,dry are in good agreement with the ATom measurements. However, the n 250,dry (Figure 4g) as estimated from CALIOP using both the OMCAM and POLIPHON algorithms is 2 to 5 times larger than in the ATom measurements. On analyzing the geographical locations of the measurements, we found that both of them are over land regions (Southern California) and encompass a mixture of urban, rural, and forest 310 continental environments. The aerosol properties can be highly variable over different land regions which perhaps is the reason behind the disagreement of the n 250,dry values.
The fourth example for the intercept on 29 April 2018 is comprised of a mixture of all four aerosol types with marine aerosols dominating from the surface to 1 km, followed by continental and smoke aerosols until 3 km, and further accompanied by mineral dust over 3 km (Figure 4d). The ATom-derived extinction coefficient (for ascending and descending flight-track segments) 315 varies by as much as 1.5 orders of magnitude at heights above 2 km. This highlights the impact of spatial heterogeneity that may occur over short distances or time periods. The CALIOP-derived humidity-corrected extinction coefficient resembles the in-situ measurements during ascent (with larger values than during descent) between 1 and 4 km altitude. Above and below that layer, the CALIOP extinction coefficient exceeds that derived from the in-situ measurements. Regarding n 50,dry , the POLIPHON estimate overlaps with the ATom measurements up to an altitude of 4 km, above which it fails to replicate the 320 increase in aerosol concentration. The OMCAM-derived profile in Figure 4h shows a similar agreement but underestimates n 50,dry at altitudes below 1 km where marine aerosols are dominant. The n 250,dry as estimated from POLIPHON and OMCAM are both in reasonable agreement with the ATom measurements.
Overall, the example cases in Figure 4 present a remarkable resemblance of the aerosol properties derived from CALIOP observations with the ATom measurements at most height levels. The examples that feature dominance of marine aerosols in 325 the lowermost 2 km illustrate the importance of applying a hygroscopicity correction and indicate that this can be realized to a reasonable degree with the kappa parametrization even when using static kappa values. In the next section, we present a statistical comparison of the extinction coefficient and ANC for all the identified intercepts. Moreover, both data sets are in better agreement at altitudes below 2 km irrespective of the dominant aerosol type. Such a result is expected as elevated aerosols above the boundary layer can be easily transported to larger distances compared to those located near the surface which counteracts the comparison approach followed in this study.

General findings
As seen from the general comparison and case studies, the aerosol extinction coefficient inferred from ATom measurement is 340 in very good agreement with the CALIPSO retrieval with the exception of a few cases where they can be significantly different.
Scenarios that may lead to large differences in the data sets are already discussed in Section 2.4 and includes the differences in the instrument sensitivities, measurement techniques, spatial and temporal resolutions, and assumptions underlying the intercept identification. In such situations, comparing the corresponding ANC may lead to misleading conclusions. Thus, while comparing the ANC, we only use those altitude bins for which the CALIOP-derived dry extinction coefficient is within ±50 % 345 of that estimated from ATom measurement. Note that the present study is not focused on the evaluation of CALIPSO products,  The comparison of n 50,dry as measured during ATom and estimated from CALIOP measurements using OMCAM and POLIPHON for the altitude bins that pass the extinction coefficient filter is shown in Figure 6. It is found that the POLIPHON estimates of n 50,dry are in better agreement with the ATom measurements with a correlation coefficient of 0.829, RMSE value of 234 cm −3 , and bias value of -96.627 cm −3 . In terms of absolute magnitude, OMCAM estimated n 50,dry are up to an order less than that of ATom, especially for aerosol concentrations below 100 cm −3 . A closer look at the aerosol-type 355 specific comparison shows that the lower values seen in OMCAM is primarily from the marine-dominated cases for which POLIPHON estimates of n 50,dry are generally in better agreement with the in-situ measurements.  (Figure 1). Also, the conversion factors for n 50,dry and n 250,dry are recalculated (Table 3 : 4) using the updated marine model following the methodology discussed in Section 2.3.2. It is interesting to note that the conversion factor estimated from the new marine model for n 250,dry is only increased by 5 %, compared to 520 % for n 50,dry . For comparing the CALIOP and Atom measurements for all the identified intersections, we only use those 240 m 385 data bins that pass the extinction-coefficient constraint (CALIOP-RH-corrected extinction coefficient within ±50 % of ATom measurement). Figure  ANC from the updated OMCAM algorithm for marine aerosol type is now at par with that from POLIPHON.

Discussion
In general, when the RH corrected extinction coefficient from CALIOP is used, both the OMCAM and POLIPHON algorithms yield values of n 50,dry and n 250,dry that are comparable to in-situ measurements for all aerosol types except for marinedominated cases. For marine-dominated retrievals, even though the n 250,dry estimated from OMCAM and POLIPHON algo-395 rithms were in good agreement with the in-situ measurements, OMCAM estimates of n 50,dry were up to an order smaller. This is perhaps the result of the limited in-situ sea salt size distribution measurements that form the marine aerosol model used in the OMCAM algorithm Choudhury and Tesche, 2022). Nevertheless, using the AERONET based marine model of (Sayer et al., 2012) in OMCAM results in an overall better agreement for both the n 50,dry and n 250,dry values with the independent airborne in-situ measurements during ATom. For retrievals dominated by polluted continental and smoke, we find a medium-high correlation between ATom measurements and CALIOP-inferred estimates of n 50,dry using both algorithms with OMCAM performing slightly better than 415 POLIPHON. For some height bins, the CALIOP estimates vary by more than a factor of 2 (especially for n 250,dry ) from the in-situ measurements. Such a variation may either occur because of the spatial and temporal heterogeneity of aerosols or due to change in the microphysical properties of the aerosols as a result of chemical or cloud processing. Also, similar to dust aerosols, the conversion factors for smoke and continental aerosols may change with age and geographical location (Ansmann et al., 2021).
satellite estimates of height resolved ANC (that are most relevant for cloud processes) and the coincident in-situ measurements for various aerosol environments has not been achieved yet. This study along with previous concurrent results (Haarig et al., 2019;Marinou et al., 2019;Georgoulias et al., 2020;Choudhury and Tesche, 2022) compliments the use of ground-based and 425 spaceborne lidar remote sensing techniques for retrieving height-resolved cloud-relevant aerosol microphysical properties.

Summary
We present a validation study of the spaceborne lidar derived aerosol number concentration using the OMCAM and POLIPHON algorithms with the airborne in-situ measurements conducted during the ATom campaigns over the Atlantic and Pacific oceans.
To identify the comparison cases, we located intercepts between the CALIPSO flight tracks and the ATom aircraft tracks with the help of HYSPLIT trajectories. Out of all intercepts, 53 were found to be suitable for comparison. On comparing the dry extinction coefficients, we found an overall good agreement between the CALIOP data and the in-situ measurements with a correlation coefficient of 0.715. Disagreement was found mostly for retrievals above 3 km altitude. Such differences are most likely due to the spatial heterogeneity of aerosol properties rather than a retrieval error. Therefore, to compare the ANC, we filtered the data sets to select only those retrievals for which the CALIOP extinction coefficient is within ±50 % of the one 435 obtained from the in-situ measurements. This constraint further increases the likelihood of comparing the same air parcel, which is crucial for parameters such as ANC that can easily vary by many orders of magnitude in space and time.
We found that the POLIPHON and OMCAM estimates of n 50,dry are in overall good agreement with the in-situ measurements with an overall correlation coefficient of 0.829 and 0.823, respectively. The agreement is seen for all the dominating aerosol type with the exception of marine aerosols, for which the POLIPHON estimates give a better agreement than the OM-nucleating particle profiling with polarization lidar: updated POLIPHON conversion factors from global AERONET analysis, Atmos.