Retrieval of UVB aerosol extinction proﬁles from the ground-based Langley Mobile Ozone Lidar (LMOL) system

. Aerosols emitted from wildﬁres are becoming one of the main sources of poor air quality on the US mainland. Their extinction in UVB (the wavelength range from 280 to 315 nm) is difﬁcult to retrieve using simple lidar techniques because of the impact of ozone (O 3 ) absorption and the lack of information about the lidar ratios at those wavelengths. Improving the characterization of lidar ratios at the abovementioned wavelengths will enable aerosol monitoring with different instruments and will also permit the correction of the aerosol impact on O 3 lidar data. The 2018 Long Island Sound Tropospheric Ozone Study (LISTOS) campaign in the New York City region utilized a comprehensive set of instruments that enabled the characterization of the lidar ratio for UVB aerosol retrieval. The NASA Langley High Altitude Lidar Observatory (HALO) produced the 532 nm aerosol extinction product along with the lidar ratio for this wavelength using a high-spectral-resolution technique. The Langley Mobile Ozone Lidar (LMOL) is able to compute the extinction provided that it has the lidar ratio at 292 nm. The lidar ratio at 292 nm and the Ångström exponent (AE) between 292 and 532 nm for the aerosols were retrieved by comparing the two observations using an optimization technique. We evaluate the aerosol extinction error due to the selection of these parameters, usually done empirically for 292 nm lasers. This is the ﬁrst known 292 nm aerosol product intercomparison between HALO and Tropospheric Ozone Lidar Network (TOLNet) O 3 lidar. It also provides the characterization of the UVB optical properties of aerosols in the lower troposphere affected by transported wildﬁre emissions.

Abstract. Aerosols emitted from wildfires are becoming one of the main sources of poor air quality on the US mainland. Their extinction in UVB (the wavelength range from 280 to 315 nm) is difficult to retrieve using simple lidar techniques because of the impact of ozone (O 3 ) absorption and the lack of information about the lidar ratios at those wavelengths. Improving the characterization of lidar ratios at the abovementioned wavelengths will enable aerosol monitoring with different instruments and will also permit the correction of the aerosol impact on O 3 lidar data. The 2018 Long Island Sound Tropospheric Ozone Study (LISTOS) campaign in the New York City region utilized a comprehensive set of instruments that enabled the characterization of the lidar ratio for UVB aerosol retrieval. The NASA Langley High Altitude Lidar Observatory (HALO) produced the 532 nm aerosol extinction product along with the lidar ratio for this wavelength using a high-spectral-resolution technique. The Langley Mobile Ozone Lidar (LMOL) is able to compute the extinction provided that it has the lidar ratio at 292 nm. The lidar ratio at 292 nm and the Ångström exponent (AE) between 292 and 532 nm for the aerosols were retrieved by comparing the two observations using an optimization technique. We evaluate the aerosol extinction error due to the selection of these parameters, usually done empirically for 292 nm lasers. This is the first known 292 nm aerosol product intercomparison between HALO and Tropospheric Ozone Lidar Network (TOLNet) O 3 lidar. It also provides the characterization of the UVB optical properties of aerosols in the lower troposphere affected by transported wildfire emissions.

Introduction
Wildfires produce substantial amounts of gaseous pollutants, such as carbon monoxide (CO), nitrogen oxides (NO x ), volatile organic compounds (VOCs), and ozone (O 3 ) as well as biomass burning particulate matter, which significantly impact the climate and air quality (Andreae and Merlet, 2001;Phuleria et al., 2005;Reid et al., 2005;Zauscher et al., 2013). Pollutants directly emitted from wildfires can affect first responders and local residents. In addition, transported wildfire emissions can lead to harmful exposures for populations in regions far away from the source fires (Cottle et al., 2014;Dreessen et al., 2016). Increases in the frequency and severity of North American wildfires significantly affect air quality by increasing the amount of particulates and O 3 in the air (Schoennagel et al., 2017). Ground-based lidars have the ability to simultaneously detect O 3 and aerosol with a high temporal and vertical resolution in order to better understand air quality exceedances that can be exacerbated by transported wildfire emissions (Aggarwal et al., 2018;Strawbridge et al., 2018;Kuang et al., 2020). On the other hand, the determination of the aerosol properties in the UVB wavelength region is of great importance to understand the effect of aerosol on UV radiation, which is linked to human health and atmospheric chemistry (Bais et al., 1993;Carlund et al., 2017;Moozhipurath and Skiera, 2020). Lidar aerosol measurements at 355 nm are often reported, but UVB aerosol properties are rarely studied by lidar (Müller et al., 2007;Nicolae et al., 2013;Haarig et al., 2018). To bridge that gap in our understanding of the impact of transported wildfire emissions on air quality and the aerosol optical properties in the UVB band, this work describes a technique to retrieve the aerosol extinction at 292 nm by comparing the data from a UV lidar along with the data from a high-spectral-resolution lidar (HSRL).
Retrieval and validation of lidar aerosol profiles in the UVB wavelength range are challenging due to three factors.
First, strong O 3 absorption at UVB wavelengths can cause large uncertainty for the retrieval of UVB aerosol. One approach to address this is to use O 3 measurements to correct the O 3 absorption before the extinction/backscatter retrieval technique is applied (Browell, 1985;Young, 1995).
Second, the aerosol extinction-to-backscatter ratio, also known as the lidar ratio, noted S 1 , is not well known for different aerosol types at UVB wavelengths. In general, a relative S 1 is needed to retrieve an accurate UVB aerosol profile. For example, Kuang et al. (2020) demonstrated the retrieval of aerosol 299 nm backscatter from the O 3 lidar raw attenuated backscatter signal using an iteration algorithm and fixed S 1 (60 sr) in the presence of smoke. However, it will introduce uncertainty for the aerosol retrieval if we use one S 1 value for different aerosol types, as S 1 is dependent upon the aerosol type and can exhibit values between approximately 10 and 90 (Omar et al., 2009;Lopes et al., 2013, Müller et al., 2007Burton et al., 2014;Haarig et al., 2018). Thus, an accurate S 1 at the UVB wavelength range is needed to obtain a realistic UVB aerosol profile retrieval.
Finally, available aerosol profiles at the UVB wavelength range to validate the retrieved aerosol result are lacking. However, aerosol profiles provided by a more common 532/355 nm aerosol lidar could be used for validation if the Ångström exponent (AE) between the UVB wavelength and 532/355 nm is available. This work will focus on addressing these three factors and retrieving the aerosol extinction at 292 nm for the Langley Mobile Ozone Lidar (LMOL) system.
The Long Island Sound Tropospheric Ozone Study (LIS-TOS) campaign was a multiagency collaborative study for the areas of Long Island Sound and the surrounding coastlines in summer 2018 that provided the perfect conditions to perform that work. The LMOL and the airborne NASA Langley High Altitude Lidar Observatory (HALO) system were both operating during the LISTOS campaign. HALO provided the extinction and the S 1 value at 532 nm thanks to a high-resolution spectroscopy lidar (HSRL) technique. As Fig. S1 in the Supplement shows, the HALO overpassed LMOL-enabled coincident measurements which, in turn, allowed the characterization of the aerosol S 1 and AE (292 and 532 nm), as explained in Sect. 3. The information about the lidar ratio at 292 nm and AE (292 and 532 nm) not only improves our UV aerosol retrieval but also improves our understanding of the aerosol optical properties at those wavelengths. During the LISTOS campaign, the case study of August 2018 was selected as an example of the UVB aerosol retrieval due to the HALO-LMOL coincident aerosol data but also because of the air quality exceedance that was likely caused by the impact of long-range transport of wildfire emissions (Rogers et al., 2020). The evaluation of the aerosol optical properties allows one to better validate their age and, therefore, their wildfire origin when compared to back trajectories.
The instruments and data used in this work are described in the next section. We use the LMOL raw and O 3 data products, HALO aerosol backscatter/extinction and S 1 data, the City College of New York (CCNY) 532 nm aerosol extinction data, and the CL51 backscatter data. The method to retrieve UVB aerosol extinction and the method used to select the optimized S 1 for UVB aerosol retrieval are presented in Sect. 3 (steps A to C in Fig. 1). The comparison between the retrieved LMOL aerosol extinction profile and the HALO aerosol extinction profile using the optimized parameter are presented in Sect. 4. The retrieved LMOL aerosol extinction comparison with the CL51 and CCNY aerosol lidar data is also presented in Sect. 4. The uncertainty for the aerosol extinction retrieval is analyzed in Sect. 5. Finally, the importance of this method is discussed in Sect. 6.
2 Instrument and data 2.1 The LMOL system LMOL is a mobile ground-based O 3 differential absorption lidar (DIAL) system that has a transmitter with a 1 kHz diode-pumped Q-switched Nd:YLF 527 nm laser to pump a custom-built Ce:LiCAF tunable UV laser to generate "on" and "off" DIAL wavelengths at 286 and 292 nm. A 40 cm diameter telescope was used to collect the backscatter signal for the far field, and a smaller-diameter wide-field offaxis parabolic mirror was used for the near-field return (De Young et al., 2017;Farris et al., 2019). Both far-field and near-field receiver channels employ analog and photon detection modes using a high-speed Licel data acquisition system to maximize the measurement dynamic range. The current configuration of LMOL can retrieve O 3 profiles in the 0.1 to 10 km range at night, with 5 to 10 min temporal averaging . During day- time, the maximum altitude reached is typically close to 5 km due to solar background light limitations. LMOL is part of the Tropospheric Ozone Lidar Network (TOLNet), a network of O 3 lidars that help evaluate air quality models and complement current and planned satellite retrievals for satellite such as the Tropospheric Emissions: Monitoring of Pollution (TEMPO) mission (Zoogman et al., 2017). LMOL generates data products following the TOLNet protocol for the acquisition, processing, and archiving of the data, thereby assuring the quality and consistency of the data products (Leblanc et al., 2016a(Leblanc et al., , 2016b. For LMOL data products, the vertical resolution (110 to 990 m) of the O 3 profiles varies with altitude to preserve a retrieval uncertainty of within ±10 %, the uncertainty of which is calculated using Poisson statistics of the backscattered photons. LMOL has been used in several campaigns, such as the Ozone Water-Land Environmental Transition Study (OWLETS) I and II, LISTOS Sullivan et al., 2019;Dacic et al., 2020), the Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) joint venture, and the Southern California Ozone Observation Project (SCOOP) . In the context of LISTOS (Wu et al., 2021), and more specifically for the present study, LMOL was deployed at Sherwood Island Park, Westport, CT (41.1182 • N, 73.3368 • W; 2.5 m a.s.l.), and obtained measurements between 12 July and 29 August 2018. To obtain the aerosol products, we used the LMOL raw data at 292 nm and the LMOL O 3 data.

The ceilometer located nearby LMOL
A ceilometer (Vaisala CL51) was installed at the Westport site co-located with LMOL (41.1173 • N, 73.3369 • W; 3 m a.s.l.) during the LISTOS campaign. A ceilometer is a single-wavelength backscatter lidar system used to monitor cloud base height and aerosol structures . A semiconductor laser (InGaAs diode laser) with a 3.0 µJ pulse energy and a repetition rate of 6.5 kHz retrieves the atmospheric backscatter at 910 nm to infer the vertical distribution of clouds and aerosols up to 15 km (Lee et al., 2018;Jin et al., 2015). The measured backscatter signal was integrated over 5 s. It is an autonomous eye-safe system that makes 24/7 observations. Although the molecular signal returns are weak because of the low-energy laser and the near-infrared wavelength, the stronger returns from aerosols and clouds can be detected. The CL51 signal is impacted by dark-current noise and daytime solar background, but it is still sufficient to measure signals from boundary layer aerosols up to 3 km (Jin et al., 2015). As a result, the ceilometer can provide the boundary layer evolution and aerosol retrievals up to 3 km for qualitative comparison with the LMOL.

The HALO aerosol measurement
The NASA airborne High Altitude Lidar Observatory (HALO) is a combined high-spectral-resolution lidar (HSRL) and H 2 O-and CH 4 -differential absorption lidar (DIAL) (Nehrir et al., 2017;Wu et al., 2021). HALO employs 1 KHz Nd:YAG pumped optical parametric oscillators to generate the DIAL wavelength for the H 2 O and CH 4 observations. The residual energy from the conversion process is employed for the HSRL technique. HALO employs the HSRL technique at 532 nm, the backscatter technique at 1064nm, and measures depolarization at both 532 and 1064 nm. An I2 vapor cell is used in the receiver to separate the molecular scattering from the total scattering (Hair et al., 2008). This allows for discrimination of aerosol scattering from molecular scattering as well as the independent retrieval of the aerosol extinction and backscatter coeffi-cient (Burton et al., 2013(Burton et al., , 2015Hair et al., 2008). The lidar extinction-to-backscatter ratio is then available from the HALO-determined aerosol extinction and backscatter coefficients. HALO data are sampled at 0.5 s temporal and 1.25 m vertical resolution. This vertical resolution for the aerosol measurement is increased to 15 m in postprocessing to increase the signal-to-noise (SNR) ratio of the intensive and extensive aerosol retrievals. Aerosol backscatter and depolarization products are averaged over 10 s horizontally, and aerosol extinction products are averaged over 60 s horizontally and 150 m vertically. The polarization and HSRL gain ratios are calculated as described in Hair et al. (2008). Operational retrievals also provide the mixing ratio of nonspherical-to-spherical backscatter (Sugimoto and Lee, 2006), the aerosol type (Burton et al., 2012), and the aerosol mixed layer height (Scarino et al., 2014). In this study, the HALO aerosol extinction data are selected when the instrument's flight measurements overpass the LMOL site.

The CCNY aerosol lidar
The CCNY lidar transmits at 1064, 532, and 355 nm with a flash lamp-pumped Nd:YAG laser with a pulse repetition rate of 30 Hz. A telescope with a 50 cm diameter collects three-wavelength elastic scatter and two Raman-scattering returns (by nitrogen and water vapor excited by a 355 nm laser). The aerosol extinction and backscatter profiles in the troposphere were retrieved, and the AE was derived to distinguish fine-mode aerosol from coarse-mode aerosol. The CCNY lidar return signal detection starts from 0.5 km with a 1 min time average and a 3.75 m vertical data-bin resolution. The planetary boundary layer (PBL) height was estimated from the 1064 nm elastic return because the backscatter signal at this wavelength is more sensitive to aerosol structures than at shorter wavelengths (Wu et al., 2019(Wu et al., , 2018(Wu et al., , 2021. The CCNY lidar was located in New York City (NYC; 40.8198 • N, −73.9483 • W) for remote sensing of the aerosol layer aloft during the LISTOS campaign.

Methodology
It is important to determine the S 1 for the LMOL 292 nm aerosol retrieval. The O 3 -corrected LMOL attenuated backscatter profile does not contain the information needed to estimate S 1 . Fortunately, the HALO observations provide the 532 nm extinction and S 1 which could help us to learn some information about the aerosol optical properties for cases where the two instruments have coincident observations.
To retrieve the S 1 , an iterative method with three main steps was used, as shown in Fig. 1. The first step is the retrieval of the aerosol extinction at 292 nm from LMOL. For that, the LMOL raw data are corrected for the O 3 absorption. The Fernald method is then used with an empirical S 1 (which is modified in subsequent iterations to explore the parameter space). For the current study, the impact of the aerosols was low enough that an iterative correction to the O 3 density was not necessary to retrieve the aerosol extinction accurately; for dense aerosols layers, the method described in Browell et al. (1985) would have been used. The second step is the retrieval of the aerosol extinction at 292 nm from HALO. The conversion of the extinction from 532 to 292 nm is done using an assumed AE (between 292 and 532 nm) which is also modified in subsequent iterations to explore the (S 1 , AE) parameter space. The third step is the comparison of the aerosol extinction from both instruments at 292 nm. The integration of the difference provides the partial aerosol optical depth (AOD) difference, referred to later as the partial AOD index. Once the plausible (S 1 , AE) parameter space has been explored, there will be a minimum to the partial AOD index which points to the best (S 1 , AE) for the observed conditions. The LMOL aerosol extinction profile related to optimized S 1 and the difference between the LMOL and HALO 292 nm aerosol profile related to the optimized S 1, and AE were also recorded for further analysis.

Method to retrieve aerosol extinction coefficient
LMOL uses the 287 and 292 nm wavelengths for O 3 DIAL measurements. The 292 nm "off" wavelength was selected for the aerosol retrieval in this work because O 3 has a smaller absorption cross section at this wavelength. The attenuated lidar signal measured by the LMOL system can be represented as follows: is the lidar return signal power; λ is the laser wavelength; C λ is the lidar system constant; β λ,a (R) is the aerosol volume backscatter coefficient; β λ,m (R) is the molecular volume backscatter coefficient; α λ,a (R) is the aerosol optical extinction coefficient; α λ,m (R) is the molecular optical extinction coefficient (without the O 3 extinction); σ λ,O 3 is the O 3 absorption cross section; N O 3 (R) is the O 3 number density; and P λ,0 is the offset, which is contributed by the sky background signal, the amplifier and digitizer offset, and the detector dark current (Fernald, 1984;Young et al., 2009). We also have α λ,m (R) = σ m N m , where σ m is the atmospheric extinction cross section, and N m is the atmospheric molecular number density. The molecular extinction coefficient and backscatter coefficient are usually calculated from a balloon measurement close to the lidar site or from a model like GEOS-5 (Sasano and Nakane, 1984).
The aerosol extinction-to-backscatter ratio (also known as the lidar ratio) is S 1 = α λ,a /β λ,a , and the molecular extinction-to-backscatter ratio is S 2 = α λ,m /β λ,m = 8π/3 (Kovalev and Eichinger, 2004). The S 1 value is dependent on the particle size, shape, and refractive index, and it usually varies from ∼ 10 to 100 sr (Sasano and Nakane, 1984). We have assumed a constant S 1 with range for the aerosol extinction retrieval (Fernald, 1972(Fernald, , 1984. The received LMOL lidar signal at 292 nm could be corrected with the O 3 profile to get the elastic lidar attenuated backscatter signal attributed to aerosol and molecular terms as shown in Eq. (2). The O 3corrected range-corrected lidar signal with background subtraction is shown as follows: We can rearrange Eq.
(2) to get the aerosol attenuated backscatter signal X(R): where Using Eq.
(3) and the aerosol and molecular extinction-tobackscatter ratio, the aerosol extinction coefficient at ranges between the lidar and calibration range R c is shown in Eq. (4) (Fernald, 1984;Sasano et al., 1985). For convenience, the equations in the following do not include λ.
In order to calculate the aerosol extinction coefficient α a (R), we need to assume S 1 and the reference value of the aerosol extinction coefficient at a calibration range R c . The reference value α a (R c ) must be known or estimated. The calibration range and the reference value could be estimated using the secant method mentioned by Li et al. (2018). We need to pay attention to the fact that all data used in the aerosol retrieval process should have the same vertical resolution. The retrieval is applied to cloud-free profiles after applying cloud screening to the data. This was done using the convolution of the O 3 -corrected attenuated backscatter signal and a Haar wavelet function to identify cloud edges and then further screening the data using a threshold to separate cloud features (Burton et al., 2010;Compton et al., 2013;Scarino et al., 2014). The aerosol extinction was retrieved for both LMOL far-field photon-counting and far-field analog signal channels. The near-field aerosol retrieval will be described in a separate study. The aerosol extinction profiles for those two channels were merged to a single profile with an overlapping altitude zone from 1.5 to 2 km. The lowest altitude for the retrieved profile is about 0.5 km, and the highest altitude for the retrieved aerosol profile is constrained by the highest altitude of reliable O 3 data.

Selection of the UVB S 1 for retrieval
As mentioned in Sect. 1, we focus on case studies from August 2018, especially during the afternoon period on 28 August 2018. The average S 1 for HALO S 1 profiles at 532 nm was calculated for afternoon data from 28 August 2018. The HALO S 1 data mentioned hereafter are the vertically averaged S 1 derived from the HALO S 1 profile. The frequency distribution of the HALO S 1 profiles for the afternoon of 28 August 2018 is shown in Fig. 2a. The mean HALO S 1 for 532 nm is ∼ 55 sr with a 1 s standard deviation of ∼ 3 sr. As Fig. 2b shows, the mean HALO S 1 for all available August measurement is ∼ 55 with a 1 s standard deviation of ∼ 6 sr. The HALO 532 nm S 1 data were screened using following criteria when calculating the average for each S 1 profile: an S 1 value larger than 10 sr and less than 100 sr.
The following paragraph will introduce the method to identify the S 1 at 292 nm and the extinction AE between 292 and 532 nm by calculating the partial AOD difference between the retrieved LMOL 292 nm aerosol extinction profile and the HALO aerosol extinction profile. The AE represents the wavelength dependency of the AOD or extinction coefficient for aerosol. The AE (noted as α λ 1 ,λ 2 ) between two wavelengths, λ 1 and λ 2 , is expressed as shown in the following equation (Wagner and Silva, 2008): Figure 3. Flow chart of the process of calculating the 292 nm S 1 and the AE between 532 and 292 nm. i is the integer increment from 2 to 18 that was used to calculate S 1 in order to make S 1 vary from 10 to 90. j is the integer increment from 5 to 25 that was used to calculate the AE in order to make the AE vary from 0.5 to 2.5. i and j could also be the index of the calculated partial AOD.
where τ 1 and τ 2 are the AOD at wavelength λ 1 and λ 2 , respectively. The ideal S 1 at 292 nm and the AE between 292 and 532 nm were determined from the retrieved LMOL aerosol extinction profiles and the aerosol profiles provided by co-located HALO measurements using a partial AOD difference method. Figure 3 shows the flow chart for five steps of this partial AOD difference method. In Step 1, the LMOL aerosol extinction, denoted using α LMOL,S 1 (i) (R), was retrieved by incrementing S 1 (i) from 10 to 90 sr in steps of 5 sr. In Step 2, the LMOL aerosol extinction, α LMOL, S 1 (i) (R), was multiplied by R (7 m in this work) to get the LMOL partial AOD at altitude R, denoted using PAOD LMOL,S 1 (i) (R). In Step 3, HALO 532 nm aerosol extinction was converted to aerosol extinction at 292 nm with AE (j ) and varied from 0.5 to 2.5 in steps of 0.1. The 292 nm HALO aerosol extinction, α HALO, AE(j ) (R), was then multiplied by R to obtain the HALO partial AOD at altitude R, denoted using PAOD HALO, AE(j ) (R). In Step 4, the relative difference of partial AOD (denoted using PAOD i,j (R)) between PAOD LMOL,S 1 (i) (R) and PAOD HALO, AE(j) (R) was calculated using Eq. (6). In Step 5, the PAOD i,j (R)) values were integrated to get the partial AOD difference index, PAODI(i, j ), using Eq. (7). In Eq. (7), R b and R t are the respective bottom and top altitudes for calculating the PAODI(i, j ). The S 1 (i), AE(j ), PAODI(i, j ), corresponding LMOL 292 nm aerosol extinction profile, and corresponding LMOL-HALO aerosol profile difference were all recorded. We use the S 1 (i), AE(j ), and PAODI(i, j ) data to find the minimum PAODI(i, j ) as well as the corresponding S 1 and AE, with the latter two terms denoted using S 1 (i c ) and AE(j c ), respectively. The LMOL 292 nm aerosol extinction profile corresponding to S 1 (i c ) is the value for the LMOL aerosol retrieval. The LMOL-HALO aerosol profile difference corresponding to S 1 (i c ) and AE(j c ) indicates the LMOL aerosol and HALO aerosol extinction comparison. This partial AOD difference method provides details on how to calculate the optimized S 1 , AE, and it corresponds to the cyan section in Fig. 1.
In order to show how the PAODI changed with the 292 nm S 1 and the AE (292 and 532 nm), we further calculated the percentage relative difference of the PAODI compared with PAODI min . An example of this partial AOD difference method at 13:17 EDT on 28 August 2018 is shown in Fig. 4. The PAODI was calculated for altitude regions from 0.5 to 3 km. The results in Fig. 4a show that the selected S 1 is 35 sr and the selected AE (292 and 532 nm) is 1.4. Therefore, an S 1 of 35 sr is the ideal choice for aerosol extinction retrieval on the afternoon of 28 August 2018. As show in Fig. 4b, the LMOL S 1 and the AE (292 and 532 nm) at (40, 1.5) and (30, 1.3) also have a PAODI value very close to PAODI min and could be a potential choice for the LMOL retrieval and comparison. Significant errors can arise when an improper S 1 is used for any UV aerosol retrieval that requires an inversion. For example, the value of PAODI using S 1 = 60 and AE = 1.4 is about 200 % of the PAODI value using S 1 = 35 and AE = 1.4. Thus, the further that S 1 deviates from the correct value, the larger the error caused for the UVB aerosol retrieval.
Using the abovementioned process, the selected 292 nm S 1 and AE (292 and 532 nm) were derived from all available co-located HALO and LMOL measurements for 5, 6, 16, 24, 28, and 29 August. The results and the HALO average S 1 at 532 nm are shown in Table 1. The altitude range for calculating the 292 nm S 1 and AE (292 and 532 nm) was from 0.5 to 3 km with the exception of the afternoon flight on 6 August, the morning flight on 16 August, and the afternoon flight on 29 August. In these cases, the altitude range from 0.5 to 2.5 km was used to avoid cloud interference that prevented proper retrieval; these instances are marked using an asterisk in Table 1. Figure 5 shows the S 1 and AE for 292 and 532 nm providing a view of the relationships. As shown in Fig. 5a and b, 532 nm S 1 varied between 40 and 70 sr, 292 nm S 1 varied between 20 and 55 sr, and the AE (292 and 532 nm) varied from 1 to 1.7. Figure 5a also shows that the 532 nm S 1 values are anticorrelated with the AE (532 and 292 nm), with a correlation coefficient of −0.72 and an R 2 value of 0.516. The anticorrelation indicates that the S 1 values are dependent on the particle size (Giannakaki et al., 2010). The 292 nm S 1 does not have a clear correlation with AE (532 and 292 nm), which is probably caused by the different aerosol absorption characteristic at 292 nm. Figure 5c shows that 292 nm S 1 values are smaller than 532 nm S 1 values for all cases listed in Table 1. The smaller S 1 values at UV wavelengths compared with those in the visible at 532 nm show the characteristic feature of aged smoke particles (Wandinger et al., 2002;Haarig et al., 2018, Müller et al., 2005Ortiz-Amezcua, 2017). This confirms the previous reports that the air parcel arriving in the northeastern US had passed over active fires in the southeastern US, the northwestern US, or the British Columbian region (Wu et al., 2021;Rogers et al., 2020;Hung et al., 2020).

Comparison of the retrieved LMOL result and the HALO aerosol extinction profile
The optimized 292 nm S 1 and AE (292 and 532 nm) selected in Table 1 have a corresponding LMOL 292 nm aerosol extinction and a 292 nm HALO aerosol profile comparison. The result of the LMOL-HALO comparison is shown in Fig. 6a-c for the afternoon of 28 August 2018. In Fig. 6a, the LMOL 292 nm aerosol extinction profile is shown in purple and the HALO aerosol extinction profile is shown in blue. As shown in Fig. 6c, the percentage difference is typically less than 10 % between 0.5 and 3 km. The gray shaded region in  Fig. 6c shows the ±10 % region. The percentage difference is larger at higher altitudes because the aerosol concentration is lower above the boundary layer. The percentage difference for all available HALO and LMOL aerosol data between 0.5 and 2.5 km was used to calculate the probability distribution function of the percentage difference for 5 % binning. The results in Fig. 6d show that the distribution of the frequency is centered about zero and exhibits a Gaussian distribution. The total number of points used for the comparison is 3146. The height of the peak of the distribution function is 0.175 (as it is normalized to 1). The median error percentage is 1.5 % with a standard deviation of 11 %. These results show that LMOL has the capability to retrieve aerosol extinction at 292 nm with reasonable accuracy. This result also provides  The HALO aerosol extinction profile is converted from the 532 nm aerosol extinction product. Panel (a) shows the LMOL and HALO aerosol extinction; panel (b) displays the difference between the LMOL and HALO aerosol extinction; panel (c) gives the percentage difference between the LMOL and HALO aerosol extinction; and panel (d) shows the error (percentage difference) probability distribution function for all available comparisons between 0.5 and 2.5 km for August 2018. In panel (d), the width between each bar shows 5 % difference.
the aerosol extinction value in the UVB wavelength range, which helps to understand the UV aerosol optical properties of transported wildfire smoke aerosol. This intercomparison is important because it illustrates the ability of the LMOL aerosol retrieval to capture a consistent aerosol feature when compared to HALO and, thus, produce relevant data for campaign analysis of the relationship between aerosols and O 3 features.

Comparisons between LMOL, the CCNY lidar, and CL51
To examine the LMOL retrieval beyond just the HALO overpass times, Fig. 7 provides a curtain plot of the 28 August LMOL 292 nm aerosol extinction compared with a co-located ceilometer CL51 910 nm backscatter signal and with the CCNY lidar (located in NYC) aerosol extinction (converted from 532 to 292 nm using an AE of 1.4). This allowed us observe boundary layer development and examine the aerosol variation features during the course of the day. The PBL height increases after 10:00 EDT and reaches a maximum at 17:00 EDT. The comparison between the CCNY aerosol extinction and the LMOL aerosol extinction shows that the retrieved LMOL UV aerosol extinction is qualitatively consistent. The difference in the aerosol extinction between the LMOL and CCNY measurements is probably caused by atmospheric variation among different locations over a distance of about 60 km. The PBL height was retrieved by applying a wavelet method to the LMOL and CCNY aerosol data (Brooks et al., 2003;Compton et al., 2013;Scarino et al., 2014). The PBL height of the ceilometer was obtained from the CL51 data product, which could be obtained from the LISTOS archive data. The PBL height is overlaid on the aerosol and O 3 curtain plot in Fig. 7a-d. LMOL-retrieved UVB aerosol extinction and the co-located CL51 aerosol backscatter show exactly the same variation for the PBL evolution except for the higher backscatter between 12:00 and 14:00 EDT. This is due to the fact that cloud screening was applied to the LMOL UVB aerosol retrieval process. This intercomparison is important because it illustrates the ability of the LMOL aerosol retrieval to capture a consistent aerosol feature when compared to other lidar systems and, thus, to produce relevant data for campaign analysis of the relationship between aerosols and O 3 features. Capturing aerosol extinction between 0.5 and 3.0 km is very useful because it will help us to retrieve the PBL height and to learn more about aerosol properties in the lower part of troposphere. Furthermore, aerosol profiling information can still play an important role in model intercomparisons and satellite retrievals.

Uncertainty
In this section, the sensitivity of the algorithm to uncertainty in the input parameters is analyzed for the 28 August 2018 case. The aerosol extinction retrieval uncertainties caused by the lidar detection noise, reference value estimation, atmospheric molecular density, O 3 concentration uncertainty, and the S 1 will be discussed. The quantitative estimation of the aerosol extinction and backscatter uncertainty is challenging, and no standardized recommendation exists (Leblanc et al., 2016b). In this work, the total uncertainty of the retrieved extinction coefficient is calculated by following standard propagation of error practices. The retrieved aerosol profile depends on several instrumental and physical parameters for the lidar system. The measurement model for the system is presented as Eq. (9). The individual values y of the quantity Y are shown in Eq. (10) (Leblanc et al., 2016b).
The combined standard uncertainty (u y ) is obtained using the individual standard measurement uncertainties associated with the input quantities in Eq. (9). As shown in Eq. (11), u y equals the positive squared root of the combined variance for all variables that are independent (Leblanc et al., 2016b): As shown in Sect. 2, the signal was used to calculate the aerosol extinction noted as X (R) and shown as Eq. (12): The detection noise uncertainty is derived from Poisson statistics associated with the probability of the detection of a repeated random event. Following Leblanc et al. (2016b), the subscript "DET" was used for detection noise. The uncertainty in the raw signal P (R) caused by detection noise could be expressed as shown in Eq. (13) and reflects purely random effects during detection (Russell et al., 1979).
It is propagated to the background-and O 3 -corrected signal X (R) by apply Eq. (11) to Eq. (12): Similarly, the O 3 uncertainty is noted as u O 3 , and it is propagated to the background-and O 3 -corrected signal X (R) as show in Eq. (15): The propagated uncertainty caused by detection noise and O 3 could be established by apply Eq. (11) to Eq. (4) as fol- Figure 8. The uncertainty budget for the LMOL (a) analog channel and (b) photon channel for the 28 August 2018 afternoon retrieval. The uncertainties are attributed to different factors: detection noise (purple), molecular number density (blue), S 1 (red), reference value (green), uncertainty of O 3 (orange), and total uncertainty (black). The uncertainty caused by using 60 sr as the S 1 is shown using a dashed gray line. lows: Thus, the total uncertainty can be established as shown in Eq. (18).
The uncertainty shown in Eq. (18) considers the impact of integral uncertainty from the targeted altitude to the reference point, as Eq. (4) includes the integral accounting for the molecular extinction and the O 3 -corrected return lidar signal of the target altitude to the reference point. u α 1 (N m ) (R) is the atmospheric molecular number density uncertainty, which we set as 1 % following the result from Kuang et al. (2020). The S 1 is assigned 35 ± 15 sr for this example, and the uncertainty of the u α 1 (S 1 ) (R) is about ±40 %. The uncertainty of the reference value is taken as 10 times for the total uncertainty analysis, as show in Eq. (18).
We calculated the uncertainties of the analog channel and the photon channel separately, so we could assess how the different parameters impacted the retrieval uncertainty for both channels. The photocurrent for the photomultiplier tube (PMT) analog mode no longer follows a strict Poisson distribution, but there still may be a quantitative estimate of this uncertainty. The uncertainty of the detection noise for the PMT analog channel is recalculated using the method mentioned in Liu et al. (2006), and the results are shown in Fig. 8a. As Fig. 8 shows, the uncertainty caused by the detection noise is small for both channels. The uncertainty caused by the reference value and the molecular number density is less than 10 % for both channels. Ozone uncertainty is 10 % for the LMOL system and generally causes less than 20 % aerosol extinction uncertainty for the analog channel and photon channel. The uncertainty of the S 1 causes about 4 %-30 % uncertainty for both the analog and photon channels. The uncertainty of the S 1 and O 3 dominate the total uncertainty for both channels. We also show the uncertainty caused by using 60 sr as S 1 for UVB aerosol retrieval for the afternoon of 28 August 2018. It was found that an S 1 of 60 would increase the aerosol retrieval uncertainty in the PBL but that the uncertainty did not change much above 2 km except in a layer located at 2.6 km.

Conclusions
For the first time, the aerosol extinction coefficient profiles, retrieved from the LMOL 292 nm attenuated backscatter using the Fernald algorithm, are compared with airborne HALO data. A partial AOD difference method was introduced to determine the optimized value for 292 nm S 1 and AE (292 and 532 nm) from these instruments. The optimized S 1 and AE (292 and 532 nm) improved the accuracy of the UVB aerosol retrieval. In addition, knowledge of these parameters can improve our understanding of the aerosol properties; for example, the case studies in the present paper demonstrated that we were in the presence of transported smoke. The intercomparison between HALO and LMOL aerosol products showed an agreement within 10 % up to 3 km after the optimization method was applied in the case of the 28 August 2018. The retrieved LMOL 292 nm aerosol was also compared with co-located ceilometer and CCNY aerosol lidar. This showed that LMOL could capture a consistent aerosol feature and mixing layer evolution. Error analysis showed that the uncertainty from O 3 and S 1 dominates the 292 nm aerosol retrieval and needs to be carefully considered in the retrievals of aerosol profiles of all of the TOLNet lidars. In cases for which there are no HALO data, a priori determinations from differing aerosol types based on this kind of analysis work will serve to provide reasonable S 1 values. Consequently, further research is needed to characterize S 1 and AE at UVB wavelengths: first, an effort should be made to determine the variation in S 1 and AE with altitude by carefully addressing the uncertainties in the HALO S 1 profile products; second, additional co-located LMOL-HSRL measurements should be done to evaluate S 1 and AE for different aerosol types (smoke, dust, marine aerosol, and pollutant aerosol). This characterization could ultimately enable the use of equipment with a better availability than HSRL instruments (e.g., micropulse lidars) in order to provide the ancillary data necessary for the aerosol extinction retrieval. Supplement. The supplement related to this article is available online at: https://doi.org/10.5194/amt-15-2465-2022-supplement.
Author contributions. LL and TAB formulated the overarching research goals. GG supported the O 3 data analysis, which was a key factor in the aerosol retrieval algorithm, and plotted Fig. 1, outlining the flow chart of the approach used in this work. LL and JS carried out the UV aerosol extinction retrieval calculation. LL undertook the S 1 and AE determination as well as the aerosol extinction comparison between LMOL and HALO. ARN provided the HALO aerosol data product and the HALO instrument introduction for the paper. YW and FM contributed CCNY lidar aerosol data and CCNY PBL height data. SK contributed to the UV aerosol retrieval algorithm. LL wrote the initial draft of the paper with contributions from all co-authors. All authors reviewed and agreed upon the final paper.
Competing interests. The contact author has declared that neither they nor their co-authors have any competing interests.
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