Retrievals of dust-related particle mass and ice-nucleating particle concentration profiles with ground-based polarization lidar and sun photometer over a central China megacity

The POLIPHON (Polarization Lidar Photometer Networking) method is a powerful pathway to retrieve the height 10 profiles of dust-related particle mass and ice-nucleating particles (INP) concentrations. The conversion factors fitted from the sun photometer observation data are the major part of the POLIPHON computations, which can convert the polarizationlidar-derived dust extinction coefficients into the dust-related particle mass and INP concentrations. For a central China megacity Wuhan (30.5°N, 114.4°E), located at the downstream area several thousands of kilometers far away from the source regions of Asian dust, dust particles always mix with other aerosols from local emission. Therefore, very few dust 15 case data sets can be available when using the column-integrated Ångström exponent (for 440-870 nm) <0.3 and aerosol optical depth (at 532 nm) >0.1 recorded by sun photometer as the filtering criteria. Instead, we present another dust-case data-set screening scheme that applies the simultaneous polarization lidar observation to verify the occurrence of dust. Based on the 33 dust-intrusion days identified during 2011-2013, the extinction-to-volume (cv,d) and extinction-to-large particle (with radius >250 nm) number concentration (c250,d) conversion factors are determined to be 0.52 × 10 −12 Mm mm and 20 0.11 Mm cm, respectively. They are both smaller than those observed at Lanzhou SACOL (36.0°N, 104.1°E), a site closer to the Gobi Desert, due to the partial dust sedimentation during transport. The conversion factors are applied in a dust event in Wuhan to reveal the typical dust-related INP concentration over East Asia city. The proposed dust-case data-set screening scheme may potentially be extended to the other polluted city sites more influenced by mixed dust.

where (=0.004 for our lidar system) is the molecular depolarization ratio that is related to the specification of the narrowband filters in the receiving unit of the lidar system [Behrendt and Nakamura, 2002]. The relative uncertainty for is 95 generally on the order of 5-10 % [Mamouri et al., 2013].

Sun Photometer and GRASP Algorithm
A sun-sky scanning spectral photometer  was installed at our observatory in April 2008 and had been operating until August 2013 due to technical failure [Zhang et al., 2021]. It detects the direct solar irradiance at eight wavelengths 100 (340,380,440,500,675,870,1020, and 1246 nm) for every 15 minutes; the AOD at each wavelength can then be calculated following the Beer-Lambert law. The uncertainties of AOD are ~0.015 at 440-1020 nm and ~0.035 at 340-380 nm [Zhang et al., 2021], which is slightly larger than those (0.01-0.02) for the AERONET field instruments [Holben et al., 1998]. The sky radiance data are not available. The fine mode fraction (FMF) of 500 nm AOD was obtained based on the method given by O'Neill et al. [2003]. 105 Generalized Retrieval of Aerosol and Surface Properties (GRASP) algorithm had been widely used in retrieving aerosol microphysical properties [Dubovik et al., 2014] and was reported to be applied in dust event observation [Benavent-Oltra et al., 2017. Although our sun photometer lacks the sky radiance observation, the GRASP-AOD application allows us to determine particle size distributions using only spectral AOD data [Torres et al., 2017]. In this study, the column-integrated particle size distribution was retrieved using the spectral AODs ranging from 380 to 1020 nm as the input to the GRASP 110 algorithm. Considering Wuhan is a megacity with plenty of local aerosol emissions [Ma et al., 2019], we assumed the complex refractive index values to reflect the mixed desert-dust characteristic in particle size distribution inversion. The real part was set to be 1.55; the imaginary part was set to be wavelength-dependent (i.e. 0.003 at 380 nm, 0.0025 at 440 nm, 0.0022 at 500 nm, 0.0014 at 675 nm, 0.001 at 870 nm, and 0.001 at 1020 nm) [Dubovik et al., 2002].

Radiosonde Data
The radiosondes (GTS1-2, made by China) were launched twice per day at 0800 Local Time (LT) (0000 UTC) and 2000 LT (1200 UTC) from the Wuhan Weather Station, located approximately 24 km from our lidar site. The profiles of temperature and pressure provided by radiosondes were used in INP concentration parameterization [DeMott et al., 2010[DeMott et al., , 2015] to convert the aerosol particle (with radius >250 nm) number concentrations (APC250) into the INP concentrations. The error 120 for measured temperature is less than 1 °C [Nash et al., 2011].

CALIOP
The Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite was launched in 2006 and carried an instrument Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) to provide the vertical information of aerosols and clouds [Winker et al., 2007]. The satellite orbit nearly passed Wuhan every day at about 0200 LT and 1400 LT 125 with the nearest subpoint occurred per 16 days (before 2018). It can measure the elastic backscatter at both 532 nm and 1064 nm and is also capable of measuring the depolarization ratio at 532 nm near nadir during both daytime and nighttime. The depolarization ratio is used to identify the dust aerosol and the ice-containing cloud because of their nonspherical shape. The color ratio, defined as the ratio of backscattering at 1064 nm to backscattering at 532 nm, is provided to represent the particle size. In this study, the CALIOP Level-2 vertical feature mask (VFM) product was used to validate the presence of dust layers 130 over Wuhan [Omar et al., 2009].

HYSPLIT Model
The Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model, based on the National Centers for Environmental Prediction (NCEP) GDAS data product, can calculate the backward trajectory of the air mass [Draxler and 135 Rolph, 2003]. In this study, three-day backward simulations were operated to check the potential source of the dust aerosol layers observed by polarization lidar over Wuhan.

Methodology
In this section, we introduce the retrieval schemes for dust-related particle mass and INP concentration. The specific steps of data processing were presented in the previous literature [Mamouri and Ansmann, 2014, 2016. Here we just present 140 the main derivation steps (Sect. 3.1). More importantly, the retrieval scheme of dust-related conversion factors over Wuhan, a megacity that is thousands of kilometers far from desert regions, is shown in detail (Sect. 3.2).

Retrieval scheme of dust mass concentration and dust-related INPC
First, aerosol backscatter coefficient β can be determined from the Mie backscatter lidar data with the Fernald Method [Fernald, 1984]. Then we need to separate the backscatter contributed by the dust component (i.e. ) from the total aerosol 145 backscatter coefficient β using the so-called 'one-step' approach [Mamouri and Ansmann et al., 2014] The primary principle is introducing two threshold values of particle depolarization ratio, non-dust particle depolarization 150 ratio = 0.05 and dust particle depolarization ratio = 0.31 [Sakai et al., 2010], to separate the respective contribution of each component (dust particle, non-dust particle, and their mixture) to the total backscatter coefficient. The particles with < are considered as non-dust particles. The particles with > are considered as pure dust particles (i.e. mineral dust). values range between and are the mix of non-dust and pure dust components. The dust backscatter coefficient can be expressed as ] 155 The subscripts 'n', 'nd', and 'p' represent 'dust', 'non-dust', and 'particle' (dust + non-dust), respectively. Therefore, the dust extinction coefficient can be calculated by: where dust lidar ratio is set to be 45 sr [Hu et al., 2020]. The uncertainty for is on the order of 20% [Mamouri and 160 Ansmann, 2014;Tesche et al., 2009].
Finally, the dust mass concentration can be computed by the equation below: where is the dust particle density (2.6 g cm -3 for Asian dust) [Wagner et al., 2009] and , is the extinction-to-volume conversion factor. The value of , can be obtained from sun-photometer-observed dust-intrusion days as discussed by Sect. 165 3.2. The uncertainty of is ≤ 60% [Mamouri and Ansmann, 2014].
To calculate the INPC, the dust extinction coefficient need to be converted to the column-integrated number concentration of large particles with radius >250 nm APC250 (here denoted as 250, ) by the expression: where 250, is the conversion factor obtained from sun photometer observation (see Sect. 3.2) during dust-intrusion days at 170 our site. The overall uncertainty for 250, is estimated to be on the order of 30% [Mamouri and Ansmann, 2015]. Based on an INPC parameterization scheme given by DeMott et al. [2010DeMott et al. [ , 2015 which is appropriate for dust-related immersion freezing regime, one can finally retrieve the height profile of INPC: where the constant a = 0.0000594, b = 3.33, c = 0.0265, and d = 0.0033. This parameterization scheme is applicable for temperatures ranging from -9 °C to -35 °C. D15 parameterization scheme is another option but explicitly for mineral dust, where the constant a d = 0.074, b d = 3.8, c d = 0.414, and d d = −9.671. This parameterization scheme is applicable for temperatures ranging from -21 °C to -35 °C. The uncertainty for INPC using the D15 is within an overall factor of 3 [Mamouri and Ansmann, 2015]. In practice, the corresponding meteorological parameter (i.e. pressure and temperature) profiles are provided by the measurement from the most recently launched radiosonde. 185

POLIPHON conversion factors over Wuhan
As mentioned in Sect. 3.1, we need to obtain the dust-related conversion factors. Ansmann et al. [2019b] reported an extended set of dust conversion factors considering all relevant deserts around the globe using the AERONET database. To obtain climatologically dust conversion factors for a given AERONET site, they filtered out all AERONET data sets with the criteria of an Ångström exponent for the 440-870 wavelength range AE <0.3 and a 532 nm (converted from 500 nm) 190 AOD >0.1. Considering the AERONET sites selected in Ansmann et al. [2019b] mostly located in/near the desert regions, the pure dust cases following the criteria given above can be found more easily (with adequate data sets >2500 for each site).
Dust frequently intruded into Wuhan over the years; however, very few sun photometer data sets can fulfill those constraints. This is caused by plenty of local aerosol emissions (especially within the boundary layer), which make the column-integrated aerosol properties observed here generally reflect a characteristic of mixed dust (dust particles mix with other urban aerosols) 195 [Shao et al., 2020;Liu et al., 2021]. It is also worthy to note that the previous gravitational sedimentation and wet deposition of dust particles during transport may modify the dust optical and microphysical properties in Wuhan and thus result in the dust-related conversion factors different from those near-desert sites.
To select the dust-containing data sets from sun photometer observation, for the first time, we employed the simultaneous ground-based polarization lidar observation as an auxiliary. Once a dust layer with δ >0.06 and layer thickness >0.9 km was 200 observed by lidar [Huang et al., 2008], we considered the simultaneous observational data sets from sun photometer available for calculating the dust-related conversion factors. For a dust-intrusion day, all these dust-containing data sets measured by sun photometer were averaged to form a representive result (AOD and later calculated particle size distribution) of this day. Here, we give an example of dust-case data-set screening scheme for a typical dust-intrusion day. Figure 2 presents the time-height contour plots of the range-corrected signal and volume depolarization ratio measured by 205 polarization lidar during 1000-1600 LT on 28 April 2011. The lidar system began to operate at ~1000 LT this day. Two distinct dust layers with δ >0.1 can be identified to be located from the surface to around 2.0 km and above 2.5 km, respectively. Hence it was a typical dust-intrusion day.
sets from an uninterrupted period of 1205-1550 LT were related to the dust intrusion. Therefore, the corresponding data sets 215 measured by sun photometer during this dust-intrusion period (1205-1550 LT) were averged to form the representive results (AOD and later particle volume size distribution) for 28 April 2011. Figure 4 shows the column-integrated particle volume size distribution (Figure 4a) and particle number size distribution (Figure 4b) derived from the averaged spectral AODs during 1205-1550 LT on 28 April 2011 based on GRASP-AOD algorithm. The particle radius ranges from 0.05 to 15 μm.
The column APC250 values are obtained by integrating the particle number (as given in Figure 4b Assuming an aerosol layer thickness of D, we can convert the above equation to: 225 where 250, and are the layer-mean large particle (with radius >250 nm) number concentration and lidar-derived dust extinction coefficient, respectively. In total, we screened 32 dust-intrusion days from the sun photometer observation during 2011-2013. As seen in Figure 5, a great correlation between 250, and was found with a linear Pearson correlation The conversion factor of 0.11 Mm cm -3 is approximately 27% smaller than the value of 0.15 Mm cm -3 obtained at Lanzhou SACOL (36.0°N, 104.1°E) AERONET site as well as at Dalanzadgad, Mongolia (see Figure 1), which are very close to the 235 source region of Asian dust [Ansmann et al., 2019b]. This discrepancy is probably due to the partial sedimentation of dust particles with large sizes before arriving in Wuhan. Another possible reason behind this is the influence of local emissions on 250, . In consequence, 0.11 Mm cm -3 could be a reasonable conversion factor for mixed dust cases in a city region.
Moreover, two other AERONET sites were reported to also have smaller 250, value as Wuhan, i.e. White Sands site (0.10 Mm cm -3 ) in North America and Birdsville site (0.11 Mm cm -3 ) in central Australia [Ansmann et al., 2019b]. 240 The column particle volume concentration value are obtained by integrating the entire particle size distribution spectrum.
The relationship between and 500 nm AOD can be linked by a so-called extinction-to-volume conversion factor , with the following equation: Assuming an aerosol layer thickness of D, we can convert the above equation to: where and are the layer-mean particle volume concentration and extinction coefficient, respectively. As seen in Figure   6, a correlation between and was found with a linear Pearson correlation coefficient of 0.653 for the period of 2011-2013. Each point in Figure 6 also represented a pair of daily value averaging all the dust-case data sets from a typical dustintrusion day (taking the day 28 April 2011 shown above as an example).The , value was 0.52 × 10 −12 Mm m 3 m −3 as 250 computed by the equation below: The conversion factor , of 0.52 × 10 −12 Mm m 3 m −3 is approximately 32% smaller than the value of 0.77 × 10 −12 Mm m 3 m −3 obtained at Lanzhou SACOL AERONET site [Ansmann et al., 2019b], suggesting that the proportion of dust particles in the atmospheric column is relatively smaller in Wuhan. In particular, those more dispersed points below the 255 dashed line seem to be more affected by anthropogenic aerosols.

Case Study on a Dust-related Heterogeneous Nucleation Process
We used the two dust-related conversion factors 250, and , retrieved at Wuhan to analyze a dust-related heterogeneous nucleation case on 31 December 2017. Figure 7 presents the time-height contour plots (1 minute/30 m resolution) of the range-corrected signal ( Figure 7b) and volume depolarization ratio δ during 0100-0700 LT (Figure 7d). The corresponding 260 profiles of the relative humidity (RH), temperature (T), horizontal wind speed (V), and wind direction from the radiosonde launched at 0800LT are shown in Figure 7a and 7c. Two distinct dust aerosol layers (below ~2 km and at ~4.5-6.5 km, respectively) were identified with peak δ values exceeding 0.1. Another slight dust layer with an enhanced δ of ~0.04 occurred up to ~8 km.
According to the backward trajectories in Figure 8, the dust layer below 2 km probably originated from the Taklimakan 265 Desert. The two aloft dust layers were probably linked to the desert regions over northwest India and Pakistan. As seen from Figure 9, the occurrence of dust over Wuhan was also verified by the aerosol subtype classification provided by the CALIOP Level-2 VFM data product. The satellite passed over Wuhan at ~1850 UTC on 30 December 2017 (0250 LT on 31 December 2017). The two aerosol layers around Wuhan, respectively located at 0-2 km and ~4-5.5 km, were distinguished as the mix of dust (marked as '2', in yellow) and polluted dust (marked as '5', in brown). 270 As seen in Figure 7d, an ice-containing cloud appeared at ~0405 LT at the altitudes where the upmost slight dust layer was located. The temperature at around 8 km was -32.5 °C as denoted by the horizontal dashed lines in Figure 7. Therefore, the dust particles were likely to trigger the heterogeneous ice formation. Figure 10 shows the height profiles of optical properties including dust and total extinction coefficient, dust and total backscatter coefficient, volume depolarization ratio, and particle depolarization ratio during the period of 0320-0350 LT. The peak dust extinction coefficient for the upmost dust layer at an 275 altitude of ~8.1 km was 2.0 Mm -1 . The peak particle depolarization ratio value for this slight dust layer was 0.16. The values of <0.3 were observed throughout the altitudes of 4-9 km, indicating the possible presence of mixed dust or fine-mode dust [Sakai et al., 2010].
In Figure 11a, the dust extinction coefficients were converted into the dust mass concentrations by multiplying by the extinction-to-volume conversion factor , and dust density. The maximum dust mass concentrations were 2.6 μg m -3 for 280 the dust layer around 8 km and 46.0 μg m -3 for the dust layer at altitudes of 4.4-5.3 km. Note that more dense dust plumes could even be observed frequently in Wuhan. The dust mass concentrations of 6.27-154.79 μg m -3 had been observed in Wuhan for the dust events from December 2012 to December 2013 [He et al., 2021a]. In Figure 11b, the dust extinction coefficients were converted into the large particle number concentrations APC250 by multiplying by the conversion factor reported similar INP concentrations at -16 °C for 13 dust events in Beijing range from 0.42 to 17.36 L -1 . As more dense dust plumes were reported to appear frequently in Wuhan [He et al., 2021a], the INPC values much larger than 2.0 L -1 as observed in this case are probably present at other times, especially in the winter when the zero isotherms can drop to a 295 lower height. This INPC level can have an important effect on ice nucleation in the atmosphere.

Discussions and Conclusions
The quantitative evaluation of dust-related INPC profiles is of particular interest for understanding the specific contribution of heterogeneous nucleation to the aerosol-cloud-interaction-induced radiative forcing. Furthermore, the understanding of INPC is also indispensable for estimating the impact of dust-related INPs on extreme precipitation [Zhang et al., 2020]. 300 However, when using the POLIPHON method to estimate the dust-related INPC profiles, the calibration of dust-related conversion factors is not easy, but of great importance, for those cities over the downstream regions of long-range transported dust plumes. They may suffer the dual impact of the emissions of local pollutions and transported dust aerosols.
Urban air pollutions (e.g. anthropogenic PM2.5 and black carbon) are generally considered not to affect the atmospheric INPC [Chen et al., 2018], thus the extraction of dust-related INP concentration using the powerful POLIPHON method is 305 possible. In addition, the dust sedimentation and particle microphysical properties modification may also take place during the transport and thus lead to the modified conversion factors over downstream cities compared with those over near-desert areas.
In this study, the retrievals of INPC and dust concentration mass profiles were realized for a central China megacity Wuhan (30.5°N, 114.4°E), located at the downstream region of long-range transported dust (see Figure 1). Different from the 310 previous screening scheme of dust occurrence data sets that simply employs the AOD at 532 nm >0.1 and Ångström exponent for the 440-870 nm wavelength range <0.3 [Ansmann et al., 2019b] as the indicators of dust occurrence, groundbased polarization lidar observation was used as a useful auxiliary to verify whether dust particles were involved in a data set measured by sun photometer. In consequence, the dust-related conversion factors explicit for Wuhan (usually mixed dust) were obtained for the first time. The extinction-to-volume conversion factor , = 0.52 × 10 −12 Mm m 3 m −3 and the 315 extinction-to-large particle (with radius >250 nm) number concentration conversion factor 250, = 0.11 Mm cm −3 . They were both smaller than those observed at Lanzhou SACOL (36.0°N, 104.1°E) AERONET site that is much more closed to the source region of Asian dust. The discrepancies are probably due to the partial sedimentation of dust particles during their several thousands of kilometers transport before arriving at Wuhan. This dust-case data-set screening scheme may potentially be extended to the other polluted city sites more influenced by mixed dust. 320 A case study on the dust-related heterogeneous nucleation process was presented. Applying the conversion factors obtained herein together with the parameterization scheme D10 and D15, the height profile of INPC and dust mass concentration before the presence of an ice-containing cloud was shown. The maximum dust mass concentration at an altitude of 8.1 km is only 2.6 μg m -3 ; the corresponding INPC here reached 2.0 L -1 and was seemed to trigger the subsequent heterogeneous ice formation. 325 In the future, the conversion parameters obtained in this study will be used to study the seasonal and long-term variation of INPC vertical distributions over Wuhan [Tobo et al., 2020]. We will also need to separate other different aerosol components and retrieve their corresponding POLIPHON conversion factors [Mamouri and Ansmann, 2017;Córdoba-Jabonero et al., 2018]. Furthermore, the observations with millimeter-wave radar can give the ice crystal number concentration information within the cloud so that may realize the possible closure study of heterogeneous ice nucleation process [Ansmann et al., 330 2019a]. Additionally, the retrieved dust mass concentration profiles are anticipated to verify the results outputted from dust models such as NMME-DREAM [Konsta et al., 2021].

Data availability
Sun photometer and ground-based polarization lidar data used to generate the results of this paper are available at the