Ice fog observed at cirrus temperatures at Dome C, Antarctic Plateau

. As the near-surface atmosphere over the Antarctic Plateau is cold and pristine, its physico-chemical conditions resemble to a certain extent those of the high-troposphere where cirrus clouds form. In this paper, we carry out an observational analysis of two shallow fog clouds forming (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) in-situ at cirrus-temperatures - that is, temperatures lower than 235 K - at Dome C, inner Antarctic Plateau. The combination of lidar proﬁles with temperature and humidity measurements from advanced 5 thermo-hygrometers along a 45-m mast makes it possible to characterise the formation and development of the fog. High su-persaturations with respect to ice are observed before the initiation of fog and the values attained suggest that the nucleation process at play is the homogeneous freezing of solution aerosol droplets. To our knowledge, this

In the former case, supercooled liquid droplets produced at higher temperatures through Cloud Condensation Nuclei (CCN) activation, -e.g. above the open ocean -are advected into a colder environment -e.g. above a continental surface, the sea-ice or an ice-sheet -and then freeze when T < 235 K. In the second case, supercooled liquid :::: water : droplets can freeze at higher 35 temperature if they contain or enter in contact with Ice Nuclei Particles (INPs). In addition to these so-called immersion and contact freezing processes, heterogeneous nucleation might occur without the presence of supercooled liquid droplets through the direct deposition of water vapor onto INPs but the occurrence of such a process in the atmosphere is still debated (Marcolli, 2014). Given the low concentrations of INPs over the Antarctic (Belosi et al., 2014), supercooled liquid droplets can be observed at ::: have ::::: been :::::::: observed :: at :::: very :::: cold : temperatures down to 248 K (Silber et al., 2019;Ricaud et al., 2020) ::::: 240 K 40 ::::::::::::::::::::::::::::::::::::::::::::::: (Silber et al., 2019;Ricaud et al., 2020;Rowe et al., 2022) and they were shown to be at the origin of fogs over the Antarctic coast (Kikuchi, 1971(Kikuchi, , 1972. Ice fogs forming locally over the Antarctic Plateau when the temperature remains well below 235 K have received much less attentionhitherto. In this cirrus-temperature regime, no supercooled water droplets are present and the fog necessarily cannot 45 have a liquid origin. In this particular case, ice crystals may form through freezing of solution aerosol particles also named haze droplets (Heymsfield and Sabin, 1989;Girard and Blanchet, 2001) when the relative humidity reaches a value that depends on the particle size and water activity. This value is above the saturation with respect to ice -so the air is supersaturated with respect to ice -but is lower than the liquid water saturation (Koop et al., 2000;Baumgartner et al., 2022). There is also evidence that solution aerosol particles can also freeze heterogeneously due to the presence of INPs (DeMott et al., 1998;Kärcher and 50 Lohmann, 2003) but this process remains poorly understood especially at very low temperatures .
The air near the surface of the Antarctic Plateau frequently experiences high supersaturations with respect to ice . The evidence of such a phenomenon is quite recent as conventional capacitive thermo-hygrometers deployed on weather stations fail to report supersaturation because the excess of water vapour with respect to saturation condenses 55 on the sampling device and the sensor . The recent development and deployment of advanced thermohygrometers able to sample supersaturations on a 45-m mast  at the French-Italian Concordia station on the Dome C, East Antarctic Plateau, paves the way for an examination of the humidity evolution during ice fog formation and could give insights into the microphysical processes -including the nucleation and growth of ice crystals -that are potentially involved.

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The objective of the present paper is to study the development of ice fog that do not have a liquid origin and do not correspond to maritime advections but that form locally at T < 235 K over the East Antarctic Plateau. Two case studies are analysed in details through an in depth examination of meteorological data at Dome C, : a : site particularly known for its very stable boundary layers and extreme temperature inversions (Vignon et al., 2017).

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The French-Italian Concordia station is located on the Dome C, high Antarctic Plateau (75°06' S, 123°20' E, 3233 m a.s.l, Local Time LT = UTC+8 h). The landscape is a homogeneous and flat snow desert where the monthly mean 2 m temperatures ranges from about 246 K in austral summer to about 208 K in the polar night in winter (Genthon et al., 2021). During austral summer, the atmospheric boundary layer experiences a marked diurnal cycle with an alternation of diurnal shallow convection -when the sun is high above the horizon -and nocturnal stable stratification. Conversely during winter, the boundary-layer 70 is almost always stably -even very stably -stratified (Genthon et al., 2013). The absence of terrain slope precludes the local generation of katabatic winds. The near-surface wind is mostly south-southwesterly and the annual 3 m mean speed is 4.5 m s −1 (Argentini et al., 2014). Occurrences of significant wind-transported snow events are seldom (Libois et al., 2014). The sets of observational data collected at the station and used in this study are described in the following sub-sections.

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Wind and temperature measurements are performed at six levels on a 45-m mast located 1-km upwind of Concordia station.
Temperature is measured using mechanically-ventilated Vaisala HMP-155 thermo-hygrometers and wind speed and direction are obtained with R. M. Young 05103 aerovanes. 30-min average data have been used in this paper. Details on data acquisition and processing are given in (Genthon et al., 2021). The downward long-wave and short-wave radiative fluxes are measured at the Dome C Baseline Surface Radiation Network (BSRN) station using two Kipp and Zonen CM22 secondary standard 80 pyranometers and two Kipp and Zonen CG4 pyrgeometers (Lanconelli et al., 2011;Driemel et al., 2018).

Lidar measurements
A tropospheric depolarization aerosol lidar (532 nm) has been operating at Dome C since 2008 (http://lidarmax.altervista.org/ englidar/Antarctic%20LIDAR.php). The lidar provides 5 min tropospheric profiles of aerosols and clouds continuously, from 130 20 to 7000 m a.g.l., with a 7.5 m vertical resolution. Further technical details are given in (Palchetti et al., 2015;Ricaud et al., 2020). Note that only the lidar backscattering signal is shown in this study but the investigation of the depolarisation ratio (not shown) reveals high values (>10%) for the two fog events analysed in this study. This suggests that the ice fogs do not contain supercooled liquid drops :::::: droplets, which is consistent with the temperature (<235 K) at which they are observed. To support the interpretation of lidar data, time-lapse webcam videos of local sky conditions are also collected.

Back-trajectory analysis
To ensure that the studied fog events correspond to local cloud formation over the Antarctic Plateau and are not associated with maritime air intrusions, we estimate air parcel Lagrangian back trajectories using the HYSPLIT modeling system (https: //www.ready.noaa.gov) applied to the Global Data Assimilation System analysis of the National Center for Environmental Prediction with a horizontal grid of 0.5 o × 0.5 o and a hourly temporal resolution. We calculate 2-day trajectories starting -140 backward in time -at the 4 closest grid points to Dome C and at two different heights near the surface: 50 m a.g.l. and 100 m a.g.l. We will see hereafter that the maximum ice fog depth during the events of interest is about 200 m. Assuming a fall velocity of ≈ 1 cm s −1 , ice crystals forming at the top of the fog layer reach the ground in less than 6 h. Therefore, a 2-day trajectory duration is sufficient to track the trajectory of all ice crystals observed ::::::::: trajectories :: of ::: the ::: air :::::: masses :::::: probed : above Dome C.   7 m s −1 . Assuming a logarithmic wind speed profile between the surface and 10-m and an aerodynamic roughness length value 160 of 1 mm (Vignon et al., 2016), this corresponds to a 3-m wind speed threshold value of 3.5 m s −1 . Note that at 2200 LT, 7 March and after 0600 LT, 8 March, the 3-m wind speed exceeds the threshold ::: and ::::: some ::::: snow ::: drift :: is :::::::: therefore ::::::: possible :::::: during :::: those ::::::: periods.
As the air is coming from the southern sector, we do not expect this fog to be associated with an oceanic intrusion. It rather corresponds to a cloud that forms locally or slightly upstream over the Antarctic Plateau. This is confirmed by the analysis 165 of air mass back-trajectories arriving at 50 and 100 m a.g.l. shown in Fig.3a. As the temperature along the trajectories never exceeds 235 K (not shown), an advection of supercooled liquid droplets towards Dome C is unlikely which confirms that the fog does not have a liquid origin Temperature measurements on the mast remain below 235 K throughout the event and one can notice a weak diurnal cycle at 3-m that is almost totally damped at 42-m (Fig. 4). A close investigation of the vertical profile of the potential temperature - very close to absolute temperature over the mast depth -reveals that the boundary layer transits between a weakly convective state during daytime to a stable state during nighttime. The fog does not have a clear radiative signature at the surface even though a slight decrease in downward longwave radiation is noticeable during the evening of 7 March (Fig B2a), which concurs with the overall decrease in air temperature (Fig 4). RHi then gradually decreases and reaches 100 % at the three levels at 0800 LT : , : 8 :::::: March (Fig. 4). The decrease starts at 2230 LT : , : 7 :::::: March at the 3-m level, a half-hour later at 18-m and 2 hours later at 42-m.
At 18-m, the decrease in RHi from 2200 LT is co-incidental with a sharp decrease in vapour partial pressure as well as a decrease in gradient of vapour partial pressure (Fig. 5c) between 3 and 18-m. The 18-m drying from 2200 LT is therefore due to the turbulent mixing near the suface with a net flux of a moisture oriented downward.

Growth and decay: 0300 LT, 8 March to 2300 LT, 9 March
From 0300 to 0800 LT, 8 March, the temperature vertical profile shows a clear night-day transition i.e. a transition from an 'exponential' shape characteristic of very stable boundary layers to a convective profile with a well-mixed layer capped by a 205 shallow temperature inversion whose height further increases during the day (Fig. 5a). A close inspection of the vertical profile of specific humidity between 3-m and the surface at 0800 LT (not shown) -assuming that the specific humidity at the snow surface equals the saturation specific humidity at the surface temperature -reveals that the vertical gradient of specific humidity and subsequently the surface flux of water vapour reverses sign and become oriented upward. The supply of water vapour from the snow surface -and possibly of drifting ice crystals since the surface wind speed exceeds the erosion threshold (Fig. 3b) -210 can therefore deposit onto the ice crystal embryos nucleated in the early morning and make them grow and become visible in the lidar signal. March, as the daytime convective boundary layer deepens in ≈ √ t (Stull, 1990). The growth of the fog is possible as the top :: in :: the :::::: higher :::: part of the boundary layer is supersaturated :: as :: its ::: top :: is :::::::::::: supersaturated ::: wrt ::: ice (Fig 2c)and ice . ::: Ice crystals can hence 215 grow by vapour deposition and sediment down to the subsaturated near-surface layers ::::: where :::: they :::::::: probably ::::: partly ::::::::: sublimate ( Fig. 2 c and 4). One ::::::::: Concurring :::: with ::::::::::::::::::  ::: (see ::::: their ::: Fig. ::: 8), ::: the ::::::::::: near-surface :: air :::::::: becomes :::::::::: subsaturated :::: wrt :: ice :::::::::: particularly :::::: during ::::::: daytime ::::: when ::: the :::::::::: near-surface ::: air :::::: warms :: by ::::::::: convective ::::::: mixing. ::: As :::: night :::: falls :::::: around ::: 19 ::: LT, : 8 ::::::: March, ::: one can then note a sharper deepening of the fog up to 200 mas night falls. The mechanisms responsible for this sudden growth cannot be directly identified from our measurements but one can nonetheless make some assumptions. As the wind speed 220 increases in the late afternoon (Fig. 3b), one could expect an enhanced vertical mixing of ice particle but a close examination of the wind speed profile from the radiosonde reveals a weak local wind shear at the top of the boundary-layer. Nonetheless, in the late afternoon, the decrease in the shallow convection intensity leads to a decrease in the capping temperature inversion strength (Ricaud et al., 2012). The weak vertical gradient of temperature at the top of the evening convective boundary layer is visible in Fig. 2b (see black arrow) whereas a second higher and stronger temperature inversion is visible at the top of the fog 225 layer and probably induced by the cloud-top radiative cooling. Izett and van de Wiel (2020) show that the growth of a radiative liquid fog layer can suddenly accelerate when the vertical gradient of temperature decreases (i.e. when the vertical gradient of saturation specific humidity decreases, see their Eq. 7). If we assume a homogeneous freezing process, the ice nucleation occurs at the Koop et al. (2000)'s threshold, that is, according to an increasing function of temperature. Subsequently, we can reasonably think that the conceptual model of Izett and van de Wiel (2020) is qualitatively valid for our ice fogs. We can there-  (Fig. 6a). Its depth then oscillates between 25 and 50 m :::: a.g.l. : and the fog vanishes at around 1400 LT, 26 August. This event is particularly interesting since its vertical extent is almost the same as the one of the meteorological mast. Note that highly reflective bands are observed during the 26 August and most of them correspond to diamond dust precipitation 'peaks' falling from the mid-troposphere. The radiosounding reveals a supersaturated layer with respect to ice 250 below 30 m a.g.l. and the :::: with : a ::::::::: maximum :::: RHi ::::: value :: of ::: 147 ::: %. ::: The : relative humidity with respect to liquid water reaches ::: also :::::: exceeds : 75% near the surface (Fig. 6c).
11 Figure 6. Same as Fig. 2 but for Event 2.   Fig. 7b shows that the 3-m wind speed remains below 4m s −1 throughout the event and never exceeds the threshold value to trigger drifting snow. Its direction slightly changes from south-westerly to a south-easterly suggesting that the air parcels reaching Dome C come from the high Antarctic Plateau (Fig. 7b) and that our measurement ::::::::::: measurements : are not affected 255 by station exhausts except during the very end of the event (see grey shading in Fig. 7c). The back-trajectories shown in Fig.   7a confirm the continental origin of the flow and as the temperature measured at the station is much lower than 235 K, a liquid-origin of the fog can be ruled out.
The time-series of observational data along the mast reveal a near-constant 3-m temperature of about 200 K during the event and confirm the absence of diurnal cycle during this period of the year. a typical 'exponential' shape to a concave shape (Vignon et al., 2017) owing to a more vigorous turbulent transport of heat towards the surface (Fig. 9). At 18-m the cooling rate is particularly intense and equals 5 K h −1 between 0800 and 1100 LT, 25 August. As an analogy with typical air parcel cooling within updraft in the mid-and high-troposphere, such a cooling rate roughly corresponds to an adiabatic air ascent of 0.10 m s −1 .
Therefore, the initiation of the second fog event is likely :::: seems ::::::: mainly due to a homogeneous freezing process starting between 3 and 42 m a.g.l :::::: aroung ::::: 0900, :: 25 ::::::: August. The density and size of ice crystals become sufficiently large for being well visible in the lidar signal a few hours later. At 0900 :::: From ::::: 1000 LT, 25 August, RHi at 18-m starts a pronounced decrease due to the vapour deposition onto newly-formed crystals and to a downward turbulent flux of water vapour as the vertical gradient 280 of vapour partial pressure between 3 and 18 m is positive (Fig. 9c).
3.2.3 Growth and decay: 1500 LT, 25 August to 1500 LT, 26 August The decrease in RHi at 42-m occurs at 1500 LT and it coincides with a decrease in temperature associated with the deepening of the weakly stable boundary layer ( Fig. 8c and 9a). The decrease in the 42-m RHi also concurs with the increase in fog layer depth visible in the lidar data between 1500 and 1800 LT, 25 August (Fig. 6a) and can therefore be attributed to the deposition 285 of water vapor onto ice crystals. The saturation is reached at 1900 LT, 25 August.
At 1200 LT, 26 August, the fog starts to dissipate from the top and the air at 42-m becomes supersaturated wrt ice (Fig.   8c). A few hours later a decrease in RHi back to saturation occurs probably due to vapor deposition onto the diamond dust preicpitation :::::::::: precipitation streaks that suddenly fall down from the low-and mid-troposphere (Fig. 6a).  of water vapour is sufficiently weak. The evolution of the fog is thereby tightly related with the ::::::: turbulent : dynamics of the boundary-layer which experiences a weak diurnal cycle in the first study case and a dynamical transition between a very stable and a weakly stable state in the second case.
Regarding the potential similarity between Antarctic ice fogs and cirrus cloudswe raised in the Introduction, this study suggests that the homogeneous freezing of solution particles, i.e. a common path to cirrus cloud formation, can be studied in 310 natural conditions near the ground surface of the Antarctic Plateau. More generally, it emphasises that Dome C is a relevant place to carry out observational studies of microphysical processes in ice clouds. Furthermore, the analysis of humidity measurements during the growing phase of fog gives access to the time-scale at which the vapour is depleted, even though it is particularly delicate to disentangle the dynamical -i.e. turbulent mixing -from the microphysical -i.e. deposition onto ice Figure 10. Conceptual scheme of the formation and growth of the two ice fogs studied in the paper. crystals -causes. The development of the fogs is indeed tightly coupled with the dynamics of the boundary-layer. This is a 315 non-negligible difference with cirrus clouds even if the dynamics thereof can be very turbulent :: in ::::: which ::: ice :::::: crystal ::::::::: properties ::::::: strongly :::::: depend :: on ::: the :::::::: dynamics :: of ::::::: gravity ::::: waves :::: (e.g., :::::::::::::::: Jensen et al., 2016) :::: and :::: local :::::::: turbulent ::::: eddies : (e.g., Gultepe and Starr, 1995).
While the available observations at Dome C make it possible to characterise the overall development of ice fogs, they do not give direct information about the type -homogeneous or heterogeneous -of the ice nucleation process and do not allow for a 320 fine understanding of the interactions between cloud microphysics, radiation and turbulent dynamics. Collecting sedimenting ice crystals during ice fog events and establishing formvar replicas thereof in the manner of Santachiara et al. (2016) would allow us to analyse the morphological structure of crystals and to perform chemical analyses of potentially remaining particles after sublimation. Running a large-eddy simulations with an advanced microphysical scheme for cold clouds and capable of simulating the boundary-layer at Dome C (Couvreux et al., 2020) would also help better understand the mechanisms driving 325 the growth and decay of the fogs. Furthermore, investigating the frequency of occurrence of very cold ice fogs at Dome C was beyond the scope of this study. This aspect would deserve further attention in the future to figure out their climatological impacts on the Antarctic Plateau.
The estimation of RHl and RHl ::: RHi from the advanced thermo-hygrometers depends on :

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the measurement of the relative humidity wrt liquid water in the heated inlet RHl h by the HMP-155 probe; the measurement of the temperature of the heated inlet T h by the HMP-155 (PT-100); the measurement of the ambient temperature T by the independent PT100 platinium resistance :::::::::: thermometer.
RHl and RHi are then calculated with the following expressions: as one standard deviation of the obtained distributions for each bin of relative humidity and temperature. In the calculation, we assume that the air reaching the hygrometer sensor in the heated inlet is ≈ 5 K warmer than the ambient air (mean over the measurement period: 4.9 K, standard deviation: 0.7 K).

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The tropospheric depolarization lidar data can be obtained at http://lidarmax.altervista.org/englidar/_AntarcticLIDAR.php. BSRN data are available on PANGAEA (Driemel et al., 2018) Author contributions. EV, LR and CG designed and conducted the study. LR and EV analysed the data and LR made the figures. MDG collected and processed the lidar data. CG collected and maintained the meteorological measurements on the mast at Dome C. AH, JBM and AB provided scientific expertise on cold microphysics and contributed to the results' interpretation. EV wrote the paper with contributions 360 from all the authors.
Competing interests. The authors declare they have no competing interests.