Sudden Sodium Layers: Their Appearanceand DisappearanceShican Qiu1,2,3, Willie Soon4, Xianghui Xue2,3 , Tao Li2,3, Wanyin Wang1,5,6, Mingjiao Jia2,3 ,Chao Ban7 , Xin Fang2,3, Yihuan Tang2,3, and Xiankang Dou2,3

1Department of Geophysics, College of the Geology Engineering and Geomatics, Chang’an University, Xi’an, China, 2KeyLaboratory of Geospace Environment, Chinese Academy of Sciences, University of Science and Technology of China, Hefei,China, 3Mengcheng National Geophysical Observatory, School of Earth and Space Sciences, University of Science andTechnology of China, Hefei, China, 4Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA, 5Gravity andMagnetic Institute, Chang’an University, Xi’an, China, 6Key Laboratory of Western China’s Mineral Resources and GeologicalEngineering, China Ministry of Education, Xi’an, China, 7Key Laboratory of Middle Atmosphere and Global EnvironmentObservation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

Abstract Temperature variation has been proposed to play an important role in the formation of thesporadic sodium layers (SSLs or NaS) in subtropic area, based on the observed significant correlationbetween SSLs and high temperatures. The icy-dust particle, which could form in the extremely coldconditions and act as absorbers of sodium species, was proposed to be a possible candidate for the sodiumreservoir of the SSLs. In this study, the University of Science and Technology of China temperature/wind lidarand the sodium fluorescence lidar at a subtropic station Hefei (31°N, 117°E), China, were used to observesodium density, temperature, and wind profiles simultaneously throughout the SSL events. Based on theobservations of two SSLs occurring on 12 and 13 May 2013, the possibility of an icy-dust layer existing andacting as the sodium reservoir is tested for the first time in details. Both events experienced an extremely coldtemperature (<150 K) several hours before the onset of SSLs, followed by a subsequently fast production ofsodium atoms during a large temperature enhancement (>40 K). An empirical model including two mainsteps is then proposed: first, sodium species are collected by an icy-dust reservoir and stored during theextremely cold phase; second, free sodium atoms could be released from the reservoir by a possible trigger.As a result, this kind of SSLs could possibly be regarded as a quasi-continuous phenomenon caused andmodulated by temperature variations with an icy-dust model that can exhibit intermittent time variationsrelated to the water vapor concentration.

Plain Language Summary Temperature variation, rather than through the mechanism ofcooccurrence of sporadic E layer (ES), has been proposed to play an important role in the formation ofthe sporadic sodium layers (SSLs or NaS) in subtropic area based on the observed significant correlationbetween SSLs and high temperatures. But the detailed process and mechanism are still unclear. Theicy-dust particle, which could form in the extremely cold temperature conditions and as absorbers ofsodium species, was proposed by previous studies to be a possible candidate for the sodium reservoir of theSSLs. However, this most promising scenario has not yet been evaluated in those earlier studies owing to alack of the relevant observations. In this study, the University of Science and Technology of Chinatemperature/wind lidar and the sodium fluorescence lidar at a subtropic station Hefei (31°N, 117°E), China,were used to observe sodium density, temperature, and wind profiles simultaneously throughout the SSLevents and activities. Based on the observations of two SSLs occurring on 12 and 13 May 2013, thepossibility of an icy-dust layer existing at the mesopause and acting as the sodium reservoir is tested andverified for the first time in details.

1. Introduction

Existing observations show that sporadic sodium layers (SSLs or NaS) have obvious regional distinctionsin occurrence frequency, duration, peak height, and seasonal and diurnal distributions, all of which indi-cate a diversity of mechanisms for SSL formation and maintenance in different latitudes and altitudes(Beatty et al., 1988; Clemesha, 1995; Collins et al., 2002; Cox et al., 1993; Daire et al., 2002; Gardneret al., 1995; Qiu et al., 2015; Zhou et al., 1993). Up to now, three mechanisms have been widely studied:the dust theory (suggesting the release of free sodium atoms from dusty surfaces by the energetic

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Journal of Geophysical Research: Space Physics

RESEARCH ARTICLE10.1029/2017JA024883

Key Points:• The possibility of an icy dust existingand acting as the sodium reservoir forsporadic Na layers is evaluated for thefirst time in details

• The possibility of an icy dust existing isdiscussed based on simultaneousobservations of sodium density andtemperature by T/W lidar

• Sporadic sodium layer is more likely tobe a quasi- continuous phenomenonas a result of alternation of the diurnaltidal phase

Correspondence to:X. Dou,dou@ustc.edu.cn

Citation:Qiu, S., Soon, W., Xue, X., Li, T., Wang, W.,Jia, M., et al. (2018). Sudden sodiumlayers: Their appearance and disap-pearance. Journal of GeophysicalResearch: Space Physics, 123. https://doi.org/10.1029/2017JA024883

Received 13 OCT 2017Accepted 16 APR 2018Accepted article online 30 APR 2018

©2018. American Geophysical Union.All Rights Reserved.

auroral particle bombardment; von Zahn et al., 1987), the ES theory (supporting the recombination ofsodium ions from a series of downward ES; Collins et al., 2002; Cox & Plane, 1998), and thetemperature-controlled theory (suggesting the triggering of sodium atoms by some means through tem-perature enhancement in a narrow altitude region due to energy damping during gravity wave breaking;Zhou et al., 1993; Zhou & Mathews, 1995). However, none of these three viable proposals seems to beable to explain the rather wide variety in specific characteristics of SSLs all over the world: Some SSLsobserved at high latitude occurring during the temperature minimum phase (Hansen & von Zahn,1990; Østerpart, 2011), SSLs occurring in a subtropic area were accompanied by no ES (Dou et al.,2009; Gong et al., 2002; Miyagawa et al., 1999), and a decrease in sodium density was also observed dur-ing auroral activity (Heinselman et al., 1998; Tsuda et al., 2013), all of which indicate a particular mechan-ism for different SSLs.

In general, the occurrence of SSLs observed in subtropical latitudes, from 20°N to 35°N, has a weak cor-relation to ES activities (Dou et al., 2009; Gong et al., 2002; Miyagawa et al., 1999; Qiu et al., 2015, 2016).These SSLs, usually lasting for a long period and locating near the centroid height of normal sodium layerat 92 km, are often detected accompanied by large temperature enhancements (Gardner et al., 1995; Liet al., 2005; Qian et al., 1998; Qiu et al., 2015, 2016). Thus, the temperature-controlled theory, instead ofthe ES theory, seems to be more appropriate for explaining the subtropical SSLs (Qiu et al., 2015, 2016).

Under the temperature theory, sodium density is thought to be influenced by a set of temperature-dependent ion-molecule gas-phase reactions (Zhou et al., 1993). The most rapid reaction for creating sodiumatoms in the mesopause, according to our knowledge, is the recombination of sodium ligand complex withfree electrons (Collins et al., 2002; Cox et al., 1993),

Naþ�X þ e�→Naþ X X ¼ O;N2;CO2;H2Oð Þ; (1)

k ¼ 1�10�6

ffiffiffiffiffiffiffiffi200T

rcm�3�molecule�1�s�1; (2)

where k is the reaction rate coefficient. However, this recombination rate is in fact inversely dependent ontemperature, which means the reaction rate would decrease with a temperature increase. At the sametime, the diffusion coefficient of sodium (kDiffusion = 152 × (300/T)�1.85 torr cm2 · s�1; Cox et al., 2001)had a direct, positive dependence on temperature. So the sodium density will probably decrease duringthe temperature enhancement episode. Therefore, it is simply difficult to invoke only the temperaturedependence for chemical reactions to explain the relatively fast generation of sodium atoms duringSSLs. Such an interpretation is in accord with some observations and model simulations showing thatthe maximum temperature had only a weak relationship with the Na peak density (Qian et al., 1998)and the Na density could even have a negative correlation to temperature above 96 km due to the dom-inance of ion-molecule chemistry there (Plane et al., 1999). In fact the scenario for a gas-phase reservoirresponsible for generating sodium atoms was rejected earlier on by Cox et al. (1993). And even Zhouet al. (1993), who first deduced the temperature theory, supported the temperature enhancement onlyas a trigger for the release of sodium from a preexisting reservoir.

The existence of a solid sodium reservoir (e.g., dust/smoke particles) for the SSLs was proposed by increas-ingly more research works and papers (Cox et al., 1993; Gu et al., 1995; Nesse et al., 2008; von Zahn et al.,1987). It was widely accepted that dust could act as a major sink of sodium atoms (Cox et al., 1993; Huntenet al., 1980). The dust particles, usually with a radius about several nanometers, had a sufficient numberdensity of hundreds to thousands particles per cubic centimeter from rocket-borne measurements ormodel simulation results (Brattli et al., 2009; Fentzke et al., 2009; Jensen & Thomas, 1991; Lynch et al.,2005; Megner et al., 2008, 2006; Robertson et al., 2009). These particles could be concentrated into anarrow layer by appropriate wind shear when the particles are charged (Nesse et al., 2008; von Zahnet al., 1987). However, in these studies, the suggested trigger responsible for the release of free sodiumatoms from the dusty surfaces was the energetic auroral particle bombardment, which might factuallybe unfeasible for subtropical SSLs. On the other hand, the formation of SSLs occurred near 95 km wereoften observed to be related to wave-like structures (Tsuda et al., 2011) and wave dissipation phenomenon(Li et al., 2005).

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We propose that the supposed sodium reservoir should contain some specific properties: it needs to haveefficient adsorption ability to store enough sodium sources, it has a fast release mechanism, and lastly, therelease process is related to a warming temperature enhancement; it might have no correlation to ES or aur-oral activities. Recently, Qiu et al. (2015) and Qiu et al. (2016) observed the following empirical scenario fortypical subtropical SSLs: extremely low temperatures below 150 K have always occurred several hours beforethe SSLs and most of these SSLs were formed or generated with a temperature maximum over 190 K. Thesestatistical results showed that the occurrence of low temperature and the corresponding subsequent tem-perature increase is a specific character of these SSLs. According to these results, formation of icy-dust parti-cles, which could form in the extremely cold weather condition and then adsorbs and accumulates sodiumspecies, and could also sublimate in the hot mesospheric weather to release free sodium atoms, was pro-posed as a candidate for the sodium reservoir (Qiu et al., 2015, 2016). However, no final conclusion was madein these two earlier studies, because simultaneous temperature observational records were not available atthat time.

Fortunately, in this work we can use the University of Science and Technology of China (USTC) T/W lidar (Liet al., 2012), as well as the sodium fluorescence lidar (Dou et al., 2009) at Hefei site (31°N, 117°E), to observesodium density, temperature, and wind profiles simultaneously throughout the SSL formation (see section 2).Based on the observations of two SSLs found occurring on 12 and 13 May 2013, the possibility of an icy-dustlayer existing at the mesopause and acting as the sodium reservoir is experimentally tested for the first timein details. An empirical (and comprehensive) model containing two main steps of the formation progressionof SSL formation and maintenance is elaborated in section 3. These results indicate that the SSLs could pos-sibly be described as a quasi-continuous phenomenon formed through temperature variations. And ourresearch essentially pointed out that for the formation of SSLs, three simultaneous conditions need to bemet, that is, a zonal wind shear, the temperature, and the water vapor cycle. If any is not met then a layer doesnot form, or, if a layer is present, and one or more of the three elements changes, then the layer disappears,hence the reasons for intermittency. The conclusion is summarized in section 4.

2. Observations and Results

On 12 and 13 May 2013, two SSLs were detected by the USTC lidar, respectively. Figures 1a and 1b show thesodium density contour images for the two events: Figure 1a shows the sodium lidar operated from 11:49 UTto 20:44 UT on 12 May, and the SSL was maintained from 17:53 UT to 20:44 UT (with no ending of the eventseen before the lidar stopped operating/observing), and Figure 1b shows the sodium lidar operated from11:59 UT to 20:39 UT on 13 May, with the SSL lasting from 16:55 UT to 19:13UT. Figures 1c and 1d showthe peak density profiles for the two events: the solid black curve in Figure 1c shows the peak height ofthe SSL on the night of 12 May located at 93.2 km, with a maximum density of 5,740 cm�3 and an intensityfactor, f (i.e., f = peak density/background density of the whole night), of about 4.0, timed around 18:38 UT.The dotted black line shows the fitted sodium density profile for the background sodium layer through thewhole night. Figure 1d shows similar results for 13 May event reaching its peak density of 4,300 cm�3 (withf = 3.5) at 94.7 km altitude timed around 17:16 UT.

Figure 2 shows the temperature profiles and distributions throughout the two nights. Figures 2a and 2b showthe temperature variations detected by the zonal (Tu) and meridional (Tv) beams on 12 May. The mesopausewent through a cold phase from the beginning of the observation till the onset of the SSL. Temperature keptbelow 160 K for almost 6 hr, with a minimum of 134.4 K ± 1.5 K for Tu at 95 km timed around 14:44 UT.Sounding of the Atmosphere with Broadband Emission Radiometry (SABER) swept Hefei at 13:41 UT, detect-ing a temperature minimum of 142.8 K at 96.8 km (29.6°N, 114.7°E), confirming the extremely cold meso-spheric weather on that day. On the other hand, from about 18:00 UT to 20:00 UT, we observed theappearance of a hot phase with large temperature enhancement in the altitude ranges between 90 and98 km. We noted that the temperature was raised above 190 K in this range, reaching a maximum of202.2 K ± 0.1 K for Tv at 97 km timed around 18:59 UT. The hot phase area overlapped the SSL region, in termsof both duration and altitude. Similar to the situations on 12 May, Figures 2c and 2d show temperature var-iations on 13 May, with a cold phase from 12 UT to 15 UT between 92 and 96 km altitude and a hot phasefrom 17 to 19 UT between 92 and 98 km region. The duration and location of temperature enhancementfor this 13 May event are also in accord to the SSL activity on 12 May.

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The near-simultaneous ES activities observed using a nearby ionosonde in Wuhan (30°N, 114°E) on 12 and 13May are shown in Figures 3a and 3b, respectively. The black squares stand for the virtual height of the echoes(h’ES) detected. These ES echoes were selected if the foES (ES layer’s critical frequency) values were greaterthan zero. On 12 May, a sequence of downward ES sustained from 07:00 UT to 13:00 UT. However, onlytwo scattered ES signals, at 17:30 UT and 17:45 UT, were recorded between 13:00 UT and the onset of theSSL. The two ES echoes had a time interval of more than 4 hr to the termination of the downward ES series,indicating a disconnection of SSL formation from ES activities. Furthermore, ES were not active at all on 13May, with no ES echoes detected during the 4 hr before the SSL.

These two SSLs have similar characteristics from the lidar profiles: the peak altitude locating near the centroidheight of the normal sodium layer (usually 92 km in subtropical area), lasting for a relatively long duration ofover 2 hr, having a large peak density and strong intensity (with f> 3), and in particular, the onset time for bothSSL events began soon after about 17:00 UT. The corresponding temperature profiles and distributions alsoexhibit a similar character, with an extremely cold phase before the onset of the SSL and anoverlappingof tem-perature enhancement during the SSL. On the other hand, ES echoes remained at zero values several hoursbefore the SSLs. All these similarities probably imply the samemechanism for these SSLs’ formation processes.

Figure 1. (a) Sodium density for 12May activity record, with the SSLmaintaining from 17:53 UT to 20:44 UT (with no endingof the event detected). (b) Sodium density for 13 May, with the SSL lasting from 16:55 UT to 19:13UT. (c)The solid black lineindicates the peak density profile of the SSL for 12 May, with a maximum density of 5,740 cm�3 (intensity factor = 4.0)narrowly located at height around 93.2 km and timed around 18:38 UT; the dotted black line indicates the fitted sodiumdensity profile of the background sodium layer through the whole night; the solid red lines with dashed lines indicate asuncertainties in temperature deduction: temperature profile at the time of the maximum density, showing a temperaturemaximum (marked as “Heating”) overlapping with the peak sodium density, and two temperature minima (marked as“Cooling”) above and below the SSL. (d) Peak density (black lines) and temperature (red lines) profiles for the 13 May SSLevent, exhibiting similar features and characteristics as those on 12 May.

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3. Discussions3.1. Possible Influences by the ES Activities

Figure 3a and 3b show the ES echoes detected by Wuhan ionosonde, which exhibits no ES echoes during the4 hr before the onset of the SSLs (the grey vertical lines mark the onset time of the SSLs). The simultaneouswind profiles observed by the USTC T/W lidar east beam and north beam on 12 and 13 May are shown inFigures 4a and 4b, respectively. The positive velocity corresponds to the eastward wind. For both events,the zonal wind shear, covers an altitude ranges from about 80 to 100 km and a time ranges from 12 UT tillthe onset of the SSL, had an opposite polarization to the required wind shear (which needs a westward windlocating above and an eastward wind below, Kirkwood & von Zahn, 1991) for gathering sodium ions through

the v* � B

!drifts in Northern Hemisphere, also indicating an inefficient condition for gathering metal ions

for the formation of ES layers. On the other hand, the formation of SSLs on 13 May 2013 observed by bothUSTC sodium lidar and T/W lidar completely overlapped with the temperature enhancement region. Thisresult is consistent with our previous studies, which suggested that SSLs in this subtropical station usuallyhad weak correlation to ES, but a close relationship to temperature variations (Dou et al., 2009, 2010; Qiuet al., 2015, 2016).

In contrast, another SSL observed on 3 June 2013 by the USTC lidar and T/W lidar shows distinct characters.The sodium density contour image and peak density profile for this comparative event are shown in

Figure 2. Temperature variation activity detected by the (a) east beam (Tu) and (b) north beam (Tv) on 12 May.Temperatures were kept below 160 K (dark blue or purple zones) for almost 6 hr, with a minimum Tu of 134.4 K 1.5 Koccurred around 95 km (Figure 2a) timed at 14:44 UT. On the other hand, from about 18:00 UT to 20:00 UT, when one observedthe occurrence a hot phasewith large temperature enhancement in the altitude ranges of 90 to 98 km. During the hot phase,the temperature was raised to above 190 K (lightest green to orange or red zones), reaching a maximum of 202.2 K 0.1 Kfor Tv at 97 km (Figure 2b) at around 18:59 UT. (c and d) Temperature variation activity recorded on 13May, with a cold phasefrom 12 UT to 15 UT between 92 and 96 km altitude and a hot phase from 17 to 19 UT between 92 to 98 km region.

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Figures 5a and 5b, respectively. Temperature profiles from the USTCT/W lidar exhibit the formation of SSL on 3 June occurring during aparticular cold weather (Figure 5c), quite different from the cases on12 and 13 May. The peak altitude locates at 97.7 km at the top ofthe sodium layer. Distinctly different from 12 and 13 May, from06:00 UT to 13:15 UT on 3 June, a sequence of ES layers descendsdownward from above 120 to 100 km, getting closer to the altitudewhere the SSL occurs (Figure 6).

From a long-term observation at Hefei, we have learned from experi-ence that SSLs occurring at a lower altitude (most likely below 96 km)often had a feature like the case on 12 and 13May, and the higher alti-tude SSLs (usually above 96 km) appeared more like the cases on 3and 13 June (Qiu et al., 2016). Therefore, the SSLs locating below96 km may have a different mechanism from those appearing above96 km. The different characters between the SSL on 3 June and thetwo typical SSLs discussed lead us to believe and propose that the for-mation for the case on 3 June probably has an ES-related formationmechanism, while the current studied cases on 12 and 13 May mayhave a close relationship to temperature variation mechanism.

3.2. The Possibility of Icy-Dust Mechanism

As discussed above, seeking out the previously undetected, preexist-ing sodium reservoir is the key observational constraint on the low-temperature phase of the model. One of the possible sodium reser-voirs identified in previous studies was thought to be thedust/smoke/aerosol particles originated from meteoric ablation (Coxet al., 1993; Nesse et al., 2008; von Zahn et al., 1987). The existenceof dust reservoir was confirmed by the simultaneous occurrence ofdust layer and sporadic metal layer detected by joint airborne rocketsand ground-based lidars (Gelinas et al., 1998, 2005). For example, a

5-km-thick positively charged dust layer was found in the vicinity of the SSL by Gelinas et al. (1998).Another research detected strong correlations between the dust density and neutral Fe profile during fourflights, suggesting that dust particles could serve as a reservoir for atomic metals (Gelinas et al., 2005).

Figure 3. The ES activities observed by the ionosonde in Wuhan (30°N, 114°E) on(a) 12 May and (b) 13 May, respectively. The black squares stand for the virtualheight of the echoes (h’ES) detected. These ES echoes were selected if the foES (ESlayer’s critical frequency) values were greater than zero. The vertical lines in eachpanel mark the time for the beginning of the SSL for the two days. The greydashed curves point out the operation duration of the sodium lidar.

Figure 4. Zonal wind profiles observed by the USTC T/W lidar on (a) 12 May and (b) 13 May. The positive velocity corre-sponds to eastward wind, and the negative velocity corresponds to westward wind. The zonal wind, in an altituderanges from about 80 km to 100 km and a time ranges from 12 UT till the onset of the SSL (roughly represented by the reddashed contour lines), shows an opposite polarization to the required wind shear for gathering sodium ions through the v

*

� B!

drifts in Northern Hemisphere. The red arrows point to the zonal wind contour regions where the SSL occurs.

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In our previous studies, we supposed that the dust reservoir to be mainly icy-dust particles and was assumedprimarily because of the possibility of icy-dust layer existing at the subtropical mesopause zone (Qiu et al.,2015). This supposition was based on the observed anticorrelation between metal layer densities and the

occurrence of mesospheric ice-related phenomena (e.g., polar meso-spheric cloud and polar mesosphere summer echo) during high-latitudesummer when the mesopause temperature fell below 150 K (Lübken &Hoffner, 2004; Plane et al., 2004; She et al., 2006; Thayer & Pan, 2006).The icy-dust particles were able to adsorb metal atoms on the surface asa thin metal film (Bellan, 2008; Fan et al., 2007; Plane et al., 2004; Raizadaet al., 2007; Thayer & Pan, 2006) or packet metal species as nuclei(Olofson et al., 2009; Plane, 2000), which were determined by rocket-bornemeasurements and numerical modeling results (Brattli et al., 2009; Havneset al., 1992, 1996; Robertson et al., 2009). The icy-dust particles, as a result,could act as an effective sink of metal layer through scavenging metal spe-cies around (Gardner et al., 2005; Plane et al., 2004; She et al., 2006; Thayer& Pan, 2006). The final fate of the icy-dust particles/layer is to sublimateunder the warm mesospheric weather condition and leaving behind aconcentrated layer of residual metal species (Plane et al., 2004), which

Figure 5. A comparative case on 3 June 2013. (a) Sodium density variations, with the SSL lasting from 13:26 UT to 14:49 UT.(b) Peak density profile for the SSL, with the peak located at 97.7 km at the top of the sodium layer. (c) Temperature profileson 3 June showing that the entire formation of the SSL maintains in a temperature minimum region. (d) Zonal wind profilesobserved by the USTC T/W lidar on 3 June.

Figure 6. ES activities observed by the Wuhan ionosonde, for the compara-tive SSL case on 3 June 2013. The grey circle stands for the altitude of theSSL and the vertical line marks the onset of the SSL.

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could probably be regarded as a seed or initial phase of sporadic metal layer. Our statistical results show thatin the subtropical station over Hefei, low temperatures below 150 K always appeared before the characteristicSSLs and most of these SSLs occurred during the phase with large temperature enhancements (Qiu et al.,2015, 2016). The water vapor mixing ratio near 93 km, discussed in our case studies, showed a sharpdecrease before the typical SSL but soon after a recovery to normal levels during the SSL (Qiu et al., 2015,2016). The variations of both temperature and water vapor concentration implied a possibility of thecoagulation and sublimation of the supposed icy dust over the subtropical mesopause region (Qiuet al., 2015).

The water vapor variations from 11 to 14May are shown in Figure 8. The water vapor concentrationmaintainsrelatively high content on 0511, with an obvious peak of over 3 ppmv at about 93 km. So the supposed icy-dust particles could form during the cold phase before the 12 May NaS (e.g., during 11 May). As discussed byprevious studies, ice particles could coagulate and grow when the water vapor saturation became greaterthan 1 (Thomas, 1996). The degree of saturation, (Sa), can be expressed as (Thomas, 1996)

Sa ¼ w H2Oð Þpexp 28:548� 6077:4=Tð Þ ¼ e6077:4=T

e28:548 �w H2Oð Þ�p;� (3)

where p is the total gas pressure in N/m2 andw(H2O) is the water vapor mixing ratio. The frost-point tempera-ture Tf, the temperature at which Sa = 1, could be deduced as (Thomas, 1996)

Tf Kð Þ ¼ 6077:437:759� loge w ppmð Þð Þ � loge p mbð Þð Þ ; (4)

where w(H2O) is expressed in units of parts per million (ppm) and p (mb) is in hPa units. Using these equa-tions, the saturation of water vapor and the critical temperature could be estimated based on direct

Figure 7. (a) Zonal wind velocity variations, by Wuhan meteor radar covering the 12–13 May interval. (b) Temperature pro-file, similar to Figure 2a and 2c, but now in the same corresponding time interval with zonal wind data given above inFigure 7a.

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observations. On 12 May, for p = 0.001 hPa (corresponding to 93 km altitude), assumingw(H2O) = 3 ppm, thecalculated critical temperature T0 = 139.5 K. The observed temperature minimum during the cold phase was134.4 K ± 1.5 K at 95 km, lower than T0. So under the temperature minimum condition, the environment couldbecome over saturated for a sustained duration, suggesting a possibility for icy dust to grow.

However, it is worth noting that even for the lowest temperature of 134 K, the calculated saturation degreeof Sa was only 6.0, not so extremely larger than 1. In fact, the estimated frost temperature and saturationdegree are highly uncertain because the imprecision in the values of total gas pressure and water vapor mix-ing ratios may add some uncertainties to the calculated values. Most previous studies, including directobservations and simulation results, support an upper limit of 150 K for ice particles in the mesopause(Aschbrenner et al., 2008; Baumgarten & Thomas, 2006; Bellan, 2008; Berger & von Zahn, 2002; Chandranet al., 2010; Chu et al., 2001, 2004; Gerding et al., 2007; Hervig et al., 2001; Jensen & Thomas, 1994;Lübken et al., 2002; Latteck et al., 2008; Merkel et al., 2009; Murray & Plane, 2003, 2004; Plane, 2000; Rapp& Lübken, 2004; Rapp et al., 2002; Taylor et al., 2002; Thomas, 1991, 2003; von Savigny et al., 2007; vonZahn, 2003; von Zahn & Berger, 2003), or even 154 K (Kirkwood et al., 1998). Even at temperatures largerthan 150 K, say at 155 K, it takes tens of minutes for a 10 nm particle to evaporate assuming a reasonablewater vapor mixing ratio (Lübken et al., 2002). So the lowest temperature of 134 K detected by the T/W lidaris indeed much lower than the upper limit of 150 K. On the other hand, studies on ice particles also showthat the existence of ice depends on several parameters and conditions. The number density of seed nucleimay be the most important condition for ice grains, followed by water vapor and then temperature (Rapp &Thomas, 2006). Results from Fentzke et al. (2009) indicate a large number density of tiny dust particles overArecibo (18.3°N, 67.3°W), which may act as the seed ice nuclei. If such an amount of tiny dusts could alsoexist over Hefei, the nucleation time needed will be much shorter than previously supposed.Furthermore, in previous studies, the ice particles are thought to must have been nucleated within 2 hr(Berger & von Zahn, 2007), which is probably not quite a long duration of cold weather. So the environmentduring the cold phase could indeed be suitable to support the formation and maintenance of icy dust,though these ice particles probably only grow to subvisible particles with tiny size. Furthermore, our T/Wlidar could only operate at night, so we must necessarily have missed the opportunity to document a longperiod of extremely low temperatures when we start operating our equipment during the night hours. Takethe case on 12 May 2013 for instance: We observed a cold temperature at the beginning of our observation,which probably did not start simultaneously with our turning on of the instruments. By contrast, the whole-day observation by T/W lidar over Fort Collins, Colorado (41°N, 105°W), shows that the cold temperature

Figure 8. The recorded variations of water vapor from 11 to 14 May. The water vapor concentration repeats a depletion-enhancement and recovery cycle, especially in exhibiting an obvious reduction of water vapor density on 12 May and areturn to the enhanced water vapor state/condition by 13 May.

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coincided well with the eastward wind and persisted as long as the eastward wind phase continued (seeFigures 1a and 1c of Li et al., 2007). Figure 7a shows the zonal wind observed by the nearest meteor radarat Wuhan, indicating an eastward wind lasting from 16 UT on 11 May to 18 UT on 12 May (marked by redoval in Figure 7a). So the corresponding cold temperature might reasonably persisted for a much longerduration (time covered by the red dashed oval in Figure 7b) than is shown by our T/W lidar nighttime obser-vation in Figure 2a.

3.3. An Empirical Model for the Typical SSLs

The temperature distributions for the two cases in May exhibit a similar character: a cold phase before theNaS and a huge enhancement of temperature during the NaS phase. Figure 8 also shows that the watervapor concentration repeats a depletion-enhancement and recovery cycle for the two cases. And ES werenot active at all on either 12 or 13 May. Based on the observations and discussions above, we concludethat this kind of subtropical SSLs might possibly have similar characteristics and hence indicate a similarmechanism: these SSLs yielded no convincing relation or connection to ES, but instead, we found a clearerspecific relationship with temperature variations. The two events were observed to undergo two mainsteps throughout the formation: first, an extremely cold weather persisting several hours before the onsetof sodium increase, and second, a large temperature warming enhancement (>40 K of temperatureincrease) during the fast generation of sodium atoms. Except for the strong correlation between therelease of sodium atoms and the enhancement of temperature, the only point of these progressions thatcould be experimentally determined was the temperature variations. However, as discussed in the intro-duction, the rate coefficient of the most rapid chemical reactions for generating sodium atoms in themesosphere have inverse dependence on temperature with the eddy diffusion having a positive anddirect correlation to temperature. So as the temperature is raised, the generation speed of the chemicalreactions would be slowed and the diffusion of Na atoms would be strengthened, which should indeedlead to an overall reduction of the sodium density. Therefore, it seems difficult to explain the sharp burstof sodium atoms by temperature enhancement alone. Then it may be proposed that the observedenhancement of sodium density during the high-temperature phase is probably caused by sodium atomsbeing released relatively quickly from an unknown sodium reservoir via a trigger.3.3.1. The Cold (Low-Temperature) PhaseThe SSLs observed on 12 and 13 May both went through an extremely cold temperature before theironset and with a subsequent large temperature enhancement after are both shown in Figure 2.Figure 8 shows that the water vapor concentration repeats a depletion-enhancement and recovery cycle,especially exhibiting an obvious reduction of water vapor density on 12 May and a recovery by 13 May.The water vapor concentration maintains a relatively high concentration on 0511. So the supposed icy-dust particles could form during the cold phase before the 0512 NaS, and as a result the water vaporconcentration later exhibits a depletion on 0512. At 05:26 UT on 0513, there is an obvious peak of watervapor. The temperature pattern and water vapor cycle are well in accord with the icy-dust reservoirdescription proposed recently by Qiu et al. (2015) and Qiu et al. (2016). Once the icy-dust particles haveformed, an updraft will allow the particles to stay for a longer time in an altitude (Reid, 1975). As aresult, during the cooling phase, the tiny icy-dust particles can counteract the gravitational settlingeffects by the upward motion and therefore achieve buoyancy in a small height range, hence effectivelypermits accumulation within a narrow layer.

The capability of the adsorption of sodium atoms on the icy-dust surface during a cold phase can be esti-mated through the collision rate. The sodium density variations throughout the cold phase before the SSLson the nights of 12 and 13 May are shown in Figures 9a and 9b, respectively. Figure 9a (dashed line)shows the difference of sodium density between at 13: 59 UT and at 13: 00 UT in the region from 94to 100 km, with the negative values standing for a reduction of sodium density; the solid line indicatesthe difference of sodium density between at 15:01 UT and at 13: 00 UT. Both curves show a sodium reduc-tion of about 400 cm�3 during the cold phase compared with the initial state of the observation. Figure 9b(dashed line) shows the deviation between sodium densities at 14:46 UT and 12:03 UT, with a maximumdensity difference of 300 cm�3; the solid line shows the deviation between sodium density at 16:01 UTand 12:03 UT, with a maximum density difference of up to 900 cm�3. From Figures 1c and 1d, the sodiumdensities of the background (dash-dotted line with asterisk symbol overlaid) for both nights at

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QIU ET AL. 10

corresponding altitudes were nearly 1,500 cm�3, so the density reduc-tion amplitude varied from about 20% to as high as 60% throughoutthe cold temperature phases. This result indicates the possibility thatthe cold phase could be interpreted as a collection step, under whichthe sodium atoms would be efficiently collected and accumulated froma yet undetected sodium reservoir, representing a substantial reductionof sodium density during this first phase.

The collision rate kT of a sodium atom with dust surface area per unitvolume A is

kT ¼ cA=4 (5)

where c ¼ffiffiffiffiffiffiffiffi8kTπm

ris themean thermal velocity of the sodium atom, k is the

Boltzmann constant, T is the environmental temperature, and m is themass of sodium atom (Hunten et al., 1980).

Form = 23 amu, 1 amu = 1.66 × 10�27 kg, and assuming the average tem-perature during the cold phase of interest equaling to 150 K, the value of kTcould be calculated. From Figure 5 of Hunten et al. (1980), the total dustsurface was A ≈ 5 × 10�10cm�1 near 95 km, so the collision rate

kT ¼ A

ffiffiffiffiffiffiffiffiffikT2πm

r

¼ 5�10�10 cm�1ð Þ�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:38�10�23�150�104 kg�s�2�cm2ð Þ

2�3:14�23�1:66�10�27 kgð Þ

s

¼ 4:65�10�6s�1

(6)

When the average background sodium density was 1,500 cm�3, thetotal equivalent collision rate is about 1500 × 4.65 × 10�6 =6.98 × 10�3 � cm�3 � s�1.

For the SSL event on 12 May, a sodium density reduction of 400 cm�3 wasdetected during about 2 hr. In theory, the duration of absorption for thesesodium atoms can be estimated to be about:

t1 ¼ 400cm�3

6:98�10�3�cm�3�s�1≈15:9hr: (7)

Similar calculations for SSL on 13 May could also be deduced. For a reduction of 900 cm�3 from a time periodfrom 12:03 to 16:01 UT, the theoretical duration estimate is about

t2 ¼ 900cm�3

6:98�10�3�cm�3�s�1≈35:8hr: (8)

The calculated time has a similar order of magnitude to the observed during for the extremely cold period ofabout 2 hr. The discrepancy could be explained by the uncertainties in the model of Hunten et al. (1980) thatthe available dust surface at 95 km might be much larger than 5 × 10�10cm�1 (Cox et al., 1993). The sug-gested dust density above 90 km was in the order of 100 cm�3 by Hunten et al. (1980), but recently, modelsimulations show that the deduced dust number density was likely to be as large as 1,000 cm�3 at 95 km(Megner et al., 2006) or even up to 105 cm�5 (Balsiger et al., 1996). And it was supposed that the total dustsurface would be much greater if the particles were not regularly spherical (Raizada et al., 2007). On the otherhand, the wind shear would affect the falling motion of charged dust significantly (Cox et al., 1993; Havneset al., 1992). As a result, dust below 90 km, with greater concentrations of sodium species coated, could con-ceivably be transported to above 95 km by an upward wind. Furthermore, Nadykto and Yu (2003) suggestedthat the uptake of neutral molecules by charged particles is much more effective for tiny particle under verycold temperature conditions (Nadykto & Yu, 2003). So the actual absorption process might be much shorterthan the theoretically calculated time duration.

Figure 9. (a) The dashed line indicates the deviation between sodium den-sity profiles at 13:59 UT and at 13:00 UT in the altitude ranging from 94 to100 km on 12 May; the solid line indicates the deviation between sodiumdensity on 15:01 UT and 13:00 UT. Both curves showed a sodium reduction ofabout 400 cm�3 during the cold phase compared with the initial state of theobservation. (b) The dashed line indicates the deviation between sodiumdensities at 14:46 UT and 12:03 UT, with a maximum difference of about300 cm�3; the solid line indicates the deviation between sodium density at16:01 UT and 12:03 UT, with a maximum difference of up to 900 cm�3.

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3.3.2. The Hot (High-Temperature) PhaseThe observation results of multiple metal atom and ion layers, exhibiting an altitude sequence (the NaS washighest, the FeS was somemeters lower than the NaS, while the CaS was a few hundredmeters lower than theFeS, and the CaS

+ was lowest, e.g., NaS > FeS > CaS > CaS+), which coincided well with the boiling point-

dependent differential ablation under the thermal ablation theory (Yi et al., 2013). This scenario further sug-gested that these metal species were directly released at the same time from a preexisting reservoir throughevaporation/sublimation process.

The observed strong temperature and wind perturbations during the SSLs suggested that gravity waves playan important role in the formation of SSLs, although the exact role still remains unclear (Qian et al., 1998). Thesupersaturated gravity wave energy must dissipate in a vertical distance of the order of the wavelength,resulting in an enhanced divergence of the vertical flux of horizontal momentum and enhanced wave dragin the same region (Fritts, 1989). The most likely mechanism for gravity wave saturation is via a shear instabil-ity in the generation of turbulence (Fritts, 1989). Dynamic stability was characterized by the Richardson num-ber Ri, which was defined as

Ri ¼ N2

S2; (9)

where N was the buoyancy frequency defined as

N2 ¼ gT

∂T∂z

þ gCp

� �; (10)

g is the gravitational acceleration with a value of 9.5 m/s2 in the mesopause region, T is the atmospheric tem-perature, and Cp is the specific heat at constant pressure with the value of 1,004 J · K

�1 · kg�1, and S is the totalvertical wind shear represented by

S2 ¼ ∂u∂z

� �2

þ ∂v∂z

� �2

; (11)

u and v are the zonal and meridional wind velocities, respectively (Li et al., 2007; Sarkhel et al., 2012; Sherman& She, 2006).

So Ri represents the ratio of the production or suppression of turbulence kinetic energy by buoyant forces(N2) to the mechanical production of turbulence kinetic energy by shear forces (S2; Nappo, 2013). Ri > 0.25is considered a sufficient condition for dynamics stability, where if the fluid is disturbed by a small vertical

Figure 10. Distributions of the calculated time-dependent Richardson numbers: the pink scatters show dynamic instabilities with 0 < Ri < 0.25; the black scattersshow convective instabilities with Ri < 0. The approximately regions of the SSLs are also shown as the background colored contours.

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QIU ET AL. 12

displacement, it will return to the initial state (Nappo, 2013). Dynamic instability would occur over the range0 ≤ Ri ≤ 0.25, and the condition for convective instability is for Ri < 0 (Nappo, 2013).

The calculated time-dependent altitude distributions of dynamic (pink scatters) and convective instabilities(black scatters) from temperature and wind velocity observed by the USTC T/W lidar, as well as the locationsof the SSLs, are shown in Figure 10. It is obvious that the dynamic instabilities (pink scatters) occur first, andthen the convective instabilities (black scatters) appear followed by a SSL, though the approximation of Riz0

0

may filter out some dynamic instabilities.

Figure 11. Time changes in momentum flux on 12 May. The blue line indicates the momentum flux; the green line indicates the zonal wind velocity. (a–l) Themomentum fluxes u0w 0 at different UTs before and after the SSL event. The red arrows point out the zero wind field during the SSL event. The red arrows pointout the zero wind field during the SSL event. An obvious momentum flux between 90 and 95 km occur for the profile at 14:45 UT (b), with a maximum absolute valueof nearly 5 m2/s2. This structure disappeared for the profiles at 17:45 UT (h), 18:45 UT (j) and 19:15 U T (k), indicating the dissipation by gravity waves.

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QIU ET AL. 13

Figure 11 shows the zonal momentum flux u0w0 variations before and after the SSL on 12 May. An obviousmomentum flux between 90 and 95 km occur at 14:45 UT (Figure 11b), with a maximum absolute value ofnearly 5 m2/s2. This structure begins to dissipate at 17:45 UT (Figure 11h) and nearly disappeared after that,indicating a gravity wave breaking. The SSL occurred at 17:53 UT, after the dissipation of the wave. In thewave theory, the breaking gravity wave will deposit momentum into the mean flow and induce vertical heatflux, leading to wind acceleration/deceleration and temperature changes around the breaking region (Liet al., 2007; Liu & Hagan, 1998). This process can produce an inversion layer (or inversion layers) in the heatingregion (s) accompanied by cooling above and below (Li et al., 2007; Liu & Hagan, 1998). Simultaneous profilesof the peak density of the SSLs and temperature on 12 and 13 May 2013 are shown in Figures 1c and 1d,respectively. The temperature profiles are similar to those which are discussed by Li et al. (2007) and Liuand Hagan (1998). All of these results provide an experimental evidence that the gravity wave breakingmay play a key role for the trigger of the SSLs.3.3.3. An Empirical Model for the Formation of Typical SSLs Over HefeiAccording to the discussions in sections 3.3.1 and 3.3.2, the formation processes for the typical subtropicalSSLs such as two events on 12 and 13 May 2013, most likely composed of two main steps: the cold (low-temperature) phase, at which the sodium species were collected efficiently by a sodium reservoir; and thehot (high-temperature) phase, yielding a temperature-induced ablation rise for the release of sodium fromthe reservoir.

In the cold phase, the sodium density is sharply reduced under the low-temperature setting, indicating thecollection of sodium atoms by some reservoir. The possible candidates for the sodium reservoir were pro-posed to be the icy-dust particles, which actually could be regarded as a particular kind of dust, collectingsodium species by packing them as nuclei or by surface absorption of sodium atoms.

During the hot (high-temperature) phase, even though there seemed to be inadequate sodium atoms gen-erated directly through the temperature-controlled chemical reactions, the high temperature itself, ortogether with some other process accompanied by the temperature enhancement, might trigger the releaseof sodium atoms from the preexisting sodium reservoir formed during the initial cold phase. Observations on12 and 13 May showed that these typical SSLs just occurred after the overturning of zonal wind (from eastdirection to west direction) and temperature (from cold phase to hot phase), indicating a nonnegligible cor-relation to the dynamical activities of tides and gravity waves. Calculations of the instabilities for different alti-tudes in section 3.3.2 (see Figure 10) show that instability occurred gradually near the SSL height before itsonset, further supporting an important role of gravity wave breaking throughout the hot phase.

Thus, we propose that the so-called SSL, which was previously suggested to be mere stochastic coincidencesor processes, is more likely to be a quasi-continuous phenomenon as a result of alternation of the tempera-ture (heating and cooling) phase. The sodium reservoir acted as a core for the formation of SSLs: during thecold phase, the sodium reservoir collected sodium species, and then released the gathered sodium in the hotphase via triggers. However, as summarized by Gardner et al. (1995), the ultimate reality for reservoir is still tobe determined based on an ever more increased innovation for direct detections. It is also worth noting thatthis ice-dust model may contain intermittent time variation because of the water vapor variations, such as thecase on 0603, 2013, as discussed in section 3.1.

4. Conclusions and Outlook

On 12 and 13 May 2013, two typical SSLs were detected by a sodium fluorescent lidar and a nearbytemperature/wind lidar at Hefei station. These two events had similar characters in duration (>2 hr), peakheight (near 92 km), intensity (factor> 3), and the onset time (about 17 UT), all of which indicated an identicalmechanism for them. Both events had experienced an extremely cold-temperature (<150 K) initiation con-dition with a density reduction several hours before the onset, compared with a relatively fast generationof sodium atoms during a large temperature enhancement (>40 K of temperature increase). Based on theobservations, the possibility of an icy dust existing at the mesopause and acting as the sodium reservoir isexperimentally tested for the first time in details and this scenario is ultimately confirmed for subtropicalSSLs studied here. During the cold phase, the temperature minimum of 134.4 K was lower than the calculatedfrost-point temperature, indicating the nucleation and growth for the water vapor. The formed icy-dust par-ticles may have a capability to adsorb enough sodium atoms in a given time period. So the SSLs were more

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QIU ET AL. 14

likely to be a subsequent phenomenon as a result of modulation of the temperature (heating and cooling)phase. An empirical model proposed in this study includes two main steps for subtropical SSLs studied here:first, sodium species were collected by a supposed reservoir and stored during the extremely cold phase; sec-ond, sodium reservoir would release free sodium atoms by a trigger, which is characterized by the tempera-ture enhancement that is in turn caused by gravity wave breaking. Our overall finding is such that threeimportant conditions regarding zonal wind shear, temperature, and water vapor cycle must be met in orderfor SSLs to form. Relatedly, if one or more of the three conditions changes, then the sodium layer disappears,which explains the occasional intermittency of the SSL phenomenon as observed.

However, since the entire model is based on the assumption that these SSLs were generated locally, the pos-sibility of sodium atoms recombining from ions in ES layers in other places and being advected to this sitecould not be completely ruled out. So the future studies should further examine the following detailed points:(a) the ES mechanism and (b) the advection of sodium atoms.

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AcknowledgmentsThis work is supported by the NationalNatural Science Foundation of China(41504177, 41674150, and 41274150),the National Key R&D Program of China(2017YFC0602202), the Open ResearchProgram of Key Laboratory of GeospaceEnvironment CAS, and the Young TalentFund of University Association forScience and Technology in Shaanxi,China (20170301). We acknowledge theuse of data from the Chinese MeridianProject for the sodium fluorescencelidar at Hefei, the ionosonde at Wuhan,and the meteor radar at Wuhan (http://data.meridianproject.ac.cn/). The watervapor content is supported by thedatabase of the Microwave LimbSounder (MLS) onboard the EOS Auraspacecraft (https://mirador.gsfc.nasa.gov/cgi-bin/mirador/presentNavigation.pl?tree=project&pro-ject=MLS&CGISESSID=cbea0de262-ce9fcd5e71ea48855f0550). The accessto the sodium density and temperaturedata by the USTC T/W lidar is referred toTao Li (litao@ustc.edu.cn). Temperatureobservation by the Sounding of theAtmosphere with Broadband EmissionRadiometry (SABER) onboard theThermosphere Ionosphere MesosphereEnergetics and Dynamics (TIMED) satel-lite is available from the open database(http://saber.gats-inc.com/browse_data.php). All coauthors thank theEditor, Alan Rodger, and two anon-ymous reviewers for their constructivecriticisms and comments, which haveled to a significant improvement of thispaper. The first author would also like tothank Hong Yan for his usefulsuggestions.

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