Formation of a bottomside secondary sodium layer associated with the passage of multiple mesospheric frontal systems

Abstract. We present a detailed investigation of the formation of a secondary sodium layer at altitudes of 79–85 km below the main sodium layer based on sodium lidar and airglow imager measurements made at Ramfjordmoen near Tromsø, Norway on the night of 19 December 2014. The airglow imager observations of OH emission revealed four passing frontal systems that resembled mesospheric bores which typically occur in ducting regions of the upper mesosphere. For about 1.5 hours, the lower altitude sodium layer had densities similar to that of the main layer with a peak around 90 km. The lower altitude sodium layer weakened and disappeared soon after the fourth front had passed. The fourth front had weakened in intensity by the time it approached the region of lidar beams and disappeared soon afterwards. The column integrated sodium densities increased gradually during formation of the lower altitude sodium layer. Temperatures measured with the lidar indicate that there was a strong thermal duct structure between 87 and 93 km. Furthermore, the temperature was enhanced below 85 km. Horizontal wind magnitudes estimated from the lidar showed strong wind shears above 93 km. We conclude that the combination of an enhanced stability region due to the temperature profile and intense wind shears have provided ideal conditions for evolution of multiple mesospheric bores revealed as frontal systems in OH images. The downward motion associated with the fronts appeared to have brought air rich in H and O from higher altitudes into the region below 85 km wherein the temperatures were also relatively high. This would have liberated sodium atoms from the reservoir species and suppressed the re-conversion of atomic sodium into reservoir species so that the lower altitude sodium layer could form and the column abundance could increase. The presented observations also reveal the importance of mesospheric frontal systems in bringing about significant variation of minor species over shorter temporal intervals.


These beam separations are of the order of the horizontal wavelengths of high frequency gravity waves. Further, many of the high frequency waves propagate with velocities in excess of 50 m/s and their periods are typically less than few 10s of minutes (Pautet et al., 2005;Narayanan and Gurubaran, 2013;Suzuki et al., 2009Suzuki et al., , 2011. All these factors make the studies of the high frequency fast moving features from different beam measurements very difficult. On the night of 19 December 2014, the lidar observations started first in the vertical beam by 13:35 UT (14:45 Central 90 European Time) and finished by 08:00 UT on 20 December 2014. Intense clouds affected the measurements after 23:00 UT. The sodium densities are measured based on the resonant back scattering signal from individual beams along with an error estimate. We consider only those measurements with density errors less than 3% of the measured value. Except in the boundaries of the sodium layer the density error is less than 2% of the measured value. We have used the sodium density data with temporal resolution of 3 min. The 96 m range resolved data are averaged to 1 km altitude steps. We mostly use the 95 measurements from vertical beam and their column integrated values as will be discussed in later sections.
Temperatures are estimated individually from each of the beam. A corresponding error estimate is also made. We consider only those temperature values with errors less than 3% of the measured value. The temperature errors are generally less than 3 K except in the bottom-and top-most regions. We consider the average of all the temperatures from the five beams within 20 minute time duration and 1 km altitude interval as the background temperature in this work. This is done to smooth the 100 fluctuations.
From the background temperature profiles we calculate the buoyancy frequency (N ) at any altitude z as given below.
where the acceleration due to gravity g is taken as 9.54 m/s 2 , T represents the temperature and C P is the specific heat at constant pressure taken as 1005 Jkg −1 K −1 . The temperature gradient in the above equation is calculated using center difference method.

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Buoyancy frequency is also known as Brunt-Väisälä frequency and is a complex quantity. The imaginary value of N indicates that the atmosphere is convectively or statically unstable. A region of higher buoyancy frequencies bounded by the lower values both above and below is a potential thermal ducting zone. Gravity waves with vertical wavelengths nearly twice of the duct width are supposed to get trapped and intensified with constructive interference. This is typical gravity wave ducting due to temperature profiles and known as thermal ducting (Hecht et al., 2001;Snively et al., 2010). However, in addition to the above of sight winds measured by the off-vertical beams in the following way.
In the equations, V mer and V zon respectively correspond to the meridional and zonal winds, V N , V S , V E , V W represent the line of sight winds from the north, south, east and west beams, respectively. θ Z stands for the zenith angle of the beams. Positive corresponds to eastward zonal and northward meridional winds while negative corresponds to westward zonal and southward meridional winds. Since the zonal and meridional winds are measured from off-vertical beams separated by about 35 to 45 km in the altitude region of interest, it is assumed that the winds are spatially uniform over the region covered by the lidar beams.

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Similar to the temperatures, we consider 20 minute averages of zonal and meridional winds in 1 km vertical spacing as the background winds. From the estimated zonal and meridional winds in each altitude, we calculated the vertical shears of zonal and meridional winds respectively, applying central difference method. Positive (negative) wind shear values in the zonal or meridional directions indicate an increase of eastward or northward (westward or southward) wind magnitudes with height.
The vertical winds are obtained from measured Doppler shifts in the vertical beam. The positive values correspond to upward 130 and negative to downward components. Since the vertical winds are smaller in magnitude and are often believed to be the result of waves, instabilities and turbulence, we do not make 20 minute averages for vertical winds. We consider the vertical winds in 3 minute temporal resolution with 1 km vertical resolution.
Another parameter we have estimated with the wind and temperature is the Richardson Number (R i ) given by the following equation: here, R i is the ratio between static stability of the atmosphere given by N 2 and the wind shears given by the denominator of equation 3. It determines whether the atmosphere is stable or susceptible to the formation of instabilities. R i becomes negative only if the N 2 is negative and it indicates that the atmosphere is convectively unstable (or statically unstable). When R i is negative it indicates definite presence of convective instabilities. Theoretical studies (Miles, 1961) showed that when R i is 140 less than 0.25, dynamical instabilities (also referred to as Kelvin-Helmholtz or shear instabilities) can occur and turbulence can be maintained when R i is less than 1 (Hecht, 2004). This is due to the destabilization by the shears. However the upper limit for initiation of the instability is being debated (Hines, 1971;Majda and Shefter, 1998) and it is quite possible for the dynamical instabilities to form when R i is less than 0.5 (Li et al., 2005;Narayanan et al., 2012). Moreover, the existence of low positive values of R i is only a necessary condition and in itself does not guarantee existence of dynamical instabilities. 145 We have calculated R i to check whether the shears are large enough to create dynamical instabilities. Since the instabilities are usually short lived, we use data with 3 minute time resolution and 1 km vertical resolution to calculate R i .

Airglow Imager
A collocated airglow imager is operated concurrently at the same location as a part of the Optical Mesosphere Thermosphere Imagers (OMTI) network (Shiokawa et al., 1999). The imager has a deep cooled 512 x 512 pixel CCD sensor and is equipped 150  The OH airglow images are 2 x 2 binned resulting in image size of 256 x 256 pixels. While binning increases the signal to noise ratio in the images, the spatial resolution is compromised in the lower elevations. Therefore, we consider the region 160 within 130 • field of view for our analysis. The raw airglow images will be curved in the off-zenith regions because they are captured with a fisheye lens in the front end. There are well established unwarping procedures (Garcia et al., 1997;Narayanan et al., 2009a). We have unwarped the airglow images and projected them in equidistance grids so that the wave parameters can be properly estimated. For unwarping, we assumed that centroid altitude of OH emission is at 86 km. Before unwarping, we to the lidar measurements. Figure 1 shows the sodium density measurements from the lidar. Note the occurrence of an intense lower altitude sodium layer between 15:00 and 17:00 UT, which almost disappeared by about 18:00 UT. This pattern is similar in all the five beams 185 and hence it is clear that the lower altitude sodium layer formed in an area larger than 35 square km, the minimum distance between the oppositely directed beams. To better investigate the time evolution of the lower altitude sodium layer, we show the 30 minute averages of sodium density profiles from the vertical beam in Figure 2. By the time of start of the lidar measurements at 13:35 UT, a secondary peak can be noticed already and it was located closer to the main sodium layer. Table 1 lists the altitudes and peak densities of the main layer and lower altitude sodium layer. The peak of lower altitude sodium layer was The variation of column abundance of sodium atoms is shown in Figure 3 along with the range-time-density plot from the vertical lidar beam. There was a gradual increase in the column abundance during the formation and intensification of the lower altitude sodium layer. This indicates that the lower altitude sodium layer is formed due to creation of sodium atoms from some reservoirs instead of from mere redistribution within the existing sodium layer. This is further consolidated by the observation 200 that the column abundance was reduced after the disappearance of the lower altitude sodium layer. An increase in column integrated density of 1.85x10 13 atoms per m 2 occurred during the formation of the lower altitude sodium layer. There was approximately 50% increase in the total column abundance by 16:40 UT compared to the earlier hours around 14:00 UT.   m/s, respectively. Because of the differing phase velocities the distance between F3 and F4 has increased as can be verified visually from images at 16:15 UT and 16:40 UT in Figure 4 and from cross sections in Figure 5. F4 became weak and almost 235 unidentifiable in images after 16:45 UT, close to its passage over zenith. Table 2 lists the characteristics of the fronts. The apparent time periods of the fronts given in the table are obtained as the ratio between the wavelengths and phase velocities. In addition to these four fronts, an east-northeastward propagating gravity wave disturbance is also noticed between 16:10 and 16:50 UT. In Figure 4, it is marked by GW with a dashed arrow indicating its propagation at 16:39 UT. Aurora started to intensify from the Northern horizon in OH images from around 16:55 UT. However, most parts of the images were clear 240 to reveal wave signatures till about 17:20 UT. The auroral features extended southward and completely masked any wave signatures that could have occurred afterwards. This can clearly be seen from Figure 6 showing the zenith intensity time series.

Secondary sodium layer in lower altitudes
The intensities are averages of 16 x 16 pixels surrounding the zenith region of the raw OH images. From Figure 6, it may be further verified that both F2 and F3 are accompanied by brightness enhancements in OH images indicating that they are bright bores. The sharp increase in intensity associated with aurora are seen from about 17:20 UT. It may be noted that there is no 245 evidence in the past that the aurora enhances OH Meinel band brightness directly. The observed enhancement is due to the entry of auroral light intensities through the broadband filter used to measure OH Meinel band emissions. Nevertheless, it is worth noting that the signatures of the fronts and the gravity wave weakened significantly by 16:50 UT, well before the aurora masked OH observations. This may also be seen from the last image in Figure 4 and the lowermost cross section in the right panel of Figure 5. 13 https://doi.org/10.5194/acp-2020-803 Preprint. Discussion started: 23 September 2020 c Author(s) 2020. CC BY 4.0 License.

Background temperature and wind conditions
Now we discuss the background temperature and wind conditions during the above mentioned observations. Figure 7(top) shows the background temperatures. The temperature profile shows a downward phase progression at the rate of 1 km/hr which might be due to the tidal effects. Of greater interest are the existence of an inversion layer close to 90 km altitude and enhanced temperatures in the lower altitudes coinciding with that of the lower altitude sodium layer. The temperature  14 https://doi.org/10.5194/acp-2020-803 Preprint. Discussion started: 23 September 2020 c Author(s) 2020. CC BY 4.0 License.  Figure 9.

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The shears in the meridional wind were much stronger than those in the zonal wind. Both Figures 8 and 9 show a downward phase progression very much similar to that seen in the temperature profiles. These large scale downward phase propagating features might be the result of tides.

Discussion
The results described above lead to the following important observations that have to be explained. 1) There was a rare formation of sodium layer in altitudes below 85 km, 2) There was an enhancement in the column abundance of sodium atoms during 285 the formation of this layer and the column abundance started to decline after its disappearance, 3) There were four consecutive mesospheric fronts coinciding with the duration of this lower altitude sodium layer observed with OH images but not with OI557.7 nm images, 4) The mesospheric fronts were associated with enhanced OH airglow intensities behind their passages and resembled bright mesospheric bores, 5) Temperatures were relatively higher in the region of lower altitude sodium layer, 6) There was a higher stability region indicating a thermal ducting structure matching with the altitudes of main sodium layer 290 16 https://doi.org/10.5194/acp-2020-803 Preprint. Discussion started: 23 September 2020 c Author(s) 2020. CC BY 4.0 License. located above the altitudes of lower altitude sodium layer, and 7) Horizontal winds had intense shears above 93 km along with a reversal in the meridional winds around 16:00 UT in the lower altitudes.
We have seen in Figures 4, 5 and 6 that the observed fronts are followed by regions of increased OH airglow indicating that they might be mesospheric bores. F1 showed formation of new undulations as well. However, no clear signatures of the fronts were seen in OI 557.7 nm emission images. This is surprising given their intense signatures in the OH emission region.

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The reason appears to be the existence of large wind shear in the region between OH and OI 557.7 nm emission layers as indicated by Figures 8 and 9. The fronts appeared to have disappeared owing to the critical level interaction between 93 and 95 km wherein the background wind speeds surpassed the speed of the observed fronts. This can be seen better with the help of Figure 11.
In the above equation, m and k stands for the vertical and horizontal wave numbers respectively, N is the buoyancy frequency, u and c denote the background wind along the wave propagation direction and the phase velocity of the wave respec-320 tively, u zz and u z indicates d 2 u/dz 2 and du/dz respectively and H is the scale height. Figure 12 shows the calculated m 2 profiles for each of the fronts with background conditions corresponding to the time of their passage over the zenith. Also lines at m 2 values indicating the vertical wavelengths of 3 km, 5 km and ∞ are shown. Since we do not know the horizontal wavenumber k for F3, the last term in equation 5 is left out when calculating its vertical wavenumber m.
Generally, a wave undergoes reflection when the m 2 turns negative in a region. When there is a region of positive m 2 325 bounded by regions of negative m 2 above and below, the wave becomes ducted. A critical level occurs when the vertical wavelength of a wave approaches 0 and this will be seen as a sharp increase in the m 2 profile. Critical levels ensure that wave energy does not propagate beyond the level but they also contributes to stronger ducting at times. Strong wave reflection may happen when the critical level exist just above a region of stronger stability. In essence, existence of critical level at the top of a duct results in a stronger duct with intense reflection of the wave because the leakage of energy through the duct is strongly 330 restricted by the critical levels situated above (Lindzen and Barker, 1985;Skyllingstad, 1991;Ramamurthy et al., 1993). This has happened in the present case as can be inferred from Figure   behind the fronts imply that these fronts were bores associated with a sudden downward push causing brightness enhancements in the underlying OH airglow.
The increase of column abundance of sodium during the formation of lower altitude sodium layer is clearly seen from Figures in sodium concentration in higher altitudes. This is also revealed by the red and green lines in Figure 13. Interestingly, there was a reduction in the sodium densities around 15:30 UT in the altitude range of 88 to 95 km corresponding to the main layer.
This time matches closely with the passage of F2 over the lidar beams. Figure 13. Column integrated sodium densities in selected altitude regions (blue and red lines) to compare with the total column abundance (black line) The positive correspondence between the sodium density and temperature variations is already well known (Zhou et al., 350 1993;Zhou and Mathews, 1995). While there was relatively higher temperature in the region of lower altitude sodium layer below 85 km, it does not occur only on this day. Temperatures in the range of 220 to 250 K are fairly common below 85 km in winter months (Lübken and von Zahn, 1991;Nozawa et al., 2014;Takahashi et al., 2015;Hildebrand et al., 2017).
To study the role of temperature in further detail, we show the sodium densities and averaged temperatures separately for the height regions corresponding to lower altitude sodium layer (81-88 km) and the main sodium layer (88-95 km) in Figure   355 14. Note that we have used temperature data with 3 minute temporal resolution herein so that we can effectively compare them with the sodium density variations. Both densities and temperatures are 3 point smoothed in the plots. Figure 14(left) shows the integrated sodium densities and average temperatures for the region of lower altitude sodium layer from 81 to 88 km. The temperatures below 83 km are noisy resulting in large fluctuations. While there are some matching regions between the densities and temperatures, the overall temperature variations differ from that of the sodium density in the lower altitude 360 sodium layer region. For instance, the sodium densities continued to decrease while temperatures were nearly stable after 17:00 UT. This further indicates that the lower altitude sodium layer was not merely due to the temperature enhancement. However, the existence of higher temperatures in the lower altitudes is indisputable (see Figure 7(top)).
20 https://doi.org/10.5194/acp-2020-803 Preprint. Discussion started: 23 September 2020 c Author(s) 2020. CC BY 4.0 License. Figure 14(right) shows similar plots as above between the altitude region of 88 and 95 km corresponding to the main sodium layer. Note that there was a temperature reduction just before 15:30 UT in this altitude region which is coincident with 365 the density reduction. F2 has crossed the zenith region around 15:35 UT. It is highly likely that this temperature reduction corresponded to the signature of the passage of F2. The density reduction in the main sodium layer altitudes might therefore be due to the sudden reduction in temperature associated with passage of F2. It is known that there may be phase delays between the temperature and airglow intensity variations during passage of mesospheric bores (Taylor et al., 1995;Pautet et al., 2018).  There was supposedly a downward force associated with the bright bores seen as fronts, which brings the minor constituents from higher altitudes to lower altitudes. This is important for constituents like O and H whose mixing ratios increase with altitude. Therefore, the downward transport will increase their concentrations in lower altitudes and affect the chemistry of the region. Indeed such a downward force and associated movement is proposed as a reason for sudden intensity variations 375 following the bore jumps (Dewan and Picard, 1998). It is believed that these bores become bright in OH emission because the OH emission peak moves to lower heights where temperatures are higher (Dewan and Picard, 1998;Medeiros et al., 2005). In addition, such a downward movement also brings in O and H from upper altitudes to lower altitudes thereby increasing their concentrations. This is because the mixing ratios of O and H increase with altitude in this region, as mentioned above. In this case, the bores are supposed to have occurred in the region between 86 and 93 km (F1 appeared to have occurred a few km 380 higher). The start of the enhanced stability region associated with the temperature inversion around 86 km seems to determine the lower boundary of the duct channel (see Figure 7). The upper boundary appears to be a combination of the temperature duct along with intense wind shears causing critical level to the propagating wavelike structures. The bores would have occurred near the center of the duct at ∼90 km from where the downward movement would have got initiated. In addition, it may be noted that the enhanced temperatures shown in Figure 7(top) at altitudes below 85 km also match well with the duration of 385 observation of the fronts. There may be a contribution from adiabatic compression immediately below the altitudes of the duct due to the downward push casued by the bores. However, a detailed investigation on this aspect is beyond the scope of present work.
It is known that higher H concentration occurring in the region with relatively higher temperature results in higher OH emission rates as per the following reaction.
The reaction R1 and its rate constant are taken from Smith and Marsh (2005). It can be seen that reaction R1 depends on temperature and higher temperatures result in higher reaction rates. Noteworthy is the fact that a downward push explains an enhancement in OH airglow. On 19 December 2014, existence of the strong thermal ducting region coincident with the altitudes of main sodium layer would have favored formation of a mesospheric bore resulting in such a downward force and 395 transport of minor species. Now, we discuss how the sodium chemistry is affected by an increased concentration of H and O due to downward transport.
At altitudes above 90 km, the densities and collisions are so low that formation of complex multi atomic molecules are often difficult. Further, during daytime higher EUV photon flux contributes to the dissociation of complex larger molecules. In lower altitudes, a larger portion of the sodium atoms react with other atoms and molecules and form reservoir species. The most 400 important reservoir species for sodium is N aHCO 3 , which liberates sodium atoms when interacting with H (Plane, 2004;Plane et al., 2015).
In addition N aOH and N aO can also liberate sodium as given below while interacting with H and O, respectively.
The reactions R2-R4 and corresponding rate constants are taken from Plane (2004);Gómez Martín et al. (2016). While the reactions R2-R4 are all dependent on temperature, the temperature dependence is weak for the reaction R4. The reaction R2 has a significant activation energy and hence is strongly dependent on temperature as can be seen from its rate expression.

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Reactions R2 and R3 clearly show that more sodium can be liberated when atomic H is transported from higher altitudes.
There is sufficient atomic H in the region between 80 and 90 km (e.g. Plane et al., 2015, Figure 4) so that a downward flux from 90 km region increases the concentration and mixing ratio of H in lower heights. Though the mixing ratio of N aHCO 3 decreases with altitude in the region between 80 and 90 km, the lower altitude sodium layer forms in the region where the N aHCO 3 and N aOH in the region and the rate with which the reactions occur will be higher when the temperature in the lower altitudes are higher. Since the temperatures were comparatively higher below 85 km more sodium atoms would have liberated resulting in a profound secondary sodium layer in the lower altitudes. Due to relatively lower values of temperature in the altitudes between 84 and 88 km, the amount of liberated sodium will be smaller in spite of the fact that the downward H flux was supposed to be present in those altitudes as well. In addition, in those heights the downward transport occurs in the 420 region of decreasing mixing ratio of N aHCO 3 , the most important reservoir species of sodium. This explains an apparent gap between the main sodium layer and lower altitude sodium layer.
The principle loss of sodium atoms below 85 km is through the formation of N aHCO 3 , N aOH, N aO, N aO 2 and meteor smoke particles. However, atomic sodium undergoes only the following two reactions directly, whose products further react with minor species in the mesosphere to produce more stable reservoirs like N aHCO 3 .

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The reactions and corresponding rates are taken from Plane et al. (2015). The reaction R6 decreases with increase in temperature and is of secondary importance compared to reaction R5. Therefore, in the region of lower altitude sodium layer wherein 430 temperatures were higher, the removal of sodium atoms by O 2 was weaker.
The two reactions above and corresponding rates are from (Smith and Marsh, 2005 O would have stopped resulting in removal of sodium by regeneration of reservoir species from atomic sodium in the lower altitudes. Further, it may be noted that the temperatures below 85 km also decreased after the disappearance of the fronts.
Because we did not have airglow imaging observations before 14:40 UT and aurorae appeared after 17:15 UT, we are unable to probe the origins of the mesospheric fronts. Moreover, the focus of the present work is towards understanding the unusual formation of lower altitude sodium layer and its relation to the observed mesospheric fronts rather than studying the formation 455 and characteristics of the mesospheric fronts themselves. The lower altitude sodium layer occurred at altitudes that are too low for the ion chemistry to play any important role and hence we did not discuss ion chemistry associated with sodium production.

Conclusions
In this work, we discuss the sodium lidar and airglow imaging observations made on 19 December 2014 from Ramfjordmoen (69.6 • N, 19.2 • E) near Tromsø, Norway. An unusual occurrence of a sodium layer below 85 km was noticed following the 460 passage of four successive mesospheric frontal events observed in OH airglow images (Figures 1-3). The fronts resembled bright mesospheric bores showing an enhancement in the OH airglow intensity following their passage (Figures 4-6). The existence of a favorable ducting region for formation of the bores was present ( Figure 12). Both temperature and wind profiles (Figures 7 and 8) contributed to the duct. The horizontal winds showed intense shearing region from ∼93 km altitudes ( Figure   9). The critical levels occurring in this region restricted the propagation of the fronts to the OI 557.7 nm airglow altitudes.

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The temperatures in the lower altitudes were in the range of 220 to 250 K during the formation of lower altitude sodium layer ( Figure 7). While this magnitude of temperatures is not uncommon in the altitudes below 85 km, on this night the temperature enhancement coincided with the duration of the fronts. An enhancement in the column abundance of sodium was also seen to occur coincidentally with the formation of the lower altitude sodium layer (Figures 3 and 13). Further analysis showed that the temperature alone cannot explain the formation of lower altitude sodium layer ( Figure 14). We explain the observations 470 consistently as follows.
The strong ducting appears to have provided favorable condition for formation of multiple mesospheric bores that are identified as the frontal features in OH images. The downward transport of air rich in H and O associated with the mesospheric bores appeared to result in enhancement of OH airglow intensity and release of atomic sodium from the reservoir species in the lower altitudes. The existence of relatively higher temperature region below 85 km compared to the temperatures in higher