The sporadic sodium layer: a possible tracer for the conjunction between the upper and lower atmospheres

. In this research, we reveal the inter-connection between lightning strokes, reversal of the electric ﬁeld, ionospheric disturbances, and a sodium layer (Na S ), based on the joint observations by a temperature/wind ( T/W , where the slash means “and”) lidar, an ionosonde, an atmospheric electric mill, a ﬂuxgate magnetometer, and the World Wide Lightning Location Network (WWLLN). Our results suggest that lightning strokes could trigger or amplify the formation of an Na S layer in a descending sporadic E layer (E S ), through a mechanism that involves the overturning of the electric ﬁeld. A conjunction between the lower and upper atmospheres could be established as follows by these inter-connected phenomena, and the key processes could be suggested to be: lightning strokes → overturning of the electric ﬁeld → E S generating Na S .


Introduction
The upper mesosphere-lower thermosphere (MLT) is the interface region for momentum and energy exchanges between the Earth's low atmosphere and outer space. However, on account of the limitations of detection methods, this region re-mains the least known part of our planet's atmosphere (Wang, 2010). Fortunately, the metal layers (especially the sodium layer), which is located between about 80-110 km, could possibly act as a window to detect the MLT parameters by means of fluorescence resonance lidars (Gardner et al., 1986;Gong et al., 2002Gong et al., , 1997. With an active chemical property, a large resonant backscatter cross section, and a high abundance of sodium atoms, the sodium layer has been widely observed and studied all over the world (Marsh et al., 2013;Collins et al., 2002;Plane, 2003Plane, , 1999. The sporadic sodium layer (SSL or Na S ), with a neutral sodium density that could double within several minutes, is the most fantastic phenomenon observed in the sodium layer. Since first reported in 1978 (Clemesha et al., 1978), many mechanisms, involving meteor injection (Clemesha et al., 1980), a dust reservoir (von Zahn et al., 1987), recombination of ions and electrons in sporadic E layer (E S ) (Cox and Plane, 1998), and hightemperature theory , have all been proposed. Because the Na S is suggested to have a connection to so many atmospheric parameters, the metric or phenomenon could be appropriate in acting as a tracer for studying the inter-connection between the middle and upper atmospheres. Up to now, a large number of observations have reported a diversity of Na S features, but the exact mechanism for Na S is probably still uncertain (Collins et al., 2002;Cox et al., 1993;Daire et al., 2002;Gardner et al., 1995;Qiu et al., 2015;Zhou and Mathews, 1995;Zhou et al., 1993).
In this research, we apply five joint observations for our case studies and statistical work: (1) one temperature/wind (T /W , where the slash means "and") lidar at Hefei (31.8 • N, 117.2 • E), providing observations of sodium density, mesopause temperature, and zonal wind; (2) an ionosonde in Wuhan (30.5 • N, 114.6 • E), detecting the E S and ionospheric echoes in different modes; (3) an atmospheric electric mill (30.5 • N, 114.5 • E), giving simultaneous electric field variations; (4) a fluxgate magnetometer (30.5 • N, 114.5 • E), probing the H, D, and Z magnetic field components; and (5) the World Wide Lightning Location Network (WWLLN), observing the location and power of a lightning stroke. The purpose of this study is to examine the possibility of Na S acting as a practical, robust tracer for the conjunction between the upper and lower atmospheres. Our results suggest that lightning strokes may have an influence on the lower ionosphere, leading to the occurrence of Na S , with the atmospheric electric field probably playing an important role.

Observations and results
2.1 An Na S event during the overturning of the electric field A sporadic sodium layer is detected on the night of 3 June 2013, by the T /W lidar (Li et al., 2012). The peak density observed by the west beam of the T /W lidar is 8650 cm −3 . This Na S event occurs much higher above the centroid height of the sodium layer (normally at about 92 km) (Qiu et al., 2016). Figure 1a shows that the sodium density begins to increase at about 13:20 UT, while the largest intensity of sodium enhancement occurs from about 14:20 UT, with a peak density located around 97.65 km at 14:37 UT. The simultaneous temperature observation by the T /W lidar reveals that this Na S occurs in a cold region (Fig. 1b), so the high-temperature mechanism appears to be inapplicable for this event.
On the other hand, the zonal wind exhibits a suitable wind shear for creating those sporadic E layers, with a westward wind above and an eastward wind below (Fig. 1c). The E S layer is predicted to form around the border of the wind shear. Observations by the ionosonde at Wuhan indeed show active sporadic E layers on that day ( Fig. 2a and b). The E S series keep traveling/propagating downward starting around 06:30 UT and decreases to a minimum value while the Na S occurs coincidently at about 13:20 UT. Thus this Na S is better explained by the E S mechanism, in accordance with our previous study which shows that an Na S higher than 96 km tends to be controlled by the E S mechanism (Qiu et al., 2016). Although the content of sodium ions in E S layers seemed to have insufficient concentration (von Zahn et al., 1989), it has also been proposed that the ions could be effectively concentrated by the wind shear (Clemesha et al., 1999;Cox and Plane, 1998;Nesse et al., 2008). On the other hand, laboratory results show that the ligand complexes of Na + q X would form and thus speed up the recombination of ions in mesopause conditions (Collins et al., 2002;Cox and Plane, 1998;Daire et al., 2002). The calculated reaction rate suggests that the formation of cluster ions is enhanced at lower temperatures, in accordance with the cold region observed in Fig. 1c where the sporadic sodium layer occurs.
More details about the atmospheric parameters are shown in Fig. 3. The time series of sodium density on the peak height display a sharp enhancement from 14:20 UT (marked by the red dashed vertical line in Fig. 3a). The atmospheric electric field detected by the mill exhibits an overturning at around 14:20 UT, alternating from a downward direction to upward (Fig. 3b). It can be clearly observed that the enhancement of sodium density occurs coincidentally with the overturning of the electric field, as highlighted by the red dashed vertical line in Fig. 3. A nearby fluxgate magnetometer provides the horizontal magnetic field H (nT) (Fig. 3c), showing disturbances at 14:15 UT. The total magnetic inten- H 2 + D 2 + Z 2 ) from fluxgate magnetometer observations (the calculated values are plotted in Fig. 3d).
It is worth noting that the overturning of atmospheric electric field discussed here is theoretically rough, since the electric field at the lower ionosphere will be modulated as well (e.g., with a value of several mV m −1 ; Seyler et al., 2004). Nevertheless, model simulations from the electrodynamics show that the upward electric field in the upper atmosphere is proportional to the source current in the troposphere (Driscoll et al., 1992) and that the upward current would continue transmitting to the heights of 100-130 km of the dynamo region where E S occurs most frequently . The model, based on rocket observations, shows that the atmospheric electric field has a similar scale and the same polarity from the ground to the altitude of the ionosphere (Abdu et al., 2003). Thus, the electric field detected by a groundbased mill could reasonably be a reflection of the actual situation in the lower ionosphere, at least for the trends and tendencies of variations.

Possible influences by the atmospheric electric circuit
The atmospheric electric circuit is formed by the ionosphere and ground surface with the dielectric medium (e.g., the neutral atmosphere) sandwiched between them (Driscoll et al., 1992;Harrison, 2020;Jánský and Pasko, 2014;Lv et al., 2004;Roble and Hays, 1979;Rycroft et al., 2000Rycroft et al., , 2007Suparta and Fraser, 2012;Tinsley, 2000). The lightning phenomena and thunderstorms, acting as the electric generator for the circuit, drive an upward current to the ionosphere. In a fair-weather regime, the electric field is directed downward to the earth surface (E > 0), making a closed global electric circuit (see Fig. A1 in the Appendix). The electric field could vary through two distinct ways as follows. The first one is the changing magnetic field explained by Faraday's law (e.g., ∇ · → E = − ∂ → B ∂t ). However, observations by the fluxgate magnetometer show that there is just a small disturbance of the magnetic field during the overturning of the electric field. The other way is the electrostatic induction following Coulomb's law ( → E = 1 4πε 0 Q r 2r ). The connection between the lightning stroke and the overturning of the electric field could be explained by the classic thunderstorm charge model through the electric imaging method based on Coulomb's law (i.e., this model could be supported by the classic electrodynamics textbook written by Griffiths, 1999). A typical thundercloud (e.g., pairs of (Q 1 , −Q 2 ) or (−Q 3 , Q 4 ) in Fig. A1), with a dipole of positive charge located above a negative charge part, which would produce an upward electric field toward the ionosphere (see more details in Appendix A).
According to the observations from WWLLN, we find two regions (red ovals A and B in Fig. 4)   area. Thus, the pairs of (Q 1 , −Q 2 ) and (−Q 3 , Q 4 ) could refer to the lightning area of part A and B in Fig. 4. Since thunderstorms could trigger the breakdown process within a rather large area (Leblanc et al., 2008) and influence the ionosphere with around more than 800 km range horizontally away from the lightning center (Johnson and Davis, 2006;Johnson et al., 1999), the whole area above might undergo a breakdown easily around Q 1 -Q 4 (e.g., the whole shadow zone in Fig. 4, involving the two strongest lightning areas and the two observing stations).
In previous studies, lightning strokes in the lower atmosphere were reported to cause a reduction of electrons of the ionosphere (Shao et al., 2013) and conversely an enhancement of sodium density in the metal layer (Yu et al., 2017). Those two scenarios are in accordance with our current results presented above, i.e., with a depletion of E S at 13:20 UT and a consequential occurrence of Na S . Although such an idea/picture was proposed a long time ago (Griffiths, 1999), this is the first time that one can apply the imaging method for observing thunderstorms to explain the link between upper and lower atmospheres through an overturning of the upward electric field. Furthermore, the results from different channels of the Wuhan ionosonde exhibit extraordinary echoes in different modes during the lightning period ( Fig. 5a-l). Figure 5ac show that, from 13:15 to 13:45 UT, the echoes gradually increase. Note that the powerful lightning period begins at 13:15 UT as well, with the sodium density enhancement occurring at about 13:20 UT. Figure 5d-g show that the most intense echo signals occur during 14:00 to 14:45 UT, while the largest intensity of sodium enhancement begins at 14:20 UT and the sodium density peaks at 14:40 UT. The overturning of the electric field also occurs at 14:20 UT. Figure 5h-j show that, from 15:00 UT to 15:30 UT, the signals weaken gradually; Fig. 5k and l show that, the echoes vanish after 15:45 UT. Afterwards, no strong stroke is detected again in the discussed area. Meanwhile, the ionospheric echoes diminish after 15:45 UT, and the overturning of the electric field also recovers at about 15:30 UT. Thus, in this case the ionospheric echoes and the lightning activities exhibit an obvious synchronous behavior.

Discussions
Normally, the midlatitude E S layers would be brought down gradually by tidal fluctuations (Mathews, 1998). The E S theory predicts that when a series of E S layers descend below 100 km, metal ions will be depleted through many chemical reactions involving ions and electrons (Cox and Plane, 1998). The main chemical reactions and corresponding rate coefficients for the sodium species under mesopause conditions are summarized in Table 1 (Cox and Plane, 1998;Jiao et al., 2017;Plane et al., 2015;Plane, 2004;Yuan et al., 2019). The application of reaction branching probabilities to Reactions (R3) to (R11) yields the following first-order rate coefficients for the neutralization rates of Na + ions (Plane, 2004): where Pr denotes the branching probability. The first-order conversion rate of k (Na + → Na) can be computed as a function of height using typical values for N 2 , O 2 , O, and CO 2 from Whole Atmosphere Community Climate Model with Na chemistry (WACCM-Na) (Yuan et al., 2019). The results are given in Fig. 6. The simulation results show that an inflection point of k (Na + → Na) comes out at around 100 km, and below that altitude, the sodium ions would recombine with electrons efficiently through cycling chemical reactions under a large k value. Then the production rate of Na could be obtained from d[Na]/dt = k (Na + → Na)[Na + ] (Plane, 2004). The number density of electrons n e could be retrieved through foE S = ω pe 2π = n e e 2 4π 2 m e ε 0 1 2 ≈ 9 10 −6 n e , with foE S in MHz and n e in cubic centimeters (Bittencourt, 2004). The foE S observed at 14:45 UT is equal to 5.75 MHz, indicating n e ≈ 1.24 × 10 4 foE S itive ions are mostly composed of metal ions, with an observed ratio of [Na + ] of 7.41 × 10 −2 (Kopp, 1997), the estimated [Na + ] equates to 3.03 × 10 4 cm −3 . The approximate value of k (Na + → Na) below 100 km is equal to 10 −4 s −1 . Then the production rate of Na d[Na]/dt = k (Na + → Na)[Na + ] is equal to 3.03 cm −3 s −1 , in accordance with the required source strength of sodium atoms of 3 sodium atoms cm −3 s −1 for the formation of Na S (Cox et al., 1993). Table 1. Ion-molecule reaction rate coefficients for Na summarized from previous reports (Cox and Plane, 1998;Jiao et al., 2017;Plane et al., 2015Plane et al., , 2004Yuan et al., 2019).
On the other hand, a link between the reverse electric field and E S variations could be established through the acceleration of electrons. In classical electromagnetism, positive particles will move along the direction of the electric field, and negative particles do the opposite (Griffiths, 1999). Since metal ions are much heavier than electrons, the ions would drag electrons to move/drift together; a process known as the bipolar diffusion (Griffiths, 1999). So during the initial phase under quasi-equilibrium conditions, the ions and electrons would co-move downward together along a southward electric field. In a partially ionized plasma, the characteristic frequencies for ions and electrons are associated with the collisions of the plasma particles with stationary neutrals (e.g., the electron-neutral collision frequency ν en and the ion-neutral collision frequency ν in ). The collision frequency ν sn for scattering of the plasma species s by the neutrals is (Shukla and Mamun, 2002) ν sn = n n σ n s V T s , where n n is the neutral number density, σ n s is the scattering cross section (which is typically of the order of 5 × 10 −15 cm 2 and depends weakly on the temperature T s ) and V T s = (k B T s /m s ) 1/2 is the thermal speed of the species s.
Then under a nonequilibrium phase (e.g., at the point of the electric field overturning), each plasma species has a different relaxation time τ = 1 ν (the time needed for reestablishing equilibrium again through collisions). The relaxation time for ions and electrons would be quite different in a partially ionized plasma with the electrons responding much faster than the heavier sodium ions do (since m i m e ). This discrepancy would cause a charge separation temporarily. The single electrons move opposite along the electric field, which means in the upward electric field they would be rapidly accelerated downward, while the ions could be regarded as essentially remaining unchanged. The electrons would reverse rapidly before the ions can respond similarly to the velocity overshoot effect for electrons. During the relaxation phase, the recombination between electrons and ions would probably be triggered through collisions because the relative impact velocity increases and the long-range attraction between the ion and electron becomes less effective.
Based on the above results, a possible mechanism for Na S could be suggested by the following four steps: (1) strong lightning strokes produce an upward atmospheric electric field toward the ionosphere; (2) the reverse of the electric field would cause a temporary charge separation, leading to a trigger of recombination between electrons and ions; (3) when the E S descends below about 100 km, the sodium ions would recombine with electrons much more efficiently through cycling chemical reactions under a large k (Na + → Na) value; (4) the E S layers generate the formation of Na S . Thus, we propose that there would probably be a connection between the lightning strokes, the overturning of the electric field, ionospheric disturbances, and also the Na S . A link between the lower and upper atmospheres could be established by carefully studying and examining these phenomena. However, we caution that the key processes for our proposed step (2) still remain quite uncertain. A more indepth modeling study concerning both plasma and neutral molecules is needed in the future.

Conclusions
In this research, we study the conjunction between the lower and upper atmospheres, through the phenomena and processes of lightning strokes, the overturning of the atmospheric electric field, ionospheric disturbance, plasma drift velocity reversal, and the formation and dissipation of sporadic sodium layer. The main findings of our results are summarized as follows: 1. The Na S event discussed in the present case study shows a close relationship with E S activities rather than conforming to the prescriptions from the competing hightemperature theory.
2. The atmospheric electric field exhibits an overturning, opposite to the fair-weather downward field in the global circuit, coincident with the depletion of E S and the consequent production of Na S .
3. A typical thunderstorm, with a positive charge located above a negative charge layer, is shown to produce an upward electric field toward the ionosphere. Two regions with heavy lightning activities nearby are found during the overturning of the atmospheric electric field.
4. Observations by the ionosonde exhibit extraordinary echoes during the lightning period, and the temporal property of the echoes behaved synchronously with lightning activities.
5. WACCM-Na model simulation results show that the calculated first-order rate coefficient k (Na + → Na) could probably explain the efficient recombination of Na + → Na in this Na S case study.
Our results support a physical connection between the lightning strokes, the overturning of the electric field, ionospheric disturbances, and possibly the Na S phenomenon as well. A link between the lower and upper atmospheres could be established as follows by the monitoring of Na S and related phenomena: lightning strokes →overturning of the electric field →E S generating Na S .

Appendix A: Calculations for the induced upward electric field in the global electric circuit
Suppose there is positive charge Q 1 at the top of a thunderstorm, with a distance of d 1 above the ground and a negative charge Q 2 at the bottom with a distance of d 2 . Since the ground surface could be regarded as an infinite conducting plane, it would generate an induced charge. The boundary condition here is Under the uniqueness theorem, we can remove the ground surface if we put the postulated image charges of −Q 1 and Q 2 to the corresponding mirror points. Then for an arbitrary point P near the boundary, the vertical electric field is equal to the following expression according to Coulomb's law (Griffiths, 1999): In the simplest case, when Q 1 is equal to Q 2 and d 1 = d 2 = d, E ⊥ varies with the distance d. If Q 2 is larger than Q 1 (Q 2 > Q 1 > 0) and the negative charge −Q 2 is closer to the observing point P (d 2 < d 1 ), E ⊥ would acquire negative values (e.g., with the upward direction). A brief simulation result is shown by Fig. A1d, exhibiting persistent negative values for E ⊥ . Data availability. The data sets of the ionosonde and the fluxgate magnetometer are publicly available from the Chinese Meridian Project database at http://data.meridianproject.ac.cn/ (Chinese Meridian Project, 2021). Observation data of the atmospheric electric field mill at Wuhan Geomagnetic Station is from the National Space Science Data Center, https://doi.org/10.12176/01.05.065 (Wuhan Geomagnetic Station, 2010). The sodium density data of the T /W lidar over Hefei is available from the National Space Science Data Center (https://doi.org/10.12176/01.05.026; University of Science and Technology of China, 2011). The lightning location and power data can be downloaded from the World Wide Lightning Location Network (http://wwlln.net/, WWLLN, 2021).
Author contributions. SQ conceived this study and wrote this paper. She also prepared Figs. 2-5 in the main text and Fig. A1 in the Appendix. NW performed data analysis. WS was in charge of the organization and polishing the English of the whole paper. GL added some materials about thunderstorms and lightning strokes. MJ prepared Fig. 1 and gave some useful comments on the content. XW wrote the response to reviewers and calculated the model simulation results. XX wrote the response to reviewers and added some materials in the discussion. TL helped with the response to reviewers. XD conceived this study and provided data from the Chinese Meridian Project.
Competing interests. The authors declare that they have no conflict of interest.
Disclaimer. Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements. This work is supported by the National Natural Science Foundation of China (nos. 41974178 and 41831071), the CNSA pre-research Project on Civil Aerospace Technologies (no. D020105), and the National Key R&D Program of China (no. 2017YFC0602202). We acknowledge the constructive reviews by both referees. Thanks to Wuhu Feng from the University of Leeds, Jianfei Wu from the University of Science & Technology of China, and Jing Jiao from National Space Science Center for their help on the model simulation. We thank Han Jin and Jin Wang for calibration of the ionograms. The first author would like to thank Hao Chen and Yandong Liu for their help on debugging programs.
Financial support. This research has been supported by the National Natural Science Foundation of China (grant nos. 41974178 and 41831071), the CNSA pre-research Project on Civil Aerospace Technologies (no. D020105), and the National Key R&D Program of China (grant no. 2017YFC0602202).
Review statement. This paper was edited by Gabriele Stiller and reviewed by two anonymous referees.