Relationship between mesospheric Na and Fe layers from simultaneous and common-volume lidar observations at Arecibo

Authors


Corresponding author: Q. Zhou, Electrical and Computer Engineering Department, Miami University Oxford OH 45056, USA. (zhouq@muohio.edu)

Abstract

[1] We compare the mesospheric Na and Fe layers by using simultaneous and common-volume lidar measurements made at the Arecibo Observatory (18.3°N, 66.75°W), Puerto Rico, in 2003. The temporal variations of the two species are highly correlated at practically all heights, although not always positively. Positive correlations occur in the bottom and top sides while negative correlation is observed in a relatively narrow region in the middle part. Chemical and dynamical effects are discussed to interpret this particular relationship between Na and Fe layers. It is shown that gas phase chemistry determines the structure of the Na and Fe layers after the metals are ablated from meteoroids entering the atmosphere. The observed region of negative correlation appears to be slightly lower than that of the expected region of negative correlation based on inert response to dynamics. It appears that such a difference may be due to temperature-dependent chemistry. Overall, the observed correlations between Na and Fe layers can be well explained by their responses to wave dynamics.

1 Introduction

[2] Sodium and iron, among the many kinds of middle atmospheric metal species, have been most extensively studied by ground-based lidar observations. During the past three decades, lidar observations of Na have been conducted widely at low-, middle-, and high-latitude sites [e.g.: Kane and Gardner, 1993; Raizada and Tepley, 2003; Gardner et al., 2005, 2011; Yi et al., 2002, 2007, 2008, 2009]. These measurements have revealed transient structures and seasonal variations in the Na layer at different latitudes and have provided crucial data for the study of middle atmosphere dynamics and chemistry. Lidar observations of the mesospheric Fe layer have also been conducted for more than two decades [e.g., Alpers et al., 1990; Kane and Gardner, 1993; Raizada and Tepley, 2003; Gardner et al., 2005; Yi et al., 2009]. These studies have revealed important information about the vertical characteristics and temporal variations of Fe layers.

[3] In the past two decades, numerous studies have been carried out to investigate the effect of chemistry on the formation of atmospheric metal layers. A sophisticated model of gas-phase chemical reactions associated with Na species under mesospheric conditions has been developed [e.g., Plane et al., 1998]. Most of the rate coefficients of the reactions incorporated into this model are supported by laboratory experiments, while some other parameters, which are difficult to obtain, are inferred from theoretical estimations. This model has been validated by lidar measurements of the Na layer at middle- and high-latitude sites [Plane et al., 1998, 1999b]. The model reproduced the layer shapes and seasonal variations of the Na layer quite well. An Fe chemical model was developed after the Na model. The main scheme of the Fe model was based on that of the Na model, and most of the rate coefficients of the reactions in this model were fitted or estimated [Helmer et al., 1998]. The Fe model reproduced the main seasonal features in most months at 40°N. Furthermore, both the Na and Fe chemical models have been used successfully to simulate many characteristics of the main features at South Pole, including density profiles, column abundance, centroid height, and root mean square layer width [Gardner et al., 2005]. Model and data comparisons indicate that gas-phase chemistry plays a major role in determining the general characteristics of the mesospheric metal layers.

[4] Atmospheric dynamical processes, such as gravity waves and tides, play crucial roles in the variations of atmospheric constituents and the chemistry of the middle atmosphere. Gardner and Shelton [1985] derived the expressions for the density response of neutral atmospheric layers to propagating waves. Zhou et al. [2005] have shown that the time variations of Na and K are caused by tides. Gardner and Liu [2010] verified that dynamical transport is important in the mesopause-region Na layer and all species are transported with the same velocity. Dynamical processes are always coupled with chemical processes. The dynamical processes of gravity wave propagation, instability, and breaking will induce density variations in all atmospheric constituents, resulting in the breaking of the existing chemical equilibrium and the establishment of a new chemical equilibrium. Walterscheid and Schubert [1989] showed that gravity waves significantly alter the mixing ratio of O3 and OH as a consequence of fast chemistry. Hickey and Plane [1995] and Xu et al. [2003] showed that the propagation of a monochromatic gravity wave could significantly affect the distributions of the chemical species in the middle atmosphere. This coupled chemical and dynamical process was suggested to account for the large transport velocities observed in the Na layer over Starfire Optical Range, New Mexico [Gardner and Liu, 2010]. Although there are still many phenomena observed in metal atom layers that are difficult to attribute to mesospheric chemistry and/or dynamics, it is widely accepted that coupled chemical and dynamical processes control the shapes, vertical distributions, and fluctuations of all metal atom layers, after the constituents containing metal species are deposited from meteoric ablation in this region.

[5] As many kinds of metal atoms and ions co-exist in the mesosphere and lower thermosphere, comparison between different layers at the same site will provide an overall understanding of the effects of chemistry, dynamics, meteor ablation, and other mechanisms on the formation and development of these layers. By using multiple lidars and sometimes radars, simultaneous and common-volume observations of different constituents have been performed at a number of sites across different latitudes [e.g., Raizada and Tepley, 2003; Raizada et al., 2011; Raizada et al., 2004; Tepley et al., 2003; Kane and Gardner, 1993; Chen and Yi, 2011]. As Na and Fe are relatively easy to observe by lidars, they have been studied most extensively [e.g., Chen and Yi, 2011; Kane and Gardner, 1993; Shibata et al., 2006; Yi et al., 2007, 2008]. Many of the Fe and Na observations are performed at the same site [e.g., Kane and Gardner, 1993; Gardner et al., 2005; Yi et al., 2009].

[6] Most closely related to the present study are the works by Yi et al. [2008] and Chen and Yi [2011]. Yi et al. [2008] presented the simultaneous and common-volume lidar observations of mesospheric Na and Fe densities over Wuhan, China (30.5°N, 114.4°E). They found that the lower boundaries of Na and Fe layers have a strong positive relationship. More recently, Chen and Yi [2011] presented more results about simultaneous ldiar observations of Na and Fe layers over Wuhan, China. They extend the study of Yi et al. [2008] about the relationship between Na and Fe from the bottom and top boundaries of the layers to the entire measurement range. They showed for the first time that an altitude-dependent relationship exists between the two metal layers. The relationship between the two species in the middle part of the metal layers appears to be very different from the bottom and upper parts. They discussed the potential for coupled chemistry and dynamical effects but did not find any mechanism to explain the observed relationship between the Na and Fe layers. The interesting results from Wuhan raise the following questions: Is the relationship at other sites similar to that observed at Wuhan? What mechanisms are responsible for the altitude-dependent relationship between Na and Fe? Our goal here is to answer these two questions.

[7] In the present study, we will first present simultaneous and common-volume lidar observations of Na and Fe layers over Arecibo Observatory (AO), Puerto Rico (18.35°N, 66.75°W). The layer shapes and relative fluctuations of these two species will then be compared in detail. We will study the relationship between the Na and Fe layers over the entire measurement range and discuss potential mechanisms to explain the relationship.

2 Instruments and Data Description

[8] All observations used in this study were made by resonance lidars at AO. To make the observation of mesospheric Na and Fe atoms, a single state-of-the-art, commercial Nd : YAG laser was used as a pump for two identical dye lasers at 50 Hz repetition rate. This was achieved by introducing a 50% beam splitter in the path of the second harmonic at 532 nm from the Nd : YAG. This resulted in an average power of 15 W to pump each of the two dye lasers. One of the dye lasers was tuned to the Na resonance wavelength at 589 nm, while the other was tuned to 572 nm and subsequently sum-frequency mixed with the residual 1064 nm infrared beam from the Nd : YAG to generate ultraviolet at 372 nm, the resonance wavelength for neutral Fe [Raizada and Tepley, 2002]. This configuration resulted in average powers of 3.5 and 0.8 W at 589 and 372 nm, respectively.

[9] The backscattered photons were collected using two Cassegrain-type telescopes that were separated by about 2 m in the horizontal direction. For Fe measurements, an EMI photo-multiplier tube (PMT), model 9863/350A, was coupled directly at the back of the telescope. The field of view (FOV) was ~2 mrad, which corresponds to a 200 m diameter spot at an altitude of 100 km. The other receiver channel dedicated for Na observations used a Hamamatsu PMT (R943-02) that was fiber optically coupled to another telescope, giving a FOV of ~0.7 mrad and resulting in 70 m spot diameter at 100 km. In both cases, the beams are pointing vertically. Thus, the observations presented in this paper are common volume and simultaneous over Arecibo. A multi-channel photon counting scaler was used to record the output signal from the PMTs.

[10] Mesopause region temperatures are observed by a potassium Doppler resonance lidar at the Arecibo Observatory [Friedman et al., 2003]. The lidar measures the spectrum of the K D1 line at three separate frequencies. The mesospheric temperature is then extracted from the spectrum information by assuming a Maxwell-Boltzmann velocity distribution for the mesospheric K [cf. She et al., 1990; Bills et al., 1991]. Its field of view also shares common volume with the Fe and Na lidars and has a field of view of 0.7 mrad.

[11] The simultaneous common-volume lidar observations of Na and Fe over AO were made mainly in 2003 and consist of five nights all together. Among these, data in two nights do not have enough overlap. The final data set used in this study includes three nights in 2003: 2–3 July, 18–19, and 22–23 December.

[12] The vertical and temporal resolutions for raw Fe data are 300 m and 2 min. while those for Na data are 75 m and 1 min. Na density errors are less than 1% for layer concentrations greater than 5000/cm3 [Zhou et al., 2005], and Fe density errors are less than 3% at the same layer concentrations. Although the Fe lidar and Na lidar have been operated over the same time periods, the starting times of Fe and Na data records are not identical on each night. For the purpose of comparison, the Na data and Fe data should match up with each other in both vertical and temporal dimensions. We first binned the Na data so that they have the same height resolution as the raw Fe data. Then we cropped the combined Na and Fe data to the same height range. The data sets were then matched in time. The final time resolution used for comparison, slightly different for each night, is about 130 s. Finally, we filtered all the data sets in the height direction using a sixth-order low-pass digital Butterworth filter, which filters out vertical wavelengths less than 1.5 km.

3 Observational Results

[13] The number densities of Na and Fe on the three nights discussed above are shown in Figure 1. Figures 1a and 1b show the results obtained on the night of 2–3 July 2003. The Na layer shown in the Figure 1a is mainly confined between 85 and 100 km. The upper and lower edges vary slightly in this night. The whole Na layer appears to be separated into two parts by an obvious border between 90 and 95 km. In the upper part, starting from the top, the density increases gradually with decreasing height and reaches the maximum just above the separating border, close to 90 km. It then decreases sharply to a local minimum at this separating border, grows slightly below the border, and remains near the lower maximum density for most part of the lower region. The Fe density shown in the corresponding Figure 1b has the same features as that of Na. The upper parts of both the Na and Fe layers have similar profiles. The densities of Na and Fe reach their local maxima at a similar altitude near the separating border in the middle region. The peak altitude lies at 94.5 km at 22:12 local time (LT = UT − 4 h). By 02:42 LT the peak has moved downward to 91.5 km. Although the peak altitude oscillates throughout the night, it is ~3 km lower at 02:42 than at 22:12 LT. In the lower parts of both Na and Fe layers, it can be seen that the bottom boundaries of both Na and Fe layers track one another closely except that the bottom contour of Fe layer is about 1 km lower than that of Na layer throughout the night. Meanwhile, the top edges of the two layers also coincide with each other most of the time. These phenomena for the top and bottom edges agree with the observations of Yi et al. [2008]. Based on these results, we infer that the Fe and Na layers may be closely related. We will calculate the cross-correlation between them in the following section.

Figure 1.

Simultaneous and common-volume observations of (a, c, and e) Na and (b, d, and f) Fe concentrations at Arecibo.

[14] The observations on 18–19 December 2003 are plotted in Figures 1c and 1d. Both the Na and Fe layers have a narrow sub-layer with prominent high density. The narrow Na layer is confined to the 89–97 km altitude region, while the Fe layer is located in the 87–94 km region. The density variation of Fe is larger than that of Na. For both metal layers, their peak altitudes ascend slightly before 02:00 LT (AST) and descend after that. The highest altitude of the Na peak is about 94 km at 02:00 LT, and the lowest altitude is about 90.5 km at 06:00 LT. For Fe, the peak is located near 92 and 89 km at those hours. Thus, the variations of peak altitude are about 3 km for both Na and Fe layers. The bottom boundaries of both Na and Fe layers track one another closely, except during the time period from about 22:00 LT to 23:50 LT. While for the top edges, it is difficult to find a clear-cut correspondence between Na and Fe layers.

[15] The data of 22–23 December 2003 (Figures 1e and 1f) shows a night in which both Na and Fe layers are broad. Figure 1f shows that the high density region of Fe layer lies mainly below 90 km throughout the night. The peak altitude is centered around 84 km before 00:00 LT. It ascends to 89 km at about 00:10 LT. At the same time, the main layer of Na shown in the Figure 1e is centered at about 90 km. The peak altitude descends from 92 km at the beginning of the observations to about 89 km after 20:00 LT. Below the top edge of Na layer, an enhanced narrow layer around 95 km exists throughout the night, but any density enhancement in the corresponding region of Fe is not obvious. The bottom edges of Na and Fe layers are quite similar for about 6 h before 01:00 LT.

[16] To have an overall view of the Na and Fe layers, we show the mean profiles of the two species in Figure 2. There is a considerable night-to-night variability for both species. In general, the similarity (within a scaling factor) between Na and Fe on the same night is stronger than the similarity of each individual species on different nights. The Na and Fe mean profiles on the night of 2–3 July 2003 show especially remarkable similarity. The most significant difference between the two profiles is the altitude of the local minimum, which is 91 km for Fe and 88 km for Na. The mean profiles on the night of 18–19 December have single peaks with the peak altitude of Fe about 2 km lower than that of Na. The mean profile of Na on 22–23 December 2003 has a strong peak at 96 km due to the narrow sporadic Na on this night. It is important to note for the subsequent discussion that the difference in the altitudes of local maxima (or minima) of the two species causes the height gradients of Fe and Na to be opposite in sign in the region around the altitudes of local maxima (or minima). The regions of opposite gradients are 88–91 and 90.5–92 km, respectively, for 2–3 July and 18–19 December 2003 while they are 88–90 and 93–96 km on the night of 22–23 December 2003.

Figure 2.

Nightly mean profiles of Na and Fe.

4 Relationship Between Na and Fe layers

[17] Chen and Yi [2011] have shown that there exists an altitude-dependent relationship between mesospheric Na and Fe layers over Wuhan, China. To verify this relationship quantitatively over AO, we have calculated the cross-correlation coefficients using the data for the entire night and plotted them against altitude in Figure 3. It is interesting to see that the profiles of all three nights have the same feature: strong positive correlation exists at the top and bottom parts while negative correlation exists in the middle altitude range. The center height of the negative correlation varies from night to night. The values of the cross-correlation on the bottom side are mostly greater than 0.80 and are larger than 0.90 in the height range from 83 to 84.5 km for all three nights, while those on the top sides are usually larger than 0.70. This indicates strong positive correlation between the Fe and Na layer at both bottom and top sides. At the same time, the values in the medium height range are negative and can reach −0.5 or less. The positive-negative-positive correlation as a function of altitude between Na and Fe is the same as that reported by Chen and Yi [2011] for lidar observations over Wuhan, China. The regions of negative values are 88.16–89.96, 90.56–93.56, and 90.54–96.24 km, respectively, for 2–3 July, 18–19, and 22–23 December 2003.

Figure 3.

Altitude variations of all night cross correlation coefficients between Na and Fe density variations on three nights. The heights of local maxima (cross) and minima (circle) of nightly mean profiles of Na (blue) and Fe (red) are labeled on the profiles. The local maxima or minima are obtained from Figure 2.

[18] We compare the altitudes of the zero points of correlation coefficients with the peak or trough altitudes at each night in Figure 2. It is found that, for the night of 2–3 July 2003, the region of negative coefficients in Figure 3 is located between the trough altitudes of the all-night mean Na and Fe profiles shown in Figure 2. For the night of 18–19 December 2003, the region of negative coefficients extends upward from about the peak altitude of all-night mean Fe profile shown in Figure 2 to a height about 1.8 km higher than the peak altitude of all-night mean Na profile shown in Figure 2. For the night of 22–23 December 2003, the region of negative coefficients is located between the peak heights of all-night mean Na and Fe profiles shown in Figure 2. The fact that the regions of negative correlation coefficients match quite well with the height range between the two peak or trough altitudes of all-night mean Na and Fe profiles implies that the negative correlation may be connected to the region of opposing vertical gradients of Na and Fe in this height range. However, the correspondence of the two height ranges during the night of 18–19 December 2003 is not in complete agreement with those of the other nights. Checking the all-night mean density profile in Figure 2, we see that the peak region of Na is relatively flat on that night between 90.6 and 93.6 km, with the density within 95% of the peak value. The small density variation means the magnitude of scale height of Na is large in this region. As the sign of the density gradient is opposite that of the scale height, we conjecture that the negative Na/Fe correlation may be connected with the sign and magnitude of scale height in this region.

[19] The all-night correlation in Figure 3 does not have information on temporal variations. By using a sliding window of 1 h, we calculate the correlation coefficient between Fe and Na at each time point and the result is shown in Figure 4. Compared to Figure 3, the correlation coefficients show variations with periods of tens of minutes. We see that, on each night, the profiles between 80 and 105 km region can be roughly divided into three regions: the positive top and bottom regions and the negative middle region. This trait is the same as that illustrated in Figure 3. For the top positive region, the bottom edge of which lies between 91 and 97 km, the values are mostly larger than 0.7 and often reach 0.9 even though there are small regions with negative values. For the bottom region, with upper edge between 85 and 90 km, the values are even larger and positive. The middle negative region usually appears between 87 and 97 km. The width and center altitude of the negative region vary throughout the night. Their values are occasionally less than −0.70. Even though the regions with negative values are narrow on the nights of 2–3 July and 18–19 December 2003, they are persistent throughout the nights.

Figure 4.

Time and altitude variations of the cross correlation coefficients between Na and Fe on three nights. The superimposed lines represent the heights of local (a) minima and (b and c) maxima of Na (white line) and Fe (black line) densities.

[20] Also plotted in Figure 4 are the heights of the local maxima (Figures 4b and 4c) and minima (Figure 4a) of Na (white lines) and Fe (black lines) densities. The two pairs of white lines in Figures 4b and 4c correspond to multiple Na density peaks in the time ranges from 21:29 to 23:10 LT on 18 December 2003 and from 19:13 to 21:48 LT on 22 December 2003 as shown in Figure 1. It can be seen that the negative regions of cross-correlation are almost enclosed by the white and black lines in Figures 4a and 4c. In Figure 4b, the region of negative correlation is somewhat wider than the region enclosed by the white and black lines, but the peak heights of the negative region match quite well with the medians of the black and white lines throughout the night. Except the time range from 23:46 to 00:54 LT, the peak heights of the negative region match quite well with the narrow region throughout the night. As Fe and Na have opposite vertical gradients in the height ranges between black and white lines, Figure 4 thus illustrates that the altitude ranges of negative correlation largely correspond to the height ranges where Fe and Na have opposite vertical gradients on a time scale of 1 h as well.

[21] Figure 4c shows that the region of positive correlation extends obviously above the peak altitude of Fe layer. From about 22:30 LT to 23:50 LT, the region of positive correlation encroaches upon most of the altitude range between the peak heights of the Fe and Na layers, which decreases the magnitude of the all-night correlation at this altitude range as shown in the right panel of Figure 3.

[22] In order to better understand the correlation between the Fe and Na layers, we show the temporal variations of the relative density variations (i.e., the ratio of deviation from mean to the mean at each height) in Figure 5. Three representative altitudes for each night are selected based on the results shown in Figure 3. The upper and lower altitudes are chosen for the maximum positive correlation, while the middle altitude is for the maximum negative correlation. The third row shows that the relative variations of Na and Fe at the lowest altitudes are virtually identical. They describe the very strong positive correlation between the bottom sides of these two metal atom layers. The first row shows that the two density variation curves also coincide quite well with each other at the highest altitudes where positive correlation occurs. The middle altitudes (second row), where the correlation between Na and Fe is generally negative, reveal opposite variations of Na and Fe. This relation is most clearly shown on the night of 18–19 December. Figure 5 demonstrates once more the close relationship that exists between Fe and Na layers, as first reported by Yi et al. [2007]. Although explicit correlation has only been reported at two sites (Wuhan 30°N and Puerto Rico 18.3°N), the close relationship between Na and Fe at the bottom boundaries of the layers can also be inferred from the reported simultaneous and common-volume lidar observations over Urbana, IL (40°N) [Kane and Gardner, 1993] and the equator [Shibata et al., 2006]. Such a ubiquitous feature clearly requires an explanation. In the following, we will discuss the impact of mesospheric gas-phase chemistry and dynamics on the relationship between Na and Fe layers.

Figure 5.

Relative variations of Na (blue line) and Fe (red line) at three selected altitudes on three nights. The black curves represent the correlation coefficients between Fe and Na at the corresponding altitude with magnitude shown by Y axis on the right of each panel.

5 Discussion

[23] Comparisons between Figures 2 and 3 have shown that the negative relationship between Na and Fe in the middle parts of metal layers is connected closely with the structure (the height of the local maxima/minima) of Na and Fe layers. Figure 4 shows that the altitude-dependent relationship is determined by the separation between local maxima and minima of Na and Fe layers. Next, we seek for the mechanisms that determine the structure and the variation of metal layers.

5.1 Effect of Gas-Phase Chemistry

[24] Mesospheric gas-phase chemistry models can reproduce the general characteristics of Na and Fe layers at middle and high latitudes [Gardner et al., 2005; Helmer et al., 1998; Plane et al., 1999a], including the lower centroid height and the smaller scale height in lower part of the Fe layer relative to that of Na. In addition, Collins et al. [2002] used a modified Na ion-molecule chemistry model to explain the formation of sporadic Na layers observed at AO. Fe ion-molecule chemical reactions have also been used by Zhou et al. [2008] to explain the close relationship between electron and iron concentrations observed over AO. These results indicate that the Na and Fe ion-molecule chemistries play essential roles in the formation of Na and Fe layers over AO. In order to explain the structures of the mean Na and Fe profiles observed by lidar over AO, we need to review them in some detail. The main reactions involving the production and loss of Fe and Na are summarized in Table 1. The neutral chemistry reactions and some of the ion-molecule chemistry reactions are adapted from the corresponding Na and Fe models reported by Plane et al. [1998, 1999a]. Table 1 also reflects the Na and Fe ion-molecule chemistries updated by Collins et al. [2002] and Zhou et al. [2008], respectively. Less important reactions are not included, because we analyze only the effects of gas-phase chemistry on the structure of Na and Fe layers.

Table 1. Main Neutral and Ionic Gas-Phase Reactions of Na and Fe in the Upper Mesosphere
No.ReactionRate CoefficientaSource
  1. aAdapted from (1) Plane et al. [1998]; (2) Collins et al. [2002]; (3) Zhou et al. [2008]; and (4) Plane et al. [1999a].
(R1)inline image4.8 × 10−30(T/200)−2.21
(R2)inline image6 × 10−102
(R3)Na · Y+ + e → Na + Y(Y = N2, CO2, O)1 × 10−6(T/200)−0.51
(R4)inline image4.1 × 10−102
(R5)Na · O+ + O → Na+ + O21 × 10−112
(R6)inline image1 × 10−112
(R7)inline image7.6 × 10−10exp(−241/T)3
(R8)inline image8.0 × 10−30(T/300)−1.523
(R9)Fe · X+ + eFe + X(X = N2, O2,  or O)5.0 × 10−7(200/T)0.53
(R10)inline image4.6 × 10−103
(R11)FeO+ + O → Fe+ + O23.2 × 10−113
(R12)Na + O3 → NaO + O21.1 × 10−9exp(−116/T)1
(R13)NaO + O → Na + O22.2 × 10−10(T/200)0.51
(R14)NaOH + H → Na + H2O4 × 10−11exp(−550/T)1
(R15)Fe + O3 → FeO + O23.44 × 10−10exp(−146/T)4
(R16)Fe + O → Fe + O21 × 10−10exp(−200/T)4
(R17)FeOH + H → Fe + H2O2.0 × 10−12exp(−5/RT)4

[25] In the upper parts of the Na and Fe layers, ion chemistry dominates. Na is formed by the neutralization of Na+ through a sequence of ion-molecule chemistry reactions (R1)–(R6). Among these, recombination with N2

display math(R1)

is the most rapid reaction of Na+ in this region because of the density of N2. The cluster ion Na•N2+ is weakly bonded, so it will ligand switch with CO2,

display math(R2)

[26] Ultimately, the cluster ion Na•CO2+ undergoes dissociative recombination with electrons to form neutral Na:

display math(R3)

[27] This type of reaction is fast, with an estimated rate coefficient around 1 × 10− 6 cm3 molecule−1 s−1 [Plane et al., 1998]. However, the neutralization of Na+ is impeded by atomic O, which dissociates Na+ from ion-molecule clusters such as Na•N2+:

display math(R4)
display math(R5)

[28] Hence, the rate of neutralization of Na+ is mainly controlled by the altitude-dependent concentrations of CO2 and O, which govern the branching between reactions (R2) and (R4) as analyzed by Collins et al. [2002]. Collins et al. emphasized that the inverse reaction of (R4)

display math(R6)

needed to be taken into account. Reaction (R4) was almost thermoneutral. In the lower thermosphere [N2] ≫ [O], reaction (R6) effectively prevents the destruction of Na•N2+ by atomic O in reaction (R4). Collins et al. [2002] have shown that the inclusion of reaction (R6) will decrease the lifetime of Na+ by 15 h.

[29] The neutralization of Fe+, shown by reactions (R7)–(R11) in Table 1, is similar to that of Na+ in some aspects. For example, the ion-molecule Fe+N2 forming reaction (R8) and dissociative recombination with a free electron (R9) to form Fe are very much like reactions (R1) and (R3) in the ion-molecular chemistry of Na+. This means N2 and electrons have a similar effect on Fe+ as they do on Na+. In addition, atomic O acts in the same way to interrupt the neutralization pathway of Fe+ through reactions (R10)–(R11), which are almost the same as reactions (R4)–(R5). In other aspects, Fe+ has somewhat different ion-molecule chemistry compared to Na+. Fe+ reacts rapidly with O3 to form FeO+:

display math(R7)

[30] Above 85 km altitude, formation of FeO+ through reaction (R7) usually dominates because the reaction rate is faster than the other recombination reaction (R8) at very low pressure [Zhou et al., 2008]. Another difference is that CO2 has little effect on the ion-molecule chemistry of Fe+.

[31] At the upper part of the Fe layer, the concentrations of O3, electrons, and atomic O essentially control the neutralization of Fe+ through reactions (R7), (R9), and (R11). Thus, when ion chemistries dominate, the dependence of both Na+ and Fe+ neutralizations on the concentration of electrons and atomic O makes Na and Fe correlate positively with each other. Meanwhile, the different dependence on CO2 and O3 between these two species limits the magnitude of cross correlation coefficient between them.

[32] Below the peak altitudes of Na and Fe, these two atomic metals are converted to their stable reservoir species (NaHCO3, NaOH, FeO3, Fe(OH)2, and FeOH) via a series of steps beginning with the oxidation of Na and Fe by O3 to NaO and FeO ((R12) and (R15) in Table 1), and subsequent processes involving O2, H2O or CO2 [Plane, 2003]. These reservoirs are converted back to Na or Fe by reactions with O and H (e.g., (R13)–(R14) and (R16)–(R17) in Table 1). O and O3 are major reactive species in this region. It has been suggested that Na and/or Fe atoms could be reduced to e-fold via oxidation by O3 within 1 min [Helmer et al., 1998]. The nighttime Na layer only exists at a height above which atomic O is also abundant [Plane, 2003]. For this reason, the small scale height on the underside of the Na layer correlates closely with the shelf of atomic O [Plane et al., 1999b]. Notice that reactions (R15)–(R16) are similar to (R12)–(R13), so we can reasonably assume that the densities of both Na and Fe on the bottom side of metal layers are controlled by odd oxygen, which leads to the high correlation between them in this region demonstrated in Figures 3 and 4. Furthermore, we can infer from this that the modulations of the lower edges of both the Na and Fe layers represent the movements of the atomic O shelf.

[33] Different chemical reaction rates determine the different background peak altitudes of Na and Fe layers. Helmer and Plane [1993] have shown that all Na is converted to free metal atoms at about 95 km. Therefore, in the region of 88–95 km, neutral chemistry dominates the loss of atomic Na while ion chemistry dominates the production of atomic Fe. Atomic O plays opposite roles in these two types of chemical reactions of Na and Fe. In the neutral chemistries of Na, atomic O works to convert atomic Na from its reservoirs (R13), while in the ion chemistries of Fe, atomic O prohibits dissociative electron recombination of molecular FeX+ (X = N2, O2, O) by reducing them back to Fe+ quickly (R10)–(R11) [Zhou et al., 2008; Plane, 2003]. Therefore, a decrease of atomic O density leads to a decrease of atomic Na density, but to an increase of atomic Fe density. By the same token, an increase of atomic O leads to an increase of atomic Na and decrease of atomic Fe. Similarly, O3 also plays an opposite role in the neutral chemistry of Na and the ion chemistry of Fe in this height range. O3 exhausts atomic Na quickly through reaction (R12), while it helps Fe+ to neutralize through reactions (R7) and (R9). Thus, chemical reactions involving odd oxygen will have contrary effects on Na and Fe in this region.

5.2 Effect of Atmospheric Dynamics

[34] In this section, we treat Na and Fe as inert tracers and consider their density variations due to gravity waves. This phenomenon is elucidated by Gardner and Shelton (1985). It is described via the following relation:

display math(1)

where Δn (∆N) and nx(N) are the density perturbations and density of the minor species (atmosphere), respectively, γ is the ratio of specific heats, and H is the atmospheric scale height. Although this equation includes the second-order nonlinear terms, the predominant term is the linear term when the background density variation is less than a few percent. The nonlinear term becomes predominant close to the height where the linear term is approximately zero.

[35] To study the relative phase and magnitude of Na and Fe fluctuations, we define the following function:

display math(2)

where sgn() is the sign function, subscripts S and F refer to Na and Fe. The first term in the equation represents the positive or negative correlation, which is decided by the sign of the gradients in both Na and Fe. The second term denotes the amplitude of the fluctuations. The combined effect is best represented by the product, because the layers are independent of each other. Denoting the scale height of the Na and Fe species as inline image and inline image, respectively, and by considering the linear term only, this function is approximated as

display math(3)

[36] Positive p-values indicate positive correlation. At the bottom sides, below both Na and Fe peak altitudes where HS and HF are both negative, p is positive. Thus, Na and Fe are positively correlated. Far above the Na and Fe peaks, where both Na and Fe have small but positive scale heights, p is also positive. The situation in the middle region is more complex. Negative p occurs in the region where the sign of inline image is opposite that of inline image. The two solutions for negative p are {0<HF<γH; HS>γH, or HS<0} and {0<Hs<γH; HF>γH, or HF<0}. In the region where both Na and Fe have a local peak and the lower of the two layers has a sufficiently small positive scale height near the peak of the upper of the layers, negative p occurs above the lower peak and extends above the higher peak altitude. This is the case of 18–19 December 2003, shown in Figure 3. In the region where both Na and Fe have a local minimum, as on 2–3 July 2003, negative p typically occurs below the higher altitude of the two local minima and extends to an altitude below the lower altitude of the two local minima. Using knowledge of the separation of the two peak altitudes and the scale heights of Na and Fe, the region of negative p can thus be estimated.

[37] To quantitatively illustrate the sign and magnitude of p, including the nonlinear effect, we consider the case where the unperturbed layers of Na and Fe have Gaussian profiles:

display math(4)

where zx, σx, and Cx are the layer peak altitude, RMS width, and column abundance, respectively. We choose (zNa, σNa, CNa) and (zFe, σFe, CFe) as (92 km, 5.8 km, 43,000 cm−2) and (89 km, 5.5 km, 124,000 cm−2), respectively, which are typical parameters for Na and Fe layers at low latitudes [Raizada and Tepley, 2003; Yi et al., 2009]. The scale heights of the Na and Fe layers are plotted versus altitude in Figure 6. Assuming an isothermal ambient atmosphere with a scale height H of 6 km, we calculate the responses of the Na and Fe layers to the effect of a −3% atmospheric fluctuation based on equation ((1)) and values of p based on equations ((2)) and ((3)) (we denote them as p and plinear, respectively, for simplicity). These results are plotted in Figure 6 and labeled on the top. It is seen that the region of negative plinear (the black solid line) occurs from 92.6 to 96 km (estimated by z1 = zNa + σNa2/γH and z2 = ZFe + σFe2/γH, respectively), where the scale height of Fe, HF, is positive but smaller than γH. The region, where the scale height of Na, HS is larger than γH, is shown by the shaded zone. plinear is positive in all other regions. The curve of p is only slightly different from that of plinear. The height of the two zero points of p are 92.3 and 95.7 km which are a bit lower than the corresponding zero points of plinear, respectively. The magnitude of p is strictly limited by the magnitudes of Na/Fe layer responses to dynamical effects. The region of negative p corresponds to the height range where the layer response of Na is positive and that of Fe is negative. The curves representing p and plinear cross at two heights: 89 and 94.3 km. In the range between these two heights, p is smaller than plinear, in other regions, p is greater than plinear. This difference shows that the nonlinear dynamical effect lowers the region of negative p for negative ΔN/N.

Figure 6.

The link of scale heights of Na and Fe with Gaussian profiles to the value of p. The scale heights of both Na (star) and Fe (circle) layer are plotted versus altitude and labeled on the bottom. The responses of Na (dotted lines) and Fe (dashed lines) layers to a 3% atmospheric fluctuation, p (red solid line) and plinear (black solid line) are plotted versus altitude and labeled by X axis on the top. The shaded zone represents the region of negative plinear.

[38] Figure 6 just shows a special case, it can be inferred that, for the other cases of Na and Fe with displaced Gaussian profiles, the wider the two peak altitudes separate, the wider the region of negative p is. The bigger the RMS width is, the farther the edge of region of negative p moves away from the peak. When the profiles of these minor constituents are the sum of two or more Gaussian profiles, the region of negative p becomes complicated. We further note that the region of negative plinear is independent of whether ΔN/N is negative or positive. Modification of plinear by the nonlinear term, however, depends on the sign of ΔN/N. With ΔN/N = −3%, we see that the nonlinear effect is to lower the region of negative correlation. In the real atmosphere, ΔN/N may change sign at different altitudes. The nonlinear effect may thus broaden or narrow the region of negative correlation defined by the linear term.

[39] The instantaneous value of p in real data is rather difficult to obtain. The averaged value can be determined through cross-correlation within a certain time duration. The above discussion assumes that Na and Fe layers are stationary during the time period when correlation is performed. With this caveat in mind, we calculate the effect of a −3% atmospheric fluctuation on the nightly mean profiles of Fe and Na based on equation ((1)) and the values of p and plinear. The results for the three nights of observation are shown in Figure 7.

Figure 7.

The responses of Na (dotted) and Fe (dashed) layers to a −3% atmospheric fluctuation. The values of p (red solid line) and plinear (black solid line) are plotted versus altitude. The blue lines represent the height ranges with negative Na/Fe correlation which are inferred from Figure 3.

[40] Figure 7 reveals where to expect the temporal cross-correlation of Na and Fe to be positive or negative due to response to dynamical effects. It is shown that the regions of negative p (red thick curve) are located between 89.36 and 90.56 km, 90.86 and 93.86 km, and 92.34 and 96.24 km, respectively for 2–3 July, 18–19, and 22–23 December 2003. These regions correspond reasonably well with the regions of negative correlation 88.16–89.96 km, 90.56–93.56 km, and 90.54–96.24 km in Figure 3, which are illustrated here with thick blue lines. Similarly, regions of positive correlation in Figure 3 agree in general with the regions of positive p in Figure 7. This result indicates that dynamic effects are essential in causing the correlation between Na and Fe layers. The nonlinear term can become significant especially when |ΔN/N| is larger than 3%. We also note that for all three nights, the region of negative density correlation is lower than the region of negative p. The altitude range difference may be due to temperature sensitive chemistry, as discussed in the next subsection.

[41] The introduction of p can also help us to understand the apparent positive correlation encroachment between 22:30 and 00:00 LT on 22–23 December in Figure 4. From the densities of the corresponding regions enclosed by rectangles in Figures 1e and 1f, we calculate the mean scale heights of Na (HS) and Fe (HF), respectively. HS is negative in the altitude range from 85 to 88 km. Between 88 and 94 km, it becomes positive and is always larger than 8.4 km (γH, where γ = 1.4 is the ratio of specific heats, H = 6 km is the assumed atmospheric scale height in this altitude range). Meanwhile, HF is negative from the altitude of 85 km to about 86 km and becomes positive above. It is less than 8.4 km in the range from the altitude of 92.3–94 km. By substituting the observed temporal mean HS, HF, and the assumed uniform H of 6 km into equation ((3)), the region of negative correlation is expected to occur only between 92.4 and 94 km. This is just the case shown in Figure 4 in the time range from 22:30 LT to 00:00 LT on 22–23 December 2003.

[42] Figure 7 allows us to examine the relative impact that a gravity wave has on one species at different altitudes and on two species at the same altitude. Gravity waves typically cause large density variations below 85 km for both Fe and Na. There is great variability from night-to-night above 95 km. What is of specific interest here is the comparison between Na and Fe, as the two species are subjected to the same gravity wave forcing at the same altitude. On 2–3 July 2003, we see that the relative variation in Fe at 89 km in Figure 7 is smaller than that in Na, which compares well with the observed relative variation at this altitude shown in Figure 5. On the night of 18–19 December 2003, Figure 7 indicates that a gravity wave does not affect Na as it does Fe at 93 km (the values for Fe and Na are, respectively, −0.14 and 0.04 at 93.3 km in the middle panel). The observed relative variation of Fe in Figure 5 for this night and altitude is clearly much larger than that of Na. On the night of 22–23 December 2003, the magnitude of dynamical response for Na is bigger than that for Fe in Figure 7 at about 95 km. Figure 5 also reveals that the relative variation for Na is larger than Fe, especially after 23:00 LT. Thus, our results clearly indicate that the influence of gravity waves is consistent with the observed relative variations of Na and Fe.

5.3 Coupled Chemistry and Dynamics

[43] The above two sections give us a reasonable explanation for the particular relationship between mesospheric Na and Fe layers: Chemistry controls the structures of the Na and Fe layers, i.e., the shape, layer width, peak altitude, and so on, while density fluctuations induced by gravity waves lead to the particular correlation relationship between the Na and Fe layers. In fact, the effects of chemistry and dynamics are not separable, as described above. Xu et al. [2003] have shown that the propagation of a gravity wave induces significant fluctuations of chemically active species such as O, O3, and H as a consequence of fast chemistry. O, O3, and H play important roles in Na and Fe chemistry as described in section 5.1. Thus, unsurprisingly, chemistry and dynamics are coupled together to act on the formation and development of the mesospheric metal layers. The significance of chemistry as compared to dynamics changes with altitude according to their relative time scales. Xu et al., [2003] showed that chemistry dominates on the bottom side of the Na layer because of the very short chemical relaxation time, and dynamics control the Na layer above because the chemical lifetime is much longer than the time scale of advection transport.

[44] Gardner and Liu [2010] analyzed the correlation between fluctuations of Na density and temperature. They derived an expression of constituent fluctuation in terms of temperature fluctuation by ignoring chemical effects and other sources. Direct dynamical transport causes almost perfect positive and negative correlation on the bottom and topside of the Na layer, respectively. Near the peak of the layer, the correlation decreases as it transitions smoothly between the bottom and topside values. However, the observed correlation between the measured Na and temperature fluctuations is much smaller in magnitude than the theoretical results. Factors that affect the correlation between Na (or Fe) and temperature include the following: (1) Wave dynamics without chemistry: Waves generate density and temperature variations simultaneously, and density and temperature variations are correlated even if the species is not sensitive to temperature. (2) Minor species response to temperature-sensitive chemistry: Waves induce changes in temperature, which in turn affects the species density.

[45] Liu and Gardner [2004] studied how the constituent number density perturbation is associated with gravity waves in terms of the concomitant temperature perturbations, while Xu et al. [2003] discussed the second effect. But it is difficult to say which mechanism is dominant. We are fortunate to have one night of simultaneous common-volume temperature data observed by K lidar on 18–19 December 2003, which will help to make clear the effects of dynamical transport. The vertical and temporal resolutions of temperature data are 0.45 km and 0.5 h, respectively. The mean errors are 4.5 K and 7.0 K at 85 km and 95 km, respectively. We combine two adjacent temperature data and three adjacent Na (and/or Fe) range cells to make them uniform in vertical resolution with a value of 0.9 km. The Na (and/or Fe) data are also combined in time to have 0.5 h temporal resolution to compare with the temperature data. The calculated correlations between temperature and Na (blue line) and Fe (red line) are shown in Figure 8.

Figure 8.

The measured correlation between temperature and Na fluctuations (blue solid curve) and that between temperature and Fe fluctuations (red solid curve) plotted versus altitude on 18–19 December 2003. The dashed curve is duplicated from the middle panel of Figure 3.

[46] The temperature/Fe correlation profiles are much like that of temperature/Na from 85 to 88 km, they are positive but less than 0.2, which is much lower than the theoretical value of 1.0 derived by Gardner and Liu [2010]. The small correlation coefficients between temperature and Na or Fe indicate that temperature plays an insignificant role in modulating the metal species in this region. The ignored chemistry and other sources in deriving the expression for the relationship between wave dynamics and constituent fluctuations may dominate in this region.

[47] The value of temperature/Na correlation begins to increase at 88 km and reaches its maximum of 0.92 near 91 km, and then decreases, becoming negative above 93 km and reaching approximately −0.72 at about 94.5 km. From about 90 to 95 km, the profile is very much like that of the theoretical results (Figure 8 in Gardner and Liu [2010] which is for correlation between temperature and density fluctuations for an inert species with a Gaussian-shaped density profile that is similar to the annual mean Na or Fe density profile). The height of maximum correlation, ~91 km is just below the peak altitude of mean Na profile (91.76 km based on Figure 2), as the theory predicts. The maximum values of 0.92 and −0.72 determined here approach the theoretical values of ±1, which indicates that dynamical effects play dominant roles at the corresponding altitudes.

[48] For temperature/Fe correlation, the value increases from 0 to about 0.45 in the height range 88–90 km and decreases sharply to its negative maximum of −0.92 just below 92 km. The beginning altitude for decreasing correlation is also near the peak height of Fe (90.26 km according to Figure 2). The correlation value remains below −0.7 above 91 km. Notice that the temperature/Fe correlation profile above 90 km is also in accordance to the profile of theoretical results. Therefore, dynamical effects caused by waves with periods longer than 0.5 h dominate above 90 km for both Na and Fe layers.

[49] In Figure 7, the observed region of negative Na/Fe density correlation is somewhat lower than the region of negative correlation for chemically inert species, i.e., the region of negative values indicated by the solid black line. We notice that the region of opposing dependence of Fe and Na on temperature is somewhat lower than that of the observed negative correlation between Na and Fe densities in Figure 8. Thus, it appears that the observed region of negative correlation is the combined result of inert response to wave dynamics and temperature sensitive chemistry. Obviously, more simultaneous density and temperature data are needed to affirm the conclusion. Nevertheless, it appears to be clear that dynamical effects, through inert response and/or dynamics-chemistry coupling, can explain the negative correlation between Na and Fe in the middle part of metal layers to a large extent.

6 Conclusion

[50] This study presents a comparison of common volume atomic Na and Fe layers measured simultaneously by resonance lidars at Arecibo. The bottom borders of the Na and Fe layers are observed to follow similar tracks for all observation times, which is similar to the results of Yi et al. [2008]. The cross-correlation between these two layers is calculated. It is found that both the top and bottom sides of the correlation profiles are positive, while the middle part is negative for all the three nights studied. This is the same as found by Chen and Yi [2011] over Wuhan, China, which indicates that this relationship may very well exist globally.

[51] We discuss the impact of chemical and dynamical effects on this particular relationship. The analysis demonstrates that gas-phase chemistry determines the structure of mesospheric Na and Fe layers after the metals are deposited by meteoric ablation in this region. The temporal correlation characteristics are intrinsically related to the vertical gradients of the metal atoms. The region of positive/negative temporal correlation agrees reasonably well with the same/opposite sign of the linear response of Na and Fe layer to dynamical effects. At the same time as dynamical effects are shown to be dominant in causing negative Na/Fe correlation, more work is needed to quantitatively analyze the impacts of dynamical, chemical, and other effects on the positive Na/Fe correlation. Furthermore, the nonlinear components of the layer density response are also required to better understand the relationship between the Na and Fe layers. Since the negative correlation is intrinsically related to the response of the metal layer density to dynamical effects, it is likely not limited to Na and Fe only but is applicable to any two metals as long as their chemical lifetimes are relatively long.

[52] The comparison of temperature/Na and temperature/Fe correlation based on one night of simultaneous common-volume observations also indicates that dynamical effects dominate in the middle parts of Na and/or Fe layers. However, the effect of temperature on Na and Fe variations appears to be less significant below 88 km. More common-volume measurements of temperature and multiple-species metal layer densities are needed to delineate the effects of inert response and dynamics-chemistry coupling.

Acknowledgments

[53] The authors would like to thank Fan Yi for his valuable comments and Alan Liu for helpful suggestions. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968) and in alliance with Ana G. Méndez-Universidad Metropolitana and the Universities Space Research Association. The study is supported by NSF grants ATM-0633418 and AGS-1042223 and Natural Science Foundation of China grants 40974085, 40674086, 40731055, 40825013, 41174127, and 41221003.