Seasonal variations of midlatitude mesospheric ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, D11304, doi:10.1029/2011JD017031, 2012

Seasonal variations of midlatitude mesospheric Na layer and their tidal period perturbations based on full diurnal cycle Na lidar observations of 2002–2008 Tao Yuan,1 C.-Y. She,2 Takuya D. Kawahara,3 and D. A. Krueger2 Received 18 October 2011; revised 27 April 2012; accepted 29 April 2012; published 8 June 2012.

[1] The Na lidar facility at Colorado State University (41 N, 105 W) started the full

diurnal cycle observations of mesopause region temperature and zonal and meridional winds as well as mesospheric Na density in May 2002. In this paper, monthly means and seasonal variations of the density of mesospheric Na based on lidar observations from May 2002 to December 2008 are reported along with the amplitude and phase of tidal period perturbations. The revealed seasonal behaviors of mesospheric Na layer are generally consistent with published nocturnal climatology, with thick layers and high abundance in winter but thin layers and low abundance near summer. Tidal amplitudes of Na density are large in February–April and August–November with a dominant peak between 85 and 90 km; they are weak in summer months (May–July). The Na density tidal phase profiles, while showing downward progression, show a significant and abrupt phase shift (ideally 180 degrees). The center altitude of this phase shifting (termed switching altitude) is found to coincide with the fractional tidal amplitude (tidal amplitude over diurnal mean) minimum about 2–4 km above the centroid altitude of the associated Na layer. Taking advantage of the established temperature tidal climatology deduced from the same data set, the tidal phase behaviors between temperature and Na density and associated fractional Na density tidal amplitudes are discussed in terms of the theoretical prediction by Gardner and Shelton (1985). Citation: Yuan, T., C.-Y. She, T. D. Kawahara, and D. A. Krueger (2012), Seasonal variations of midlatitude mesospheric Na layer and their tidal period perturbations based on full diurnal cycle Na lidar observations of 2002–2008, J. Geophys. Res., 117, D11304, doi:10.1029/2011JD017031.

1. Introduction [2] The mesospheric Na layer, along with the other atomic metal layers (Fe, K, Ca, etc.), is the result of meteoric ablation and the relevant atmospheric chemical reactions [Plane et al., 1999; Plane, 2004; Kane and Gardner, 1993; von Zahn et al., 2002]. The Na layer has been long studied by ground-based resonance lidars at various locations all over the world [Simonich et al., 1979; Collins et al., 1994; States and Gardner, 1999; She et al., 2000]. In fact, Gibson and Sandford [1971] reported seasonal variation of Na density as early as 1971. The most recent observations from satellite instruments give the global distributions of the Na layer

1 Center of Atmospheric and Space Sciences, Utah State University, Logan, Utah, USA. 2 Physics Department, Colorado State University, Fort Collins, Colorado, USA. 3 Department of Information Engineering, Shinshu University, Nagano, Japan.

Corresponding author: T. Yuan, Center of Atmospheric and Space Sciences, Utah State University, Logan, UT 84322, USA. ([email protected]) ©2012. American Geophysical Union. All Rights Reserved.

[Fussen et al., 2010; Gumbel et al., 2007], providing an unprecedented data set for understanding this important layer in the mesopause region of the atmosphere. However, such data sets are limited by the satellite’s sampling scheme and most of the ground-based investigations are based on nighttime observations. Thus comprehensive mesospheric Na layer studies based on significant numbers of full diurnal measurements are rare. With the improvement of lidar technology, daytime Na density profiles by Na lidar have been achieved and tidal period perturbations of Na density were deduced based on limited Na lidar diurnal cycle observations [Chen et al., 1996; States and Gardner, 1999; Clemesha et al., 2002]. Due to the complexity of the generation of mesospheric Na, there is no consensus on whether such perturbations are driven by solar thermal tides [Batista et al., 1985] or by photochemical effects [States and Gardner, 1999]. Nonetheless, Clemesha et al. [2002] found strong correlations between the Na density tidal period perturbations and those of the meridional wind and concluded that Na density tidal perturbations are indeed driven by solar thermal tides. [3] The Na lidar at Colorado State University located at Fort Collins (40.6 N, 105 W), which was relocated to Utah State University in summer of 2010 and continues its operation, had achieved the daytime temperature measurement

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YUAN ET AL.: Na LAYER TIDES AND MEAN VALUE

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Figure 1. (a) The Na lidar-observed Na layer (FWHM) thickness, (b) Na abundance, and (c) layer centroid height variations during one Na lidar diurnal cycle observation from 21 to 24 February 2006. The diamonds are lidar measurements; the crosses are reconstructed Na layer variations using the mean and tidal components retrieved from the harmonic least squares fitting algorithm. The vertical bars are uncertainty-derived from the least squares fitting. capability in 1996 [Chen et al., 1996]. It started its regular full diurnal cycle observations of temperature and zonal and meridional winds as well as Na density in May 2002. In this paper, seasonal variations of mesospheric Na density along with its monthly mean tidal period perturbations are deduced based on a total of 4,838 h of full diurnal cycle observations from May 2002 to December 2008 with 2 km and 4 km vertical resolution, respectively, for nighttime observation and for sunlit condition. Coupled with the studies of mean states and tidal perturbations of temperature and zonal and meridional winds deduced from the same data set, as well as from earlier publications based on shorter data sets [Yuan et al., 2008a, 2008b, 2010], the tidal influences on the observed Na density tidal period perturbations can be better understood. [4] The organization of this paper is as follows. Lidar observations and associated data analysis are outlined in section 2. The seasonal variations of the mean mesospheric Na layer, as well as its amplitudes and phases of diurnal and semidiurnal tidal period perturbations are reported in section 3. The relationship between Na density perturbations and temperature tidal perturbations is discussed in section 4 in the theoretical framework of Gardner and Shelton [1985], which provides an analytical relation between Na density and atmospheric density perturbations. We compare the lidar observed fractional Na density perturbations and the

calculated ones based on the above linear theory in section 5. This study is summarized in section 6.

2. Lidar Observation and Analysis [5] The least squares fitting algorithm with tidal period modulations (24 h, 12 h, 8 h, and 6 h) is applied at each altitude for the full diurnal cycle (continuous observations longer than 24 h) of lidar observations, yielding mean fields, and amplitudes and phases of tidal period perturbation profiles within the mesopause region. Using hourly binned data removes the short-period gravity wave (GW) perturbation. Possible bias due to the long-period planetary wave effect is minimized by using the monthly mean of multiyear observations. For multiyear lidar data harmonic analysis, hourly mean Na density profiles within the same month of different years are binned according to the local time sequence of respective years, before the fitting algorithm is applied. The detailed data analysis algorithm and system description have been given in published literature [She et al., 2004; Arnold and She, 2003]. [6] Figure 1 shows one set of lidar observations of the mesospheric Na layer from 21 to 24 February 2006 (days 052–055 of the year) and the results after applying a least squares fit. The lidar measurements (diamonds, one per hour) of the mesospheric Na layer full width at half maximum

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Table 1. Monthly Distribution of Full Diurnal Cycle Lidar Observation Between 2002 and 2008 at Fort Collins, Colorado Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Number of sets 11 11 7 7 9 10 10 15 25 22 17 14 Number of hours 365 316 213 297 315 312 483 399 719 610 403 406

(FWHM) (Figure 1a), Na abundance (Figure 1b), and the layer centroid height (Figure 1c) all clearly show tidal period modulations. These hourly data are weighted equally in the fitting analysis. We then reconstructed the hourly profiles from the resulting mean and tidal period perturbations. From these we computed the Na layer parameters for each hour and plotted them (crosses) in the same figure, which show good agreement between the Na layer observations and the reconstructed layer variations. The vertical bars indicate the uncertainty of the layer parameters derived from the uncertainties of harmonic analysis. Also given in this figure (and Table 2) are the amplitudes of the mean, diurnal (A24), semidiurnal (A12), terdiurnal (A8), and quadiurnal (A6) variations for each parameter. The tidal period modulations of Na layer thickness (FWHM) during this period are 1.36 km and 1.52 km for diurnal and semidiurnal period, respectively. The magnitudes of these two tidal components of the Na abundance are similar with values well over 10% of the mean value. The variation of the centroid height of the layer, although clearly showing tidal modulations, is not surprisingly small (a few hundred meters). Overall, the quadiurnal components are much less significant than the others, whereas the terdiunal components can sometimes be considerable. However, to uncover the mesospheric Na layer’s seasonal variations, considerably more data are essential to extract major diurnal tidal modulations and to minimize the transient variability either due to interactions with gravity waves [Xu and Smith, 2004] or modulation in mean state by planetary waves [Liu et al., 2007].

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[7] By December 2008, close to 5000 h of such full diurnal cycle lidar observations well distributed over the year, had been acquired. The monthly distribution of the full diurnal data sets is given in Table 1, where for each month, the number of sets of multiple day continuous observations and the total numbers of hours of such observations are given. Part of the data set had been utilized to study the seasonal variations of the mean fields and tidal perturbations in temperature and horizontal winds [Yuan et al., 2006, 2008a, 2008b]. Most recently, the comparison between temperature tidal measurements from the Na lidar and those from TIMED/SABER instrument [Yuan et al., 2010] shows generally good agreement, suggesting that the lidar observed climatology of tidal period perturbations based on this data set is a good indication of the solar thermal tidal wave modulations in the midlatitude mesopause region.

3. Seasonal Variations of Na Density and Tidal Period Perturbations [8] Using the harmonic analysis for each month, Figure 2 shows the seasonal behavior of monthly diurnal mean (tidalremoved) Na density in the mesopause region. For each month we model the diurnal mean Na density profile, ns(z), by a Gaussian function, from which the layer parameters, centroid altitude, z0, abundance, C0, and RMS width, s0 are determined: " # C0 ðz z0 Þ2 ns ðzÞ ¼ pffiffiffiffiffiffi exp : 2s20 2ps0

ð1Þ

[9] We use a Gaussian model and all available data (70 to 120 km) so that the results are consistent with and can be applied to the earlier theoretical study discussed in section 4. In Appendix A we discuss the difference in abundance by using data between 70 and 120 km and by using data between 80 and 105 km. Also discussed is the difference in Na layer parameters (using abundance as an example)

Figure 2. The seasonal variations of diurnal mean Na density. The tick positions to the left and right of the letter labeling a month mark the start and end of the month. 3 of 13


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Table 2. Seasonal Variation of Diurnal Mean Na Layer Over Fort Collins, Colorado Parametera

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

z0 C0 s0 A24b Α12c

90.0 5.46 6.45 3.25 3.86

91.8 3.76 4.90 8.99 7.70

92.0 3.48 4.49 5.36 6.83

91.9 2.91 4.41 5.97 1.37

90.6 2.15 4.88 2.04 1.12

90.0 1.63 4.25 1.65 1.04

91.3 2.36 5.09 2.47 1.67

91.6 3.14 4.66 3.68 2.53

91.5 3.0 4.40 3.96 5.61

90.8 4.61 4.51 3.58 6.94

90.7 5.71 4.88 4.16 3.78

90.3 7.46 6.04 3.46 3.90

Parameter (unit): z0, centroid altitude (km); C0, abundance (1013 m2); s0, RMS width (km). Diurnal amplitude: A24 (108 m3). c Semidiurnal amplitude: A12 (108 m3). a

b

deduced from the Gaussian fitting and by direct statistical calculations. [10] As Figure 2 shows, the Na layer is thicker and stronger in the winter months and thinner and much weaker in summer months. The monthly mean abundance, RMS width and centroid altitude of the diurnal mean Na density, are listed in Table 2 with standard deviations from the annual mean values of 1.7 1013/m2 for Na abundance,

0.68 km for RMS width and 0.74 km for centroid height. The abundance reaches its maximum in December with RMS maximum width in January due to the warm winter temperature in the mesopause region [Plane et al., 1999]. From Table 2, we can see that the centroid altitude of the mesospheric Na layer has an obvious seasonal cycle. It is at its lowest altitude in January and June (90.0 km) and rises to its highest altitude in March (91.9 km) and second-highest

Figure 3. The monthly mean Na density diurnal tidal amplitude profiles (red lines) and semidiurnal amplitude (green lines) showing their seasonal variations. 4 of 13

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Figure 4a. Diurnal tidal phase profiles of Na density (diamonds) and temperature (asterisks) for each month of the year as a function of local solar time (LST, in h).

altitude in August (91.6 km), showing high centroid in equinoctial months and low centroid near solstice. The RMS width of the layer is wider in winter (6.45 km in January, and 6.04 km in December) but shrinks to its minimum near summer solstice (4.25 km in June) while the Na abundance follows the same seasonal changes. The theory (chemistry) behind the mesospheric Na layer’s abundance and density seasonal variations is well stated in the literature [Plane et al., 1999; Plane, 2004]. Basically, the reservoirs for atomic sodium are mostly NaHCO3 below 96 km whereas they are Na+ above. While the conversion from NaHCO3 to atomic Na has strong positive correlation with in situ temperature (correlation coefficient larger than 0.8), the conversion from Na+ to Na is slightly negatively correlated with temperature (correlation coefficient 0.2) and thus less sensitive to temperature, due to their different temperature dependence of chemical reaction rates. Therefore, the cold (warm) temperature in the mesopause region during summer (winter) induces much smaller (larger) Na abundance. Although the revealed seasonal variation of the mesospheric diurnal mean Na layer is similar to that based on nocturnal only observations [She et al., 2000] with the earlier (classic) data set (1990–1999), there are noticeable differences. Since

this is not the emphasis of this paper, we further discuss the possible causes for these differences in Appendix A. [11] Figure 3 shows the seasonal variations of monthly diurnal (red) and semidiurnal (green) amplitudes of Na density. Diurnal amplitudes are large in February–April and August–November with a dominant peak between 85 and 90 km; they are weak in summer months (May–July). The same statement can be made for semidiurnal tidal amplitudes, except for April when the semidiurnal amplitude is comparable to those in summer months and is about 5 times weaker than the diurnal amplitude. The maximum peaks of the diurnal and semidiurnal Na density tides occur in February at 89 km with amplitudes of 9.0 108 m3 and 7.7 108 m3, respectively, while the minimum peaks occur in June with amplitude of 1.7 108 m3 at 84 km for the diurnal component and 1.3 108 m3 at 96 km for the semidiurnal component. The altitude dependence of semidiurnal and diurnal tidal amplitudes for February, March, and August–November appears to be nearly the same. For the months of June and December, the tidal amplitude profiles appear to be wavy, and for many other months (February–April and August–November) the tidal amplitude profile has a double peak with the larger one

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Figure 4b. Same as Figure 4a except for semidiurnal tide. slightly below the centroid height near 90 km and the smaller one near 95 km or above. These somewhat bizarre features of Na density tidal amplitude profiles are very different from the temperature and wind tidal amplitudes [Yuan et al., 2006, 2008b], especially for the semidiurnal component, whose amplitudes typically increase as altitude increases with a faster rate of increase above 90–95 km. As to be explained in sections 4 and 5, these wavy Na density tidal amplitudes are a direct reflection of the corresponding fractional tidal amplitude (tidal amplitude over diurnal mean) that is dramatically modified from the fractional atmospheric perturbation by a multiplicative function that depends on altitude, scale height and Na layer centroid height and RMS width. [12] In Figures 4a and 4b, we show the diurnal (Figure 4a) and semidiurnal (Figure 4b) tidal phase profiles for each month. Because the Na density will tend to follow the atmospheric density [Gardner and Shelton, 1985; Hickey and Plane, 1995], we plot the related atmospheric temperature tidal phase (asterisks) along with the Na density tidal phase (diamonds) to facilitate the explanation and discussion in section 4. Overall, the Na density tidal period perturbations show downward phase progression for most of the

year. Below the Na layer’s centroid height, the Na density semidiurnal tidal phase profiles (Figure 4b) follow those of the temperature well for many months of the year (phase difference around or less than 90 degrees). Although the behavior of the two diurnal components appears to be similar between January and April (Figure 4a) the differences are nontrivial for the rest of the year. Above the layer’s centroid height, there appear sudden and significant phase shifts (most of them are close to 180 degrees relative to temperature tidal phase profiles for semidiurnal perturbations). Here, we term the altitude at the middle of this rapid phase shifting (or phase jump) process as the switching altitude to simplify further discussion. We discuss the relationships between Na density tidal amplitude, the density tidal phase jump and temperature tidal perturbations in section 4.

4. Relationships Between Observed Na Density and Temperature Tidal Period Perturbations [13] Gardner and Shelton [1985] have discussed the perturbation of atmospheric and sodium densities in response to the passage of gravity waves in the mesopause region. They

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assumed that chemistry can be ignored and that the minor species, including Na atoms, move with the atmosphere which has an unperturbed exponentially decreasing atmospheric density, Ns(z) = N0ez/H, with scale height H and air density of N0 near the surface of earth. They also assume the mesospheric Na layer has a Gaussian Na density profile ns(z) with centroid altitude z0 and standard deviation (or RMS width) s0 as described in equation (1). They gave succinct relationships between the fractional Na density perturbation, Dn/ns and the fractional atmospheric density perturbation, DN/Ns in response to the propagating gravity waves. In the first order, these perturbations are related as

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periods of about 12 h or less [Gardner and Voelz, 1987; Senft and Gardner, 1991]. In addition, the period of diurnal tide is longer than 2p/f 18.4 h, where f is the Coriolis parameter (or inertial frequency) at Fort Collins, Colorado (40.6 N, 105 W). We therefore apply the formulation of Gardner and Shelton [1985] to semidiurnal and diurnal tidal period perturbations in this paper, and expect better agreement in the semidiurnal density tides. [16] As the atmosphere obeys the ideal gas law, the fractional atmospheric density perturbation, DN/Ns, where Ns is the unperturbed atmospheric density at an altitude in question, may be related to fractional pressure perturbation, Dp/ p, and temperature perturbation, DT/T, resulting from pas Dn 1 gH ðz z0 Þ DN Dp DN DT ¼ ; ð2Þ sage of a wave, as Ns ¼ p T . Since the pressure per1 ns g1 Ns s20 turbation is relatively small and our Na lidar does not where g is the ratio of specific heats, 1.4 for atmosphere. If measure pressure perturbations directly, to proceed further, the nonlinear effect is included through second order, their we assume that the pressure perturbation is negligible compared to temperature perturbation for simplicity, and replace relationship becomes DN DT Ns by T in equations (2) and (3). We acknowledge that Dn 1 gH ðz z0 Þ DN after the passage of a wave perturbation, the atmosphere will ¼ 1 Dp Dz ns g1 Ns s20 2 quickly restore itself to hydrostatic balance, i.e., p ¼ H . 2 2 2 2 1 g H 3gH g H DN 2 þ 1 2 ðz z0 Þ þ ðz z0 Þ : Strictly speaking, the fractional pressure perturbation may be Ns 2s0 2s20 2s40 ðg 1Þ2 negligible only when the vertical wavelength is much shorter ð3Þ than the scale height, i.e., lz < < H, a condition not necessarily true for longer wavelength semidiurnal tidal period [14] Whether the linear or higher-order theory is used, the perturbations. DT [17] With DN fractional Na perturbation, though related to the fractional Ns T and observed s0 along with altitudeatmospheric perturbation, is modified dramatically by a dependent DT (tidal period perturbation in temperature), T function that depends on the interplay of Na layer para- (monthly mean temperatures) and H, we can calculate the meters, zo and so. The fractional Na perturbation can magnitude of fractional Na density perturbations from (2) undergo a 180 phase shift near this point z0. On the other and (3), and compare them with the observed fractional Na hand, the fractional Na perturbation can be arbitrarily small density tidal amplitude. With this approximation, the atmoregardless of the fractional atmospheric perturbation, creat- spheric density perturbation is 180 degrees out of phase of ing more complex variation in Na density perturbation than the associated temperature perturbation. Since, unlike the mean atmospheric density, Ns (z), the Na mean density, ns the corresponding atmospheric density perturbation. [15] While Gardner and Shelton [1985] were interested in (z), first increases with altitude and then decreases above the deducing atmospheric density responses from the observed centroid altitude. To satisfy continuity, equations (2) and (3) Na density responses, the lidar observations reported here predict that the Na density and temperature tidal perturbapermit observation of both Na perturbations and atmospheric tions should be in phase below the switching altitude, z with 2 perturbations by observing the impact of waves on atmo- zz0 = s0/gH (typically 2–4 km above the centroid altispheric temperature (as well as on zonal and meridional tude) and 180 degree out of phase above it. This sharp phase winds). Therefore we can use observed properties of both switch is not only confirmed by modeling [Xu and Smith, atmospheric and Na density perturbations to investigate the 2004] but also found in the observed Na density tidal validity of these relations on the one hand, and to aid the phase profiles as indicated above. Inspecting the observed understanding of Na density tidal perturbations with these phase relations for semidiurnal tides (Figure 4b), we find relations on the other. We therefore need to relate the excellent agreement in January, February, and March, and atmospheric density perturbations to the observed tempera- reasonably good agreement in July, August, September, ture perturbations. For the interest of this paper, the wave October, November, and December, though the agreement perturbation in question has either diurnal or semidiurnal in April, May, and June is relatively poor. Since either Dp/p tidal period. Because of the assumption that the diffusion or chemical effects may not be completely negligible, there time of the minor constituent forming the atmospheric layer may be a phase shift between Dp/p and DT/T. The deviais much greater than the period of the atmospheric waves tions from the predictions for summer months are to be inducing the observed density perturbations, the analysis is expected, since for these months chemical effects are relamore applicable for semidiurnal tidal period perturbations. tively more important and the vertical wavelength of semiIndeed, previous works have concluded that Gardner and diurnal tide are much longer [Yuan et al., 2008b]. We note Shelton’s [1985] assumption of horizontally uniformity that the seasonal model of the Na layer incorporating may be relaxed. It is only necessary for the horizontal dis- chemistry [Plane et al., 1999] showed discrepancies in placement imparted by the gravity waves to be small com- summer months, especially in June and July, when the pared to the horizontal scale length of the unperturbed Na modeled centroid altitude is 2–3 km above that of observalayer, which is easily satisfied for all gravity waves with tion. Since the centroid altitudes by full diurnal observations 7 of 13

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Figure 5a. Comparison of Na density fractional semidiurnal tidal amplitudes between predictions via linear (equation (2), blue line) and nonlinear (equation (3), red line) relations and lidar observation (black line) for March, June, September, and December, representing four seasons. reported here are in general agreement with those previously reported from nighttime only observations, this discrepancy between model and observation in summer remains an open question.

5. Fractional Na Tidal Perturbations [18] In Figure 5a, we present the above three types of fractional semidiurnal Na density tidal modulation (lidar observed in black, the one deduced from equation (2) in blue and the one deduced from equation (3) in red) for March, June, September, and December, representing four seasons. By comparing tidal amplitudes in Figure 5a to the corresponding tidal phases in Figure 4b, we find for all the four cases considered that the minimum of the fractional semidiurnal tidal amplitude occurs at the phase switching altitude. [19] From Figure 4b, we determine the dominant vertical wavelength of the semidiurnal tide from its phase profile to be 35 km, 350 km, 49 km and 36 km for March, June, September, and December, respectively. Due to the considerable long vertical wavelength of temperature semidiurnal tide in June, the uncertainty of lz determined from the tidal phase profile is quite large for this month. By using the phase between 85 km and 95 km, lz for June semidiurnal tide may be estimated to be between 300 and 400 km. The density and temperature phases for March as shown in Figure 4b behave ideally, as the vertical wavelength of the Na density semidiurnal tide is the same as its temperature

counterpart, lz 35 km, and stay in phase with each other below the switching altitude near 93 km. This leads a strikingly good agreement between calculated (linear or nonlinear) and observed Na density fractional semidiurnal tidal amplitudes as shown in Figure 5a. We note that due to the structure of the nonlinear term in equation (3), the nonlinear correction above the altitude of the minimum fractional density tide is negligible, while it is noticeable but small below this height. The agreement between calculated and observed fractions in June is marginal, because not only the density and temperature semidiurnal tidal phase are very different, but they are 90 degrees out of phase within most of the mesopause region. In addition, the extremely long vertical wavelength during the month makes it impossible to fulfill the already relaxed approximation of lz < < H in the linear theory. As a result, the agreement between calculated and observed densities below minimum fractional amplitude is poor. The agreement in September and December is also fairly good, when the vertical wavelength and the degree of in phase between the two components share similar features as those of March (in December the vertical wavelength is shorter, lz 36 km and stay mostly in phase below 92 km; in September, lz 49 km, and in phase below 92 km). Similar analysis may be carried out for other months. Judging from the comparison between semidiurnal density and temperature tidal phases shown in Figure 4b, we expect that as in March, the agreement in January and February should also be excellent, while the agreement in summer months below the altitude of minimum fractional amplitude will be

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Figure 5b. Same as Figure 5a except for diurnal tidal amplitudes.

poor. In summary, for semidiurnal tidal components, whenever the vertical wavelength is relatively short and the two components (Na density and temperature) are nearly in phase with each other below the switching altitude, this theoretical relationship between fractional atmospheric density perturbation and fractional Na density perturbation represents the observations well. This is not the case in summer, as chemistry then likely plays an important role below 87 km [Xu and Smith, 2004]. [20] However, the period of diurnal tide may be too long to apply equations (2) and (3), as pointed out by Gardner and Voelz [1987], and in addition, there exists some considerable phase shift between diurnal Na density and temperature tides as can be seen in Figure 4a. Nonetheless, there still exists a reasonably sharp phase switching altitude in diurnal density tide for about half of the months. Unfortunately, unlike the semidiurnal tides, most of the phase jumps are less than 180 with the phase difference between density and temperature diurnal tides below the switching altitude. We present the comparison between calculated and observed diurnal tidal amplitude of Na density for March, June, September, and December in Figure 5b, representing four seasons. It is clear that the agreement is reasonably good for March and September between 90 and 100 km, while the agreement for June and December is marginal or poor. This difference may be anticipated based on the difference between the density and temperature diurnal phase plots in Figure 4a. Similar to the discussion on the semidiurnal component, the vertical wavelength of the diurnal

temperature tide for both March and September is about 34 km and there exists a clear phase switching altitude and the temperature and density tide are roughly in phase below it, with a difference of 20 for March and 50 for September. On the other hand, there exists no clear sharp phase switching in June or December, and the minimum phase shift between diurnal density and temperature tides along the profile is 65 for December and 120 for June, leading to poor agreement. By comparing the fractional tidal amplitudes in Figure 5b to the corresponding tidal phases in Figure 4a, we find that the minimum of the fractional diurnal tidal amplitude occurs at the phase switching altitude for the cases when the rapid phase shifting and amplitude minimum are clearly observed (March and September), the two out of four cases considered in Figure 5b. Examining the diurnal phase plots (Figure 4a), we expect that January, February, April, and November also produce good agreement between calculated and observed fractional diurnal Na density perturbations in addition to March and September. However, for many months, the calculated and observed Na density diurnal tidal period perturbations still differ significantly, implying the limitation of this relationship (equation (2) and equation (3)) and the possibilities that more processes should be involved in the study. For example, a theoretical study using an improved tidal model, such as Hough Mode Extension analysis [Oberheide and Forbes, 2008], to account for the complex phase difference between atmospheric density and temperature, along with a more complete accounting of the relationships between Na density and

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atmospheric density perturbations, which models nonlinear interactions [Xu and Smith, 2004] and includes both damping and chemistry effects, appears to be desirable. [21] The complexity of the Na density tidal amplitude profiles in Figure 3 is actually a direct reflection of the corresponding fractional Na density tides, which depends on fractional atmospheric density tide but modified dramatically by a function that depends on the interplay of Na layer parameters, zo and so creating additional minima. This makes it very difficult to deduce the fractional atmospheric perturbation from the corresponding Na perturbation at certain altitudes. For this reason, these wave perturbations in Na density are not an ideal proxy for atmospheric waves of interest. If the linear theory of Gardner and Shelton [1985] works perfectly, there is one additional sharp minimum in the profile. Deviation from the linear theory gives rise to multiple additional minima as seen, for example, in the December profiles of Figures 5a and 5b. To appreciate this relationship, we need only to realize that tidal perturbation is the product of fractional (relative) tide and the mean (background) density. Since the altitude variation of the mean Na density is mild and gradual, a minimum in the fractional amplitude gives rise to a minimum in the perturbation itself. For example, a clear minimum at 94 km is seen in the observed fractional amplitudes of both diurnal and semidiurnal tides for March and September in Figures 5a and 5b and a clear minimum is also seen in the corresponding Figure 3, giving rise to the double peaked profiles of March and September with a dip near 94 km. In December plots in Figures 5a and 5b, two minima are seen in lidar observed fractional diurnal amplitude at 89 and 101 km (Figure 5b), and three minima in the observed semidiurnal amplitude at 80, 88, and 95 km (Figure 5a), and the same minima are also seen in the Na density tidal amplitude profiles in December (Figure 3), giving rise to the wavy profiles observed. Similarly, for June, though the signal above 98 km is weak, we can see clearly the first minimum occurs at 88 km for diurnal tide and at 90 km for semidiurnal tide in Figures 3 and 5a.

6. Summary [22] Since the CSU Na lidar started full diurnal cycle observations of mesopause region Na density, temperature and horizontal winds in May 2002, the system has enabled many MLT dynamics studies based on its relatively large data set. Here, utilizing Na lidar full diurnal cycle observations of Na density from May 2002 to December 2008, we have deduced the mesospheric Na density tidal period perturbations and seasonal variations of the diurnal mean mesospheric Na layer. The mean Na density shows maxima near winter solstice and minimum around summer solstice, which is consistent with its seasonal behavior revealed by nocturnal lidar observations during 1990s [She et al., 2000]. The layer centroid height drops to its lowest point (90.0 km) in January, then, increases to its peak in March (91.9 km), followed by another minimum in June (90.0 km) and a secondary maximum in August (91.6 km). The Na layer also has large RMS width and high abundance in winter and the opposite scenario is found in June. [23] The newly reported diurnal and semidiurnal amplitude of Na density tidal amplitudes are observed to be large in February–March and August–December with a dominant

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peak between 85 and 90 km and small in summer months (May–July). While the diurnal and semidiurnal amplitudes are comparable in most months, in April, however, the diurnal amplitude is more than 5 times stronger than the semidiurnal amplitude. Unlike the temperature and wind tidal amplitudes [Yuan et al., 2006, 2008b], the observed amplitude profiles reveal a complex structure including a double-peak (or single sharp minimum) structure in many months other than December and summer months. In December and June, the profiles are particularly wavy with multiple extremes. [24] Unlike the temperature tide, the deduced tidal phase profiles of Na density, while showing downward phase progression most of the year, exhibit rapid phase shifts typically between 90 degrees and 180 degrees mostly during nonsummer months, at an altitude, termed the switching altitude, 2–4 km above associated Na layer centroid. In most cases, especially in semidiurnal tides, we find that the minimum of observed fractional tidal amplitude occurs near the switching altitude. For these cases when a clear phase switching and a minimum in fraction amplitude are clearly observed at nearly the same altitude, the formulation of Gardner and Shelton [1985] with the assumptions of negligible pressure perturbations and chemical effects, can be used to calculate and reproduce such fractional perturbation profiles that are in good agreement with the observed fractional Na density semidiurnal tidal amplitude many months of the year and diurnal amplitude for some months. The same formulation and a more recent model simulation [Xu and Smith, 2004] both predict this sudden and dramatic phase shift in the Na density tidal phase profile. This proves that the Na density tidal period perturbations are mostly driven by atmospheric dynamic sources. This said, we point out that there are months when the observed profiles differ from the prediction of Gardner and Shelton’s [1985] model, implying the limitation of this early study and calling for additional theoretical and modeling work. Since the switching altitude is essentially the altitude where the Na mixing ratio (Na density divided by the atmosphere density) has zero vertical gradient, from the dynamics view point, the Na mixing ratio perturbations may be more relevant than the Na density perturbations.

Appendix A: Parameters of Monthly Mean Na Layers [25] The parameters of a diurnal mean Na layer, abundance, centroid altitude, and RMS width, can be computed directly from the statistical definition of these quantities or by fitting the associated profile to a Gaussian curve. Since for a given 24 h period, the Na density profile usually does not have a Gaussian shape, the results calculated from these two methods could be quite different. However, for the monthly mean Na density profile, the Gaussian function is a good approximation, and we thus expect the resulting parameters to be quite similar. In this paper, to better compare with the theory [Gardner and Shelton, 1985], we use a Gaussian fitting to determine the monthly mean Na layer parameters with data between 70 and 120 km, a region that contains nearly all atmospheric Na atoms. This appendix addresses the questions of how well a Gaussian fits the observed monthly mean profile and what is the impact of

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Table 3. Monthly Mean Na Layer Abundances: Comparison Between Different Data Sets and Analysesa Itemb 1 2 3 4 5 6

Abundance c

C0(D) Abd(D)c C0(N)c DDN = 1–3 C0(D)d Abd(N)d

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

5.46 5.34 5.26 0.20 5.17 5.12

3.76 3.72 3.56 0.20 3.72 4.17

3.48 3.46 3.26 0.22 3.46 3.66

2.91 2.90 2.53 0.38 2.90 2.65

2.15 2.13 2.07 0.08 2.13 2.12

1.63 1.63 1.55 0.08 1.61 1.70

2.36 2.33 2.47 0.11 2.34 2.10

3.14 3.11 2.92 0.22 3.11 2.68

3.00 2.99 2.81 0.19 2.99 3.47

4.61 4.62 4.39 0.22 4.57 4.46

5.71 5.70 5.51 0.20 5.64 5.97

7.46 7.36 7.06 0.40 7.16 5.04

Parameters (unit): abundance (1013 m2). Items 1–5 based on 2002–2008 full diurnal cycle observations, 6 based on 1990–1999 nocturnal observations. c With data between 70 and 120 km. d With data between 80 and 105 km. a

b

tidal perturbations on the nightly mean profiles. The abundance for each monthly diurnal mean determined by Gaussian fit and by direct calculation are shown, respectively, as items 1 and 2 in Table 3, with item 1 taken from Table 2; their differences are between 0% for June and 2.2% for January. That a Gaussian profile can represent the monthly mean Na density profile very well can be seen in Figure A1, where we show the months of October (Figure A1a) and November (Figure A1b) with highest resulting Pearson’s correlation coefficient, R, of 0.9998 and 0.9997 respectively, and the months of July (Figure A1c) and January (Figure A1d) with lowest R values of 0.9973 and 0.9966, respectively. It is clear that the differences between data points and fitted curves are small for all months, and a Gaussian curve fits the diurnal mean profiles well.

[26] To discern the difference in abundance between a diurnal mean layer and a nighttime mean layer is much more difficult. This is in part because the length of nighttime lidar observation for each night is usually different, thereby contaminating the extent of tidal perturbations. For the investigation here, we consider a set of ideal nighttime monthly mean profiles, which are the 12 h averaged profiles (between 18 h, LST and 6 h, LST) from the same diurnal data set used in this paper. The abundance of this ideal nighttime data set is shown as item 3 in Table 3, with the difference between the diurnal mean and the ideal nighttime mean, DDN, given as item 4. Other than the month of July, we see positive differences with the largest difference in December, 0.4 1013 m2. The positive difference, yielding a higher abundance during the daytime sector, is consistent with the

Figure A1. The observed monthly diurnal mean Na density profiles and their associated Gaussian fits. Showing here are two months with excellent fits, (a) October and (b) November, along with two months with very good fits, (c) July and (d) January. The goodness of fit may be seen by their Pearson’s correlation coefficient R = 0.9998, 0.9997, 0.9973, and 0.9966, respectively. 11 of 13

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phase of diurnal tide falling in the daytime hours (between 6 h and 18 h) as shown in Figure 4a. In particular, the diurnal tidal phase between 83 and 93 km in April is centered near noon, where its corresponding amplitude is large (peaked at 88 km). However, the negative difference in July is puzzling. Though the diurnal tidal amplitude in July is relatively small, its phase nonetheless also occurs in the daytime sector. Therefore, the diurnal tide cannot be the sole root cause of the observed negative difference. Since neither 12 h nor 6 h tidal period perturbation can contribute to a 12 h average of our ideal nighttime mean, we need to investigate the terdiurnal tidal period perturbations. Since our full diurnal data set is able to determine the tidal period perturbation, and if the tidal reconstruction is perfect without residual, the difference should be equal to the sum of 24 h and 8 h tidal contributions averaged over the daytime sector (from 6 h to 18 h LST), we thus made an attempt to consider or even quantify these tidal contributions for April and July. Of course, both Gaussian fit and tidal reconstructions are not perfect, and we must consider their uncertainties. The Gaussian fitted abundances for diurnal mean and nocturnal mean (C0(D) and C0(N), respectively, in Table 3) have uncertainties; taking them into account, we can express the difference for the above two scenarios (DDN in Table 3) as 0.38 (0.04) 1013 m2 for April and 0.11 (0.08) 1013 m2 for July. Assuming conservatively, the mean percentage uncertainty of the tidal amplitude equals that of the tidal contribution to the associated abundance, we find diurnal and terdiurnal tidal contributions to abundance of 0.299 (0.047) 1013 m2 and 0.019 (0.015) 1013 m2 for April, and 0.122 (0.027) 1013 m2 and 0.010 (0.007) 1013 m2 for July. The total tidal contribution is then 0.32 (0.06) 1013 m2 for April and 0.11 (0.03) 1013 m2 for July. Since uncertainties exist in both tidal amplitudes and phases, the actual uncertainty will be larger than what we assumed. Though this exercise points to the right direction, unfortunately, it does not allow for a precise accounting of the difference in DDN we deduced. For example, unlike April, the terdiurnal contribution is negative in July, but its magnitude is smaller than the uncertainty of the associated diurnal contribution. [27] To quantitatively account for the difference between the full diurnal observations taken between 2002 and 2008 (items 1–5 in Table 3) and the nocturnal observations between 1990–1999 (item 6 in Table 3) is extremely difficult, if not impossible. Since our earlier work based on the classic data set, used only nighttime data between 80 and 105 km [She et al., 2000] and computed the Na layer parameters directly (as opposed to Gaussian fitting), we first calculate abundances based on the current data set by excluding the altitude region below 80 km and above 105 km, and take the results from our earlier work; they are listed, respectively as items 5 and 6 in Table 3. Comparing the abundance between item 5 and item 1, it is clear that excluding data from the edges of the Na layer does not change abundance for most months, except in January and December with values smaller by 5.5% and 4.1%, respectively, because the Na layers in winter months extend beyond these altitudes. For abundances based on the classic data set, we point out that, in July, the abundance listed here has been changed to 2.10 1013 m2 from the published value of 1.2 1013 m2. That the latter is a typo may be

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checked by calculating it from the published Na density in the same column in Table 2 of She et al. [2000]; it is also evident from She et al. [2000, Figure 2], in that Na density in July is more abundant than that in June. Even with this correction, the difference between the direct statistics calculated abundances (item 2 and item 6 in Table 3) ranges from 15% in September to +37% in December. In addition, the historic data were unfortunately analyzed with a different vertical resolution of 3.7 km, and the derivation of monthly mean profiles was done differently (see She et al. [2000] for details). The fact that the dwell time each night in the classic data set is different (ranging from 4 to 13 h) makes it impossible to quantitatively assess the associated tidal effects. Noticeably, the December abundance has increased by 37% in the current data set and it is higher than the November abundance (the other way around in the classic data set). It seems that these differences cannot be accounted for by either excluding the Na layer edge altitudes or by the unknown tidal effects. While this potential longterm change in Na layer is an interesting and, possibly, a real effect, without a more thorough reanalysis of classic data and careful study, a definitive conclusion is not possible. [28] Acknowledgments. The work done at Colorado State University was supported by NSF grant ATM-0545221 and NASA award NNX07AB64G. The work achieved at Utah State University was supported by NSF grant ATM-1041571. C.-Y. She acknowledges helpful discussions with C. S. Gardner on his early publications.

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