The lunar tides in the mesosphere and lower thermosphere over Brazilian sector

Author’s Accepted Manuscript The lunar tides in the mesosphere and lower thermosphere over Brazilian sector A.R. Paulino, P.P. Batista, L.M. Lima, B.R. Clemesha, R.A. Buriti, N. Schuch www.elsevier.com/locate/jastp

PII: DOI: Reference:

S1364-6826(15)30037-7 http://dx.doi.org/10.1016/j.jastp.2015.08.011 ATP4263

To appear in: Journal of Atmospheric and Solar-Terrestrial Physics Received date: 14 May 2015 Revised date: 21 August 2015 Accepted date: 22 August 2015 Cite this article as: A.R. Paulino, P.P. Batista, L.M. Lima, B.R. Clemesha, R.A. Buriti and N. Schuch, The lunar tides in the mesosphere and lower thermosphere over Brazilian sector, Journal of Atmospheric and Solar-Terrestrial Physics, http://dx.doi.org/10.1016/j.jastp.2015.08.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The lunar tides in the mesosphere and lower thermosphere over Brazilian sector A. R. Paulinoa,∗, P. P. Batistab , L. M. Limaa , B. R. Clemeshab , R. A. Buritic , N. Schuchd a

b

Universidade Estadual da Paraiba, Campina Grande/PB - Brazil Instituto Nacional de Pesquisas Espaciais, Sao Jose dos Campos/SP - Brazil c Universidade Federal de Campina Grande, Campina Grande/PB -Brazil d Centro Regional Sul de Ciencias Espaciais, Santa Maria/RS -Brazil

Abstract Meteor radar observations at S˜ao Jo˜ao do Cariri (7.4oS; 36.5o W), Cachoeira Paulista (22.7o S; 45o W) and Santa Maria (29.7o S; 53.7o W) have permitted estimates to be made of winds in the mesosphere and lower thermosphere (MLT) over the Brazilian sector simultaneously. Using horizontal winds the semidiurnal lunar tide is determined from January 2005 to December 2008 for these three sites. The lunar tide is observed to reach amplitudes as large as 8 m/s. In general, the amplitude increases with height and the phase decreases with height, corresponding to an upwardly-propagating tide. The estimated vertical wavelengths are variable for some month, like December at Cachoeira Paulista for northward wind, April and June at Santa Maria for eastward wind, which indicates possible mode coupling and reflection. Characteristics similar to those seen in the Northern Hemisphere have been observed in June ∗

Corresponding author Email address: [email protected] (A. R. Paulino)

Preprint submitted to JASTP

August 28, 2015

and October at S˜ao Jo˜ao do Cariri, in December at Cachoeira Paulista, in March at Santa Maria and in August at all observation sites, which suggest the presence of antisymmetric modes. Different behaviour has been observed in the amplitudes, phases and vertical wavelengths at each station, indicating latitudinal variation even from the low to the equatorial region. Keywords: Lunar semidiurnal tides, Atmospheric tides 1. Introduction 2

The atmospheric lunar tide is generated in the lower atmospheric region primarily by the gravitational forcing of the moon on the Earth-Ocean-

4

Atmosphere system and propagates vertically achieving large amplitudes in the mesosphere and lower thermosphere (MLT region). The vertical motion

6

of the oceans at the lower atmosphere boundary is an important mechanism for generation the lunar tide. In the MLT region there are several observa-

8

tional series made with radar measurements and more recently with satellite measurements that have contributed to the understanding of the structure

10

and characteristics of this oscillation in the whole Earths atmosphere. Both ground-based and satellite observation have revealed many important fea-

12

tures of the lunar tide. Ground-based measurements are convenient for studying in detail the sea-

14

sonality, long term variability, and vertical structure at different geographic points around the world. This type of technique has provided several studies

16

on lunar tides. For instance, radar measurements have shown that this oscil2

lation shows seasonal and year to year variation (e.g., Stening et al. (2003); 18

Niu et al. (2005); Sandford et al. (2006)). These characteristics can be explained by changes in the background atmosphere i.e., changes in the wind

20

and temperature (e.g., Stening et al. (1997a); Fejer et al. (2010); Paulino et al. (2012a)). Since the lunar tides can be modified by the conditions of the mid-

22

dle atmosphere, and the forcing is well known, their determination is important, because it can help in understanding how the conditions of the middle

24

atmosphere act upon the tides while they propagate through this region. Some studies have made comparisons of the lunar tide using winds ob-

26

tained with radar measurements at two sites, for example, Stening et al. (1994) analyzed the lunar tide at Saskatoon (52o N, 107o W) and Adelaide

28

(35o S, 138oE). Niu et al. (2005) have compared the lunar tide at Wuhan (31o N, 114o E) and Adelaide from 2002 to 2003. The objective of these

30

works was to study symmetry of the lunar tide with respect to the equator. Sandford et al. (2006) have made a comparative study of the lunar tide using

32

two stations at different latitudes (high and middle latitudes). At high latitude, Sandford et al. (2007) have compared the lunar tide from two stations

34

separated by about 150o longitude. Other studies have been made at equatorial and low latitudes region (e.g.,

36

Stening et al. (1997b, 2003); Sandford and Mitchell (2007); Stening and Vincent (1989)). However, all of these studies were made in different periods of time.

38

Since the lunar tide has a well known year to year variability it is necessary to do these studies in coincident periods. 3

40

Winds in the MLT region have been measured in Brazil since 1999 at Cachoeira Paulista (CP - 23o S, 45o W) and since 2004 at S˜ao Jo˜ao do Cariri

42

(SJC - 7.4o S, 36.5o W) and Santa Maria (SM - 29.7o S, 53.7o W) using meteor radars. Simultaneous measurements for these stations were collected

44

from 2005 to 2008. These observations in the same period of time offer an opportunity to compare the behaviour of the lunar tide at equatorial and low

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latitudes over Brazil. The present work investigates simultaneous measurements of the lunar semidiurnal tide, which has a period of 12.420lunar hours

48

or 1.9323 cycles per day, from these stations. 2. Instrumentation and Methodology

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The data used in this study have been measured in the MLT region by all-Sky interferometric meteor radars (SkiYmet) at three Brazilian stations:

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S˜ao Jo˜ao do Cariri (7.4o S, 36.5o W), Cachoeira Paulista (22.7o S, 45o W) and Santa Maria (29.7o S, 53.7o W). The data were recorded from January

54

2005 to December 2008. The meteor radars use five two-element Yagi receiving antennas, which are set up as an asymmetric cross, and one three

56

elements Yagi transmitter antenna [see Hocking et al. (2001), for further details]. These radars operate at 35.24 MHz and transmit 2144 pulses per

58

second. The transmitted signals are reflected by meteor ionized trails from meteoroids impinging on Earth‘s upper atmosphere. These meteor echoes

60

can be detected by the receiving antennae array. The radial drift velocity can be determined from the Doppler shift of the returned signal from meteor 4

62

trails, since it is assumed that the environment where the trail are formed, moves due to the neutral wind. The number of useful meteor echoes detected

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per day is typically between 1000 and 3000. The sampling of meteor changes during the day, where the maximum detection rate is observed at around

66

6:00 local time and the minimum is around 18:00 local time. The number of useful meteor detections makes it possible to obtain hourly wind value in 3

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km bins from 82 to 107 km (Clemesha et al., 2001). In the present work, the northward and eastward winds are estimated in

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hourly time bins for seven atmospheric height intervals of 4 km thickness, with a height overlap of 0.5 km, centered at 81 km, 84 km, 87 km, 90 km, 93

72

km, 96 km, and 99 km. Monthly mean tidal amplitudes and phases are calculated for each height using the least squares method of Malin and Schlapp

74

(1980), where the winds are assumed to consist of a mean wind and sinusoidal solar (diurnal, semidiurnal and terdiurnal components) and lunar

76

tidal (semidiurnal component) oscillations, as can be seen from the following equation:

 V = V0 + A1 cos

78

2π t − φ1 24



 + A2 cos

2π t − φ2 12



 + A3 cos

2π t − φ3 8



 + A4 cos

2π τ − φ4 12

 (1)

where V0 is the mean wind, t is the solar time and τ is the lunar time. The lunar time is given by τ = t − ν and ν is the lunar age, which is equal to

80

0 at the new moon (e.g., Stening et al. (1994, 2003); Sandford and Mitchell (2007); Paulino et al. (2012b)). 5

82

Amplitudes, phases and vertical wavelengths calculated for the lunar semidiurnal tide are compared with those estimated for the Vial and Forbes

84

(1994) lunar semidiurnal tide model. This model includes forcing by the Moons gravitational attraction on the atmosphere, as well as a dynamical

86

effect caused by the vertical motion of the lower boundaries. A wave number S = 2 is used in the model, and their parameters do not vary from year to

88

year, because the model was run only for 1993. Moreover, the parameters do not vary throughout the month, so the results provided for each month are

90

representative values of 15th day of each month (see Vial and Forbes (1994)). 3. Results and Discussion

92

The monthly-means observed amplitudes and phases for each month from successive years (2005-2008) were vector averaged to yield a composite year.

94

Figure 1 shows the monthly mean amplitudes for each height bin and for each available month between 2005 and 2008. Panels (a) - (c) show the northward

96

amplitudes and panels (g) - (i) show the eastward amplitudes for S˜ao Jo˜ao do Cariri (SJC), Cachoeira Paulista (CP) and Santa Maria (SM), respectively.

98

Panels (d) - (f) and (j) - (l) indicate the northward and eastward amplitudes predicted by the Vial and Forbes (1994) model for the latitudes of the three

100

Brazilian sites. At SJC, the amplitudes [panels (a) - (g)] increase with height for both

102

components, except in January for the northward component where amplitudes reached values between 3 m/s and 6 m/s for practically all heights. 6

104

The northward amplitudes are larger than the eastward from January to March and from August to November. The eastward component is larger in

106

April (∼ 4 m/s), in June (∼ 4 m/s) and in December (∼ 5-6 m/s) above 93 km. The smallest amplitudes for the northward component are observed

108

from May to July for all heights and in June below 96 km. However, for the eastward component, amplitudes smaller than 2 m/s are observed from

110

August to October for all altitudes and February, April, May and July for altitudes below 90 km. In March, August, September, October, November

112

and December for heights above 93 km are observed northward amplitudes with values higher than 3m/s. However, for the eastward component this

114

feature is observed in June, November and December. In January the highest amplitude during the year for the northward com-

116

ponent is observed at SJC with values as large as 6 m/s, whereas, for the eastward amplitude, it is verified in December. The monthly mean ampli-

118

tudes observed at SJC for the northward wind do not show the outstanding semiannual variation predicted by the Vial and Forbes (1994) model at 08o

120

S [panel (d)]. The model predicts maximum amplitudes for the northward component in winter and summer months of the southern hemisphere, how-

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ever the observations showed a minimum in winter months and a maximum in January with a secondary peak in November. The observed monthly mean

124

values for the eastward component are larger than the values predicted by the model during the year, but the mean values of the northward amplitude have

126

the same magnitude as those predicted by the model for this component. 7

Sandford and Mitchell (2007) using meteor radar data obtained at Ascen128

sion Island (8o S, 14.4o W) from 2001 to 2005 determined the lunar semidiurnal tide in the wind components from 78 km to 100 km and observed

130

monthly-mean amplitudes broadly similar to those obtained at SJC (between ∼ 1.5 and 3 m/s). In general, they found northward amplitudes in winter-

132

time and summertime larger than the eastward component. At SJC this feature is similar only for summertime. Stening et al. (1997b) have reported

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the lunar tide using horizontal winds over Christmas Island (2o N, 203o E) from 1990-93. The mean amplitude observed was about 2 m/s. The mean

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amplitudes observed at SJC are larger than at Christmas Island. However, the periods when these three studies (Ascension Island, SJC and Christmas

138

Island) were conducted are different. Furthermore, the monthly mean values shown here includes January 2006 that showed an unusual enhancement at

140

these stations that could be a response for the sudden stratospheric warming (Paulino et al., 2012a).

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The observed northward component at CP [panel (b)] shows four clear peaks along the year, between February and March (for practically all heights),

144

May and June (above 90 km), October and December (above 90 km) and January (below 90 km). In April and from July to October for all heights,

146

and between May and June for heights below 90 km the northward amplitudes are smaller than ∼ 2 m/s. For eastward wind, values of this order

148

are obtained from January to March, May and June for altitudes below 90 km, and in August for all altitudes. The northward wind is larger than the 8

150

eastward, except for January above 90 km. For the model, in both components at 22o S [panels (e) and (k)], predicted

152

amplitudes are smaller than the observed during the year. The model shows, for the northward component, peaks similar to those observed in January

154

and from October to December, but the predicted amplitudes are smaller. The model predicts semiannual variation for the eastward component above

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90 km with maximum amplitudes in the summer months and from July to August, but the observations showed maximum amplitude in the summer

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months and from April to May above 90 km. At SM [panels (c) and (i)], the results for both components show a semi-

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annual variation with maximum in October-February (above 90 km) and in April-May (above 93 km), but the values for the northward component are

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larger, reaching values as large as 8 m/s. Values of the northward amplitudes varying between 1.0 m/s and 2.5 m/s are obtained between June, July

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and September for all altitudes and from December to May below 87 km, however for eastward component similarly low values are observed below 90

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km for all months, except in October. During winter months for altitudes below 85 km for the eastward component is observed a peak with amplitudes

168

varying between ∼ 2.5 m/s and ∼ 4m/s. The model showed a semiannual variation for both components at 30o S with maximum amplitudes in the

170

summer months and from July to August, but in the data for Santa Maria this feature is observed in the summer months and from April to May. For

172

the model, values for both components vary between ∼ 1 m/s and ∼ 8 m/s. 9

Niu et al. (2005) found that the largest northward lunar tidal amplitude 174

at Adelaide (35o S; 138o E) occurred in January-February with a second peak in November. The largest eastward amplitude was observed in January-

176

February and in October. This analysis was made for 2002-2003 using horizontal winds from 80 to 98 km. The results for Adelaide are similar to SM for

178

the northward component and in January-February for the eastward component. It is important to note that these studies are not for the same years.

180

So the differences are maybe due to the well known year to year variability of the lunar tide.

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Figure 2 shows the amplitudes (left panels) and phases (right panels) for northward (solid line) and eastward (dashed line) components for a single

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year 2005 at SJC (top panel), CP (middle panel) and SM (bottom panel). The error bars, in this Figure, indicate the standard deviation of the mean.

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In both components at SJC a semiannual variation is clear, with maximum amplitudes in summer and winter months for the northward component. This

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feature is predicted by the model at 8o S for the northward component [Figure 1(d)] at 93 km. For the eastward component the maximum amplitudes are

190

observed in April and August. In contrast, the model does not suggest a semiannual variation for the eastward component at 8o S [Figure 1(j)]. The

192

semiannual variation observed for a single year is not observed in the averaged amplitude (Figure 1). The reason, maybe, is the self-cancellation of the

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seasonal fluctuation and/or inter-annual variability in the phase eventually present in the data. 10

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The northward amplitudes at CP are maximum in February, June and November. However, the eastward amplitudes are larger in June, July, Octo-

198

ber and November. The amplitude values for eastward wind are smaller than 2 m/s from January to May and the amplitudes are varying between 3 m/s

200

and 5 m/s from June to December. For 93 km the predictions of the model [Figure 1(e) and 1(k)] do not agree with the observations. The amplitudes at

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SM showed peaks in February, April, August and November for the northward component and in February, July and November for the eastward. The

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model predicted minimum values in April, but maximum values in August and November for the northward wind [Figure 1(f)]. The result suggested

206

by the model at 30o S for the eastward component [Figure 1(l)] at 93 km is similar to the observed. With respect to the phase (right panels of Figure

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2) at SJC, the eastward and northward components are in phase in January, February, September, November and December. The eastward phase leads

210

the northward in March and July by about 3h, and in April and May by 2h. However, in June, August and October the eastward phase occurred later

212

than the northward by about 3h, 5h and 4h, respectively. At CP the eastward and northward components are in phase in January

214

and July. The eastward phase leads the northward by about 2h in February, October and November, 3h in September, 4h in April, 5h in March and 6h

216

in May and June. Moreover, in August and December the eastward phase is later than the northward by about 2 and 3h, respectively.

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At SM the eastward phase leads the northward in April and May (3h), 11

February and October (∼ 4h), June, July and September (∼ 6h). In January, 220

November and December the components were practically in phase. But, in March the eastward phase lags the northward by around 6h.

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The phase relation between northward and eastward winds for SJC show characteristics of the equator according to classical tidal theory, from Novem-

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ber to February and in September. Behavior characteristic of the Southern Hemisphere is observed from March to May and in July, and characteristic

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of the Northern Hemisphere in June, August and October. At CP the lunar phase has Southern Hemisphere characteristics from February to June and

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from September to November. Behavior characteristic of the Northern Hemisphere is observed in August and December at CP and in March and August

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at SM. SM shows behavior characteristic of the Southern Hemisphere from February to July and in October, however in September and from November

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to January characteristics of the Equator are observed. Stening et al. (1997b) studied the lunar tide at Christmas Island using

234

all data together (1990-1993) and they observed that the phase of the two components was about 6 hours different above 82 km in May, August and

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December, corresponding to Equator characteristics. Stening et al. (2003) have also observed these three different characteristics for the phase relation

238

between eastward and northward components at Jakarta (6.4o S; 106.7o E). They suggested that the characteristic of the Northern hemisphere in the

240

Southern hemisphere may occur due to an invasion across the equator by Northern hemisphere conditions and the effect of antisymmetric tides. 12

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Figures 3 and 4 present height versus monthly mean profiles of northward (Fig. 3) and eastward (Fig. 4) phase for SJC (square + black line), CP

244

(circle + red line) and SM (star + blue line). Error bars, in Figures 3 and 4, represent the uncertainties in the calculation plus the variability from

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year to year for the lunar semidiurnal tide. Upward propagating phases are observed for the northward component at SJC in the months of January,

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from March to May, June (84-93 km), July, August (> 87 km), September (< 93), October (< 90 km), and December. Over CP upward propagating

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phases are observed in March, April (< 87 km), May (> 87 km), from June to August, September (> 84 km) and October (< 90 km). SM shows the

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same characteristics for northward wind in January (84-93 km), February (> 93 km), May (> 84 km), June (> 87 km), July (< 93 km), August (> 84

254

km) and December (> 87 km). For eastward wind (Fig. 4) upward propagating phases are observed at

256

SJC in January (< 87 km), February (< 87 km), March (< 96 km), April (> 87 km), May, June, August (> 90 km), September (< 93 km), October

258

and December. For CP these conditions are obtained in January (> 87 km), February (> 90 km), May (> 84 km), June (87 km-96 km), July (< 96

260

km), August (> 90 km), September, October, November (> 84 km) and December. For SM phase decreasing with height is observed in January (>

262

87 km), February (< 90 km), March (> 90 km), April, May (> 90 km), June, July, August, September (< 96 km), October, November (< 96 km)

264

and December. 13

In some months, as for the northward component, at SJC in June (> 93 266

km) and October (> 90 km), at CP in September (< 84 km), at SM in May (< 84 km), July (93 km) and December (< 84 km) phase progression in the

268

opposite direction is observed. We also observed, a changing direction of the phase propagation in the eastward component at SJC in March (> 96 km),

270

at CP in January (< 87 km), February (< 90 km), March (> 93 km), May (> 84 km) and August (> 87 km), at SM in May (< 84 km). Phase progression

272

in the opposite direction is indicative of reflection or mode coupling. Phase increasing with height is observed for the eastward component at

274

SJC in July, August (below 87 km) and in November. Similar behavior is observed for the northward component in February (below 90 km) and

276

October (above 90 km). This also occurs at CP in January (87-96 km) for northward and for eastward component in January (below 84 km) and August

278

(above 90 km). At SM the phase progress increasing with height is verified for northward components in January (above 90 km), February (from 81-93

280

km), March (above 90 km), April (from 81-99 km) and for eastward wind in May (below 87 km).

282

Some studies have pointed to indications of reflection or mode coupling as well in different periods (e.g., Stening et al. (1987); Stening (1989) and

284

Stening and Vincent (1989)). The vertical phase progression allows the determination of the vertical

286

wavelength of the lunar semidiurnal tide for each month. This estimative has been made by least mean square straight line fit. In order to eliminate 14

288

outliers, the points very far from this adjusted line have been removed and a new vertical wavelength was determined. Table 1 shows the height range

290

used to estimate the vertical wavelength for each component and site. In parentheses are shown the height removed from vertical phase profile.

292

Figure 5 shows the observed [panels (a) and (b)] and modeled [panels (c) and (d)] vertical wavelength for northward (left side) and eastward (right

294

side) components over SJC (square + black line), CP (circle + red dashed line) and SM (star + blue dash dot dot line). For the model 8o S (square +

296

black line) has been used for SJC, 22o S (circle + red dashed line) for CP and 30o S (star + blue dash dot dot line) for SM. This Figure shows the ver-

298

tical wavelength for the cases in which the lunar tide is upward propagating. Blank space indicate either very long wavelength (>130 km) or downward

300

propagation conditions. Very long vertical wavelength for northward components are observed in

302

February and March for CP, April for SJC and SM, and November for SJC and CP. Whereas, for eastward component, these conditions are observed in

304

March for CP, April, May, July and November for SJC and September for CP.

306

Northward vertical wavelengths shorter than about 30 km were observed at SJC in June and December, at CP in July, August and September, and

308

at SM in June, August and September. For the eastward wind, wavelengths shorter than about 30 km are obtained in August at SJC, in May and August

310

at CP and in March, April and November at SM. 15

The estimated vertical wavelengths showed values from 30 km to 50 km 312

for northward component in February, March, May, July, August, September and October at SJC; in April, May, June and October at CP and in January

314

and July at SM. For eastward wind those values are observed at CP in February, June and July and at SM from May to September.

316

Vertical wavelength varying from 50 km and 120 km are observed for northward wind in January at SJC, in January and December at CP and

318

in February, March, May and from October to December at SM. For the eastward component similar behaviors are obtained from January to March,

320

June, October and December at SJC; in January, April and from October to December at CP and in January, February, October and December at SM.

322

The values predicted by the model for the northward component are greater than those observed at SJC from May to August and December;

324

and for the eastward wind from June to August and December. At CP for this component agreement with the model is observed in May-August,

326

but in October and January the values presented by the model are larger. Besides, at SM the model predicted values larger than observed from May to

328

September and January. A similar discrepancy was observed for the eastward wind at SJC from January to March, June, August to October and December;

330

and at CP in January, February, April-September, August, from October to December. For the eastward wind at SM these feature are verified for all

332

months, except January. In general, SM has vertical propagation conditions are better than the 16

334

other sites, because the mean vertical wavelengths at this site in both components are smaller than 130 km during practically all the year. However,

336

the prediction of the model showed very long wavelength for this latitude in February, March, October and November for both components and in De-

338

cember for the northward wind. In the southern hemisphere winter months (June-August) we observed vertical wavelengths smaller than 40 km for the

340

northward wind for all of the three sites. On the other hand, for the eastward component this feature is observed at the three sites only in August. In June

342

the eastward wind wavelength at SJC was 59.91 ±3.17 and for the other sites it was smaller than 40 km. In July at SJC the phase increased with

344

height, at CP the wavelength was 48.89±2.00 km and at SM 53.58±3.98. The model prediction for eastward component at a latitude similar to those

346

of the three locations of this study is larger than 70 km for this time and for the northward component the model showed wavelengths larger than 60 km

348

at SJC and SM, only CP presented values smaller than 40 km. In Southern hemisphere summer (December-February) the lunar tide ex-

350

hibited good propagating conditions for the three sites, except in February at CP for northward component. In this period, a small value is observed in

352

December at SJC (27.32±2.50 km) and a large value is observed in December at SM (96.84±14.45 km). Better agreement with the model in this time

354

interval is observed in January for all three sites and at SJC in February and December.

356

In some months, like December (51.02±2.93 km below 87 km and 92.96±22.63 17

km above 93 km) at CP for the northward wind, April (15.52±0.88 km below 358

87 km and 33.52±9.64 km above 90 km) and June (18.60±0.40 km below 87 km and 43.06±6.20 km above 90 km) at SM for eastward wind, the ob-

360

served vertical wavelengths indicate possible reflections, because the time of the maximum becomes slightly later at greater heights.

362

Sandford and Mitchell (2007) estimated the zonal and meridional vertical wavelengths for Ascension Island and they observed that the wavelengths are

364

generally between ∼ 50 and 80 km but range from a minimum of 12±2 km in October to a maximum of 150±60 km in February.

366

Stening and Vincent (1989) studied the lunar semidiurnal tide at Adelaide during 1983-1985 and verified that in December the eastward wind has

368

a mean vertical wavelength of about 25 km below 92 km. Above 92 km the wavelength becomes much longer with some possible reflection as the time

370

of maximum becomes slightly later at greater heights. In June the eastward wavelength at 78 km - 90 km was 38 km with a phase discontinuity around

372

88 km. In August they showed vertical wavelength of 36 km above 88 km for northward component and below this height phase progresses in the opposite

374

direction indicating reflection or mode coupling. In March the vertical wavelength was 48 km for the eastward wind above 88 km, below this height there

376

was again evidence of oppositely directed phase progression. At Saskatoon, Stening et al. (1987) obtained eastward vertical wavelengths of about 25 km

378

above 87 km using all eastward wind from 1980-1983, while for 1984-1985 the wavelength was 81 km or more. In March the wavelength was about 30 18

380

km to 40 km from 93-102 km. The theoretical vertical wavelength was calculated based on the classical

382

tidal theory for three sites studied here. The wavelength in units of scale height is given by

384



2π

1/4[4h−1 n (κH+dH/dx)−1]

where H is the scale height, hn is equivalent depth, κ = (γ − 1)/γ and 386

γ = Cp /CV . The equivalent depth used was 7.07 km for the (2,2) Hough mode, 3.26 km for the (2,3) Hough mode, 1.85 km for the (2,4) Hough mode,

388

1.19 km for the (2,5) Hough mode and 0.83 for the (2,6) Hough mode [for more information see Tsuda et al. (1981) and Chapman and Lindzen (1970)].

390

The results were compared with the observed wavelengths and the associated Hough modes for each month.

392

It is important to note that this analysis is just a roughly estimate of possible Hough modes because identification of a particular mode is difficult

394

due to the presence of mode coupling and/or reflection of the tides [Stening (1989)]. The estimated Hough modes are shown in Table 2. In general,

396

the lunar semidiurnal tide is mainly associated with (2,3), (2,4), and (2,2). However, in some months the Hough modes (2,5) and (2,6) are important.

398

Few months show the predominance of only one mode and in most of the cases the characteristics of the wavelengths allow the presence of two or three

400

modes. The presence of only either symmetric or antisymmetric modes was not observed. In July for the eastward wind at SJC and in April for the 19

402

northward component at SM the phase progressed increasing with height. Tsuda et al. (1981) determined the lunar semidiurnal tide using meteor

404

radar winds at Kyoto and verified that the wavelength range is from 40 to 75 km which corresponds to the (2,3) and (2,4) mode. Forbes (1982)

406

verified theoretically that similarly to the solar-thermal semidiurnal tide, the lunar semidiurnal tide for solstice conditions in the MLT region is mainly

408

associated with the (2,4) predominant mode with secondary contributions from (2,2), (2,3) and (2,5) modes. The (2,2) mode is the more important

410

below 70 km and above 120 km, but in the latter case there is a strong secondary contributions from the (2,3) mode. For equinox conditions similar

412

characteristics are obtained, except that the antisymmetric (2,3) and (2,5) modes are absent.

414

Forbes et al. (2013) reported that the characteristics of the seasonallatitudinal distribution of lunar tidal temperature amplitudes observed in the

416

9 year (2002-2011) mean tidal climatology obtained from TIMED-SABER observations are in large part explicable in terms of the (2,2) and (2,4)

418

Hough modes with additional contributions from the (2,4) and (2,5) Hough modes. However, in the MLT region the growth of the (2,2) modes is re-

420

tarded facilitating the dominance of the (2,3) mode. In several months of this analysis the presence of the (2,3) mode is observed. Also, from global

422

TIMED/SABER temperature measurements, Paulino et al. (2013) verified that the lunar semidiurnal tide presented an asymmetric behavior in rela-

424

tion to the equator during the year, which suggest that asymmetric modes 20

contribute significantly to this oscillation. Furthermore, they observed a sig426

nificant longitudinal variability that reveals the existence of non-migrating components in addition to the dominant migrating tide.

428

Stening et al. (1994) reported that Hough decomposition of the simulated results of Vial and Forbes (1994) indicates, at least, 83% of the lunar ampli-

430

tude can be attributed to the (2,4) and lower-order modes. This could be an explanation for the discrepancies observed between the present observation

432

and model predictions of the wavelengths in the MLT. 4. Conclusions

434

The lunar semidiurnal tide at three Brazilian sites has been measured by meteor radar during the years 2005 2008. The northward amplitudes

436

were larger than the zonal during almost all of year. The observed phase generally decreases with height, corresponding to an upwardly-propagating

438

tide. However, evidences of reflection or mode coupling have also been observed for some months for all stations. Characteristics of the Northern

440

Hemisphere have been observed in June and October at SJC, in December at CP, in March at SM and in August at all observation sites, which suggests

442

the presence of antisymmetric modes. Different behaviour has been observed in the amplitudes, phases and vertical wavelengths at each station, indicat-

444

ing latitudinal variation even for the comparatively small range of latitudes explored. The model does not represent well the mean variations observed

446

at three latitudes. However, in 2005, the model gives results agreeing with 21

the observation for northward components at SJC. This may be an indica448

tion of the influence of year-to-year variation. In general, SM has vertical propagation conditions better than the other sites, because the mean vertical

450

wavelengths for this site in both components are smaller than 130 km during practically all the year.

452

5. Acknowledgments The authors thank the CEDAR database that kindly supplied the data

454

of the Vial and Forbes (1994) model of the lunar semidiurnal tide and the Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq -

456

Brazil) for the financing of this study under contracts 460624/2014-8 and 166286/2013-3.

458

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26

Figure 1 Contour plot of the lunar semidiurnal tide amplitude for north540

ward and eastward components during the period between 2005 and 2008 from S˜ao Jo˜ao do Cariri SJC (a, g), Cachoeira Paulista CP (b, h), Santa

542

Maria SM (c, i), Model 08 S (d,j), Model 22 S (e, k), and Model 30 S (f, l). Color scale represents amplitude.

544

Figure 2

Amplitude and Phase at 93 km over S˜ao Jo˜ao do Cariri

(black solid line for northward and black dashed line for eastward), Cachoeira 546

Paulista (red solid line for northward and red dashed line for eastward) and Santa Maria (blue solid line for northward and blue dashed line for eastward)

548

in 2005. Figure 3 Variation of the northward phase of the lunar tide with height.

550

Black line is for S˜ao Jo˜ao do Cariri, red line is for Cachoeira Paulista, and blue line is for Santa Maria.

552

Figure 4 As for Figure 3 but for eastward component. Figure 5 Vertical wavelength for the northward (left side) and eastward

554

(right side) wind components. Top panels are for observations and bottom panels are for Vial and Forbes (1994) model.

556

Table 1 The height ranges used to estimate the vertical wavelength for northward and eastward components at S˜ao Jo˜ao do Cariri, Cachoeira

558

Paulista and Santa Maria. Table 2 Estimative of Hough modes for lunar semidiurnal tide at S˜ao

560

Jo˜ao do Cariri, Cachoeira Paulista and Santa Maria.

27

Figure 1: Contour plot of the lunar semidiurnal tide amplitude for northward and eastward components during the period between 2005 and 2008 from S˜ ao Jo˜ ao do Cariri SJC (a, g), Cachoeira Paulista CP (b, h), Santa Maria SM (c, i), Model 08 S (d,j), Model 22 S (e, k), and Model 30 S (f, l). Color scale represents amplitude.

28

Figure 2: Amplitude and Phase at 93 km over S˜ ao Jo˜ ao do Cariri (black solid line for northward and black dashed line for eastward), Cachoeira Paulista (red solid line for northward and red dashed line for eastward) and Santa Maria (blue solid line for northward and blue dashed line for eastward) in 2005.

29

Figure 3: Variation of the northward phase of the lunar tide with height. Black line is for S˜ ao Jo˜ ao do Cariri, red line is for Cachoeira Paulista, and blue line is for Santa Maria.

30

Figure 4: As for Figure 3 but for eastward component.

31

Figure 5: Vertical wavelength for the northward (left side) and eastward (right side) wind components. Top panels are for observations and bottom panels are for Vial and Forbes (1994) model.

32

Month Height - SJC (N) January 81 - 99 February 90 - 96 March 84 - 99 April 84 - 99 May 81 - 96 June 84 - 93 July 81 - 99 August 81 - 99 September 81 - 99 October 81 - 90 November 81 - 99 December 81 - 99

Height - SJC (E)

Height - CP (N)

81 93 81 84 81 81 81 87 81 81 81 81

81 87 81 81 81 84 81 81 84 81 87 81

-

93 99 96 99 99 99 99 99 99 96 99 99

Height - CP (E)

- 87 87 - 99 - 99 90 - 99 - 99 81 - 93 - 99 (87, 90) 81 - 99 (84, 87) - 99 81 - 99 - 99 87 - 96 -99 81 - 96 - 99 90 - 99 - 99 81 - 99 - 99 81 - 96 - 99 81 - 99 - 99 87 - 99

Height - SM (N)

Height - SM (E)

84 93 84 84 84 84 81 81 81 81 93 87

81 81 81 81 90 81 81 81 81 81 81 87

-

90 99 90 99 99 99 93 99 99 (87) 96 99 99

-

99 99 99(90) 99 99 99 99 99 99 99 99 99

Month Jan Feb Mar Abr May Jun Jul Aug Sep Oct Nov Dec

S˜ao Jo˜ao northward (2,3)(2,2) (2,3)(2,4) (2,3)(2,4) (2,2) (2,4) (2,5)(2,6) (2,4) (2,3)(2,4) (2,3)(2,4) (2,3)(2,4) (2,3)(2,2) (2,5)(2,6)

do Cariri eastward (2,2)(2,3) (2,2)(2,3) (2,2)(2,3) (2,2)(2,3) (2,2)(2,3) (2,2)(2,3) (2,6) (2,4)(2,5) (2,2)(2,3)

Cachoeira Paulista northward eastward (2,3)(2,4)(2,5) (2,2)(2,3) (2,2) (2,4)(2,5)(2,6) (2,2) (2,2)(2,3) (2,4)(2,5) (2,2)(2,3) (2,3)(2,4)(2,5) (2,4)(2,5)(2,6) (2,3)(2,4)(2,5) (2,4)(2,5)(2,6) (2,6) (2,4)(2,5)(2,6) (2,5)(2,6) (2,4)(2,5)(2,6) (2,5)(2,6) (2,2)(2,3) (2,4)(2,5) (2,2)(2,3) (2,2) (2,2)(2,3) (2,2)(2,3) (2,3)(2,4)(2,5) (2,2)(2,3)

1

Santa Maria northward eastward (2,3)(2,4) (2,2)(2,3)(2,4) (2,3)(2,4) (2,2)(2,3)(2,4) (2,3)(2,4) (2,5)(2,6) (2,5)(2,6) (2,3)(2,4) (2,2)(2,3)(2,4) (2,5)(2,6) (2,5)(2,6) (2,5)(2,6) (2,2)(2,3)(2,4) (2,6) (2,5)(2,6) (2,6) (2,5)(2,6) (2,3)(2,4) (2,2)(2,3)(2,4) (2,3)(2,4) (2,5)(2,6) (2,3)(2,4) (2,2)(2,3)(2,4)