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CHAPTER 5

Characteristics of tidal variability in the mesosphere:

Signature of Terdiurnal tide

5.1 Introduction It is well known that gravity waves and tides are very important carrier of energy

and momentum from the lower atmosphere to the upper atmosphere and they modify the

dynamical condition of the concerned ambient atmosphere. Because of that they have got

significant importance in active research and become a interesting topic of frontline

research in recent few decades (Hines, 1960; Chapman, 1970; Reisin and Scheer et al,

1996; Fritts and Alexander, 2003; Taori et al, 2007). Tides are generated due to

absorption of incoming solar radiation by the atmospheric molecules, e.g. ozone, water

vapor, carbon dioxide etc. and also geared by the latent heat forcing in the atmosphere,

mostly in lower atmosphere and change the structure and dynamics of mesopause region.

Nature of migrating tide is well studied theoretically which shows the periodicities are

sub-harmonics of solar day, i.e. 24, 12, 8, 6, 4 hour etc. and they propagate westward due

to the relative motion of sun relative to earth (Chapman and Lindgen, 1970). Modeling

studies by several investigators (Bernard, 1981; Forbes and Vial, 1989; Hagan et al,

1995) have enriched our knowledge of tidal structure and their variability to some extent.

Interaction between tides and gravity waves is also strong enough to cause short term

tidal variability (Walterscheid, 1981; Fritts and Vincent, 1987; Lu and Fritts, 1993;

Nakamura et al, 1997; Beard et al, 1999).

Study of tides using airglow emissions was pioneered by Fukuyama, 1976;

Petitdidier and Teitelbaum, 1977. Airglow emission (OH layer ~ 87 km, O2 layer ~ 94

Km, Na layer ~ 89 km etc.) is an effective tool for performing upper atmospheric

variability study. As airglow is a passive remote sensing tool for acquiring information of

mesospheric processes, it can be used to obtain tidal characteristics of periodicity less

than 12 hour (Taylor et al, 1999) very efficiently. Thus routine measurement of

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mesospheric airglow emissions can give more insight in tracing out tidal variability and

their effect on global scale processes and associated change.

There are several reports of observation of diurnal and semi-diurnal tides in

mesospheric regions at various geographical locations with various ground based

instruments, e.g. LIDAR (Liu et al, 2007; Taylor et al, 1999), RADAR (Zhang et al,

2003), Airglow (Won et al, 2007) as well as space based instruments (Smith et al, 2000)

but still detection of terdiurnal tide lacks of measurement. Observation of terdiurnal tide

was first detected by meteor echo (Revah, 1969). After that very few investigators have

reported its occurrence in low latitude (Taori et al, 2005), mid-latitude (Wiens et al,

1995; She et al, 2002) and in high latitude (Younger et al, 2002; Wu et al, 2005b).Using

Radar, structure, characteristics of terdiurnal tide was extensively studied by Thayaparan

et al, 1997 throughout the year and the investigators got significant dominance around

spring and winter compared to the other times of the season. Taylor et al, 1999 also

obtained the large amplitude of terdiurnal tide at the same time mentioned before from

mid latitude stations (40 - 42oN) with very less or no evidence of diurnal and semi-

diurnal tidal components. Pendleton et al, 2000 have done comparative study of

terdiurnal tide in two mid latitude sites in OH nightglow emission.

The generation of terdiurnal wave is not very much understood still today.

Complex interaction mechanisms are responsible for the creation of the terdiurnal tide.

Probable reasons may be thermal excitation by solar heating (Chapman and Lindzen,

1970) or due to non-linear interaction between diurnal and semi-diurnal tides (Smith,

2000) or due to combination of two factors mentioned before (Glass and Fellous, 1975;

Teitelbaum et al, 1989) or due to interaction of tides with gravity waves (Miyahara and

Forbes, 1991).

5.2 Observation In the present study we have chosen late-winter dataset from a low latitude station

Maui, Hawaii (20.8o N, 156.2o W) to investigate the characteristics of terdiurnal tide

component in mesospheric OH and O2 airglow emission temperatures. The systematic

observation was actually a part of Maui Mesosphere and Lower Thermosphere (MALT)

program which was started since November, 2001. All the clear night data has been

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incorporated for analysis of both the OH and O2 emissions. We have used nocturnal data

of February-2003 which includes 20 clear nights with observation period greater than five

hours.

5.3 Data analysis and Results The nocturnal temperature data for the concerned month has been analyzed for

investigating long period terdiurnal tide signature. Figure 5.1 shows one typical nocturnal

temperature profile with respect to UT in hour for O2 and OH on UT Day - 40. It is clear

from the plot that the data is dominated by long period wave with short period

oscillations are superposed on it. A simple sinusoidal model has been used to fit best the

observed data.

)2(T

tSinBAYfit×

×+=π 5.1

where A is the DC level of the temperature data, which is nearly equal to the mean

temperature value, B is the observed wave amplitude, T is the period of the oscillation

and t is the time of variation of the data. Best fit result shows T ~ 7.04 ± 0.04 and 8.65 ±

0.04 hour, B ~ 5.14 ± 0.28 and 7.28 ± 0.25 K and A ~ 200 ± 0.2 and 198.5 ± 0.2 K for

OH and O2 respectively.

Figure 5.2 shows the ensemble of the temperature profiles of the whole month (20

Days) after taking half hourly average to smooth the profiles from short period

oscillations for OH and O2. O2 data exhibits larger range of variability compared to OH

data. On the other hand OH data exposes more consistent nocturnal variation for all the

nights shown here in comparison with O2 where variability is somewhat zigzag in

fashion. One should note the dominant long period oscillations are significant in both the

profiles (OH and O2).

To elucidate monthly nocturnal wave feature we have carried out average of all

the night profiles to a single temperature profile for both the OH and O2 temperature data

which is shown in Figure 5.3. Again best fit model as described before has been applied

to both the profiles and the best fit wave parameters comes out to be T ~ 7.52 ± 0.8 and

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Figure 5.1 Nocturnal Temperature patterns of O2 and OH have been shown with a

best sinusoidal fit to the data on the UT Day-40, 2003.

7.00 ± 0.11 hour, B ~ 3.13 ± 0.33 and 3.82 ± 0.55 K, A ~ 202.46 ± 0.24 and 198.41 ±

0.41 K for OH and O2 respectively. The observed phase difference between O2 and OH

temperature is ~ 1 hour which signifies the downward phase progression of upward

propagating wave.

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Figure 5.2 Ensemble of the nocturnal temperature profiles with respect to UT hour

for all the days of the month after taking half hourly average to smooth the short period

features for both the O2 and OH. More consistent pattern is observed in OH in

comparison with O2.

For better quantification of the terdiurnal tidal component on the nocturnal

variation pattern we have performed continuous wavelet analysis on the OH and O2

monthly averaged temperature data. Wavelet analysis reveals the conspicuous variability

pattern of wave amplitude with respect to time span of observation and the periodicities

(Torrence and Compo, 1998). We have used complex Morelet as a mother wavelet for

analysis which is actually a plane wave modulated by a Gaussian envelope to find out the

time-period spectrum of a non-stationary signal. The wavelet coefficient deduced by

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Figure 5.3 Same plot as defined in Figure 5.1, but here monthly average temperature

profiles have been plotted.

integrating the product of time series data and mother wavelet over all the time span is

actually signifying the concerned wave amplitude. The upper and middle panels show the

O2 and OH spectra respectively. The bottom panel represents the cross wavelet spectrum

which indeed describes the common wave packets present at the time of observation in

both the altitudes (87 and 94 km).

Both the spectra (O2 and OH) reveal a number of wave packets existing in the

nocturnal temperature. O2 wavelet spectrum indicates a dominant 6 - 8 hour wave for

most of the time of observation, whereas OH spectrum exhibits almost same wave (6 - 9

hour) characteristics and they are existing around ~ 5 - 7, 8 - 10, 11 - 14 UT hour and also

in the late night hours. Several common wave-packets are also observed in the spectra

with less magnitude. Evident from the cross wavelet spectrum, is the dominant 7 hour

periodicity wave around 5.5, 9, 12.5 UT hour.

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Figure 5.4 Top and middle panels are showing wavelet spectra of O2 and OH

average temperature profiles which is shown in Figure 5.3. Both the spectra show ~ 6 - 9

hour periodicity waves dominating over the nights. Bottom panel describes the cross

wavelet spectrum deduced from the OH and O2 wavelet spectra to figure out the common

wave features between two.

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5.4 Discussion In the present study we have investigated the terdiurnal tidal variability in the

nocturnal temperature data derived from OH and O2 airglow emission intensities in the

 

Figure 5.5 Same plot as described in Figure 5.2 but here temperature data is filtered

through a band pass digital filter centered at 8 hour with lower cut-off ~7 hour and

higher cut-off ~ 9 hour.

month of February, 2003 in Maui, Hawaii (20.8oN, 156.2oW ) using MTM. Results show

large day to day variability with a clear signature of terdiurnal tide for the whole month

of observation.

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To classify the terdiurnal component separately from other waves and tidal

features we have extracted the eight hour wave component with the help of a band pass

digital filter centered around 8 hour and lower cut off ~ 7 hour and higher cut off ~ 9

hour, after applying to the nocturnal temperature data profiles of the month for O2 and

OH. The ensemble of the filtered nocturnal profiles has been plotted in Figure 5.5.

 

Figure 5.6 This plot is same with Figure 5.3 except the fact that the profile is deduced

from the 8 hour filtered temperature profiles as shown in Figure 5.5. Amplitudes are

somewhat lesser compared to Figure 5.3 because of the omission of the other wave

components.

It is interesting to note the smoother variation of all the profiles for both OH and O2. It is

quite acceptable that the range of variability for both OH and O2 has been reduced to

some extent because of the cancellation of contribution of the wave periodicities less than

7 hour and greater than 9 hour to the concerned 8 hour wave component. Here we have

accepted only the waves with periodicities ranges between 7 and 9 hour.

Figure 5.6 depicts the monthly mean temperature profile of the filtered O2 and OH

data and also the best fit analysis is done which is same as the analysis done in Figure

5.3. The best fit model parameters are found to be T ~ 7.68 ± 0.06 and 7.01 ± 0.1 hour, B

~ 2.5 ± 0.18 and 2.72 ± 0.31 K, A ~ 202.28 ± 0.13 and 198.3 ± 0.23 K for OH and O2,

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Figure 5.7 Wave characteristics of terdiurnal tide have been shown here. Top panel

is showing amplitude variability observed in all the days. Second panel is showing phase

variation of the terdiurnal wave for OH and O2 Third panel is showing vertical

wavelengths deduced from the phase differences between OH and O2. Wave growth

factor is plotted in the bottom panel.

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respectively. It is noteworthy that almost same periods are obtained in both the unfiltered

and filtered data (OH and O2 temperature) but amplitudes are somewhat less in filtered

data with compared to the unfiltered one because of absence of the contribution from the

other wave components and it also corroborate the dominance of the 7 - 8 hour wave

features in the nocturnal variability throughout the month.

To characterize the terdiurnal tide we have calculated tidal amplitude, phase,

vertical wavelength and growth factor for all the days of the observing month (Feb, 2003)

with 8 hour filtered temperature data described before, which is shown in Figure 5.7. The

upper panel shows the 8 hour wave amplitude with respect to the corresponding days of

the month. The plot shows large variability in the amplitude for both OH and O2. O2

amplitudes show relatively larger value compared to the OH ones with a maximum ~ 19

K, whereas OH values show a maximum around ~ 10 K. Taori et al, 2005 found the

variability of tidal amplitude in the range ~ 5 - 17 K with average ~ 5.5 K which agrees

with our observed variability (~ 2 - 19 K). Using airglow imager and Na Lidar

observation in a mid latitude station during spring and fall equinox, Taylor et al, 1999

obtained variability of 8 hour component ~ 1.5 - 15 K and they concluded the dominance

of 8 hour wave is due to interplay of diurnal and semi-diurnal tidal components.

Pendleton et al, 2000 observed significant amplitude up to ~ 15 K for OH layer

observation in a mid latitude station during fall equinox, which is close to our observed

ones. Using Lidar temperature measurement She et al, 2002 showed that the variability

lies between ~ 1- 4 K which is quite low compared to other observations.

Phases of 8 hour tide have been shown in the second panel (from the top) for OH

and O2 with respect to UT days of the month. It is important to note that all the nights

show O2 phase leads ahead the OH one which validates the downward phase progression

with a mean phase shift ~ 1 hour. Taori et al, 2005 have found prominent phase shift ~ 1

hour among the two emission heights which matches exactly with our obtained value.

Vertical wavelengths (VW) have been derived with the values from phase

difference between OH (~ 87 Km) and O2 (~ 94 Km) and plotted in third panel (from the

top). Values of VW show significant day to day variability (~ 14 - 112 Km) with an

average of ~ 46 Km. Vertical wavelength obtained by several investigators match more

or less with our observed values. Thayaparan et al, 1997 observed VW ~ 30 ± 7 Km in

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February, 1995 from a mid-latitude station. Using Meteor Radar measurement Younger et

al, 2002 found VW ~ 31 ± 5.2 Km (in zonal wind) and 31.1 ± 5.8 Km (in meridional

wind) during winter season. Wu et al, 2005b have found VW for terdiurnal wave in a

high latitude station ~ 35 km. Taori et al, 2005 obtained a large variability of VW (~ 26 -

110 km) with a mean value ~ 63 km, which matches very well with our obtained VWs.

The growth factor (GF), a measure of wave amplitude growth/attenuation as the

altitude goes high, has been shown in bottom panel of Figure 5.7. From the plot it is clear

that most of the nights (GF > 1) show significant growth of 8 hour wave as it reaches

from 87 Km to 94 Km with a maximum value ~ 4.6 on UT Day-43 with a monthly

average ~ 1.6. It should be noted that some nights are dominated by significant wave

dissipation between these two layers as indicated by the plot. Taori et al, 2005 observed

GF variability ~ 0.6 - 1.9 in the same location in July, 2002 which is lesser compared to

our observed ones.

Very few investigators have studied the characteristics of terdiurnal tide so far.

Younger et al, 2002 have shown seasonal characteristics of terdiurnal tide using Meteor

Radar observation in polar mesosphere and they observed increase of tidal amplitude

with altitude. Using satellite based wind observation Smith et al, 2000 found terdiurnal

wave amplitude maximizes during spring and fall equinox in mid-latitude. Also using

radar observation Thayaparan et al, 1997 found significant contribution of 8 hour tide

during spring and winter season and less dominance during summer and fall time. Zhao

et al, 2005 found different seasonal pattern of 8 hour tide variability unlike other

investigators.

5.5 Summary Our present study in a low latitude site using best fit analysis of monthly averaged

data reveals the presence of terdiurnal tide in nocturnal temperature pattern of O2 and OH

airglow emissions with strong day to day variability in the mesosphere region during late

winter time. Wavelet analysis has been carried out on the monthly averaged temperature

data which shows quasi 8 hour wave dominance in both the layer in nocturnal

temperature pattern throughout the night. Cross wavelet analysis shows a strong quasi 8

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hour (~ 7 hour) wave, which exists in two altitudes (at 87 km and at 94 km)

simultaneously.

We have further analyzed the data by applying a band pass digital filter centered

at 8 hour and width ~ 2 hour. Monthly mean temperature profile shows ~ 1 hour phase

difference among OH and O2 layer with leading O2 phase over OH which indicates

downward phase progression. For characterization of the 8 hour wave we have derived

amplitude, phase, vertical wavelength and wave growth factor. Our observed terdiurnal

amplitude shows significant high value during the period of observation and it is well

compared with observations of other investigators performed previously. Observed

phases (in UT hour) of filtered O2 and OH temperatures show significant spread over the

nocturnal time span of the month. Vertical wavelength reveals larger range of variability

with compared to the most of the investigators mentioned before with an average value of

~ 46 ± 5 km. Growth factors as we obtained, indicate most of the nights are conducive for

large wave growth (mean ~ 1.6) for quasi 8 hour wave because of supportive dynamical

condition.

****End****

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