Earth Planets Space, 57, 393–398, 2005
The terdiurnal tide in the mesosphere and lower thermosphere over Wuhan
Guangxin Zhao1,2,3, Libo Liu1, Baiqi Ning1, Weixing Wan1, and Jiangang Xiong1
1Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China
2Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China
3Graduate School of the Chinese Academy of Sciences, China
(Received August 25, 2004; Revised April 18, 2005; Accepted April 18, 2005)
Winds measured by an all-sky meteor radar have been used to investigate the terdiurnal tide in the mesosphere
and lower thermosphere (MLT) region over Wuhan (30.6◦N, 114.4◦E). We present a climatology of the terdiurnal
tide at low-mid latitude site during the period of April 2002 to December 2004. The terdiurnal peak is distinct in
the long-term power spectrum of the wind. The monthly and seasonal mean maximum amplitudes have values
of 7 m/s and 5 m/s, respectively. The short-term amplitudes can occasionally reach up to 30 m/s, and at times
the terdiurnal tide is as large as the diurnal and semidiurnal ones. It seems that the meridional component is
more regular than the zonal one. An obvious annual variation is observed in the meridional phases with a phase
leading in winter than that in summer. The annual variation for the terdiurnal tidal amplitude is not obvious, and
is variable from year to year in our observations. This seasonal trend is slightly different from earlier studies at
Key words: Meteor radar, terdiurnal tide, mesospheric dynamics, nonlinear interaction.
Ground-based and satellite-based measurements and the-
oretical studies have greatly enriched our knowledge on the
diurnal (24-hour) and semidiurnal (12-hour) tides in the
mesosphere/lower thermosphere (MLT) region (e.g., Bur-
rage et al., 1995; Hagan et al., 1999; Manson et al., 1999).
However, there are still very limited studies on the terdiur-
nal (8-hour) tide in the MLT region, partly because of the
relatively small amplitude of the terdiurnal tide compared
to the diurnal and semidiurnal ones, as generally expected.
However, some workers have shown that the amplitude of
the terdiurnal tide is often comparable to that of the diur-
nal and/or the semidiurnal tides (Manson and Meek, 1986;
Cevolani, 1987; Reddietal., 1993; Teitelbaumetal., 1989).
Midlatitude observations suggest that the amplitude of the
terdiurnal tide is largest in winter or near winter months
(Manson and Meek, 1986; Teitelbaum et al., 1989; Thaya-
paran, 1997; Smith, 2000; Namboothiri et al., 2004). The
latest modeling studies of the terdiurnal tide also exhibit the
maximum amplitudes in winter (e.g., Akmaev, 2001; Smith
and Ortland, 2001). However, the polar meteor radar obser-
vations at Esrange (68◦N, 21◦E) show the maximum ampli-
tude in autumn (Younger et al., 2002).
The origin of the terdiurnal tide is still uncertain. Some
authors think that the terdiurnal tide cannot be completely
explained by the solar thermal driving. They found a more
irregular phase variation and shorter wavelength in sum-
mer than in winter, and that the short vertical wavelength in
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ences (SGEPSS); The Seismological Society of Japan; The Volcanological Society
of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sci-
summer was not consistent with solar driven modes (Glass
and Fellous, 1975; Manson and Meek, 1986; Cevolani,
1987; Teitelbaum et al., 1989). However the phase varia-
tions in summer can be explained by a nonlinear interac-
tion between the diurnal and semidiurnal tides (Glass and
Fellous, 1975; Teitelbaum et al., 1989). At some certain
times, the observed short-term terdiurnal tidal amplitudes
are correlated to those of the diurnal and semidiurnal tides,
and its vertical wave number is equal to the sum of the
vertical wave numbers of the diurnal and semidiurnal tides
(Cevolani, 1987; Thayaparan, 1997; Younger et al., 2002),
which supports the interpretation of nonlinear interaction.
Furthermore, some researchers presented that interactions
between the diurnal tide and gravity waves can also produce
near 8-hour and 12-hour oscillations (Miyahara and Forbes,
1991; Thayaparan et al., 1995).
In this study, the meteor radar wind data recorded at
Wuhan (30.6◦N, 114.4◦E) over the interval of April 2002
to December 2004 are analyzed to determine the terdiurnal
tide. The meteor radar system and data analysis are de-
scribed in Section 2. Then we present the short-term vari-
ations, monthly and seasonal amplitudes and phases of the
terdiurnal tide in Section 3. And the discussions and con-
clusions are made in Section 4.
2.Wuhan Meteor Radar and Data Analysis
An all-sky interferometric meteor wind radar began to be
operated at Wuhan (30.6◦N, 114.4◦E), China, with a peak
power of 7.5 kW, a duty cycle of 10% at a frequency of
38.7 MHz, a pulse repetition frequency of 1980 Hz and a
height resolution of typically <2 km since January 2002.
This system is almost identical to the Buckland Park meteor
394 G. ZHAO et al.: THE TERDIURNAL TIDE OVER WUHAN
radar in Australia (Holdsworth et al., 2004). A mean daily
meteor count recorded by the Wuhan meteor radar is about
2500–3000, and almost all meteor echoes appear in the
altitude region from 70 km to 110 km with the peak echo
counts near 91 km. Continuous observations have been
carried out from March 2002 to December 2004, apart from
a data gap of 56 days from February 26 to April 22 in 2003.
The observed meteor echoes are divided into five height
ranges 79–84, 84–88, 88–92, 92–96 and 96–101 km. Con-
sidering the mean height of all meteors recorded over the
entire period, the five height ranges are centered on 81.4,
86.1, 90.0, 93.9 and 98.5 km, respectively.
sured radial velocities, azimuths, zeniths and ranges in each
height range are used to infer zonal and meridional wind
components in a 1-hour window by applying a least-squares
fitting algorithm (Hocking et al., 2001). Then two meth-
ods are used to analyze the terdiurnal tide. The Lomb peri-
odogram analysis (Lomb, 1976) was used to verify the exis-
tence of evident peaks with periods near 8 hour. And a har-
monic analysis based on a least-squares fit was performed
to retrieve the amplitudes and phases of the terdiurnal tide.
In the harmonic analysis, the hourly mean data were fitted
to mean, 24-, 12- and 8-hour components. We used a 2-days
window, stepped by 1 day, and a fit for a given height inter-
val is performed only if there are data for at least 32 hours
in the 2 day data set.
Existence of the terdiurnal tide
Figure 1 gives the amplitude spectrum calculated from
the entire time series of meridional winds measured at 90.0
km in the period of April 2002 to December 2004. The 24-,
12- and 8-hour period peaks are clearly evident. The 24-
and 12-hour peaks represent the well-known diurnal and
semidiurnal tides. But we should be aware of that the 8-
hour oscillation in Fig. 1 can also be used to address other
waves with periods near 8-hour, such as gravity waves and
Lamb waves. Although the gravity waves play an important
role in oscillations in period band between 5 and 10 hours,
the peak at 8-hour rises markedly above the gravity-wave
background. And that any gravity waves with period near
8-hour may have random phases, so they would self-cancel
interval from April 2002 to December 2004.
The Lomb periodogram of meridional winds at 90 km in the
or submerge in a spectrum analysis using a so long time
series. This suggests that the 8-hour signal in Fig. 1 is not
primarily gravity waves.
The intradiurnal Lamb waves are observationally and
theoretically studied at polar region in the last two decades
(Hernandez et al., 1995; Forbes et al., 1999; Portnyagin et
al., 2000). Among them, the second symmetric mode with
period near 8.6 hours and the second antisymmetric mode
with period near 7.2 hours have similar periods to the ter-
diurnal tide. Forbes et al. (1999) suggested that the Lamb
waves may exist at middle latitudes by numerical simula-
tions, and it would be easy to confuse these waves with
terdiurnal tide for its limited lifetime. The 8-hour peak
in Fig. 1 should be interpreted as a terdiurnal tide rather
than Lamb waves for two factors (Younger et al., 2002).
First, Fig. 1 indicates a motion whose period is exactly 8
hours, but the Lamb waves only have similar periods to
tides. Second, the Lamb waves are not permanent atmo-
spheric phenomena and their lifetimes are limited, so they
can be easily concealed in a spectrum calculation using a
time series longer than two years. These factors suggest
that a terdiurnal tide really exists and it ought to be a per-
manent phenomenon in the atmosphere, as most authors
suggested (Thayaparan, 1997; Smith, 2000; Younger et al.,
2002; Namboothiri et al., 2004). We should note that the
gravity waves and Lamb waves may be as significant as ter-
diurnal tide in short terms, and may affect the day-to-day
variation of the terdiurnal tide by the superposition with the
Although the terdiurnal tide seems to be a persistent mo-
tion, the strong terdiurnal tide activity only appears from
time to time and usually last from 2 to 10 days. In this part,
we would show some examples of short-term daily ampli-
tude variations of this strong terdiurnal tide activity. Four
16-day continuous data sets of the terdiurnal tidal ampli-
tude at 93.9 km are presented on the left panel in Fig. 2. For
the purpose of comparison, the amplitudes of diurnal and
semidiurnal tides over the same period are also given. The
amplitude spectra, obtaining from Lamb periodogram anal-
ysis (Lomb, 1976), for the corresponding period are plotted
on the right panel of Fig. 2.
In these figures, the short-term daily amplitudes of the
terdiurnal tide can reach values as large as 20–30 m/s, and
that the terdiurnal tide occasionally has comparable am-
plitude with the diurnal and semidiurnal ones. Amplitude
spectra also show the existence of significant peaks at peri-
ods near 8 hours. Large day-to-day variability is found in
the tidal amplitudes. The amplitude variations of the ter-
diurnal tide in December 10–25, 2003 (bottom panel) are
correlated to those of the diurnal and semidiurnal tides, with
correlation values of 0.64 and 0.73, respectively, which sup-
ports the suggestion that the terdiurnal tide could be par-
tially generated by nonlinear interaction between the diur-
nal and semidiurnal tides (Teitelbaum et al., 1989; Thaya-
paran, 1997). But in other three examples, the correlation
values are quite low. Furthermore, this amplitude variation
may also be affected by the superposition of the terdiurnal
tide with gravity waves of comparable period, or result from
the resonant interaction among the diurnal, semidiurnal and
G. ZHAO et al.: THE TERDIURNAL TIDE OVER WUHAN 395
Fig. 2. Daily amplitude variations of the diurnal, semidiurnal and terdiurnal tides (left panel) and the corresponding amplitude spectra (right panel) for
the 16 days time series at 93.9 km.
terdiurnal tides at the mesopause region.
3.3Monthly mean and annual variations
Figure 3 gives the monthly mean amplitudes and phases
of the terdiurnal tide obtained at 86.1, 90 and 93.9 km from
April 2002 to December 2004. The phase of the terdiur-
nal tide is defined as the local time in hours after midnight
when the amplitude is maximal. The monthly tidal averages
are calculated by taking a vector average of the daily tidal
values. The monthly amplitudes display that the meridional
component is generally stronger than the zonal one. The
meridional terdiurnal tidal amplitudes are 2–7 m/s, and the
zonal ones are usually 1–5 m/s. There is not an obvious
season pattern in the zonal amplitudes. In 2003, the zonal
amplitudes seem to be slightly larger in winter and smaller
in summer. For the meridional amplitudes, the annual vari-
ation manner is variable from year to year. Obvious ampli-
tude maximums are found during late winter of 2003 and
early spring of 2004 (January–March). But in 2002, there
are not obvious seasonal pattern with comparative ampli-
tudes in most months. In 2004, enhanced meridional am-
plitude appeared in August. The larger meridional ampli-
tude in April 2003 may be partly come from that a vector
average we have used to calculate the monthly mean and
only eight daily tidal values are obtained in that month for
a data gap. This season pattern is some different from most
early observations in mid-latitudes those reported large am-
plitudes in or near winter months and small amplitudes in
summer (Manson and Meek, 1986; Teitelbaum et al., 1989;
Thayaparan, 1997; Smith, 2000; Namboothiri et al., 2004),
and also different from the polar region results at Esrange
ber/October (Younger et al., 2002). The observed differ-
ences may be geographical reasons because our observa-
tions are made at a lower latitude station compared to oth-
The phases of the meridional component are more regu-
lar than those of the zonal one. An obvious annual varia-
tion appears in the meridional phases with a phase in winter
leading that in summer. The phases are usually stable in
the summer and winter with phase transition in March and
September. This pattern is repeated in three years shown
here. The meridional phases for the three heights show
396 G. ZHAO et al.: THE TERDIURNAL TIDE OVER WUHAN
altitudes of 86, 90, 94 km, respectively.
Monthly mean amplitudes and phases of the terdiurnal tide at
a roughly similar behavior, but this feature is less obvi-
ous in the zonal phases. The regular annual variation in
meridional phases and the similar behavior at three separate
heights support the interpretation that the terdiurnal tide is a
real and permanent motion in the atmosphere. Under most
conditions, the phases of three heights only undergo a little
change, indicating large vertical wavelengths.
The similar phase variation manner has also been ob-
served at Wakkanai by Namboothiri et al. (2004).
at London, no obvious phase annual variation is observed
(Thayaparan, 1997). At Esrange, a distinct season varia-
tion in phases is visible in both the zonal and meridional
components, but the season pattern seems to consist of rel-
atively constant equinoctial values separated by solsticial
transitions (Younger et al., 2002), which is contrary to our
result with relatively constant solsticial values separated by
equinoctial transitions. Furthermore, the phases of merid-
ional component are less organized than the zonal ones at
Wakkanai and London. But in our results, the zonal phases
are more regular than the meridional ones.
3.4 Seasonal variations
Figure 4 presents the season behavior of height variations
ysis, the data from 2002–2004 were classified into spring
(March, April and May), summer (June, July and August),
fall (September, October and November) and winter (De-
cember, January and February). The seasonal averages of
tide are calculated by taking a vector average of the monthly
mean values. We present the amplitudes and phases in the
top and bottom panels, respectively.
The zonal amplitudes are usually less than 3 m/s except
at 98.5 km in winter. The amplitudes in winter are slightly
larger than those in other three seasons above 90 km, and
the minimum amplitude appears in fall. Above 90 km,
the winter amplitudes show an abrupt increase with height,
changing velocity from ∼1 m/s below 90 km to near 4 m/s
at 98.5 km. The fall amplitudes are usually less than 1m/s
except at 81.4 km with a little larger value. It is noticeable
that the spring amplitudes decrease with height below 90
km and increase above this height, reaching a minimum
value (near 0 m/s) at 90 km, and a phase jump appears at
the same height.
The meridional amplitudes are in the range of 2–5 m/s,
and are larger than the zonal one in all seasons. This may
be partly resulted from a vector average we have used, be-
cause the meridional phases are more regular than the zonal
ones (see Fig. 3). The meridional amplitudes in winter,
spring and summer have comparable values in our results.
Many observations at mid latitudes show that the winter
amplitudes are obviously larger than the summer ampli-
tudes (Thayaparan, 1997; Namboothiri et al., 2004). But
this characteristic is not distinct at Wuhan. In fact, the
summer amplitudes of the meridional component at Wuhan
are larger than the winter ones at most heights except near
94 km. The fall amplitudes are again the smallest one at
heights above 85 km (about 2 m/s) for the meridional com-
ponent. It is noted that a phase transition from summer
to winter appears between September and November (see
Fig. 3), which can affect the seasonal average amplitudes
by taking a vector average. The height dependence of the
fall amplitudes is not obvious, but the amplitudes in other
three seasons generally increase with height (the winter am-
plitudes attain maximum at 94 km and decrease above this
The phase of the terdiurnal tide is presented at the bot-
tom panel of Fig. 4. The meridional phase profiles are more
regular and smooth than the zonal ones, and phase jumps
are often found in the zonal phases, especially a big phase
jump appears at 90 km in spring. For both the zonal and
meridional components, the winter phases are earliest. Fur-
thermore, the meridional phases are generally earlier than
the zonal phases. The mean phase differences are about 2
hours in spring, summer and fall, and become smaller in
winter. A downward phase propagation is found in most
cases. A linear trend is evident in the spring and summer
phases of the meridional component, corresponding a verti-
cal wavelength of ∼150 km.
4. Discussions and Conclusions
In this paper, we have presented a general picture of
the terdiurnal tide in the MLT region over Wuhan (30.6◦N,
114.4◦E). The terdiurnal tide seems to be a permanent fea-
ture of the mid-latitude MLT region. Although the monthly
and seasonal mean values of the terdiurnal tide are signif-
icantly smaller than the diurnal and semidiurnal tides, the
short-term amplitudes are comparable to the diurnal and
semidiurnal ones at times. Strong day-to-day variations ex-
ist in the present study, and large amplitudes can occasion-
ally reach up to 30 m/s. To specify the mechanisms pro-
ducing short-time variations is difficult, probably due to the
G. ZHAO et al.: THE TERDIURNAL TIDE OVER WUHAN 397
Fig. 4. Seasonal mean amplitudes and phases of the terdiurnal tide measured over Wuhan.
existence of several mechanisms involved: direct thermal
excitation by solar heating; non-linear interaction between
the diurnal and semidiurnal tides; tidal and gravity wave
interaction; wave propagation characteristics; and tidal am-
plitude modulation by planetary waves.
The nonlinear interaction between the diurnal and semid-
iurnal tides is suggested as an important mechanism to
cause the terdiurnal tide by several authors (Glass and Fel-
lous, 1975; Teitelbaum et al., 1989; Thayaparan, 1997).
The observational evidence for tide interactions involve that
the short time amplitude variations are correlated to those of
lengths of the terdiurnal, semidiurnal and diurnal tides meet
the relation . In our observation, we also find some exam-
ples of short time amplitude variations correlation, such as
the bottom panel of Fig. 2 (more examples are not shown
here). Interaction between diurnal tide and gravity waves
was considered to be another origin to produce oscillations
near 8-hour (e.g., Miyahara and Forbes, 1991; Thayaparan
et al., 1995). Thayaparan (1997) surmised that such inter-
action might explain at least some of the large amplitudes
observed over London. Together with the direct thermal
driven mechanism by solar, each one of these mechanisms
may play an important role at certain times of year, and they
can also coexistent at some time.
Some authors reported a phase jump associated with a
minimum in the amplitude, and they explained that this
phenomenon is the result of the superposition of two waves
of different origin (Teitelbaum et al., 1989; Thayaparan,
1997). Two such examples in our research are presented
in Fig. 5. For these two cases, we can see the minimum
amplitude at 90 km accompanied by a phase jump at the
same height. Further, Younger et al. (2002) found that some
of the amplitude fluctuations of the terdiurnal tide appear
quasi-periodic in character. They also gave an example
that the 8-hour tidal amplitudes vary with a quasi-2-day
period, and explained this as a result of a nonlinear coupling
between tides and planetary waves.
The monthly mean amplitudes of the terdiurnal tide are
∼2–7 m/s for the meridional component and ∼1–5 m/s for
the zonal component, which are similar to the results at
London (Thayaparan, 1997). But another midlatitude ob-
servation at Wakkanai (45.4◦N, 141.7◦E) has given monthly
amplitudes up to 15 m/s. The annual variation for the ter-
diurnal tidal amplitude is not obvious, and is variable from
year to year in our observations. A more long term observa-
tion is needed to understand well the season pattern of the
terdiurnal tide at Wuhan. An obvious annual variation ap-
pears in the meridional phases with relatively constant sol-
sticial values separated by equinoctial transitions, and this
pattern is repeated in the years shown here.
Compared to other studies at higher latitudes stations, the
significant differences. For example, the amplitudes during
winter are larger than those during summer, as many mid
latitude observations reported (Manson and Meek, 1986;
Teitelbaum et al., 1989; Thayaparan, 1997; Smith, 2000;
Namboothiri et al., 2004), which is not clear at Wuhan.
398 G. ZHAO et al.: THE TERDIURNAL TIDE OVER WUHAN Download full-text
Fig. 5. Height profiles of the amplitude and phase of the terdiurnal tide during March 31 to April 15, 2002 (top panel), and July 4–19, 2002 (bottom
sites, observational period and observational manner.
In general, we only give a primary picture of the terdiur-
nal tide at mid-low latitude. More observations are needed
to investigate the season pattern in our site and more com-
parisons with other stations are also needed to understand
the latitude and longitude difference of the terdiurnal tide in
Acknowledgments. This research was supported by the KIP Pi-
lot Project (kzcx3-sw-144) of Chinese Academy of Sciences, Na-
tional Natural Science Foundation of China (40134020) and Im-
portant Basis Research Project of China (G2000078407).
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