PUBLICATIONS
Journal of Geophysical Research: Atmospheres
RESEARCH ARTICLE
10.1002/2013JD020150
Key Points:
• Investigation of relation of
nonmigrating tides and stationary
planetary waves
• Amplitudes of these tides and
waves in midlatitude stratosphere
vary in synch
• Seasonal variations of migrating tides
are not controlled by the interaction
Evidence for nonmigrating tides produced
by the interaction between tides and stationary
planetary waves in the stratosphere
and lower mesosphere
Jiyao Xu1, A. K. Smith2, Mohan Liu1, Xiao Liu1, Hong Gao1, Gouying Jiang1, and Wei Yuan1
1
State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences,
Beijing, China, 2Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, Colorado, USA
Abstract
Correspondence to:
Jiyao Xu,
[email protected]
Citation:
Xu, J., A. K. Smith, M. Liu, X. Liu, H. Gao, G.
Jiang, and W. Yuan (2014), Evidence for
nonmigrating tides produced by the
interaction between tides and stationary planetary waves in the stratosphere
and lower mesosphere, J. Geophys. Res.
Atmos., 119, 471–489, doi:10.1002/
2013JD020150.
Received 7 MAY 2013
Accepted 20 DEC 2013
Accepted article online 25 DEC 2013
Published online 27 JAN 2014
In this work, 11 years (2002–2012) of Thermosphere, Ionosphere, Mesosphere Energetics, and
Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) global temperature
data are used to study the nonlinear interaction between stationary planetary waves (SPWs) and tides in the
stratosphere and mesosphere. The holistic behavior of the nonlinear interactions between all SPWs and tides is
analyzed from the point of view of energetics. The results indicate that the intensities of nonmigrating
diurnal, semidiurnal, terdiurnal, and 6 h tides are strongest during winter and almost vanish during summer,
synchronous with SPW activity. Temporal correlations between the SPWs and nonmigrating tides for these four
tidal components are strong in the region poleward of 20° and below about 80 km. In the tropics, where the
SPWs are very weak in all seasons, the correlations are small. Bispectral analysis between triads of waves and
tides shows which particular interactions are likely to be responsible for the generation of the nonmigrating
tides that are largest in the midlatitude stratosphere. Based on the more limited SABER observations at high
latitudes, the correlations there are similar to those in midlatitudes during spring, summer, and autumn; there
are no high-latitude observations by SABER in winter. These results show that nonlinear interactions between
SPWs and tides in the stratosphere and the lower mesosphere may be an important source of the nonmigrating
tides that then propagate into the upper mesosphere and lower thermosphere.
1. Introduction
In recent years, numerous studies have shown that nonmigrating tides are prevalent in the middle and upper
atmosphere [e.g., Oberheide et al., 2006; Wu et al., 2008]. Several mechanisms for forcing these tides have
been proposed and investigated: topographical forcing [Zhang et al., 2010a], longitudinal variations in latent
heat release [Oberheide and Forbes, 2008; Zhang et al., 2010b], and nonlinear interaction between planetary
waves and migrating tides [Teitelbaum and Vial, 1991; Pancheva et al., 2002; Chang et al., 2011]. The process of
wave-wave interactions and the generation of secondary “child” waves when a planetary wave and tide are
present have been investigated in theoretical studies [e.g., Beard et al., 1999; Angelats I Coll and Forbes, 2002].
If the secondary wave is able to propagate vertically, the nonmigrating tide can be seen far from the location
of the original wave-tide interaction.
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XU ET AL.
Hagan and Roble [2001] simulated the global structures of the diurnal tides using the thermosphereionosphere-mesosphere electrodynamics-general circulation model and found evidence that the interaction between the migrating diurnal tide (DW1) and stationary planetary waves produce nonmigrating
diurnal tides (S0 and DW2). Angelats i Coll and Forbes [2002] investigated the source of the semidiurnal
tides with zonal wave numbers of 1 and 3 (SW1 and SW3) that are often observed in the southern
hemisphere mesosphere and lower thermosphere in summer. They used a three-dimensional nonlinear
spectral model to study the interaction between the planetary wave and tides. The good agreement
between model results and observations supports the conclusion that SW1 and SW3 originate from tideplanetary wave (PW) interactions. Modeling by Yamashita et al. [2002] showed that the SW1 propagated
from the northern hemisphere winter stratosphere to the summer mesosphere at the South Pole.
The theoretical and modeling evidence for the possibility of generating nonmigrating tides through the
interaction of tides with stationary planetary waves (SPWs) is compelling but does not guarantee that this
process is responsible for the observed nonmigrating tides. However, observational evidence for the
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020150
importance of this process is building. Much of the observational evidence for tide-PW interactions has come
from studies linking tides in the mesopause region with planetary waves in the winter stratosphere. One
particularly striking result is the large nonmigrating semidiurnal amplitudes in the southern high-latitude
summer [Angelats I Coll and Forbes, 2002] and their temporal correlation with northern hemisphere planetary
waves [Murphy et al., 2009]. A similar correlation has been seen for PWs in the southern hemisphere winter
stratosphere and the net semidiurnal (migrating plus nonmigrating) tide at a single radar site [Smith et al.,
2007]. Xu et al. [2009b] found the link to be asymmetric between the hemispheres; because of their much
larger amplitudes, the northern hemisphere SPW has a larger impact on the generation of semidiurnal
nonmigrating tides than do southern hemisphere SPW.
Lieberman et al. [2004] used temperature profiles observed by the Limb Infrared Monitor of the Stratosphere
on the Nimbus 7 satellite from November 1978 until February 1979 to study the short-term variations in
diurnal tides and PWs in the northern hemisphere lower mesosphere. They presented evidence that
PW-migrating tide interactions are a source of the DW2 nonmigrating tide. As in the studies cited
above, the primary evidence is a temporal correlation between the DW2 and PW1 amplitudes during
the winter of 1978–1979 in the northern hemisphere.
The observational studies mentioned above show that correlation studies support the hypothesis that
interaction of SPWs in the winter stratosphere and lower mesosphere with migrating tides is a source for
nonmigrating tides. The observational cases have treated either the diurnal or semidiurnal tides; most have
looked at the nonmigrating tide far from the source, in the upper mesosphere of the same or
opposite hemisphere.
In this paper, we focus on the nonmigrating tides at the source, i.e., in the latitude and altitude region where
the planetary waves are present. Temperatures measured by SABER (Sounding of the Atmosphere using
Broadband Emission Radiometry) are used to analyze the nonlinear interaction between SPWs and tides. We
emphasize the holistic response to the interaction between SPWs and tides. In other words, we look at the net
response of all nonmigrating tides, not limited to the results of a single pair of migrating tides and SPW. The
potential energy summed over all nonmigrating tides is used as a single parameter to investigate the general
behavior of the nonmigrating tides.
The rest of the paper is organized as follows: Section 2 presents the data set and describes the calculation of
the SPWs and tides. The results showing the impact of interactions between SPWs and tides are given in
section 3. Section 4 looks at the contributions of specific pairs of tides and SPW in the generation of
nonmigrating tides. Section 5 gives the summary.
2. Data Set and the Method of Calculating SPWs and Tides
The structures of tides and stationary waves are derived from temperatures observed by SABER , one of the
payloads on the TIMED (Thermosphere, Ionosphere, Mesosphere Energetics, and Dynamics) satellite [Russell
et al., 1999]. SABER measurements began on 25 January 2002 and are ongoing. SABER temperature data
provide information for investigating the global structure of the dynamics at high-vertical resolution from the
lower stratosphere to the lower thermosphere. Version 1.07 temperature data [Remsberg et al., 2008] from
February 2002 to July 2012 are used in this work.
TIMED precesses in local time. The combination of ascending and descending data over a 60 day period
provides 24 h of local time coverage [e.g., Xu et al., 2007, 2009a]. The latitude coverage of SABER is from
53°N to 83°S or from 53°S to 83°N; the range changes about every 60 days. With this observation pattern,
we can perform continuous analysis on the tides and SPWs from 50°S to 50°N. The observations at high
latitudes (poleward of 53°) are sampled for 60 day periods but only on alternate yaw cycles. However, this
is sufficient for a 24 h coverage. Therefore, we perform the calculations for alternate 60 day periods for
high latitudes.
Before the analysis, the temperature profiles are sorted into overlapping latitude bins that are 10° wide with
centers offset by 5° extending from 85°S to 85°N and longitude bins that are 10° wide. Profiles are interpolated in
the vertical with 1 km spacing from 20 km to 110 km. Analysis is performed for each day using a 60 day sliding
window (low to middle latitudes) or intermittent 60 day periods (high latitudes).
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The atmospheric temperature can be expressed as the combination of the zonal daily mean and wave perturbations in longitude and/or time. We include perturbations due to the migrating and nonmigrating tides,
stationary planetary waves, and transient planetary waves for each latitude bin and each 60 day window.
T ðλ; tÞ ¼ T þ ∑ ∑ An;s cos nΩt þ sλ þ φn;s þ ∑ Bk cosðkλ þ ϕ k Þ
n s
k
6
∑ C m cosðωm t þ jm λ þ ψ m Þ
(1)
m¼1
The first term on the right side of equation (1), T ¼
2π
1
2π ∫ ∫ T ðλ;
0
tÞdtdλ is the zonal daily mean temperature.
Note for this term, as well as for the wave terms in equation (1), data from a full 60 day window are used to
construct the daily time-dependent values of T(λ,t) used in the analysis. The second term is the tides; n (=1, 2,
3, and 4) denotes the subharmonics of a solar day, representing 24 h, 12 h, 8 h, and 6 h periods, respectively.
Multiple zonal wave numbers are included for each tide so the term represents both migrating and
nonmigrating tides. In the representation here, we use a range of zonal wave numbers s that depends on the
tidal frequency; (sn) ranges from 8, … 2, 1, 0, 1, 2, … to 8. Positive values of s indicate westward
propagating. An,s is the amplitude, λ is the longitude (in radians), t is universal time in days, Ω = 2π/day is the
frequency of the 24 h tide, and φn;s is the phase. The tidal notation follows that of Forbes et al. [2003]. The third
term of equation (1) represents the stationary planetary waves. Bk is the amplitude and ϕ k is the phase
(longitude), k =1, 2, … 8 is the zonal wave number. The last term is the transient planetary waves. The six
strongest transient planetary waves are included. Cm are the amplitudes, ωm are the frequencies of the
planetary waves, jm are the zonal wave numbers, and ψ m are the phases of the six strongest PWs. The method
of calculation of PWs is given below.
Least square fitting is used to simultaneously extract the zonal mean temperature, the amplitudes and phases
of the SPW, the amplitudes and phases of migrating and nonmigrating tides with periods of 24 h, 12 h, 8 h,
and 6 h, and the amplitudes and phases of transient planetary waves. The range of zonal wave numbers for
stationary planetary waves is from 1 to 8 and the range for tides is ±8 from the migrating tidal wave number.
Transient and travelling planetary waves can be quite variable in amplitude and phase. Several steps are
needed for the calculation of the transient planetary waves. The first step is to fit the first three terms
(mean temperature, tides, and stationary planetary waves) to the data for each 60 day window. A fit is then
performed on the residuals to the fit to determine the waves present that have periods from 2 to 30 days,
incremented by 1 day and zonal wave numbers from 4 to 4. The six strongest planetary waves are selected
and included in a new fit to equation (1). The steps are iterated until they converge. The traveling planetary
waves are included for completeness but are not considered further in this paper.
3. Correlation Between SPWs and Nonmigrating Tides
In this study, we look exclusively for nonmigrating tides that are at the same latitude and altitude as the SPW.
This approach is in contrast to other observational investigations of nonmigrating tidal sources associated
with SPWs [e.g., Lieberman et al., 2004; Murphy et al., 2009]. Our analysis is intended to focus on the generation
of the tides. At a distance from the source region, tidal amplitudes are influenced by both the sources and the
conditions for propagation from the source. The amplitude at the location of the source will be affected only
by the generation, not the propagation, of the tides. However, note that the nonmigrating tides that are
present in our analysis may not have been generated precisely where they are observed. They also could
have propagated from a different part of the atmosphere, such as from the troposphere.
As described in section 2, all analysis uses averages over 60 days because this time interval is necessary to
separate SPW from tides in the SABER data. Therefore, we only consider those tides and waves that remain
steady over these long times. Short-period phenomena, such as the interaction of tides with 2 day or 16 day
waves, will not contribute to the signals presented here.
To investigate the in situ nonlinear interaction between the SPWs and tides in the stratosphere and lower
mesosphere, we give the latitudinal distributions of the SPWs first. As an example, we take the wave number
1 SPW, which is the strongest stationary planetary wave (see the discussion below). Figure 1 gives the distributions of SPW with wave number 1 in the stratosphere and lower mesosphere. The stationary planetary
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(a)
2002
2003
2004
2005
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2009
2010
2011
2012
80
Amp.
(K)
14
LATITUDE
60
40
12
20
10
0
8.0
-20
6.0
-40
4.0
-60
2.0
0.0
-80
2002
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YEAR
(b)
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Amp.
(K)
14
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40
12
20
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0
8.0
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0.0
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(c)
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Amp.
(K)
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LATITUDE
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40
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8.0
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(d)
2002
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Amp.
(K)
14
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60
40
12
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8.0
-20
6.0
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4.0
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YEAR
(e)
2002
2003
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Amp.
(K)
14
LATITUDE
60
40
12
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0
8.0
-20
6.0
-40
4.0
-60
2.0
-80
0.0
2002
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2009
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YEAR
Figure 1. Latitudinal distribution of the amplitude (K) of SPWs of wave number 1 from 2002 to 2012. (a–e) The altitudes of 75 km, 65 km,
55 km, 45 km, and 35 km, respectively. The white areas indicate the absence of observations.
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Figure 2. Global distributions of the amplitude (K) of SPWs of wave number (left) 1 and (right) 2 in (top) December–January and (bottom)
June–July averaged over the period from 2002 to 2012.
wave amplitudes are strong during the wintertime (December–January in the northern hemisphere and
June–July in the southern hemisphere) in the middle and high latitude and almost vanish during the
summertime. For instance, the amplitude of SPW with wave number 1 is less than 0.2 K at 45 km and 45°N
during summer. In the tropics, the SPW amplitude is very weak during all seasons. In order to show the
latitude-height distribution of the SPW, Figure 2 gives the amplitudes of SPWs of wave numbers 1 and 2 in
December–January and June–July, averaged over the period from 2002 to 2012; these two waves are the
major components of SPWs. Both Figures 1 and 2 show that the SPWs in northern hemisphere winter are
stronger than those in southern hemisphere winter. These results are consistent with the statistics of the
climatology of SPWs by Barnett and Labitzke [1990]. Figures 1 and 2 indicate that the SPWs in temperature
are strongest at 45 km, which is near the stratopause. Because SABER has complete and continuous observation only equatorward of 53°, we first take the northern hemisphere upper stratosphere: 45 km, 45°N
as an example to show the tidal and SPWs at a single location. At this location, SPWs are very strong and so
the in situ SPW-tide interaction should be strong also. From the variations at this latitude and altitude, we
can see temporal relations between the tidal amplitudes, SPW amplitudes, and variations in the potential
energies. A statistical view, using correlations in time, is then extended to the global middle atmosphere.
The correlations indicate that the relationships that are seen at 45 km, 45°N apply over broad regions of
both hemispheres.
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Figure 3. The 11 year average zonal wave number distributions of (first row) SPWs, (second row) diurnal tides, (third row) semidiurnal tides, (fourth row) terdiurnal tides, and (fifth row) 6 h
tides at 45 km altitude and 45°N for four seasons (from left to right: December–January, March–April, June–July, and September–October). The vertical dashed line marks the migrating tide.
For tides, minus and positive wave numbers means eastward and westward propagating. The scale changes from panel to panel.
The multiyear averaged (from 2002 to 2012) temperature for each zonal wave number for SPWs and tides at
four seasons (December–January, March–April, June–July, and September–October) at 45 km, 45°N are shown
in Figure 3. From the first row of Figure 3, we can see that the SPWs are very strong in wintertime and very
weak in summertime, which is also shown in Figure 1. During winter, wave number 1 has the largest amplitude; its averaged value reaches about 7.2 ± 1.02 K at 45 km and 45°N. During summer, the amplitudes of
SPWs are less than 0.15 ± 0.028 K. These features of the SPWs are consistent with the summary of SPWs in
temperature by Barnett and Labitzke [1990], (see Figure 2 in their paper). The amplitude of SPW1 in temperature in the wintertime is also consistent with the results of Mukhtarov et al. [2010], (see Figure 4 of their
paper showing the average from 2002 to 2007 from SABER observation).
From the second row of Figure 3, we can see that the diurnal migrating tide (wave number 1) is the strongest
of the diurnal tide components in most seasons. The amplitudes are 1.9 ± 0.27 K (December–January),
3.5 ± 0.34 K (March–April), 2.9 ± 0.10 K (June-July), and 2.0 ± 0.15 K (September–October). The amplitudes are
approximately consistent with the results of migrating diurnal tides by Sakazaki et al. [2012] from analysis of
SABER observations for five years: 2002–2006.
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Figure 4. Time series of the total potential energy of SPWs (thick black line shown in all panels). (a–d) Give the potential energies of the
nonmigrating (thick blue line) and migrating (green line) tides and their sum (red line) for (from top to bottom) the diurnal, semidiurnal,
terdiurnal, and 6 h tides at 45°N and 45 km. The left axis is for the energy of SPWs; the right axis is for tides. (e) The squared buoyancy
frequency (right axis) and the temperature (left axis) at 45°N and 45 km.
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Figure 3 exhibits a very interesting feature of the nonmigrating tides. During summer (June–July), the diurnal tide
at this location is almost completely made up of wave number 1, the migrating component. In contrast, during
winter (December–January), the diurnal tide includes a range of wave numbers; nonmigrating components are
much larger and have amplitudes similar to that of the migrating tide. The semidiurnal tides show a similar distribution; the winter average indicates that the migrating tide is actually smaller than several of the nonmigrating
tides. Some of the same features are evident for the terdiurnal and 6 h tides, including large seasonal variability
and variations in the relative magnitudes of nonmigrating and migrating tides. The seasonal differences indicate
that migrating tides for these periodicities are larger during the winter and spring.
The SPWs and tides include propagation from below, in situ forcing, and nonlinear wave generation by SPW-tide
and tide-tide interactions. For example, the migrating and nonmigrating diurnal tides can propagate from below,
be forced by diurnally varying ozone heating, which reaches peak amplitude in the stratopause region [e.g., Xu
et al., 2010, 2012], and be produced by the interactions between the SPWs and other diurnal tides, diurnal tides
with semidiurnal tides, etc. Tides and SPWs are also affected by interactions with the background atmosphere
and with internal gravity waves [e.g., McLandress, 2002; Ortland and Alexander, 2006]. From Figure 3, it is evident
that numerous migrating and nonmigrating tides and SPWs are present simultaneously during all seasons except
summer. Therefore, the nonlinear interaction process includes nonlinear coupling between many different waves
and tides. Nonlinear interactions between SPWs and migrating tides do not change the frequency of tides but
can produce nonmigrating tides and can therefore broaden the zonal wave number spectra of the tides.
For simplifying the description of SPWs and tides in the text and figures, we use {n, s} to represent frequency
and zonal wave number, respectively, for both SPWs and tides. Here n = 0 for SPWs, and n = 1, 2, 3, and 4 for
diurnal, semidiurnal, terdiurnal, and 6 h tides.The s is the wave number. The interaction of two primary waves,
{n1, s1} and {n2, s2}, would generate secondary waves with frequencies and wave numbers that are the sum,
{n1 + n2, s1 + s2}, and difference, {n1 n2, s1 s2}; this can be expressed by
fn1 ; s1 g fn2 ; s2 g → fn1 þ n2 ; s1 þ s2 g þ fn1 n2 ; s1 s2 g:
Taken as a whole, the potential for wave and tide interactions and nonmigrating tide generation is complex.
There are dozens of SPW-tidal pairs that could in principle contribute to the generation of the observed
nonmigrating tides. Consider a case where there are initially only two waves: {0, 1} and {1, 1}. The interaction
between them can generate the child waves, {1, 2} and {1, 0}. Then {1, 2} and {1, 0} can become parent waves
and interact with {0, 1} and {1, 1} to produce {1, 3}, {1, 1}, {2, 3}, {2, 1}, and so on. As a result, there can be many
different waves and tides simultaneously present through the interactive process. Wave energy transfers
from one wave to another through the nonlinear interactions. If the propagation of waves from other regions
is also involved, the situation is even more complex.
For our first look at this process, we turn to a holistic approach and investigate the net activity of tides and SPWs
to characterize the interactions between them. We use the potential energy in order to have a single parameter
that represents the behavior of multiple tides. The wave potential energy per unit mass (J/kg) can be used to
measure the wave activity using the SABER temperature data. The wave potential energy per unit mass Ep is
defined as follows:
1 g2 T’ 2
2 N2 T̄
Ep ¼
(2)
where N2 is the squared buoyancy frequency, g is the acceleration of gravity, and T ’ is the deviation in temperature from the zonal and time mean. The overline indicates the temporal and zonal mean. The potential
energy can be defined separately for individual waves or tides. Here we use the potential energy for SPWs
and tides to represent the intensities of wave activity. The total potential energies are denoted Ep,p for the
sum of all SPWs, E np;t for all tides, E np;mt for migrating tides, and E np;nt for nonmigrating tides. These quantities
can be calculated using the amplitudes of waves as follows:
E p;p ¼
E np;t ¼
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1 g2 1 1 2
∑B
2 N2 T 2 2 k k
1 g2 1 1 2
∑A ;
2 N2 T 2 2 s n;s
©2013. The Authors.
n ¼ 1; 2; 3; and 4
(3a)
(3b)
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Figure 5. The same as Figure 4, but for a composite year averaged from 2002 to 2012.
E np;mt ¼
E np;nt ¼
1 g2 1 1
An;n 2 ;
2 N2 T 2 2
1 g2 1 1 X
An;s 2 ;
2 N2 T 2 2 s≠n
n ¼ 1; 2; 3; and 4
n ¼ 1; 2; 3; and 4
(3c)
(3d)
As in equaion (1), n = 1, 2, 3, and 4 denotes diurnal, semidiurnal, terdiurnal, and 6 h tides.
Figure 4 shows a time series of the potential energy terms from 2002 to 2012 for the location shown in
Figure 3 (45 km, 45°N). Each of the rows corresponds to a different tidal period. The thick black line (same in
each of the first four rows) gives the time variations of the potential energy of SPWs. The other curves are the
potential energies of the migrating (green line), the nonmigrating (thick blue line), and the sum of migrating
and nonmigrating (red line) tides for the respective tidal periods (from the top: diurnal, semidiurnal,
terdiurnal, and 6 h periods). From Figure 4, we can see that the potential energies of SPWs and tides have
regular seasonal variations. In Figure 4, the squared buoyancy frequency (N2) and the zonal daily mean
temperature (T) are also given (the last row). The averaged values of the squared buoyancy frequency and the
zonal daily mean temperature are about 4.2 ± 0.2 104 and about 258 ± 10 K, respectively. Therefore, the
seasonal variations of the potential energies are mainly associated with variations in the wave activity, not by
buoyancy frequency variations.
In order to present the seasonal variation of the relationship between the different time series of the
energies in detail, Figure 5 gives a time series of the annual cycle of the potential energy terms at the
same location in a composite year averaged from 2002 to 2012. Figures 5a, 5b, 5c, and 5d show
diurnal, semidiurnal, terdiurnal, and 6 h tides, respectively. From Figures 4 and 5, we can see that the
seasonal variations of potential energies of nonmigrating tides for the four tidal periods are well
correlated with the potential energy of SPWs. The nonmigrating tidal components for each tidal period
almost vanish during summer, coincident with the disappearance of the SPWs, and reach maxima
during winter when SPWs are largest. For the 6 h tides (Figures 4d and 5d), the total potential energies
of tides (migrating plus nonmigrating) are also well correlated with the SPWs since the migrating tides
make only small contributions.
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Figure 6. Global distributions of the correlation coefficients between the potential energy of SPWs and the potential energies of
nonmigrating (a) diurnal, (b) semidiurnal, (c) terdiurnal, and (d) 6 h tides over the period from 2002 to 2012.
For the semidiurnal, terdiurnal, and 6 h periods at this location, there is a wintertime maximum for not only
the nonmigrating tides but also the total tides. This is not the case for the diurnal tide. The dominant diurnal
tide is the migrating tide; its seasonal variation shows a maximum in spring. From Figures 4a and 5a, we can
see that the nonmigrating diurnal tides are present only when there are planetary waves. During winter, the
SPWs are very strong, the migrating diurnal tide does not vanish, and the nonmigrating diurnal tides are
strong. During spring, the migrating diurnal tide is strong, the SPWs are weak but do not vanish, and there is a
small peak in the energy of the nonmigrating diurnal tides.
Figure 6 gives the global distributions of the correlation coefficients for the temporal variations of the potential energy of SPWs with the potential energies of nonmigrating diurnal, semidiurnal, terdiurnal, and 6 h
tidal components over the period from 2002 to 2012. Correlations between the SPWs and nonmigrating tides
are large and positive for all four tidal periods in the region poleward of 20°N and below about 80 km. For
most of the midlatitudes of the northern hemisphere below 80 km, the correlation coefficients are larger than
0.6. At 45°N and 45 km, the correlation coefficients for the diurnal, semidiurnal, terdiurnal, and 6 h components are 0.78 ± 0.072, 0.69 ± 0.073, 0.80 ± 0.059, and 0.78 ± 0.052, respectively. Figure 6 also shows that the
correlation coefficients are very small in the tropics.
The t test is used to estimate the significance level of the correlation coefficient. Because 60 day windows are
used for the analysis of SABER data, according to the most stringent criterion, the absolute independent
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number of the data for one year is 365/60 ≈ 6. The degrees of freedom (d.f.) of 11 year data (from 2002 to
2012) is larger than n = 60. Therefore, we take the d.f. of the data to be n = 60. For 95% significance level of the
correlation, the correlation coefficient should be
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
jr j
n 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ≥ 2:0;
1 r2
where r is the correlation coefficient. The above equation shows that when |r| ≥ 0.25, the result is significant
at the 95% level. From Figure 6, we can see that, in the region poleward of 20° latitude and below about
80 km altitude, the correlation coefficients are larger than this value. Therefore, the correlation of the SPWs
and nonmigrating tides is significant at the 95% significance level.
From Figure 6, we can also see that the correlation coefficients are slightly smaller in the southern hemisphere than in the northern hemisphere but, even so, are larger than 0.5 over most of the midlatitude region
below 80 km. This asymmetry between the hemispheres is probably produced by the asymmetry of the SPWs
in the two hemispheres and fits with the analysis of Xu et al. [2009b]. Figures 1 and 2 show that the SPWs in
northern hemisphere winter are stronger than those in southern hemisphere winter. This can explain the low
correlation coefficient between the SPWs and tides shown in Figure 6.
It is well known that the SPWs are strong in the high-latitude stratosphere and lower mesosphere. To observe
these, we face the limitation that the TIMED/SABER observations for high latitudes (poleward of 53°) are
sampled only on alternate yaw cycles with periods of 60 days. The timing of the northward and southward
periods of observations repeats annually. SABER observed the northward region on periods centered on
February (day 45), June (day 160), and October (day 285) and the southward regions on periods centered on
April (day 105), August (day 225), and December (day 345) of each year. These 60 day observations are long
enough for 24 h coverage. Therefore, we have the opportunity to investigate the activities of SPWs and tides
in the high-latitude regions of the two hemispheres alternately every two months. Unfortunately there are no
high-latitude observations by SABER during midwinter so we cannot get information about the relationship
between SPWs and tides in the place and time where SPWs are largest.
Figure 7 shows the temperature amplitudes for the average over the period at each season for 65°N and
45 km for comparison with Figure 3. Despite the limited data, the higher latitude results in Figure 7 are similar
to the midlatitude results in Figure 3. During summer, the SPWs are very weak and the nonmigrating tides at
all four periodicities are also very weak. The nonmigrating tides are stronger during the spring and autumn
when SPWs are large.
4. Identification of Interaction Pairs Between SPWs and Tides
The previous section uses the holistic behavior of tides and SPWs, as defined by the potential energies, to
characterize the interactions between them. In this section, we investigate the wave-wave interaction pairs
that contribute to the patterns seen in the potential energies. We seek to identify the most effective in situ
nonlinear interaction pairs.
The nonlinear interaction between waves can produce secondary waves with sum and difference
frequencies and quadratic phase coupling [Beard et al., 1999]. Here the higher-order spectral technique of bispectral analysis [Beard et al., 1999] is used to investigate the nonlinear coupling between
waves. The analysis follows that of Beard et al. [1999] but, whereas their time series were constructed
from hourly data, here we use time series consisting of the daily wave and tide amplitudes and
phases, as defined in equation (1). The bispectral analysis gives a peak where there is coherent variation of the time series of three waves: the two primary, or parent, waves and the secondary, or child,
wave. In the discussion that follows, we start with a particular secondary wave representing a
nonmigrating tide and then compare the bispectral analysis results for all SPW and/or tide triads that
fit the theoretical criteria for generating it by SPW-tide or tide-tide interaction. A higher bispectral
power for a specific wave triad indicates that the waves in question have higher amplitudes and are
varying together; they are therefore more likely to have contributed to the generation of the specific
nonmigrating tide.
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Figure 7. As in Figure 3, but for the latitude of 65°N and altitude of 45 km. The statistical calculations using 60 day window are centered at
day 45 (February), day 160 (June), and day 285 (October) for the northern hemisphere. (During midwinter, there are no SABER observations
for high latitudes.)
Now we take a detailed look at the nonlinear interactions associated with the generation of the strongest
nonmigrating tides for each tidal period. We again take 45 km and 45°N as an example to investigate the in
situ wave-wave nonlinear interaction.
4.1. Nonmigrating Diurnal Tides
There are many different SPW-tide or tide-tide pairs that can generate nonmigrating tides with 24 h periods:
SPWs-diurnal tides, semidiurnal tides-diurnal tides, terdiurnal tides-semidiurnal tides, and terdiurnal tides-6 h
tides with multiple combinations of zonal wave number for each. From Figure 3, we can see that
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Figure 8. Bispectral amplitudes for the generation of nonmigrating diurnal tides with (top )wave number of 0 and (bottom) wave number 2
at the latitude of 45°N and altitude of 45 km. The results are shown for all wave pairs with amplitudes 5% or higher of that from the largest
contribution.
nonmigrating diurnal tides with wave numbers 0 and 2, denoted as {1, 0} and {1, 2}, respectively, are the
strongest nonmigrating diurnal tides. For the five periods (stationary, diurnal, semidiurnal, terdiurnal, and 6 h)
and up to 17 zonal wave numbers (sn from 8 to 8) in our analysis, we can identify 63 wave pairs that could
in principle give rise to the {1, 0} tide. Figure 8 compares the bispectral amplitudes of the possible wave
coupling pairs with the largest signals; results are shown for all triad values with magnitudes that are at least
5% of the value of the maximum contribution. The largest peak in the bispectra that includes the (top) {1, 0}
tide has a magnitude of 5.4 and includes the primary waves {0, 1} {1, 1} , i.e., SPW with wave number 1 and
the migrating diurnal tide. There is also a contribution to the bispectra from the interaction between the
migrating diurnal tide and nonmigrating semidiurnal tide with zonal wave number 1, {1, 1} {2, 1} → {1, 0}.
Additional smaller contributions involve interaction of SPW with nonmigrating diurnal tides {0, 1} and {1, 1}.
The largest contribution to the bispectra of the {1, 2} tide is {0, 1} {1, 1} → {1, 2}, again, the interaction of SPW
with wave number 1 and the migrating diurnal tide. There is also a contribution from {1, 1} {2, 3} → {1, 2},
again, involving a nonmigrating semidiurnal tide. There are other smaller contributions from interactions
involving SPW and nonmigrating diurnal tides. The large magnitudes of the dominant terms confirm the
existence of significant quadratic phase coupling between the migrating diurnal tide and the SPWs. The
nonlinear interaction between the SPW with wave number 1 and the migrating tide is the main contributor
for producing the two largest nonmigrating diurnal tides, those with wave numbers of 0 and 2. The smaller
but not negligible contributions from the interaction of the migrating diurnal tides with nonmigrating
semidiurnal tides were not expected.
Figure 9 shows the latitudinal distribution of the amplitudes of diurnal tides with wave number 1, 0, and 2
at 45 km. The (top) migrating diurnal tide has nonzero amplitude at all times in the middle and high
latitude at 45 km that can reach about 3–4 K. This amplitude is approximately consistent with the results
for the migrating diurnal tide by Sakazaki et al. [2012], (Figure 6 in their paper) from analysis of SABER
observations and Modern Era Retrospective-Analysis for Research and Applications reanalysis data. From
Figure 9, we can see that the amplitudes of the nonmigrating diurnal tides with wave numbers 0 and 2 at
this altitude are strong in the middle and high latitude during wintertime. Combining this observation
with the SPW variability in Figure 1 and the bispectral analysis results in Figure 8, we conclude that the
seasonal pattern in these nonmigrating tides can be attributed to the nonlinear interaction between the
migrating diurnal tide and SPWs.
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(a)
(b)
(c)
Figure 9. Latitudinal distributions of the temperature amplitude (K) of diurnal tides with (a) wave number 1, (b) wave number 0, and
(c) wave number 2 at altitude of 45 km from 2002 to 2012.
The latitudinal distribution of the bispectral amplitude for {0, 1) {1, 1} → (1, 0} and {0, 1) {1, 1} → (1, 0} at
several altitudes are shown in Figure 10. The values at 45 km are largest; the curves for other altitudes are
multiplied by a factor of four so that the latitudinal variation can be seen. The figure shows that the amplitudes are small in low latitudes and increase sharply toward the high latitude limit of the analysis (45°) in both
hemispheres. From the figure, we can see that the nonlinear interactions between SPWs and tides are
strongest near the stratopause (around 45 km) and decrease toward lower and higher altitudes. The altitude
of the peak is near the peak of the temperature perturbations associated with SPW (Figure 2). It is also near
the peak of the diurnally varying heating due to absorption of solar radiation by ozone [e.g., Xu et al., 2010],
which contributes to the forcing of the migrating tide.
For the eastward travelling nonmigrating diurnal tide with wave number 1 at this altitude and latitude, the
main source is the interaction between the SPW with wave number 1 and the nonmigrating diurnal tide with
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Figure 10. Latitudinal variations of bispectral amplitude for (left) {0, 1} {1, 1} → {1, 0} and (right) {0, 1} {1, 1} → {1, 2} at 25, 35, 45, 55, and
65 km. Note that the values shown for 25, 35, 55, and 65 km are four times the bispectral magnitudes.
wave number 0. The main sources for the nonmigrating diurnal tide with wave number 3 are the interactions
between SPW {0, 1} and the nonmigrating diurnal tide {1, 2} and between {0, 2} and {1, 1}.
4.2. Nonmigrating Semidiurnal Tides
Interactions between SPWs-semidiurnal tides, diurnal tides-diurnal tides, diurnal tides-terdiurnal tides, and
semidiurnal tides-6 h tides may produce the nonmigrating semidiurnal tides. Figure 3 indicates that the
strongest nonmigrating semidiurnal tides are those with wave numbers 1 and 3, {2, 1} and {2, 3}. Figure 11
shows the bispectral amplitudes that have magnitudes greater than 10% of the maximum value for the
possible wave-wave coupling pairs for generation of these two semidiurnal tides.
Figure 11. The same as Figure 8, but for nonmigrating semidiurnal tides with (top) wave number of 1 and (bottom) wave number 3. The
results are shown for all wave pairs with amplitudes 10% or higher of that from the largest contribution.
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Figure 12. The same as Figure 8, but for nonmigrating terdiurnal tides with (top) wave number of 2 and (bottom) wave number 4. The results are shown for all wave pairs with amplitudes 10% or higher of that from the largest contribution.
For nonmigrating tide {2, 1}, Figure 11 indicates that there is high-quadratic phase coupling between the
migrating semidiurnal tide {2, 2} and SPW {0, 1}. From the figure, we can see that the interaction between
diurnal tides {1, 0} and {1, 1} may also make a large contribution to generation of {2, 1}.
For the nonmigrating tide {2, 3}, the interaction between diurnal tides {1, 1} and {1, 2} may make the strongest
contribution to generation of {2, 3}. Figure 11 also shows that the interactions of the wave number 1 SPW with
migrating and nonmigrating semidiurnal tides also contribute to the generation of {2, 3}.
The amplitudes of nonmigrating semidiurnal tides with wave numbers 1 and 3 (not shown) have latitudinal
distributions that are similar to that of the nonmigrating diurnal tides shown in Figure 9. These two
nonmigrating tidal components almost vanish during summer, coincident with the disappearance of the
SPWs, and reach maxima during winter when SPWs are largest. This is an additional confirmation of the
findings in section 3.
We also calculate the bispectra for other nonmigrating semidiurnal tides. For the nonmigrating semidiurnal
tides {2, 0} and {2, 4}, the largest contributions come from the interactions between the SPW {0, 1} and the
semidiurnal tide {2, 1} and between the SPW {0, 1} and the semidiurnal tide {2, 3}, respectively.
4.3. Nonmigrating Terdiurnal Tides
The interactions between SPWs and terdiurnal tides, diurnal tides and semidiurnal tides, and between diurnal
tides and 6 h tides, are possible sources for producing the nonmigrating terdiurnal tides. For the strongest
nonmigrating terdiurnal tides, {3, 2} and {3, 4}, Figure 12 gives the bispectral amplitudes of the wave-wave
coupling pairs for generation of these two terdiurnal tides whose magnitudes are within 10% of the
maximum signal.
For the (top) {3, 2} tide, Figure 12 indicates that the interaction involving {0, 1} and {3, 3} has the maximum
contribution for this tide. Figure 12 also shows that the interactions between {1, 1} and {4, 3} and between {1, 1}
and {2, 1} have relatively large values of bispectral amplitude.
For the (bottom) nonmigrating tide {3, 4}, Figure 12 shows that the interaction between {0, 1} and {3, 3} gives
the largest magnitude. The interactions between {0, 1} and {3, 5}, {1, 1} and {4, 5}, and {1, 1} and {2, 3} may also
have an impact on the nonmigrating terdiurnal tide {3, 4}.
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Figure 13. The same as Figure 8, but for nonmigrating 6 h tides with (top) wave number of 3 and (bottom) wave number 5. The results are
shown for all wave pairs with amplitudes 10% or higher of that from the largest contribution.
4.4. Nonmigrating 6 h Tides
Figure 13 gives the bispectral amplitudes of the largest wave-wave coupling pairs for generation of two
nonmigrating 6 h tides: (top) {4, 3} and (bottom) {4, 5}, which are the strongest nonmigrating 6 h tides. The
analysis indicates that the interactions between the diurnal tides and terdiurnal tides may be major sources
for producing the nonmigrating 6 h tides. For instance, the interaction between {1, 1} and {3, 2} is the strongest source for the tide {4, 3}. For the generation of the tide of {4, 5}, the interaction between {1, 1} and {3, 4} has
the largest value. We also investigated the nonmigrating 6 h tides {4, 2} and {4, 6}. The results (not shown) show
that interactions between the diurnal tides and terdiurnal tides are the major sources for their generation as well.
The analysis of the 6 h nonmigrating tides indicates that the interactions between SPWs and 6 h tides are
weak. This is probably due to the small amplitudes of the migrating 6 h tides. The present analysis strongly
suggests that the generation of the observed nonmigrating 6 h tides is the result of nonlinear interactions
between diurnal and terdiurnal tides.
4.5. Interpretation of the Bispectral Magnitudes
The discussion in this section is based on the magnitudes of bispectra of the nonlinear wave and tide interactions. These values are relevant for investigating tide generation by wave-tide and tide-tide interactions.
However, some caution is needed in the interpretation of these quantities. Large values of bispectral magnitude only indicate that there is a high degree of quadratic phase coupling between the two primary and the
secondary waves. High bispectral magnitudes may indicate the generation or strengthening of the secondary
wave but could also imply a weakening of the secondary wave through the interaction of the same two
primary waves. To thoroughly investigate the interpretation of this analysis method, it should be applied to
numerical modeling simulations where independent information about wave interactions can be compared
with the bispectral results.
The only atmospheric information that we use is temperature. It is well known that planetary waves and tides
can also have large perturbations in horizontal and vertical winds. Interactions that involve winds cannot be
directly investigated with the current analysis. However, if such interactions generate nonmigrating tides, the
winds from the generated tide will induce temperature perturbations that then can be seen in SABER data.
Without simultaneous temperature and wind information, we cannot assess to what extent our analysis omits
or modifies the pattern of nonmigrating tide generation.
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It is worth noting that, in Figures 3 and 7, the distribution of nonmigrating tide amplitudes are asymmetric
relative to the migrating tides, especially for the semidiurnal, terdiurnal, and 6 h tides. The tides with lower
wave numbers have higher amplitudes than those with higher wave numbers. From the present analysis, we
cannot determine the cause of this asymmetry.
Finally, we must emphasize that, although the high correlations between the nonmigrating tides and SPWs
given in this work provide support for the role of interactions in generating nonmigrating tides, the impact of
the interactions on the global distribution of the tides still needs to be studied in detail, especially by
modeling simulations. We also have not addressed the propagation of the nonmigrating tides away from the
source region and therefore cannot determine which tidal wave numbers are likely to be seen at locations
that are remote in latitude or altitude from the winter stratosphere and lower mesosphere.
5. Summary
In this paper, we use 11 years (2002–2012) of TIMED/SABER global temperature data to analyze the activities
of SPWs and tides in the stratosphere and lower mesosphere. The main purpose is to evaluate the production
of nonmigrating tides by in situ nonlinear interaction between SPWs and tides. We analyze the holistic
behaviors of the nonlinear interactions between SPWs and tides from the point of view of energetics. This
work gives global features from 50°S to 50°N and limited high-latitude results.
The results indicate that the amplitudes of nonmigrating tides with diurnal, semidiurnal, terdiurnal, and 6 h periods in the midlatitude upper stratosphere are strongest during winter and almost vanish during summer, synchronous with the amplitudes of SPWs. For these four tidal periods, correlations between the SPWs and the total
of nonmigrating tides are strong below about 80 km in the region from 20° to 53°, which is the limit of the SABER
year-round observations. In the tropics, where the SPWs are very weak in all seasons, the correlations are small.
Analysis with the limited available data for high latitudes shows similar results for spring, summer, and autumn;
there are not sufficient SABER observations to evaluate the tidal structure in high-latitude midwinter.
We also use bispectral analysis to identify strong wave-wave interaction pairs for producing nonmigrating tides in
the stratospheric extratropics. The results reveal that the nonlinear interactions between SPWs and migrating
tides are the major sources for the generation of nonmigrating diurnal, semidiurnal, and terdiurnal tides.
However, interactions between migrating and nonmigrating tides also appear to contribute to the generation of
some of the nonmigrating tides. For the generation of the nonmigrating 6 h tides, interactions between diurnal
and terdiurnal tides may be the major contributor. SPWs have an indirect role in this process: they produce the
nonmigrating diurnal and terdiurnal tides that then interact to produce the nonmigrating 6 h tides.
The results shown here focus on the nonmigrating tides at the location where SPWs are present. Therefore,
these results are relevant for the generation of the nonmigrating tides by nonlinear interactions between
SPWs and tides in the stratosphere and the lower mesosphere. The correlation coefficients between the
potential energy of SPWs and the potential energies of nonmigrating tides are large in the stratosphere
andthe lower mesosphere (see Figure 6). The very strong temporal correlation between the presence of
stationary planetary waves and of nonmigrating tides in the midlatitude stratosphere and lower mesosphere
is an evidence for the generation of nonmigrating tides by wave-tide interaction. The analysis shows that this
correlation is strong only in the extratropics in winter when planetary wave activity is high. At this season and
latitude range, the amplitudes of migrating tides are not necessarily at their maximum.
Another possible candidate for generation of the nonmigrating tides is the diurnally varying ozone
heating, which peaks near the stratopause [e.g., Xu et al., 2010, 2012]. SPWs can modulate the distribution
of ozone and also the heating; the longitudinal asymmetries in heating then can act to generate
nonmigrating tides. The asymmetric ozone heating may contribute to the observed nonmigrating tides
but it is difficult to know from observational analysis because the altitude of the heating maximum is close
to the altitude where the bispectral analysis indicates that the direct impact of interactions between SPW
and tides is strongest.
The propagation of the nonmigrating tides into or out of a region can also contribute to the nonmigrating tides
seen in that region. In this paper, we do not address the propagation of the nonmigrating tides, whichcould
carry them to other altitudes and latitudes. We also do not have any way to ensure that the nonmigrating tides
that we observe were generated in situ rather than propagated from elsewhere in the atmosphere.
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Acknowledgments
This work is supported by the National
Science Foundation of China (41331069,
41274153), the Chinese Academy of
Sciences (KZZD-EW-01-2), and the
National Important Basic Research
Project of China (2011CB811405) and
the project is also supported by the
Specialized Research Fund for State Key
Laboratories. The National Center for
Atmospheric Research is sponsored by
the National Science Foundation. The
computations were performed by
Numerical Forecast Modelling R&D and
VR System of State Key Laboratory of
Space Weather and Special HPC
workstand of Chinese Meridian Project.
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References
Angelats i Coll, M., and Forbes, J. M. (2002), Nonlinear interactions in the upper atmosphere: The s = 1 and s = 3 non-migrating semidiurnal
tides, J. Geophys. Res., 107(A8), 1187, doi:10.1029/2001JA900179.
Barnett, J. J., and K. Labitzke (1990), Climatological distribution of planetary waves in the middle atmosphere, Adv. Space Res., 10, 63–91.
Beard, A. G., N. J. Mitchell, P. J. S. Williams, and M. Kunitake (1999), Nonlinear interactions between tides and planetary waves resulting in
periodic tidal variability, J. Atmos. Sol. Terr. Phys., 50, 252–265.
Chang, L. C., S. E. Palo, and H.-L. Liu (2011), Short-term variability in the migrating diurnal tide caused by interactions with the quasi 2 day
wave, J. Geophys. Res., 116, D12112, doi:10.1029/2010JD014996.
Forbes, J. M., X. Zhang, E. R. Talaat, and W. Ward (2003), Nonmigrating diurnal tides in the thermosphere, J. Geophys. Res., 108(A1), 1033,
doi:10.1029/2002JA009262.
Hagan, M. E., and R. G. Roble (2001), Modeling diurnal tide variability with the National Center for Atmospheric Research thermosphere –
ionosphere – mesosphere - electrodynamics general circulation model, J. Geophys. Res., 106, 24,869–24,882.
Lieberman, R. S., J. Oberheide, M. E. Hagan, E. E. Remsberg, and L. L. Gordley (2004), Variability of diurnal tides and planetary waves during
November 1978–May 1979, J. Atmos. Sol. Terr. Phys., 66, 517–528.
McLandress, C. (2002), The seasonal variation of the propagating diurnal tide in the mesosphere and lower thermosphere. Part 1: The role of
gravity waves and planetary waves, J. Atmos. Sci., 59, 893–906.
Mukhtarov, P., D. Pancheva, and B. Andonov (2010), Climatology of the stationary planetary waves seen in the SABER/TIMED temperatures
(2002–2007), J. Geophys. Res., 115, A06315, doi:10.1029/2009JA015156.
Murphy, D. J., T. Aso, D. C. Fritts, R. E. Hibbins, A. J. McDonald, D. M. Riggin, M. Tsutsumi, and R. A. Vincent (2009), Source regions for Antarctic
MLT non-migrating semidiurnal tides, Geophys. Res. Lett., 36, L09805, doi:10.1029/2008GL037064.
Oberheide, J., and J. M. Forbes (2008), Tidal propagation of deep tropical cloud signatures into the thermosphere from TIMED observations,
Geophys. Res. Lett., 35, L04816, doi:10.1029/2007GL032397.
Oberheide, J., Q. Wu, T. L. Killeen, M. E. Hagan, and R. G. Roble (2006), Diurnal nonmigrating tides from TIMED Doppler Interferometer wind
data: Monthly climatologies and seasonal variations, J. Geophys. Res., 111, A10S03, doi:10.1029/2005JA011491.
Ortland, D. A., and M. J. Alexander (2006), Gravity wave influence on the global structure of the diurnal tide in the mesosphere and lower
thermosphere, J. Geophys. Res., 111, A10S10, doi:10.1029/2005JA011467.
Pancheva, D., et al. (2002), Global-scale tidal variability during the PSMOS campaign of June-August 1999: Interaction with planetary waves,
J. Atmos. Sol. Terr. Phys., 64, 1865–1895, doi:10.1016/S1364-6826(02)00199-2.
Remsberg, E. E., et al. (2008), Assessment of the quality of the Version 1.07 temperature-versus-pressure profiles of the middle atmosphere
from TIMED/SABER, J. Geophys. Res., 113, D17101, doi:10.1029/2008JD010013.
Russell, J. M., III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin (1999), An overview of the SABER experiment and preliminary
calibration results, Proc. SPIE Int. Soc. Opt. Eng., 3756, 277–288.
Sakazaki, T., M. Fujiwara, X. Zhang, M. E. Hagan, and J. M. Forbes (2012), Diurnal tides from the troposphere to the lower mesosphere as
deduced from TIMED/SABER satellite data and six global reanalysis data sets, J. Geophys. Res., 117, D13108, doi:10.1029/2011JD017117.
Smith, A. K., D. V. Pancheva, N. J. Mitchell, D. R. Marsh, J. M. Russell III, and M. G. Mlynczak (2007), A link between variability of the semidiurnal
tide and planetary waves in the opposite hemisphere, Geophys. Res. Lett., 34, L07809, doi:10.1029/2006GL028929.
Teitelbaum, H., and F. Vial (1991), On tidal variability induced by nonlinear interaction with planetary waves, J. Geophys. Res., 96,
14,169–14,178, doi:10.1029/91JA01019.
Wu, Q., D. A. Ortland, T. L. Killeen, R. G. Roble, M. E. Hagan, H.-L. Liu, S. C. Solomon, J. Xu, W. R. Skinner, and R. J. Niciejewski (2008), Global
distribution and interannual variations of mesospheric and lower thermospheric neutral wind diurnal tide: 2. Nonmigrating tide,
J. Geophys. Res., 113, A05309, doi:10.1029/2007JA012543.
Xu, J., A. K. Smith, W. Yuan, H.-L. Liu, Q. Wu, M. G. Mlynczak, and J. M. Russell III (2007), Global structure and long-term variations of zonal mean
temperature observed by TIMED/SABER, J. Geophys. Res., 112, D24106, doi:10.1029/2007JD008546.
Xu, J., A. K. Smith, H.-L. Liu, W. Yuan, Q. Wu, G. Jiang, M. G. Mlynczak, J. M. Russell III, and S. J. Franke (2009a), Seasonal and quasi-biennial
variations in the migrating diurnal tide observed by Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics (TIMED),
J. Geophys. Res., 114, D13107, doi:10.1029/2008JD011298.
Xu, X., A. H. Manson, C. E. Meek, T. Chshyolkova, J. R. Drummond, C. M. Hall, C. Jacobi, D. M. Riggin, M. Tsutsumi, and R. E. Hibbins (2009b),
Relationship between variability of the semidiurnal tide in the Northern Hemisphere mesosphere and quasi-stationary planetary waves
throughout the global middle atmosphere, Ann. Geophys., 27, 4239–4256.
Xu, J., A. K. Smith, G. Jiang, and W. Yuan (2010), Seasonal variation of the Hough modes of the diurnal component of ozone heating evaluated
from Aura Microwave Limb Sounder observations, J. Geophys. Res., 115, D10110, doi:10.1029/2009JD013179.
Xu, J., A. K. Smith, G. Jiang, W. Yuan, and H. Gao (2012), Features of the seasonal variation of the semidiurnal, terdiurnal and 6-h components
of ozone heating evaluated from Aura/MLS observations, Ann. Geophys., 30, 259–281, doi:10.5194/angeo-30-259-2012.
Yamashita, K., S. Miyahara, Y. Miyoshi, K. Kawano, and J. Ninomiya (2002), Seasonal variation of non-migrating semidiurnal tide in the polar
MLT region in a general circulation model, J. Atmos. Sol. Terr. Phys., 64, 1083–1094.
Zhang, X., J. M. Forbes, and M. E. Hagan (2010a), Longitudinal variation of tides in the MLT region: 1. Tides driven by tropospheric net
radiative heating, J. Geophys. Res., 115, A06316, doi:10.1029/2009JA014897.
Zhang, X., J. M. Forbes, and M. E. Hagan (2010b), Longitudinal variation of tides in the MLT region: 2. Relative effects of solar radiative and
latent heating, J. Geophys. Res., 115, A06317, doi:10.1029/2009JA014898.
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