Introduction
The quasi 2-day wave (QTDW) is one of the most striking
dynamical features in the mesosphere and lower thermosphere. The QTDW was
first reported by using a meteor wind radar at Sheffield,
UK. He found significant oscillations with periods of approximately 51 h from UK radar
data. Even earlier, QTDWs were discovered over Mogadishu
near the Equator. The QTDW at mid-latitudes is
characterized by a clear maximum in summer, with one or several bursts of a
few weeks each. At high latitudes the wave shows a different behavior
compared to at mid-latitudes, e.g., with maxima during winter
. The QTDW has been frequently observed by
ground-based
e.g.,
and satellite instruments . Additionally, several
numerical studies simulated possible excitation processes
.
Regarding possible forcing mechanisms, suggested
the QTDW to be a manifestation of a Rossby gravity normal mode in an
isothermal windless atmosphere with wave number 3; however, this mechanism
could not explain its burst-like behavior. Applying a one-dimensional
stability analysis introduced baroclinic instability as an
excitation mechanism. supported this theory by using a
two-dimensional quasi-geostrophic model and found a QTDW with wave numbers
2–4 and maxima at middle and high latitudes. However, this result did not
resemble all the characteristics of the observed wave. Hence,
combined both mechanisms in numerical experiments and found a QTDW excitation
in the winter hemisphere by planetary wave activity. Crossing the Equator to
the summer hemisphere the QTDW is then enhanced by baroclinic instability
connected with the easterly mesospheric wind jet .
A hemispheric asymmetry has been observed
e.g., with stronger amplitudes in the Southern
Hemisphere (SH) compared to in the Northern Hemisphere (NH). The meridional
component tends to be slightly larger than the zonal one at mid-latitudes
or of similar magnitude . The period of
approximately 2 days varies between 43 and 56 h in the NH
. Generally, periods can be divided into three
groups as suggested by ; see also and
. The dominating one has periods of approximately 48 h with
wave numbers 2 and 3. The second group has much shorter periods of about
42–43 h. Different wave numbers such as 2, 3 and 4 are reported. The
last group covers periods longer than 48 h and peaks at 52 h with wave
numbers 2 and 3. In the SH these three groups could not be observed and
periods are close to 48 h with wave number 3 . explored phase locking relative to the sun
and suggested nonlinear interactions with diurnal tides. This is also
supported by recent studies e.g.,. A possible correlation of QTDW amplitudes with the
11-year solar cycle has been found by , who explained this
finding by a stronger mesospheric wind shear during solar maximum.
In the following we present analyses of the QTDW from a meteor radar (MR) at
Collm (51∘ N, 13∘ E) which was started in 2004.
Earlier, the low-frequency (LF) spaced receiver method was applied at
Collm, from the late 1950s until 2007. This was based on the reflection
of commercial LF radio waves in the lower ionospheric E region. This led to
regular daily gaps due to increased absorption during daylight hours. These
gaps are especially long in summer. The measurements had been used earlier to
obtain a QTDW climatology over Collm . However, the
limitations of the LF method may give rise to potential artifacts, namely
uncertainties of the amplitude and possible effects on the analyzed phases
resulting from the data gaps. Therefore, here the MR winds are analyzed and
can be used to evaluate the earlier results because meteor winds are observed
continuously throughout the day. Possible MR data gaps owing to small meteor
count rates especially at the uppermost and lowermost heights are shorter and
more regularly distributed than the LF data gaps. Collm MR wind data from
2004 to 2013 have already been analyzed with respect to the climatology
of a 2-day oscillation by , but their analysis is based
on a fixed period of 48 h. This may lead to different amplitudes and
phases. In the present study, the actual periods of the QTDW over Collm are
calculated in order to improve the results of . Compared
with , further information about the mid-latitude QTDW can be
obtained with greater accuracy than the earlier LF measurements, in
particular because the amplitude and phase uncertainties due to daytime data
gaps of LF measurements will be avoided. Background shear obtained from the
prevailing winds observed by the radar is used as a proxy for baroclinic
instability.
Measurements and data analysis
A commercial VHF MR, distributed under the brand name SKiYMET All-Sky
Interferometric Meteor Radar; is operated at Collm Observatory
(51∘ N, 13∘ E) since late summer 2004 to measure
mesopause region winds, replacing the earlier LF drift measurements
e.g.,. The MR operates at 36.2 MHz and has a pulse
repetition frequency of 2144 Hz which is effectively reduced to 536 Hz
due to a 4-point coherent integration. The peak power is 6 kW. The
transmitting antenna is a 3-element Yagi with a sampling resolution of
1.87 ms and an angular and range resolution of about 2∘ and
2 km, respectively. The receiving interferometer consists of five
2-element Yagi antennas arranged as an asymmetric cross. This allows
calculating the azimuth and elevation angle from phase comparisons of the
individual receiver antenna pairs. Together with range measurements, the
meteor trail position is detected. The radar uses the Doppler shift of the
reflected VHF radio wave from ionized meteor trails in order to measure the
radial velocity along the line of sight of the radio wave. The radar and data
collection procedure is described by .
The meteor trail reflection heights vary between 75 and 110 km with a
maximum around 90 km e.g.,. To analyze the wind field,
the received meteors and corresponding radial winds are binned in six height
gates centered at 82 km (80.5–83.5 km), 85 km
(83.5–86.5 km), 88 km (86.5–89.5 km), 91 km
(89.5–92.5 km), 94 km (92.5–96.0 km) and 98 km
(96.0–100.5 km). With regard to the uppermost height gate,
showed that, owing to the vertical distribution of meteor
count rates, nominal and mean heights are not necessarily the same and that
the uppermost gate has a nominal height of 98 km which refers to a mean
height of about 97 km. The radar measurements deliver half-hourly mean
horizontal wind values that are calculated by a least squares fit of the
horizontal half-hourly wind components to the individual radial wind under
the assumption that vertical winds are small . An outlier
rejection is added. The climatology of background winds and tides as measured
by the Collm radar is presented in .
The periods of the QTDW are obtained from Lomb–Scargle periodogram analyses
that are based on 11 days of meridional half-hourly wind data each. This
method is chosen due to unevenly spaced data that mainly result from too few
meteors during some half-hourly time intervals, especially at the upper and
lower height gates during the afternoon. The period of maximum amplitude
between 40 and 60 h was defined as the most probable period of the QTDW
for the respective 11-day time interval. This period range is chosen in
accordance with the results of who did not observe longer or
shorter periods. Note that there are cases with more than one maximum in the
selected period interval, and the lower ones are disregarded here even if
they should be close to 48 h. The periodograms are calculated for the
meridional component because the meridional QTDW amplitudes are observed to
be larger than the zonal ones . This is also
justified because for large amplitudes the period difference is generally
small and <2 h in about 75 % of all cases with large amplitudes. Hence,
the underestimation of zonal amplitudes is small and, as will be described in
Sect. 3.1, the zonal amplitude is smaller than the meridional one even when
using QTDW periods that are based on a periodogram analysis for the zonal
component. An example periodogram analysis for the meridional component is
shown in Fig. , using data of a time interval centered on 25
July 2010. In this case, the amplitude maximum between 40 and 60 h is
found at a period slightly larger than 40 h, which represents the QTDW
period for this date.
Lomb–Scargle periodogram of the meridional wind for
a time interval of 11 days centered on 25 July 2010 (91 km altitude). The
QTDW period for this day is set to the one with the maximum amplitude between
40 and 60 h, illustrated by the vertical dotted line.
To obtain amplitudes and phases of the QTDW a least-squares fit has been
applied to the zonal and meridional horizontal half-hourly winds, which
includes the prevailing wind, tidal oscillations of 24, 12 and 8 h,
and the individual period of the QTDW as obtained from the periodogram
analysis of the meridional wind. Each individual fit is again based on 11
days of half-hourly mean winds and the results are attributed to the center
of this data window. Note that if shorter data windows were used, the
resulting amplitudes would be reduced. In particular, this is the case if
there are 2-day bursts within the 11-day window which are not coherent. This
has been discussed by who used both 11- and 5-day windows
for their analysis. Choosing windows that are too small would thus include more
irregular fluctuations, while the chosen 11-day window usually covers several
cycles within a QTDW burst. For the example presented in Fig. ,
the resulting amplitude of the QTDW is 27.6 m s-1 at a period of
40.5 h. After analyzing the QTDW parameters in an 11-day window, the
window was shifted by 1 day. The least-squares fit was performed for both
the zonal and the meridional wind component, and for each height gate
separately. The following results are based on these data.
Results
The upper and lower panels of Fig. present the mean seasonal cycle
of QTDW amplitudes. Here, we also present the total amplitudes as a
combination of zonal and meridional components. The upper panel of
Fig. refers to an altitude of 91 km (gate 4). It shows the
total amplitudes of each year in light gray, starting in September 2004 and
ending in August 2014. The black lines show the 10-year average for total
(straight), meridional (dashed) and zonal (dotted) amplitudes and the red
line shows 45-day adjacent averages of the 10-year mean total amplitude. As
previously reported in the literature, we find a strong summer and a weaker
winter maximum. The first increase of the summer burst starts during May,
where the year 2006 shows a strikingly strong burst. Maximum amplitudes are
usually reached at the end of July and beginning of August, where the
long-term average amplitudes (red curve) exceed 15 m s-1. The maxima
during individual bursts (gray curves) can be even larger and in some years
they reach up to 40 m s-1. The winter QTDW appears much weaker with
average amplitudes between 5 and 10 m s-1.
Upper panel: total annual amplitudes between September
2004 and August 2014 (light gray). Average values of the years 2004–2014
in black for total (straight), meridional (dashed) and zonal (dotted)
components. The 45-day adjacent average for the total annual amplitude is in red.
The blue curve denotes the vertical shear of zonal wind including standard
error. Data refer to an altitude of 91 km. Lower panel: contour plot of
the 10-year mean amplitudes over height in an annual cycle. The horizontal
lines (black) mark the six height gates. Data are interpolated in between.
Periodograms of the meridional amplitude for the
years 2004–2014 at 91 km altitude. Each day represents the center of an
11-day analysis of horizontal wind data. The white line follows the period
of maximum amplitude between 40 and 60 h if amplitudes are larger than
6 m s-1.
The vertical zonal wind shear, which has been calculated from the difference
of the respective prevailing wind components at 94 and 88 km, is added
as a blue line. On a long-time average, the QTDW amplitudes start to increase
when the shear reaches its maximum. In Sect. , we show
that wind shear, taken here as a proxy for baroclinic instability, may act as
a source of the QTDW. However, this relation is not observed in winter where
the QTDW is assumed to appear due to instabilities of the polar night jet
e.g.,.
Distribution of QTDW periods in summer (May–Aug) for the years
2005–2014. Black: amplitudes larger 15 m s-1 only. Gray:
amplitudes between 10 and 15 m s-1. White: amplitudes smaller than
10 m s-1.
Generally, the meridional amplitude in Fig. is larger than the
zonal one. One may argue that this is due to the fact that we define the
period of the QTDW as the period of maximum meridional amplitude (see
Fig. ). This ensures strong meridional amplitudes at the chosen
period but may result in smaller zonal amplitudes if the maximum zonal value
is found at another period. To prove that the larger meridional component is
not attributed to the analysis method we performed the same analysis but
determined the period of the QTDW from the zonal component (not shown here).
As a result, the meridional QTDW amplitude is still larger than the zonal
one.
The lower panel of Fig. combines the mean seasonal cycles of all
six height gates in a contour plot where the respective heights of the gates
are indicated by horizontal lines. The seasonal cycle is similar at different
height gates except for the uppermost one. The summer amplitudes maximize at
about 88 km height which is close to the value reported by
. The winter maximum is strongest at higher altitudes in
late winter where 10 m s-1 can be exceeded, so that at the upper
height gate, the amplitude difference between summer and winter decreases.
The distribution of meridional amplitudes during the years 2004–2014
as obtained from the Lomb–Scargle periodograms is shown in
Fig. . As in Fig. , they refer to an
altitude of 91 km. The white line denotes the period of maximum amplitude
between 40 and 60 h. Note that this curve determines the period that is
taken as the real QTDW period for further analyses. Having a look at the
summer season it is apparent that in certain years the QTDW appears in one
single burst (such as 2007, 2010 or 2012) with typical seasonal maxima
at the end of July or beginning of August. In other years, QTDW activity is
split into two or more bursts (e.g., 2005, 2006, 2009). The largest
amplitudes are usually found between June and August; however, in some years
(e.g., 2006, 2009, 2014) significant amplitudes are also observed in
May. The running spectrum for 2006 is a typical example for a strong summer
QTDW with two main bursts where the periods vary between more or less 40
and 52 h. At the onset of the summer wave in May and when it vanishes in
August, the periods are longer than during the event. This feature from long
periods to shorter ones and back to long ones is also seen in other years
such as 2007 and 2012. In 2005 and 2009 the period is also largest at
the onset of the wave burst and lowest at the maximum of the wave, but it is
more variable in between.
In each winter from 2005 to 2014 slightly increased amplitudes of the
QTDW can be seen. The 10-year mean winter maximum is small and the amplitudes
are, on average, only about 2 times as large as during the September
minimum, which is comparable to earlier observations
e.g.,. The winter oscillations are irregular: they are
particularly large in January 2006, 2012 and 2013. In some cases the
enhancement already starts at the end of the previous year, e.g., large
amplitudes in December 2011 continue in January 2012. Several studies
e.g., suggest a possible relation between
QTDW amplitudes and the strong major sudden stratospheric warming in January
2006. The 2012 and 2013 maxima are also found during winters of major
stratospheric warmings: however, during the 2009 stratospheric
warming no QTDW enhancement is seen in the measurements. In some years (e.g.,
2009, 2011, 2012) amplitudes also maximize in November or December.
Periods are very short in January with 44 h or less and they increase
until February where they often reach 52 h or more.
In the following we concentrate on the more intense summer QTDW, referring to
the months of May–August. In order to investigate the distribution of
periods with respect to the amplitudes, Fig. shows histograms
of periods for different magnitudes of the amplitude where boundary periods
(≤41 h or >59 h) are omitted. Dark bars denote only larger
amplitudes while white bars include days of all amplitudes. The histogram
refers to an altitude of 91 km during summer (May–August). As a result,
intervals with large QTDW amplitudes tend to exhibit shorter periods. The
median for large amplitudes (black columns) is 47.9 h but the median for
all amplitudes including small ones (white) is 49.3 h. For amplitudes
larger than 15 m s-1 (black columns), the lower and upper quartiles
are 45.8 and 52.7 h, respectively. For larger periods, smaller
amplitudes dominate. Furthermore, we find a clear maximum at 47–48 h and
two secondary maxima at 42–43 h and 50–51 h. The latter two maxima are
not statistically significant but, together with the primary maximum, they
correspond to the three maxima presented by .
In the following we show summer QTDW data for amplitudes of at least
15 m s-1. Figure shows the relative amplitude
differences Δv see between zonal and meridional
QTDW amplitudes at 91 km altitude given by
Δv=2vz-vmvz+vm⋅100%,
where the index z refers to the zonal and the index m to the meridional
component of the QTDW. Hence, positive (negative) Δv values denote larger
zonal (meridional) amplitudes and the value denotes the percentage of
amplitude differences from the mean amplitude. The mean and median of summer
relative amplitude differences amount to -46.8 and -39.0 %,
respectively. The 5 and 95 % percentiles are P5=-114.5 % and
P95=2.6 %, respectively. Thus, the meridional component tends to be
larger than the zonal one. Note that the meridional amplitude also tends to
be slightly larger due to the fact that the periods of the QTDW were chosen
from the maximum meridional amplitude. However, this effect is small. If we
calculate the relative amplitude differences using the periods at maximum
zonal amplitude we obtain P5=-75.5 % and P95=17.1 %, which
qualitatively leads to the same conclusion that the meridional amplitude is
larger.
The phase differences between zonal and meridional QTDW components at
91 km altitude are shown in Fig. . The histogram includes
the results for amplitudes larger than 15 m s-1 in black and white
for summer (May–August) and the rest of the year, respectively. The small
number of the latter shows that large amplitudes do mainly appear in summer.
A Gaussian fit was applied to the summer histogram. As a typical feature of
that distribution, mean (102.2∘), median (101.1∘) and mode
(102.4∘) are all of similar value. These values are only slightly
larger than 90∘ and hence the zonal and meridional components are
nearly in quadrature. Other height gates have Gaussian modes that are up to
10∘ larger compared to the 91 km altitude.
Histogram of the 91 km (gate 4) relative
amplitude differences Δv of zonal and meridional components for
amplitudes larger than 15 m s-1. Black bars: summer (May–August)
data, 460 days considered. White bars: rest of the year (January–April,
September–December) data, 17 days considered. Positive values denote
larger zonal than meridional amplitudes.
Histogram of the 91 km (gate 4) phase
differences of zonal and meridional components for amplitudes larger than
15 m s-1. Black bars: summer (May–August) data, 460 days
considered. White bars: rest of the year (January–April,
September–December) data, 17 days considered.
Figure (left panel) shows the means and standard deviations of
the phase difference at all six height gates for amplitudes larger than
15 m s-1. The standard deviation of the uppermost gate is almost
twice as large as those of the lower gates. Considering the lower gates, the
means are comparable to the one at 91 km, slightly higher than
90∘. However, the standard deviation of about 30∘ is large.
The right panel of Fig. shows the profile of the mean QTDW
zonal and meridional amplitudes as well as their differences. At 82 km the
meridional amplitude is only slightly larger than the zonal one. For greater
altitudes, the difference is increasing up to a height of 91 km and almost
constant above.
Vertical wavelengths λz were calculated for each 11-day interval
when the amplitudes at the 91 km altitude were larger than 15 m s-1
by
λz=PdT/dz,
where P is the period and dT / dz is the vertical gradient of the
phase T. For this analysis, the same period has to be used for each height
gate to obtain consistent phases. Therefore, for wavelength calculation, we
repeated the QTDW analysis for each height gate with the period found for
91 km. The vertical phase gradients were calculated by applying linear
fits of phase over height. The histogram in Fig. shows all
wavelengths smaller than 400 km. Indeed, we obtain a few very large
(“infinite”) wavelengths that are not presented when the phase does not
significantly change with altitude, i.e., when the wave does not propagate
vertically. This is true in about 12 % of all cases considered. For the
values smaller than 400 km, a lognormal probability density function is
applied. This fit is accepted by several statistical hypothesis tests such as
a Kolmogorov–Smirnov, Anderson–Darling and a chi-squared test. The mode of
the fitted lognormal function is 77 km whereas the median and mean of the
data set for < 400 km are much larger with 106 and 127 km, respectively.
Left panel: mean phase difference (black) between
zonal and meridional components for 2004–2014 and their standard deviations.
Right panel: zonal (red) and meridional (green) mean amplitudes for 2004–2014 and
their standard deviations. Amplitude difference with standard deviation in
blue. For both panels only dates with total amplitude > 15 m s-1
are used.
Connection with background wind shear
introduced the idea that the origin of the QTDW is baroclinic
instability of the easterly jet in the summer mesosphere. A necessary
condition for that is that the northward gradient of quasi-geostrophic
potential vorticity qy must change sign somewhere in the flow domain to
enable instability . This condition is given in the summer
mesospheric jet in an altitude of about 70 km. Here, the vertical zonal
wind profile has a minimum or, in other words, the easterly winds to reach a
maximum. In order to investigate possible baroclinic instability by analyzing
MR measurements from higher altitudes, a proxy needs to be determined because
the wind maximum is outside the measurement range. We analyze the vertical
wind shear of the zonal wind above the jet as a measure of its strength and
hence for baroclinic instability.
We apply superposed epoch analyses in two ways. First, the key events are
defined from the time series of the amplitude. Therefore, the time series is
filtered using a Lanczos low-pass filter with 30 weights and a cutoff
period of 20 days. When the low-pass filtered amplitudes show a maximum of
at least 10 m s-1, a time window of the original time series from
20 days before the event until 10 days after the event is considered.
Second, the key events are defined from the time series of the wind shear
which was again low-pass filtered with a cutoff period of 20 days. Maxima
of at least 3 m s-1 km-1 are considered and the time window
from -10 to +20 days is used. For each approach, separately, the time
windows are averaged over all key events in both variables, amplitude and
wind shear. Note that the maximum of the key variable is not necessarily
placed at day 0 since the maximum of the low-pass filtered values was set
to day 0 but not the real time series. The results for an altitude of
85 km are shown in Fig. . If the QTDW was amplified by
baroclinic instability, a maximum of the amplitudes would be expected to
appear shortly after a maximum of wind shear as reported by
or . In Fig. , both methods of
the epoch analysis show that the amplitude maximizes about 10–15 days
after a maximum of wind shear. These results are consistent with the
conclusion of : the QTDW is propagating eastward, opposite to
the wind direction in the jet. With increasing amplitude, it tends to act
against its origin and diminishes the wind shear.
When the wind shear is too weak for amplification the amplitude decreases
again. However, considering the large error bars in our data we can only
speak about tendencies. The effect is not clear enough to prove the
hypothesis of baroclinic instability as a forcing mechanism. Furthermore, the
results shown here at 85 km altitude become less significant for higher
altitudes.
Histogram of daily vertical wavelengths during
summer (May–August) for the time period from 2005 to 2014 (red bars)
where only dates with total amplitude > 15 m s-1 are used.
Wavelengths longer than 400 km are not shown (this refers to 56 days out
of 460). A fitted lognormal probability density function in black.
Inter-annual variability
A correlation of QTDW amplitudes to the 11-year solar cycle was found in
low frequency measurements by and recently by
using satellite measurements. Both report larger amplitudes
during solar maximum. Due to the deep solar minimum in 2008 and 2009 an
analysis of the inter-annual variability of the QTDW is of special interest.
Figure presents the F10.7 solar radio flux (black) and
vertical zonal wind shear at 85 km (pink) in the upper part. The lower
part shows the total amplitudes at the four height gates between the 85 and
94 km altitudes. These parameters are given for summer (upper panel) and
winter (lower panel). The seasonal mean data presented in
Fig. are shown each as a 4-month average from May to
August and from November to February while the year of the winter refers to
the one of the respective January.
Superposed epoch analysis of vertical wind shear of the
zonal prevailing wind in blue and QTDW total amplitudes in red at 85 km
altitude, including standard error. The 10-day adjacent averages of the
amplitude are in dark red and wind shear in dark blue. Upper panel: maxima in wind
shear > 3 m s-1 km-1 are considered as key events. Lower
panel: maxima in QTDW amplitude > 10 m s-1 are considered as key
events.
Seasonal mean QTDW total amplitudes for summer
(May–August, upper panel) and winter (November–February, lower panel, the
year refers to the one of the respective January) for different altitudes in
orange, green, blue and red. Error bars denote the standard error given by
the standard deviation of the 11-day analyses during one season divided by
the square root of independent samples (11 per season). Seasonal mean
F10.7 solar radio fluxes and their standard deviations given in solar flux
units (sfu) where 1 sfu = 10-22 Wm-2 Hz-1 (black) and
zonal wind shear of the prevailing wind at 85 km and their standard errors
(pink) are added.
In summer, the amplitudes qualitatively show similar inter-annual variability
at each altitude with a major maximum in 2006 and two minor maxima in
2009 and 2012. The correlation with the solar cycle is weak and
insignificant. However, the correlation of the seasonal mean total amplitudes
with the wind shear at 85 km altitude is stronger with correlation
coefficients from R=0.4 to 0.7. The zonal amplitude has a slightly larger
correlation coefficient for all height gates; the meridional one is slightly
smaller. However, either of them only differs by about 0.1.
report that gravity wave interactions reach particularly
high altitudes in 2008 and hence further increase the shear which is also
visible in Fig. . However, this does not seem to affect the
QTDW in summer.
In winter, amplitudes at different altitudes are not always as homogeneous as
in summer. However, there is a clear peak in all altitudes during winter
2005/2006 when a major stratospheric warming was observed. This is in good
agreement with the general view that enhanced planetary wave activity can
cause stratospheric warmings. The correlation between QTDW winter amplitudes
and solar radio flux in the lower height gates is slightly higher than in
summer but still not significant. Correlation coefficients vary between
-0.4 and +0.4, where zonal amplitudes tend to have negative values and
meridional ones tend to have positive values. The opposite holds for the
correlation with wind shear. Here, meridional amplitudes tend to be
negatively correlated (up to R=-0.7) and zonal ones positively (up to
R=0.7). However, for different altitudes, the values differ significantly
and most correlations turn out to be insignificant. This is in accordance
with the general view that the winter QTDW is a result of instability of the
polar night jet and that the QTDW is originating from the lower atmosphere
instead of being determined by the mesospheric circulation.
As presented in the periodograms in Fig. , the appearance of
the QTDW is not uniform in each year. This is why one might expect a seasonal
mean not necessarily to be representative enough to describe the QTDW. Thus,
we also compare different ways to describe seasonal mean QTDW activity during
a season such as (1) the maximum total amplitude during a season, (2) the
mean of the squared total amplitudes during a season as an estimate for
energy, and (3) the mean of amplitudes minus a threshold value of
6 m s-1, while negative values are set to zero. This latter value is
taken from the “noise floor” visible in Fig. during the
equinoxes.
As a result, the estimates (2) and (3) behave very similar to the
seasonal mean values concerning magnitudes and sign of the correlation
coefficients for correlations with solar radio flux and vertical shear of the
zonal wind.
Using the maximum as an estimate, the correlation with solar radio flux in
summer turns out to be slightly positive for most altitudes with
R≈0.2 in the lower height gates. However, this is still no clear
correlation and thus the results more or less correspond with those obtained
for other estimates. The same holds for summer, where positive values for
zonal and negative values for meridional amplitudes dominate. The correlation
between wind shear and seasonal maxima is mostly weaker than that obtained for
seasonal means by about 0.2.
To conclude, differences obtained with the four methods are not very large.
Thus, the obtained relation between QTDW amplitudes and wind shear is robust
and independent from the chosen method.
Discussion and conclusion
The QTDW is analyzed from Collm VHF meteor radar data. The considered time
series begins after the installation of the radar in 2004 when it replaced
earlier LF measurements and continues until 2014.
On a 10-year average, the QTDW has amplitudes of about 15 m s-1 in
summer when analyzed on an 11-day basis, and single bursts can reach values
of 40 m s-1. These values are comparable to those obtained by
, but they presented MR measurements at low latitudes. In
winter, a secondary maximum with amplitudes of 5–10 m s-1 is
observed. These observations combined with the fact that e.g.,
and report a strong winter QTDW at high
latitudes indicate that the influence of the winter QTDW becomes stronger
with increasing latitude. The periods of the QTDW tend to be longer in winter
than in summer. Some years show a typical signature of periods during summer
bursts that change in length from long to short and back to long while
shorter periods are generally associated with larger amplitudes. Similar
features were observed by and by long-term measurements at
Saskatoon, Canada, by . and
, however, observed shortening periods during the
respective bursts, while found continuously increasing
periods during a burst.
Phase differences between the zonal and meridional component turn out to be
slightly larger than 90∘, which indicates that the wave is nearly but
not exactly circularly polarized. This value is a bit larger than the one
reported by . The zonal and meridional amplitudes are of
comparable size at 82 km altitude but they change with height in a way
that the meridional ones tend to be larger by about 50 %. This coincides
with the results of, e.g., and but it
could not be seen in the earlier LF measurements .
Vertical wavelengths were calculated from the vertical phase gradients. The
mode of a fitted lognormal distribution is 77 km, while the median
wavelength is 106 km. These values are comparable to those obtained by
. Smaller values below 80 km are reported, e.g., by
, or . Even larger values
are found by and but these were obtained in
the Southern Hemisphere. What all studies have in common is the fact that
very large, almost “infinite” values were occasionally obtained, which is
also the case over Collm. This indicates that the wave does not propagate
vertically in these cases.
Furthermore, we find a connection between vertical zonal wind shear and QTDW
amplitudes by applying superposed epoch analyses. They show a maximum of
amplitudes about 10 days after a maximum of zonal wind shear at 85 km
altitude. Also, a maximum of zonal wind shear is found about 10–15
days before the amplitude maximizes at 85 km. In the long-term mean annual
cycle, zonal wind shear reaches a maximum when the QTDW starts to amplify. Also,
in an inter-annual view, the correlation between zonal wind shear and
amplitudes of the QTDW is high in summer but not in winter where the QTDW is
assumed to be amplified by instability of the polar night jet
e.g.,. Since shear is
taken here as a proxy for baroclinic instability we conclude that the QTDW
over Collm is at least to a certain degree forced by instability of the
summer mesospheric jet, as reported by , using satellite
measurements too. Also, observed increasing QTDW amplitudes
above regions of negative quasi-geostrophic potential vorticity.
Between QTDW amplitudes and the 11-year solar cycle a positive correlation
is found in winter. In summer it is weaker and correlation coefficients tend
to be negative. However, the correlation is not that clear. This can be
explained by considering the results of . They found a
positive correlation of zonal wind shear and solar cycle except during solar
minimum when correlation turns out to be negative. This may also hold for the
QTDW due to the possible amplification by baroclinic instability. As the
strong solar minimum in 2009 is centered in the analyzed time series, longer
observations are necessary to draw further conclusions.