Airglow spectrometers, as they are operated within the Network for the Detection
of Mesospheric Change (NDMC; https://ndmc.dlr.de, last access: 1 November 2020), for example, allow the derivation of rotational
temperatures which are equivalent to the kinetic temperature, local thermodynamic
equilibrium provided. Temperature variations at the height of the airglow layer
are, amongst others, caused by gravity waves. However, airglow spectrometers do
not deliver vertically resolved temperature information. This is an obstacle
for the calculation of the density of gravity wave potential energy from these measurements.
As Wüst et al. (2016) showed, the density of wave potential energy can
be estimated from data of OH∗-airglow spectrometers if co-located
TIMED-SABER (Thermosphere Ionosphere Mesosphere Energetics Dynamics, Sounding of the Atmosphere using Broadband Emission Radiometry) measurements are available, since they allow the calculation of the
Brunt–Väisälä frequency. If co-located measurements are not
available, a climatology of the Brunt–Väisälä frequency is an
alternative. Based on 17 years of TIMED-SABER temperature data (2002–2018),
such a climatology is provided here for the OH∗-airglow layer height and for
a latitudinal longitudinal grid of 10∘×20∘ at
midlatitudes and low latitudes. Additionally, climatologies of height and thickness
of the OH∗-airglow layer are calculated.
Introduction
This is the succeeding publication to Wüst et al. (2017a),
where the angular Brunt–Väisälä (BV) frequency was
calculated for the OH∗-layer height between 43.93–48.09∘ N
and 5.71–12.95∘ E using Thermosphere Ionosphere Mesosphere Energetics
Dynamics, Sounding of the Atmosphere using Broadband Emission Radiometry
(TIMED-SABER) data from 2002 to 2015. The choice of the geographical region,
which includes the Alps, was due to the location of the five Network for the
Detection of Mesospheric Change (NDMC) stations: Oberpfaffenhofen (48.09∘ N,
11.28∘ E), the Hohenpeißenberg observatory (47.8∘ N,
11.0∘ E), the Environmental Research Station Schneefernerhaus (47.42∘ N,
10.98∘ E), Germany, and the observatories in Haute-Provence (43.93∘ N,
5.71∘ E), France, and Sonnblick (47.05∘ N, 12.95∘ E), Austria. We described
seasonal variations of the three parameters, height and full width at half
maximum (FWHM) of the OH∗ layer as well as the BV frequency
weighted according to the parameters of the OH∗ layer and
provided a climatology of the yearly course of this BV frequency.
Now, the data basis is extended to global TIMED-SABER measurements. Overall, 3 more years (2016–2018)
are included in the analysis which changed slightly compared to Wüst et
al. (2017a): instead of calculating the Gaussian-weighted BV frequency, the
BV frequency is now weighted with the volume emission rate of the OH-B (1.6 µm)
channel of SABER. Furthermore, the geographical position of the SABER
measurements at 86 km height is taken into account (in our preceding
publication, any part of the SABER profile needed to fit the geographical
selection criteria).
The angular BV frequency N, which is, for example, needed for calculation of
the density of gravity wave potential energy, varies with the temperature
T and its vertical gradient (e.g. Andrews, 2000):
NT,dTdz=gTdTdz-Γd,
where Γd=g/cp (with g equal to acceleration due to gravity,
cp the specific heat capacity of air at constant pressure) is the dry-adiabatic
lapse rate defined as the vertical adiabatic temperature decrease. In most cases,
its value is given as 9.8 K km-1. However, the acceleration due to gravity, g, is slightly height
dependent and determines together with the specific heat capacity at constant
pressure, cp, the dry-adiabatic lapse rate. g reaches a value of
approximately 9.55 m s-2 at 86 km height; therefore, the vertical
adiabatic temperature decrease is approximately 9.5 K km-1 there.
g also depends on the geographical position due to the fact that the Earth is not a perfect sphere
but oblate. Since the variation in the Earth radius is less than 86 km (only
approximately one quarter of it), this effect is of minor importance and therefore
neglected here.
Measurement techniques which provide vertical temperature profiles therefore allow
the direct calculation of the BV frequency and of further
parameters such as the density of wave potential energy (see, e.g. Kramer et
al., 2015; Mzé et al., 2014; Rauthe et al., 2008, to mention just a few).
OH∗ spectrometers, however, deliver information about
temperature always vertically averaged over the OH∗ layer.
OH∗ imaging systems provide in most cases only brightness
maps (e.g. Sedlak et al., 2016, and Hannawald et al., 2016, 2019, who
addressed a small part of the sky, and Garcia et al., 1997, who
operated an all-sky system). An exception is here Pautet et al. (2014), who
worked with narrow-band filters and could derive temperature maps. At a
poorer horizontal resolution scanning OH∗ spectrometers can also deliver
horizontally resolved temperature information (see, e.g. Wachter et al., 2015;
Wüst et al., 2018). However, also in these cases, the temperature is
vertically averaged over the OH∗ layer; the BV frequency cannot be calculated.
So, one needs to rely on temperature climatologies or on complementary
temperature measurements. The latter should be of higher accuracy in most
cases, if the coincidence in time and space of the complementary and the
original measurement is good enough (see Wendt et al., 2013, for the
quantification of typical temperature differences due to miss time and
miss distance). Since complementary measurements are rare and not available
at every NDMC station and at every time, a climatology of the BV frequency
based on global satellite-based measurements is very valuable. Approximately
85 % of all spectrometers and photometers listed in the database of NDMC address
at least one of the various OH emissions (Schmidt et al., 2018); thus,
TIMED-SABER OH-B channel and temperature measurements are used for the BV
frequency climatology. The OH-B channel covers the wavelength range from
1.56 to 1.72 µm, which includes mostly the OH (4-2) and OH (5-3)
vibrational transition bands. The peak altitude difference for adjacent
vibrational levels is approximately 500 m (e.g. Adler-Golden, 1997; von Savigny et
al., 2012) and therefore negligible compared to the FWHM, which is typically
cited to be 8.6km±3.1km (Baker and Stair, 1988). Of course,
a climatology based on global satellite measurements always provides averaged
information. Effects of processes which vary during one night, such as gravity
waves, or those which change significantly from year to year are not (or
only to a small extent) included (due to the thickness of the
OH∗ layer, at least small-scale variations cancel
out; see, e.g. Wüst et al., 2016). Especially tides can affect
the BV frequency significantly since they are able to change the
temperature and also the temperature gradient. Mukhtarov et al. (2009)
showed, for example, that the amplitude of the diurnal migrating (meaning
Sun-synchronous) tide varies during the year but maximizes at the equatorial
mesosphere with amplitudes of 19 K at 90 km height. The amplitude is
lower at midlatitudes. The vertical wavelength in this height range is
approximately 20 km. The amplitude of the semi-diurnal migrating tide
shows another latitudinal structure at 90 km height with maxima of
approximately 9 K, which are reached around 40∘ N/S (Pancheva
et al., 2009). The vertical wavelengths are larger in summer (∼38–50 km)
than in winter (∼25–35 km). These results concern tides propagating
to the west. The eastward-propagating diurnal and semi-diurnal tides are,
for example, investigated in Pancheva et al. (2010a). They are characterized
by smaller amplitudes. Therefore, we additionally provide an uncertainty
range of the BV frequency due to tides in this publication.
Data and analysis
We use TIMED-SABER temperature and OH-B channel data (volume emission rate;
VER) in version 2.0 for the years 2002 to 2018. It was
downloaded from the SABER homepage (http://saber.gats-inc.com/, last access: 6 December 2019). In order not to
duplicate information, the reader is referred to our preceding publication
(Wüst et al., 2017a) and publications therein for more details about
TIMED-SABER (Mertens et al., 2004; Mlynczak, 1997; Russell et al., 1999),
the retrieval of kinetic temperatures (Dawkins et al., 2018; Garcia-Comas et
al., 2008; López-Puertas et al., 2004; Mertens et al., 2004, 2008;
Remsberg et al., 2008) and a comparison between SABER v2.0 temperature and
ground-based lidar data (Dawkins et al., 2018). Since the OH∗
spectrometers only allow measurements during nighttime, we calculate the exact
local time (by adding 4 min to UTC for every longitudinal degree) and
require SABER measurements between 18:00 and 06:00 LT (local
time).
The squared BV frequency Ni2 is computed for each SABER profile at
every available height and weighted with the OH VER. The result is called
the OH∗-equivalent BV frequency in the following. From time to time, a
maximum in the VER is observed around 40 km height and the respective
profile shows strong oscillations. These profiles are excluded from further
analysis steps.
Furthermore, information about the OH∗ layer is derived
from the OH VER profiles. The centroid height is denoted as the
OH∗ height in the following and the FWHM is calculated
by determining the maximum of the OH VER and subtracting the lower
height from the upper height where half of the maximum is reached
for the first time (starting at the height of maximal OH VER).
In the following, the OH∗ height, the FWHM and
the OH∗-equivalent BV
frequency are mapped to a 20∘(longitude)×10∘(latitude)
grid. The data are ascribed to the midpoints of the respective intervals. Here,
the geographical position of the SABER measurement at 86 km height
is taken into account. Then, the daily mean of each parameter is calculated
for every grid cell. This is done for all years. It is assumed that every
year is a leap year; this facilitates further calculations.
Due to the yaw cycle of SABER, data gaps are visible at higher latitudes and
all investigations in this publication include the latitudinal range of
52∘ S to 52∘ N.
Results and discussion
All three parameters (the OH∗-layer height, the FWHM and
the OH∗-equivalent BV frequency) vary with latitude, longitude,
day of year (DoY) and local time. In this section, the results will be first
described qualitatively based on some examples. Then, the annual development
of the OH∗-equivalent BV frequency will be approximated and the respective
mathematical function will be provided.
Variations of <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> height, FWHM and <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-equivalent BV frequency
Since the BV frequency depends on temperature, which changes strongly with
DoY and latitude, one would expect that the BV frequency varies more with
these two parameters than with longitude. Both the latitudinal and the
temporal dependence of the temperature are strongly determined by the
residual circulation (see, e.g. Garcia and Solomon, 1985, who give
a concise overview in their introduction about the development of our knowledge
concerning the mean meridional circulation). The residual circulation
consists of horizontal and vertical movements. The higher the latitude, the
more important the vertical movement and the less important the horizontal
one becomes. The vertical movement influences the temperature through
adiabatic warming or cooling but also the downward transport of atomic
oxygen (the dominating species for the formation of OH∗)
from heights above the OH∗ layer and therefore the
OH∗ height and thickness (e.g. Shepherd et al., 2006):
a downward movement leads to a lower and brighter OH∗ layer,
and vice versa. On average, the OH∗ layer is thicker (thinner)
during a prevailing downward (upward) movement (e.g. Liu and Shepherd, 2006).
Therefore, it is not surprising that an annual cycle is clearly visible in
the temporal development of all three parameters at midlatitudes. It dominates
the development of the OH∗ height and the OH∗-equivalent
BV frequency during the year at all longitudes for 45∘ N (Fig. 1a),
for example. The FWHM additionally shows a period of approximately 60 d
in every season but summer. At low latitudes, the annual cycle is less pronounced.
At all longitudes for 5∘ N, for example, a semi-annual cycle and
superimposed oscillations with smaller periods of approximately 60 d (especially
for the FWHM and the OH∗-equivalent BV frequency) gain importance for the
development of the three parameters during the year or even dominate it
(Fig. 1b).
OH∗-layer
height (a, d), FWHM (b, e) and OH∗-equivalent
BV frequency (c, f) are shown for the latitudinal band of 45±5∘ N (a–c)
and 5±5∘ N (d–f) depending on longitudinal bands (longitude ±10∘,
colour coded) and DoY. The data are averaged for each DoY. Additionally,
they are subject to a 31-point sliding mean. In order to facilitate
comparison, the scales of the plots referring to 45±5∘ N and 5±5∘ N are identical.
The annual development of the OH∗-layer height, the FWHM
and the OH∗-equivalent BV frequency varies to some
extent also with longitude. For the different longitudes, the yearly
latitudinal means over the three parameters range between
approximately 85 and 87 km, 7.0 and 8.25 km, and 0.020 and
0.023 s-1 (Fig. 2). The longitudinal variability (peak-to-peak
difference) is at maximum approximately 1.5 km (approximately 2 %
relative to 86 km) for the OH∗-layer height,
approximately 1 km (approximately 13 % relative to 7.6 km) for
the FWHM and approximately 0.001 s-1 (approximately 5 % relative to 0.0215 s-1) for the OH∗-equivalent
BV frequency (Fig. 2). The graphs referring to the different longitudes
spread more for 5∘ N than for 45∘ N (Fig. 1).
OH∗-layer height (a), FWHM (b)
and OH∗-equivalent BV frequency (c)
are averaged over all years and plotted for the latitudinal bands
45±5∘ S to
45±5∘ N, 50–52∘ N/S (colour coded). Please
be aware that the axes of the respective plots of Figs. 1 and 2 are not
identical.
Therefore, the approximation of the annual development of the OH∗-equivalent
BV frequency will be calculated on a latitude–longitude grid, which is
10∘×20∘. The number of values per grid cell
and year varies strongly. For high latitudes (53∘ N or
∘ S and more), the OH∗-equivalent BV frequency can be provided for
half a year and less due to the TIMED yaw cycle. Thus, these latitudes are
excluded from further investigations. For midlatitudes and low latitudes, data gaps
exist only for individual days. For the climatology of the OH∗-equivalent BV
frequency, which is based on 17 years of TIMED-SABER data, approximately 80–190
values are available per grid cell and day at maximum. The number of values
and the variation in the number of values per grid cell over the year is
higher for midlatitudes compared to low ones. The average number of values
per grid cell and day ranges between approximately 45 (for low latitudes) and 85 (for
midlatitudes).
Possible reasons for the variations of the <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>
height, the FWHM and the <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-equivalent BV frequency
In the following, we discuss the possible origin of the oscillations
described above. Here, we have to discriminate between natural phenomena and
possible artefacts due to the yaw cycle of TIMED in order to chose a correct
mathematical approximation of the annual development of the BV frequency.
The 60 d oscillation
The overpass time of TIMED-SABER varies with DoY (Fig. 3, only nightly
overpasses considered): TIMED flies by a little bit earlier every day with
respect to a fixed geographical position and has a yaw cycle of 60 d, i.e.
the viewing direction of the instrument changes every 60 d, and the overpass
time at a specific geographical position is the same every 120 d for the
same viewing direction (ascending or descending part of the orbit). If the
observed parameter has a fixed daily cycle, an artificial 120 d oscillation
can be generated in the respective time series. Zhang et al. (2006) showed
such a periodicity in SABER temperature measurements at 86 km height in
their Fig. 2a. If the viewing direction is neglected, the overpass time is
identical every 60 d. In this case, an artificial 60 d oscillation could be
generated in the respective time series.
Local overpass time of TIMED for the grid cells at 5∘ N,
10∘ E (dark grey), and 45∘ N, 10∘ E (light
grey), for the year 2002 between 18:00 and 06:00 LT. A negative
local time means that the respective profile was recorded before midnight
(-2 LT = 22:00 LT, -4 LT = 20:00 LT, -6 LT = 18:00 LT).
Daily averages are not computed; this plot shows the individual measurements (959 for 5∘ N and 1626 for
45∘ N).
The BV frequency depends not only on temperature but also on the
vertical temperature gradient. Changes in temperature and its vertical
gradient can affect the development of the BV frequency during the night but
they do not necessarily need to (if both temperature and vertical
temperature gradient, increase (or decrease) simultaneously, their effect on
the BV frequency can also cancel out; see Eq. 1). Approximating
linearly the temporal dependence of temperature and its vertical gradient
during nighttime for 5∘ N gives -0.94 K h-1 and -0.25 K km-1 h-1
(Fig. 4a and b; the squared correlation coefficient R2 is 6 % and 17 %).
For 45∘ N, the parameters increase on average by 0.81 K h-1
and 0.04 K km-1 h-1 during the night (Fig. 4c and d; R2 is
3 % and 0.4 %). Assuming a linear behaviour of both the temperature
and its vertical gradient, an effect on the BV frequency cannot be derived
for 45∘ N. For 5∘ N, the BV frequency shows a temporal
dependence (Fig. 4e), which is the condition for a sensitivity to the yaw
cycle. Even though the respective R2 values are very low, the
result is consistent with our observations (Fig. 1c and f).
Temperature and vertical temperature gradient, both VER weighted,
for 5∘ N (a, b) and 45∘ N (c, d) for
the year 2002. The nomenclature concerning the local time agrees with the one
explained in the caption of Fig. 3. Panel (e) shows the development
of the BV frequency during the night for 5∘ N, 10∘ E
(black), and 45∘ N, 10∘ E (grey), based on the linear
approximation of temperature and its vertical gradient.
Let us have a closer look on the variability of temperature and its vertical
gradient during night. During one night, both parameters are influenced
amongst others by tides. As shown by Pancheva et al. (2009) and Mukhtarov et al. (2009) based on 5 years of TIMED-SABER observations, the amplitude of the
diurnal and semi-diurnal tide varies from month to month and so does their
influence on the BV frequency. From April to July, the amplitudes of both
tides show a common minimum at 90 km height and 40∘ N, whereas the
diurnal tide is maximal in February and March as well as in August and
September. The semi-diurnal tide reaches its highest amplitudes from
November to February. These results are supported by Silber et al. (2017),
who show in their Fig. 7 that tidal amplitudes in general are relatively
low during summer for 4 years of GRIPS (Ground-based Infrared
P-branch Spectrometer) data in Tel Aviv (32.1∘ N, 34.8∘ E).
Also the phases of the diurnal and semi-diurnal tides vary to some extent
(see again Pancheva et al., 2009, and Mukhtarov et al., 2009, for measurements
between 50∘ S and 50∘ N). Silber et al. (2017) depict in
their Fig. 9 that the phases of the diurnal and the semi-diurnal tide are
at least over some time relatively stable (the tides are approximated by a
cosine starting at 12:00 LT; the phases approach values near zero on average).
A nearly linear relation between observation time and temperature (vertical
temperature gradient) can only be expected if the diurnal tide dominates
over the semi-diurnal and its phase is 06:00 or 18:00 LT (00:00 or 12:00 LT)
in the case that the tide is approximated by a cosine. The weighting with
VER smears the signals. Temperature and temperature gradient should show different
variations during the year due to tides. The low amplitudes during summer are
captured by the strength of the 60 d oscillation in the OH∗-equivalent BV frequency time series.
These effects probably explain the low R2 values and lead to
the large spread around the linear regression shown in Fig. 4a–d.
Tidal influence could also explain the oscillation of approximately 60 d in the FWHM
at 45∘ N during parts of the year. Compared to the calculation of
the OH∗-layer height and of the BV frequency, the FWHM is not
weighted by the VER (see Sect. 2), and therefore it is more sensitive to individual
variations of the OH VER profile. Amongst others, these individual
variations are due to tides which systematically influence the temperature
and its gradient but also the downward mixing of atomic oxygen. Only during
selected time intervals (e.g. approximately DoY 90–120, 220–250 and 330–365; see
Fig. 3) are profiles sensed at different times of the night (time difference of approximately 4 h)
available. Comparing Figs. 3 and 1b, one can see, for example, around DoY
30–40 that the gradient of the FWHM changes its sign when the observation
time jumps in this case from approximately 18:00 to 06:00 LT.
However, oscillations with slightly shorter periods than 60 d (approximately
50 d) are also observed in measurements which are not affected by a 60 d yaw
cycle as, for example, Rüfenacht et al. (2016) showed based on horizontal wind
values derived from a ground-based Doppler wind radiometer. Those
measurements refer to the altitude range between the mid-stratosphere (5 hPa)
and the upper mesosphere (0.02 hPa); low, middle and high latitudes are addressed
in the publication. The observed periods between 20 and 50 d are subject to
temporal variations. The reason for these oscillations is not
clear. The authors discuss a link to solar forcing; however, they point out
that solar forcing might influence the atmospheric wave pattern only in an
indirect way. Therefore, it is possible that we see a mixture
of natural and artificial effects in our data. However, we cannot distinguish
between them and ignore the 60 d oscillation for our BV climatology.
Comparing the large-scale dynamics (tides and planetary waves) of low and
midlatitudes, there are prominent differences. Offermann et al. (2009)
showed in their Fig. 8 that tidal motions in general gain more and more
importance in comparison to planetary waves at approximately 90 km height the lower
the latitude is. At 20∘ N, tidal waves cause more variability than
stationary planetary waves. Compared to travelling planetary waves, tidal
variations lie in the same range (Offermann et al., 2009). We can conclude
that at low latitudes the effect of tidal motions on temperature is at least
of the same order of magnitude as the influence of planetary waves.
Concerning the temperature gradient, we can argue as follows: the influence
of waves on the temperature gradient depends on the vertical wavelength (the
larger the wavelength, the smaller the influence of waves with the same
amplitude) and the amplitude of the wave (the larger the amplitude, the
greater the influence of waves with the same vertical wavelength). The
vertical phase velocity determines how fast the influence is changing. The
mean vertical wavelength of the 5 d Rossby wave, for example, is approximately
50–60 km according to Pancheva et al. (2010b), who investigated TIMED-SABER
temperature measurements for 6 full years from January 2002 to December
2007, while the vertical wavelengths of tides are mostly in the same range
or slightly smaller and reach approximately 30 km at minimum as, for example, Zhang et
al. (2006) showed for case studies and Forbes et al. (2008), who used
TIMED-SABER temperature measurements from March 2002 to December 2006.
Additionally, the periods of tides are smaller compared to planetary wave
periods; tides have a larger vertical phase velocity. That means that at low
latitudes, tides influence the temperature gradient and its change during
night stronger than planetary waves. This agrees qualitatively with the
results shown in Fig. 4.
Annual and semi-annual variation
As mentioned above, visual inspection of Fig. 1 depicts at least one additional
oscillation with a semi-annual period besides the annual cycle
and the 60 d variation. Semi- and even ter-annual periods are observed by
other authors and in different parameters (for the semi-annual cycle in
different parameters in the mesosphere and higher but not specifically for
airglow, see, e.g. the introduction of Silber et al., 2016). Based on
WINDII (Wind Imaging Interferometer) measurements between 60∘ N
and 60∘ S from 1991 to 1997, Shepherd et al. (2006) showed in their
Fig. 1 a semi-annual variation in the OH emission rate between approximately
20∘ N and 20∘ S with maxima in spring and autumn. The
authors attribute this oscillation to the semi-annual variation of the
downward mixing associated with the variation in amplitude of the diurnal
tide. Liu and Shepherd (2006) pointed out that the column-integrated
emission rate is inversely related to the peak height for WINDII data
between 40∘ S and 40∘ N, and developed an empirical model
for predicting the altitude of the peak of the OH nightglow emission. Here,
they included amongst others sinusoidal annual and semi-annual variations.
Mulligan et al. (2009) transferred this model to Longyearbyen (78∘ N,
16∘ E) and found amplitudes unequal to zero for the annual and semi-annual
modes. For low latitudes, von Savigny (2015) showed minima in the OH∗
height in spring and autumn. Annual, semi- and ter-annual oscillations are also
observed in temperature: as published by Höppner and Bittner (2007) in
their Fig. 2 for Wuppertal, Germany (51∘ N, 7∘ E), in 1993,
the OH∗ temperature derived by the ground-based
GRIPS does not show just an annual cycle; it is characterized
by a kind of plateau at DoY 40–80 (February and March) and DoY 260–300
(September and October). Therefore, the authors approximate the overall
yearly course as (quasi) annual, (quasi) semi-annual and (quasi) ter-annual
sinusoidal (see also Bittner et al., 2000, 2002). Those plateaus can also be
observed using GRIPS data at other stations, e.g. in Tel Aviv (see Wüst
et al., 2017b), and if the temperature data are averaged over some years
(tested for the Environmental Research Station Schneefernerhaus (UFS) and
not shown here).
Approximation of the <inline-formula><mml:math id="M155" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-equivalent BV frequency
In order to provide qualitative results, the harmonic analysis (one-step mode; see, e.g. Wüst and Bittner, 2006) is applied to the
time series of OH∗-equivalent BV frequency averaged over each
DoY and separated according to latitude and longitude. In order to avoid the
approximation of the 60 d oscillation, which might be due to sampling tides
at different phases as discussed above, the period range which the harmonic
analysis uses is restricted to 180–366 d. That means tidal effects are not
included here. The number of oscillations is chosen to be two. The results
are summarized in Table 1, and two examples for the approximation are shown
in Fig. 5. The quality of approximation (that means 1-σres2σ2,
where σ2 is the variance of the original time series and σres2
is the variance of the residual time series, so the original time series minus the
approximation) is plotted versus latitude in Fig. 6. In most cases, the two oscillations
show periods in the range of an annual and semi-annual cycle. As already mentioned above,
using the latitudes of 5∘ N and 45∘ N, the importance of the 60 d
oscillation, which is not adapted, increases with decreasing latitude. Therefore, the
quality of approximation over all longitudes reaches its minimum near the Equator (Fig. 6).
The asymmetry in the quality of approximation between the Northern Hemisphere and
the Southern Hemisphere is remarkable. This agrees quite well with asymmetries in
tidal activity observed, for example, by Vincent et al. (1989). Those authors
investigated radar wind observations which refer to 80–100 km height in
Adelaide (35∘ S, 138∘ E) and Kyoto (35∘ N, 136∘ E),
two places which are symmetrically located around the Equator. The diurnal tidal
winds in Adelaide have a larger amplitude than in Kyoto (factor 2–3). However,
the reason for this behaviour is not entirely clarified. There exist hemispheric
differences in tidal forcing but also differences in the middle atmosphere winds
through which the tides must propagate and finally differences in dissipation.
Concerning the amplitudes of the semi-diurnal tide, the authors found out that they are in general
smaller at both sites than the amplitudes of the diurnal tide. During local
summer, the amplitudes are larger in Adelaide. For many latitudes,
longitudinal differences are clearly visible in the quality of
approximation. However, when taking a ±10 % interval around the approximation, all data are covered in nearly all cases (Fig. 7).
Period (T), amplitude (A) and phase (φ) of the two oscillations
which explain the variability of the daily OH∗-equivalent BV frequency
values (averaged over all years) best for a latitudinal and longitudinal
gridding of 10∘ and 20∘. They oscillate around the
respective mean. The OH∗-equivalent BV frequency (s-1) can be estimated by
the mean+∑i=12Aisin2πTi⋅DoY-φi. Due to leap years, the total amount of days for 1 year is set to 366, which
means 1 March is DoY 61 for every year. The harmonic oscillation explains the variability in the time series of
daily OH∗-equivalent BV frequency values to a different extent. The
respective value is provided in the column “quality of approximation”.
Additionally, the fraction of data which lies within intervals of ±5 %
or ± 10 % around the harmonic approximation is given.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±5 %±10 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -51102.19366.00.24-1.56192.60.13-1.680.870.920.99-51302.18366.00.23-1.61189.30.12-1.620.870.950.99-51502.18366.00.22-1.62187.90.11-1.510.850.930.99-51702.17366.00.21-1.61188.90.10-1.600.830.930.99-51902.18366.00.22-1.59190.30.09-1.590.870.940.99-511102.18366.00.22-1.58188.40.10-1.560.830.930.98-511302.17366.00.24-1.56189.80.12-1.620.880.950.99-511502.15366.00.22-1.58190.30.11-1.580.860.941.00-511702.15366.00.22-1.59189.30.11-1.710.860.930.98-511902.15366.00.23-1.58188.90.12-1.690.880.930.98-512102.15366.00.25-1.58188.40.13-1.670.890.930.99-512302.14366.00.24-1.58186.10.10-1.610.900.960.99-512502.15366.00.25-1.54189.30.10-1.660.900.950.99-512702.16366.00.24-1.54189.30.11-1.690.860.930.99-512902.17366.00.23-1.56188.40.11-1.770.860.920.99-513102.17366.00.22-1.56188.90.11-1.770.900.941.00-513302.17366.00.22-1.55189.30.11-1.760.880.940.98-513502.18366.00.22-1.54191.20.11-1.660.860.940.99-45102.18366.00.16-1.52201.90.05-1.900.720.910.99-45302.18366.00.17-1.55195.40.05-1.770.800.931.00-45502.18366.00.15-1.56195.40.04-1.530.760.940.99-45702.17366.00.14-1.50204.70.03-1.800.690.921.00-45902.17366.00.15-1.49192.10.03-2.040.800.961.00-451102.18366.00.16-1.50194.50.04-1.810.840.961.00-451302.18366.00.18-1.51193.50.05-1.820.860.961.00-451502.16366.00.16-1.50193.10.04-1.710.800.951.00-451702.16366.00.15-1.51191.70.04-1.930.810.961.00-451902.16366.00.16-1.46193.50.05-1.850.820.961.00-452102.16366.00.17-1.48194.00.05-1.760.830.961.00-452302.16366.00.15-1.51190.30.04-1.850.810.961.00-452502.17366.00.14-1.45192.10.03-1.840.770.951.00-452702.18366.00.13-1.44186.10.04-1.920.730.941.00-452902.18366.00.15-1.47184.20.06-1.970.790.941.00-453102.16366.00.15-1.52191.20.05-2.030.820.961.00-453302.16366.00.14-1.50195.40.04-2.140.760.951.00-453502.18366.00.15-1.51200.10.04-2.060.710.931.00-35102.22365.50.07-1.12180.00.041.930.270.800.96-35302.22315.70.08-0.72180.00.041.790.430.861.00-35502.22256.00.080.17180.00.031.160.390.801.00-35702.21229.00.050.17366.00.04-0.510.270.821.00-35902.21328.20.05-0.59180.00.041.970.330.881.00-351102.22350.60.07-1.06180.00.032.130.470.941.00-351302.23354.40.09-1.21180.00.022.620.600.981.00-351502.22323.60.06-0.76180.00.021.770.390.941.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±5 %±10 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -351702.20275.10.040.30180.00.021.720.240.951.00-351902.21333.40.07-0.71180.00.022.150.450.951.00-352102.23366.00.09-1.16180.00.011.710.630.981.00-352302.23312.40.05-0.67180.00.011.740.370.961.00-352502.24199.10.031.28366.00.02-0.190.170.941.00-352702.23325.90.030.16180.00.023.030.160.931.00-352902.20350.60.06-0.88180.00.033.110.450.941.00-353102.19342.70.08-1.04180.00.032.440.540.941.00-353302.19222.90.050.61366.00.02-0.900.280.861.00-353502.21215.90.040.73366.00.02-1.280.160.790.97-25102.20180.00.041.97366.00.03-0.710.230.921.00-25302.20245.70.05-0.13366.00.03-0.330.430.981.00-25502.21213.60.060.55366.00.04-0.400.420.971.00-25702.21180.00.051.63366.00.03-0.450.350.941.00-25902.19180.00.041.69366.00.020.040.260.951.00-251102.20334.30.03-0.50180.00.021.650.290.991.00-251302.22354.80.06-1.17180.00.021.440.480.981.00-251502.21208.00.030.70366.00.02-0.770.190.971.00-251702.19180.00.041.56292.40.031.610.310.981.00-251902.19366.00.030.42188.90.011.270.190.981.00-252102.22366.00.05-0.79221.50.01-1.060.360.971.00-252302.24265.80.040.43180.00.020.570.200.981.00-252502.25366.00.041.45192.10.031.500.270.971.00-252702.22366.00.051.28180.00.032.740.400.971.00-252902.19324.10.030.74180.00.022.860.230.981.00-253102.18335.20.04-0.47180.00.022.480.330.981.00-253302.19180.00.041.83366.00.02-0.970.240.931.00-253502.21180.00.062.15238.70.03-1.790.230.901.00-15102.13180.00.01-1.49363.70.01-2.970.040.951.00-15302.12366.00.03-1.50180.00.01-1.130.180.931.00-15502.13303.10.03-0.58180.00.01-0.040.200.981.00-15702.13212.20.041.54180.00.040.020.130.971.00-15902.11366.00.012.15180.00.010.170.050.931.00-151102.11180.00.02-0.67245.70.010.260.050.921.00-151302.13366.00.06-1.41197.70.03-0.590.360.921.00-151502.13180.00.040.38366.00.03-1.930.270.951.00-151702.12366.00.042.47180.00.021.000.240.941.00-151902.10361.30.031.55232.70.01-1.460.160.911.00-152102.13184.20.04-0.95366.00.03-0.910.220.931.00-152302.15366.00.03-1.79180.00.02-1.220.200.951.00-152502.15366.00.052.15236.40.010.980.280.981.00-152702.14366.00.061.78233.10.01-0.890.340.951.00-152902.11307.70.022.68180.00.01-1.370.050.931.00-153102.11361.80.03-1.17231.30.01-1.190.110.911.00-153302.13274.60.04-1.26187.50.012.330.200.961.00-153502.14348.80.03-3.09204.70.010.740.220.981.00-5102.06180.00.04-0.97366.00.042.470.210.821.00-5302.05180.00.04-1.16366.00.012.800.150.821.00-5502.04180.00.03-1.42366.00.012.060.080.831.00-5702.04306.30.032.46180.00.02-1.170.130.811.00-5902.04249.90.043.00180.00.02-0.600.180.770.99
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±5 %±10 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -51102.04205.60.05-1.80366.00.021.410.170.820.97-51302.05181.40.05-1.01366.00.02-1.060.200.821.00-51502.04187.00.04-0.83366.00.01-2.840.210.901.00-51702.05310.10.05-3.01180.00.010.280.290.881.00-51902.05299.80.053.04215.00.010.120.200.851.00-52102.05194.90.05-1.24366.00.02-1.620.190.861.00-52302.05180.00.05-1.06366.00.02-2.400.250.851.00-52502.05227.60.04-2.41366.00.022.650.170.861.00-52702.06249.50.04-2.43180.00.02-0.240.200.831.00-52902.04180.00.04-0.39366.00.022.790.140.851.00-53102.03267.60.03-0.91180.00.02-0.850.100.841.00-53302.04314.30.04-2.05180.00.02-0.650.140.841.00-53502.06345.50.052.99180.00.02-0.820.210.841.005102.05349.70.071.84180.00.02-1.050.300.790.995302.03297.90.062.16180.00.03-0.580.290.820.995502.02265.80.062.50180.00.03-0.470.300.741.005702.04269.00.082.47180.00.03-0.580.350.730.985902.06275.60.092.50180.00.03-0.630.430.780.9951102.06266.20.092.70180.00.02-0.580.440.821.0051302.05234.50.06-2.66366.00.030.480.330.831.0051502.03232.70.07-3.07180.00.020.200.320.810.9951702.08317.10.052.62180.00.02-0.030.280.871.0051902.09366.00.051.94180.00.010.350.330.981.0052102.05235.50.04-2.67366.00.010.800.260.951.0052302.03220.10.06-2.87180.00.020.040.280.861.0052502.05241.50.053.00180.00.02-0.270.220.801.0052702.07249.50.042.85180.00.030.030.200.891.0052902.06240.10.042.81180.00.04-0.030.220.891.0053102.03253.20.042.61180.00.02-0.090.160.851.0053302.04258.30.042.70180.00.02-0.200.190.851.0053502.06344.60.061.97180.00.02-1.030.310.821.0015102.12366.00.081.57228.00.021.690.570.961.0015302.10366.00.071.55242.90.010.640.470.951.0015502.09360.90.071.51180.00.01-0.560.420.931.0015702.12352.00.071.58180.00.01-0.590.480.931.0015902.15362.70.081.65180.00.01-0.270.570.961.00151102.15366.00.091.68180.00.010.850.500.911.00151302.12366.00.081.62180.00.011.190.410.881.00151502.10291.00.062.26180.00.01-0.340.390.931.00151702.16366.00.051.92180.00.010.420.290.961.00151902.17366.00.061.64194.90.021.180.390.971.00152102.14363.20.081.55246.20.011.330.580.971.00152302.11333.40.091.81180.00.02-1.560.590.941.00152502.13356.70.061.41180.00.01-2.440.410.951.00152702.16366.00.051.52218.70.010.800.300.981.00152902.14318.50.052.00180.00.02-0.910.390.971.00153102.11273.70.062.45180.00.01-1.040.450.961.00153302.12298.90.072.02180.00.01-1.510.520.971.00153502.13357.10.081.66213.60.022.610.650.981.0025102.20366.00.071.44199.60.031.460.360.931.0025302.18366.00.061.39193.10.041.150.400.941.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±5 %±10 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. 25502.18366.00.051.40190.70.041.120.420.971.0025702.20180.00.051.49366.00.051.460.500.991.0025902.24366.00.071.67187.00.051.070.500.961.00251102.21366.00.071.87191.20.051.180.530.961.00251302.18366.00.071.81188.90.041.310.490.941.00251502.17366.00.051.86182.80.021.110.420.971.00251702.22366.00.061.80184.70.031.110.400.961.00251902.24366.00.071.66194.90.051.130.490.971.00252102.22366.00.101.54191.70.031.300.680.971.00252302.21366.00.111.50201.90.011.890.710.971.00252502.23366.00.081.30187.50.031.790.560.961.00252702.25366.00.061.40191.70.031.310.390.961.00252902.22366.00.051.76192.10.021.180.250.961.00253102.19366.00.051.87200.50.012.190.340.991.00253302.20366.00.061.59199.10.012.350.430.981.00253502.22366.00.071.52206.60.021.850.410.931.0035102.23366.00.081.49196.80.021.820.390.861.0035302.22366.00.081.51195.40.031.620.410.891.0035502.22366.00.081.49198.20.021.200.330.881.0035702.23366.00.081.50191.70.030.940.390.901.0035902.24366.00.101.67191.20.030.810.520.871.00351102.21366.00.121.73199.10.030.730.580.901.00351302.20366.00.121.72199.60.020.730.610.931.00351502.20366.00.111.70194.50.020.700.620.941.00351702.23366.00.111.66202.40.020.690.610.921.00351902.24366.00.121.64199.60.031.030.620.921.00352102.23366.00.141.56193.10.031.280.730.941.00352302.23366.00.141.55197.30.021.420.750.951.00352502.24366.00.131.49201.40.021.580.700.941.00352702.25366.00.111.51194.90.011.640.590.931.00352902.23366.00.071.75200.10.011.460.370.921.00353102.21366.00.071.84180.00.023.130.420.921.00353302.23366.00.091.71180.00.02-2.810.470.911.00353502.24366.00.101.58185.10.023.090.460.851.0045102.20324.50.192.02180.00.05-1.610.840.911.0045302.20315.20.172.13180.00.04-1.480.810.891.0045502.20304.50.162.22180.00.04-1.470.800.891.0045702.20310.50.172.18180.00.04-1.270.830.921.0045902.21311.00.192.22180.00.04-1.130.850.901.00451102.20316.60.202.16180.00.04-1.190.860.921.00451302.19311.90.202.21180.00.04-1.270.860.921.00451502.19328.20.202.02180.00.04-1.290.880.941.00451702.19330.60.201.99180.00.04-1.390.890.951.00451902.19344.60.211.80180.00.04-1.550.890.951.00452102.19353.40.231.72180.00.04-1.400.910.951.00452302.18354.40.241.68180.00.04-1.460.900.961.00452502.20351.10.251.68180.00.04-1.550.900.930.99452702.20348.30.221.74180.00.04-1.600.880.941.00452902.19341.30.181.88180.00.04-1.530.840.941.00453102.18332.90.172.01180.00.04-1.790.830.941.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±5 %±10 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. 453302.19327.80.182.04180.00.04-1.670.840.931.00453502.21330.60.191.98180.00.05-1.590.840.911.0051102.20285.40.262.50180.00.06-1.410.810.780.9851302.20279.80.252.54180.00.05-1.550.830.780.9851502.21279.30.242.57180.00.05-1.660.820.800.9851702.21282.10.232.56180.00.05-1.430.830.820.9951902.22280.20.252.59180.00.05-1.380.840.790.99511102.21276.50.252.65180.00.05-1.330.810.780.98511302.20274.60.252.68180.00.05-1.450.820.780.98511502.20278.80.252.60180.00.05-1.450.840.810.98511702.20276.00.262.64180.00.05-1.550.820.780.98511902.19284.90.262.48180.00.06-1.600.850.780.98512102.18302.60.282.25180.00.07-1.510.880.830.99512302.17316.60.312.05180.00.08-1.570.900.830.99512502.18319.90.332.01180.00.08-1.580.880.800.98512702.17323.10.302.01180.00.08-1.570.900.840.99512902.18311.00.272.14180.00.07-1.730.880.860.98513102.18294.20.252.39180.00.06-1.770.840.820.96513302.17291.90.252.43180.00.05-1.630.850.790.99513502.19287.70.262.47180.00.06-1.580.840.780.98
Comparison of the approximation of the BV frequency (solid line) with the approximated values for two different bins. The dashed line refers to the ±10 % interval around the approximation.
Quality of approximation as shown in Table 1 versus latitude. All
longitudes are plotted but not separated by colour in order to keep the
figure clear.
Fraction of data within ±5 % and ±10 % intervals
around the approximation.
As mentioned above, tidal effects are not included in the approximation of
the OH∗-equivalent BV frequency. However, an uncertainty range of the
OH∗-equivalent BV frequency due to these effects is additional useful
information. In order to estimate it, SABER profiles which refer to the same
night (between 18:00 and 06:00 LT) and are separated by 6 h at minimum are
collected for all years (2002–2018) at each grid point. Since tides have periods
in the range of 6 h and more (the dominating ones have
periods of 12 and 24 h), we argue that the difference of the
OH∗-equivalent BV frequency within these hours during
one night is mainly due to tides. Of course, also gravity waves still play
a role in this period range. Since our gridding is relatively coarse for
gravity waves, we assume that gravity waves increase and decrease the
OH∗-equivalent BV frequency in one pixel so that
their effect cancels out over time. This is not true for
larger-scale phenomena. The mean difference per hour over all years is
calculated at each grid point. The results are averaged over latitude
afterwards (Table 2). The amount of data per latitude
measurement is on the order of magnitude of 10 000.
As mentioned above, tidal activity varies during the year.
Therefore, the provision of monthly values would make more sense. However,
especially at midlatitudes and high latitudes, SABER profiles which refer to the same
night separated by 6 h at least are not evenly distributed over the
year or not available every month. The uncertainty range provided in Table 2
can therefore be regarded as a rather rough estimate. With respect to an
OH∗-equivalent BV frequency of 0.02 s-1, the results
are in the range of approximately 1 %–2 %. For a night of 12 h, tidal effects sum up to approximately 21 % at
maximum (meaning for low latitudes). We can assume that the approximation
of the OH∗-equivalent BV frequency refers to midnight, so the tidal effects
can be approximated by ±11 % for the whole night in this case.
Shown are the mean difference per hour and its variance for the
OH∗-equivalent BV frequency measured during the same night
for the different latitudinal intervals (-45±5∘ until
+45±5∘, -51±1∘ and
+51±1∘).
As mentioned at the beginning, this is the succeeding paper to Wüst
et al. (2017a) where the authors proposed an approximation of the
OH∗-equivalent BV frequency for the Alpine region more
exactly for 43.93–48.09∘ N and 5.71–12.95∘ E based
on three oscillations. The question, which naturally arises now, is how the two
different approximations, the one of Wüst et al. (2017a) and one
proposed here, compare. The following differences exist in methods and data
basis: the pixel size of Wüst et al. (2017a) is approximately
5∘×7∘ and therefore less than 25 % of the pixel size
applied here. Wüst et al. (2017a) use three oscillations and SABER data
from 2002 to 2015; we use two oscillations and SABER data from 2002 to 2018.
Furthermore, instead of calculating the Gaussian-weighted BV frequency, the
OH∗-equivalent BV frequency is now weighted with the
volume emission rate of the OH-B channel of SABER. Then, the geographical position of the SABER
measurements at 86 km height is taken into account (in our preceding
publication, any part of the SABER profile needed to fit the geographical
selection criteria). Finally, the dry-adiabatic lapse rate is assumed to be
9.8 K km-1 in Wüst et al. (2017a); now, it is 9.5 K km-1
since the height dependence of g is taken into account here. As Fig. 8 shows,
the two approximations agree for the majority of the year within an uncertainty
of 5 %. This is in the range of the natural variability (see Table 1).
There is an offset visible, which is due to the height dependence of the
dry-adiabatic lapse rate. Furthermore, the data disagree especially where the
ter-annual oscillation used by Wüst et al. (2017a) has a maximum.
This oscillation is not used here since tests showed that it appears very
prominently at low latitudes in order to approximate at least in part the
oscillation of approximately 60 d. Even though temperature data at midlatitudes also
show a slight ter-annual course as discussed above, it is not clear until
which latitude the ter-annual oscillation might be real and from which
latitude on it might be artificial. Therefore, we propose to use the values
of Wüst et al. (2017a) for investigations which do not comprise a direct
comparison with results from stations not within 43.93–48.09∘ N
and 5.71–12.95∘ E. In any other case, the values of this
paper should be applied.
Comparison of the approximation of the BV frequency in the Alpine
region as it was proposed by Wüst et al. (2017a) based on three
oscillations (black) and in this paper (grey, values of the pixel at
45∘ N and 10∘ E are used).
Even though a climatology of the OH∗-layer height and its FWHM is not in the
focus of this paper, it might be of interest for some scientific
groups. Therefore, the harmonic analysis is applied to the time series of
daily mean values of the OH∗-layer height and of the FWHM in the same way as
it was used for the approximation of the BV frequency. The results are
listed in Tables A1 and A2.
Summary and outlook
We provide a climatology of the OH∗-equivalent
BV frequency based on 17 years of TIMED-SABER data for midlatitudes and low latitudes on a
10∘×20∘ grid. This is done in order to facilitate the
estimation of the density of gravity wave potential energy from airglow temperature
measurements independent of co-located measurements which deliver vertical
temperature profiles. This paper is the succeeding work of Wüst et al. (2017a),
who published a climatology for the Alpine region only.
Especially at low latitudes, a prominent 60 d oscillation is present in the
time series of daily OH∗-equivalent BV frequency averaged over
all years. This might be an artificial signal due to a combination of the yaw
cycle of SABER and strong tidal activity. Physical reasons for the annual and
semi-annual oscillations, which are also present in the data, are known. Therefore,
an analytical formulation for the approximation of the daily
OH∗-equivalent BV frequency based on the superposition of a
mean value and two further oscillations (in most cases a nearly annual and
a nearly semi-annual) is provided. It is estimated based on a harmonic analysis
approach, and the approximation is usually better than ±10 %. An
uncertainty range for tidal influences during one night is calculated,
which indicates that in the tropics sometimes uncertainties of up to
±11 % can occur. An improvement over our previous work is
that additional formulations for daily values of the OH∗-layer
height and thickness are also given.
Same as Table 1 but for the OH∗-layer height. Please
note that OH∗-layer height is less variable
during the year, and therefore the fraction of data around the approximation is
provided for intervals of ±1 % and ±2 %.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±1 %±2 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -511086.43340.41.30-1.51187.90.320.200.780.901.00-513086.43358.51.45-1.57208.90.38-0.770.790.930.99-515086.39361.31.43-1.58194.90.30-0.160.800.910.99-517086.20347.81.27-1.46187.90.240.590.670.880.98-519086.16355.71.34-1.45213.60.26-0.490.740.920.98-5111086.16362.31.52-1.51216.80.30-0.890.800.930.99-5113086.14366.01.69-1.51219.20.33-1.060.850.930.99-5115086.07354.81.47-1.41210.80.38-0.580.780.910.99-5117086.04355.31.43-1.47208.00.27-0.420.780.900.98-5119086.03351.11.41-1.40203.30.42-0.360.780.890.99-5121086.11355.31.44-1.47196.30.39-0.150.790.890.99-5123086.17350.61.44-1.57180.00.290.580.780.870.98-5125086.26350.61.48-1.55180.90.310.620.810.911.00-5127086.29338.01.29-1.40207.00.40-0.670.720.850.98-5129086.28334.31.37-1.44197.70.38-0.310.760.860.99-5131086.30348.31.40-1.59183.30.330.430.800.901.00-5133086.32343.21.34-1.56180.00.300.830.800.920.99-5135086.31295.11.15-1.08181.90.270.320.700.890.98-451086.37257.41.04-0.40180.00.460.090.730.901.00-453086.39274.21.09-0.64180.00.480.110.760.911.00-455086.38292.41.07-0.80180.00.510.320.770.911.00-457086.26261.10.98-0.35180.00.420.150.710.921.00-459086.23273.71.02-0.50180.00.370.280.760.951.00-4511086.28304.91.11-0.94180.50.460.380.820.961.00-4513086.34349.71.40-1.42186.50.450.220.860.951.00-4515086.19304.51.29-0.94180.00.510.420.790.880.99-4517086.06270.01.19-0.46180.00.490.220.780.901.00-4519086.11263.41.08-0.34180.00.590.080.720.861.00-4521086.20272.31.10-0.55180.00.550.140.730.891.00-4523086.24280.71.01-0.70180.00.440.270.730.911.00-4525086.25284.40.99-0.74180.00.410.330.720.931.00-4527086.32272.81.00-0.65180.00.420.120.690.881.00-4529086.21290.51.22-0.92180.00.450.300.750.871.00-4531086.20262.11.09-0.45180.00.460.200.710.871.00-4533086.26252.70.97-0.28180.00.420.250.690.901.00-4535086.30249.00.95-0.15180.00.440.200.700.921.00-351086.47240.10.82-0.98366.00.70-0.940.650.881.00-353086.52259.70.96-0.28180.00.72-0.040.700.881.00-355086.55254.10.95-0.13180.00.72-0.040.670.871.00-357086.51235.50.79-0.87366.00.63-0.940.630.871.00-359086.51240.60.72-0.85366.00.54-0.910.630.911.00-3511086.61254.60.85-0.23180.00.53-0.030.670.901.00-3513086.70321.31.04-1.15180.00.510.350.780.931.00-3515086.59271.81.15-0.48180.00.650.170.750.871.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±1 %±2 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -3517086.33248.51.050.01180.00.730.040.710.881.00-3519086.31235.50.860.18180.00.71-0.120.690.901.00-3521086.49243.90.85-0.04180.00.71-0.150.690.911.00-3523086.55262.10.78-0.35180.00.61-0.050.630.891.00-3525086.52255.10.72-0.17180.00.57-0.060.560.890.99-3527086.56270.90.73-0.49180.00.56-0.090.570.880.99-3529086.33328.21.12-1.20180.00.630.470.780.901.00-3531086.26256.01.09-0.25180.00.690.040.700.871.00-3533086.26216.40.89-0.27366.00.53-0.980.690.901.00-3535086.35222.90.79-0.43366.00.51-0.960.610.881.00-251086.57183.30.44-0.49366.00.38-1.700.370.891.00-253086.71366.00.58-1.55196.80.48-0.990.510.921.00-255086.74366.00.60-1.60196.30.52-0.990.460.861.00-257086.73261.10.44-0.78183.70.43-0.900.260.790.99-259086.69264.80.39-1.05186.10.30-1.020.230.830.99-2511086.69340.40.44-1.59198.70.32-1.190.280.850.99-2513086.86366.00.74-1.69201.40.33-1.180.440.851.00-2515086.84366.00.81-1.56187.90.40-0.320.510.830.99-2517086.62366.00.42-1.78180.00.410.050.360.871.00-2519086.45186.10.42-0.57366.00.09-2.310.290.941.00-2521086.69184.70.53-0.70366.00.19-1.660.400.921.00-2523086.84180.00.55-0.59366.00.39-1.600.440.891.00-2525086.81180.00.45-0.72366.00.32-1.810.340.901.00-2527086.77180.00.40-0.92366.00.34-2.020.300.881.00-2529086.62366.00.66-1.84195.90.41-1.320.460.871.00-2531086.52366.00.68-1.67197.30.48-1.170.480.861.00-2533086.49188.40.46-0.61366.00.38-1.470.320.841.00-2535086.48187.50.47-0.42366.00.35-1.500.380.891.00-151086.33187.50.88-1.79339.00.33-2.810.660.921.00-153086.40180.00.89-1.50338.00.29-2.470.630.931.00-155086.43180.00.81-1.50366.00.33-2.170.590.911.00-157086.35180.00.56-1.56366.00.35-2.020.370.841.00-159086.21180.00.53-1.45366.00.39-2.020.370.831.00-1511086.23180.00.51-1.59340.40.34-2.070.380.871.00-1513086.46366.00.73-1.73193.10.39-1.770.420.821.00-1515086.55366.00.77-1.62198.70.49-1.650.470.841.00-1517086.40184.20.42-1.65366.00.25-2.100.230.831.00-1519086.29195.90.67-2.15332.40.15-3.070.420.871.00-1521086.48190.70.78-1.86280.20.15-1.620.490.891.00-1523086.52180.00.79-1.42366.00.30-1.900.550.891.00-1525086.42180.50.95-1.66355.70.25-2.560.640.921.00-1527086.47180.00.87-1.79334.30.37-2.690.610.921.00-1529086.47180.00.75-1.70348.80.41-2.710.600.931.00-1531086.29180.00.81-1.72343.20.34-2.240.590.901.00-1533086.27180.00.69-1.59340.40.31-2.110.520.901.00-1535086.31180.90.66-1.58339.40.25-2.600.520.931.00-51085.59189.31.31-1.83351.60.48-3.090.780.891.00-53085.57184.71.42-1.69328.20.37-2.910.810.901.00-55085.46180.01.34-1.65311.50.35-2.450.780.911.00-57085.35180.01.15-1.65313.80.36-2.170.670.831.00-59085.32180.01.07-1.54317.50.33-1.930.640.851.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±1 %±2 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -511085.59180.01.08-1.58285.40.41-1.980.630.831.00-513085.94180.00.98-1.56309.10.46-1.500.600.841.00-515085.99180.00.82-1.42366.00.52-1.750.560.821.00-517086.06185.60.81-1.64333.40.34-2.260.510.861.00-519086.11184.20.72-1.80320.30.35-2.700.500.891.00-521086.00180.00.87-1.62314.70.29-1.800.550.881.00-523085.77180.01.17-1.53366.00.46-2.010.700.861.00-525085.55180.01.38-1.63366.00.29-1.990.810.931.00-527085.67180.01.18-1.62315.70.35-2.240.780.951.00-529085.73180.01.15-1.61340.40.48-2.630.790.951.00-531085.54180.01.17-1.68341.80.41-2.530.760.911.00-533085.49180.01.12-1.57360.40.41-2.510.760.931.00-535085.53181.91.21-1.61335.70.49-2.870.760.911.0051085.54201.41.37-2.19366.00.102.030.740.870.9953085.37204.21.46-2.21366.00.101.300.740.870.9955085.14198.71.47-1.98366.00.140.280.720.830.9857085.07194.51.38-1.84366.00.20-0.330.610.750.9659085.40194.51.25-1.79366.00.14-0.910.610.780.99511085.86196.31.14-1.82298.90.13-1.580.570.830.98513086.11194.00.98-1.70366.00.15-0.550.500.800.99515085.95187.51.04-1.62366.00.24-0.810.550.810.99517086.26183.70.94-1.35366.00.31-1.950.580.851.00519086.48180.50.67-1.43366.00.27-2.480.490.891.00521086.26181.90.83-1.62366.00.15-1.710.560.901.00523085.86182.81.21-1.71366.00.16-1.410.730.911.00525085.63181.41.37-1.68366.00.26-0.530.810.941.00527085.81180.01.18-1.59366.00.16-1.190.740.921.00529085.82186.11.17-1.74366.00.15-2.760.740.911.00531085.55189.31.21-1.93317.10.11-2.620.730.911.00533085.40184.71.21-1.65366.00.08-1.900.740.901.00535085.44192.61.29-1.96312.90.08-2.490.760.921.00151086.42203.80.78-2.24366.00.150.760.550.911.00153086.36203.30.79-2.03366.00.180.600.510.871.00155086.13200.50.89-1.81366.00.310.210.500.820.99157086.06194.00.77-1.57366.00.34-0.150.470.850.99159086.37184.70.77-1.26366.00.20-0.440.520.891.001511086.66180.00.67-0.77286.80.151.320.390.861.001513086.67184.20.51-0.80330.60.151.000.280.881.001515086.45180.00.67-1.21366.00.28-0.710.540.921.001517086.64180.00.76-1.17366.00.39-1.520.620.941.001519086.91180.00.56-1.14366.00.31-1.740.460.911.001521086.86180.00.58-0.99267.20.190.990.400.921.001523086.55186.50.79-1.55314.30.191.100.600.931.001525086.41185.60.90-1.69366.00.280.270.680.941.001527086.53180.00.72-1.45361.30.24-0.450.610.951.001529086.53180.00.82-1.16249.90.130.980.580.951.001531086.32181.40.75-1.24257.90.061.020.520.931.001533086.16184.70.82-1.50366.00.16-0.660.560.911.001535086.34192.10.78-1.82332.40.120.550.620.951.00251086.83180.00.45-0.36366.00.301.260.310.861.00253086.79180.00.51-0.20326.40.201.080.290.861.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±1 %±2 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. 255086.70180.00.48-0.19358.10.170.700.290.891.00257086.60180.00.43-0.28366.00.23-0.040.350.951.00259086.75180.00.52-0.23336.60.160.130.350.911.002511086.84180.00.67-0.09259.70.260.400.390.891.002513086.81180.00.52-0.02283.00.28-0.280.350.891.002515086.63366.00.48-1.27180.00.44-0.510.490.921.002517086.71180.00.56-0.59356.70.39-1.210.520.941.002519086.96180.00.61-0.49298.40.22-0.460.420.911.002521087.04180.00.57-0.31297.90.101.100.400.931.002523086.95180.00.60-0.58355.70.351.170.560.951.002525086.83189.30.56-1.05366.00.370.600.540.951.002527086.79180.00.52-0.35366.00.180.120.420.931.002529086.76180.00.63-0.25339.00.13-0.940.440.911.002531086.71180.00.52-0.18358.50.20-1.490.430.961.002533086.68180.00.46-0.43366.00.14-0.940.350.941.002535086.77180.00.51-0.57352.00.251.250.340.891.00351086.58180.00.680.57366.00.631.320.650.931.00353086.56180.00.720.69366.00.481.290.630.941.00355086.54180.00.660.62366.00.401.230.550.931.00357086.44180.00.630.58366.00.310.980.500.921.00359086.49180.00.730.57366.00.291.170.550.911.003511086.52180.00.770.63366.00.131.160.550.911.003513086.57180.00.710.59291.40.220.390.500.941.003515086.50180.00.590.47317.10.27-0.180.410.931.003517086.58180.00.620.37312.90.230.370.410.921.003519086.72180.00.560.39335.70.211.140.370.901.003521086.83180.00.600.38366.00.391.140.500.921.003523086.82180.00.600.27366.00.511.170.580.951.003525086.72366.00.551.04180.00.560.140.620.941.003527086.63180.00.580.23366.00.400.890.510.941.003529086.52180.00.720.49366.00.210.390.540.921.003531086.45180.00.730.55366.00.250.670.600.941.003533086.53180.00.640.54366.00.371.030.590.951.003535086.64180.00.620.46366.00.591.310.620.931.00451086.34366.00.971.35180.00.720.800.780.941.00453086.36366.00.861.33180.90.720.770.780.961.00455086.37366.00.791.34182.30.660.820.740.961.00457086.35180.00.670.91365.10.651.350.740.961.00459086.35180.00.690.79366.00.651.400.720.961.004511086.30180.00.710.86364.10.611.440.670.941.004513086.29180.00.590.89361.30.551.270.630.961.004515086.25366.00.551.21180.00.531.000.570.931.004517086.24366.00.651.31180.00.590.970.650.911.004519086.27366.00.881.37180.00.670.990.730.901.004521086.33366.01.081.39180.50.710.880.780.921.004523086.35366.01.121.38181.90.720.820.800.921.004525086.31366.00.961.30180.50.690.810.800.941.004527086.27366.00.731.21180.00.700.890.740.961.004529086.24180.00.740.85358.10.581.150.700.951.004531086.14180.00.690.88354.40.651.210.660.951.004533086.24366.00.831.23180.00.630.780.750.951.00
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±1 %±2 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. 4535086.35366.00.901.32180.00.690.730.800.961.00511086.38366.01.201.34180.00.480.980.760.911.00513086.40366.01.111.33180.00.460.960.730.891.00515086.44366.01.001.34182.80.440.990.720.911.00517086.43366.00.881.34181.40.451.080.690.930.99519086.41366.00.921.40180.00.400.980.690.920.995111086.28366.00.911.35180.00.421.060.680.931.005113086.18366.00.961.40180.00.361.250.680.891.005115086.10366.01.081.39180.00.351.270.700.890.995117086.04366.01.311.43180.00.361.320.750.880.995119086.02366.01.531.39180.00.461.340.800.850.995121085.97366.01.741.43180.00.501.270.830.881.005123085.99366.01.701.42180.00.551.110.840.871.005125086.04366.01.451.43180.00.531.250.810.890.995127086.08366.01.211.38180.00.541.300.730.880.995129086.15366.01.101.26180.00.471.330.700.890.995131086.09366.01.151.26180.00.361.160.700.890.995133086.16366.01.181.28180.00.351.030.740.890.995135086.27366.01.151.32180.00.450.830.740.901.00
Same as Table 1 but for the FWHM. Please note
that FWHM is more variable during the year, and therefore the fraction of
data around the approximation is provided for intervals of ±7.5 %
and ±15 %.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±1 %±2 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -51107.50366.00.741.78191.70.601.220.510.680.97-51307.48366.00.821.63191.70.601.230.600.710.96-51507.54366.00.681.58189.30.471.370.480.700.94-51707.57366.00.671.61194.00.381.200.320.680.96-51907.53366.00.671.69194.50.361.250.360.630.95-511107.51366.00.791.67193.50.481.230.550.690.96-511307.58366.00.771.69194.00.451.130.490.660.95-511507.65366.00.721.60193.50.461.160.460.670.94-511707.69366.00.751.61191.70.511.150.530.680.98-511907.66366.00.781.58191.20.601.230.580.720.97-512107.68366.00.851.63190.70.611.080.620.730.97-512307.76366.00.801.68189.30.481.220.650.800.98-512507.71366.00.941.73189.80.491.370.660.760.96-512707.70366.00.971.73188.90.531.190.640.670.95-512907.75366.00.951.70188.40.531.030.660.710.96-513107.66366.00.871.67193.50.590.730.650.770.96-513307.59366.00.761.72188.90.510.960.610.760.98-513507.57366.00.681.93189.30.401.260.460.690.94-45107.55366.00.431.69190.70.330.840.280.640.95-45307.57366.00.511.55193.50.331.050.360.720.98-45507.57366.00.501.52199.60.291.090.320.740.98-45707.66366.00.451.54199.10.240.800.250.680.96-45907.61366.00.511.75200.50.180.680.290.710.96-451107.58366.00.621.76203.30.240.920.390.750.98-451307.55366.00.631.75199.60.280.930.450.750.98-451507.72366.00.471.85204.20.161.100.290.730.99-451707.76366.00.441.77201.90.160.820.270.800.97-451907.67366.00.551.84196.80.240.880.400.800.98-452107.69366.00.611.74196.30.300.880.470.790.99-452307.71366.00.521.79198.70.220.670.370.800.98-452507.66366.00.581.92199.10.220.640.380.740.97-452707.66366.00.551.86192.10.370.770.390.700.96-452907.76366.00.621.82180.00.320.820.510.760.99-453107.76366.00.461.69187.50.340.860.420.790.98-453307.65366.00.451.69188.90.360.600.400.770.99-453507.58366.00.411.79193.50.260.700.260.720.96-35107.39366.00.252.07180.00.21-0.380.100.600.90-35307.41366.00.281.90180.00.21-0.940.130.630.92-35507.43366.00.272.05180.00.26-1.330.150.690.90-35707.47180.00.24-1.09366.00.201.970.100.680.91-35907.48366.00.211.84180.00.15-0.670.070.620.92-351107.40366.00.311.72180.00.12-0.760.130.660.93-351307.33366.00.321.83180.00.16-0.170.160.690.94-351507.42331.00.272.54180.00.17-1.310.140.690.95-351707.54180.00.25-1.01366.00.212.790.150.740.94-351907.44366.00.372.33180.00.17-1.050.240.760.96-352107.30366.00.422.13180.00.03-0.630.290.780.97-352307.36351.10.182.24180.00.10-1.130.080.760.97-352507.38322.20.19-2.90180.00.15-0.710.090.730.95
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±7.5 %±15 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -352707.49180.00.290.30366.00.243.060.160.660.93-352907.69359.90.432.11180.00.270.060.330.740.96-353107.73366.00.321.85180.00.17-0.310.180.720.95-353307.67180.00.29-0.60366.00.151.960.120.690.93-353507.45180.00.26-0.23366.00.151.370.080.600.89-25107.48180.00.150.02366.00.112.180.050.680.96-25307.53366.00.242.21180.00.11-1.540.110.710.96-25507.48366.00.192.41180.00.13-1.550.070.670.97-25707.49180.00.18-1.13366.00.152.380.070.660.94-25907.59366.00.151.61180.00.10-1.370.040.650.95-251107.50363.70.251.43239.70.100.960.090.690.96-251307.34365.50.351.49180.00.12-1.490.170.610.95-251507.46180.00.16-1.25366.00.141.700.050.650.93-251707.55180.00.17-0.51366.00.13-2.770.070.710.96-251907.47366.00.222.75180.00.110.180.120.780.98-252107.20366.00.262.27180.00.090.730.180.810.98-252307.17238.70.12-1.71180.00.070.880.050.720.97-252507.33263.90.21-0.48180.00.20-0.300.130.720.96-252707.51219.60.270.05366.00.12-3.000.140.680.96-252907.69359.90.212.87180.00.170.580.130.750.98-253107.68366.00.302.34236.40.090.810.120.750.98-253307.59180.00.25-0.52225.20.191.560.040.690.95-253507.47180.00.37-0.14244.80.271.190.100.670.95-15107.73180.00.191.94365.50.181.340.180.851.00-15307.75366.00.211.69186.50.201.850.180.840.99-15507.74180.00.132.50346.90.122.160.070.790.99-15707.75366.00.131.82180.00.132.540.070.750.98-15907.94180.00.201.99366.00.141.560.110.760.98-151107.88180.00.232.16361.30.211.430.190.800.98-151307.79366.00.381.33197.30.261.960.280.751.00-151507.84292.40.261.13180.00.132.850.160.780.98-151708.02334.80.180.36180.00.052.750.080.791.00-151907.92366.00.191.63198.70.172.120.150.840.99-152107.65366.00.381.63204.70.201.700.310.831.00-152307.62366.00.181.13184.70.141.270.120.830.99-152507.75305.90.14-0.82180.00.031.340.070.831.00-152707.77366.00.17-2.64186.50.152.690.140.861.00-152907.85366.00.222.42180.90.162.680.180.841.00-153107.81181.90.252.88366.00.221.780.250.830.99-153307.72274.20.211.78180.90.112.450.180.901.00-153507.71356.70.230.67180.00.161.920.180.841.00-5107.73280.20.111.90180.00.11-2.840.060.720.99-5307.74180.00.14-2.86254.60.09-2.600.040.780.98-5507.73366.00.10-1.62180.00.06-3.000.020.730.98-5707.72303.10.26-1.50180.00.172.630.160.780.98-5907.82283.50.37-1.40180.00.192.410.230.750.97-51107.81238.70.40-0.49180.00.252.870.240.750.97-51307.91211.70.390.94366.00.19-2.810.280.770.99-51508.05228.00.430.19180.00.32-2.900.320.790.98-51708.09249.50.280.26180.00.26-2.590.230.791.00-51908.13180.00.353.14366.00.080.760.210.810.99
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±7.5 %±15 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. -52108.09200.10.392.56366.00.241.080.290.740.98-52308.03180.00.37-3.07366.00.190.720.240.750.99-52507.90180.00.46-2.68366.00.19-1.230.320.770.97-52707.70180.00.46-2.77366.00.13-1.640.320.770.98-52907.70180.00.34-2.76304.00.14-2.010.180.740.98-53107.70184.70.29-2.80289.60.042.710.170.800.98-53307.73180.00.23-2.48366.00.150.770.130.750.99-53507.74276.50.141.44180.00.13-2.760.080.720.985107.85366.00.30-0.94180.00.28-2.580.220.750.985307.85180.00.25-2.60366.00.24-1.220.180.720.975507.77366.00.35-1.38180.00.16-3.020.180.690.965707.74325.40.49-1.36180.00.162.540.290.680.955907.77329.60.60-1.38180.00.232.530.410.670.9751107.86332.40.68-1.57180.00.242.570.520.770.9951308.00338.50.58-1.76180.00.242.550.540.851.0051508.02333.80.60-1.60180.00.342.820.520.810.9951707.89364.10.51-1.63180.00.28-2.910.480.831.0051907.99348.80.46-1.70180.00.192.880.390.831.0052108.19245.30.34-0.21180.00.30-2.900.300.851.0052308.12180.00.33-3.10366.00.27-1.370.270.800.9952507.93180.00.42-2.81366.00.27-1.320.350.780.9852707.79180.00.44-2.89366.00.29-1.520.380.780.9952907.77366.00.39-1.64180.00.34-3.040.390.780.9953107.70366.00.20-1.84180.00.20-2.760.150.790.9853307.74180.00.23-2.73366.00.12-1.030.110.720.9853507.77366.00.23-1.08180.00.20-2.660.160.740.9815107.86351.10.36-1.36180.00.081.700.240.790.9815307.94359.00.43-1.45184.70.123.010.330.770.9915507.90352.00.43-1.47180.50.182.860.380.841.0015707.82353.00.52-1.57180.00.112.270.410.801.0015907.78354.40.50-1.41180.00.183.050.400.790.99151107.89366.00.55-1.55180.00.17-2.910.360.720.98151307.96363.70.50-1.65180.50.153.060.280.710.96151507.87331.00.37-1.50180.00.082.310.300.850.99151707.54366.00.37-1.41180.00.05-2.520.260.810.99151907.60366.00.55-1.51221.50.07-1.570.400.760.98152107.83350.60.60-1.57180.00.131.770.450.760.99152307.85348.30.47-1.43180.00.131.870.380.820.99152507.78366.00.19-2.21205.60.07-2.860.080.800.99152707.74180.00.092.90366.00.04-1.950.020.770.98152907.78282.10.29-0.62180.00.152.880.240.830.99153107.87331.50.41-1.38180.00.142.020.390.881.0053307.78310.50.41-1.22180.00.131.530.400.861.00153507.77344.60.43-1.33180.00.131.200.390.850.9925107.54366.00.15-1.79206.10.07-1.430.030.620.9125307.57366.00.23-1.81189.30.12-2.240.070.680.9225507.55366.00.24-1.92198.70.11-2.290.080.660.9525707.46180.00.19-1.81366.00.14-2.080.090.710.9525907.44366.00.21-1.00180.00.21-2.020.110.670.93251107.57366.00.30-0.82185.10.24-1.890.180.700.93251307.64366.00.36-1.08187.90.12-1.610.190.750.96251507.48366.00.26-0.80198.20.10-1.660.140.790.99
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±7.5 %±15 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. 251707.21366.00.37-0.95206.10.21-1.630.180.660.95251907.20366.00.49-1.19199.10.24-1.440.320.710.96252107.35366.00.55-1.45199.10.12-1.240.370.690.99252307.39366.00.49-1.53192.10.12-0.960.320.700.96252507.36180.00.21-0.88366.00.20-2.230.110.670.94252707.36202.40.20-1.60365.50.04-2.000.050.630.93252907.50366.00.14-0.72208.40.09-1.220.030.670.95253107.56240.60.19-0.71366.00.17-0.680.120.740.98253307.49243.40.29-0.21180.00.110.700.160.650.96253507.44276.00.20-0.72180.00.110.750.080.630.9235107.37366.00.19-1.41204.70.17-1.160.060.610.9335307.38366.00.24-1.46200.50.18-1.210.090.670.9235507.33366.00.19-1.41204.20.12-1.540.050.620.9135707.28366.00.22-1.26197.70.20-1.700.080.640.9235907.28366.00.32-0.96191.70.25-1.670.150.610.92351107.40366.00.48-0.93187.00.22-1.300.300.720.95351307.47366.00.48-0.88180.00.21-0.580.350.750.96351507.39366.00.46-0.83192.60.17-1.220.300.730.96351707.22366.00.45-0.92201.90.19-1.560.260.670.96351907.19366.00.58-1.10201.00.22-1.440.340.680.96352107.24366.00.65-1.27195.40.23-1.500.440.710.97352307.25366.00.66-1.30198.20.24-1.530.430.700.96352507.26366.00.48-1.43199.60.28-1.630.270.650.95352707.30181.90.24-1.08366.00.18-1.170.130.710.95352907.45180.00.20-0.58355.70.14-0.430.090.720.96353107.42366.00.27-1.05180.00.200.070.170.730.96353307.30366.00.32-1.20180.00.180.590.170.650.94353507.25366.00.29-1.30198.20.16-0.460.110.570.9245107.47337.10.61-1.08180.00.291.170.480.780.9745307.44339.90.53-1.10180.00.301.110.420.720.9745507.42260.20.43-0.82366.00.31-0.730.380.700.9745707.38320.30.52-0.82180.00.251.240.390.740.9645907.35314.30.60-0.69180.00.261.240.430.740.94451107.46311.50.60-0.63180.00.241.050.450.740.98451307.50294.70.56-0.35180.00.250.860.450.780.97451507.51334.30.63-0.83180.00.281.060.530.800.98451707.43322.20.59-0.77180.00.311.140.520.780.97451907.41346.00.73-1.11180.00.321.090.590.790.98452107.43362.70.83-1.29180.00.271.230.620.730.99452307.49366.00.96-1.39180.00.231.030.630.720.98452507.53366.00.93-1.48180.00.190.780.580.690.96452707.67366.00.67-1.31206.60.21-1.300.440.720.98452907.66366.00.54-1.26188.40.20-0.330.390.750.99453107.59366.00.62-1.27180.00.240.700.450.730.98453307.52359.00.70-1.22180.00.331.100.530.730.99453507.44349.20.67-1.20180.00.301.320.480.680.9751107.40262.50.93-0.16180.00.310.820.580.640.9551307.38249.50.73-0.39366.00.37-0.880.570.660.9351507.36253.20.59-0.40366.00.34-0.630.470.690.9251707.27248.50.730.16180.00.280.730.490.540.8051907.25245.30.59-0.06366.00.27-0.690.410.640.93
Continued.
Lat.Long.MeanFirst oscillation Second oscillation Quality ofFraction (∘)(∘)(10-2 s-1)approximationof data PeriodAmp.PhasePeriodAmp.Phase±7.5 %±15 %(d)(10-2 s-1)(rad)(d)(10-2 s-1)(rad)around approx. 511107.31232.20.570.26366.00.20-0.800.410.710.94511307.32230.80.650.30366.00.21-0.810.470.680.95511507.34230.80.620.26366.00.22-0.710.460.700.95511707.31227.60.710.29366.00.25-0.850.550.710.95511907.32234.50.760.03366.00.32-0.930.570.670.94512107.41259.30.88-0.11180.00.291.100.580.630.94512307.54290.51.00-0.64180.00.371.210.670.630.95512507.63327.31.07-1.16180.00.371.270.680.690.95512707.65347.81.05-1.36180.00.420.860.660.690.95512907.69347.40.91-1.28180.00.380.930.610.730.95513107.61329.60.95-1.00180.00.451.030.660.700.96513307.60317.50.86-0.82180.00.431.120.600.640.95513507.44266.70.97-0.24180.00.350.860.610.620.94Data availability
The data are accessible via the SABER homepage (http://saber.gats-inc.com/coin.php, SABER team, 2019).
Author contributions
MGM and JMR were responsible for the TIMED-SABER data.
JHY provided selected algorithms for the analysis of SABER data. SW formulated
the research goals, analysed the data, wrote the paper and discussed it especially with MB and MGM.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The work of Sabine Wüst was funded by the Bavarian State Ministry for
the Environment and Consumer Protection.
We thank Oleg Goussev (DLR) and Verena Wendt for their assistance in SABER
data preparation.
We thank the anonymous reviewers for the valuable comments.
Financial support
This research has been supported
by the Bavarian State Ministry for the Environment
and Consumer Protection (VoCaS-ALP (grant no. TKP01KPB-70581)
and AlpEnDAC II (TUS01UFS-72184)). The
article processing charges for this open-access publication
were covered by a Research Centre of the Helmholtz
Association.
Review statement
This paper was edited by Martin Riese and reviewed by two anonymous referees.
References
Adler-Golden, S.: Kinetic parameters for OH nightglow modeling consistent
with recent laboratory measurements, J. Geophys. Res., 102, 19969–19976,
1997.
Andrews, D. G.: An introduction to atmospheric physics, Cambridge University
Press, Cambridge, UK, 2000.
Baker, D. J. and Stair Jr., A. T.: Rocket measurements of the altitude
distributions of the hydroxyl airglow, Phys. Scripta, 37, 611–622, 1988.
Bittner, M., Offermann, D., and Graef, H.-H.: Mesopause temperature variability
above a midlatitude station in Europe, J. Geophys. Res., 105, 2045–2058,
2000.
Bittner, M., Offermann, D., Graef, H.-H., Donner, M., and Hamilton, K.: An
18-year time series of OH rotational temperatures and middle atmosphere
decadal variations, J. Atmos. Sol.-Terr. Phy., 64, 1147–1166, 2002.Dawkins, E. C. M., Feofilov, A., Rezac, L., Kutepov, A. A., Janches, D.,
Höffner, J., Chu. X., Lu, X., Mlynczak, M. G., and Russell III, J.:
Validation of SABER v2.0 operational temperature data with ground-based
lidars in the mesosphere-lower thermosphere region (75–105 km), J. Geophys.
Res.-Atmos., 123, 9916–9934, 10.1029/2018JD028742, 2018.Hannawald, P., Schmidt, C., Sedlak, R., Wüst, S., and Bittner, M.: Seasonal and intra-diurnal variability of small-scale gravity waves in OH airglow at two Alpine stations, Atmos. Meas. Tech., 12, 457–469, 10.5194/amt-12-457-2019, 2016.Hannawald, P., Schmidt, C., Sedlak, R., Wüst, S., and Bittner, M.: Seasonal and intra-diurnal variability of small-scale gravity waves in OH airglow at two Alpine stations, Atmos. Meas. Tech., 12, 457–469, 10.5194/amt-12-457-2019, 2019.Höppner, K. and Bittner, M.: Evidence for solar signals in the
mesopause temperature variability?, J. Atmos. Sol.-Terr. Phy., 69,
431–448, 10.1016/j.jastp.2006.10.007, 2007.Forbes, J. M., Zhang, X., Palo, S., Russell, J., Mertens, C. J., and
Mlynczak, M.: Tidal variability in the ionospheric dynamo region, J.
Geophys. Res., 113, A02310, 10.1029/2007JA012737, 2008.Kramer, R., Wüst, S., Schmidt, C., and Bittner, M.: Gravity wave
characteristics in the middle atmosphere during the CESAR campaign at Palma
de Mallorca in 2011/2012: Impact of extratropical cyclones and cold fronts,
J. Atmos. Sol.-Terr. Phy., 128, 8–23, 10.1016/j.jastp.2015.03.001,
2015.
Garcia, F. J., Taylor, M. J., and Kelley, M. C.: Two-dimensional spectral
analysis of mesospheric airglow image data, Appl. Optics, 36, 7374–7358,
1997.Garcia, R. R. and Solomon, S.: The effect of breaking gravity waves on the
dynamics and chemical composition of the mesosphere and lower thermosphere,
J. Geophys. Res., 90, 3850–3868, 10.1029/JD090iD02p03850, 1985.García-Comas, M., López-Puertas, M., Marshall, B. T.,
Wintersteiner, P. P., Funke, B., Bermejo-Pantaleón, D., Mertens, J.,
Remsberg, E. E., Gordley, L. L., Mlynczak, M. G., and Russell III, J. M.: Errors in Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) kinetic temperature caused by non-local-thermodynamic-equilibrium model parameters, J. Geophys. Res., 113, D24106, 10.1029/2008JD010105,
2008.Liu, G. and Shepherd, G. G.: An empirical model for the altitude of the OH
nightglow emission, Geophys. Res. Lett., 33, L09805, 10.1029/2005GL025297, 2006.López-Puertas, M., Garcia-Comas, M., Funke, B., Picard, R. H., Winick,
J. R., Wintersteiner, P. P., Mlynczak, M. G., Mertens, C. J., Russell III,
J. M., and Gordley, L. L.: Evidence for an OH (υ) excitation mechanism of
CO2 4.3 µm nighttime emission from SABER/TIMED measurements, J. Geophys. Res., 109, D09307, 10.1029/2003JD004383, 2004.Mertens, C. J., Schmidlin, F. J., Goldberg, R. A., Remsberg, E. E., Pesnell,
W. D., Russell III, J. M., Mlynczak, M. G., López-Puertas, M.,
Wintersteiner, P. P., Picard, R. H., Winick, J. R., and Gordley, L. L.:
SABER observations of mesospheric temperatures and comparisons with falling
sphere measurements taken during the 2002 summer MaCWAVE campaign, Geophys.
Res. Lett., 31, L03105, 10.1029/2003GL018605, 2004.
Mertens, C. J., Fernandez, J. R., Xu, X., Evans, D. S., Mlynczak, M. G., and
Russell III, J. M.: A new source of auroral infrared emission observed by
TIMED/SABER, Geophys. Res. Lett., 35, 17–20, 2008.Mlynczak, M. G.: Energetics of the mesosphere and lower thermosphere and the
SABER experiment, Adv. Space Res., 20, 1177–1183, 10.1016/S0273-1177(97)00769-2, 1997.Mulligan, F. J., Dyrland, M. E., Sigernes, F., and Deehr, C. S.: Inferring hydroxyl layer peak heights from ground-based measurements of OH(6-2) band integrated emission rate at Longyearbyen (78∘ N, 16∘ E), Ann. Geophys., 27, 4197–4205, 10.5194/angeo-27-4197-2009, 2009.Mukhtarov, P., Pancheva, D., and Andonov, B.: Global structure and seasonal
and interannual variability of the migrating diurnal tide seen in the
SABER/TIMED temperatures between 20 and 120 km, J. Geophys. Res., 114,
A02309, 10.1029/2008JA013759, 2009.Mzé, N., Hauchecorne, A., Keckhut, P., and Thétis, M.: Vertical
distribution of gravity wave potential energy from long-term Rayleigh lidar
data at a northern middle latitude site, J. Geophys. Res., 119,
12069–12083, 10.1002/2014JD022035, 2014.Offermann, D., Goussev, O., Donner, M., Forbes, J. M., Hagan, M., Mlynczak,
M. G., Oberheide, J., Preusse, P., Schmidt, H., and Russell III, J. M.:
Relative intensities of middle atmosphere waves, J. Geophys. Res., 114,
D06110, 10.1029/2008JD010662, 2009.Pancheva, D., Mukhtarov, P., and Andonov, B.: Global structure, seasonal and interannual variability of the migrating semidiurnal tide seen in the SABER/TIMED temperatures (2002–2007), Ann. Geophys., 27, 687–703, 10.5194/angeo-27-687-2009, 2009.
Pancheva, D., Mukhtarov, P., and Andonov, B.: Global structure, seasonal and
interannual variability of the eastward propagating tides seen in the
SABER/TIMED temperatures (2002–2007), Adv. Space Res., 46, 257–274, 2010a.Pancheva, D., Mukhtarov, P., Andonov, B., and Forbes, J. M.: Global
distribution and climatological features of the 5–6-day planetary waves
seen in the SABER/TIMED temperatures (2002–2007), J. Atmos. Sol.-Terr.
Phy., 72, 26–37, 10.1016/j.jastp.2009.10.005, 2010b.
Pautet, P.-D., Taylor, M., Pendleton, W., Zhao, Y., Yuan, T., Esplin, R.,
and McLain, D.: Advanced mesospheric temperature mapper for high-latitude
airglow studies, Appl. Optics, 53, 5934–5943, 2014.Rauthe, M., Gerding, M., and Lübken, F.-J.: Seasonal changes in gravity wave activity measured by lidars at mid-latitudes, Atmos. Chem. Phys., 8, 6775–6787, 10.5194/acp-8-6775-2008, 2008.Remsberg, E. E., Marshall, B. T., Garcia-Comas, M., Krueger, D.,
Lingenfelser, G. S., Martin-Torres, J., Mlynczak, M. G., Russell III, J. M.,
Smith, A. K., Zhao, Y., Brown, C., Gordley, L. L., Lopez-Gonzalez, M. J.,
Lopez-Puertas, M., She, C.-Y., Taylor, M. J., and Thompson, R. E.:
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, 10.1029/2008JD010013, 2008.Rüfenacht, R., Hocke, K., and Kämpfer, N.: First continuous ground-based observations of long period oscillations in the vertically resolved wind field of the stratosphere and mesosphere, Atmos. Chem. Phys., 16, 4915–4925, 10.5194/acp-16-4915-2016, 2016.Russell III, J. M., Mlynczak, M. G., Gordley, L. L., Tansock Jr., J. J., and
Esplin, R. W.: Overview of the SABER experiment and preliminary calibration
results, in: Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III, Denver, CO, United States, 19–21 July 1999, Proc. SPIE, 3756, 277–288, 10.1117/12.366382, 1999.SABER team: SABER data Version 2.0, available at: http://saber.gats-inc.com/coin.php, last access: 6 December 2019.Schmidt, C., Dunker, T., Lichtenstern, S., Scheer, J., Wüst, S., Hoppe,
U. P., and Bittner, M.: Derivation of vertical wavelengths of gravity waves in the MLT-region from multispectral airglow observations. J. Atmos. Sol.-Terr. Phy., 173, 119–127, 10.1016/j.jastp.2018.03.002, 2018.Sedlak, R., Hannawald, P., Schmidt, C., Wüst, S., and Bittner, M.: High-resolution observations of small-scale gravity waves and turbulence features in the OH airglow layer, Atmos. Meas. Tech., 9, 5955–5963, 10.5194/amt-9-5955-2016, 2016.Silber, I., Price, C., and Rodger, C. J.: Semi-annual oscillation (SAO) of the nighttime ionospheric D region as detected through ground-based VLF receivers, Atmos. Chem. Phys., 16, 3279–3288, 10.5194/acp-16-3279-2016, 2016.Silber I., Price, C., Schmidt, C., Wüst, S., Bittner, M., Pecora E.:
First ground-based observations of mesopause temperatures above the
Eastern-Mediterranean Part I: Multi-day oscillations and tides. J. Atmos.
Sol.-Terr. Phys., 155, 95–103, 10.1016/j.jastp.2016.08.014, 2017.Shepherd, G. G., Cho, Y.-M., Liu, G., Shepherd, M. G., and Roble, R. G.:
Airglow variability in the context of the global mesospheric circulation, J.
Atmos. Sol.-Terr. Phy., 68, 2000–2011, 10.1016/j.jastp.2006.06.006,
2006.Vincent, R. A., Tsuda, T., and Kato, S.: Asymmetries in mesospheric tidal
structure. J. Atmos. Terr. Phys., 51, 609–616, 10.1016/0021-9169(89)90058-5, 1989.von Savigny, C.: Variability of OH(3–1) emission altitude from 2003 to 2011:
Long-term stability and universality of the emission rate-altitude
relationship, J. Atmos. Sol.-Terr. Phy., 127, 120–128, 10.1016/j.jastp.2015.02.001, 2015.von Savigny, C., McDade, I. C., Eichmann, K.-U., and Burrows, J. P.: On the dependence of the OH∗ Meinel emission altitude on vibrational level: SCIAMACHY observations and model simulations, Atmos. Chem. Phys., 12, 8813–8828, 10.5194/acp-12-8813-2012, 2012.Wachter, P., Schmidt, C., Wüst, S., and Bittner, M.: Spatial gravity
wave characteristics obtained from multiple OH(3–1) airglow temperature time
series, J. Atmos. Sol.-Terr. Phys., 135, 192–201, 10.1016/j.jastp.2015.11.008, 2015Wendt, V., Wüst, S., Mlynczak, M. G., Russell III, J. M., Yee, J.-H.,
and Bittner, M.: Impact of atmospheric variability on validation of
satellite-based temperature measurements, J. Atmos. Sol.-Terr. Phy., 102,
252–260, 10.1016/j.jastp.2013.05.022, 2013.Wüst, S. and Bittner, M.: Non-linear resonant wave–wave interaction
(triad): Case studies based on rocket data and first application to
satellite data, J. Atmos. Sol.-Terr. Phy., 68, 959–976, 10.1016/j.jastp.2005.11.011, 2006.Wüst, S., Wendt, V., Schmidt, C., Lichtenstern, S., Bittner, M., Yee,
J.-H., Mlynczak, M. G., and Russell III, J. M.: Derivation of gravity wave
potential energy density from NDMC measurements, J. Atmos. Sol.-Terr. Phys.,
138, 32–46, 10.1016/j.jastp.2015.12.003, 2016.Wüst, S., Bittner, M., Yee, J.-H., Mlynczak, M. G., and Russell III, J. M.: Variability of the Brunt–Väisälä frequency at the OH∗ layer height, Atmos. Meas. Tech., 10, 4895–4903, 10.5194/amt-10-4895-2017, 2017a.Wüst, S., Schmidt, C., Bittner, M., Price, C., Silber, I., Yee, J.-H.,
Mlynczak, M. G., and Russell III, J. M.: First ground-based observations of
mesopause temperatures above the Eastern-Mediterranean Part II:
OH∗-climatology and gravity wave activity, J. Atmos. Sol.-Terr. Phy., 155, 104–111, 10.1016/j.jastp.2017.01.003, 2017b.
Wüst, S., Offenwanger, T., Schmidt, C., Bittner, M., Jacobi, C., Stober, G., Yee, J.-H., Mlynczak, M. G., and Russell III, J. M.: Derivation of gravity wave intrinsic parameters and vertical wavelength using a single scanning OH(3-1) airglow spectrometer, Atmos. Meas. Tech., 11, 2937–2947, 10.5194/amt-11-2937-2018, 2018.Zhang, X., Forbes, J. M., Hagan, M. E., Russell III, J. M., Palo, S. E.,
Mertens, C. J., and Mlynczak, M. G.: Monthly tidal temperatures 20–120 km
from TIMED/SABER, J. Geophys. Res., 111, A10S08, 10.1029/2005JA011504,
2006.