Atmos. Chem. Phys., 20, 11979–12010, 2020
https://doi.org/10.5194/acp-20-11979-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
Comparative study between ground-based observations and
NAVGEM-HA analysis data in the mesosphere and lower
thermosphere region
Gunter Stober1,2 , Kathrin Baumgarten2,3 , John P. McCormack4 , Peter Brown5,6 , and Jerry Czarnecki2
1 Institute
of Applied Physics, Microwave Physics, University of Bern, Bern, Switzerland
of Atmospheric Physics at the University of Rostock, Kühlungsborn, Germany
3 Fraunhofer Institute for Computer Graphics Research IGD, Rostock, Germany
4 Space Science Division, Naval Research Laboratory, Washington, DC, USA
5 Dept. of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada
6 Western Institute for Earth and Space Exploration, University of Western Ontario, London, Ontario, Canada
2 Leibniz-Institute
Correspondence: Gunter Stober (gunter.stober@iap.unibe.ch)
Received: 30 October 2019 – Discussion started: 19 November 2019
Revised: 17 August 2020 – Accepted: 31 August 2020 – Published: 26 October 2020
Abstract. Recent studies have shown that day-to-day variability of the migrating semidiurnal solar (SW2) tide within
the mesosphere and lower thermosphere (MLT) is a key
driver of anomalies in the thermosphere–ionosphere system.
Here, we study the variability in both the amplitude and
phase of SW2 using meteor radar wind and lidar temperature observations at altitudes of 75–110 km as well as wind
and temperature output from the Navy Global Environmental Model – High Altitude (NAVGEM-HA), a high-altitude
meteorological analysis system. Application of a new adaptive spectral filter technique to both local radar wind observations and global NAVGEM-HA analyses offers an important
cross-validation of both data sets and makes it possible to
distinguish between migrating and non-migrating tidal components, which is difficult using local measurements alone.
Comparisons of NAVGEM-HA, meteor radar and lidar observations over a 12-month period show that the meteorological analyses consistently reproduce the seasonal as well
as day-to-day variability in mean winds, mean temperatures
and SW2 features from the ground-based observations. This
study also examines in detail the day-to-day variability in
SW2 during two sudden stratospheric warming, events that
have been implicated in producing ionospheric anomalies.
During this period, both meteor radar and NAVGEM-HA
winds show a significant phase shift and amplitude modulation, but no signs of coupling to the lunar tide as previous
studies have suggested. Overall, these findings demonstrate
the benefit of combining global high-altitude meteorological
analyses with ground-based observations of the MLT region
to better understand the tidal variability in the atmosphere.
1 Introduction
There is a growing need to understand the global wind field
from the surface up to the lower thermosphere (0–100 km)
and beyond as well as its day-to-day variability due to meteorological processes. Planetary waves and atmospheric tides
are dominant drivers at the mesosphere and lower thermosphere (MLT) that provide a highly variable dynamical lower
boundary to the thermospheric–ionospheric system, e.g., at
the equatorial dynamo region at altitudes from 100 to 150 km
(see, e.g., Akmaev, 2011, and references therein). The upward propagation of these drivers from their source regions
near the surface into the MLT region is determined in large
part by the global wind field. Accurate assessments of both
daily and seasonal variability in winds and tidal modes has
therefore become necessary for better understanding lower
atmospheric forcing of the thermosphere–ionosphere system.
At midlatitudes and polar latitudes, planetary waves provide a significant contribution to the variability of the winter MLT and play a major role in vertical coupling pro-
Published by Copernicus Publications on behalf of the European Geosciences Union.
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cesses between the different atmospheric layers. For example, during sudden stratospheric warmings (SSWs) (Matsuno, 1971; Andrews et al., 1987), the whole middle atmosphere (stratosphere–mesosphere) responds to sudden reversals of the zonal wind from eastward to westward and
back to eastward accompanied by an increase of the stratospheric temperature and a mesospheric cooling (see, e.g.,
Chandran et al., 2014; Zülicke et al., 2018, and references
therin). SSWs are often studied using general circulation
models (GCMs), which are either free running (e.g., GAIA,
WACCM and KMCM; Jin et al., 2012; Liu et al., 2010;
Becker, 2017; Zülicke et al., 2018) or nudged to reanalysis fields (e.g., the Whole Atmosphere Community Climate
Model with specified dynamics, SD-WACCM; Marsh, 2011;
Stray et al., 2015; Limpasuvan et al., 2016). Manney et al.
(2008, 2009) characterized the SSW in 2006 as a vortex displacement and the SSW in 2009 as a vortex splitting event
making use of global satellite observations (Microwave Limb
Sounder; MLS) and data-assimilated reanalysis mostly at the
stratosphere and lower mesosphere. Matthias et al. (2013) investigated the role of planetary waves in the evolution of vortex splitting and displacement events combining satellite data
and ground-based observations.
Atmospheric tides are generated in the troposphere and
stratosphere mostly through the absorption of sunlight by water vapor and ozone (e.g., Lindzen, 1979). They have been
studied theoretically (e.g., Chapman and Lindzen, 1970;
Forbes, 1982; Wang et al., 2016) and from observations (e.g.,
Portnyagin et al., 1993; Merzlyakov et al., 2009; Oberheide
et al., 2009, 2011, and references therein) for decades. More
recent studies analyzed the response of the semidiurnal tide
during SSWs using ground-based instruments and nudged
GCM data or investigated the relative importance and impact
of the semidiurnal lunar tide during SSWs with the TIME
general circulation model (GCM) and WACCM (Pedatella
et al., 2012; Pedatella and Maute, 2015). However, atmospheric tides propagate from their source region up to the
MLT through a constantly varying altitude-dependent wind
and temperature field, which significantly modifies the phase
of the tides, depending on their vertical wavelength, as well
as the vertical wavelength itself.
In this study, we compare local meteor radar (MR) wind
observations as well as lidar temperature measurements
with meteorological analyses produced with NAVGEM-HA
(Navy Global Environmental Model – High Altitude), a data
assimilation and modeling system that extends from the surface to the lower thermosphere. NAVGEM-HA fields were
available from December 2009 to December 2010 and during the winter season of 2012/13 from December 2012 to
March 2013. Recent studies (Eckermann et al., 2018; McCormack et al., 2017) have presented an initial cross-validation
of the mesospheric winds from NAVGEM-HA for two winter seasons using worldwide-distributed MR measurements.
Here, we extend these initial comparisons to include seasonal mean winds (30 d median) from NAVGEM-HA and
Atmos. Chem. Phys., 20, 11979–12010, 2020
G. Stober et al.: Tidal variability
from three MRs at midlatitudes to high latitudes for the year
2010. Time series of both NAVGEM-HA analyzed winds and
MR measurements are decomposed into daily mean winds,
tides and GW residuals using a recently introduced analysis technique called adaptive spectral filter (ASF) (Stober
et al., 2017; Pokhotelov et al., 2018; Wilhelm et al., 2019;
Baumgarten and Stober, 2019). This technique is designed
to extract daily mean winds and tidal variations on a day-today basis. In addition to MR measurements, we also present
the first comparison between midlatitude temperature observations from a resonance lidar and NAVGEM-HA analyzed
temperatures for the 2010 period.
Meteorological analysis data, such as NAVGEM-HA, provide a much more realistic forcing of the upper atmosphere
due to tides and mean winds compared to current versions of
other comprehensive models. Chandran and Collins (2014)
investigated SSW events using SD-WACCM nudged with
reanalysis fields from the GEOS-5.2 reanalysis system up
to an altitude of about 40 km. However, at altitudes above
70–80 km, the nudged model started to substantially deviate from the observed wind climatologies (Wilhelm et al.,
2019). In particular, the nudged model showed a wind reversal from eastward to westwards winds between 70 and
80 km, which is not confirmed from the wind climatologies.
Such reversal of the zonal wind can be also found in other
comprehensive models or mechanistic models (Smith, 2012;
Becker, 2012). Liu (2016) shows a comparison among several GCMs indicating that there are substantial deviations at
the mesosphere and upper atmosphere, although each of the
GCMs was nudged up to the lower stratosphere (see also
Pedatella et al., 2014, for more details). Only the Groundto-Topside Model of Atmosphere and Ionosphere for Aeronomy (GAIA) (Jin et al., 2012; Liu et al., 2014) showed during
winter eastward winds at the MLT. Previously, the extended
Canadian Middle Atmosphere Model (eCMAM) model was
also cross-validated with ground-based meteor radar observations to investigate mean winds and tides and their amplitude and phase behavior at equatorial latitudes (Du et al.,
2007; Ward et al., 2010). They found a remarkably good
agreement between the model and the local observations using 60 d running means underlining the value of such comparisons. The focus of the present study is to examine the degree of agreement between day-to-day and seasonal variability in migrating semidiurnal westward-migrating tide with
zonal wave number 2 (SW2) between a global meteorological analyses of the MLT region and ground-based observations as a means to, ultimately, better understand the origins
of this variability.
Finally, we perform a detailed comparison of SW2 variability from both NAVGEM-HA and meteor radar observations during the SSWs in 2009/10 and 2012/13, focusing
in particular on how the amplitude and phase of semidiurnal variability in both data sets respond to changes in the
background wind. Overall, the results of these comparisons
show very good agreement between NAVGEM-HA analyzed
https://doi.org/10.5194/acp-20-11979-2020
G. Stober et al.: Tidal variability
winds and MR observations, highlighting the utility of combining global high-altitude data assimilation products with
ground-based observations of the MLT to lend new insight
into the causes of semidiurnal tidal variability over daily to
seasonal timescales. Such short time variations are essential
for the understanding of the forcing from below the thermosphere and ionosphere (Liu, 2016).
Therefore, the paper is structured as follows. First, we describe the observations for winds and temperatures in the
MLT region and the corresponding meteorological analysis
data in Sect. 2. Section 3 provides a detailed explanation
of the methodology used for the data analysis. Section 4
presents the results for the climatology, comparing mean
winds simultaneously seen in the meteor radar data at different locations with the NAVGEM-HA analysis data accompanied with available temperature measurements from a resonance lidar at one midlatitude location. The results are also
discussed for the semidiurnal tide for the whole year (2010)
as well as during the winter seasons of 2010 and 2013 in
Sect. 5. Finally, the findings are summarized and a conclusion is given in Sect. 6.
2 Data description
2.1
Wind observations
In this study, we compare the 3-hourly global synoptic wind
and temperature analyses from NAVGEM-HA with meteor
radar observations collected at three different latitudes in Andenes (69◦ N, 11◦ E) in Norway, Juliusruh (54.3◦ N, 13◦ E)
in Germany and Tavistock (Canadian Meteor Orbit Radar;
CMOR) (43.2◦ N, 80.7◦ W) in Canada. All three meteor
radars use the same software for meteor detection and classification as described in Hocking et al. (2001). All systems
were almost continuously in operation for the analyzed periods. Only the Andenes system shows some data gaps, mainly
due to the more extreme weather conditions in northern Norway, which caused some damage to the antennas and from
time to time a power outage. A more detailed description of
the CMOR radar can be found in Brown et al. (2008). A summary of the Juliusruh and Andenes MR is found in Stober
et al. (2012) and Wilhelm et al. (2017).
MLT winds are obtained with a temporal resolution of 1 h
and a vertical resolution of 2 km using the wind retrieval
algorithm presented in Stober et al. (2018), which is a further development of the wind analysis presented in Hocking
et al. (2001). The wind analysis contains a full error propagation of the statistical uncertainties and a physical error model
based on the vertical and temporal shear as a spatiotemporal
Laplace filter for each wind component. Contrary to many
other meteor radar wind analysis, the algorithm also solves
for the vertical wind velocity. The obtained mean vertical velocities show values of a few centimeters per second and are
mainly used as quality control for successful convergence of
https://doi.org/10.5194/acp-20-11979-2020
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the wind fit. In the present study, we use four meteors as a
minimum for a successful wind fit.
2.2
Temperature observations
At Kühlungsborn (54◦ N, 12◦ E), around 118 km southwest
of the meteor radar at Juliusruh, a resonance lidar was in operation until 2012 to observe temperatures in the MLT region. The potassium lidar measures the Doppler broadening
of the 770 nm potassium D1 resonance line by scanning with
a narrowband Alexandrite ring laser. The system is fully daylight capable. Further details can be found in von Zahn and
Höffner (1996) and Fricke-Begemann et al. (2002).
The extent of the potassium layer in the atmosphere limits the range of heights at which temperatures can be determined. In this work, temperatures are determined for heights
between 80 and 105 km. The integration time of the data used
here is 1 h with a shift of 15 min. The vertical resolution is
1 km. In addition to the resonance lidar, also a Rayleigh–
Mie–Raman (RMR) lidar was operated during the night at
the same location until 2013. This lidar used the second harmonic output of a Nd:YAG laser at 532 nm. The temperatures
are calculated under the assumption of hydrostatic equilibrium from the Rayleigh backscatter which is proportional to
the atmospheric air density (Hauchecorne and Chanin, 1980).
The initial temperature value for integration is taken from the
resonance lidar (Alpers et al., 2004). The temperatures from
the RMR lidar cover an altitude range between 22 and 90 km.
But as the focus of this study is on the MLT region, we use
these temperatures only above 70 km. Here, daily mean temperatures as a composite between 2003 and 2012 are used
to describe the mean temperature field during the year in the
MLT region. A full description of the seasonal variation has
been published in Gerding et al. (2008).
2.3
NAVGEM-HA meteorological analyses
NAVGEM-HA is a high-altitude numerical weather prediction (NWP) system extending from the surface to ∼ 116 km
altitude that provides atmospheric winds, temperatures and
constituent information. It is based on the operational system described in Hogan et al. (2014), which combines the
NAVGEM global spectral forecast model with a hybrid fourdimensional variational (4D-Var) data assimilation algorithm
(Kuhl et al., 2013).
In addition to standard operational meteorological observations in the troposphere and stratosphere, NAVGEMHA assimilates satellite-based observations of temperature,
ozone and water vapor in the stratosphere, mesosphere
and lower thermosphere (McCormack et al., 2017). The
NAVGEM-HA output is on a 1◦ latitude and longitude grid,
respectively. The temporal resolution of the data output fields
is 3 h. NAVGEM-HA uses a fixed top-level pressure of 6 ×
10−5 hPa (e.g., McCormack et al., 2017; Eckermann et al.,
2018, and references therein), which corresponds to an apAtmos. Chem. Phys., 20, 11979–12010, 2020
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proximate altitude of 116 km. However, at the upper three
model levels, an enhanced diffusion is applied to reduce the
effects of wave reflection. These layers effectively act as a
“sponge layer” and are not included in the data analysis.
The forecast model component of NAVGEM-HA incorporates the same implicit fourth-order horizontal diffusion of
vorticity, divergence and virtual potential temperature used
in its predecessor system (NOGAPS-ALPHA) to suppress
growth of unrealistic variances near the truncation scale, as
described in McCormack et al. (2015). Default values for the
diffusion result in an effective e-folding time of 24 h at the
highest wave number (here T119). In the top three model
levels, the diffusion is ramped up to produce an effective
e-folding of 2 h at the top level. In the 74-level version of
NAVGEM-HA used in this study, this region of enhanced diffusion (sponge layer) covers levels with p < 1 × 10−3 hPa or
95 km in pressure altitude.
In an initial validation study, McCormack et al. (2017)
used NAVGEM-HA output interpolated to geometric altitudes up to 95 km for the mean winds and up to 90 km for
the wave analysis. In the present study, vertical profiles of
NAVGEM-HA analyzed winds and temperatures are converted from the model vertical grid in geopotential altitude to
a geometric altitude grid as done in Eckermann et al. (2009)
up to 94 km altitude. Above this level, NAVGEM-HA vertical resolution degrades significantly, as the vertical grid spacing increases from ∼ 3 km near 80 km altitude to more than
5 km near 100 km altitude. To date, NAVGEM-HA winds and
tides up to 90 km altitude have been shown to be in good
agreement with both ground-based MR observations, as reported in McCormack et al. (2017), Eckermann et al. (2018)
and Laskar et al. (2019), and with independent satellite-based
wind observations, as reported in Dhadly et al. (2018). The
present study extends these initial validation studies to include, for the first time, validation with two independent
ground-based data sets over a 12-month period.
In this study, we use a fixed geometric altitude grid (based
on the World Geodetic System 84 model) with a maximum
altitude of 94 and 2 km vertical resolution at the MLT to
match the meteor radar data. We convert the geopotential altitudes of NAVGEM-HA to geometric altitudes. However, we
note that the geopotential altitude of the highest usable output
level, neglecting the sponge layer effects noted above, has a
geometric altitude between 92 and 89 km. As a consequence,
tidal amplitudes above 90 km altitude should not be considered as geophysical and are caused by the extrapolation to
the geometric altitude grid and sponge layer effects. Further,
the vertical constraint implemented in the ASF amplifies this
effect even more.
At mesospheric altitudes, NAVGEM-HA assimilates satellite measurements from the Thermosphere, Ionosphere,
Mesosphere Energetics and Dynamics (TIMED) and Aura
satellites and radiances from the Defense Meteorological
Satellite program (DMSP) (Eckermann et al., 2018). Systematic differences between the meteorological analysis and the
Atmos. Chem. Phys., 20, 11979–12010, 2020
G. Stober et al.: Tidal variability
ground-based wind and temperature data herein may have
different origins. There could be intrinsic differences due to
the model physics leading to such deviations, or the assimilated data may show some systematic differences in relation
to the observations used for the comparison. Further, considering that the true state of the atmosphere of temperature
and winds remains elusive, it is hard to determine which of
the observational techniques provides a better representation
of this true state. Thus, it is essential to assess some of the
systematic differences which can arise due to the methodology employed for the comparison, e.g., whether applying
different diagnostics or different spatiotemporal sampling of
the instruments makes a large difference. Validation and assessment of potential biases between the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER)
temperatures and ground-based lidar measurements can be
found in Xu et al. (2006) and Dawkins et al. (2018). A crosscomparison of the MLS and SABER temperatures is presented in Schwartz et al. (2008). A detailed description of
how the data assimilation in NAVGEM-HA treats the temperature biases between both satellites is given in Eckermann
et al. (2018).
Another important point affecting the comparison is the
availability of the assimilated data. Above 90 km, fewer
satellite observations can be assimilated. Further, it has to
be noted that the spatial coverage of the assimilated SABER
temperatures varies due to the yaw cycle of the spacecraft,
which changes the observing geometry every 60 d providing a variable latitudinal coverage. From 52◦ S to 52◦ N, the
satellite collects constant measurements, whereas the higher
latitudes depend on the yaw cycle and alternate between up to
82◦ S and 82◦ N latitudinal coverage. This yaw cycle pattern
may affect the quality of NAVGEM-HA analyses at Juliusruh
and Andenes.
3 Local and global diagnostics
One of the challenges comparing different data sets is the
use of a common diagnostic to ensure that all observations
and the meteorological analysis data are treated in the same
way. In particular, observational data can be more difficult to
be analyzed due to data gaps or uneven temporal sampling.
Atmospheric tidal and planetary wave amplitudes are often obtained from Fourier-based techniques (e.g., Stockwell
et al., 1996; Torrence and Compo, 1998). In the case of unevenly sampled data, Lomb–Scargle periodograms are used
(Lomb, 1976; Scargle, 1982), which provide a amplitude–
power spectrum and a significance level but without phase
information. For observational data, it is also very common
to derive the tidal information of amplitude and phase with a
least-squares fit (Lima et al., 2007) or by a multiple regression analysis assuming, for instance, a circular polarization
for the semidiurnal tide (Jacobi et al., 2008).
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A commonly used approach to extract tides is a harmonic
analysis:
u, v, T = u0 , v0 , T0 +
3
X
n=1
an sin
2π
2π
· t + bn cos
· t ; (1)
Pn
Pn
here u, v and T are the zonal wind, meridional wind and
temperature, an and bn are the tidal Fourier coefficients,
Pn = 24, 12, 8 stands for the tidal periods in hours, and t is
the time of the observation either in UTC or local time, whatever is preferred. Harmonic tidal analysis works well for time
series of several days or months but assumes a constant mean
background wind, tidal amplitude and phase for the selected
period. Recent studies of mean winds and tides using meteor
radar, lidar and satellite observations indicate that tides have
a fairly intermittent amplitude and phase character (Stober
et al., 2017; Baumgarten et al., 2018; Baumgarten and Stober, 2019; Dhadly et al., 2018).
The adaptive spectral filter (ASF) aims to be a simple and
general diagnostic to decompose time series in 1-D (temporal filter) (Stober et al., 2017) or 2-D (temporal–spatial filter) (Baumgarten and Stober, 2019). The technique is based
on least squares and hence applicable to unevenly sampled
data, and no additional zero padding needs to be applied for
data gaps as long as sufficient observations are available in
the remaining adapted time window. Another benefit of the
least-squares implementation is given in the error propagation to the derived quantities through the covariance matrix.
The term “adaptive” in this context relates, similar to the
wavelet technique, that the window length adapts to the number of wave cycles for each frequency component that is fitted. The MR and NAVGEM-HA time series are decomposed
into daily mean winds, diurnal tide, semidiurnal tide, terdiurnal tide and gravity wave residuum using the ASF.
The ASF uses a sliding window and fits each tidal component applying a scaling factor of 1.3 accounting for the
number of wave cycles and no de-trending is applied. The
scaling factor determines the window length that is used for
the fitting for each frequency component. Here, we applied
a window length of 31 h for the diurnal tide, whereas the
semidiurnal tide is determined using a 16 h window and so
forth for the terdiurnal tide. At first, the daily mean wind and
the diurnal tidal (amplitude and phase) components are determined considering also a semidiurnal and terdiurnal tide.
In the next step, the semidiurnal tide is fitted using a regularization by the previously determined daily mean wind and
diurnal tide and adapting the window length. The same procedure is repeated for the terdiurnal tide, respectively. Due to
the short window length, the bandwidth for each tidal component is rather wide and may also include some gravity wave
contributions. It turns out that just applying temporal filtering leads to some contamination of the obtained tidal amplitudes and phases due to inertia gravity waves with short (less
than 10 km) vertical wavelengths (see Appendix A). However, there are also some studies from polar latitudes using
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lidar and radar observations from McMurdo or Scott bases
(77.8◦ S, 166.7◦ E) and from Syowa station (39.6◦ E, 69.0◦ S)
indicating the presence of gravity waves with vertical wavelengths of 22–23 km (Chen et al., 2013) or periods close to
the semidiurnal tide (Shibuya et al., 2017). However, Davis
et al. (2013) has shown that the diurnal and semidiurnal tides
typically have vertical wavelengths larger than 20 km. Hence,
we constrain our tidal amplitudes and phases by assuming
that the phase of the diurnal and semidiurnal tide only gradually changes with altitude using a 16 km vertical retrieval
kernel. The mean winds are constrained by a 10 km vertical
retrieval kernel to avoid issues during the summer wind reversal from westward winds to eastward winds.
We optimized these vertical wavelength values considering the results of previous studies using meteor radars investigating the vertical wavelengths of tides (Yu et al., 2013;
Davis et al., 2013; Fritts et al., 2019). These earlier studies showed that the vertical wavelengths for most of the
tidal modes are much larger than 25 km. Only Yu et al.
(2013) found, for some Hough modes, vertical wavelengths
shorter than 25 km. To avoid a potential contamination of
shorter tidal wavelengths in our vertical retrieval kernel, we
did not implement a hard cut-off vertical wavelength. Instead, we just constrained the smoothness of the vertical tidal
phase within the averaging kernel and even allowed a gradual change. An example of the ASF(2D) tidal fit compared
to ASF(1D) is presented in Fig. A1.
The vertical regularization constraint is an essential feature
of the ASF compared to many other diagnostic techniques
based on wavelet or Fourier methods. Previous studies based
on lidar observations (e.g., Ehard et al., 2015; Baumgarten
et al., 2017, and reference therin) already investigated how
the potential gravity wave energy changes with the applied
filtering. Temporal filters tend to underestimate inertia gravity waves due to their long periods combined with short vertical wavelengths, whereas vertical filters are designed to eliminate the tidal contribution due to their large vertical wavelengths. As a consequence, this filter underestimates gravity waves with comparatively large vertical wavelengths. The
ASF is much less prone to such biases due to the combination
of spatiotemporal information for the specific waves.
Since NAVGEM-HA produces global wind and temperature fields, we can extract tides as global waves and separate migrating and non-migrating tidal modes. The migrating tides are DW1 (diurnal westward wave number 1), SW2
(semidiurnal westward wave number 2) and TW3 (terdiurnal westward wave number 3); all other tidal modes are
non-migrating tidal components (e.g., Forbes et al., 2008;
Miyoshi et al., 2017, and references therein). The migrating
and non-migrating tidal components are obtained using the
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G. Stober et al.: Tidal variability
following function:
3 X
3
X
2π
asi · sin s · λ −
·t
Pi
s=−3 i=1
2π
+bsi · cos s · λ −
·t
+ further waves,
Pi
u, v, T = u0 , v0 , T0 +
(2)
where s is the zonal wave number (negative eastward, positive westward), λ denotes the longitude at a fixed latitude
circle, Pi indicates the periods of the diurnal, semidiurnal
and terdiurnal tides, and asi and bsi are the Fourier coefficients for each wave number s and period Pi . The zonal
mean zonal and meridional wind and the zonal mean temperature are given by u0 , v0 and T0 . The function also includes longer period waves such as the quasi-two-day wave
(QTDW) with wave number s = 1, 2, 3 and stationary planetary waves with wave number s = 1, 2, 3 (Baumgarten and
Stober, 2019; Schranz et al., 2020).
Daily mean tides for all the components are obtained by
using a 3 d window around a central day, which is sufficient to still see some day-to-day variability and to determine potential phase drifts of each tidal component. The
global tidal phase for all tidal components is referenced to
the Prime Meridian (Greenwich). Although NAVGEM-HA
provides validated wind and temperature products from ∼ 18
up to ∼ 94 km altitude, we focus our comparison on the MLT
region and mostly on the available MR observations. A detailed discussion of the QTDW or planetary waves is beyond
the scope of this paper and we leave these for other studies.
4 Results
In the first two parts of the results, we show the mean state
of the atmosphere during the year in the MLT region using
winds and temperatures from observations and NAVGEMHA data. Next, the seasonal variation of the semidiurnal tidal
component derived with the adaptive spectral filter is presented for each location. In addition to this, the analysis is
also done for two examples of sudden stratospheric warming in the winters of 2009/10 and 2012/13 to determine how
well the observed variations in the MLT winds correspond to
the NAVGEM-HA analysis data as well as to determine the
day-to-day variability of the semidiurnal tide.
4.1
Mean winds
Figure 1 shows the time variation of the zonal and meridional winds at the three locations (Andenes, Juliusruh and
Tavistock) from hourly meteor radar observations (left column) and the corresponding 3-hourly NAVGEM analyzed
winds (center column) for the same location and each latitude as zonal mean values (right column). Daily mean winds
are calculated and small-scale variations such as tides and
gravity waves are removed by the adaptive spectral filter, and
Atmos. Chem. Phys., 20, 11979–12010, 2020
planetary waves are effectively filtered using a 30 d running
median. The climatologies are based on the same time periods for MR winds and NAVGEM-HA and include December
2009 to December 2010 with periodic boundary conditions.
In general, there is good agreement of the seasonal wind
pattern between the meteor radar wind observations and the
NAVGEM-HA data. At all three locations, the zonal wind
observations show the typical eastward winds in winter and
the prominent wind reversal in spring. In particular, the seasonal asymmetry of the spring transition as well as the gradual change of the summer wind reversal altitude seen in the
meteor radar winds is well reproduced in the NAVGEM-HA
analyses.
During summer, a strong transition between westward and
eastward winds occurs between 80 and 90 km altitude. The
transition height decreases from high latitudes to midlatitudes. Above 90 km altitude, the eastward jet reaches wind
velocities of about 40 m s−1 for all stations. The meridional
winds during winter are typically northward, while they are
southward during the summer. Similar behavior is seen in
the NAVGEM-HA analysis data, but here the magnitude of
the winds is to some extent larger compared to the meteor
radar observations. Although the general morphology of the
seasonal pattern is well captured in NAVGEM-HA, there are
some differences in the wind reversal altitudes in summer in
both wind components, which would affect the gravity-wavebreaking altitudes and hence the altitude of the resulting momentum deposition.
Furthermore, the altitude where the zonal wind reverses
during summer decreases not as much with latitude as indicated from the meteor radar observations for the different
locations. Some differences occur between the NAVGEMHA locally analyzed winds compared to the zonal-averaged
NAVGEM-HA analyzed winds for each latitude of the meteor radar stations. Short-term variations during winter are
much more visible in the locally analyzed winds; this is especially true for the meridional wind case.
4.2
Mean temperatures
Until now, only NAVGEM-HA wind products have been extensively validated with independent ground-based measurements. To extend this validation to MLT temperatures, we
next perform a similar comparison using NAVGEM-HA temperature analyses and a co-located potassium lidar instrument at Kühlungsborn. The composite daily mean lidar temperatures over the period 2003–2012 are shown in Fig. 2
together with the NAVGEM-HA analyzed temperatures between 2009 and 2010. Both data sets show the same seasonal temperature pattern with the lowest temperatures during summer. The mesopause, where the lowest temperatures
occur during the year, is estimated from the lidar data and
found around 88 km in summer and just above 100 km in
winter. For the NAVGEM-HA analyzed temperatures, the altitude of the mesopause is in nearly the same altitude range.
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Figure 1. Comparison of mean winds above Andenes, Juliusruh and Tavistock (CMOR) using a 30 d running median with periodic boundary
condition using the same dates for NAVGEM-HA and the meteor radar observations. The left panels show the meteor radar observations.
The central panels show the NAVGEM-HA analysis fields for the same locations and periods. The right panels display the zonal mean zonal
and meridional winds for each latitude.
In general, the temperature values are in very good agreement with each other, although we note that the temperatures
observed by lidar near 70 km are larger than the NAVGEMHA temperature. At the upper edge of the NAVGEM-HA
data, there is also a temperature enhancement during summer, which is not seen in the lidar data.
4.3
Semidiurnal tides
In this section, we investigate the seasonal variation of the
semidiurnal wind tide based on the calculation with the adaptive spectral filter. This component is the most dominant tidal
component at the MLT and the latitudes analyzed herein
(Chapman and Lindzen, 1970). The results for the semidiurnal tidal amplitude and phase for the stations at Andenes,
Juliusruh and Tavistock are shown in Figs. 3, 4 and 5, respectively. Every data set is compared to the NAVGEM analyzed
https://doi.org/10.5194/acp-20-11979-2020
tidal fields from a local and from a global perspective as already done for the mean winds and temperatures.
The observations from all stations indicate a clear winter amplitude maximum. A second maximum is also evident during September. The amplitudes are smallest during
November and April. Only Tavistock exhibits a significant
semidiurnal tidal amplitude for April compared to the meteor
radars at higher latitudes, and we note that the tidal amplitudes above Tavistock are also even stronger during fall than
during winter. Compared to the other locations, the winter
maximum above Tavistock is less pronounced. In general,
the amplitudes during winter are strongest for midlatitudes
(Juliusruh).
The NAVGEM-HA analyzed amplitudes reveal the same
temporal variability over the year as from the observations.
Above an altitude of 90 km, the amplitudes from NAVGEMHA show a significant increase which is not seen in the obAtmos. Chem. Phys., 20, 11979–12010, 2020
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4.4.1
Figure 2. Comparison of mean temperatures above Kühlungsborn.
Panel (a) shows the temperatures derived from the potassium lidar.
Panel (b) shows the NAVGEM-HA analysis field for the same location.
servations. This was also visible in the temperature data of
NAVGEM-HA compared to the lidar data.
In addition to the amplitudes of the semidiurnal tides, the
annual phase behavior of those tides was also calculated using the spectral adaptive filter. In general, for every location,
the phase of the semidiurnal tide is drifting and variable over
the year. During winter, the phases are continuously changing; at the beginning of March, the phase shows a sudden
jump, which is evident in every location of the observations
and the meteorological analysis. This behavior reverses during October–November, exactly when the atmospheric circulation reverses again from summer to winter conditions. A
similar phase progression is visible from the NAVGEM-HA
locally analyzed data as well as from the global fields.
4.4
Day-to-day variability during a sudden
stratospheric warming
Having established that NAVGEM-HA wind and temperature analyses capture many of the salient features in the seasonal variation of both meteor radar wind and lidar temperature observations, we now examine the shorter-term variations in both data sets. Specifically, we examine the dayto-day variability of the mean winds, the semidiurnal tidal
amplitudes and phases from the meteor radar winds during
the SSW that took place in 2010 and 2013 in comparison
to NAVGEM-HA analyzed data from a local perspective as
well as from a global view. To do so, we apply the same ASF
analysis procedure to both meteor radar and NAVGEM-HA
data at a high-latitude (Andenes) and a midlatitude (Juliusruh) location.
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Winter season 2009/10
During the winter of 2009/10, a major sudden stratospheric
warming occurred at the end of January when the polar vortex was markedly displaced from the pole (Stober et al.,
2012) and then separated into two unequally strong lobes
(e.g., Dörnbrack et al., 2012; Jones et al., 2018). Following previous studies involving NAVGEM-HA, we mark the
onset of the SSW as occurring on 27 January (McCormack
et al., 2017). Mean winds, the semidiurnal tidal amplitude
and phase are shown in Fig. 6 from the meteor radar observations above Andenes as well as for the corresponding locally analyzed NAVGEM-HA data. In Fig. 7, the same results
are shown for the station at midlatitudes above Juliusruh.
Stronger changes in the winds are visible for Juliusruh than
for Andenes. Even the semidiurnal amplitudes are stronger at
midlatitudes, which agrees with the stronger seasonal variation of the semidiurnal tidal amplitude above Juliusruh. After
the onset of the sudden stratospheric warming, the semidiurnal tidal amplitudes show an enhancement at the beginning
of February, which is visible at both stations and in both wind
components.
The semidiurnal tidal phases show a large day-to-day variability during the winter period, which is in general stronger
at high latitudes than at midlatitudes. After the central date
of the sudden stratospheric warming, the tidal phase shows
a sudden increase which lasts only a few days. After these
days, the phase shows a recovery where they become more
stable again just as before the sudden stratospheric warming.
The NAVGEM-HA analyzed winds exhibit the same shortterm variability during the 2009/10 winter at both stations for
the winds as well as for the semidiurnal tide. Even the phase
enhancement after the central date of the SSW is remarkably well reflected by the NAVGEM-HA data. Some differences occur above an altitude of 85 km, where NAVGEMHA data reveal larger magnitudes in the winds as well as
larger amplitudes for the semidiurnal tide as previously seen.
Figure 8 shows global NAVGEM-HA results for both the Andenes and Juliusruh station locations. The global analyzed
NAVGEM-HA data indicate much less variability during the
winter compared to the locally analyzed data. But the central
date of the SSW is more easily identified in the winds than
was the case for the locally analyzed winds. However, the
main features for the semidiurnal tide stay the same. The amplitudes show an increase after the central date of the SSW
and the phases reveal a change for a few days at both locations. In contrast to the locally analyzed data, the phases
from the global NAVGEM-HA fields slowly change during
the winter. But, in general, the agreement with the MR observations is still good.
4.4.2
Winter season 2012/13
The winter season of 2012/13 was also characterized by a
major sudden stratospheric warming. In this case, the onhttps://doi.org/10.5194/acp-20-11979-2020
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Figure 3. Comparison of semidiurnal seasonal zonal and meridional amplitude (two upper rows) and phase (two lower rows) tidal climatology
using a 30 d running median with periodic boundary condition. The left panels show the meteor radar observations above Andenes (69◦ N,
11◦ E). The central panels show the NAVGEM-HA analysis fields for the same period. The right panels visualize the zonal mean tidal
amplitude and phase of the SW2. The labels A12 and p12 correspond to the semidiurnal amplitude and phase using the local diagnostic.
Figure 4. Same as Fig. 3 but for Juliusruh.
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Figure 5. Same as Fig. 3 but for CMOR.
set of the SSW occurred on 7 January using again the definition presented in McCormack et al. (2017). During the
SSW, the vortex was split into two lobes (Coy and Pawson,
2015). Again, mean winds, the semidiurnal tidal amplitudes
and phases are shown in Figs. 9 and 10 for high latitudes and
midlatitudes, respectively.
In this winter season, the mean zonal winds at high latitudes are stronger, especially after the SSW, than at midlatitudes, which is opposite to what was seen in the winter season of 2009/10. The mean meridional winds are similar in
strength for both stations. Nevertheless, the semidiurnal tide
again shows stronger amplitudes at the midlatitude station
than at high latitudes. At Andenes, we see a distinct increase
of the amplitudes after the SSW, which was already seen in
the winter season of 2009/10, while in general, at Juliusruh,
a larger tidal activity is visible. Here, before and during the
central date of the SSW, the tidal amplitudes decrease in the
first place due to the strong changing winds. Afterward, the
semidiurnal tidal amplitudes increase again, more than during the entire winter.
The semidiurnal tidal phases show again a large variability
during the whole time. A few days after the central date of the
sudden stratospheric warming, a sudden increase of the phase
is visible in the same way as for the winter of 2009/10. The
locally analyzed NAVGEM-HA data reveal structures during
this winter period similar to those from the observations. It
is evident from every data set that the mean winds, as well
as the amplitudes, are slightly overestimated in NAVGEMHA. The NAVGEM-HA analyzed tidal phases exhibit also
a sudden change after the SSW, though not as strong as
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from the observations, but this might be due to a general
more disturbed winter period compared to the year 2009/10.
The globally analyzed data from NAVGEM-HA are shown
in Fig. 11. As was the case for the 2009/10 winter, in this
winter season, the winds from a global perspective are much
stronger and uniformly distributed over the winter months,
except for the wind reversal during the SSW, which is visible
at the beginning of January.
5 Discussion
5.1
NAVGEM-HA and MR mean wind and
temperature climatology
The comparison of the NAVGEM-HA mean winds and the
meteor radar climatologies at Andenes, Juliusruh and CMOR
is remarkable up to an altitude of 94 km. The assimilation
of satellite-based middle atmospheric temperature and constituent observations enables NAVGEM-HA to capture the
main features of the seasonal wind climatologies such as the
weak eastward winds during the winter and the asymmetry of the seasonal pattern between the spring and autumn
wind reversals, as well as the gradual descent of the summer wind reversal between the mesospheric westward winds
and the higher-altitude thermospheric eastward jet. Our analysis shows that the initial good agreement reported during
the winter months in McCormack et al. (2017) extends to
seasonal timescales and provides further cross-validation of
the NAVGEM-HA winds with globally distributed and available meteor radar wind observations.
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Figure 6. Comparison of meteor radar observations and NAVGEM-HA above Andenes during the winter of 2009/10 for daily mean zonal
and meridional winds (two upper panels), semidiurnal tidal zonal and meridional amplitude (middle panels) and semidiurnal tidal phases
(two lower panels). The labels A12 and p12 correspond to the semidiurnal amplitude and phase using the local diagnostic.
The MLT mean wind climatology is still afflicted with a
high degree of uncertainty when comparing different GCMs,
although nudged to the same reanalysis data sets. Pedatella
et al. (2014) compared several GCMs and showed that not
even the sign of the mean wind seems to agree between the
models at the MLT. Further, the seasonal morphology at midlatitudes and high latitudes was not well reproduced by some
models compared to the climatologies published from meteor radars (Portnyagin et al., 2004; Wilhelm et al., 2019).
In particular, the seasonal asymmetry of the zonal wind circulation from the winter to the summer conditions and back
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to the winter regime seems to be problematic for the GCMs.
Comparing the seasonal morphology of the zonal and meridional winds between NAVGEM-HA and other comprehensive GCMs, such as WACCM or SD-WACCM (Smith, 2012;
Chandran and Collins, 2014), and the meteor radar and lidar
data, indicates a much better agreement for the meteorological analysis for altitudes beyond 80 km. Similar results have
been found by comparing meteor radar winds to free-running
mechanistic GCM (Pokhotelov et al., 2018). Previous studies
comparing eCMAM with ground-based meteor radar observations at low latitudes and on seasonal timescales revealed
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Figure 7. The same as Fig. 6 but for Juliusruh.
similar good agreement for mean winds and diurnal tidal amplitude and phases (Du et al., 2007; Ward et al., 2010). The
good agreement between NAVGEM-HA and ground-based
wind observations shown in Sect. 4 indicates that global
data assimilation products in the MLT can provide a valuable benchmark for evaluating the performance of “wholeatmosphere” GCMs extending into the thermosphere. These
products could improve understanding of the large discrepancies among different models noted above by offering insight
regarding where these models deviate most from a validated
high-altitude meteorological analyses.
The general thermal structure and seasonal climatology
are also well reproduced in NAVGEM-HA for the lidar
Atmos. Chem. Phys., 20, 11979–12010, 2020
observations presented in Fig. 2 at the midlatitude station
of Kühlungsborn. The meteorological analyses captures the
seasonal course of the altitude variation of the mesopause.
Further, we identified a small offset between the lidar and
the NAVGEM-HA temperatures. The analysis data tend towards slightly warmer temperatures compared to the resonance lidar. These slightly higher temperatures in NAVGEMHA may also explain the higher wind magnitudes relative to
the MR observations.
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11991
Figure 8. Comparison of global NAVGEM-HA above Andenes and Juliusruh during the winter of 2009/10 for daily zonal mean zonal
and meridional winds (two upper panels), zonal mean semidiurnal tidal zonal and meridional amplitude (middle panels) and zonal mean
semidiurnal tidal phases (two lower panels).
5.2
NAVGEM-HA and MR mean wind semidiurnal
tidal comparison
At MLT heights, tidal amplitudes grow large and contribute
significantly to the daily variability of the zonal and meridional winds. At midlatitudes and polar latitudes, the semidiurnal tide is the most prominent tidal wave in the MLT that
can be observed throughout the course of the year (Porthttps://doi.org/10.5194/acp-20-11979-2020
nyagin et al., 2004; Pokhotelov et al., 2018; Wilhelm et al.,
2019).
In principle, local observations (single measurements)
cannot distinguish between migrating and non-migrating
tidal components and only observe a total tide. Earlier studies (e.g., Portnyagin et al., 2004) have investigated the global
nature of the diurnal and semidiurnal tide at polar latitudes
using a chain of radars at approximately 70◦ N. They found
very good agreement between monthly tidal amplitudes and
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Figure 9. Comparison of meteor radar observations and NAVGEM-HA above Andenes during the winter of 2012/13 for daily mean zonal
and meridional winds (two upper panels), semidiurnal tidal zonal and meridional amplitude (middle panels) and semidiurnal tidal phases
(two lower panels). The labels A12 and p12 correspond to the semidiurnal amplitude and phase using the local diagnostic.
phases for all stations along the latitudinal circle. Recently,
there have been some attempts to separate migrating and
non-migrating tides using globally distributed chains of meteor radars (He et al., 2018) assuming theoretical tidal wave
fields consisting of migrating and non-migrating components. However, due to the small number of meteor radars
at the latitudinal circles, the analysis still contains a high degree of ambiguity.
Atmos. Chem. Phys., 20, 11979–12010, 2020
Combining the benefits of high-resolution local measurements with global meteorological analysis data solves this
problem. The comparison of the semidiurnal tidal climatology reveals that NAVGEM-HA reproduces the seasonal morphology of the tidal amplitudes for both wind components up
to an altitude of 90 km applying the ASF tidal diagnostic. The
local ASF diagnostic shows remarkable agreement between
the global tidal analysis of the migrating SW2 tide in magni-
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11993
Figure 10. The same as Fig. 9 but for Juliusruh.
tude and phase. The non-migrating semidiurnal components
show only very small and often negligible amplitudes. The
agreement of the phase of the SW2 tide between the global
and local measurements seems to be better at lower latitudes
of CMOR and Juliusruh compared to Andenes.
Ward et al. (2010) performed a similar validation of the
tidal amplitude and phase behavior using the eCMAM at low
latitudes. However, they used much longer windows of 60 d
to compute average amplitudes and phases. They also found
the seasonal change of the tidal phase and remarkable good
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agreement between the ground-based lidar and radar data and
the model.
The comparison of NAVGEM-HA and the meteor radar
indicates that tidal phase is variable on the seasonal scale
showing already significant shifts and drifts within a week.
Previously, for local observations, this phase variability was
assumed to be the result of a superposition of migrating and
non-migrating tidal modes. However, comparing the global
tidal fit obtained from NAVGEM-HA of the SW2 tide reflects
this behavior as well. These continuous phase changes have
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Figure 11. Comparison of global NAVGEM-HA above Juliusruh (left column) and Andenes (right column) during the winter of 2012/13
for daily zonal mean zonal and meridional winds (two upper panels), zonal mean semidiurnal tidal zonal and meridional amplitude (middle
panels) and zonal mean semidiurnal tidal phases (two lower panels).
severe implications for the analysis of tides at midlatitudes
and high latitudes from satellites, which usually requires averaging over several weeks to cover all local times.
5.3
NAVGEM-HA and MR winds and tidal day-to-day
variability and lunar tides during SSW events
Besides comparing mean winds, we also investigated the
day-to-day variability of the semidiurnal tide during two winAtmos. Chem. Phys., 20, 11979–12010, 2020
ter seasons with a major SSW event at the midlatitude location of Juliusruh and polar latitudes above Andenes. In 2010,
there was a vortex displacement event (e.g., Stober et al.,
2012; Matthias et al., 2013), which was already validated by
a cross-comparison of the mean winds and waves in McCormack et al. (2017) using several worldwide-distributed meteor radars. The second SSW event occurred during winter
of 2012/13 and evolved as a vortex splitting event (e.g., Xu
and San Liang, 2017).
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Daily mean winds and tidal amplitudes were diagnosed
by the ASF. The meteorological analysis of NAVGEM-HA
reproduces the general day-to-day variability of winds and
even shows a high level of agreement for individual planetary waves passing over the stations. In particular, the timing
of the SSW event itself with the zonal wind reversal and the
formation of an elevated stratopause is well captured. Similar to the zonal and meridional wind climatologies, the meteorological analysis tends to show higher magnitudes of the
wind speeds. Previous comparisons of wind observations to
model data, such as ECMWF or MERRA2, were limited to
a maximum altitude of approximately 70–75 km and below
(Rüfenacht et al., 2018), and thus we omit here any further
detailed discussion.
Another very important aspect of this study is the phase
variability on a day-to-day basis. The ASF provides information on the phase stability of tides with basically the same
resolution as the original measurement time series. Very often, tidal phases are assumed to be stable over long periods of
up to several months in the analysis. However, for instance,
the TIMED satellite requires 60 d to cover all local times due
to its orbit geometry (Zhang et al., 2006; Oberheide et al.,
2011). Our results indicate that during an SSW the phase of
the SW2 tide is significantly altered on a global scale as well
as on a regional or local scale as the dynamics of the middle
atmosphere change (e.g., Manney et al., 2009; Matthias et al.,
2012). Fuller-Rowell et al. (2016) discussed three possible
mechanisms to understand these changes of the tide; FullerRowell et al. (2010) and Jin et al. (2012) attributed the change
of the migrating tidal phase to changes of the mean winds in
the middle atmosphere, whereas Pedatella and Forbes (2010)
suggested non-migrating tides as a source of the SW2 phase
variability. Other studies favor an amplification of the lunar
tide during an SSW (Fejer et al., 2010; Forbes and Zhang,
2012). We discuss these three aspects using the results obtained from the ASF decomposition of the local and global
measurements and meteorological analysis data with a particular emphasis on the suggested lunar tide amplification.
Thus, we are introducing a holographic analysis and lunar
orbit parameters as proxy of the lunar forcing. Furthermore,
we are determining the zonal and vertical wave numbers as
well as the period of the semidiurnal tide and their temporal evolution to separate a potential lunar forcing from the
solar-driven semidiurnal tide.
At first, we investigate the non-migrating tidal components
(see Figs. B1–B4) derived from NAVGEM-HA winds. It appears that only the SW1 and SW3 tides show a response to
the SSW event depending on the latitude and how the SSW
evolved. This is consistent with previous studies (Du et al.,
2007; Liu et al., 2010). The SE1, SE2, SE3 and S0 semidiurnal tides show much smaller amplitudes and are negligible compared to the SW2 tide, in particular, at polar latitudes. Another interesting aspect when comparing the migrating and non-migrating tides from NAVGEM-HA is the
winter seasonal phase behavior of the SW2 tide. The phase
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11995
of the tide drifts by several hours from December to March,
which correlates with the mean wind morphology. Apparently, the change of the phase of the semidiurnal tide is not
explained by a superposition of migrating and non-migrating
tides. However, this needs to be examined in more detail and
is beyond the scope of this paper.
Secondly, we are discussing in detail the suggested lunar
tide amplification after an SSW introducing a holographic
diagnostic and the lunar orbit elevation as proxy of the lunar
forcing. Fejer et al. (2010) investigated vertical plasma drifts
above Jicamarca and found a drift in local time of the semidiurnal oscillation during SSWs, which was attributed to the
lunar tide, assuming that all other tidal waves remained stationary and monochromatic. Later, Forbes and Zhang (2012)
proposed that the lunar tide enhancement is a result of the
Pekeris resonance effect that is shifted towards the lunar tide
period M2 of 12.42 h due to changes in the mean zonal winds
and vertical temperature structure caused by the SSW. They
tested the proposed physical mechanism on satellite observations from SABER, CHAMP and GRACE and the steadystate Global Scale Wave Model (GSWM) for a case study and
the SSW in 2009. To separate the lunar tide from the semidiurnal SW2 tide, they used a window of 24 d to ensure sufficient frequency resolution and assumed monochromatic and
stationary tidal waves within the window. Later, Zhang and
Forbes (2014) claimed that the lunar tides seem to enhance
during nearly every SSW event arguing that the Pekeris resonance has a rather broad peak, and thus the resonance conditions are satisfied for all SSW events, although Forbes and
Zhang (2012) pointed out that a very specific thermal and dynamic structure is required to satisfy the resonance condition.
In the following, we investigate the phase variability of
the semidiurnal tide introducing a holographic analysis for
the SSW 2012/13 and discuss a potential connection to the
Pekeris resonance (Zhang and Forbes, 2014). Similar to other
holographic analysis, we use the phase differences between
a coherent reference wave and the observed wave field, that
propagated through the atmosphere, to infer small deviations
in frequency that are not resolvable by standard Fourier techniques. The day-to-day variability, obtained from the ASF,
indicates that the tidal phases are not stable with time and
show significant inter-day variability, which appears to be related to changes in the zonal wind in the middle atmosphere
driven by the polar vortex and planetary waves. Considering
that a time-dependent phase corresponds to a frequency shift,
it is possible to convert this temporal phase variability into a
period change and hence to estimate the spectral line shape
of the tide or to derive a holographic representation of the
temporal evolution on a day-to-day basis.
The hologram is derived considering that the tide can be
represented by a cosine wave with amplitude A (e.g., semidiurnal tide), a mean frequency w and a time-dependent phase
φ(t):
A(t) = A cos (wt + φ(t)) .
(3)
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G. Stober et al.: Tidal variability
Figure 12. Holographic reconstruction of the semidiurnal tidal
phase variability. The hologram shows the periods using a timevariable phase, which is equivalent to a frequency shift or change in
period. The white contour lines indicate the lunar tides M2 (12.42 h)
(solid line) and N2 (12.66 h) (dashed line). The lunar orbit as elevation angle (−90 to 90◦ ) for Juliusruh is plotted as a solid black
line.
Although the true functional form of the time-dependent
phase might be unknown, we can express this function as
a Taylor series at a certain point in time t:
φ(t) = φ0 +
dφ
· t + . . ..
dt
(4)
Truncating the Taylor series at the first order and inserting
them in Eq. (3) leads to
dφ
A(t) = A cos wt + φ0 +
·t .
(5)
dt
Rearranging the terms according to their time dependence
leads to
dφ
· t + φ0 .
(6)
A(t) = A cos w +
dt
It is now straightforward to numerically obtain the timedependent phase change dφ/dt using a central differences
approach in the complex domain.
In Fig. 12, we show a holographic reconstruction based on
the ASF decomposition of the semidiurnal tide. This technique only assumes monochromaticity within the adopted
window length (less than a day for the semidiurnal tide)
and thus captures non-stationary processes on an inter-day
basis. The hologram shows that during the SSW event in
2012/13, the phase behavior of the semidiurnal tide itself was
shifted to the period range that was expected for the lunar
tide M2 (solid white line) and N2 (dashed white line). Further, we overlaid the lunar orbit as elevation angle for the geographic location of Juliusruh to search for a potential connection of the semidiurnal phase variability and the moon
Atmos. Chem. Phys., 20, 11979–12010, 2020
Figure 13. The same as Fig. 12 but for the global tidal analysis of
the SW2.
position on the sky. The hologram for the global diagnostic
is shown in Fig. 13. The main differences in the holograms
between the local MR observations and the global tidal fields
from NAVGEM-HA are attributed to the decomposition of
the global fields into migrating and non-migrating tides. As
shown in Figs. B1–B4, there is an excitation of the nonmigrating tides (SW1 and SW3), which leads to the differences in the holographic reconstruction. The local diagnostic
shows the superposition of all tidal components. However,
the global diagnostic also indicates the frequency shifts of the
SW2 tide to periods that can match the predicted Pekeris lunar tide resonances. However, as indicated by the white lines,
these phase shifts happen frequently during a winter season
and are neither correlated with the lunar orbit nor accompanied by a tide enhancement. The effect of the SSW is visible in both holograms up to 10 d after the onset of the SSW,
which is also the time delay corresponding to the amplification of the semidiurnal tide after the SSW.
Moreover, Forbes and Zhang (2012) reported a delay of
5–7 d between the occurrence of the lunar tide amplification and the central day of the SSW event. This delay of approximately 5–7 d is consistent with the holographic analysis, which also shows that the frequency/period shift towards
the lunar tide frequency/period (M2 and N2) occurs after the
SSW event (central day), at the beginning of the formation
of an elevated stratopause or when the polar vortex begins to
restore, however, well before the semidiurnal tide enhancement. This time span also corresponds to the response time
of the semidiurnal tide to a transient forcing, which was estimated to be between 6 and 10 d (Vial et al., 1991) for comparisons to steady-state models.
Many recent studies have investigated lunar tides with
window lengths that are long enough to ensure an unambiguous frequency resolution to separate the lunar tide from the
semidiurnal tide, which requires at least 21 d or more (e.g.,
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Forbes and Zhang, 2012; Chau et al., 2015; Conte et al.,
2017; He et al., 2018; Siddiqui et al., 2018, and reference
therein). The ASF analysis indicates that there is a considerable inter-day tidal variability in amplitude and phase, which
poses a challenge to the signal processing. Such intermittent
behavior suggests that long windows (longer than even a day)
might lead to spurious results and do not allow a separation
of the different waves from each other. The zonal wind reversal and accompanied cooling at the MLT during a SSW last
only for a few days (much shorter than the typical window
length used for the lunar tides) and cause significant changes
in the zonal mean wind at midlatitudes and polar latitudes
altering the propagation conditions for the tides. As a consequence, such a long window would not allow one to capture
SSW effects, which themselves cause changes in the semidiurnal tide. Thus, if one does not notice that an SSW occurred,
one cannot know whether the 12.42 h tide is lunar or a semidiurnal tide that was altered by the SSW.
These shortcomings are also mentioned and discussed in
(Forbes and Zhang, 2012; Zhang and Forbes, 2014). They
fitted the lunar tide, for instance, on the residuals of SABER
measurements after removing the semidiurnal tide by a 12 d
running mean, which still is too long given the huge phase
variability of the tide. The caveats of the steady-state model
GSWM are also discussed in Forbes and Zhang (2012). In
particular, the steady-state assumption seems to be not fully
met during an SSW, recalling the results from Vial et al.
(1991), as the whole event lasts only 3–4 d at the MLT.
The next aspect we did investigate is a potential correlation between the phase shifts from the holographic analysis
and the lunar orbit. Thus, the lunar azimuth, elevation and
lunar distance were evaluated, regardless of whether an SSW
occurred or not. Holographic analysis of the S2 phase shifts
frequently shows periods close to the M2 tide, indicated by
the white contour lines, but no obvious correlations to the lunar position or the other orbital parameters were found. This
behavior is also reproduced for the global hologram.
Finally, we examined the properties of the semidiurnal tide
with respect to the frequency and vertical wavelength at the
MLT before and during the SSW as well as during the amplitude enhancement after the SSW. This was mainly to underline that we can derive all wave properties of the SW2 tide
combining local and global diagnostics, which are the zonal
wave number, the vertical wave number and the frequency
on a inter-day basis. The vertical wavelength of the semidiurnal tide was about 50–60 km before the SSW at altitudes between 74 and 100 km (see Fig. C1). The same vertical wavelength was observed during the tide enhancement, whereas
during the SSW event the vertical wavelength suddenly increased to 150–600 km at Juliusruh and then decreased just
as suddenly after the wind reversal but before the tide enhancement. The global zonal mean diagnostic exhibits similar vertical wavelengths before and after the SSW, but the
sudden response in vertical wavelength due to the SSW was
less pronounced. However, the hologram also shows that the
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mean period of the S2/SW2 tide before the SSW and during
the tide enhancement is centered around 12.0 h. This does
not indicate a lunar tide enhancement due to the Pekeris resonance effect, which would require a 12.42 h period. Only
during the SSW event itself, there is an increase in the vertical wavelength and the shift of the period towards the M2
period visible, pointing to a lunar tide signature that could be
interpreted as Pekeris resonance. However, this needs to be
investigated with comprehensive models to account for the
complex dynamics associated with a SSW.
Previous analysis of the lunar tide facilitating multi-year
observations from meteor radars by Sandford et al. (2006)
showed that the signal is much weaker compared to the total S2 tide. Their spectral analysis also confirms that tides
show some spectral broadening. Such a line broadening is
also found in our holographic analysis.
Figure 14 shows the histograms of the frequency distributions obtained from the holograms. Figure 14a–b are computed from the meteor radar observations at Juliusruh (zonal
and meridional) and Fig. 14c–d from the global diagnostic
using NAVGEM-HA at the same latitude (zonal and meridional, respectively). The spectral line shape seems to agree
from their general morphology, in particular, the line width.
The dashed vertical line denotes the period of the lunar tide
M2, which lies in the natural line width of the SW2 tide.
However, the peak of the spectral line obtained from the meteor radar observations at Juliusruh shows two side peaks
that can be associated with the vortex splitting event and
are related to the planetary wave activity during the winter
of 2012/13. Due to instrumental effects, the number of measurements is not equally distributed over the winter season,
leading to an apparent double peak structure (this was validated looking at other meteor radar data that are not used in
this study). The same plot obtained from NAVGEM-HA at
the Juliusruh location shows a fully symmetric spectral line
shape similar to the global diagnostic. During the vortex displacement event in the winter season of 2009/10, the spectral
line at Juliusruh was entirely symmetric similar to the global
diagnostic for both cases. The global diagnostic is not prone
to this type of effect as all longitudes are included in the analysis, and hence these particularities average out. In the case
of lunar tide amplification, the global diagnostic should reveal a shoulder at the M2 period or asymmetry around the
dashed vertical line, which seems to be not present.
Finally, and similar to previous studies (Fuller-Rowell
et al., 2010, 2016), we attribute the day-to-day variability
of the semidiurnal tidal amplitudes and phases to changes
of the zonal winds in the middle atmosphere altering the
vertical propagation conditions. Although atmospheric tides
are global-scale waves, their vertical propagation depends on
the regional meteorological situation. As a consequence, the
observed period or phase at the MLT can be altered. Due
to the long horizontal wavelength of the semidiurnal tide, a
change in the wind pattern in the middle atmosphere manifests as changes in phase for a single station measurement
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Figure 14. Histograms for the zonal and meridional frequency shift due to a temporal variable phase derived from the holograms from
December 2012 to March 2013. Panels (a, b) show the local meteor radar observations at Juliusruh and panels (c, d) the global diagnostic
inferred from NAVGEM-HA.
accompanied by a change of the vertical wavelength of the
tide. The holographic reconstruction shows that the day-today variability of phase is equivalent to a Doppler shifting
of the intrinsic tidal frequency, which causes the line broadening at the MLT. Furthermore, an SSW is also associated
with a large exchange of air masses between midlatitudes
and polar latitudes, which leads to a significant enhancement of the ozone volume mixing ratio inside the polar cap
(Schranz et al., 2020) and thus provides a potential source to
increase the tidal forcing of the semidiurnal tide. Further, this
strong meridional coupling also provides a sufficient strong
response to explain the low-latitude response to the SSW.
This aspect needs to be researched in more detail but provides a reasonable approach to explain the semidiurnal tide
enhancement after the SSW and the observed low-latitude
responses (Fejer et al., 2010).
6 Conclusions
In this study, we cross-validate NAVGEM-HA meteorological analyses with ground-based meteor radar and lidar observations at midlatitudes and high latitudes. For the validation,
we performed a detailed analysis of mean winds and temperatures and atmospheric tides using a recently developed
tool called adaptive spectral filter (ASF), which is designed
to capture the intermittent tidal behavior and provide vector
information for mean winds and tides for climatologies. We
present a comparison of mean winds, temperatures and the
semidiurnal wind tide and its phase behavior and a detailed
discussion of the day-to-day variability of the semidiurnal
tide during two SSW events in 2009/10 and 2012/13 combining global and local diagnostics. We discussed our results
in the context of previous studies, in particular, on the lunar
tide amplification during SSWs, and have outlined potential
issues due to the day-to-day semidiurnal tidal variability.
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The agreement between MR/lidar climatologies and
NAVGEM-HA analysis data is remarkably good compared to
the seasonal wind and temperature pattern of comprehensive
models. NAVGEM-HA tends to show slightly higher wind
speeds and temperatures compared to the ground-based instruments. NAVGEM-HA reproduces the seasonal asymmetry of the zonal wind at midlatitudes and high latitudes. The
temperature and wind fields in NAVGEM-HA are realistic
compared to ground-based sensors up to an altitude of 90 km
(geometric altitude). However, our comparison also confirms
that the availability of satellites observations for the data
assimilation in NAVGEM-HA has an impact on the overall agreement. Further, the meteorological analysis reflects
the seasonal phase behavior of the semidiurnal tide, which
is constantly changing. These continuous phase changes are
important and need to be considered when analyzing satellite
observations or spectral analysis using long windows.
NAVGEM-HA reflects the day-to-day variability of the
wind and semidiurnal tide amplitude and phase behavior during SSW events. The combination of NAVGEM-HA meteorological analysis data and ground-based observations allowed us to develop new diagnostics to retrieve atmospheric
information and to investigate physical processes. The crossvalidation suggests that the global fields of NAVGEM-HA
provide a realistic boundary to nudge other GCMs coupling
the middle atmosphere to the upper atmosphere. In particular,
the good agreement of the tidal phases is an essential quality benchmark for the lower forcing of the thermosphere and
ionosphere through atmospheric tides. The day-to-day tidal
variability (amplitude and phase) of the semidiurnal tide is
associated with changes in the wind pattern in the middle atmosphere altering the vertical propagation conditions of the
tide. This is in agreement with previous studies by FullerRowell et al. (2010, 2016) and Jin et al. (2012).
Further, we did investigate a potential lunar tide amplification through the Pekeris resonance effect as proposed by
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Forbes and Zhang (2012) and Zhang and Forbes (2014). The
ASF and holographic analysis permit to determine the different phases of the SSW in 2012/13 and the tidal response
in much more detail with respect to the timing. The tidal enhancement after the SSW, which was in many previous studies termed to be a lunar tidal enhancement, shows essentially
a period around 12.0 h (see holograms) and has the same vertical wavelength of about 50–60 km as the semidiurnal tide
before the SSW. The global diagnostic also confirms a wave
number 2 structure. Further, there are no signs of a coupling
and phase relation to the lunar orbit during this time.
However, during the SSW, there is a phase shift of the
semidiurnal tide towards the 12.42 h period, and the dynamical and thermal structure could be suitable to shift the Pekeris
resonance towards a period of 12.42 h as well, as outlined in
Forbes and Zhang (2012) and Zhang and Forbes (2014). The
increased vertical wavelength of about 150–400 km and the
time span of 3–5 d during this phase of the SSW might be
the result of the resonance and may indicate the presence of
a lunar tidal mode, but this needs to be confirmed by tidal
modeling and is beyond the discussion herein. However, the
amplitude of this tidal mode is still much smaller than a typical semidiurnal tide but might be larger than the average lunar amplitude of about 1–4 m s−1 (Sandford et al., 2006).
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Holographic analyses provide a new method to investigate the frequency behavior using short windows in the time
domain while keeping a localized measurement of the frequency resolution. Further, we were able to provide a quantitative spectral measurement of the spectral variability for the
semidiurnal tide, which pointed out that the lunar tide (M2)
lies well within the spectral line shape. This now has some
implications for epoch analysis of the lunar tide from local
observations. The holograms show that there are frequently
shifts of the semidiurnal tide towards the M2 (12.42 h) that
are disconnected from the lunar orbit, which means the lunar
tide can hardly be inferred from such an analysis without additional information, for instance, the vertical wavelength of
the lunar tide.
In this work, we have demonstrated the value of meteorological analysis data from NAVGEM-HA for investigating
the day-to-day variability of tides in a global context and for
local meteor radar observations. Such data sets are essential for nudging thermospheric and ionospheric models for
space weather applications. Further, we emphasized that new
analysis techniques are required to infer the tidal variability
or to separate lunar tides from the semidiurnal tide. Holographic reconstructions and spectral line models for atmospheric tides might be part of such a solution.
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Appendix A: Comparison of ASF with and without
vertical regularization
Here, we provide two examples comparing a tidal amplitude
fit for the zonal and meridional components using the 1-D
ASF and the 2-D ASF with vertical regularization to demonstrate how a potential contamination of gravity waves with
short vertical wavelengths is reduced. The time difference
between the two left panels and the two right panels is 6 h.
Figure A1. Here, we show observations from 1 February 2010 and the Juliusruh meteor radar. The dashed lines indicate the tidal solution by
applying only temporal fitting and the solid lines show the ASF solution with vertical regularization for the diurnal and semidiurnal tides.
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Appendix B: Tidal components from global
NAVGEM-HA analyzed winds
In addition to the semidiurnal tide, which is locally observed
from the meteor radar as well as from NAVGEM analyzed
winds, here we provide the results for the westward- and
eastward-propagating non-migrating semidiurnal tidal components (SW1, SW3, SE1, SE2, SE3) as well as for the stationary semidiurnal tide (S0) during the winters of 2009/10
and 2012/13 for the stations in Andenes and Juliusruh from
the global fields of NAVGEM-HA.
Figure B1. Non-migrating tides derived from global NAVGEM-HA winds above Andenes during the winter of 2009/10 for SW1 and SW3
(two upper panels), SE1 and SE2 (middle panels), and SE3 and S0 (two lower panels) tidal components.
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Figure B2. The same as Fig. 13 but for the winter of 2012/13.
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Figure B3. The same as Fig. 13 but above Juliusruh and for the winter of 2009/10.
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Figure B4. The same as Fig. 13 but above Juliusruh and for the winter of 2012/13.
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Appendix C: Vertical wavelength from MR and
NAVGEM-HA
Vertical wavelengths were derived from the vertical profiles
of the phases of the semidiurnal tidal fit for every day. In
the case of the meteor radar, the fit is performed at altitudes
between 74 and 100 km. The NAVGEM-HA data were analyzed in the altitude range from 70 to 90 km. However, as
we estimate the vertical wavelengths from a rather thin atmospheric layer at the MLT, the uncertainty of the obtained
wavelengths scales with the wavelength itself. There is a tendency for the uncertainties to be larger for wavelengths beyond 250 km.
Figure C1. Time series of the vertical wavelength of the semidiurnal tide at Juliusruh and Andenes. The two upper panels (a, b) denote the
meteor radar observations for both locations. The lower panels (c, d) are obtained from NAVGEM-HA.
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Data availability. The meteor radar can be obtained from Gunter
Stober upon request from the Leibniz Institute for Atmospheric
Physics. The NAVGEM-HA data used in this study can be obtained
from https://map.nrl.navy.mil/map/pub/nrl/navgem/iap (last access:
September 2020, U.S. Naval Research Laboratory, 2020). The lidar
observations are available upon request from Kathrin Baumgarten.
Author contributions. The manuscript was edited by and discussed
with all authors. The conceptual idea of the manuscript was developed by GS, KB and JM. The meteor radar data analysis was
performed by GS. KB partly computed the lidar temperatures and
analyzed both lidar data sets. PB contributed with the CMOR radar
data, read and edited the manuscript and helped with the discussions. JC provided support in the data analysis and helped discuss
the results.
Competing interests. The authors declare that they have no conflict
of interest.
Acknowledgements. We gratefully acknowledge Michael Gerding,
Michael Priester and Torsten Köpnick for the maintenance and operation of the lidar systems at IAP, as well as all students for helping
in lidar operation. We appreciate the support from Josef Höffner in
computing the resonance lidar temperatures. We acknowledge the
technical support of the IAP technicians in the operation of the meteor radars.
Financial support. This work is supported by the University of
Bern Institute of Applied Physics and the Oeschger Center for
Climate Change Research. The data analysis is supported by the
ARISE2/ARISE-IA project (available at: http://www.arise-project.
eu, last access: October 2020) and received funding from the European Community’s Horizon 2020 programme (grant no. 653980).
Kathrin Baumgarten is supported by the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) under project
LU1174/8-1 (PACOG) of the research unit FOR1898 within the Research Unit MS-GWaves. The work at the Naval Research Laboratory was supported by the chief of naval research and by a grant of
computer time from the High Performance Computing Modernization Program.
Review statement. This paper was edited by William Ward and reviewed by three anonymous referees.
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