ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-36-1597-2018Comparison of gravity wave propagation directions observed by mesospheric
airglow imaging at three different latitudes using the
M-transformComparison of gravity wave propagation directionsPerwitasariSeptisepti.perwitasari@gmail.comNakamuraTakujiKogureMasaruTomikawaYoshihiroEjiriMitsumu K.ShiokawaKazuoNational Institute of Polar Research, Tokyo, 190-8518, JapanDepartment of Polar Science, SOKENDAI (The Graduate University for
Advanced Studies), Tokyo, 190-8518, JapanNational Institute of Aeronautics and Space (LAPAN) of Indonesia,
Bandung, 40173, IndonesiaInstitute for Space-Earth Environmental Research, Nagoya University,
Nagoya, 464-8601, JapanSepti Perwitasari (septi.perwitasari@gmail.com)30November20183661597160518September201820September20187November201812November2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://angeo.copernicus.org/articles/36/1597/2018/angeo-36-1597-2018.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/36/1597/2018/angeo-36-1597-2018.pdf
We developed user-friendly software based on Matsuda et al.'s (2014) 3D-FFT
method (Matsuda-transform, M-transform) for airglow imaging data analysis as
a function of Interactive Data Language (IDL). Users can customize the range
of wave parameters to process when executing the program. The input for this
function is a 3-D array of a time series of a 2-D airglow image in
geographical coordinates. We applied this new function to mesospheric airglow
imaging data with slightly different observation parameters obtained for the
period of April–May at three different latitudes: Syowa Station, the
Antarctic (69∘ S, 40∘ E); Shigaraki, Japan (35∘ N,
136∘ E); and Tomohon, Indonesia (1∘ N, 122∘ E).
The day-to-day variation of the phase velocity spectrum at the Syowa Station
is smaller and the propagation direction is mainly westward. In Shigaraki,
the day-to-day variation of the horizontal propagation direction is larger
than that at the Syowa Station; the variation in Tomohon is even larger. In
Tomohon, the variation of the nightly power spectrum magnitude is remarkable,
which indicates the intermittency of atmospheric gravity waves (AGWs). The
average nightly spectrum obtained from April–May shows that the dominant
propagation is westward with a phase speed <50 m s-1 at the Syowa Station and
east-southeastward with a phase speed of up to ∼80 m s-1 in
Shigaraki. The day-to-day variation in Tomohon is too strong to discuss
average characteristics; however, a phase speed of up to ∼100 m s-1 and faster is observed. The corresponding background wind
profiles derived from MERRA-2 indicate that wind filtering plays a
significant role in filtering out waves that propagate eastward at the Syowa
Station. On the other hand, the background wind is not strong enough to
filter out relatively high-speed AGWs in Shigaraki and Tomohon and the
dominant propagation direction is likely related to the
distribution and characteristics of the source region, at least in April and May.
Introduction
Atmospheric gravity waves (AGWs) or buoyancy waves are oscillations caused by
the vertical displacement of an air parcel, which is restored to its initial
position by buoyancy. These waves, which primarily originate in the lower
atmosphere, propagate into the upper mesosphere and lower thermosphere (e.g.,
Lindzen, 1981; Matsuno, 1982; Fritts, 1984; Fritts and Alexander, 2003). The
study of AGWs is important because these waves transport energy and momentum
vertically and drive the general circulation up to ∼100 km. The AGWs
greatly affect the global temperature structure through general circulation.
Therefore, improved understanding of AGWs characteristics and their
implementation in numerical models, such as climate models, is very
important to improve such models and increase their precision. However,
quantitative observational studies are progressing slowly, partly because of
the difficulties related to investigating global AGW characteristics. One
difficulty is that AGWs cover a very broad spectrum (the wave periods range
from minutes to hours and spatial scales extend up to thousands of
kilometers). Although satellite observations can provide a global view of AGW
phenomena, they are limited to the portion of AGWs with a large scale because
of the low horizontal and/or vertical resolutions of the instruments
(Alexander, 1998; Wright et al., 2016). Therefore, studies using ground-based
measurements with high horizontal and/or vertical resolutions are essential
to reveal the global characteristics of AGWs.
Among various ground-based observations, airglow-imaging observations have
been proven to be very effective in determining both the energy and
propagation characteristics. In the last few decades, airglow imagers have
been deployed at various latitudes to study AGWs in equatorial, midlatitude,
and polar regions (e.g., Shiokawa et al., 2009; Suzuki et al., 2007; Matsuda
et al., 2014, 2017). Such long-term observations provide a huge amount of
data. However, the lack of sophisticated analysis methods prevents
quantitative studies based on complete worldwide datasets that have been
collected with great effort.
A new analysis algorithm has been developed by the National Institute of
Polar Research (NIPR) group to obtain the power spectrum in the horizontal
phase velocity domain from long-series data of airglow imagers, as shown in
Matsuda et al. (2014; Matsuda-transform, here M-transform). The M-transform method
transforms airglow-intensity image data to a power spectrum in the horizontal
phase velocity domain. This method can handle a huge amount of data.
Therefore, the time consumption and manpower required for the analysis of
such a huge amount of airglow data are reduced. This method has been
successfully applied to Antarctic Gravity Wave Instrument Network (ANGWIN)
imagers that are used to study the characteristics of mesospheric AGWs over
Antarctica, as reported by Matsuda et al. (2017). Takeo et al. (2017) and
Tsuchiya et al. (2018) applied this method to 16-year airglow imaging data
from Shigaraki (35∘ N, 136∘ E) and Rikubetsu
(44∘ N, 144∘ E), Japan, to study the horizontal phase speed
and propagation direction at midlatitudes.
Despite the high success of this method's application, several subroutines
must be separately executed in the original program, which is not
user-friendly. Therefore, we developed a simple user-friendly function based
on Matsuda et al.'s (2014) method that can be handled by users with different
backgrounds and programming skills. We encourage AGW research groups to use
the program for the analysis of their data and produce results in a uniform
format (power spectrum in the phase velocity domain). This will make it
easier to compare the AGW phase velocities and energy distributions of
different locations, that is, of different latitudes and longitudes. This
paper is organized as follows. Section 2 describes the M-transform function
and its use. Section 3 shows the comparison of phase speed spectra obtained
with the M-transform application for different airglow datasets with
different observation parameters recorded at different latitudes: Syowa
Station (69∘ S, 40∘ E), Shigaraki (35∘ N,
136∘ E), and Tomohon Observatory (1∘ N, 122∘ E).
The conclusions of this paper are provided in Sect. 4.
M-Transform function
The M-transform function is a 3-D FFT function using Interactive Data
Language (IDL; http://www.exelisvis.com/ProductsServices/IDL.aspx, last
access: 15 September 2018), which is used to
analyze airglow imaging data based on the method developed by Matsuda et
al. (2014). This method requires time series of airglow images in 3-D array
format, which have been preprocessed to have fixed intervals of image pixels
(dx, dy) and time (dt). These preprocessed
images should be obtained through common airglow image preprocessing, that
is, (1) star removal, (2) correction of the Van Rijhin effect if necessary,
and (3) projection onto a geographical coordinate system in equal distances
in latitudinal and longitudinal directions (e.g., Kubota et al., 2001; Suzuki
et al., 2007). It is also recommended to normalize the airglow intensity
values to compare the power spectral values of different datasets. For this
purpose, ((I-I‾)/I‾), where I is the image intensity
of each pixel, should be used in the input array. Our M-transform code
applies 2-D prewhitening to the images to reduce the contamination of higher
wavenumbers with lower-wavenumber peaks of the red AGW spectrum. It also
applies the 2-D Hanning window to reduce the harmonics of the window function
in the horizontal direction (Coble et al., 1998). Matsuda et al.'s (2014) new
method transforms the power spectrum density (PSD) in the wave number domain
(k, l, ω) to the phase velocity domain (νx, νy,
ω) based on the following equations:
vx=ωk/(k2+l2),vy=ωl/(k2+l2),
where vx and vy are the orthogonal projections of the phase
velocity onto zonal and meridional axes, respectively ((νx,νy)=c(sinφ,cosφ), where c and
φ are the phase speed and azimuth (east from north) of the phase
velocity). Note that νx and νy are not the phase velocities in
the zonal or meridional directions or cross sections; ω is the
frequency; and k and l are the zonal and meridional wavenumbers,
respectively. Finally, the phase velocity spectrum is integrated over the
frequency and results in a 2-D phase velocity spectrum.
Description of M-transform function on IDL.
Program description NameMatsuda_transformPurposeCalculate horizontal phase velocity spectra from airglow intensity image data using 3-D FFTCalling sequenceResult=Matsuda_transform(Img)InputsImg: time series of 2-D airglow data in geographic coordinates (x, y, t)Input keywords(a) dx, dy, dt: image resolution in x (m), y (m), and time (s)(b) LH_min, LH_max: minimum and maximum horizontal wavelength (m) to be processed(c) T_min, T_max: minimum and maximum wave period (s) to be processed(d) Vp_min, Vp_max: minimum and maximum horizontal phase speed (m s-1) to be calculated(e) zpx, zpy, zpt: dimension of the zero-padded image size in x, y, and t to improve the intervals of k, l, and ω(f) min1, max1: minimum and maximum phase velocity spectra to be plotted(g) Interpolation: select interpolation methodOutputs2-D phase velocity spectra (vx, vy)RemarksRequires equal sampling interval time resolution (dt)
The original program developed by Matsuda et al. (2014) consisted of several
subroutines, which were used to calculate the 3-D FFT, create an
interpolation table, perform the interpolation, and separately plot the
results. The users had to set the wave parameters in each subroutine and had
to run it one by one, making the process complicated and inefficient.
Furthermore, once the users failed to compile one of the subroutines, the
program failed to run and the users had to check the subroutine one by one
again. Therefore, a simple, hassle-free one-line-command software with
adjustable input keywords is necessary to efficiently apply this method.
Table 1 shows the description of the M-transform function and Fig. 1 shows
how to run the program. To run this function, the user can simply use the
calling sequence “Result=Matsuda_transform(Img)”, where “Img” is the
3-D array of the preprocessed images in geographic coordinates (x, y,
t). The image resolutions (dx, dy, dt),
wave parameters (horizontal wavelength, LH), wave period (T), phase speed
(Vp), and size of zero padding (zpx, zpy, zpt) can be adjusted by
setting input parameter keywords. The default image resolution is 1 km in
both zonal (dx) and meridional (dy) directions. The
default image interval time (dt) is 60 s. The default minimum and
maximum values of the wave parameters are 5≤LH≤100 km, 8≤T≤60 min, and 0≤Vp≤150 m s-1. The default
output of this program is a 2-D phase velocity spectrum. The default
interpolation method of this new function is the Delaunay triangulation
method (e.g., Dwyer, 1987; Su and Scot Drysdale, 1997). One restriction of
this program is that it requires an equal time interval (dt). This
may not be the case for practical observations, where filter rotations or
background (or dark) images for the calibration are obtained from the
observation sequence. In that case, users have to interpolate the image to
obtain a constant dt interval before applying this function. More
details on the function development are provided elsewhere.
Flow chart showing the input, how to run the program, and the output
format.
Figure 2 shows an example of the use of the M-transform function. The input
consists of airglow data over the Syowa Station obtained on 20 September 2011
(the same dataset as used in Matsuda et al., 2014), which have the following
dimensions: x=400 km, y=400 km, t=21 min (×3 min).
Because the image time resolution was 3 min, the dt input keyword
was set to dt=180 s. The default values were used for the other
wave parameters. The IDL console shows the input, calling sequence, total
calculation time, and output. The output is a 2-D phase velocity spectrum
(right panel). The horizontal axis is vx, the vertical axis is vy,
and the color bar shows the PSD on a logarithmic scale. The phase velocity
spectrum shows dominant propagation in the southwestward direction, which
agrees with the wave propagation observed in the airglow preprocessed image
movie in the Supplement as that reported by Matsuda et al. (2014). The total
calculation time of the M-transform function for 21 images with 400×400 pixels was ∼1.4 min using a personal computer. The calculation
was performed on a MacBook Pro with a dual core 2.8 GHz Intel Core i7
processor with 4 MB cache size and 16 GB memory, while the program was
single-threaded.
Summary of airglow imagers used in this study.
Station name (country)Syowa (Antarctic)Shigaraki (Japan)Tomohon (Indonesia)Location69∘ S, 40∘ E35∘ N, 136∘ E1∘ N, 122∘ EInstitutionNational Institute of Polar Research (NIPR)Nagoya UniversityNational Institute of Aeronautics and Space (LAPAN)Airglow emissionNa (589.6 nm)OI (557.7 nm)OI (557.7 nm)Sampling interval (dt) (min)15.52.5Image size (km)400×400400×400400×400Minimum wave period (T_min) (min)16.516.516.5Maximum wave period (T_max) (min)606060
Example of how to use the Matsuda-transform (M-transform) program,
showing the input, calling sequence, total calculation time, and output as
2-D phase velocity spectrum.
Comparison of the phase velocity spectra obtained with the M-transform
function for different airglow datasets at three different latitudes
We applied this new M-transform function to various airglow datasets obtained
at three different latitudes. Table 2 shows the summary of each airglow
imager used in this analysis. Syowa Station (69∘ S, 40∘ E)
data represent airglow data in the polar region, while Shigaraki
(35∘ N, 136∘ E) and Tomohon (1∘ N,
122∘ E) data represent the midlatitude and equatorial regions,
respectively. We used the Na (589.6 nm) airglow emission obtained at the
Syowa Station and OI (557.7 nm) airglow emission recorded in Shigaraki and Tomohon.
Day-to-day variation of 2-D phase velocity spectra for
April–May 2013 at the Syowa Station (a), in
Shigaraki (2011) (b), and in Tomohon (2016) (c).
Panel (c) is the same as that for 5 May 2016, but with a different
color bar level to better visualize the dominant wave propagation direction.
We observed 9 clear-sky nights at the Syowa Station from April to May 2013,
10 clear-sky nights in Shigaraki from April to May 2011, and 5 clear-sky
nights in Tomohon from April to May 2016. The Syowa data were the same dataset
as that reported by Matsuda et al. (2017). The image size for each
observation site was 400×400 km and the sampling intervals
(dt) were 1 min (Syowa), 5.5 min (Shigaraki), and 2.5 min
(Tomohon). The different sampling intervals limit the maximum phase velocity
to be analyzed; that at Shigaraki was the smallest. To avoid an aliasing
effect on the 2-D phase velocity spectrum, we selected the period minimum
(T_min) to be at least 2 times larger than the
sampling interval (2×dt). In this study we set
T_min to 3×dt. Because the
dt of Shigaraki data was 5.5 min, we set the
T_min to 16.5 min for all datasets to obtain the same
frequency range. This setting can be easily altered by changing the input
keyword (T_min) when running the function. The defaults
were used for the other wave parameters.
(a) Average day-to-day variation of the 2-D phase velocity
spectrum of AGWs observed at Syowa, in Shigaraki, and in Tomohon.
(b) Average zonal wind profiles (positive: eastward) and
(c) average meridional wind profiles (positive: northward) of GWs
observed during clear nights from MERRA-2 data.
Figure 3 shows the day-to-day variation of 2-D phase velocity spectrum
results for (a) Syowa Station, (b) Shigaraki, and (c) Tomohon. The top and
left represent the north and east respectively. The day-to-day plot at Syowa
Station shows a lack of eastward gravity wave (GW) propagation and a dominant
westward propagation, which is probably due to the filtering effect by the
eastward polar night jet, as described in Matsuda et al. (2014). However, the
azimuth direction with large power spectral density was not always the same;
a much narrower azimuth distribution was observed on 13 and 14 May. This
suggests that the distribution of the GW sources was limited on these days
and changed from day to day. On the contrary, the 2-D phase velocity spectrum
for Shigaraki shows a lack of westward propagation and dominant eastward and
southward propagations. The strong spectrum based on Shigaraki data has a
much larger day-to-day azimuth variation than that for Syowa, suggesting that
the distribution of the wave source region varied more in Shigaraki, at least
in this season's April and May. The day-to-day variation of the propagation
direction was even stronger in Tomohon. At the same time, a significant
day-to-day variation of the magnitude of the power spectrum was observed. The
power was the weakest on 13 April; it was much stronger on 5 May and is
overscaled in the plot. The last panel in Fig. 3c was plotted with the
maximum color level; it is ∼30 times larger than the others. Such a
significant day-to-day variation indicates the intermittency of the GWs.
Figure 4a shows the average nightly spectrum at each observation site plotted
on the world map. The average phase velocity spectrum at the Syowa Station
shows a distinct westward propagation with a phase speed below
50 m s-1. In Shigaraki, AGWs propagate dominantly in the
east-southeastward direction and reach phase speeds up to ∼80 m s-1. The AGWs in Tomohon show a preferred propagation direction,
that is, they are moving southeastward with phase speeds of up to ∼100 m s-1. It should be noted that the plot for Tomohon is highly
affected by a single day, 5 May. This also indicates the intermittency of
GWs, which suggests that the net momentum transportation highly depends on
the very strong GWs with smaller occurrence frequency.
One can discuss the AGW propagation by comparing the 2-D phase velocity
spectrum and background conditions along the propagation path. Figure 4b and
c show the zonal and meridional wind profiles, respectively, obtained from
Modern-Era Retrospective Analysis for Research and Applications (MERRA-2;
Gelaro et al., 2017) for each observation site. The profiles were averaged
over the clear nights of the observed AGWs. The zonal wind over the Syowa
Station, which was averaged over nine clear-sky nights, shows strong eastward
wind up to ∼50 m s-1 around ∼50 km, which could filter
out the waves propagating eastward. A similar conclusion was reported by
Matsuda et al. (2017), who applied a GW blocking diagram (Taylor et al.,
1993; Tomikawa, 2015) by using horizontal wind data from MERRA and the
medium-frequency (MF) radar to discuss the preferred wave propagation
direction observed in the phase velocity spectrum. They concluded that
eastward-propagating AGWs are restricted to propagating up to the mesopause
due to critical-level filtering.
In contrast to the strong zonal wind at the Syowa Station, the average zonal
wind profile in Shigaraki over 10 clear nights shows relatively weak
westward wind with a speed of up to ∼30 m s-1 at ∼50 km
altitude. Previous studies of the seasonal directionality of AGWs in
Shigaraki showed that east–west propagation anisotropy is usually caused by
wind filtering of the mesospheric jet (e.g., Nakamura et al., 1999; Ejiri et
al., 2003; Takeo et al., 2017). However, the westward wind in our current
case for April–May 2011 is not stronger than 30 m s-1 above the
stratosphere; it is not strong enough to filter out all GWs with westward
propagation. The average tropopause eastward jet is as strong as
60 m s-1. If the GW source is associated with such an eastward jet
structure, the horizontal phase velocity distribution of generated GWs should
shift eastward. This could also be the reason for the lack of
westward-propagating AGWs, especially those with higher phase velocities such
as over 40 m s-1.
The average zonal wind in Tomohon is small (<20 m s-1) and likely
has a limited impact on the much faster AGW phase speed (∼100 m s-1). However, Fig. 4a shows that the GWs over Tomohon have a
dominant southeastward propagation. As already discussed, this distribution
is affected by the spectrum of a single day and should be highly affected by
the location of the strong wave source on that day. Haffke et al. (2016)
reported that the Intertropical Convergence Zone (ITCZ) is located above the
Equator between March and April and starts to move north of the Equator in
May, which could explain the dominant southward propagation of AGWs observed
on 5 May 2016 (Fig. 3c). The scenario in which the distribution of the source
location has a more significant effect on the AGW propagation direction than
the background wind in the equatorial region agrees well with results
reported by Nakamura et al. (2003). They reported AGW characteristics for
Tanjungsari, Indonesia (107.9∘ E, 6.9∘ S) and based on the
analysis of Geostationary Meteorological Satellite (GMS) data they concluded
that the distribution of tropospheric clouds that are located mainly in the
opposite direction of the wave propagation plays a more significant role than
the relatively weak background wind. The meridional wind at each observation
site has a weak velocity (<5 m s-1) and likely has almost no impact
on the wave propagation direction.
Conclusion
We developed a user-friendly IDL function based on Matsuda et al.'s (2014)
3-D FFT method for airglow data analysis. This function efficiently deals
with extensive amounts of imaging data obtained in different years and at
various observation sites without bias caused by the analysis by different
research groups and treats the dynamical and physical effect of AGWs by precisely
reflecting the amplitude, area, and lifetime of each AGW event with a
reasonable execution time. It can also be applied for airglow data with
different observation parameters such as the image sampling interval. This
new function was applied to airglow imaging data obtained from April–May of
selected years at three different latitudes: Syowa Station (69∘ S,
40∘ E), Shigaraki (35∘ N, 136∘ E), and Tomohon
(1∘ N, 122∘ E). By comparing the 2-D phase velocity spectra
of each site, we found that the day-to-day variation in Shigaraki is larger
than that at the Syowa Station. The day-to-day variation in Tomohon has an
even greater variability than the other two sites, which suggests that the
distribution of the source region in Shigaraki and Tomohon is likely more
variable than at the Syowa Station. We also found that the day-to-day
variation in Tomohon includes a significant variation of the phase spectrum
magnitude, which indicates the intermittency of AGWs. The average nightly
spectrum shows a dominant westward wave with a phase speed <50 m s-1
at the Syowa Station and an east-southeastward propagation with a phase speed
of up to <80 m s-1 in Shigaraki. Southeastward propagation was
observed in Tomohon; however, this result is highly affected by a single day
with an extremely strong power spectrum. The phase speed in Tomohon reaches
up to ∼100 m s-1, which is larger than that at the other two
sites. The comparison of the 2-D phase velocity spectra with background wind
profiles derived from MERRA-2 data revealed that wind filtering plays a more
significant role in filtering out eastward-propagating waves at the Syowa
Station. On the other hand, the background winds in Shigaraki and Tomohon are
not strong enough to filter out AGWs that propagate in the opposite direction
of the observed wave propagation. This shows that the dominant propagation
directions observed in Shigaraki and at the Tomohon Observatory are likely
related to the distribution and characteristics of the source region. We
demonstrated the distinct difference in the GW propagation characteristics at
three different latitudes based on the phase velocity spectra. These results
indicate the usefulness of phase velocity spectra for the characterization
and comparison of GW characteristics at different sites and the effectiveness
of the new M-transform function for airglow imaging data obtained at these
locations. The comparison made in the current study is limited to the period
of April–May, for which enough preprocessed clear-night data were available.
In the future, we plan to extend this comparison and include data for all
seasons and months with more global coverage.
The M-transform function code and airglow data used in this
study are stored in the NIPR repositories and can be provided on request. The
MERRA-2 data used in the analysis can be freely accessed at
https://disc.gsfc.nasa.gov/datasets/ (last access: 27 November 2018)
(Gelaro et al., 2017).
The supplement related to this article is available online at: https://doi.org/10.5194/angeo-36-1597-2018-supplement.
SP developed the code, did the analysis and led the writing
of the paper. TN came up with the original idea and contributed heavily
to the discussion of the analysis results. MK did the preprocessing image of
Syowa airglow data, helped modify the code and contributed to the
discussion of the results. YT and MKE contributed to the discussion and
helped edit the paper. KS provided the Shigaraki airglow data and
contributed to the discussion of the results.
The authors declare that they have no conflict of
interest.
Acknowledgements
The airglow imaging at Syowa was carried out by the Japanese Antarctic
Research Expedition (JARE) of the Ministry of Education, Culture, Sports,
Science and Technology (MEXT). The airglow imager in Tomohon is operated by
the National Institute of Aeronautics and Space (LAPAN), Indonesia. The
airglow imager in Shigaraki is operated by Institute for Space-Earth
Environmental Research (ISEE), Nagoya University, in collaboration with the
Research Institute for Sustainable Humanosphere, Kyoto University. This
research was supported by JSPS KAKENHI grants (JP 15H02137, JP 15H05815, and
JP 16H06286), projects KP-1 and KP-301 of the National Institute of Polar
Research (NIPR), and by the JSPS Core-to-Core Program, B. Asia-Africa Science
Platforms. This research was supported by the National Institute of Information
and Communications Technology (NICT) Foreign Researcher Invitation Program.
The MERRA-2 data used in this study have been provided by the Global Modeling
and Assimilation Office (GMAO) at NASA Goddard Space Flight Center. This
publication was supported by an NIPR publication subsidy. Edited by: Petr Pisoft Reviewed by: two
anonymous referees
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