Shunsen Gong

Su Lu

Xunjie Zhang

Yong Ai

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Characteristics of atmospheric density spectra in the mesopause region at Wuhan, China during March 1996

Earth Planets Space, 50, 383–386, 1998
383
Copy right ©  The Society of Geomagnetism and Earth, Planetary and Space Sciences
(SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan;
The Geodetic Society of Japan; The Japanese Society for Planetary Sciences.
Characteristics of atmospheric density spectra in the mesopause region
at Wuhan, China during March 1996
Yong Ai1, Xunjie Zhang2, Su Lu1, and Shunsen Gong2
1Department of Radio Physics, Wuhan University, Wuhan 430072, China
2Wuhan Institute of Physics and Mathematics, The Chinese Academy of Science, Wuhan 430071, China
(Received September 13, 1997; Revised February 2, 1998; Accepted February 20, 1998)
Sodium layers (75–105 km) were measured by Na lidar on three nights from 1 to 3 of March 1996. The lidar data
were used to calculate the Na density profiles and the atmospheric density spectra. The vertical wave number
spectra exhibit power-law shapes with average slopes of –2.38 and magnitude at m =2π/(3 km) of 8.40 × 105 (m2s–
2)/(cyc/m) in the mesopause region.
1.  Introduction
Gravity waves have a significant influence on the wind,
temperature and density structure of the middle and upper
atmosphere. During the past decade wave activity has been
studied extensively, using both radar and lidar techniques
(Beatty et al., 1992; Senft et al., 1993; Manson et al., 1997).
These observations have provided important information on
wave amplitudes, periods and wavelengths and on the sta-
tistical characteristics of the wave spectra. In February
1996, Wuhan Institute of Physics and Mathematics installed
a Na lidar at Wuhan observatory (30°32′ N, 144°22′ E). The
system was operated as a Rayleigh and Na lidar for 3 days
from 1 to 3 March 1996. The description of Na lidar system
and the measurements of the shapes of sodium layers in the
mesopause regions have been summarized by Gong et al.
(1997) and Ai et al. (1998). In this paper we present our
measurements of gravity wave atmospheric density spectra
in the mesopause regions.
2.  Lidar System and Experimental Data
Figure 1 is a block diagram of the Na lidar system. The
pulsed laser is tuned to the D2 resonant absorption line of Na
at a wavelength near 589 nm which is in the yellow-orange
region of the visible spectrum. Kiton red dye was used in the
dye laser. Laser pulse energy is about 50 mJ, pulse width is
about 10 ns, photon counter operated with a 1.28 μs receiver
range-gate which corresponds to a range bin length of 192
m. The Na lidar system was operated during the nights of 1–
3 March 1996. The experiments lasted 144 minutes each
night. The lidar observed at zenith and the raw data consist
of photon count profiles obtained by accumulating the
returns from 4800 laser pulses collected over a period of 4
min. A typical photon count profile is plotted in Fig. 2. The
resonant scattering from the Na layer between about 80 and
105 km is clearly evident. The nonzero count level is caused
primarily by background noise from scattered moonlight
and starlight. The high photon count levels below 60 km
result from Rayleigh (i.e. molecular) and Mie scattering by
air molecules and aerosols. There were no clouds during any
of the observations. From the raw data and by using refer-
ence temperature and pressure data from a March 1986
middle atmosphere model (30°N), we calculated absolute
Na density profiles from which it is possible to deduce the
relative atmospheric density perturbations.
3.  Atmospheric Density Spectra
Because the atmospheric transmittance depends on the
clarity of the lower atmosphere and is not easy to measure,
the absolute Na density is usually compute by normalizing
the Na photocounts by the Rayleigh photocounts at an
altitude free of aerosols, typically 30–35 km. The absolute
Na density can be written as (Liu, 1989)
ρ
σ ρ
σs
a sz
z z
z
N z N R t
N z N R t
( ) = ( ) ( ) −[ ]( ) −[ ] ( )
2
2 1
R R
R eff
B L
R R B L
Δ
Δ
where Ns(z) = expected number of Na and background
photons detected in the range interval (z – Δz/2, z + Δz/2);
NR(zR) = expected number of Rayleigh scattering and
background photons detected in the range interval (zR – Δz/
2, zR + Δz/2); ρs(z) = Na density at range z (m–3); ρa(zR) =
atmospheric density at the normalizing altitude zR (m–3); NB
= expected photocount per range bin per pulse due to
background noise and dark counts; σeff = effective Na
backscatter cross section (m2); σR = Rayleigh backscatter
cross section (m2); RL = laser pulse rate (s–1); Δt = integra-
tion time (s).
According to Eq. (1), from the raw data we can get the
absolute Na density distributions, and we also can get Na
density perturbations rs(z, t)
r z t
z
z
z z
zs
s s,( ) = ( )( )
= ( ) − ( )
( ) ( )
ρ
ρ
ρ ρ
ρ
′
0
0
0
2
Letter
384 YONG AI et al.: CHARACTERISTICS OF ATMOSPHERIC DENSITY SPECTRA IN THE MESOPAUSE REGION
Fig. 1.  Block diagram of Na resonance fluorescene lidar system.
Fig. 2.  Lidar photon count profile observed at 21:08 LST of 2 March
1996.
whereρ0(z) is unperturbed Na profile. The prime denotes the
perturbation quantity.
It has been shown that a reasonably accurate model for the
unperturbed Na layer is a Gaussian profile (Gardner and
Voelz, 1987)
ρ
σ π σ0
0
0
0
2
0
22 2
3z
C z z( ) = − −( )
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
( )exp
where C0 = Na column abundance (~5 × 109 cm–2); z0 = layer
centroid height (~92 km); σ0 = r.m.s. layer width (~4.3 km).
The distribution of Na density with altitude and the
changing relation of the profiles with time is shown in Fig.
3. The profiles have been plotted on a linear scale at 4 min
intervals. The wavelike structure in the profiles is caused by
the wind perturbations associated with low-frequency inter-
nal gravity wave. If the vertical extent of the Na layer is large
compared to the vertical correlation length of the density or
wind perturbations, then the vertical wavenumber spectra of
the Na Fs(kz) and atmospheric density fluctuations Fa(kz) are
related (Liu, 1989)
F k
R k t
L
F ks z
s z
a z( ) =
( )
≈ ( ) ( )
,
2
2
1
4
μ
where
Fig. 3.  The distribution of Na density with altitude and the changing relation of the profiles with time that observed on 2 March 1996. The profiles
have been plotted on a linear scale at 4 minutes intervals.
A. YONG et al.: CHARACTERISTICS OF ATMOSPHERIC DENSITY SPECTRA IN THE MESOPAUSE REGION 385
μ
γ
γ σ
2
2
0
2 2
1
1 12
5=
−( )
+ ( )⎡⎣⎢ ⎤⎦⎥
( )
HL / /
and Rs(kz, t) is the Fourier transforms of rs(z, t)
R k t r z t e dzs z s
ik z
z L
z L
z, , .
/
/( ) = ( ) ( )
−
+
∫
0
0
2
2
6
In Eq. (5), σ0 = r.m.s. thickness of the unperturbed Na
layer (~4.3 km), z0 = centroid height of the unperturbed Na
layer (~92 km), H = atmospheric scale height (~6 km), γ =
ratio of specific heats (1.4).
Although Rayleigh and Na lidar measure density, the
gravity wave polarization and dispersion relation can be
used to relate the mean-square atmospheric density pertur-
bations and density power spectra Fa(kz) to the mean-square
horizontal wind perturbations <u2> and horizontal wind
power spectra Fu(kz) (Liu, 1989).
u z t
g
N
a
a
2
2 2
7,( ) ≈ ⎛⎝
⎞
⎠
⎛
⎝⎜
⎞
⎠⎟
( )ρ
ρ
′
F k
g
N
F ku z a z( ) ≈ ⎛⎝
⎞
⎠ ( ) ( )
2
8
where N is buoyancy frequency, here we take N value of 2π/
(300 s).
The vertical wave number spectra for 1, 2 and 3 March
1996, averaged over the respective observation periods and
for the altitude range from 84 km to 99 km, are plotted in Fig.
4. The photon noise floors have been subtracted and the
power law fits over the wave number range m = 2π/(10 km)
to 2π/(1 km) are also plotted on each spectra. For reference
the saturated power spectral density Fs(m) = N2/(6 m3)
predicted by linear instability theory also plotted in Fig. 4.
4.  Discussion
The slopes of the vertical wave number spectra in the
mesopause varied from –2.17 to –2.65, the mean slope is –
2.38. The magnitudes in this paper at m = 2π/(4 km) varied
from 3.74 × 105 (m2/s2)/(cyc/m) to 2.05 × 106 (m2/s2)/(cyc/
m). Senft and Gardner (1991) reported their observations
that the m-spectra shapes were highly variable at Urbana.
The slopes varied from –2.20 to –3.55 with an annual mean
of –2.90 and the spectral magnitude at m = 2π/(4 km) varied
by more than a factor of 10 throughout the year with
maximum values in summer and an annual mean of 4.4 × 105
(m2/s2)/(cyc/m). Beatty et al. (1992) reported a mean of –
2.98 and 2.9 × 105 (m2/s2)/(cyc/m), respectively, for the mean
slope and magnitude for all of the Arecibo data.
Because the lidar observation period each day was only
lasted about 2.4 hours, so the contents of long period wave
(T > 2.4 hours) could not be received by our lidar. In addition
the atmospheric density spectra averaged for the altitude
range only from 84 to 99 km, the contents of long vertical
Fig. 4.  Vertical wavenumber power spectra of the atmospheric density
perturbation associated with internal gravity waves in the mesopause
region. The spectra were inferred from Na lidar data collected at
Wuhan on 1 (a), 2 (b), and 3 (c) March 1996. The straight lines are linear
regression fits to the spectra for 1 to 10 km wavelength. The saturated
power spectral density model is also plotted in the figure.
386 YONG AI et al.: CHARACTERISTICS OF ATMOSPHERIC DENSITY SPECTRA IN THE MESOPAUSE REGION
Table 1.  Comparison of the magnitudes of the spectra.
Fu (2 π/(5 km)) Fu (2 π/(4 km)) Fu (2 π/(3 km)) Fu (2 π/(1 km))
(m/s) 2/(cyc/m) (m/s) 2/(cyc/m) (m/s) 2/(cyc/m) (m/s) 2/(cyc/m)
1 March 6.3 × 10 5 3.74 × 10 5 1.82 × 10 5 8.98 × 10 3
2 March 3.31 × 10 6 2.05 × 10 6 1.13 × 10 6 8.14 × 10 4
3 March 1.47 × 10 6 1.07 × 10 6 5.63 × 10 5 5.09 × 10 4
Mean 1.80 × 10 6 1.16 × 10 6 6.25 × 10 5 4.70 × 10 4
Fs  (m) model 8.84 × 10 6 4.75 × 10 6 2.08 × 10 6 7.50 × 10 4
wavelength waves (λz > 15 km) were not included in the
spectra. These two reason may explain why the slopes in this
paper are a little shallower than the values measured at other
sites.
The magnitudes of the spectra in this paper and the
saturated power spectral model are summarized in Table 1.
The lidar values are artificially depressed by a factor of
0.5~0.75 (Senft et al., 1993) because the data were filtered
with a cutoff frequency of 2π/(1 h) and a cutoff wavelength
2π/(1 km) before the spectra were computed. The lidar m-
spectra do not include gravity wave energy in the frequency
range 2π/(1 h) to N. Thus, if we account tor filtering effects,
the lidar spectra of 2 March are saturated at the range of m
> 2π/(3 km). From Table 1 we can see that the magnitude of
2 March is much big than 1 and 3 March, which may show
an enhanced wave activity occurred during the observation.
5.  Conclusions
The vertical wavenumber spectra shown in Fig. 4 are
generally within a factor of 1 to 8 of the saturated spectrum
for vertical scales from 10 km to 1 km, suggesting general
consistency with the saturated spectral model in spectral
amplitude. Also apparent are variations in the wavenumber
spectra from day to day. It reveals that the wave activities in
the mesopause region at Wuhan are strong.
Unfortunately, the signal levels below 60 km altitude
were not adequate to compute many of the gravity wave
parameters from the upper stratosphere data. For more
detailed studies of dynamics in the mesosphere and strato-
sphere, much more powerful lidars are required.
Acknowledgments.  The authors wish to express their sincere
appreciation to Dr. M. Ishii (C.R.L.) for his valuable help in
writing this paper. The work was supported by the funds of the
Chinese Academy of Science.
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Y. Ai (e-mail: aiyong@public.wh.hb.cn), X. J. Zhang, S. Lu, and S. S.
Gong


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Characteristics of atmospheric density spectra in the mesopause region at Wuhan, China during March 1996

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