Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 335—342
335
Simulation of response of sodium layer to the
propagation of gravity wave
XU Jiyao
Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of
Sciences, Beijing 100080, China (email:[email protected])
Received January 23, 2003
Abstract A time-dependent two-dimensional photochemical-dynamical coupling gravity
wave model of sodium layer is developed, which combines the sodium photochemical
theory, a time-dependent two-dimensional atmospheric photochemical model, a
two-dimensional gravity wave model, and the International Reference Ionosphere model
(IRI-95)with the diabatic process induced by photochemical reactions and the transport of
chemical species by gravity waves included. The pseudospectral method is used in the
horizontal direction, the finite difference approximations are used in vertical direction z
and time t. And FICE method is used to solve the model. The simulation results indicate
that intense perturbations of the sodium layer can be induced by the propagation of
gravity waves. The results are consistent with the observations.
Keywords: gravity wave, photochemistry, nonlinear, numerical simulation, mesopause, sodium layer.
DOI: 10.1360/ 02ye0455
The gravity wave is one of the most important phenomena of atmospheric waves.
Owing to the exponential decrease in the atmospheric density, the amplitude of gravity
wave increases as it propagates from lower altitude to higher altitude. When the gravity
wave reaches mesopause region, in some cases, the gravity wave breaks and produces
turbulence. Therefore, the gravity wave is one of the most important atmospheric waves.
The sodium layer, which is located in the region between about 80 km to more than
100 km, is often disturbed by gravity waves which propagate from lower part of atmosphere. Because atomic sodium can be detected directly by lidar, the sodium layer becomes a very important trace medium for studying the atmospheric dynamics. With the
development of lidar technology, the lidar becomes an important tool for detecting the
dynamical fluctuations in the mesopause region.
However, besides the effect of atmospheric dynamical transport, the sodium layer is
affected by the photochemical process and the background chemical species. At the
same time, the effect of the ion chemical reactions in the lower ionosphere cannot be
ignored. Therefore, the sodium layer cannot be simply regarded as a tracer of atmosCopyright by Science in China Press 2004
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Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 335—342
pheric dynamics. In order to explain the results of observation, the photochemical process must be considered.
Hickey and Plane[1] studied the sodium layer fluctuations induced by gravity waves
using a linear chemical-dynamical model of sodium layer. The model was under the approximation of WKB. The linear theory can provide the characteristics of the amplitude
and phase of the fluctuation. Therefore, the linear theory is one of the most important
methods for studying atmospheric waves. However, the linear theory can only be applicable to the small amplitude waves. In the middle atmosphere, especially in the
mesopause region, the assumption of the small amplitude is not correct in some cases.
On the other hand, the linear theory supposes that the atmospheric parameters vary little
over one vertical wavelength of the gravity wave. However, in the mesopause region,
some profiles of important chemical species, such as O, H, and Na, have very large vertical gradient. Therefore, a time-dependent, nonlinear, photochemical-dynamical coupling gravity wave model of sodium layer is required.
Because the photochemical reaction rates depend on the temperature, in the simulation, we must consider the non-isothermal atmosphere. On the other hand, as the gravity
wave propagates upwards, the amplitude of the gravity wave exponentially increases.
The nonlinear and compressible processes of the gravity wave cannot be ignored. In addition, the middle atmospheric photochemistry is a nonlinear system. Therefore, the
model should be a nonlinear, compressible, diabatic, and nonhydrostatic model.
The numerical simulation is an efficient tool to study a nonlinear complex system.
In addition, at present, the lidar can only make observations above the lidar station. It is
difficult to get the whole physical structure of gravity waves. However, the numerical
simulation can give the two-dimensional or three-dimensional spacial and temporal
evolution of the gravity wave. In this paper, a time-dependent two-dimensional gravity
wave model of sodium layer is developed, which is composed of the sodium photochemical theory, a time-dependent two-dimensional atmospheric photochemical model,
a two-dimensional gravity wave model, and the International Reference Ionosphere
model (IRI-95).
In this paper, we will study the response of the sodium layer to gravity waves using
the time-dependent two-dimensional gravity wave model of the sodium layer.
1
The photochemical-dynamical coupling gravity wave model of sodium layer
The photochemical-dynamical coupling gravity wave model of sodium layer is
composed of 4 models: a time-dependent two-dimensional gravity wave model, a
time-dependent two-dimensional atmospheric photochemical model, the sodium photochemical model, and the International Reference Ionosphere model (IRI-95).
The time-dependent two-dimensional gravity wave model is a nonlinear model
which takes into account the non-isothermal and compressible atmosphere. The diabatic
process induced by the photochemical reactions is also included in the model.
Copyright by Science in China Press 2004
Simulation of response of sodium layer to the propagation of gravity wave
337
The background photochemical model includes the important photochemical reactions in the middle atmosphere and lower thermosphere. The transport processes induced
by gravity waves and the turbulence diffusion and the molecular diffusion are included
in the model. In the calculation, oxygen compounds ( O3, O3p, O1D ), hydrogen compounds( H, OH, HO2 ), nitrogen compounds ( N, NO, NO2, NO3, N2O5, HNO3 ) and
chlorine compounds ( Cl, ClO, HCl, HOCl) are calculated. The middle atmospheric
photochemical model is a nonlinear, time-dependent, two-dimensional model, which
accounts for the variation of solar zenith angle during daylit hours. Therefore, it can
simulate the diurnal variation of the photochemistry. Details of the photochemical
scheme are discussed in our previous papers[2,3].
The combination of the time-dependent two-dimensional gravity wave model and
the middle atmospheric photochemical model yields a time-dependent photochemical-dynamical coupling gravity wave model[4]. The model can simulate the fluctuations
of winds, temperature and the atmospheric chemical species.
The sodium photochemical part in the photochemical-dynamical coupling gravity
wave model of sodium layer is a two-dimensional photochemical model of the sodium
layer. The photochemical continuity equation for sodium species i is
∂qi
∂q
∂q
1
1
+ u i + w i = ∇ ⋅ ( ρ K zz ∇qi ) + ( Pi − Li ) , i = 1, 2, Λ, J ,
∂t
∂x
∂z ρ
ρ
(1)
where qi = ni / ρ is the mixing ratio of the chemical species i. ni is the density; ρ is the
atmospheric density; Kzz(z) is the diffusion coefficient; u and w are the wind speed in
horizontal and vertical direction, respectively; Pi and Li are the production rate and loss
rate for chemical species i, which can be calculated by the equations of the photochemical reactions of the sodium layer. The neutral photochemical reactions, the ion chemical
reactions, the photolysis and the photoionization are involved in the sodium photochemical model. These reactions have close relationships with the neutral chemical species (such as O3, O(3p), and H) and ions (such as O2+, NO+ and electron ). Therefore, the
sodium layer couples with the ionospheric E and D regions. Nine chemical species,
which are Na, NaO, NaO2, NaO3, NaOH, NaCO3, NaHCO3, Na+ and Na+X are calculated in the time-dependent two-dimensional model of the sodium layer. On the other
hand, in order to keep the conservation of total number of sodium atom N0, the total
number of sodium atom in the sodium layer is controlled by
N0 = [Na]+[NaO]+[NaO2]+[NaO3]+[NaOH]+[NaCO3]+[NaHCO3]+[Na+]+[Na+X]. (2)
Various compositions of Na layer are partitioned among the total number of sodium
atom through the photochemical reactions.
Eqs. (1) and (2) show that the photochemical reactions, the dynamical transport and
the diffusion process are included in the model of the sodium layer. The dynamical fluctuations can be calculated by the gravity wave model. The profiles of the background
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Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 335—342
chemical species can be calculated by the time-dependent two-dimensional chemical
model.
The fourth part of the photochemical-dynamical coupling gravity wave model of
sodium layer is the ionospheric model. Many researches indicate that the sodium layer is
[6,7]
closely related with the ionosphere . Therefore, the effect of the ion species should be
considered in the sodium layer model. The ion species and its diurnal variation are calculated by the International Reference Ionosphere model (IRI-95).
The solution method of this model is the same as our photochemical-dynamical
gravity wave model in our previous paper[4].
Considering the atmospheric uniformity in horizontal direction, the pseudospectral
method is used in the horizontal direction. The calculation domain in the horizontal direction is one wavelength.
However, in the vertical direction, the temperature, winds and the profiles of
chemical species vary with altitude. And the boundary condition is not periodic in the
vertical direction. Therefore, the finite difference approximations are used in the vertical
direction and in time. The vertical grid size is 0.2 km, and the domain of the model extends from the ground to 170 km.
The solution method used here is similar to the Full-Implicit-Continuous-Eulerian
(FICE) scheme[8,9].
2
Results of the simulation
Fig. 1 gives the undisturbed profile of
density of atomic sodium Na, where the peak
of Na density is at about 90 km. The peak
density of Na is about 3000 cm−3. This simulation results are consistent with average
characteristics of observations.
Fig. 1. The undisturbed profile of Na density.
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Now, we can study the response of sodium layer to the gravity wave. In the simulation, we take the initial atmosphere as a
realistic vertical temperature profile and the
atmosphere is at rest. The temperature profile
is taken from the U. S. Standard Atmosphere.
The initial perturbation is a Gaussian gravity
wave packet at 50 km (i.e. the center of the
maximum energy density of the wave packet
is at 50 km):
Simulation of response of sodium layer to the propagation of gravity wave
339
2
⎡
⎛ z − z0 ⎞ ⎤
⎛ z − z0 ⎞
T ′ ( x, z , t = 0 ) = T0′ ( z0 ) sin ( k x x + k z ( z − z0 ) ) exp ⎢ − ln 2 ⎜
⎟ ⎥ exp ⎜
⎟ , (3)
λ
⎢⎣
⎝ 2H ⎠
⎝ z ⎠ ⎦⎥
where z0 = 50 km; kx = 2π/lx and kz = 2π/lz are the wave numbers in the horizontal and
vertical directions, respectively. The horizontal wavelength lx is 100 km, the vertical
wavelength lz is 10 km, and the half width of the wave packet λz is 15 km. T0′ ( z0 ) is
the amplitude of initial temperature perturbation. In the simulation, we take T0′ ( z0 ) =
1K. The initial perturbation quantities, u ′ ( x, z, t = 0 ) , w′ ( x, z , t = 0 ) ,
p ′ ( x, z , t = 0 )
and ρ ′ ( x, z , t = 0 ) , are derived from T0′ ( z0 ) using the polarization equations for a
linear gravity wave.
Fig. 2 shows the propagation of the gravity wave in the non-isothermal atmosphere.
The figure gives the horizontal wind at 5 times (0, 3000, 6000, 9000 and 12000 s). When
the simulation time is 12000 s, the gravity wave reaches near a height of 100 km. The
amplitude of the horizontal wind fluctuation is about 50 m/s.
Now, we study the response of sodium layer to the propagation of gravity wave.
First, the simulation result of the spacial distribution of the sodium layer fluctuation induced by the gravity wave is discussed. Fig. 3 shows the two-dimensional distribution of
the Na density fluctuation at 12000 s of simulation. The figure indicates that the profile
of Na density is intensely modulated by the gravity wave. The amplitude of the perturbation reaches above 1000 cm−3. The region of the largest fluctuation of the sodium density
is located in 84—88 km. This makes the variation of larger than 2000 cm−3 in sodium
density.
In order to show the time evolution of the sodium layer fluctuation when the gravity
wave propagates through the mesopause region, the simulations during 9000—12000 s
is taken as an example, Fig. 4 gives the profiles of sodium layer for a fixed horizontal
position at 2-min intervals. The figure shows the variation of Na density at x = 50 km.
The figure shows obvious downward phase propagation, which is an important feature
of an upward propagation of gravity wave. Many observations validate this characteris[10]
tic of the gravity wave propagation . At the same time, the altitude of the atomic sodium density peak is intensely disturbed by the gravity wave. On the other hand, fig. 4(a)
indicates that during 11500—12000 s, there are double peaks in Na density profile. The
two peaks of atomic sodium density are located at 95 and 90 km respectively. The double and multi-peak structure of the sodium layer and the intense variation of the altitude
[11—14]
of atomic Na density peak are often observed by lidar system
. The simulation in
this paper proves that the complex structure of the sodium layer is induced by the
propagation of gravity waves.
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Fig. 2. The fluctuation of horizontal wind at 5 times (a) 0; (b) 3000 s; (c) 6000 s; (d) 9000 s; (e) 12000 s.
3
Discussion
In this paper, a time-dependent, two-dimensional, nonlinear, photochemicaldynamical gravity wave model of sodium layer is developed. It is composed of 4 models:
the dynamical gravity wave model, the middle atmospheric photochemical model, the
Na layer photochemical model and the ionospheric model. Using this model we studied
the effect of the gravity wave propagation on Na layer. Simulation indicates that the
gravity wave propagation can induce intense perturbation of the Na layer and can proCopyright by Science in China Press 2004
Simulation of response of sodium layer to the propagation of gravity wave
341
Fig. 3. The fluctuation of the density of atomic sodium at 12000 s.
Fig. 4. The variation of the sodium density with times during 9000—12000 s of simulation. (a) The fluctuation of
Na density; (b) the density of Na.
duce a complex structure of the sodium layer. This phenomenon is consistent with observations.
However, in the model advanced in this paper, the International Reference Ionosphere model (IRI-95) is used for calculating the ions O2+, ON+ and electron densities in
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Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 335—342
ionospheric E layer. And the geomagnetic effect is ignored. In this model, except the
diurnal variation of ionosphere, the perturbations of the ionosphere induced by gravity
waves cannot considered at present. This may lead to an inaccuracy on the topside of
sodium layer. We will study the effects of perturbation of the ionosphere on the Na layer
in the near future.
Acknowledgements This research was supported by National Natural Science Foundation of China (40225011),
the National Research Project (G2000078407), and project of CAS (KZCX3-SW-217).
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