- Email: [email protected]
temperature ratio, η
Gravity waves from O2 nightglow during the AIDA ‘89 campaign II : numerical modeling of the emission rate/temperature ratio, q S. P.
ZHAEU’G,R.
H. WRENSand G. G.
SHEPHERD
Institute for Space and Terrestrial Science, York University, 4850 Keele St., North York, Ontario. Canada M3J 3KI
Abstract-The dependence of q. the ratio of emission rate fluctuation to temperature ~ucfuation, on the gravity wave parameters and chemical parameters is developed using a model for the O2 airglow’s response to a gravity wave. The model is in the Eulerian frame of reference using the traditional linearization and perturbation method. Two photochemical mechanisms, the three-body recombination mechanism and the two-step transfer mechanism, and two kinds of waves, evanescent and internal, are separately discussed in detail. Results of the model are compared with other existing models of q(02) and found to be in agreement. The predictions of this model agree fairly well with the available gravity wave measurements in the magnitude of q, but the predicted phases are somewhat larger than those normally observed.
theory which was later made specific to the Oz(b’Z) and to the OH airglow layers by TARASKK and SHEPHERD (1992a,b). Meanwhile, WALTERSCHEID er Variations in airglow brightness have been attributed to gravity wave activity for many years (e.g. HINES, al. (I 987) advanced yet another theory of p specifically for the OH airglow. Whereas the Weinstock treatment 1964; NOXON,1978; KRASSOVSKY, 1972), but a rigorinvokes non-linear considerations, the HINES and ous understanding of the relationship between the TARASICK(1987) approach avoids this by mapping dynamical and the chemical aspects has not yet emerged. Observations of the OH Meinel and the O2 the Eulerian equations back to unperturbed heights. WALTERSCHEID ef (II. (1987) begin with an Eulerian atmospheric airglow layers by optical spectrometers reference frame but restrict their concerns to a fixed allow for the measurement of the chemically related altitude. variable, that is, integrated column emission rate, and A choice of which of the above theoretical forthe dynami~dlly related variable, that is, mean layer rotational temperature, simultaneously. KRASSOVSKY mulations best represents observable realities has so far been hindered by a lack of relevant experimental (1972) related the chemical and the dynamical conmeasurements. Although cepts by defining the parameter q, the ratio of the many simultaneous measurements of emission rate and rotational temfractional fluctuation of the emission rate to the fracperature have been reported for both the O? atmotional fluctuation of the temperature, in his study of OH airglow. Since the temperature perturbations in a spheric and OH Meinel bands of the airglow, they have almost always been made at a single point in the gravity wave are linked to the corresponding persky, and hence provide periods as their only measured turbations of density, pressure, and velocity through wave parameter. As pointed out by TARASIC~ and the polarization equations set down by HJNES(1960), HINES(I 987) measurements of only g and period allow the further linking of perturbations of temperature to the modeler to choose the wavelength as a free parthose of emission rate through q makes emission rate ameter, and therefore do not allow the adequate testa useful quantity with which to study the impact of ing of any theory. An opportunity to test these gravity waves on the state of the mesopause/lower thermosphere region of the atmosphere. An applitheories more rigorously as they apply to the O2 atmospheric case was provided by the MORTI measurecation of this principle is to be found in the following ments made during the AIDA ‘89 campaign in Puerto paper, paper III, by WAKC rt ul. (1993). The concept of ye was employed by WEINSTOCK Rico. Here the corresponding wave components in (1978) to explain NOXON’S(1978) O2 atmospheric airboth column emission rate and mean rotational temperature were analyzed to find 1 and the period, as glow measurements. HINES and TARASIC~(1987) and usual, but also horizontal wave velocity and conseTARASICKand HINES (1987) provided an alternate 377
yuently all of the kinematic wave characteristics, These characteristics and the methods of obtaining them from the MORTI data are described in the preceding paper, paper I by ZHANG et al. (1993), where it is also shown that none of the theories mentioned above is able to predict q in both magnitude and phase to within the measurement uncertainty when the full characterization is taken into account. The inconsistencies between the existing theories and the AIDA ‘89 measurements of paper I stimulated the present work, the purpose of which is to present a numerical chemical-dynamical model of q in the O2 atmospheric nightglow for both internal gravity and evanescent waves. Following the derivation of WaLTERSCHEIDet (11.(1987) for q in the OH Meinel nightglow. this model employs the usual linearization and perturbation methods in an Eulerian reference frame. Two different photochemical excitation mechanisms for the 0,(6’Z:) atmospheric nightglow are included separately in order to determine whether gravity wave observations of any kind can provide a means of evaluating their relative i~n~orta~lce. THE EXCITATION MECHANISMS FOR O,(b’Z$)
The excitation mechanism for the O>(b’X:) has been debated for some years. Two mechanisms have been proposed, and we will treat both separately. The first one is the three-body recombination. also called the direct excitation (the Chapman mechanism), in which : O+O+M(02-t-Nz)
-+ 02(h’E:)+M
(I)
(CHAPMAN, 1931). Although no longer having widespread support, this proposal is simple enough to allow for inclusion in models in closed mathematical form, and so has been covered in the theoretical papers of W~INST~CK( 1978) and HIKF~and TARASICK (1987). The second, more widely accepted, proposal is the two-step process, also called the transfer excitation (the Barth mechanism). in which :
O+O+M(OzfN?)
+02((.‘C,; )+M,
02((.‘C,, )102 --+O,(h’q)+O,
(2)
(SOLHEIMand LLEWELLYN,1979; GREERet al., 1981; T~RR er crl., 1985 : MURTA<;Hef al., 1990). The actual identification of the precursor state, here designated as 02(c’Cti ) is still open to question, but the method does not depend upon the specific state. In either case the atmospheric bands result from o&?‘c:)
-+ O&Y’C;)+hv.
(3)
When quenching of O,(h’Z:) by atmospheric O2 and N, is included. the volume emission rate (photons
cm-’ s- ‘) for the three-body recombination expressed as
may be
(MCDAIX if n(., 1986), and for the two-step transfer mechanism it may be expressed as
6 =~ _~ _. k,A,[01’([0~1+[Nzl)[o,~____ ~.~~~.~~~~~~ (A2+f@[02]+K>?[N2])(C
~[O,]+c’“‘[O1) (cm-‘s-‘)
(5)
(M~RTA~H et al., 1990; MCDADEet a!., 1986), where k, = 4.7 x 10-~~(300/~)2
cm6s
’
(6)
is the rate coefficient for three-body recombination of atomic oxygen ; and [O](cm-7) is the number density of atomic oxygen, [O,](cm-‘) is the number density of molecular oxygen, [N,](cm-I) is the number density of nitrogen. c A 0.1, the Fraction of recombinations, il 1 = 0.079 s ‘, the (@O) band transition probability. <4>= 0.083 s- ‘, the inverse radiative lifetimeofO,(h’C,i ). K$ =4.0x 10 “cm”s ‘. therate coefficient for quenching of 02(b’Xl) by atmospheric 0 2, KN~=27~10-‘5 cm3 s.- ‘, the rate coefficient 2 .for quenching of OJb’Z:) by atmospheric N,, Co2 = 7.5, the empirical parameter defined and evaluated by MCDADEet al. (1986), Co = 33, the empirical parameter also defined and evaluated by M~DADE ef lli. (1986). Using the three-body recombination the volume emission rate produces a peak altitude of 95-96 km, and using the two-step transfer processes the peak is at about 94 km. The thickness of this emission layer is calculated to be about 8 km. BASIC EQLATIONS AND SOLUTIONS OF WAVE MOTION
In order to obtain a reasonably simple solution For gravity waves in the atmosphere, we use the conventional assumptions (HINES, 1960; HOUGHTON, 1986; WALTERSCHEID et al., 1987) : the atmosphere is isothermal and motionless in the absence of waves; the motion of waves is adiabatic; the Coriolis term, the friction term, molecular diffusion, and eddy diffusion are ne.glected; and all equations are linearized. The wave solutions of T’/T, (temperature), P’/PO (pressure}. IV/N,, (density), w’ (vertical velocity) and C:’ (horizontal velocity) are expressed as complex numbers in the form :
Gravity
waves from O2 nightglow
during
campaign
II
379
where time t, coordinates x and z-, horizontal and vertical wave numbers k, and k= are all real numbers. The constant r, a real number, will be found, w is the circular frequency of the wave, and C is the speed of sound. The primes and naughts denote perturbed and unperturbed quantities, respectively. The basic equations of wave motion for the major gas (HOUGHTON, 1986) have two solutions. The first one is :
where H is the scale height of the major gas, g is the acceleration of gravity, and 11is the ratio of the specific heat of air at constant pressure to the specific heat of air at constant volume, for dry air y = 1.4. Also ~t)~is the Brunt-V~is~l~ frequency, w,, is the acoustic cutoff frequency, and C is the speed of sound. If the atmosphere is in hydrostatic equilibrium, then C2 = Hg-f. Since k; = 0, there is no phase variation in the vertical : waves associated with this solution are called cvanescent waves. The a is a function of the wave frequency and the wavelength. There are two c( values given by equation (8) corresponding to two waves which have the same period and wavelength but different amplitudes. Numerical calcutation shows the two values of a are both positive while the wave period is between 20 and 360 min and the wavelength is between 100 and 2000 km. The argument of the square root in equation (8) is almost zero for long period waves. With o’ <
The second equation of equation (9) is well known as the dispersion relationship. The waves associated with this solution are called internal waves (HINES, 1960). The Brunt-VBidIl frequency is the maximum frequency of internal waves, Generally, the wave speed of the internal wave is lower than that of the evanescent wave. Using notation similar to that of WALTERSCHE~D et al. (1987) we derive
The parameter,/; is a complex number for the internal wave, and a real number for the evanescent wave, that is
(for internal waves),
(for evanescent waves).
i IS)
(15’)
The five variables, T’fT,, P’fPo, N’fN,, ii’ and H”, have different amplitudes and phases which depend on wave periods, wavelengths. and the scale height of the major gas. Tables I and 2 are numerical examples of the ratios of P’fP,, N’fN,, V and w’ to T’J7;,. THE WAVEPERTURBATION IN ATOMICOXYGEN Figure 1 shows the vertical profiles of the number densities of atomic oxygen, molecular oxygen, and nitrogen calculated by the MS&86 model (HEDIN, 1987). Unlike molecular oxygen and nitrogen, atomic oxygen is not in hydrostatic equilibrium; the distribution of atomic oxygen strongly depends on photochemical processes. The profile of the volume emission rate of the 0, airglow, as shown in Fig. 1, is clearly related to the profile of atomic oxygen. Assuming that all species have the same tcmperature and velocity as the background major gas (WALTERSCHJSID et al., 1987), the continuity equation of atomic oxygen is
where n is the density of atomic oxygen that n = n,+n’, and P’ and L’ are the perturbation parts of the production and loss of atomic oxygen. respectively. At night P’ = 0, and the loss L’ is so much
380
Table 1. Polarization
factors*
for waves generated Amplitude
in lower atmosphere
ratio
with period
120 min
Phase difference -
100 200 300 400 500 600 700 800 900 IO00 1100 1200 1300 1400
1500 1600 1700
1800 1900 2000 2100
*Using
-4.0 -8.1 - 12.2 - 16.5 -20.9 -25.5 - 30.5 -35.8 -41.7 -48.3 - 55.8 -64.7 -15.6 - 89.6 - 109.4 - 141.3 -211.3
0.111 0.222 0.334 0.445 0.556 0.667 0.779 0.890 1.001 1.113 1.224 1.335 1.446 1.558
- x - x YL - *x, --‘10 - ,Co -CC - 71
2.125 1.863 2.946 I.497 3.545
I .669 I.780 1.892
1.379 4.121 1.308
1.000 1.000 1.000
0.999 0.999 0.999 0.999 0.999 0.999 0.999
1.580 1.580 I .580 I.580 1.580 1.580 1.580 1.580 1.580 1.580 1.580 1.580 1.580 I .5x0 I.580
1.125 0.863 1.946 0.497 2.545 0.379 3.121 0.308
0.0249 0.0296 0.0 100 0.0363 0.0008 0.0384 0.0112 0.0397
1.676 1.470 2.202 I.119 2.517 0.979 2.787 0.884
1.000 1.ooo t .ooo I .ooo 1.000 1.000 1.000
factors*
for waves generated Amplitude
80 60 40 30 30
- 87”
1.580 -84 -80’ --77’ -74” -70“ -67 -64 -60 -56‘ -52, -48 -44’ -39’ -33’ -27‘ -19
_-88”
- 174’ - 167’ - 161’ -154 - 148 - 141 -134‘ - 127 -120 --II? - 105‘ --96 -87 -78 -67‘ -54 -38
-86” -85’ -83’ -81’ - 79’ -77 -76 - 74” -72’ -71 -- 69 -68 -67’ -66’ -67 - 70’
- 87’ -84” -80’ - 71“ -74 - 70 -67‘ -64.’ -60’ -56’ -52 -48‘ - 44’ -39“ - 33’ -27 -19
0 0’ oi 0’ 0 0 0 0
-90 - (10 -90 - 90’. 90‘ -90 90 -90
0’ o-’ 0’ 0” 0” 0’ 0 0
0’ 0 0 0’ 0 0 0 0
the scale height H = 5.730 km. the speed of sound = 276 m/s.
Table 2. Polarization
360 340 320 300 280 260 240 220 200 180 160 140 120 100
1.580
0.0633 0.063 1 0.0627 0.062 1 0.0613 0.0604 0.0593 0.0580 0.0565 0.0548 0.0528 0.0505 0.0480 0.0450 0.0416 0.0376 0.0329
ratio
~-..____I 1.000 0.0211 1.000 0.0223
-6.7 -7.1 -7.6 -8.1 -8.7 -9.3 - 10.1 - 1 I.1 - 12.2 - 13.6 - 15.4 - 17.7 -20.9 -25.5 -33.1 -48.4 - 110.4
0.186 0.196 0.209 0.223 0.239 0.257 0.278 0.304 0.334 0.371 0.417 0.477 0.556 0.667 0.834 1.110 I.661
0.999 0.998 0.99 I
0.0237 0.0252 0.0270 0.0291 0.0314 0.0342 0.0376 0.0417 0.0467 0.0530 0.0613 0.0725 0.0881 0.1096 0.1250
- Z’ - Z> - nj -CC
3.569 I.368 10.31 1.076
2.569 0.368 9.311 0.076
0.0050 0.1544 0.7400 0.2634
1.000 1.000 1.000 1.000 1.ooo 1.000 1.000 1.ooo 1.000 1.000 1.000
1.000
in lower atmosphere
with & = 500 km
Phase difference .-- .____~
____- 169” -169” - 168. - 167’ -166 -- 165’ -164 - 163‘ - 161 -159 -156” -152 - 148’ -141’ -131” - 113” -67’
-87’ -87 -87 -86“ - 86” -86 -- 85 -85 -85’ -84’ -83’ -82’ -81 - 79,. -76’ -12 -67
-85 -84’ - 84’ -84’ -83’ -83” - 82“ -81“ -80 -79 -78”
1.572
-85 -84 -84 -84‘ -83’ -83 -82‘ -81% -80‘ -79’ - 78” - 76’ -74 - 70“ - 65’-56“ -33’
2.534 0.971 4.881 0.509
0 0, 0‘ 0’
0 0 0 0“
90 -90 90‘ -90
0 0’ 0’ 0”
1.581 1.581 1.58L I.581 1.581 I.581 I.581 I.581 I.581 I.581 I.580 I.%0 1.580 1.579 1.578
i .577
* Using the scale height H = 5.730 km, the speed of sound
= 276 m/s.
-76’ -74‘ -70‘ -65’ -56’ - 33.‘
Gravity
waves from O2 nightglow
during
campaign
3x1
II
120
110
100
90
0
2
4
6
6
10
12
Fig. 1, Vertical profiles of the volume emission rate of the OL airglow emission using the two-step transfer mechanism, temperature, number densities of atomic oxygen, molecular oxygen, and nitrogen calculated
by MSIS-86 model.
smaller than the other terms in equation (16) by comparison (less than I/1000) that it may be neglected. Substituting equations (IO), (11) into (16) yields
THE RATIO $ = @‘/I&) : ( r,i T,,)
In a ground-based measurement such as the kind described by ZHANGrt al. (1993), the apparent emission rate, B, is given by ,
where
B=
s0
Edr,
(20)
and the measured temperature, T,, is weighted by the apparent emission rate as and
H,, is the scale height of atomic oxygen. Obviously if DW = - I. that is, H,, = H, the scale height of atomic oxygen equals the scale height of the dominant gas, and ,fh =,fi. However below 99 km, D is positive (Table 3 and Fig. I) meaning that the scale height of atomic oxygen is negative, whereas the scale heights of major gases, O2 and Nz, are always positive. Then ,f6 is quite different from f3. For example, at 94 km altitude, D % 0.8 x 10-4mm ’ and H x 5.730 km, from equation (17) we havef, = - 1.4f,+2.5.
where c is the volume emission rate, and T(.Y,:) is measured along the line of sight. This physical situation is identical to that invoked by WEINSTOCK(1978) and by HINES and TARASICK(1987). If the viewing direction is 0 degrees from the vertical, then it is easy to transfer dr into d; by setting dv = secOd_ and x = _x,+ z tan 8, where _v, is a constant. The effect of non-zero 0 is studied by TARASICKand HINES (1987) who showed that for waves with period longer than 30 min, the effect is negligible at least for fI < 45‘.
3x2
S. P. ZHANG et (11.
Table3.Atmospheric parameters
-~ 85 86
87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 IO3 104 105 106 107 108 109 110
10.13 9.192 X.216 7.244 4.312 5.447 4.663 3.968 3.362 2.840 2.395 2.018 I.700
2.656 2.403 2.141
0.464 0.716 1.046 1.452 1.921 2.432 2.959 3.474 3.950 4.366 4.708 4.968 5.143 5.236 5.254 5.205 5.097 4.941 4.744 4.516 4.264 3.884 3.612 3.334 3.056 2.782
I.880 1.630 1.399 1.190 1.006 0.845 0.708 0.591 0.492 0.409 0.340 0.282 0.233 0.193 0.159 0.131 0.107 0.088 0.071 0.058 0.046 0.037 0.030
1.433 1.208 1.019 0.860 0.725 0.612 0.515 0.433 0.364 0.305 0.255 0.212 0.176
0.262 0.261 0.261 0.260 0.258 0.257 0.255 0.254 0.251 0.249 0.247 0.244 0.241 0.237 0.233 0.229 0.224 0.219 0.214 0.208 0.202 O.lY6 0.189 0.182 0.176 0.16Y
0.730 0.710 0.686 0.659 0.627 0.592 0.554 0.514 0.472 0.431 0.389 0.349 0.312 0.276 0.243 0.213 0.186 0.162 0.140 0.121 0.103 0.088 0.075 0.063 0.053 0.045
5.43x 4.609 3.881 3.230 2.660 2.167 1.740 1.370 1.053 0.783 0.552 0.352 0.181 0.034 -0.093 -0.207 -0.306 -0.399 -0.481 -0.555 -0.631 -0.700 -0.770 -0.834 -0.897 -0.960
0.992 0.987 0.979 0.967 0.951 0.929 O.YOl 0.868 0.829 0.786 0.740 0.692 0.644 0.596 0.549 0.505 0.462 0.423 0.385 0.351 0.318 0.294 0.266 0.241 0.217 0.196
-
*z, = [0,]/[N2]; fee,seeequation (30):$ D = 0.001 x([O],+I:[O],-137).
f)m ';SD*, seeequation
Hence, we will only deal with the simplest case of 0 = 0.
The parameter q is a ratio of two quantities integrated over the thickness of the layer, it is more simpfe
Under these conditions, a fractional sion rate perturbation will be
to conceive of the corresponding equivalent point within the layer, where we define
apparent
emis-
for a
(25)
(22) and substitute (24) yields
Jo
equations
(25) and (7) into equation
and a fractional measured temperature perturbation for an isothermal atmosphere (T,, is constant) will be (26)
T‘Y
(23)
B<,
The parameter ye,therefore, may be expressed as
‘I = ~~~)~(~~
= J;;;L. 0
*n
(24) 0
Equation (26) shows that if p did not depend on z (which will be discussed later), then q = p. As indicated in equation (12), the ratio of the density Auctuation of the major gas to the temperature ffuctuation caused by a wave is f3. The phase off; can be nearly 180’ for waves with short horizontal wavelength (Table I). which means that the Ruc-
Gravity
waves from O? nightglow
tuations of density and temperature can be in opposite phase. However, we cannot simply infer that the fluctuations of the apparent emission rate and the measured temperature are in opposite phase, because both the relationship between the apparent emission rate fluctuation and the major gas density fluctuation, and the relationship between the measured temperature and the in situ temperature are complex. The emission rate and the measured temperature depend not only on the fluctuation of the major gas density but also on the fluctuations of the minor gas density and the temperature.
during
campaign
II
383
2. p in the two-step transfer mechanism From equation (5) the linearized volume emission rate for the two-step transfer mechanism becomes
1
T’ -2 T . (35)
N’
where
I p in the three-hodJ~ reaction mechtmism
(37)
The volume emission rate of OZ from the threebody combination is given in equation (4). We use II, N. 2, N and k* as [O]. [N,], [O?], and k,, respectively, where
Here /I<,is an empirical parameter depending on Co, and C”. Substituting equations (12) and (17) into (35) yields
(27) Since x, does not change much in this region (Table 3) we may assume it to be a constant, so that the linearized perturbation expression fort: becomes
s: = [(1+8,11h+(z-r,,-B,),/;-2],T:. &I and gives P = ( 1+ B
= [2-&-lL-~W1 c = c,, 1+2; [
+(I-a,)m;’
(1
0
-2;
0‘I
,
(38) 0
(28)
+lL)l.f?
+ (I +8”)(1 +DH)
? (39)
(Y-1)
where
Comparing equations (34) and (39) the difference between the ps of the three-body mechanism and the two-step mechanism is PI?-\rcpl= We may therefore mechanisms :
(the unperturbed (k*)’
= -2kz
F~
part of k, in equation (the perturbed
p = (1 -a,,-‘DH),I;+ (4)),
part of k ,),
0
(31)
-a&2];.
(33)
0 According to equations (25) and (If?), equation gives p = ?fhf(l -%).f;-2 = (l-r,-2DH)fi+
2(1+DH) ~ ~ ;,_,
-2.
+
( ] -
b,,)(.f
2”;_;H) i
(33)
(34)
(40)
-.fh).
use one equation
of p for the two
-2
.
(32)
Here %(.indicates the quenching effects by O2 and N,, and LX,,= 0 implies no quenching is included. Substituting equations (I 2) and (17) into (28) yields the fractional volume emission rate perturbation as ;I = [2f;,+(I
PC?-hod,)
(41)
with /I,, = 1, i 0 ( B,, < 1,
for the three-body for the two-step
mechanism
;
mechanism.
Equation (41) shows that p depends on z through the three parameters, D, CI,, and PO, which represent the vertical distribution of the atomic oxygen density, the quenching effect, and the photochemical mechanism, respectively. The values of these three parameters are listed in Table 3 using the MSIS-86 model for 6 April 1989 midnight at 18”N, 293”E. Both s(, and /I0 are between zero and one and monotonically
s. P.
384
ZHANG
decrease as the altitude increases. This means that quenching (cc,) happens most’ty in the lower part of the emission layer and the three-body mechanism (&,> fits the lower part of the emission layer better than the upper part. It is worth noting that /I, = 1 is equivalcnt to C” = 0 in equation (37). The D value monotonically decreases, too, but from positive to negative. Positive D corresponds to an increasing density of atomic oxygen with altitude, and negative D to a decreasing density of atomic oxygen. In principle we need only substitute this equation (41) For p into equation (26) and integrate to complete the calculation of rl. In practice the integratjon is performed nur~~erica~ly as in the following section.
NUMERICAL 1.
PREDICTION
OF q
Emission layer with constant D, x,, and /&
In order to investigate 4 and the influence on q from D, r,, and pO, we first treat the emission layer as a layer
in which these three parameters are constant, making p independent of z. From equation (28) we have
YI
Ni.
tj = p = pr + ipi = 1~1e”,
where pf and pi are the real part and the imaginary part of p, respectively. Positive dpmeans the apparent emission rate leads the measured temperature, negative d, means the reverse. The numerical results of q are shown in Figs 224 where the horizontal wavelength Ir, is chosen as 200, 400,600, . . ,200O km, and the intrinsic period varies from 10 to 360 min. The calculations are only for upward propagating internal waves. a. R~.s~4lts,f#rthe ~ha~rna~ rnec~lun~stn. fn Fig. 2a and 2b, the vafue of q is calculated by the Chapman mechanism using the values of I), z, and r”;,at altitudes of 94,95 and 96 km separately. As mentioned above, the peak of the O2 emission profile is at about 95 km according to the Chapman mechanism, so the three cases represent the layer just below the peak of the O2 emission profile, the layer at the peak, and the layer just above the peak. In the layer at 95 km, I?] is almost a constant 4.6. and (1,is almost 0’. It implies that q is unresponsive to the wavelength and wave period.
(a) 5.5
E =
2000
km
5
0
(42)
200
100
Period
(min.)
Fig. 23. The value of /pi in the two-step mechanism calculated by using the values of D, a, and j$, at altitudes of 95 km (below), 94 km (middle), and 93 km (above) for horizontal wavelengths I, = 200, 400, 600. 800. 1000, 1200. 1400, 1600. 1800 and 2000 km. The wave period used is the intrinsic period.
2-
-x s
o-
-2
; -4
= ‘200
km
0
A*
=
Period
km
300
200
100
2000
(min.>
Fig. 2b. As in Fig. 2a, the value of Q1cakxkited by using the values off), q, and p0 at altitudes (below), 94 km (middle), and 93 km (above).
of 95 km
6
r =
=
200
2000
km
km
100
200 Period
300
(min.)
Fig. 3a. The value of jpl in the three-body mechanism calculated by using the values of D, LX$, and /& at altitudes of 96 km (below), 95 km (middle), and 94 km (above) for horizontal wavelengths i., = 200, 400, 600. 800. 1000, 1200. 1400. 1600. 1800 and 2000 km. The wave period used is the intrinsic period.
Fig. 3b. As in Fig. 3a, the value of @ calculated by using the values of D, n, and &, at altitudes of96 km (below), 95 km (middle). and 94 km (above). I
(a)
’
”
I
.
a
’
6
Zbokm
A,
=
km L
4 0
*
I
I
a
I
2QO Period (min.)
100
s
‘1
x
f
300
Fig. 4a. The value of p in the two-step mechanism without the quenching term calculated by using the values of IJ and POat altitudes of 94 km (below). 93 km (middle), and 92 km (above) for horizontal wavelengths 1, = 200,400.601), 800, 1000, 1200. 1400, 1600, 18fY.land 2000 km. The wave period used is the
intrimir wrinrt
Gravity
waves from O? nightglow
I
(b) 200
”
during
campaign
II
387
,a
”
km
I A,
=
2900
s km
2
0
8
-2
-4
200 Period
(min.)
Fig. 4b. As in Fig. 4a, the value of @ calculated by using the values of D and /I<,at altitudes of 94 km (below), 93 km (middle). and 92 km (above).
The value of Irl( from the lower layer is between 4.9 and 5.6, and the value of @ is between 0 and 3.6 For a fixed horizontal wavelength, 1~1increases with increasing wave period, but when the period is greater than a certain value (depending on I,), 1~1is almost constant. For a fixed period, 1~1 increases when the horizontal wavelength decreases. The fluctuation of the emission rate leads the fluctuation of the measured temperature by a few degrees. For a fixed horizontal wavelength, I@,1increases first with increasing period. after reaching a maximum value (-3.6 ) and then gradually tends to 0 The value of InI from the upper layer is between 3.7 and 4.3, and the value of @ is between - 3.6 and 0~. The fluctuation of the measured temperature leads the fluctuation of the emission rate. The value of 1~1 decreases when the wave period increases for a fixed wavelength. b. Results ,fbr the Burth mechunism. In Fig. 3a and 3b, the values of q are calculated by the Barth mechanism using the values of D, CI,and PC,at altitudes of 93, 94 and 95 km separately. The peak of the emission profile is at 94 km by the Barth mechanism. The
figures have features similar to those of Fig. 2a and 2b with slightly different ranges of 1111 and 0,. c. Results ,for the Chapman mechanism without qwnching @cts. Since the quenching effect increases the altitude of the peak of the emission layer by about 1 km, the peak of the emission profile is at about 94 km when a, = 0 and /I$ = 1. In Fig. 4a and 4b, the values of 7 arc calculated using the values of D at altitudes of 93, 94 and 95 km separately. Therefore, those figures show how D changes p. 2. Emission buyer in N reulistic utmosphcre The three parameters, D, M,,and /IO, in the O2 layer are not in fact constants, and so p is a function of altitude. A sample of how p varies with altitude in both magnitude and phase is shown for the specitic combination of E., = 1000 km and P = 120 min in Fig. 5. The phase is seen to be positive below the altitude of peak emission rate (95 km in this case) and becomes rapidly more negative with increasing altitude above the peak, whereas the magnitude decreases monotonically from the bottom to the top of the layer. For ground-based measurements the ver-
388
S.
P.
ZHANG 6’1al
GO
85
1.~1and
#* of p
Fig. 5. The vertical distributions of lpi and @ (degree) of p for a wave with period = 120 min and /1, = 1000 km in the Chapman mechanism.
tical integration of these two curves gives the phase and magnitude of r]. In practice, we calculate v directly by integrating equation (26) using the MSIS-86 atmospheric model. The calculations for 9 using the two excitation mechanisms are shown separately in Figs 6 and 7. Figure 6 shows q calculated using the three-body reaction mechanism for an emission layer given by equation (4) between 85 and 110 km altitude, which includes 99% of the total 0, volume emission. The ranges of period and horizontal wavelength are selected to limit J., to being greater than 10 km to be relevant to MORTI observations. The range of Jqj is from 4.4 to 9.7, and the range of tf, is from - 80 to 0‘ fn Fig. 7 5 is calcufated using the two-step transfer mechanism for an emission layer given by equation (5) between 85 and 108 km altitude, which also includes 99% of the total O2 volume emission. The range of 1~1is from 3.9 to 9.9, and CDfrom -84 to 0 The differences between Figs 6 and 7 are small, indicating that measurements of v will not help to resolve any questions about the relative importance of the chemical excitation mechanism. In both cases both lr?l and @ vary slowly and smoothly as functions of period and horizontal wavelength, but more slowly
for longer wavelengths. The temperature fluctuations lead the column emission rate fluctuations for all wavelengths and periods shown, and the lead diminishes as the horizontal waveIength increases. The absolute value of the phase difference at any wavelength decreases as the period decreases, which means as the phase speed increases, or as the waves approach evanescence. At a fixed period, we see that the phase of q approaches zero and the magnitude increases as the wavelength increases. The integrated values of q, particularly @, are much greater than the results from a uniform emission layer with the values of D, tl, and & at altitude of 95 km (three-body mechanism) or 94 km (two-step mechanism). The large @ is caused by the upper part of the emission layer, mainly above 97 km altitude (Fig. 5).
Since p, and k, are zero for evanescent waves, CDcan be either 0 or 180 depending on pI > 0 or p, c 0. For example, waves with a horizontal wavelength of 2000 km and a wave period less than 134 min, are evanescent. Table 4a and 4b give the 4 values calculated for an emission layer from 85 to I10 km altitude and from a uniform layer at 9.5 km by the three-
Gravity
-80
-A,
=
200
waves from 0: nightglow
during campaign
389
II
km
(b)
/
.
I,
*
100
I
*
/
a
*
200 Period
,
‘
300
(min.)
Fig. 6. The value of /?/ and cf, in the two-step mechanism calculated by numerically integrating equation (26) for an emission layer from 85 to 108 km for horizontal wavelengths I, = 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800 and 2000 km. The wave period used is the intrinsic period. Table 4a. The q values for short period evanescent waves using the three-body reaction mechanism (A, = 2000 km) O3 layer at 94 km Period
.-
(min) ~.__
-.._
130 120 110 100 90 80 70 60 50 40 30 28 26 24 22 20 IO 8 6
IYI*
4.54 4.53 4.51 4.48 4.45 4.40 4.34 4.24 4.07 3.74 2.86 2.47 1.57 0.80 1.71 15.9 5.54 5.12 4.83
0: layer
CD
l&t
@
0' 0’ 0 0’ 0’ 0’ 0 0‘ 0 0 00 I) 0 I80
4.56 4.57 4.57 4.57 4.57 4.51 4.57 4.57 4.57 4.57 4.57 4.57 4.57 4.57 4.57
0’ 0 0’ 0 0’ 0‘ 0‘ 0: 0; 0’ 0’ 0“ 0’ 0’ 0’
180 0 0 0
4.57 4.58 4.58 4.58
;:
__
0” 0’
4.34 4.82 5.35 6.00 6.87 8.06 9.79 12.48 17.01 25.85 49.34 59.78 75.86 104.4 171.3 550.4 22.17 Il.19 3.31
0’ 0 0 0 0 0 0 0’ 0“ 0 0’ 0‘ 0’ 0 0‘ 0 180” 180” 180”
: 85- 110 km
3.85 3.73 3.67 3.64 3.61 3.59 3.58 3.56 3.55 3.54 3.54 3.54 3.54 3.54 3.54 3.52 3.47 3.43 3.31
0’ 0“ 0‘ 0” 0” 0 0’ 0 0” 0 0 0 0 0” 0’ 0’ 0” 0 0;
!\\i s. P. .&Al'%
390
et Ui.
Q-““l”“l”“l”4
-20
-40
A,
=
2000
km
I
-60
-00
-A,
=
I 200
km
\
0
100
200
300
a
100
200
300
12
2 Period
(min.)
Fig. 7. The value of 1~1and Q, in the three-body mechanism calculated by numerically integrating equation (26) for an emission layer from 85 to 110 km for horizontal wavelengths A, = 200, 400, 600, 800, 1000. 1200, 1400, 1600, 1800 and 2000 km. The wave period used is the intrinsic period.
Table
4b. The 9 values for short period transfer mechanism
evanescent waves (A, = 2000 km)
0, layer at 94 km Period (min)
using the two-step
0: layer:
85-108
km
__
130 120 110 100 90 80 70 60 50 40 30 28 26 24 22 20 10 8 6 *When
f --5 -~
141* 4.44 4.42 4.40 4.37 4.33 4.28 4.21 4.09 3.90 3.52 2.52 2.07 1.39 0.17 2.69 18.9 5.58 5.11 4.77 a =
m 0: O’> 0’ 0’. 0 0‘ 0” 0 0” 0’ 0” 0’ 0” 0” 180’ 180” 0” 0” 0
1/2H-&
IsIt
@
Id*
@
lrll+
@
4.46 4.47 4.41 4.47 4.47 4.47 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.49
0 0‘ 0 0’ 0 0 0‘ 0’ 0’ 0’ 0 0’ 0’ 0’ 0’ 0” 00” 0‘
4.21 4.69 5.21 5.85 6.70 7.87 9.58 12.21 16.66 25.24 48.42 58.68 74.47 102.5 168.2 540.6 21.82 11.04 3.30
0 0” 0 0’ 0 0‘ 0‘ 0‘ 0’ OF 0’ 0 0” 0’ 0 0’ 180“ 180 180
3.73 3.62 3.56 3.53 3.50 3.48 3.47 3.46 3.45 3.44 3.43 3.42 3.42 3.42 3.42 3.42 3.37 3.32 3.20
0’ 0’ 0, 0’ 0’ 0’ 0‘ 0 0’ 0’ 0 0 0 0 0’ 0 0 0’ 0’
-: z h,(m,,/ru
T.- -I)-_(W’-u~)/C’:
twhen
z = 1/2H+
Gravity
waves from 0: nightglow
body model, and from 85 to 108 km and from a uniform layer at 94 km for the two-step model, respectively. There are two sets of results corresponding to two c( values given by equation (8). The first set of results is given for 2 with the negative sign in equation (8). In this case (~1 has a wide range, from 3 to 550, and there is a singularity at a period near 20 min. where r = o’/g in the function_f\. The measured temperature fluctuations may then have the same phase as the emission rate fluctuations or be totally out of phase. The second set of results is given for the positive sign in equation (8). In this case q is almost constant in magnitude at 3.5 with zero phase. For evanescent waves with increasing period, the difference between these two solutions decreases. DISCUSSION
Because the 0, atmospheric band is weaker in intensity and therefore more difficult to analyze than the OH emission, the available observations of gravity waves from the 0, airglow which measure both periods and wavelengths are more scarce than those of OH (see for example, TAYLOR rt d., 1991). We will compare our theoretical predictions of q with the observations of 9 by ZHANG d al. (1993) in paper I. then with those reported by VIERECK and DEEHR (1989) to evaluate our model.
during
campaign
II
I. Comparison with AIDA
391
‘89 observations
Thirteen gravity waves in the 0, nightglow were measured by MORTI during the AIDA ‘89 campaign in Puerto Rico (17’57’N, 66”52’W) and analyzed to give q and the kinematic wave characteristics in paper I. The comparison of the observed and the predicted q by integrating equation (26) are listed in Table 5a using the Chapman mechanism, and Table 5b using the Barth mechanism. There are two sets of calculated q, the first one corresponds to zero wind speeds, and the second one corresponds to the wind speeds mcasurcd by BIRD (~1a/. ( 1993) from the O’S emission layer 3 km higher. The predicted q values by both mechanisms agree fairly well with the 1~1values but poorly with @values. According to Fig. 6.3b (or Fig. 6.4b) the agreements are improved significantly if the predictions are made for a uniform layer at about 96 km (or 95 km), but of course such a picture does not seem to be realistic. We note that the integrated v in Table 5 are similar for the specific MORTI cases to the TH90 ‘1 predictions given in paper I. Two cases of evanescent waves are listed in Tables 5, on 1 l/l2 April and 4/5 May. The measurements gave 1~1of 3.7 and 4.0, respectively, and Q = 0’ for both, corresponding to 3.9 for the solution with the positive sign in s( both nights, and 4.5 for the negative
Table 5a. Comparison of the observed reaction
P Date
(min)
516 April
q by MORTI and the predicted 4 using the three-body for an emission layer between X5 and 110 km
mechanism
126
I&
@
(observed) 3.5
(m/s) 0
-I
5.50 5.87 6.01 6.72
-32 -38, -40 -48
+57% +68% + 34% +49%
-31 -37’ -38’ -46’
0
4.97 4.75
-19’ -13
-10% -14%
-12; -6
0
3.92 3.91
0 0
4.83 8.34
0
4.79 4.87
+15
X/9 April
46
4.5
-2
308
5.5
-1
0 1-20 -34
I l/l2 April
160
3.7
- 16 -6
30 April/ 3!4 May
1 May
150 340
4.8 5.5
-0 -0
278
3.5
-0 +14
0 0
f6% +6%
+I6 +I6
- 15’ -57’
+ 1% f52%
-15’ -57
-14 ~ 16
+37% +39%
-14 - 16‘
415 May
106
4.0
-0
0
3.91
5/h May
162 82
4.8 5.2
-0 -0
0 0
5.75 5.71
-36’ -36’
+20% + 10%
- 36’ -36
617 May
132
5.0
-0’
0
7.02 5.97 4.57 4.50
-50 -39’ -7’ -5
f40% + 19% +20/o 0
-50 -39’ -7‘ -5
4.90
-17
f7%
-20 80
4.5
0
-0 -15
8,‘9 May
138
4.6
-0
0
0
-2%
0’
~ 17’
392
S. P. ZHaNG et al. Table 5b. Comparison
of the observed q by MORTI and the predicted 7 using the two-step mechanism for an emission layer between 85 and 108 km
P
@
Id
u
III -III, (predicted)
A@
(m/s)
126
3.5
- I”
46
4.5
-2
0 +15 0 +20
4.96 5.45 5.63 6.51
-43’ - 50” -52’ - 59”
+42% + 56% +25% +46%
-42’ -49’ -50 - 51”
308
5.5
-1’
0
4.30 4.08
-29” -21”
-22% -26%
-22 -14’
0
3.85 3.84
0’ 0’
-+4% f4%
+16’ fl6’
(min)
516 April
-34 160
11/12 April
@
(observed)
Date
8/9 April
I&
transfer
3.1
- 16’ -6
r
150 340
4.8 5.5
-0’ -0;
0 0
4.15 8.69
- 24” -67’
- 14% +58%
-24 -67’
314 May
278
3.5
-0’
0 +14
4.11 4.19
- 22” -26’
fll% +20%
-22 -26
4/5 May
106
4.0
-0”
0
516 May
162 82
4.8 5.2
-0’ -0”
0 0
3.84 5.28
0’ -48’
5.24
617 May
132
5.0
N 0”
0
6.95 5.58 3.96 3.93 4.22
-21’
30 April/l
May
-20 80
4.5
0
-0 -15
S/9 May
138
4.6
-0’
in Tables 5. The physical results seem to favor the positive sign solution in these cases, but both solutions are not very different. sign but are not listed
2. Comparison with Viereck and Deehr ‘s observations VIERECKand DEEHR (1989) reported a large number of observations carried out at Fairbanks, Alaska (64”N, 145”W), U.S.A. and Longyearbyen, Svalbard (78’N, 16”E), Norway. As mentioned in paper I, they did not distinguish between internal waves and evanescent waves in their measurements. Most waves they measured had periods of less than 1 h. For these waves, the Ipj was mostly between 0 and 2, and the phase difference was about 180”. Our calculations show, as in Tables 4, that the 180” phase difference is possible for evanescent waves using the negative sign in CI,and we can get small 1~1with this condition for a thin layer but not an integrated one. For a few long-period (longer than 2.8 h) waves in their measurements 1~1was between 2 and 7, and the phase was about 0”. Assuming those waves to be internal, the phase value again agrees with our prediction for a uniform layer, but the measured 1~1value has a wider range than that predicted. 3. Comparison with other theories As mentioned in paper I, the n value predicted by WEINST~CK (1978) was between - 0.1 and 1.1, which
0
-4%
0
-41’
+lo% + 1%
-48’ -47’
-61” -51” - 13” _ 9”
+39% +12% - 12% -13%
-61“ -51 -13 _ 9”
-8%
- 21’,
does not agree with our prediction. His theory was criticized by HINES and TARASICK (1987), and we will not re-examine it. HINES and TARASICK (1987) (HT87) used a semiLagrangian method in a frame of reference that moved up and down with the wave. The virtue of their method is that since we measure vertically integrated quantities, the altitude of the layer is not important, and their method leads to an analytical solution for the non-quenching three-body photochemical mechanism. We have taken the more direct Eulerian approach suggested by WALTERSCHEID et al. (1987). In our work, the physical quantities are represented at a given altitude. For both analyses using exactly the same atmosphere and the Chapman mechanism without quenching, it can be proved mathematically that the formulas of r] from the two methods, in our case the integral of equation (26), are identical. When quenching is involved with the Barth mechanism, which was discussed by TARASICK and SHEPHERD (1992a), the situation is much more complicated, and the identity of these two approaches is difficult to prove mathematically. Numerical calculations for this case with different periods and wave speeds resulted in the graph of Fig. 8. Comparison with the equivalent fig. 3 of TARASICK and SHEPHERD (1992a), shows no significant differences.
Gravity
waves from O2 nightglow during campaign II
Since the present study is based on the work of WALTERSCHEIDet al. (1987), it shows, as might have been expectkd, that the HT87 and the WALTERSCHEID et 01. (1987) approaches are fundamentally the same, provided the integration is over the full thickness of the layer in both cases. It also shows that neither approach provides an adequate explanation of the phase of rl. It is worth noting that the Walterscheid method was extended by HICKEY (1988) to include eddy dissipation in his study of waves in the OH layer. Hickey’s results showed that at horizontal wavelengths comparable to those seen by MORTI in 03, that is, 1000 km, and periods of several hours, the phase of? did in fact become zero. Similar calculations for the 0, layer have not been performed, but they would seem to be the next logical step. CONCLUSION
The present study is an attempt to satisfy the need shown by ZHANC et al. (1992) for an improvement in our understanding of the dynamical
393
the perturbed and mean integrated column emission rates, respectively, of the 0, (&l) band, and T’ and T, the brightness weighted temperatures integrated through the O2 nightglow layer. The model used is an extension of one presented for the OH layer by WALTERSCHEID et al. (1987), but employing O,(b’&+) excitation chemistry and integration over the whole layer. The results show 1~1as a smoothly varying number, depending upon wavelength and period, that lies in the range 3.9-8.3 for waves of the kind reported by ZHANC et al. (1993). which is somewhat larger than the observed values, in the range 3.5-5.5. Whereas the measured phases ranged from - 16 to 0 , this model predicted -67-O Evanescent waves give good agreement for predicted and measured q, slightly favoring the positive option for x in equation (8). The model is in fact shown to be numerically equivalent to the one by HINES and TARASICK (1987) and further developed by TARASICK and HINES (1990) and TARASICK and SHEPHERD (1992a). In neither development is there a significant difference between the ‘1predictions for the Chapman and the Barth mechanisms, suggesting that the weaknesses are probably not chemical. Rather, the neglect of all dissipative effects may be the cause of the discrepancies.
10
I
6
6
x A,
/
P
=
150
m/s
4
_L 2
0
I
I
1
10 Period
Fig. 8. Variation
100
(P/P,)
of (~1 with wave period for horizontal
wave speeds 60, 100 and 150 m/s
394
S. P.
ZHANG
It is of considerable interest that 1~1 as predicted comes as close as it does to the observed ratio in view of the assumptions made. The importance of these models is that (~1 is in fact shown to be a well-behaved function. Then by equations (1 I)-( 14) all of the state variables of the gravity wave that relate to T//T, also relate to B’/B_ through n. and the use of ontical vhotometry for the study of these waves is justified. An example that employs equation (14) for horizontal perturbation velocity is described in the accompanying paper by WANG et al. (1993). Still others are \,
_
.,
I
et al.
possible as suggested by the polarization factors and phases listed for specific wavelength-period combinations in Tables 1 and 2.
Aclinow,leajqmenfs-The Institute for Space and Terrestrial Science is a designated Centre of Excellence of the Province of Ontario, Canada. S. P. Zhang was supported by a grant from the Natural Science and Engineering Research Council of Canada. The authors wish to thank the guest editor, C, 0. H’mes. for a significant contribution to the tinal version of ihis work.
.
REFERENCES BIKII J. C.. TEPLEY C. A. and SHEPHEKI~ G. G.
1993
CHAPMANS.
1931
GREER R. G. H., LLEWELLYNE. J., S~LHEIMB. H. and WITT G. HEDINA. E.
1981
HICKEYM. P.
1988
HINESC. 0.
1960
HINESC. 0.
1964
HINESC. 0. and TARASICKD. W.
1987
HOUGHTON J. T.
1986
KRASS~VSKY V. 1.
1972
MCDAIX I. C., MURTAGHD. P., GREER. R. G. H., DITKINSON,P. H. G., WITT, G., STEGMAN, J., LLEWELLYNE. J., THOMASL. and JENKINSD. B. MURTAGHD. P., WITT G., STEGMAN J.. MCDA~E I. C., LLEWELLYNE. J., HARRISF. and GREEKR. G. H. NOXONJ. F.
1986
SOLHEIMB. H. and LLEWELLYNE. J.
I979
TARASI~KD. W. and HINESC. 0.
1987
TARASICKD. W. and SHEVHERD G. G.
1992a
TARASICKD. W. and SHEPHERDG. G.
1992b
TAYLORM. J., ESPY P. J., BAKERD. J., SICA R. J.. NEAL P. C. and PENDLETON W. R. JR
1991
T~RR M. R., TORR D. G. and LAHEKR. R.
1985
VIERE~KR. A. and DEEHRC. S.
1989
I987
1990
1978
Optical measurement of neutral winds during AIDA ‘89. J. atmos. WV. Phys. 55, 313. Some phenomena of the upper atmosphere. Proc. R. SW. Lord. (A) 132, 353. The excitation of 02(b’Z:) in the nightglow. Planet. Space Sri. 29, 168 1. MSIS-86 thermospheric model. J. ,qeophy,s. RES. 92, 4649. Wavelength dependence of eddy dissipation and Coriohs force in the dynamics of gravity wave driven fluctuations in the OH nightglow. J. geophys. Rrs. 93, 4089. Internal atmospheric gravity waves at ionospheric heights. Gun. J. Phys. 38, 1441. Ionospheric movements and irregularities. Research in Geophysics, Vol. I. p. 299, H. ODISHAW(cd.). MIT. Press, Cambridge, U.S.A. On the detection and utilization of gravity waves in airglow studies. Planet. Space Sci. 35, 851. The Physics of Atmosphere.r. Cambridge University Press, Cambridge, U.K. Infrasonic variations of OH emission in the upper atmosphere. Ann. Geophys. 28, 736. ETON 2 : quenching parameters for the proposed precursors of O,(h’X,q+) and 0(‘S) in the terrestrial nightglow. Planet. Spuce Sci. 34, 789. An assessment of proposed 0(‘S) and 02(b’X: ) nightglow excitation parameters. Planet. Spaw Sci. 38, 43. Effect of internal gravity waves upon night airglow temperatures. Geophys. Res. Let/. 5, 25. An indirect mechanism for the production of 0( ‘S) in the aurora. Planet. Space Sci. 27,473. On the detection and utilization of gravity waves in airglow studies. Planet. Space Sci. 35, 85 I The effects of gravity waves on complex airglow chemistries I : OZ(h’Xd ) emission. J.,qeoph~s. Rrs. 97(A3), 3185. The effects of gravity waves on complex airglow chemistries 11: OH emission. J. geopl~~s. Rex. 97(A3), 3195. Simultaneous intensity, temperature and imaging measurements of short period wave structure in the OH nightglow emission. Planer. Space Sci. 39, I 171. The O2 atmospheric ((M) band and related emissions at night from Spacelab I. J. geophys. Res. 90, 8525. On the interaction between gravity waves and the OH Meinel (62) and the 0, atmospheric (&I) bands in the polar night airglow. J. yeophys. Rex. 94, 5397
Gravity
waves from 0: nightglow
WALTEKSCH~II)R. L., SCHUBEKTG. and STRAUSSJ. M.
1987
WANGD. Y., ZHANGS. P., WRENSR. H. and SHEPHEKDG.G.
1993
WEINSTOCK
197x
ZHANCi
J.
S. P.. PETEKSOKR. N., WENS R. H. and
SHEPHEKD G.
G.
I993
during
campaign
II
395
A dynamicalxhemical model of wave-driven fluctuations in the OH nightglow. J. yeophys.Res. 92, 1241. Gravity waves from O2 nightglow during the AIDA ‘89 campaign III : effects of gravity waves saturation. J. u~mos. [err. Phjs. 55, 397. Theory of the interaction of gravity waves with 02( ‘X) airglow. J. geophy.7. Res. 83, 5175. Gravity waves from O2 nightglow during the AIDA ‘89 campaign I : emission rate/temperature observations. .I. uin7o.Y. /err. Ph,lY. 55, 355.
ZHAEU’G,R.
H. WRENSand G. G.
SHEPHERD
Institute for Space and Terrestrial Science, York University, 4850 Keele St., North York, Ontario. Canada M3J 3KI
Abstract-The dependence of q. the ratio of emission rate fluctuation to temperature ~ucfuation, on the gravity wave parameters and chemical parameters is developed using a model for the O2 airglow’s response to a gravity wave. The model is in the Eulerian frame of reference using the traditional linearization and perturbation method. Two photochemical mechanisms, the three-body recombination mechanism and the two-step transfer mechanism, and two kinds of waves, evanescent and internal, are separately discussed in detail. Results of the model are compared with other existing models of q(02) and found to be in agreement. The predictions of this model agree fairly well with the available gravity wave measurements in the magnitude of q, but the predicted phases are somewhat larger than those normally observed.
theory which was later made specific to the Oz(b’Z) and to the OH airglow layers by TARASKK and SHEPHERD (1992a,b). Meanwhile, WALTERSCHEID er Variations in airglow brightness have been attributed to gravity wave activity for many years (e.g. HINES, al. (I 987) advanced yet another theory of p specifically for the OH airglow. Whereas the Weinstock treatment 1964; NOXON,1978; KRASSOVSKY, 1972), but a rigorinvokes non-linear considerations, the HINES and ous understanding of the relationship between the TARASICK(1987) approach avoids this by mapping dynamical and the chemical aspects has not yet emerged. Observations of the OH Meinel and the O2 the Eulerian equations back to unperturbed heights. WALTERSCHEID ef (II. (1987) begin with an Eulerian atmospheric airglow layers by optical spectrometers reference frame but restrict their concerns to a fixed allow for the measurement of the chemically related altitude. variable, that is, integrated column emission rate, and A choice of which of the above theoretical forthe dynami~dlly related variable, that is, mean layer rotational temperature, simultaneously. KRASSOVSKY mulations best represents observable realities has so far been hindered by a lack of relevant experimental (1972) related the chemical and the dynamical conmeasurements. Although cepts by defining the parameter q, the ratio of the many simultaneous measurements of emission rate and rotational temfractional fluctuation of the emission rate to the fracperature have been reported for both the O? atmotional fluctuation of the temperature, in his study of OH airglow. Since the temperature perturbations in a spheric and OH Meinel bands of the airglow, they have almost always been made at a single point in the gravity wave are linked to the corresponding persky, and hence provide periods as their only measured turbations of density, pressure, and velocity through wave parameter. As pointed out by TARASIC~ and the polarization equations set down by HJNES(1960), HINES(I 987) measurements of only g and period allow the further linking of perturbations of temperature to the modeler to choose the wavelength as a free parthose of emission rate through q makes emission rate ameter, and therefore do not allow the adequate testa useful quantity with which to study the impact of ing of any theory. An opportunity to test these gravity waves on the state of the mesopause/lower thermosphere region of the atmosphere. An applitheories more rigorously as they apply to the O2 atmospheric case was provided by the MORTI measurecation of this principle is to be found in the following ments made during the AIDA ‘89 campaign in Puerto paper, paper III, by WAKC rt ul. (1993). The concept of ye was employed by WEINSTOCK Rico. Here the corresponding wave components in (1978) to explain NOXON’S(1978) O2 atmospheric airboth column emission rate and mean rotational temperature were analyzed to find 1 and the period, as glow measurements. HINES and TARASIC~(1987) and usual, but also horizontal wave velocity and conseTARASICKand HINES (1987) provided an alternate 377
yuently all of the kinematic wave characteristics, These characteristics and the methods of obtaining them from the MORTI data are described in the preceding paper, paper I by ZHANG et al. (1993), where it is also shown that none of the theories mentioned above is able to predict q in both magnitude and phase to within the measurement uncertainty when the full characterization is taken into account. The inconsistencies between the existing theories and the AIDA ‘89 measurements of paper I stimulated the present work, the purpose of which is to present a numerical chemical-dynamical model of q in the O2 atmospheric nightglow for both internal gravity and evanescent waves. Following the derivation of WaLTERSCHEIDet (11.(1987) for q in the OH Meinel nightglow. this model employs the usual linearization and perturbation methods in an Eulerian reference frame. Two different photochemical excitation mechanisms for the 0,(6’Z:) atmospheric nightglow are included separately in order to determine whether gravity wave observations of any kind can provide a means of evaluating their relative i~n~orta~lce. THE EXCITATION MECHANISMS FOR O,(b’Z$)
The excitation mechanism for the O>(b’X:) has been debated for some years. Two mechanisms have been proposed, and we will treat both separately. The first one is the three-body recombination. also called the direct excitation (the Chapman mechanism), in which : O+O+M(02-t-Nz)
-+ 02(h’E:)+M
(I)
(CHAPMAN, 1931). Although no longer having widespread support, this proposal is simple enough to allow for inclusion in models in closed mathematical form, and so has been covered in the theoretical papers of W~INST~CK( 1978) and HIKF~and TARASICK (1987). The second, more widely accepted, proposal is the two-step process, also called the transfer excitation (the Barth mechanism). in which :
O+O+M(OzfN?)
+02((.‘C,; )+M,
02((.‘C,, )102 --+O,(h’q)+O,
(2)
(SOLHEIMand LLEWELLYN,1979; GREERet al., 1981; T~RR er crl., 1985 : MURTA<;Hef al., 1990). The actual identification of the precursor state, here designated as 02(c’Cti ) is still open to question, but the method does not depend upon the specific state. In either case the atmospheric bands result from o&?‘c:)
-+ O&Y’C;)+hv.
(3)
When quenching of O,(h’Z:) by atmospheric O2 and N, is included. the volume emission rate (photons
cm-’ s- ‘) for the three-body recombination expressed as
may be
(MCDAIX if n(., 1986), and for the two-step transfer mechanism it may be expressed as
6 =~ _~ _. k,A,[01’([0~1+[Nzl)[o,~____ ~.~~~.~~~~~~ (A2+f@[02]+K>?[N2])(C
~[O,]+c’“‘[O1) (cm-‘s-‘)
(5)
(M~RTA~H et al., 1990; MCDADEet a!., 1986), where k, = 4.7 x 10-~~(300/~)2
cm6s
’
(6)
is the rate coefficient for three-body recombination of atomic oxygen ; and [O](cm-7) is the number density of atomic oxygen, [O,](cm-‘) is the number density of molecular oxygen, [N,](cm-I) is the number density of nitrogen. c A 0.1, the Fraction of recombinations, il 1 = 0.079 s ‘, the (@O) band transition probability. <4>= 0.083 s- ‘, the inverse radiative lifetimeofO,(h’C,i ). K$ =4.0x 10 “cm”s ‘. therate coefficient for quenching of 02(b’Xl) by atmospheric 0 2, KN~=27~10-‘5 cm3 s.- ‘, the rate coefficient 2 .for quenching of OJb’Z:) by atmospheric N,, Co2 = 7.5, the empirical parameter defined and evaluated by MCDADEet al. (1986), Co = 33, the empirical parameter also defined and evaluated by M~DADE ef lli. (1986). Using the three-body recombination the volume emission rate produces a peak altitude of 95-96 km, and using the two-step transfer processes the peak is at about 94 km. The thickness of this emission layer is calculated to be about 8 km. BASIC EQLATIONS AND SOLUTIONS OF WAVE MOTION
In order to obtain a reasonably simple solution For gravity waves in the atmosphere, we use the conventional assumptions (HINES, 1960; HOUGHTON, 1986; WALTERSCHEID et al., 1987) : the atmosphere is isothermal and motionless in the absence of waves; the motion of waves is adiabatic; the Coriolis term, the friction term, molecular diffusion, and eddy diffusion are ne.glected; and all equations are linearized. The wave solutions of T’/T, (temperature), P’/PO (pressure}. IV/N,, (density), w’ (vertical velocity) and C:’ (horizontal velocity) are expressed as complex numbers in the form :
Gravity
waves from O2 nightglow
during
campaign
II
379
where time t, coordinates x and z-, horizontal and vertical wave numbers k, and k= are all real numbers. The constant r, a real number, will be found, w is the circular frequency of the wave, and C is the speed of sound. The primes and naughts denote perturbed and unperturbed quantities, respectively. The basic equations of wave motion for the major gas (HOUGHTON, 1986) have two solutions. The first one is :
where H is the scale height of the major gas, g is the acceleration of gravity, and 11is the ratio of the specific heat of air at constant pressure to the specific heat of air at constant volume, for dry air y = 1.4. Also ~t)~is the Brunt-V~is~l~ frequency, w,, is the acoustic cutoff frequency, and C is the speed of sound. If the atmosphere is in hydrostatic equilibrium, then C2 = Hg-f. Since k; = 0, there is no phase variation in the vertical : waves associated with this solution are called cvanescent waves. The a is a function of the wave frequency and the wavelength. There are two c( values given by equation (8) corresponding to two waves which have the same period and wavelength but different amplitudes. Numerical calcutation shows the two values of a are both positive while the wave period is between 20 and 360 min and the wavelength is between 100 and 2000 km. The argument of the square root in equation (8) is almost zero for long period waves. With o’ <
The second equation of equation (9) is well known as the dispersion relationship. The waves associated with this solution are called internal waves (HINES, 1960). The Brunt-VBidIl frequency is the maximum frequency of internal waves, Generally, the wave speed of the internal wave is lower than that of the evanescent wave. Using notation similar to that of WALTERSCHE~D et al. (1987) we derive
The parameter,/; is a complex number for the internal wave, and a real number for the evanescent wave, that is
(for internal waves),
(for evanescent waves).
i IS)
(15’)
The five variables, T’fT,, P’fPo, N’fN,, ii’ and H”, have different amplitudes and phases which depend on wave periods, wavelengths. and the scale height of the major gas. Tables I and 2 are numerical examples of the ratios of P’fP,, N’fN,, V and w’ to T’J7;,. THE WAVEPERTURBATION IN ATOMICOXYGEN Figure 1 shows the vertical profiles of the number densities of atomic oxygen, molecular oxygen, and nitrogen calculated by the MS&86 model (HEDIN, 1987). Unlike molecular oxygen and nitrogen, atomic oxygen is not in hydrostatic equilibrium; the distribution of atomic oxygen strongly depends on photochemical processes. The profile of the volume emission rate of the 0, airglow, as shown in Fig. 1, is clearly related to the profile of atomic oxygen. Assuming that all species have the same tcmperature and velocity as the background major gas (WALTERSCHJSID et al., 1987), the continuity equation of atomic oxygen is
where n is the density of atomic oxygen that n = n,+n’, and P’ and L’ are the perturbation parts of the production and loss of atomic oxygen. respectively. At night P’ = 0, and the loss L’ is so much
380
Table 1. Polarization
factors*
for waves generated Amplitude
in lower atmosphere
ratio
with period
120 min
Phase difference -
100 200 300 400 500 600 700 800 900 IO00 1100 1200 1300 1400
1500 1600 1700
1800 1900 2000 2100
*Using
-4.0 -8.1 - 12.2 - 16.5 -20.9 -25.5 - 30.5 -35.8 -41.7 -48.3 - 55.8 -64.7 -15.6 - 89.6 - 109.4 - 141.3 -211.3
0.111 0.222 0.334 0.445 0.556 0.667 0.779 0.890 1.001 1.113 1.224 1.335 1.446 1.558
- x - x YL - *x, --‘10 - ,Co -CC - 71
2.125 1.863 2.946 I.497 3.545
I .669 I.780 1.892
1.379 4.121 1.308
1.000 1.000 1.000
0.999 0.999 0.999 0.999 0.999 0.999 0.999
1.580 1.580 I .580 I.580 1.580 1.580 1.580 1.580 1.580 1.580 1.580 1.580 1.580 I .5x0 I.580
1.125 0.863 1.946 0.497 2.545 0.379 3.121 0.308
0.0249 0.0296 0.0 100 0.0363 0.0008 0.0384 0.0112 0.0397
1.676 1.470 2.202 I.119 2.517 0.979 2.787 0.884
1.000 1.ooo t .ooo I .ooo 1.000 1.000 1.000
factors*
for waves generated Amplitude
80 60 40 30 30
- 87”
1.580 -84 -80’ --77’ -74” -70“ -67 -64 -60 -56‘ -52, -48 -44’ -39’ -33’ -27‘ -19
_-88”
- 174’ - 167’ - 161’ -154 - 148 - 141 -134‘ - 127 -120 --II? - 105‘ --96 -87 -78 -67‘ -54 -38
-86” -85’ -83’ -81’ - 79’ -77 -76 - 74” -72’ -71 -- 69 -68 -67’ -66’ -67 - 70’
- 87’ -84” -80’ - 71“ -74 - 70 -67‘ -64.’ -60’ -56’ -52 -48‘ - 44’ -39“ - 33’ -27 -19
0 0’ oi 0’ 0 0 0 0
-90 - (10 -90 - 90’. 90‘ -90 90 -90
0’ o-’ 0’ 0” 0” 0’ 0 0
0’ 0 0 0’ 0 0 0 0
the scale height H = 5.730 km. the speed of sound = 276 m/s.
Table 2. Polarization
360 340 320 300 280 260 240 220 200 180 160 140 120 100
1.580
0.0633 0.063 1 0.0627 0.062 1 0.0613 0.0604 0.0593 0.0580 0.0565 0.0548 0.0528 0.0505 0.0480 0.0450 0.0416 0.0376 0.0329
ratio
~-..____I 1.000 0.0211 1.000 0.0223
-6.7 -7.1 -7.6 -8.1 -8.7 -9.3 - 10.1 - 1 I.1 - 12.2 - 13.6 - 15.4 - 17.7 -20.9 -25.5 -33.1 -48.4 - 110.4
0.186 0.196 0.209 0.223 0.239 0.257 0.278 0.304 0.334 0.371 0.417 0.477 0.556 0.667 0.834 1.110 I.661
0.999 0.998 0.99 I
0.0237 0.0252 0.0270 0.0291 0.0314 0.0342 0.0376 0.0417 0.0467 0.0530 0.0613 0.0725 0.0881 0.1096 0.1250
- Z’ - Z> - nj -CC
3.569 I.368 10.31 1.076
2.569 0.368 9.311 0.076
0.0050 0.1544 0.7400 0.2634
1.000 1.000 1.000 1.000 1.ooo 1.000 1.000 1.ooo 1.000 1.000 1.000
1.000
in lower atmosphere
with & = 500 km
Phase difference .-- .____~
____- 169” -169” - 168. - 167’ -166 -- 165’ -164 - 163‘ - 161 -159 -156” -152 - 148’ -141’ -131” - 113” -67’
-87’ -87 -87 -86“ - 86” -86 -- 85 -85 -85’ -84’ -83’ -82’ -81 - 79,. -76’ -12 -67
-85 -84’ - 84’ -84’ -83’ -83” - 82“ -81“ -80 -79 -78”
1.572
-85 -84 -84 -84‘ -83’ -83 -82‘ -81% -80‘ -79’ - 78” - 76’ -74 - 70“ - 65’-56“ -33’
2.534 0.971 4.881 0.509
0 0, 0‘ 0’
0 0 0 0“
90 -90 90‘ -90
0 0’ 0’ 0”
1.581 1.581 1.58L I.581 1.581 I.581 I.581 I.581 I.581 I.581 I.580 I.%0 1.580 1.579 1.578
i .577
* Using the scale height H = 5.730 km, the speed of sound
= 276 m/s.
-76’ -74‘ -70‘ -65’ -56’ - 33.‘
Gravity
waves from O2 nightglow
during
campaign
3x1
II
120
110
100
90
0
2
4
6
6
10
12
Fig. 1, Vertical profiles of the volume emission rate of the OL airglow emission using the two-step transfer mechanism, temperature, number densities of atomic oxygen, molecular oxygen, and nitrogen calculated
by MSIS-86 model.
smaller than the other terms in equation (16) by comparison (less than I/1000) that it may be neglected. Substituting equations (IO), (11) into (16) yields
THE RATIO $ = @‘/I&) : ( r,i T,,)
In a ground-based measurement such as the kind described by ZHANGrt al. (1993), the apparent emission rate, B, is given by ,
where
B=
s0
Edr,
(20)
and the measured temperature, T,, is weighted by the apparent emission rate as and
H,, is the scale height of atomic oxygen. Obviously if DW = - I. that is, H,, = H, the scale height of atomic oxygen equals the scale height of the dominant gas, and ,fh =,fi. However below 99 km, D is positive (Table 3 and Fig. I) meaning that the scale height of atomic oxygen is negative, whereas the scale heights of major gases, O2 and Nz, are always positive. Then ,f6 is quite different from f3. For example, at 94 km altitude, D % 0.8 x 10-4mm ’ and H x 5.730 km, from equation (17) we havef, = - 1.4f,+2.5.
where c is the volume emission rate, and T(.Y,:) is measured along the line of sight. This physical situation is identical to that invoked by WEINSTOCK(1978) and by HINES and TARASICK(1987). If the viewing direction is 0 degrees from the vertical, then it is easy to transfer dr into d; by setting dv = secOd_ and x = _x,+ z tan 8, where _v, is a constant. The effect of non-zero 0 is studied by TARASICKand HINES (1987) who showed that for waves with period longer than 30 min, the effect is negligible at least for fI < 45‘.
3x2
S. P. ZHANG et (11.
Table3.Atmospheric parameters
-~ 85 86
87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 IO3 104 105 106 107 108 109 110
10.13 9.192 X.216 7.244 4.312 5.447 4.663 3.968 3.362 2.840 2.395 2.018 I.700
2.656 2.403 2.141
0.464 0.716 1.046 1.452 1.921 2.432 2.959 3.474 3.950 4.366 4.708 4.968 5.143 5.236 5.254 5.205 5.097 4.941 4.744 4.516 4.264 3.884 3.612 3.334 3.056 2.782
I.880 1.630 1.399 1.190 1.006 0.845 0.708 0.591 0.492 0.409 0.340 0.282 0.233 0.193 0.159 0.131 0.107 0.088 0.071 0.058 0.046 0.037 0.030
1.433 1.208 1.019 0.860 0.725 0.612 0.515 0.433 0.364 0.305 0.255 0.212 0.176
0.262 0.261 0.261 0.260 0.258 0.257 0.255 0.254 0.251 0.249 0.247 0.244 0.241 0.237 0.233 0.229 0.224 0.219 0.214 0.208 0.202 O.lY6 0.189 0.182 0.176 0.16Y
0.730 0.710 0.686 0.659 0.627 0.592 0.554 0.514 0.472 0.431 0.389 0.349 0.312 0.276 0.243 0.213 0.186 0.162 0.140 0.121 0.103 0.088 0.075 0.063 0.053 0.045
5.43x 4.609 3.881 3.230 2.660 2.167 1.740 1.370 1.053 0.783 0.552 0.352 0.181 0.034 -0.093 -0.207 -0.306 -0.399 -0.481 -0.555 -0.631 -0.700 -0.770 -0.834 -0.897 -0.960
0.992 0.987 0.979 0.967 0.951 0.929 O.YOl 0.868 0.829 0.786 0.740 0.692 0.644 0.596 0.549 0.505 0.462 0.423 0.385 0.351 0.318 0.294 0.266 0.241 0.217 0.196
-
*z, = [0,]/[N2]; fee,seeequation (30):$ D = 0.001 x([O],+I:[O],-137).
f)m ';SD*, seeequation
Hence, we will only deal with the simplest case of 0 = 0.
The parameter q is a ratio of two quantities integrated over the thickness of the layer, it is more simpfe
Under these conditions, a fractional sion rate perturbation will be
to conceive of the corresponding equivalent point within the layer, where we define
apparent
emis-
for a
(25)
(22) and substitute (24) yields
Jo
equations
(25) and (7) into equation
and a fractional measured temperature perturbation for an isothermal atmosphere (T,, is constant) will be (26)
T‘Y
(23)
B<,
The parameter ye,therefore, may be expressed as
‘I = ~~~)~(~~
= J;;;L. 0
*n
(24) 0
Equation (26) shows that if p did not depend on z (which will be discussed later), then q = p. As indicated in equation (12), the ratio of the density Auctuation of the major gas to the temperature ffuctuation caused by a wave is f3. The phase off; can be nearly 180’ for waves with short horizontal wavelength (Table I). which means that the Ruc-
Gravity
waves from O? nightglow
tuations of density and temperature can be in opposite phase. However, we cannot simply infer that the fluctuations of the apparent emission rate and the measured temperature are in opposite phase, because both the relationship between the apparent emission rate fluctuation and the major gas density fluctuation, and the relationship between the measured temperature and the in situ temperature are complex. The emission rate and the measured temperature depend not only on the fluctuation of the major gas density but also on the fluctuations of the minor gas density and the temperature.
during
campaign
II
383
2. p in the two-step transfer mechanism From equation (5) the linearized volume emission rate for the two-step transfer mechanism becomes
1
T’ -2 T . (35)
N’
where
I p in the three-hodJ~ reaction mechtmism
(37)
The volume emission rate of OZ from the threebody combination is given in equation (4). We use II, N. 2, N and k* as [O]. [N,], [O?], and k,, respectively, where
Here /I<,is an empirical parameter depending on Co, and C”. Substituting equations (12) and (17) into (35) yields
(27) Since x, does not change much in this region (Table 3) we may assume it to be a constant, so that the linearized perturbation expression fort: becomes
s: = [(1+8,11h+(z-r,,-B,),/;-2],T:. &I and gives P = ( 1+ B
= [2-&-lL-~W1 c = c,, 1+2; [
+(I-a,)m;’
(1
0
-2;
0‘I
,
(38) 0
(28)
+lL)l.f?
+ (I +8”)(1 +DH)
? (39)
(Y-1)
where
Comparing equations (34) and (39) the difference between the ps of the three-body mechanism and the two-step mechanism is PI?-\rcpl= We may therefore mechanisms :
(the unperturbed (k*)’
= -2kz
F~
part of k, in equation (the perturbed
p = (1 -a,,-‘DH),I;+ (4)),
part of k ,),
0
(31)
-a&2];.
(33)
0 According to equations (25) and (If?), equation gives p = ?fhf(l -%).f;-2 = (l-r,-2DH)fi+
2(1+DH) ~ ~ ;,_,
-2.
+
( ] -
b,,)(.f
2”;_;H) i
(33)
(34)
(40)
-.fh).
use one equation
of p for the two
-2
.
(32)
Here %(.indicates the quenching effects by O2 and N,, and LX,,= 0 implies no quenching is included. Substituting equations (I 2) and (17) into (28) yields the fractional volume emission rate perturbation as ;I = [2f;,+(I
PC?-hod,)
(41)
with /I,, = 1, i 0 ( B,, < 1,
for the three-body for the two-step
mechanism
;
mechanism.
Equation (41) shows that p depends on z through the three parameters, D, CI,, and PO, which represent the vertical distribution of the atomic oxygen density, the quenching effect, and the photochemical mechanism, respectively. The values of these three parameters are listed in Table 3 using the MSIS-86 model for 6 April 1989 midnight at 18”N, 293”E. Both s(, and /I0 are between zero and one and monotonically
s. P.
384
ZHANG
decrease as the altitude increases. This means that quenching (cc,) happens most’ty in the lower part of the emission layer and the three-body mechanism (&,> fits the lower part of the emission layer better than the upper part. It is worth noting that /I, = 1 is equivalcnt to C” = 0 in equation (37). The D value monotonically decreases, too, but from positive to negative. Positive D corresponds to an increasing density of atomic oxygen with altitude, and negative D to a decreasing density of atomic oxygen. In principle we need only substitute this equation (41) For p into equation (26) and integrate to complete the calculation of rl. In practice the integratjon is performed nur~~erica~ly as in the following section.
NUMERICAL 1.
PREDICTION
OF q
Emission layer with constant D, x,, and /&
In order to investigate 4 and the influence on q from D, r,, and pO, we first treat the emission layer as a layer
in which these three parameters are constant, making p independent of z. From equation (28) we have
YI
Ni.
tj = p = pr + ipi = 1~1e”,
where pf and pi are the real part and the imaginary part of p, respectively. Positive dpmeans the apparent emission rate leads the measured temperature, negative d, means the reverse. The numerical results of q are shown in Figs 224 where the horizontal wavelength Ir, is chosen as 200, 400,600, . . ,200O km, and the intrinsic period varies from 10 to 360 min. The calculations are only for upward propagating internal waves. a. R~.s~4lts,f#rthe ~ha~rna~ rnec~lun~stn. fn Fig. 2a and 2b, the vafue of q is calculated by the Chapman mechanism using the values of I), z, and r”;,at altitudes of 94,95 and 96 km separately. As mentioned above, the peak of the O2 emission profile is at about 95 km according to the Chapman mechanism, so the three cases represent the layer just below the peak of the O2 emission profile, the layer at the peak, and the layer just above the peak. In the layer at 95 km, I?] is almost a constant 4.6. and (1,is almost 0’. It implies that q is unresponsive to the wavelength and wave period.
(a) 5.5
E =
2000
km
5
0
(42)
200
100
Period
(min.)
Fig. 23. The value of /pi in the two-step mechanism calculated by using the values of D, a, and j$, at altitudes of 95 km (below), 94 km (middle), and 93 km (above) for horizontal wavelengths I, = 200, 400, 600. 800. 1000, 1200. 1400, 1600. 1800 and 2000 km. The wave period used is the intrinsic period.
2-
-x s
o-
-2
; -4
= ‘200
km
0
A*
=
Period
km
300
200
100
2000
(min.>
Fig. 2b. As in Fig. 2a, the value of Q1cakxkited by using the values off), q, and p0 at altitudes (below), 94 km (middle), and 93 km (above).
of 95 km
6
r =
=
200
2000
km
km
100
200 Period
300
(min.)
Fig. 3a. The value of jpl in the three-body mechanism calculated by using the values of D, LX$, and /& at altitudes of 96 km (below), 95 km (middle), and 94 km (above) for horizontal wavelengths i., = 200, 400, 600. 800. 1000, 1200. 1400. 1600. 1800 and 2000 km. The wave period used is the intrinsic period.
Fig. 3b. As in Fig. 3a, the value of @ calculated by using the values of D, n, and &, at altitudes of96 km (below), 95 km (middle). and 94 km (above). I
(a)
’
”
I
.
a
’
6
Zbokm
A,
=
km L
4 0
*
I
I
a
I
2QO Period (min.)
100
s
‘1
x
f
300
Fig. 4a. The value of p in the two-step mechanism without the quenching term calculated by using the values of IJ and POat altitudes of 94 km (below). 93 km (middle), and 92 km (above) for horizontal wavelengths 1, = 200,400.601), 800, 1000, 1200. 1400, 1600, 18fY.land 2000 km. The wave period used is the
intrimir wrinrt
Gravity
waves from O? nightglow
I
(b) 200
”
during
campaign
II
387
,a
”
km
I A,
=
2900
s km
2
0
8
-2
-4
200 Period
(min.)
Fig. 4b. As in Fig. 4a, the value of @ calculated by using the values of D and /I<,at altitudes of 94 km (below), 93 km (middle). and 92 km (above).
The value of Irl( from the lower layer is between 4.9 and 5.6, and the value of @ is between 0 and 3.6 For a fixed horizontal wavelength, 1~1increases with increasing wave period, but when the period is greater than a certain value (depending on I,), 1~1is almost constant. For a fixed period, 1~1 increases when the horizontal wavelength decreases. The fluctuation of the emission rate leads the fluctuation of the measured temperature by a few degrees. For a fixed horizontal wavelength, I@,1increases first with increasing period. after reaching a maximum value (-3.6 ) and then gradually tends to 0 The value of InI from the upper layer is between 3.7 and 4.3, and the value of @ is between - 3.6 and 0~. The fluctuation of the measured temperature leads the fluctuation of the emission rate. The value of 1~1 decreases when the wave period increases for a fixed wavelength. b. Results ,fbr the Burth mechunism. In Fig. 3a and 3b, the values of q are calculated by the Barth mechanism using the values of D, CI,and PC,at altitudes of 93, 94 and 95 km separately. The peak of the emission profile is at 94 km by the Barth mechanism. The
figures have features similar to those of Fig. 2a and 2b with slightly different ranges of 1111 and 0,. c. Results ,for the Chapman mechanism without qwnching @cts. Since the quenching effect increases the altitude of the peak of the emission layer by about 1 km, the peak of the emission profile is at about 94 km when a, = 0 and /I$ = 1. In Fig. 4a and 4b, the values of 7 arc calculated using the values of D at altitudes of 93, 94 and 95 km separately. Therefore, those figures show how D changes p. 2. Emission buyer in N reulistic utmosphcre The three parameters, D, M,,and /IO, in the O2 layer are not in fact constants, and so p is a function of altitude. A sample of how p varies with altitude in both magnitude and phase is shown for the specitic combination of E., = 1000 km and P = 120 min in Fig. 5. The phase is seen to be positive below the altitude of peak emission rate (95 km in this case) and becomes rapidly more negative with increasing altitude above the peak, whereas the magnitude decreases monotonically from the bottom to the top of the layer. For ground-based measurements the ver-
388
S.
P.
ZHANG 6’1al
GO
85
1.~1and
#* of p
Fig. 5. The vertical distributions of lpi and @ (degree) of p for a wave with period = 120 min and /1, = 1000 km in the Chapman mechanism.
tical integration of these two curves gives the phase and magnitude of r]. In practice, we calculate v directly by integrating equation (26) using the MSIS-86 atmospheric model. The calculations for 9 using the two excitation mechanisms are shown separately in Figs 6 and 7. Figure 6 shows q calculated using the three-body reaction mechanism for an emission layer given by equation (4) between 85 and 110 km altitude, which includes 99% of the total 0, volume emission. The ranges of period and horizontal wavelength are selected to limit J., to being greater than 10 km to be relevant to MORTI observations. The range of Jqj is from 4.4 to 9.7, and the range of tf, is from - 80 to 0‘ fn Fig. 7 5 is calcufated using the two-step transfer mechanism for an emission layer given by equation (5) between 85 and 108 km altitude, which also includes 99% of the total O2 volume emission. The range of 1~1is from 3.9 to 9.9, and CDfrom -84 to 0 The differences between Figs 6 and 7 are small, indicating that measurements of v will not help to resolve any questions about the relative importance of the chemical excitation mechanism. In both cases both lr?l and @ vary slowly and smoothly as functions of period and horizontal wavelength, but more slowly
for longer wavelengths. The temperature fluctuations lead the column emission rate fluctuations for all wavelengths and periods shown, and the lead diminishes as the horizontal waveIength increases. The absolute value of the phase difference at any wavelength decreases as the period decreases, which means as the phase speed increases, or as the waves approach evanescence. At a fixed period, we see that the phase of q approaches zero and the magnitude increases as the wavelength increases. The integrated values of q, particularly @, are much greater than the results from a uniform emission layer with the values of D, tl, and & at altitude of 95 km (three-body mechanism) or 94 km (two-step mechanism). The large @ is caused by the upper part of the emission layer, mainly above 97 km altitude (Fig. 5).
Since p, and k, are zero for evanescent waves, CDcan be either 0 or 180 depending on pI > 0 or p, c 0. For example, waves with a horizontal wavelength of 2000 km and a wave period less than 134 min, are evanescent. Table 4a and 4b give the 4 values calculated for an emission layer from 85 to I10 km altitude and from a uniform layer at 9.5 km by the three-
Gravity
-80
-A,
=
200
waves from 0: nightglow
during campaign
389
II
km
(b)
/
.
I,
*
100
I
*
/
a
*
200 Period
,
‘
300
(min.)
Fig. 6. The value of /?/ and cf, in the two-step mechanism calculated by numerically integrating equation (26) for an emission layer from 85 to 108 km for horizontal wavelengths I, = 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800 and 2000 km. The wave period used is the intrinsic period. Table 4a. The q values for short period evanescent waves using the three-body reaction mechanism (A, = 2000 km) O3 layer at 94 km Period
.-
(min) ~.__
-.._
130 120 110 100 90 80 70 60 50 40 30 28 26 24 22 20 IO 8 6
IYI*
4.54 4.53 4.51 4.48 4.45 4.40 4.34 4.24 4.07 3.74 2.86 2.47 1.57 0.80 1.71 15.9 5.54 5.12 4.83
0: layer
CD
l&t
@
0' 0’ 0 0’ 0’ 0’ 0 0‘ 0 0 00 I) 0 I80
4.56 4.57 4.57 4.57 4.57 4.51 4.57 4.57 4.57 4.57 4.57 4.57 4.57 4.57 4.57
0’ 0 0’ 0 0’ 0‘ 0‘ 0: 0; 0’ 0’ 0“ 0’ 0’ 0’
180 0 0 0
4.57 4.58 4.58 4.58
;:
__
0” 0’
4.34 4.82 5.35 6.00 6.87 8.06 9.79 12.48 17.01 25.85 49.34 59.78 75.86 104.4 171.3 550.4 22.17 Il.19 3.31
0’ 0 0 0 0 0 0 0’ 0“ 0 0’ 0‘ 0’ 0 0‘ 0 180” 180” 180”
: 85- 110 km
3.85 3.73 3.67 3.64 3.61 3.59 3.58 3.56 3.55 3.54 3.54 3.54 3.54 3.54 3.54 3.52 3.47 3.43 3.31
0’ 0“ 0‘ 0” 0” 0 0’ 0 0” 0 0 0 0 0” 0’ 0’ 0” 0 0;
!\\i s. P. .&Al'%
390
et Ui.
Q-““l”“l”“l”4
-20
-40
A,
=
2000
km
I
-60
-00
-A,
=
I 200
km
\
0
100
200
300
a
100
200
300
12
2 Period
(min.)
Fig. 7. The value of 1~1and Q, in the three-body mechanism calculated by numerically integrating equation (26) for an emission layer from 85 to 110 km for horizontal wavelengths A, = 200, 400, 600, 800, 1000. 1200, 1400, 1600, 1800 and 2000 km. The wave period used is the intrinsic period.
Table
4b. The 9 values for short period transfer mechanism
evanescent waves (A, = 2000 km)
0, layer at 94 km Period (min)
using the two-step
0: layer:
85-108
km
__
130 120 110 100 90 80 70 60 50 40 30 28 26 24 22 20 10 8 6 *When
f --5 -~
141* 4.44 4.42 4.40 4.37 4.33 4.28 4.21 4.09 3.90 3.52 2.52 2.07 1.39 0.17 2.69 18.9 5.58 5.11 4.77 a =
m 0: O’> 0’ 0’. 0 0‘ 0” 0 0” 0’ 0” 0’ 0” 0” 180’ 180” 0” 0” 0
1/2H-&
IsIt
@
Id*
@
lrll+
@
4.46 4.47 4.41 4.47 4.47 4.47 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.48 4.49
0 0‘ 0 0’ 0 0 0‘ 0’ 0’ 0’ 0 0’ 0’ 0’ 0’ 0” 00” 0‘
4.21 4.69 5.21 5.85 6.70 7.87 9.58 12.21 16.66 25.24 48.42 58.68 74.47 102.5 168.2 540.6 21.82 11.04 3.30
0 0” 0 0’ 0 0‘ 0‘ 0‘ 0’ OF 0’ 0 0” 0’ 0 0’ 180“ 180 180
3.73 3.62 3.56 3.53 3.50 3.48 3.47 3.46 3.45 3.44 3.43 3.42 3.42 3.42 3.42 3.42 3.37 3.32 3.20
0’ 0’ 0, 0’ 0’ 0’ 0‘ 0 0’ 0’ 0 0 0 0 0’ 0 0 0’ 0’
-: z h,(m,,/ru
T.- -I)-_(W’-u~)/C’:
twhen
z = 1/2H+
Gravity
waves from 0: nightglow
body model, and from 85 to 108 km and from a uniform layer at 94 km for the two-step model, respectively. There are two sets of results corresponding to two c( values given by equation (8). The first set of results is given for 2 with the negative sign in equation (8). In this case (~1 has a wide range, from 3 to 550, and there is a singularity at a period near 20 min. where r = o’/g in the function_f\. The measured temperature fluctuations may then have the same phase as the emission rate fluctuations or be totally out of phase. The second set of results is given for the positive sign in equation (8). In this case q is almost constant in magnitude at 3.5 with zero phase. For evanescent waves with increasing period, the difference between these two solutions decreases. DISCUSSION
Because the 0, atmospheric band is weaker in intensity and therefore more difficult to analyze than the OH emission, the available observations of gravity waves from the 0, airglow which measure both periods and wavelengths are more scarce than those of OH (see for example, TAYLOR rt d., 1991). We will compare our theoretical predictions of q with the observations of 9 by ZHANG d al. (1993) in paper I. then with those reported by VIERECK and DEEHR (1989) to evaluate our model.
during
campaign
II
I. Comparison with AIDA
391
‘89 observations
Thirteen gravity waves in the 0, nightglow were measured by MORTI during the AIDA ‘89 campaign in Puerto Rico (17’57’N, 66”52’W) and analyzed to give q and the kinematic wave characteristics in paper I. The comparison of the observed and the predicted q by integrating equation (26) are listed in Table 5a using the Chapman mechanism, and Table 5b using the Barth mechanism. There are two sets of calculated q, the first one corresponds to zero wind speeds, and the second one corresponds to the wind speeds mcasurcd by BIRD (~1a/. ( 1993) from the O’S emission layer 3 km higher. The predicted q values by both mechanisms agree fairly well with the 1~1values but poorly with @values. According to Fig. 6.3b (or Fig. 6.4b) the agreements are improved significantly if the predictions are made for a uniform layer at about 96 km (or 95 km), but of course such a picture does not seem to be realistic. We note that the integrated v in Table 5 are similar for the specific MORTI cases to the TH90 ‘1 predictions given in paper I. Two cases of evanescent waves are listed in Tables 5, on 1 l/l2 April and 4/5 May. The measurements gave 1~1of 3.7 and 4.0, respectively, and Q = 0’ for both, corresponding to 3.9 for the solution with the positive sign in s( both nights, and 4.5 for the negative
Table 5a. Comparison of the observed reaction
P Date
(min)
516 April
q by MORTI and the predicted 4 using the three-body for an emission layer between X5 and 110 km
mechanism
126
I&
@
(observed) 3.5
(m/s) 0
-I
5.50 5.87 6.01 6.72
-32 -38, -40 -48
+57% +68% + 34% +49%
-31 -37’ -38’ -46’
0
4.97 4.75
-19’ -13
-10% -14%
-12; -6
0
3.92 3.91
0 0
4.83 8.34
0
4.79 4.87
+15
X/9 April
46
4.5
-2
308
5.5
-1
0 1-20 -34
I l/l2 April
160
3.7
- 16 -6
30 April/ 3!4 May
1 May
150 340
4.8 5.5
-0 -0
278
3.5
-0 +14
0 0
f6% +6%
+I6 +I6
- 15’ -57’
+ 1% f52%
-15’ -57
-14 ~ 16
+37% +39%
-14 - 16‘
415 May
106
4.0
-0
0
3.91
5/h May
162 82
4.8 5.2
-0 -0
0 0
5.75 5.71
-36’ -36’
+20% + 10%
- 36’ -36
617 May
132
5.0
-0’
0
7.02 5.97 4.57 4.50
-50 -39’ -7’ -5
f40% + 19% +20/o 0
-50 -39’ -7‘ -5
4.90
-17
f7%
-20 80
4.5
0
-0 -15
8,‘9 May
138
4.6
-0
0
0
-2%
0’
~ 17’
392
S. P. ZHaNG et al. Table 5b. Comparison
of the observed q by MORTI and the predicted 7 using the two-step mechanism for an emission layer between 85 and 108 km
P
@
Id
u
III -III, (predicted)
A@
(m/s)
126
3.5
- I”
46
4.5
-2
0 +15 0 +20
4.96 5.45 5.63 6.51
-43’ - 50” -52’ - 59”
+42% + 56% +25% +46%
-42’ -49’ -50 - 51”
308
5.5
-1’
0
4.30 4.08
-29” -21”
-22% -26%
-22 -14’
0
3.85 3.84
0’ 0’
-+4% f4%
+16’ fl6’
(min)
516 April
-34 160
11/12 April
@
(observed)
Date
8/9 April
I&
transfer
3.1
- 16’ -6
r
150 340
4.8 5.5
-0’ -0;
0 0
4.15 8.69
- 24” -67’
- 14% +58%
-24 -67’
314 May
278
3.5
-0’
0 +14
4.11 4.19
- 22” -26’
fll% +20%
-22 -26
4/5 May
106
4.0
-0”
0
516 May
162 82
4.8 5.2
-0’ -0”
0 0
3.84 5.28
0’ -48’
5.24
617 May
132
5.0
N 0”
0
6.95 5.58 3.96 3.93 4.22
-21’
30 April/l
May
-20 80
4.5
0
-0 -15
S/9 May
138
4.6
-0’
in Tables 5. The physical results seem to favor the positive sign solution in these cases, but both solutions are not very different. sign but are not listed
2. Comparison with Viereck and Deehr ‘s observations VIERECKand DEEHR (1989) reported a large number of observations carried out at Fairbanks, Alaska (64”N, 145”W), U.S.A. and Longyearbyen, Svalbard (78’N, 16”E), Norway. As mentioned in paper I, they did not distinguish between internal waves and evanescent waves in their measurements. Most waves they measured had periods of less than 1 h. For these waves, the Ipj was mostly between 0 and 2, and the phase difference was about 180”. Our calculations show, as in Tables 4, that the 180” phase difference is possible for evanescent waves using the negative sign in CI,and we can get small 1~1with this condition for a thin layer but not an integrated one. For a few long-period (longer than 2.8 h) waves in their measurements 1~1was between 2 and 7, and the phase was about 0”. Assuming those waves to be internal, the phase value again agrees with our prediction for a uniform layer, but the measured 1~1value has a wider range than that predicted. 3. Comparison with other theories As mentioned in paper I, the n value predicted by WEINST~CK (1978) was between - 0.1 and 1.1, which
0
-4%
0
-41’
+lo% + 1%
-48’ -47’
-61” -51” - 13” _ 9”
+39% +12% - 12% -13%
-61“ -51 -13 _ 9”
-8%
- 21’,
does not agree with our prediction. His theory was criticized by HINES and TARASICK (1987), and we will not re-examine it. HINES and TARASICK (1987) (HT87) used a semiLagrangian method in a frame of reference that moved up and down with the wave. The virtue of their method is that since we measure vertically integrated quantities, the altitude of the layer is not important, and their method leads to an analytical solution for the non-quenching three-body photochemical mechanism. We have taken the more direct Eulerian approach suggested by WALTERSCHEID et al. (1987). In our work, the physical quantities are represented at a given altitude. For both analyses using exactly the same atmosphere and the Chapman mechanism without quenching, it can be proved mathematically that the formulas of r] from the two methods, in our case the integral of equation (26), are identical. When quenching is involved with the Barth mechanism, which was discussed by TARASICK and SHEPHERD (1992a), the situation is much more complicated, and the identity of these two approaches is difficult to prove mathematically. Numerical calculations for this case with different periods and wave speeds resulted in the graph of Fig. 8. Comparison with the equivalent fig. 3 of TARASICK and SHEPHERD (1992a), shows no significant differences.
Gravity
waves from O2 nightglow during campaign II
Since the present study is based on the work of WALTERSCHEIDet al. (1987), it shows, as might have been expectkd, that the HT87 and the WALTERSCHEID et 01. (1987) approaches are fundamentally the same, provided the integration is over the full thickness of the layer in both cases. It also shows that neither approach provides an adequate explanation of the phase of rl. It is worth noting that the Walterscheid method was extended by HICKEY (1988) to include eddy dissipation in his study of waves in the OH layer. Hickey’s results showed that at horizontal wavelengths comparable to those seen by MORTI in 03, that is, 1000 km, and periods of several hours, the phase of? did in fact become zero. Similar calculations for the 0, layer have not been performed, but they would seem to be the next logical step. CONCLUSION
The present study is an attempt to satisfy the need shown by ZHANC et al. (1992) for an improvement in our understanding of the dynamical
393
the perturbed and mean integrated column emission rates, respectively, of the 0, (&l) band, and T’ and T, the brightness weighted temperatures integrated through the O2 nightglow layer. The model used is an extension of one presented for the OH layer by WALTERSCHEID et al. (1987), but employing O,(b’&+) excitation chemistry and integration over the whole layer. The results show 1~1as a smoothly varying number, depending upon wavelength and period, that lies in the range 3.9-8.3 for waves of the kind reported by ZHANC et al. (1993). which is somewhat larger than the observed values, in the range 3.5-5.5. Whereas the measured phases ranged from - 16 to 0 , this model predicted -67-O Evanescent waves give good agreement for predicted and measured q, slightly favoring the positive option for x in equation (8). The model is in fact shown to be numerically equivalent to the one by HINES and TARASICK (1987) and further developed by TARASICK and HINES (1990) and TARASICK and SHEPHERD (1992a). In neither development is there a significant difference between the ‘1predictions for the Chapman and the Barth mechanisms, suggesting that the weaknesses are probably not chemical. Rather, the neglect of all dissipative effects may be the cause of the discrepancies.
10
I
6
6
x A,
/
P
=
150
m/s
4
_L 2
0
I
I
1
10 Period
Fig. 8. Variation
100
(P/P,)
of (~1 with wave period for horizontal
wave speeds 60, 100 and 150 m/s
394
S. P.
ZHANG
It is of considerable interest that 1~1 as predicted comes as close as it does to the observed ratio in view of the assumptions made. The importance of these models is that (~1 is in fact shown to be a well-behaved function. Then by equations (1 I)-( 14) all of the state variables of the gravity wave that relate to T//T, also relate to B’/B_ through n. and the use of ontical vhotometry for the study of these waves is justified. An example that employs equation (14) for horizontal perturbation velocity is described in the accompanying paper by WANG et al. (1993). Still others are \,
_
.,
I
et al.
possible as suggested by the polarization factors and phases listed for specific wavelength-period combinations in Tables 1 and 2.
Aclinow,leajqmenfs-The Institute for Space and Terrestrial Science is a designated Centre of Excellence of the Province of Ontario, Canada. S. P. Zhang was supported by a grant from the Natural Science and Engineering Research Council of Canada. The authors wish to thank the guest editor, C, 0. H’mes. for a significant contribution to the tinal version of ihis work.
.
REFERENCES BIKII J. C.. TEPLEY C. A. and SHEPHEKI~ G. G.
1993
CHAPMANS.
1931
GREER R. G. H., LLEWELLYNE. J., S~LHEIMB. H. and WITT G. HEDINA. E.
1981
HICKEYM. P.
1988
HINESC. 0.
1960
HINESC. 0.
1964
HINESC. 0. and TARASICKD. W.
1987
HOUGHTON J. T.
1986
KRASS~VSKY V. 1.
1972
MCDAIX I. C., MURTAGHD. P., GREER. R. G. H., DITKINSON,P. H. G., WITT, G., STEGMAN, J., LLEWELLYNE. J., THOMASL. and JENKINSD. B. MURTAGHD. P., WITT G., STEGMAN J.. MCDA~E I. C., LLEWELLYNE. J., HARRISF. and GREEKR. G. H. NOXONJ. F.
1986
SOLHEIMB. H. and LLEWELLYNE. J.
I979
TARASI~KD. W. and HINESC. 0.
1987
TARASICKD. W. and SHEVHERD G. G.
1992a
TARASICKD. W. and SHEPHERDG. G.
1992b
TAYLORM. J., ESPY P. J., BAKERD. J., SICA R. J.. NEAL P. C. and PENDLETON W. R. JR
1991
T~RR M. R., TORR D. G. and LAHEKR. R.
1985
VIERE~KR. A. and DEEHRC. S.
1989
I987
1990
1978
Optical measurement of neutral winds during AIDA ‘89. J. atmos. WV. Phys. 55, 313. Some phenomena of the upper atmosphere. Proc. R. SW. Lord. (A) 132, 353. The excitation of 02(b’Z:) in the nightglow. Planet. Space Sri. 29, 168 1. MSIS-86 thermospheric model. J. ,qeophy,s. RES. 92, 4649. Wavelength dependence of eddy dissipation and Coriohs force in the dynamics of gravity wave driven fluctuations in the OH nightglow. J. geophys. Rrs. 93, 4089. Internal atmospheric gravity waves at ionospheric heights. Gun. J. Phys. 38, 1441. Ionospheric movements and irregularities. Research in Geophysics, Vol. I. p. 299, H. ODISHAW(cd.). MIT. Press, Cambridge, U.S.A. On the detection and utilization of gravity waves in airglow studies. Planet. Space Sci. 35, 851. The Physics of Atmosphere.r. Cambridge University Press, Cambridge, U.K. Infrasonic variations of OH emission in the upper atmosphere. Ann. Geophys. 28, 736. ETON 2 : quenching parameters for the proposed precursors of O,(h’X,q+) and 0(‘S) in the terrestrial nightglow. Planet. Spuce Sci. 34, 789. An assessment of proposed 0(‘S) and 02(b’X: ) nightglow excitation parameters. Planet. Spaw Sci. 38, 43. Effect of internal gravity waves upon night airglow temperatures. Geophys. Res. Let/. 5, 25. An indirect mechanism for the production of 0( ‘S) in the aurora. Planet. Space Sci. 27,473. On the detection and utilization of gravity waves in airglow studies. Planet. Space Sci. 35, 85 I The effects of gravity waves on complex airglow chemistries I : OZ(h’Xd ) emission. J.,qeoph~s. Rrs. 97(A3), 3185. The effects of gravity waves on complex airglow chemistries 11: OH emission. J. geopl~~s. Rex. 97(A3), 3195. Simultaneous intensity, temperature and imaging measurements of short period wave structure in the OH nightglow emission. Planer. Space Sci. 39, I 171. The O2 atmospheric ((M) band and related emissions at night from Spacelab I. J. geophys. Res. 90, 8525. On the interaction between gravity waves and the OH Meinel (62) and the 0, atmospheric (&I) bands in the polar night airglow. J. yeophys. Rex. 94, 5397
Gravity
waves from 0: nightglow
WALTEKSCH~II)R. L., SCHUBEKTG. and STRAUSSJ. M.
1987
WANGD. Y., ZHANGS. P., WRENSR. H. and SHEPHEKDG.G.
1993
WEINSTOCK
197x
ZHANCi
J.
S. P.. PETEKSOKR. N., WENS R. H. and
SHEPHEKD G.
G.
I993
during
campaign
II
395
A dynamicalxhemical model of wave-driven fluctuations in the OH nightglow. J. yeophys.Res. 92, 1241. Gravity waves from O2 nightglow during the AIDA ‘89 campaign III : effects of gravity waves saturation. J. u~mos. [err. Phjs. 55, 397. Theory of the interaction of gravity waves with 02( ‘X) airglow. J. geophy.7. Res. 83, 5175. Gravity waves from O2 nightglow during the AIDA ‘89 campaign I : emission rate/temperature observations. .I. uin7o.Y. /err. Ph,lY. 55, 355.