The Middle atmosphere

Editors' Note It has been for some time the editorial policy of this journal to publish occasional special issues containing articles which have either been presented at a symposium or are devoted to a topic of recognized current interest. This particular issue contains 29 articles dealing with various aspects of the region of the Earth's atmosphere known as the Middle Atmosphere - a region including the upper stratosphere and the mesosphere and comprising roughly the altitude range between 30 and 90 km. The Middle Atmosphere is a region where radiative, photochemical and dynamical processes are interlinked in intriguing ways. Because of the growing awareness that this region is particularly sensitive to both natural and man-made perturbations, there has been an upsurge of research activity in the present decade in what is essentially an interdisciplinary area. It is the hope of the editors that the articles in this volume will help in giving the reader a glimpse of the scope and nature of the problems, of the extent and current status of the progress achieved, and of what lies ahead in this rapidly developing subject. These articles were solicited by the editors as invited contributions from experts in their respective specialities. In content they represent either original contributions or reviews of accomplished work or, as was left to the choice of the authors, appropriate combinations of both. It is our distinct pleasure to thank the authors for their valuable contributions and their cooperation in meeting an early deadline, as well as the anonymous referees for their pertinent comments. The expert secretarial assistance of Ms. Elizabeth Schwalm has been chiefly instrumental in bringing out this volume on schedule.

Los Angeles and Washington, D.C. August 1979

S. V. VENKATESWARAN N. SUNDARARAMAN Guest Editors

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Solar UV Radiation and its Absorption in the Mesosphere and Stratosphere By MARCELNICOLET1'2) A b s t r a c t - Solar radiation of A > 175 nm and of Lyman-alpha at 121.6 nm is absorbed in the mesosphere and stratosphere by molecular oxygen (A < 242 nm) and also by ozone molecules at A > 200 nm. This paper describes the photodissociation processes resulting from absorption in the Schumann-Runge bands and Herzberg continuum of molecular oxygen and also in the Hartley, Huggins and Chappuis bands of ozone. Special consideration is given to differences between the stratospheric and mesospheric problems.

Key words: Ultraviolet radiation; Photodissociation; Schumann-Runge bands; Herzberg continuum; Ozone bands. L

Introduction

In order to study the photochemical action of solar radiation on stratospheric and mesospheric constituents, it is convenient to divide the solar spectrum in spectral ranges related to the molecular oxygen and ozone absorptions. The radiation of wavelengths less than 100 nm is absorbed by nitrogen and oxygen in the thermosphere; it leads essentially to ionization processes and is, therefore, not considered here. Only X rays of wavelengths less than 1 nm can penetrate into the atmosphere below 100km, and lead indirectly to the dissociation of molecular constituents. The radiation of wavelengths less than 242 nm is absorbed by molecular oxygen and leads to its photodissociation. The principal photodissociation continuum (Schumann-Runge continuum) at A < 175 nm corresponds to a complete absorption of the solar radiation in the thermosphere and will not be considered in this analysis. An important solar line, Lyman-~ at 121.6 nm, is situated in a so-called atmospheric window since the 02 absorption cross section is only of the order of 10-2o cmL Such a radiation is absorbed in the mesosphere. The second important spectral range, between 200 nm and 175 nm, is related to the 0 2 Schumann-Runge band system which includes 18 bands, ( 2 - 0 ) to (19-O), subject to the predissociation process. In this spectral region, the mean absorption cross sections are a function of the temperature and number of O2 absorbing molecules. 1) Ionosphere Research Laboratory, The Pennsylvania State University, University Park, Pa. 16802, USA. 2) Present address: 30 Avenue Den Doorn, B-180 Brussels, Belgium.

4

Marcel Nicolet

(Pageoph,

The absorption, which is essentially a mesospheric process, also plays a role in various stratospheric photodissociations. From 200 to 242 nm, the 02 absorption, which is related to the Herzberg continuum with low absorption cross section (from 10 -24 to 10 -23 cm 2) occurs in the stratosphere. In addition, the ozone absorption must be introduced since this spectral region belongs to the spectral range of the 03 Hartley band. The simultaneous absorption by 02 and 08 must be considered in the stratosphere. In the mesosphere, the 03 absorption is practically negligible since the total number of ozone molecules is very small for low solar zenith angles. At wavelengths less than 310 nm corresponding to the 03 Hartley band, the ozone molecule has its principal absorption which occurs in the stratosphere. Its limit near 310 nm must be determined with precision, since the photodissociation process in the Hartley band, which is

03 + hv(A < 310 n m ) - + O2(1Ag) + O(1D)

(1)

leads to the production of O(~D) atoms responsible, particularly below 50 km, for the production of OH from H20, CH4 and H2, and also of NO from N20. At ~ > 310 nm, the Oa Huggins bands correspond to the limit of its ultraviolet absorption. The spectral range to be considered should be between 310 n m a n d 400 nm since it corresponds also to various limits of the absorption spectrum of H202, H2CO, NO2, N20~, HNO2, HNOa, C1ONO2, HOCI . . . . . In the visible region (410-850 nm), the Chappuis bands play an important role leading to the 03 photodissociation in the lower part of the atmosphere, troposphere and lower stratosphere. At ~ > 300 nm, various effects such as the Rayleigh scattering and the albedo must be introduced. In particular, the photodissociation rates of 03; ratio n(O)/n(03), of NOz, ratio n(NO2)/n(NO), and the absolute concentration of the other constituents absorbing in that spectral region are strongly affected by the Rayleigh scattering and albedo effects. Thus, the photodissociation problem is related to a knowledge of the solar flux and its possible variations in certain spectral regions, the exact determination of the vertical distribution of the atmospheric optical depth of 02 and Oa, the measurement of the absorption cross sections and photodissociation quantum yields for each constituent, and the introduction of the atmospheric conditions related to the radiation scattering and a l b e d o .

H. 02 Absorption The absorption cross section in the Herzberg continuum is known with an accuracy which is not greater than 25~ (Fig. 1). At A > 230 nm the 02 cross section is not known with sufficient precision; but since the ozone absorption is maximum in this

Vol. 118, 1980)

Solar UV Radiation Absorption in Mesosphere and Stratosphere

5

15

.~ ~0

: .....................

o

i?i!!~

02

-

INUUM

.....

g

/

"

= 10 200

I

210

I

,

220 230 WAVELENGTH ( nm )

i

2/,0

Figure 1 Experimental data on 02 absorption cross sections in the Herzberg continuum, x DITCHBURN and YOUNG (1962). (:30GAWA (1971). [] I-IASSONand NICHOLLS (1971). 9 SHARDANANO (1977).

Table 1 Mean value o f solar flux (q, photons cm-2 sec-1); mean cross section (o, cm 2 for 500 c m - 1) and 02 photodissociation coefficients (j, sec- 1) at the top o f the Earth's atmosphere in the spectral range o f the 02 Herzberg continuum (A(A) = average wavelength in A o f the spectral range, + 250 cm- 1) A(A) 2010 2030 2051 2072 2094 2116 2139 2162 2186 2209 2234 2259 2286 2312 2339 2367 2395 2424

q~ 1.44 x 1012 1.80 2.08 2.45 5.09 7.12 9.23 8.42 1.20 • 1013 1.22 1.77 1.60 1.96 1.97 1.70 2.00 1.77 1/2 (2.58)

ao2

j~

1.50 x 10 -23 1.25 1.00 9.80 • 10 -24 9.20 8.50 7.85 7.05 6.15 5.50 4.75 4.05 3.35 2.70 2.20 1.65 1.20 0.75

2.16 • 10 -11 2.25 2.08 2.40 4.68 6.05 7.25 5.94 7.38 6.71 8.4l 6.48 6.57 5.32 3.74 3.30 2.12 9.80 • 10 -12

6

Marcel Nicolet

(Pageoph,

10 Z

N ( O 2 } ~< 2 x J019 C m , O- IO2) = 10~29cm 2 ~2xlO

C~

19 c m 2, l o g TO2 = A l o g N I O ; J . B

~) UJ q

"T" p..

U3 O

n

.

o ~

5x~0 ~

0

m
Uaa

\

~(1)\

0

4

+

/~(j)

I VW In the matrix U, the important elements are the diagonal elements. Any row is determined from the previous rows following the arrows indicated. In the ease of a single absorbing gas, fi would be the absorption cross-section,/3, and U would include the desired number densities of this gas. These determinations start from Ull and the associated air mass Mn. If the latter quantity is small, the divisions by it that are subsequently carried out will yield large optical depths which, in turn, yield small differential transmissions. A chain reaction on the other transmissions sets in. Inaccuracies in M~I will get amplified creating an instability in the problem. These diff• could be avoided by choosing a sufficiently wide layer 1 but at the expense of vertical resolution at the high altitudes. Rather than following the kind of forward recursion just discussed, it may be more advantageous to utilize a backward recursion starting from the atmospheric layer of lowest altitude sounded. This upward building process must end at the highest altitude where the air mass is accurately known. The ratio between this air mass and that determined from the computations could then be used as a normalization constant for the entire profile. Thus, in the case of a single constituent, the cause of the ill-conditioning can be traced to the low air mass at the high altitudes. We have suggested two ways of overcoming it. When several absorbing gases are present, the number densities can no longer be included in U, and the ~'s which must incorporate them are truly absorption

50

A.L. Fymat and C. B. Smith

(Pageoph,

coefficients, not cross-sections. All that one can get is the vertical profile of the composite/3 at each sounding wavelength. This would also be the case if monodispersions of aerosols are also present (providing their refractive index is known). The set of fl's thus determined is the one that enters in the inversion of equations (6) and (7) below. In the case ofpolydispersions of aerosols, the corresponding/3 further depends on the size distribution which is an additional unknown of the problem [see equation (5)]. Providing the high altitude air mass ,problem has been taken care of, the system in equation (6) is already in a convenient form for solution by successive determination of the extinctions/3,(h) at decreasing altitudes. As discussed earlier, the choice of a nonuniform discretization of the atmosphere into layers having more uniform masses does provide an alternative approach which could allow stable direct recovery of extinction profiles independently for each layer, if the altitude layers are suitably selected. The penance to be paid when using such an approach is the coarser vertical resolution at the high altitudes. There are, however, several advantages to this direct method other than its numerical simplicity. First, it does not require prior estimates of the extinction profiles for the constituents. Second, for the absorbing gases, it can make use of the constituents cross-sections for the recovery of the gas number densities;enough channels must remain available for recovery of effective aerosol parameters. This is preferable to the naive assumption that the channels are most sensitive to just one constituent. Third, many wavelengths can be processed independently, whether or not future SAGE wavelengths are at the peak response of any constituent sought.

B. Sounding above 25 km altitude In the case of SAGE I, at each of the altitudes of interest, we can write for the composite extinction factor [see equations (4) and (5)]: [3 = ~N, or

/32 /33

/3~

= [tiM(A2) fiN(h2) /~0(h2) ~/JM(A3) 0 /~o(A3)

\~(~)

o

NN ,

(7a)

No] N.

o

where, as earlier, A1 -- 0.385 tzm, h2 = 0.45 t~m, A3 = 0.6/~m and A4 = 1.0 tzm are the four SAGE I channels. Referring again to Fig. 2 and also to Fig. 4 of CM in which the atmospheric transmission versus tangent altitude is graphed, we see immediately that the sounding channel 3,4 transmits almost all the incident solar radiation. This near-unity transmission renders h4 inefficient as an atmospheric sounding channel. This is rather an advantage than a drawback for, instead of the system (la), we can use the system: /3z /33

= |/3M()tZ) /3U(ZZ) /30(A2) \/~M(A3) 0 L(h3)]

NN . No

(7b)

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

51

Thus, if the matrix/~ is well-behaved, this system could be inverted uniquely to yield the required number densities at each atmospheric level. The reconstruction, altitude by altitude, of the vertical profiles of these parameters will be discussed below. As indicated earlier, one can use either Method No. 1 or Method No. 2 in arriving at the solution. What is important, however, is that/3M = NM~M follows a power law variation in altitude (see, for example, Fig. 5 of CM which displays the vertical extinction profiles for Rayleigh, 03, NO2 and aerosols). The power exponent is slightly different on either side of ~ 40 km. Thus, only two determinations of the molecular extinction are sufficient for completely characterizing this parameter above this altitude. Likewise, from ,-,40 km down to 10 km, two similar determinations are also sufficient; the latter could be obtained in the range ~ 30-40 km. In summary, in the absence of aerosol incursions above 25 km, it is possible to recover ArM, NN and No from the solution of equation (7b), and to further determine the molecular contribution in the region ~ 10-30 km from that at higher altitudes. This would then reduce the number of unknowns at these lower altitudes for which all of the available sounding channels could be used. In the presence of higher altitude aerosols, the problem is less well determined, as discussed earlier.

B. Sounding below 25 km altitude The molecular extinction contribution having been determined, it could be subtracted from the measurements. The analogue of system (7) would be: -

\

[33 ~M(A3) ] \ ~o(~3)[3A(A3][Na] )

(3)

Even using the above device for determining the molecular density, and solving only for the extinctions, the problem is clearly underdetermined by one order (an additional order would be added if NO2 were present in the lower atmosphere). Indeed, there are five unknowns /~A(;~), /3A(A2), /]A()~a), /3A()q) and No to be recovered from only four measurements. Additional measurements would not resolve this ambiguity because each measurement, say at Z = '~5, would introduce a further unknown /JA(;~5). The only way out of this difficulty is to attempt to retrieve the ozone independently of the aerosol, and to provide as many sounding wavelengths as desired values of the aerosol extinction. For a follow-on experiment, we suggest using a pair of ozone channels between which the ozone extinction is greatly variable while the aerosol extinction variation is relatively negligible. If NO2 were also present, the same technique utilizing a close pair of wavelengths in the absorption band could likewise be used for recovering the number density vertical profile of this constituent. Assuming that this approach is followed, all four channels could be used for the aerosol. We illustrate below in great detail what type of aerosol information (beyond the extinction coefficients) could be extracted from these four wavelength measurements.

(a) 10"1 m:

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MAXIMUM ENVELNPE SOLUIK)N

It ~tJIlUd

lO-~

IO-t

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i~~

PARIlCLE RADIUS {MICRONS)

(i)

Figure 3 Illustrating the results of seven numerical inversion techniques applied to S A G E simulated data ()t = 0.385/,m, 0.45 t,m, 0.60 txm and 1.0/zm) for the reconstruction of the aerosol size distribution. Case of a background aerosol model (log-normal distribution with rg = 0.0725, ag = 1.86 and N

=

10 cm-3).

(a) simulated extinction data and extinctions recomputed from the inverted size distributions. (b) actual size distribution and computed averages (arrows on the abscissa scale indicate sizes most sensitive to S A G E sounding channels). (c) inverse solution using the actual distribution as a prior estimate. (d)-(j) inverse solutions using no prior estimates.

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

g

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(Pageoph,

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(;)

c,

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Figure 4 S a m e as Fig+ 3 for a v o l c a n i c a e r o s o l m o d e l ( l o g - n o r m a l , r~ = 0.097, % = 2.02, N = 10 c m - 3 ) .

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

55

D. Numerical experiments for aerosol inversion using four SAGE wavelengths For the following study, we have retained the SAGE I wavelengths, and have assumed that they are all available for the aerosol problem. Our objective was to determine what kind of aerosol information could be retrieved from 4 wavelengths. Our library of inversion routines, developed previously, includes: (i) minimum deviation method, (ii) minimum norm method, (iii) monotonic non-negative method, (iv) matrix inversion method with two-smoothing constraints (as applied by Yamamoto and Tanaka), (v) maximum entropy method (SMtTH, 1978), (vi)linear programming method with non-negative least squares, (vii) weighted-average method, and (viii) minimization search method. We have applied the first seven methods for the two aerosol models (background, volcanic). Our results and conclusions, assuming spherical aerosols of known refractive index, are presented below. Figure 3(a) shows the ' d a t a ' as the variation of extinction coefficient with the four wavelength channels. It also exhibits the extinction recomputed from the inverted size distributions presented in the next Figures and retrieved using each of the seven inversion methods. We also illustrate the maximum envelope solution. All eight results fit exactly the data and, consequently, we have reproduced only one of them. Because of this exact fit, we are confident that our inversions do provide a good test of the information content and parameter estimation at these wavelengths. Figure 3(b) displays the true log-normal model distribution for the background aerosol. The distribution parameters: r~ = geometric radius, % = standard deviation, N = number density, tLa = first moment of the distribution, A = geometrical area of the polydispersion (related to the second moment), and V = polydispersion volume are also shown. The 'average' distribution showing averages at 4 radius values is also indicated for information. The inverted distributions using the different methods are graphed in Figs. 3(c) through 3(j) in which the values of the distribution parameters have been reported and summarized in Table 2. In Fig. 3(c) only, the true distribution was used as a prior estimate, as was done in the inversions illustrated by Chu and McCormick. All other inversions use zero as a prior estimate. Figure 4 displays the corresponding results and information for the volcanic aerosol model. Table 2 illustrates the following points (i) if good a priori information is known about the solution, it is possible to perform reasonably good inversions (see method 1 and Figs. 3c and 4c). If no such information is available, there will be as many solutions as inversion methods tried ; (ii) the Minim u m Deviance method has performed best among all methods applied. Nevertheless, its results are not very accurate; and (iii) in practice, among methods providing physically meaningful solutions, no single method could be preferred to all others. The well-known non-uniqueness of the solution is here well represented. In addition, (iv) the data were assumed to be exact; experimental and numerical noise would add to the uncertainty in the solution; and (v) in all inversions, we further assumed that we knew the values of the minimum and maximum radius of the distribution (0-1.0 t*m in the case studied), and we made

56

A.L. Fymat and C. B. Smith

(Pageoph,

sure that 99~o of the distribution is contained in this interval. In practice, this information is not available a priori and this would further compound the non-uniqueness features of numerical inversions.

V. Proposedstrategyfor follow-on experiments The above analysis of the SAGE I concept has suggested the following possible improvements for follow-on experiments: (i) a different data sequence strategy with a faster scanning rate of the solar disk at the high altitudes where the uncertainty is largest (this is also the source of the mathematical ill-conditioning of the data inversion problem); (ii) additional sounding channels at the shortest possible wavelengths (A < 0.385/~m) that would be more sensitive to the bulk of the aerosol sizes. The determination of the minimal number of such channels remains to be investigated; (iii) a pair of additional ozone sounding channels on the short-or-long-wavelength side of the Chappuis absorption band, or one channel on each side of the band center, or even on the, shorter wavelength Hartley-Huggins band; (iv) possibly different data inversion strategies that utilize not only the near altitude separation between NO2 and aerosol contributions (as proposed in SAGE I) but also the power law variations in both altitude and wavelength of the molecular extinction; and (v) different data inversion methods. These several suggestions could be incorporated in SAGE II and subsequent experiments for a larger and less ambiguous scientific return of the data. With regard to the last suggestion, we have already indicated how the profiles could be reconstructed from the bottom up to the top of the atmosphere. The same idea could be implemented using our minimization search inversion approach (FVMAT, 1976). It has been applied recently by MILL and DRAVSON (1978) for recovering both a constant and a variable CO2 mixing ratio profile from transmittance data with random errors, and for reconstructing CF2CI2 vertical profiles from solar occultation data near 930 cm- 1. Another important improvement would consist in adjoining to the transmission measurement a forward scattering measurement. A complete description of this other technique can be found in FVMAT and MEASE (1978). Our reasons are the following (i) forward scattering is a very efficient sensor of particle size, much more so than scattering at larger angles, (ii) it is not too sensitive to the particle shape or orientation, (iii) it is little sensitive to the particle refractive index, particularly for angles close to the exact forward direction; this influence of the refractive index can be represented fairly simply in terms of the extinction efficiency of the aerosol (FYMAT and MEASE, 1979), (iv) it rests on a completely different physical phenomenon than transmission, and thus can provide an independent confirmation or invalidation of the transmission experiment result, (v) a closed form analytical solution of the data inversion problem is available, and (vi) it utilizes basically the same geometry as the

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

57

occultation experiment. Extensive numerical tests o f this inverse solution have shown that: - The inversion formula o f FYMAT (1978) for forward scattering enables one to reconstruct the size distribution without a priori modeling of, or information on, the distribution. - Examination o f the integrand only o f the inverse formula, evaluated progressively as the data is being received, provides meaningful instruction as to (i) when to terminate the experiment as it would provide no additional useful data, (ii) whether the dispersion under examination consists o f mono-sized particles, and what is the n u m b e r o f its modes. - A size resolution o f a few tenths o f a micron can be achieved with proper selection o f the forward scattering cone half-width, and by the angular resolution with which this cone is scanned. -Moderately strong r a n d o m and systematic noise values are without serious effect as well as multiple scattering, source non-monochromaticity, instrument bandwidth, and finite field-of-view owing to the great stability o f the inverse solution. - The mode radius seems to be always locatable even with only a few measurements. These several advantages appear to us to be o f such an importance as to warrant the most serious consideration o f a satellite forward scattering experiment.

REFERENCES CHU, W. P., in Inversion Methods in Atmospheric Remote Sounding, (Academic, New York 1977), A. Deepak, Ed. CHtI, W. P. and MCCORMICK,M. P. (1979), Appl. Opt. 18, 1404-1413. DEEPAK, A., ed., Inversion Methods in Atmospheric Remote Sounding (Academic, New York 1977), 505 pp. FYMAT, A. L. (1976), Phys. Earth & Planet, Inter. 12, 273-282. FYMAT, A. L. (1978), Appl. Optics, 17, 1676-1677. FYMAT, A. L. and ZUEV, V. E., eds. Remote Sensing of the Atmosphere: Inversion Methods and Applications (Elsevier, New York 1978), 327 pp. FYraAT, A. L. and MEASE,K. D. (1979), Appl, Opt. (in press). MILL, J. D. and DRAYSON,S. R., in Remote Sensing of the Atmosphere: Inversion Methods and Applications (Elsevier, New York 1978), A. L. Fymat and V. E. Zuev, eds., 123-135. PEPIN, T. J., in Inversion Methods in Atmospheric Remote Sounding (Academic Press, New York 1977), A. Deepak, ed. PINNICK, R. G., ROSEN,J. M. and HOFMANN,D. J. (1976), J. Atmos. Sci. 33, 304. SCHUERMAN,D. and GREENBERG,J. M. (1974), Appl. Opt. SMITH, C. B. (1978), Ph.D. dissertation, Univ. of Calif., San Diego. TWOMEY, S. (1977), Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York), 243 pp. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhiiuser Verlag, Basel

Instantaneous Global Ozone Balance Including Observed Nitrogen Dioxide By SUSAN SOLOMON, HAROLD S. JOHNSTON, MARTA KOWALCZYK, a n d IVAN WILSON1)

Abstract - The catalytic destruction of stratospheric ozone by the oxides of nitrogen is believed to be an important part of the global ozone balance. The lack of sufficient measurements of NOx concentrations has impeded efforts to quantify this process. Recent measurements of stratospheric nitrogen dioxide from ground-based stations as well as aircraft and balloons have provided a first approximation to a global distribution of NO2 vertical columns at sunset. These observed vertical columns have been translated into time-dependent vertical NO2 profiles by means of a one-dimensional atmospheric photochemical model. Using recent observations of air temperature and ozone along with this information, the independent instantaneous (one second) rates of ozone production from oxygen photolysis, P(O3), of ozone destruction from pure oxygen species (Chapman reactions) L(Ox), and of ozone destruction by nitrogen oxides L(NOx) were estimated over the three-dimensional atmosphere. These quantities are displayed as zonal average contour maps, summed over various latitude zones, summed over various altitude bands, and integrated globally between 15 and 45 kin. Although the global summation between 15 and 45 km by no means telIs the complete story, these numbers are of some interest, and the relative values are: P(O3), 100; L(Ox), 15; L(NOx), 45 + 15. It is to be emphasized that this relative NO~ contribution to the integrated ozone balance is not a measure of the sensitivity of ozone to possible perturbations of stratospheric NOx; recent model results must be examined for current estimates of this sensitivity. Key words: NO2 distribution; Ozone destruction by NO~.

1. Introduction The importance of the oxides of nitrogen in affecting the stratospheric ozone balance has been a subject of interest in atmospheric chemistry for several years (CRUTZEN, 1970). Recently, NOXON (1978, 1979) and NOXON et al. (1979) have presented measurements of the stratospheric c o l u m n of nitrogen dioxide, NO2, at n u m e r o u s latitudes and seasons. There are now several NO2 profiles up to the middle stratosphere observed from balloons (ACKERMAN et al., 1975; FONTANELLA et al., 1974; OGAWA, 1979; MURCRAY et al., 1974; HARRIES et al., 1976; EVANS et al., 1977; EVANS et al., 1978; GOLDMAN et al., 1978; DRUMMOND and JARNOT, 1978). DOTscrt (1978) has reviewed all of the available data on the vertical ozone distribu1) Department of Chemistry, University of California, and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, Califoria 94720, USA.

Vol. 118, 1980)

Instantaneous Global Ozone Balance

59

tion measured with chemical sondes and one year of ozone data obtained by backscattered ultraviolet radiation from the Nimbus 4 satellite. We have taken these recent measurements of temperature, ozone, and nitrogen dioxide; and using a photochemical model we have translated the observed NO2 columns to time-dependent vertical profiles, which were then extended to global stratospheric distributions. We then examined the global distribution of the rate of NOx catalyzed destruction of ozone by the method of instantaneous rates. The method of instantaneous rates has been described previously (JOHNSTON and WHITTEN, 1973, 1975; JOHNSTON,1975). Briefly the observed distribution of temperature, oxygen, ozone, and incoming solar radiation outside the atmosphere are used to calculate photolysis rates on a grid containing 1 km vertical intervals, 10~ latitude intervals, and 15~ longitude intervals. Rayleigh scattering and albedo effects are treated by the method of ISAKSENet al. (1976). The concentration of O(3P) is calculated at each grid point using the steady-state approximation. At each grid point three independent components of the global ozone balance were evaluated: (a) The rate of ozone production from the photolysis of oxygen, P(O3), which is 2j[O2] as can be seen from the pair of reactions

net:

O~ + hv(h < 242 nm)---> O + O

(slow)

(O + O 2 + M-->O3 + M) • 2

(fast)

(l)

302 + hv --->203

(b) The rate of ozone destruction by the pure oxygen family of reactions, L(O~), which is 2k[O][O3] on the basis of

net:

03 + hv(uv, vis) --> 02 + O

(fast)

O + 03--> 02 + 02

(slow)

(2)

203 + hv --> 302

(c) The rate of ozone destruction by the oxides of nitrogen, L(NOx), which is 2k'[O][NO2] as can be seen from NO + O a - ~ NO2 + 02

(fast)

03 + hv(uv, vis) --~ 02 + 0

(fast)

(3)

NO2 + O--> NO + 02 net:

203 + hv -+ 302

In each of the above cases the loss or production of ozone resulting from the catalytic cycle is given by the rate determining step in each cycle. One might protest that the Ox, NOx, HO~, and C1X families of reactions are coupled, and as a consequence the ozone production and losses cannot simply be identified as 2j[O~], 2k[O][O3], and 2k'[O][NO2]. It is true that the O~, NO~, HOx, and C1X families are strongly coupled, but it is appropriate to review the nature of the coupling and to note what retains its identity during the interactions. Suppose the

60

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

photochemistry of the stratosphere is represented by m chemical species, A1, A~. . . . . Am, and n photolytic and chemical reactions with rate constants, Jl,J2 . . . . . kn, at each grid point of the model. A change in the concentration of a chemical substance As may change the concentrations of many, perhaps all, other species. If changing A~ causes a change in local temperature, all temperature-dependent rate constants would be affected. If changing As causes a change in the ozone profile, the distribution of solar radiation in the atmosphere and the photolytic rate constants j would be altered. As an example, an increase in nitric oxide changes the concentrations of HOx species through the reaction HOO + N O - + HO + NO2 and changes the concentrations of CIX species through the reaction CIO + NO -+ C1 + NO2. Thus the concentrations of various species At are coupled to each other, and by feed-back mechanisms the values of temperature dependent rate constants may be affected. However, there are some things that are not changed when species concentrations are altered, in particular the identity of the n photochemical reactions in the model. The set of photochemical reactions can be expressed in terms of linear combinations of these reactions. With care, a set of linear combinations of reactions can be found such that the net effect of each is either (i) an increase in two molecules of ozone, (ii) a decrease in two molecules of ozone, or (iii) no change in ozone (JOHNSTONand PODOLSKE, 1978). Reactions (1), (2), and (3) represent such linear combinations of reactions. The measured ozone and nitrogen dioxide concentrations are the observed results of all the various coupled chemical processes and of atmospheric transport. At each grid point of the sunlit atmosphere, three components of the ozone balance can be evaluated from 2j[O2]obs, 2k[O]o~1o[O3]obs, and 2k'[O]~c[NO2]ob~. These quantities have been zonally averaged, vertically summed, and expressed as total global rates and as global rates in 5 km altitude bands. In this work, then, we have examined the contributions made by NOx and Ox processes to the natural global ozone balance.

2. Observational data

D~TSCn'S (1978) data were supplied as temperature and ozone partial pressures on a pressure grid from 0.5 to 250 rob, each 10 degrees of latitude from the south to the north pole, and for each month of the year. Data for three months were averaged to give seasonal averages, i.e., March, April, May; spring, etc. For each of the four seasons, the data were converted to ozone mixing ratios and ozone concentrations using the barometric equation to yield altitudes at I km intervals starting from the 250 mb level and interpolating between the given pressure levels. For altitudes below 250 rob, earlier distributions were used (DfOTSCH, 1969; JOHNSTON and WHITTEN, 1973). Examples of the global spring and winter temperature distributions are given in Fig. I. The corresponding ozone mixing ratios (ppbm) and concentrations in units of 1012 molecules cm -3 are presented as Figs. 2 and 3 respectively. The concentration of atomic oxygen was calculated at each grid point of the

Vol. t 18, 1980)

61

Instantaneous Global Ozone Balance TEMPERATURE, K

-L----~-'-~-----'~ 40 ~

26o- ~ 2 5 0

~

5 zo

280 -90 Fell

-60

-50

0

30

60

90-90 -60 Spring Summer

-30

0

30

60

90 Winter

LATITUDE

Figure 1 Temperature in the troposphere and stratosphere. The south pole is - 9 0 ~ and the north pole is 90 ~ One panel is the average of DOTscn's (1978) values for March, April, May; the other is the average of Dec., Jan., Feb.

atmosphere and for each of the four seasons. The orientation of the sun relative to the earth was that for spring and fall equinox and winter and summer solstice. A zonal average of the atomic oxygen concentration over daylight hours was obtained for each grid point of altitude and latitude, and representative results are given in Fig. 4. OZONE MIXING RATIOS (PPMV)

I

t

-90 Fell

-60

-50

0

50

60

60 90 -90 Spring Summer

-30

0

LATITUDE Figure 2 Ozone mixing ratios (parts per million by volume).

30

60

90 Winter

62

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, OZONE CONCENTRATION, I012 MOLECULES CM"3

50 4O

:30

c~ 20 LO

0

L

-90 Fall

I

I

-60

I

J

k

-50

I

I

I

0

I

L

:30

I

I

J

60

I

4

t

I

i

90-90 -60 Spring Summer

I

I

I

-30

I

I

I

I

0

i

I

50

I

I

I

I

60

I

90 Winter

LATITUDE

Figure 3 Ozone concentration in units of 10TM molecules cm -a. Observational data are now available that give a first approximation to the global distribution of stratospheric NO2 (NoxoN et al., 1979; NoxoN, 1979). The measurements were made from the ground or from aircraft during the twilight period using Rayleigh-scattered sunlight from overhead. This gave changes in the NO2, visible, absorption-spectrum through long optical paths in the stratosphere as the sun moved OXYGEN ATOM CONCENTRATION, MOLECULES CM-3

E hi tm

-

50

F--

;_, 20

IE 3E tE

I

-90 Fell

-60

-30

0

50

60

90-90

-60

-30

0

30

60

Spring Summer LATITUDE

Figure 4 Atomic oxygen concentration, 12 hour, daytime average. 3E9 = 3 x 109.

90

Winter

Vol. 118, 1980)

Instantaneous Global Ozone Balance

63

Table 1 Vertical column of stratospheric nitrogen dioxide in units of 10is molecules cm-2 as read from Figs. 1, 2, 3, and 6 of NOXON (1979)

Season

Noxon Fig.

Date

SP

1

4/75

3/77

10/76

3

F

2

3/77

1

10176

3

Lat. Deg.

NO2 1015

77 N 63 N 48 N 43 N 41 N 37 N 27 N 17 N 12 S 31 S 35 S 65 N 53 N 49 N 40 N 14 S

4.9 2.8 2.8 4.6 3.9 3.7 3.1 2.3 2.2 4.4 5.5 1.9 1.9 2.3 3.9 2.6 2.5 2.6 2.5 2.2 2.1 2.9 3.6 4.2 3.5 3.2 4.0 4.0 5.0 4.5

44 N 42 N 40 N 20 N 65 N 53 N 49 N 40 N

Season

Noxon Fig.

Date

SU

1

7/75

3

W

1

2/77

3

6

2/77

Lat. Deg.

NO2 1015

82 N 76 N 69 N 59 N 53 N 40 N 65 N 53 N 49 N 40 N 57 N 56 N 55 N 52 N 51 N 48 N 47 N 46 N 45 N 44 N 43 N 65 N 53 N 49 N 40 N 56 N 49 N 44 N 40 N 30 N

6.9 6.1 5.3 5.4 5.2 5.7 5.1 4.4 4.6 4.9 1.3 1.2 1.4 1.4 1.1 1.1 2.3 1.9 3.2 3.5 3.8 1.3 1.4 2.7 2.3 1.4 1.1 3.0 3.7 3.8

from 88 ~ to 97 ~ with respect to the vertical. The spectral changes d u r i n g sunset (or sunrise) gave the value of the stratospheric NO2 vertical c o l u m n as p r i m a r y information a n d gave a n estimate of the altitude of m a x i m u m NO2. In this article we interpret N o x o n ' s stratospheric NO2 c o l u m n as being that between 15 and 50 kin. At mid-latitudes, NoxoN et al. (1979) reported AM a n d PM c o l u m n s of nitrogen dioxide as well as the altitude of its m a x i m u m concentration. D u r i n g the day the stratospheric NO2 c o l u m n increases by approximately a factor of two, p r e s u m a b l y as the c o m p o u n d s N205, HNO3, CIONO2, and possibly H O O N O 2 are photolyzed. NoxoN (1979) presented the global behavior of NO2 in a series of figures. As a f u n c t i o n of latitude, his Fig. 1 gave representative m e a s u r e m e n t s of the late a f t e r n o o n vertical c o l u m n of stratospheric NO2. We read these points from the graph a n d listed them in Table 1. I n N o x o n ' s Fig. 2, the NO2 c o l u m n s at Cusco, Peru, 14~ ~vere

64

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, NITROGEN DIOXIDEVERTICAL COLUMN I0

I

'

I

I

I

l

l

l

I

l

l

l

l

l

I

l

E

g "6 B

0

~6

6 .E

5:

~~

~

(D I

z

] -90

-60

-30

~

T

I

0 Lotitude

I

I

t

l

30

l 60

90

Figure 5 Observed PM vertical columns of stratospheric nitrogen dioxide, fall-spring: (i) NoxoN (1979), Fig. 1; [] NOXON, Fig. 2; A NOXON, Fig. 3; D. HARRIES e t al. (1976); C. MURCRAY et al. (1974); B. OGAWA (1979); A. ACKERMANet al. (1974). The line is that used as the primary case for this study. Sensitivity studies were made with NO~ columns 2/3 and 4/3 of this line.

given over a nine day period; the late afternoon columns read from the graph are in Table 1. At four stations (40~ 49~ 53~ and 65~ enough data were taken to provide 12 month variation of the NO2 columns, and these data are given as Noxon's Fig. 3. For each of our four seasons (winter solstice, spring equinox, summer solstice and fall equinox), we read the value of the NO2 column from Noxon's smooth NITROGEN DIOXIDE VERTICAL COLUMN OJ

E

u

I0

I

I

I

I

~

I

I

[

I

I

I

I

I

I

I

I

9 8

7 -(D

F F

6

OH

F

--

o

"6

5

E:

4

E

z

E

G

A

0

" 9

3

0 -90

~

I -60

I

I

[ -30

t

I

I

0 Lalitude

~

I

l 30

I

J

I 60

b 90

Figure 6 O b s e r v e d PM vertical c o l u m n s o f s t r a t o s p h e r i c n i t r o g e n dioxide, w i n t e r - s u m m e r : Q , NOXON (1979), Fig. I; ~ , N o x o N , Fig. 3; O , N o x o N , Fig. 6. G. GOLDMAN et al. (1978); E. EVANS et aL (1977) ; F. EvANs e t al. (1978); H. DRUMMOND a n d J ARNOT (1979). T h e line as d e s c r i b e d in Fig. 5.

Vol. 118, 1980)

Instantaneous Global Ozone Balance

et

Z ~

0

~4 O0

~o r ZZ O0

~

~z

._= ,,4 ~.~

65

66

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

curve in his Fig. 3, and these points are included in Table 1. Also the data points in Noxon's Fig. 6 are listed in Table I. For the relatively few NO2 columns observed in the southern hemisphere, (SH), Noxon found a gross symmetry with respect to the corresponding season in the northern hemisphere, (NH). To extend the data base, we reflected all observed points in Table 1 to the other hemisphere with a six month phase shift. The points in Table 1 are plotted in Fig. 5 to represent the observed NO2 stratospheric columns for spring (NH), fall (SH) and in Fig. 6 to represent summer (SH), winter (NH). The vertical distributions of stratospheric nitrogen dioxide as observed from balloons typically go from a lower altitude o f 12 to 20 km to an upper altitude of 28 to 40 km. The profile measured by DRUMMOND and JARYOT (1978) extended from 20 to 50 km. Some of these measurements were made at sunset, some at sunrise, and some at noon. Noxon's stratospheric NO2 columns of Table 1 and Figs. 5 and 6 refer to late afternoon conditions and essentially to the NO2 between 15 and 50 kin, and the column provided by the balloon profiles are not strictly comparable. We filled in the gaps in the lower stratosphere, or upper stratosphere, or both to give extended balloon profiles from 15 to 50 km by using estimates from the photochemical model. In the cases where the balloon profile did not correspond to late afternoon conditions, we ran the photochemical model from sunrise to sunset to obtain a model value for the PM/AMratio for the NO2 column. The values, typically about two, were used to scale the observed column to PM conditions. Table 2 contains the resulting columns from the observed NO~ profiles and the value of the corresponding column scaled as described above. Each balloon study is labeled by a letter A through H in Table 2, and these letters appear as data points on Figs. 5 and 6. Entry A in Fig. 5 is based on ACKEgMAN et al. (1975) from 20 to 36 km, on FONTANELLA et al. (1974) from 15 to 20 kin, and on a model-based extension from 36 to 50 km, and this balloon-based column agrees with or may be somewhat smaller than Noxon's results. At the other extreme, Harries' column is far greater than Noxon's column for the corresponding latitude and season, Fig. 5 (JoHNsToN and PODOLSKE, 1978, pointed out that the NO2 from Harries column destroyed ozone above 30 km much faster than it was produced by sunlight and was probably not representative of general conditions). The other observed PM nitrogen dioxide columns scaled to 15 to 50 km lie somewhat above Noxon's NO2 columns, although in general not more than the + 20~o error that Noxon estimated for his method. Considering both Noxon's results and the balloon results, we derived the lines in Figs. 5 and 6 to use as the present estimate of the global and seasonal stratospheric NO2 columns between t5 and 50 kin. Certain sensitivity studies were carried out where the curves of Figs. 5 and 6 were scaled by the factor 2/3 or by the factor 413. 3. Photochemical model calculations

Originally we intended to treat the NO2 distribution 100~o empirically, using (i) the vertical columns from Figs. 5 and 6, (ii) two as a universal PM/AM ratio with

Vol. 118, 1980)

Instantaneous Global Ozone Balance

67

linear change with time during the day at all altitudes, (iii) Noxon's observed altitudes of maximum NO2, and (iv) a Gaussian function (or = 7 km) derived from balloon measurements to give the vertical NO2 profile. This procedure was carried through for one calculation of global instantaneous rates. Its assumptions were tested against a time-dependent photochemical model, and the assumptions were not sustained. The rate of change of NO2 between AMand PM was found not to be uniform with altitude. Model calculations do not yield an NO2 profile which is Gaussian in shape. The rapid rise in the concentration of O(3P) with increasing altitude, as shown in Fig. 4, causes the maximum rate of the O + NO2 reaction to occur at a higher altitude than the maximum NO2 concentration. In order to evaluate the global contribution of this process to the natural ozone balance, it is essential to know the nitrogen dioxide concentrations at high stratospheric altitudes, where there are few measurements. It was felt that model extrapolation of the N02 profile above the highest altitude of NO2 measurement was more reliable than an empirical extrapolation from the limited set of observations. As a result of these considerations, we decided to take the observed PM vertical columns of NO2 as primary data and to use a photochemical model to establish the PM/AMratio, the change of NO2 during the day, and the vertical distribution of the NO~. The model used includes one-dimensional atmospheric motion and photochemistry; it was obtained from the Lawrence Livermore Laboratory as their 1974 model (CHANG, 1974; CHANG et al., 1974), and we modified it to include additional species and reactions. Twenty species are treated time-dependently (03, O, HO, HOO, H20, H202, N20, NO, NO2, NO3, N205, HNO3, CH4, CO, C1, C10, C1ONO2, HC1, CF2C12, CFC13) and three species are treated by steady-state approximations [O(1D), N, H]. A natural background of 2 ppbv of total chlorine is prescribed, including CF2C12 and CFC13 in lieu of natural CHaC1. The vertical eddy diffusion function of STEWARTand HOFFERT(1975) is used. The differential equations for each atmospheric species are solved using the Gear method. The chemical reactions and rate constants are given in Table 3. Model calculations were performed to obtain reference NO2 profiles for three zones: polar, mid-latitude, and tropical regions. For the mid-latitude region, the model was run, using a constant sun at half intensity, for 30 years. Diitsch's ozone was taken as the initial distribution, and runs were made with four different sets of boundary values for NO and NO~. Each of these runs was followed by three days of diurnal calculations with a maximum time step of 200 sec and where the photolysis rates varied continually according to the computed solar angle and radiation flux. This produced four sets of stratospheric evening NO2 profiles, for which the columns bracketed the range observed by Noxon. From these four profiles we derived linear interpolation factors that gave the NO2 profile at any time of day starting from a given PM vertical column. For tropical and polar regions, we could not expect a one-dimensional eddydiffusion model to give reasonable results. Our goal is not to model ozone but only

68

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

I'~

I"~

0

0

0

+

'~

5g

gLg$%%~

~ ~3 2" .............

2222~

~3 oo

.....

~,

, , , o&g~,

9

o

8

+

~9

+

+

o

~:++z6zO=5 ~o O+ +

o++~ zoo o

zos

6tn

e

== += 6 c 7 6++o+= ~ o o=~t

tee

t~

t = t6:~=o

++

:~ c ? l " + ~t +c ~+ =+ od +

o+t:~ O "~ 0+

t+ ~'+s

d o z + + o z z +o+ + ~ + ~ 6 +

+ ~ o + +=+z+=+= d ~ 1 7 6+1+7 6 + o + o+9+ ~ + o ~=~c~++c~====+~+oo+=+c~==

+++oo+++o o6ozzzzz~=uob=b===oooozzzz:=ozzoob~

Vol. 118, 1980)

Instantaneous Global Ozone Balance

oz

69

o,

z

z

z

r~

m

r~


.
~ ~ m . ~ ,-. ;;" ,-.' > ~ o . . ~ ~'~"o ~ ~ o ' = u o= - ~o ~o 0 o

z._c ~ = o ~n o ~,-... ~ = ~ . ~ . n ~

_o E ~ . o'" ~" ~

~

~

z ~

~,~o'~

-~~ ~~ = ~ = o ~

~ 8 ='= - o'" "-:=,-

o.=

: ~= =~ III ~o ""~

~,.~ ~ o ~ ~ I .,~ = , . . _ , ~

~..~ r o o.,.o = .~.~

~ 0,.s o','~.- 0 ~ , .-4 o ~ m

"u'~

8

o

93

94

R.C. Whitten, O. B. Toon, and R. P. Turco

(Pageoph,

the dominant processes for the oxidation of SO2 into H2SO4 does not yet exist. As a result, reaction sequences like that listed in Table I must usually be used. Fortunately, reaction schemes can be readily expanded with advances in sulfur photochemistry. Heterogeneous reactions may also be important. FRIEND et al. (1973), have pointed out that SO2 could react directly with sulfuric acid droplet surfaces to produce additional dissolved sulfates; the process would require the presence in solution of a buffering agent such as ammonium ions. Sulfur radicals, such as HSOa, might also be absorbed or react directly on aerosol surfaces. Again, we have insufficient information to be sure; however, we may reasonably assume that some of the nitrogenbearing sulfates that have been detected are formed by heterogeneous reactions. It is important to mention at this point that extensive sensitivity tests (ToON et aL, 1979) have shown that the precise fate of sulfur radicals formed in the stratosphere may not be critical to the simulation, as long as they eventually stick onto aerosol particles and are chemically transformed into sulfate.

Microphysical processes

Theoretical treatments of nucleation and growth by condensation and coagulation of aqueous sulfuric acid solution droplets under stratospheric conditions are available. It is generally assumed in the literature that the aerosol particles are formed in situ by heterogeneous heteromolecular nucleation of H2SO4 and water vapors onto condensation nuclei or Aitken particles. Recently, CADLE and KIANG (1977) reviewed current scientific knowledge of atmospheric Aitken particles. The Aitken nuclei are assumed to be transported by eddy diffusion from the troposphere to the stratosphere or to be deposited in situ by aircraft or rocket engines. If the stratosphere is supersaturated with respect to an aqueous H2SO4 solution, the Aitken particles are rapidly nucleated in times of the order of 10~ sec or tess, depending on the supersaturation, the nucleus composition and size, and other factors (P. HAMILL, private communication). (Model calculations are quite insensitive to this time as long as it is less than 107 see.) HAMILL et al. (1977a), have shown that under ambient stratospheric conditions, homogeneous nucleation or nucleation onto molecular ions may be slower than the heterogeneous process. However, large ions consisting of a charged core surrounded by a cluster of polar molecules such as H~O, HNOa, and H2SO4 have been detected in the lower stratosphere (ARNOLD and HENSCHEN, 1978); such ions might act as effective nucleation sites for aerosol particles (CAsTLEMAN et aL, 1979). Complexes of sulfur radicals might also act as condensation nuclei in the stratosphere (FmF.ND, private communication). Once nucleated, the droplets grow by heteromolecular condensation of sulfuric acid and water vapors; the nonacidic material of the nucleus becomes a (solid or dissolved) droplet core and remains so until the H2SO4 and H 2 0 are evaporated. Even so, the core surface may remain activated for some time due to incomplete

VoI. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

95

drying. HOPPEL(1976) and HAMILLet al. (1977b), have shown that the droplet growth rate is controlled by the rate of impingement of sulfuric acid molecules, and that the droplet is always in equilibrium with the ambient atmospheric water vapor. If the partial pressure of sulfuric acid vapor surrounding the droplet is greater than the droplet vapor pressure, there is a net uptake of incident H2SO4 molecules; conversely, if the vapor pressure is greater, there is a net loss of H2SO~ from the droplet and evaporation occurs. The droplet simultaneously absorbs or evaporates just enough water vapor to maintain a constant mass fraction of H2SO4 in solution (because the amount of water vapor in the stratosphere is much greater than the amount of H~SO4). Particle coagulation has an effect somewhat similar to condensation in that it causes particle growth. However, it is dissimilar in that it involves droplets rather than single molecules sticking to another droplet. In the stratosphere, where aerosol sizes are usually less than 1 t~m, only coagulation due to Brownian motion need be considered; that is, coagulation due to turbulence and coalescence due to differences in fall velocities can be neglected. The coagulation kernel for particles of different size has been derived by FUCHS (1964); the kernel is a function of the molecular diameters for air and H2SO4, the particle sizes, densities and sticking coefficients, and the kinematic viscosity of air. In modeling coagulation, one should include coagulation of condensation nuclei with droplets, but may omit coagulation of nuclei with nuclei because of the much lower probability of their colliding and sticking to each other in the stratosphere. During sedimentation in the lower atmosphere, droplets are always at or very close to their terminal fall velocities and retain their approximately spherical shape if they do not freeze (because at small velocities, surface tension can maintain a nearspherical shape). Hence, the fall velocities are given very accurately by the StokesCunningham formula (e.g., KASTEN, 1968). The aerosol particles are, of course, also transported by atmospheric motions. For droplet sizes representative of the lower stratosphere, one can, to a very good approximation, assume that the mean particle velocity due to drag by atmospheric motion is equal to the local mean atmospheric velocity.

3. Stratospheric aerosol models Model elements The particle size distribution, which is in general a function of time t, altitude z, and radius r, is described by continuity equation of the form

dn ~-

( ~g) ~n +n V-V+~r -= O-t + V.(nv) +~(gn)

= Sn

(1)

where n is the particle concentration per unit radius (particles cm-3 sec-1), g is the

96

R.C. Whitten, O. B. Toon, and R. P. Turco

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particle growth rate (cm see-1), SN is the net particle source/sink term due to nucleation, coagulation washout, etc. (particles cm -3 sec-1), and v is the particle velocity. The rate of change of n due to coagulation is given by an expression analogous to the collision integral of gas dynamics which specifies the volume rate at which particles are 'scattered' (i.e., coagulated) into a radial 'element' less the rate of'scattering' out of the element. Then equation (1) can be written

~n ~ (dn) ~--~ + V. (nv) + ~ (gn) = ~-

+ S;

(2)

coag~

the coagulation integral, (dn/dt)ooa~., will be discussed later. A similar continuity equation is satisfied by the condensation nuclei. The spatial flux ~b denoted by (nv) in equation (2) is conveniently decomposed into three parts: a sedimentation flux dps = -v~n~z

(3a)

where vs is the fall velocity and ~z is a vertical unit vector; a flux due to atmospheric bulk motion dpa = v~n

(3b)

where va is the atmospheric bulk velocity; and an eddy flux, representative of sub-grid scale motions

(3c) where na is total atmospheric number density and D i s the eddy diffusion tensor. The growth and evaporation of aerosol droplets affect the concentrations of sulfur-bearing gases in the atmosphere. The rate at which H2SO4 molecules condense on and evaporate from droplet surfaces is determined by the particle growth rate and the total particle surface area available. The net rate at which acid molecules condense onto existing particles can be expressed in the (equivalent chemical kinetic) form

dna dt

P~

-

L~n~,

(4)

where P, and L~ are the specific sulfuric acid production rate (molecules cm-a sec-1) and loss rates (molecules sec- 1), respectively, which may be related to the growth rate g and aerosol concentration n by appropriate integrals over particle sizes. The term dn~/dt also represents the net rate of loss of sulfuric acid from the droplets. Hence, if a model is to be interactive between aerosol and vapor, the terms P~ and L~n~ must be included in the kinetic equation for H2SO4 vapor. As we shall see later, it is important to include these terms because condensation can severely deplete H2S04 vapor in the lower stratosphere, moderating the growth rate of aerosol particles.

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

97

The model of Junge, Chagnon,and Manson I n their p a p e r r e p o r t i n g the first definitive m e a s u r e m e n t s o f t h e stratospheric aerosols, JUNGE ( t 9 6 I ) also p r e s e n t e d a simple m o d e l t h a t was r e m a r k a b l y c o m p l e t e with respect to i m p o r t a n t phYSical processes in view o f the capabilities o f the c o m p u t e r s o f t h a t era. Specifically, they included t r a n s p o r t by vertical diffusion a n d sedimentation, a n d coagulation. They expressed the vertical flux, ~ o f particles as

et al.

0 ((n) n r~ = -naD exp [-f; (vs/D)dzr] -~z

exp

[f~ (vJD) dz']}

(5)

where D is the vertical c o m p o n e n t (D~z) o f the e d d y diffusion tensor. The steady-state f o r m o f the continuity e q u a t i o n was then solved for the particles u n d e r the a s s u m p t i o n t h a t D is a constant, t h a t vs varies inversely with air density, a n d that there were b o t h

CONCENTRATION, NUMBER cm -3 .01 .1 I 3O

--

DOWNWARD DI FFUSI NG PARTICLES

a

9

UPWARD DI FFUSING PARTICLES UPWARD DI F FUSI NG PARTICLES WITH COAGULATION

I 2 20

\.7.D

i 10

=JLt .1

1.0

= 2000

D -lOOO t

t J l J Jl[

i tl

i

.1

1.0

CONCENTRATION (RELATIVE), NUMBER cm -3

Figure 3 Vertical profiles of particle concentration calculated for diffusion-sedimentation equilibrium for particles of 0.15/~m radius and 2.0 g cm -a density using the model of JUNGE (1961). The eddy diffusion coefficients, D, are in units of cm 2 sec -I. The dashed curves ( . . . . . ) represent upward diffusion of particles from a constant source at 30 km altitude and an effective sink (washout) at the tropopause. The broken curve ( - - . - - ) represents qualitatively the shift in the dashed ( . . . . . ) curves when coagulation is introduced. The vertical bars and heavy solid line connecting their midpoints represent a profile of particles collected by impactor on November 21, 1959; the measurements are roughly representative of 0.15/~m particles.

et aL

98

R.C. Whitten, O. B. Toon, and R. P. Turco

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stratospheric and tropospheric sources of particles; the sources were taken into account by fixing the number density at 30 km and 10 km. Some calculated number densities of particles with radii of 0.15 tzm are shown in Fig. 3; the particles of stratospheric origin (see 'b' curves) are assumed to be rapidly removed by washout at the tropopause. As seen in Fig. 3, JUNGEet al. (1961) found that at altitudes below 24 km the predicted vertical distribution of 0.15 tzm particles was in rough qualitative agreement with observational data when an eddy diffusivity of 2000 cm 2 sec-1 was used. Because of computational limitations, they were able to give only a qualitative assessment of the coagulation process for upward-diffusing fine particles. For this case, they used an approximate steady-state expression d2n

D-d~z2+ an 2 = 0,

(6)

where a is a coagulation coefficient, which depends on the particle mean free path, and on the air viscosity and temperature. The solutions have the form 6D n = a(z + Zo)2

(7)

where Zo is an empirical constant. A typical vertical distribution for the upwarddiffusing particles is shown by curve c in Fig. 3. JUNGE et al. (1961), concluded from their studies that sedimentation and diffusion, and particle growth by coagulation satisfactorily describe the evolution of particle distributions in the stratosphere. They also concluded that there are three major populations of stratospheric aerosol particles: those with radii < 0.1/zm, probably of tropospheric origin; those with radii between 0.1 and 1 tLm, most likely formed within the stratosphere, probably by oxidation of SO2 and H2S; and those with radii > 1/zm, of extra-terrestrial origin. We now know (e.g., TURCO et al., 1979a) that particle growth by condensation and shrinkage by evaporation are also important microphysical processes. Nevertheless, the model analysis performed by JUNGEet al. (1961), did identify many of the important sources and processes of stratospheric aerosols and helped to explain several features of their experimental data, particularly the vertical distribution of the' large' particles (i.e., particles with radii between 0.15 and 2 t~m). The model o f Burgmeier and Blifford

BURGMEIERand BLIFFORD(1975) had a rather limited objective in their studies: to simulate the 'aging' of aerosols by coagulation and by growth resulting from surface-gas reactions in the presence of regenerating particle sources. They also calculated mean particle residence times in the absence of particle sources. Then Burgmeier and Blifford sought to estimate changes in particle size distributions as they evolved by growth and sedimentation. The aerosol continuity equation used by

The Stratospheric Sulfate Aerosol Layer

Vol. 118, 1980)

99

Burgmeier and Blifford, -On(r, - t) =

Ot

f

rl21/3

K[(r s - r'~ 113, r']n[(r 3 - r'S) 1Is, t ]n(r', t) Ta r 2

[,rb

x (r ~ --r,,)2/s dr' - n(r, t) Jr K(r, r')n(r', t) dr' a

}r

o~

vs ) n(r, t) - ~(r, t) -~r + S(r, t),

(8)

where n(r, t) is the concentration of particles with radii between r and r + dr, K(r, r') is a coagulation kernel, vs(r) is the sedimentation fall velocity, l is a length parameter characteristic of the layer depth (nominally taken to be 100 m), a is the rate of growth due to the reactions of gases on the particle surface, and S(r, t) is a particle source term. The authors were able to ignore gas phase chemistry because all processes leading to particle formation and growth were implicitly absorbed into the empirical terms S(r, t) and a(r, t). The first integral on the right-hand side of equation (8) accounts for accretion of particles in the size range r, r + dr due to coagulation of smaller particles, and the second integral accounts for coagulative loss of particles in that size range. The source term was so constructed that it returned to the atmosphere a total mass equal to that removed by sedimentation, ensuring the size distribution for the source to be the initial size distribution for the calculation, n(r, 0). The continuity equation was then solved numerically for various forms of the initial concentration and size distribution. Burgmeier and Blifford used the model to study aerosol 'aging' and aerosol residence times by simulating the time evolution of various initial size distributions. Of several such distributions considered, only that of BIGG et al. (1972) was consistent with the residence time of 2 yeats estimated by TELEGADASand LIST (1969) from radioactivity measurements. The authors also concluded that, with sources proportional to the initial size distribution, the spectra of BIGGet al. (1972), and of FRIEND (1966) were capable of maintaining their original forms; on the other hand, the spectrum of JUNGE et al. (1961) became significantly depleted in the small size range. For sources that were not proportional to the initial particle size spectrum, BURGME1ER and BLIFFORD(1975) found a tendency for the spectrum to approach the shape of the source. This behavoir was somewhat stronger with the larger particle concentrations of Bigg et al. than with those of Friend or Junge et al. The time evolution of a ' Bigg' initial spectrum is shown in Fig. 4. (Note that the distribution is expressed in the form dn/d log r.)

The model of Kritz In his Ph.D dissertation, KRITZ (1975a) undertook a somewhat more general analysis of aerosols than those outlined above, particularly with respect to particle formation and growth. In order to simplify the treatment of the aerosol particle

100

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t, days

10

j

10 z

/

30

/

/

t

CC "'

I

I

Z

-5 C3

lO4

I

/ I

]

10-6 ,01

ol rad, #m

Figure 4 Changes in the size distribution of Bigg over a period of 30 days. Note that the distribution is given by dn/d (log r). (After BURGMHERand BLIFFORD, 1975.) continuity equation, he adopted a Lagrangian formulation

Dn(r, t) Dt

1 rD n(r, t) - ~ 1 n(r, t) + f coag. -- ~ [gn(r, t)] + S(r, t),

(9)

where ~'D and ~-~ are, respectively, the particle residence times against diffusion and sedimentation. The term f coag. represents the coagulation integrals (first two terms

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

101

on the right-hand side of equations (8)), g is the particle growth rate due to accretion of sulfuric acid molecules by the particle surfaces, and S(r, t) is a source term as in equation (8). Gas phase chemistry was assumed to lead to the formation of sulfur trioxide (SO3) from the oxidation o f other sulphur compounds such as sulfur dioxide (SO2). The S Q molecules were then assumed to either form new aerosol particles (via heteromolecular homogeneous nucleation) or to be accreted by existing aerosol particles. The simulation of diffusion and sedimentation by the use of residence times, while admittedly crude, was acceptable for Kritz's limited study of the rates of aerosol processes. To facilitate solution of the coagulation integrals, Kritz employed the logarithm of the particle mass (log m) rather than radius as the variable of integration. The particle size distribution was divided into a series of bins, i = 1, 2 . . . , s p a n n i n g the particle mass range considered such that the log rn~ were in arithmetic progression. The coagulation integrals were then discretized in a manner similar to that used by TuRco et al. (1979a) and discussed below; the coagulations kernels were computed using formulas given by FucI-IS (1964). With a given size distribution as an initial condition, the populations of the bins were allowed to evolve by time-stepping the finite difference analog of equation (9). Rather than treat growth as a separate process, Kritz incorporated it into the coagulation integral. Heterogeneous nucleation (growth) processes were modeled by including a special size bin whose population was set equal to the ambient concentration of SO3. Coagulation of an SO3 molecule with a particle in any aerosol size bin was assumed to be equivalent to growth, and the ambient SOa concentration adjusted by taking the difference between its rate of formation from SO2 and rate of loss to particles. The formation of new particles via homogeneous processes (the S term in equation (9)) was accounted for by increments to the population of the first aerosol size bin. KRITZ (1975a) used this model to simulate a number of possible scenarios related to the formation of the background stratospheric aerosol in order to determine the effects of various postulated rates and mechanisms of aerosol formation on the particle size spectrum of the resultant aerosol populations. The principal conclusions of the study were that the large particles characteristic of the background stratospheric aerosol layer are formed by the growth of a small population of'pre-existing' Aitken particles, and that a principal factor controlling the final size (and number) of the large particles thus formed is the number of Aitken particles (i.e., growth sites) originally present. However, the model could not distinguish between growth caused by the condensation of SO3 and water vapor on the particles (heterogeneous nucleation) and that resulting from the direct uptake and oxidation of SO2 within the particles (presumably in the presence of NHa, as proposed by FRIEND et al., 1973). Coagulation, while effective in limiting the population of smaller particles (~0.05/x radius), was found to be too slow to be a significant factor in the formation of the large particles or in materially reducing their number. The production of large particles was also found to be relatively insensitive to the rate of aerosol formation, so long as these rates were of the same order or fast relative to the ~ 1-year residence

102

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times characteristic of the lower stratosphere. KRITZ(1975b) also tested the possibility that the requisite 'pre-existing' Aitken nuclei population might be produced in the stratosphere via a ' self-limiting' homogeneous heteromolecular nucleation of sulfuric acid-water nuclei but concluded that this was unlikely. The model o f Rosen, Hofmann, and Singh

ROSEN et al. (1978) based their model on solutions to a form of equation (9) in which the residence times are replaced by operators representing eddy diffusion and sedimentation: 9D ~ -~z DnA 1 0 -- -->-

7s

~Z

v~.

n21

(10a) (10b)

Further important approximations were also made: coagulation kernels are independent of particle size, H2SO4 vapor is distributed with a narrow Gaussian profile centered at 20 km, and gas phase chemistry can be neglected. Even with these assumptions, Rosen et al. were able to obtain analytic solutions that were in rough qualitative agreement with observed size distributions and vertical height distributions of aerosols. They found, however, that the predicted condensation nuclei (CN) profile was not in good agreement with observation. When they adjusted the input parameters so as to being the CN profile into better agreement with measurements, other profiles, such as the large particle (radius >0.15/~m) mixing-ratio profile became unacceptable. A search for a reasonable set of parameters that would bring the model into essentially complete agreement with the measurements was unsuccessful. The occurrence of a particle mixing-ratio peak at 20 km was, of course, due largely to the assumption of an H2S04 concentration peak at 20 km. Despite its defects, the model of Rosen et al. represents an improvement over earlier models in that aerosol height and size distributions, as they are affected by coagulation, could be studied in greater detail. The model o f Turco and coworkers

TURCO et al. (1976, 1979a) developed a stratospheric aerosol model which includes the following processes: vertical eddy diffusion, sedimentation, nucleation, vapor condensation and evaporation, coagulation, and interactive sulfur gas phase chemistry. 'Interactive' means that sulfuric acid vapor formed by chemical reactions is coupled to the liquid phase abundance in aerosols through equation (4). Turco et al. consider two classes of particles separately: aerosol droplets and condensation nuclei. They also follow the evolution of core material in the droplets, which consists of accumulated nucleus material. The corresponding set of continuity equations, which have the

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

103

general form of equation (2), were recast into finite difference equations for computer solution. Because stratospheric aerosol particles can span several orders of magnitude in radius, TuRco et al. (1979a) represented their model size range (radii of 0.001 to 2.56 tzm) with a set of geometrically increasing particle size categories (also see the discussion of Kritz's model). As did JUNGE et al. (1961), Turco et aL combined the particle diffusion and sedimentation terms into the form

~tot~1

Dt~ Oz (~n),

(lla)

where n ~ exp [J~ Vs(z'),az ,]j. /z = na(0)

(1 lb)

Using equations (l l) reduces 'numerical' or artificial diffusion problems which normally arise when sedimentation fluxes are calculated. Artificial diffusion also arises in the finite difference formulation of droplet growth, and a suitable means must be employed to minimize it. In the scheme of TuRco et aL (1979a), the particle population of bin i is given by f T,+1 ni,~ l(r) dr, l

where (12)

n~,~+l(r) = n~,i+l r

During a time step at a given height, the constants h and a are calculated by adjusting them to fit the total particle surface areas in bins i and i + 1, i'espectively. One then finds that the finite difference approximation to the growth term in equation (2) can be written for the ith bin as

en,J -ffl~rowth

n,-1 ~,-1

ni

(13)

~,

where the ~-~are the time-dependent parameters which depend on the mean growth rate of particles in a bin and on bin populations. This approach can effectively inhibit spurious particle growth resulting from 'numerical' diffusion. Lack of computer capacity prohibits a detailed treatment of the size distribution of the cores within each droplet size bin. An alternative approach developed by Turco et al. uses the first and second total core volume moments for the inclusions in each size particle. Continuity equations analogous to equation (2) can be derived for the core volume moments. For coagulation, the assumption of a discrete particle size spectrum gives

104

R . C . Whitten, O. B. Toon, and R. P. Turco

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satisfactory results and is easy to use. In this case, one writes the coagulation loss term in equation (2) as (14)

= -- n, ~ K, jn~( Vff V 0 + ooag, loss

j~;~

and the gain term as

On'+11 ~t

(15)

= n, E K~yny(VJlV~)O,y

= coag. gain

3" ~ i

(o,j = 1 if i ~ j ;

O~j = 89 if i = j ) .

The factor 0ij is a symmetry factor which eliminates double summing in computing self-coagulation rates. The treatment for coagulation of condensation nuclei with droplets is slightly different; the reader is referred to TURCO et al. (1979a) for details. Using the model of TURCO et aL (1979a), TooN et al. (1979) have made some rather extensive comparisons of model predictions with aerosol observations. For example, Fig. la shows model predictions of typical vertical distributions of the dominant sulfur-bearing gases, including the effects of aerosols. The mixing ratio of COS is constant in the troposPhere (which is indicative of a long lifetime in this 40

I

I

I

I

I

I

I

I

SPRING 1973 LATITUDE AVERAGE DATA 35

i

30

E25

'yV

2o

15

10

S I

I

.2

I

I

.4

I

~

.6

I

]

]

.8

i

10

SO4 MASS MIXING RATIO, 10"6/ag/mg AIR

Figure 5 Observed and calculated aerosol sulfate mass mixing ratios (rag SOg/kg air). The observations (LAZRUS and GANDRUD, 1974), made with filters, have been averaged over latitude from pole to pole. The error bars give the extreme values found at individual latitudes.

Vol. 118, 1980) 40

The Stratospheric Sulfate Aerosol Layer I

I

I

I I

I

I

I

I

I

I

...... n

I

1 I

I

I

I

I

JUNGE et al. 1961

.__

KP, S E L A U

-- -- --

PODZIMEK

[]

30

105

etal.

1974

e t al. 1 9 7 5

CADLE AND LANGER 1975 t

ea 1-20

. . . . . ;"

-i:

-

ROSENAND HOFMANN 1977

0

10

% 1%

-

M O D E L RESULTS I

I

1

I I

10

I

I

I

I I

100

I

I

I

I

I

I

1000

I

I

I

10,000

TOTAL PARTICLE MIXING RATIO, PARTICLES/mg AIR

Figure 6 Observed and calculated total particle number mixing ratios (particles/rag air). The data were obtained over a period of 15 years by various investigators using condensation chambers. The large spread in the data may be partly due to real differences in aerosol abundances and partly due to different sampling techniques. region) and then decreases uniformly with height above the tropopause. The predictions fit the recent stratospheric measurements of INN et al. (1979) quite well. Sulfur dioxide concentrations decrease rapidly above the tropopause due to upward diffusion and rapid oxidation by OH. Interestingly, SO2 increases in the region where COS is photolyzed, and again at higher altitudes where H2SO4 is photolytically decomposed, although this latter process is speculative because H2SO4 vapor absorption cross sections in the dissociating region below 250 nm are undetermined. Sulfuric acid vapor has an interesting distribution in that its lowest concentrations occur in the vicinity of the aerosol layer. The aerosol particles strongly absorb H2SO4, significantly affecting its local abundance. This result suggests that aerosol models that do not include interactive gas-particle processes for H2SO4 may be quite inaccurate in their predictions for the sulfate layer. Some of the steady-state model predictions of the properties of the ambient stratospheric aerosol layer, and comparisons with experimental data, are shown in Figs. 5 to 9. Interestingly, even though T O O N et al. (1979) did not attempt to tune their model by varying some of the uncertain physical parameters, the predictions for the five aerosol characteristics shown in Figs. 5 to 9 are reasonably good. It is pertinent to note that most of the data employed here were obtained during a volcanically quiescent period in 1973-74. The steady-state model predictions are presumed to represent an average global state for the quiescent aerosol layer.

106

R.C. Whitten, O. B. Toon, and R. P. Turco

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40 SUMMER (~ = O WINTER SPRING MODEL RESULTS

35

30

E ..~

25

E3 II-~ w

20

15

10

51

I 0

I 2

I

I 4

I

I 6

I

I 8

I

I 10

~

I 12

LARGE-PARTICLE (r > 0.15/~m) MIXING RATIO, PARTICLES/mg AIR

Figure 7 Observed and calculated mixing ratios of particles with radii >0.15 /zm. The observations (HoFMANNet aL, 1975a) were made using a light-scattering particle counter. A large number of measurements were made over Wyoming; the mean value and a measure of the standard deviations are presented for different seasons. The sulfate mass-mixing ratios shown in Fig. 5 indicate that the model gives roughly the same amount of sulfate mass in the aerosol layer as has been observed. Predicted and measured total particle mixing ratios in the stratosphere are shown in Fig. 6. The scatter in the experimental data could be indicative of variability in atmospheric vertical transport rates in this case. Figure 7 illustrates that the calculated concentrations of large particles (radii > 0.15 txm) are in accord with a number of stratospheric in situ measurements. Figure 8 shows that the size distribution of the large particles (represented by the concentration ratio of particles with radii >0.15/xm to those with radii >0.25 t~m) are also in agreement with observations. In both Figs. 7 and 8, there is a substantial range of measured values, with the model calculation being generally representative of the data. Finally, the computed particle size distributions at 16 and 20 km are compared

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer 40

I

I

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9 '1 ~'~

35

t

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[

107 I

22 FLIGHTSOVER LARAMIE, WYOMING ~ 32 FLIGHTS WORLDWIDE MODEL RESULTS

30

E 25

/

a I'm I'-

~

/

I I

2o

15

10

0

2 4 6 8 RATIO OF PARTICLES > 0.15 #m RADIUS TO THOSE > 0.25 .um RADIUS

10

Figure 8 Observed and measured concentration ratios of particles with radii >0.15/~m to those with radii > 0.25/zm. The observations (PINNICKet al., 1976) were made with a light-scattering particle counter. Numerous flights were made over Wyoming and worldwide. The average value and a measure of the standard deviation are illustrated. to several empirical size distributions in Fig. 9. Evidently, the model reproduces the observed stratospheric aerosol properties quite well (under volcanically quiescent conditions). Model o f Cadle, Kiang, and Louis CADLE et al. (1976) constructed a two-dimensional (meridional plane) model designed to simulate the global dispersion of volcanic eruption clouds. No processes other than transport by atmospheric motions were included in the model. Hence, particle formation, growth, coagulation, and even sedimentation were ignored. Despite these drastic simplifications, the model proved useful in a qualitative way for assessing the rate and degree of meridional spreading of the injected material from several eruptions. As the material from a simulated equatorial eruption ( A g u n g ) s p r e a d poleward, the predicted altitude of peak concentration steadily decreased, as observed for ambient aerosols (e.g., ROSEN et al., 1975). A simulation of a high-latitude eruption (Bezymainny) suggested that the material will tend to stay at high latitudes until it is eventually lost by downward transport into the troposphere.

108

R.C. Whitten, O. B. Toon, and R. P. Turco

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AT 16 km ___• MODEL RESUL" AT 20 km - - - = EXPONENTIAL -log NORMAL o ZOLD ___ r

r~

10-,V

Z O I,
0.15 tzm to the number with radius > 0.25 tzm. Key: 1 = very sensitive; sensitivity study calculations differ more than observed variability 2 = moderately sensitive; sensitivity study calculations differ as much as observed variability 3 = insensitive; sensitivity study calculations differ less than the observed variability model calculations are discussed at length by TURCO et al. (1979a) a n d TOON et al. (1979).

Growth and coagulation I n Figs. 10(a-d) the results of the reference model of TURCO et al. (1979a) a n d the calculations of four o b s e r v a b l e s - t o t a l particle n u m b e r mixing ratio, largeparticle n u m b e r mixing ratio, aerosol mass-mixing ratio, and particle size ratio (particles with radii > 0.15/zm to those with radii > 0 . 2 5 / z m ) - are c o m p a r e d with model calculations in which growth and coagulation have been omitted. Omission of growth from a model produces a small increase in the total n u m b e r of particles, partly because the particles are smaller and their rate of sedimentation is slower. The total particle mass a n d the n u m b e r of large particles are, of course, reduced dramatically. G r o w t h itself c a n n o t change the total n u m b e r of particles. It is only because of the effect of particle size o n the sedimentation a n d coagulation processes that a change occurs when growth is omitted. The small residual layer r e m a i n i n g in the n o - g r o w t h case illustrated in Figs. 10(a-d) is mainly a r e m n a n t of the initial conditions r e m a i n i n g after 5 years of simulated decay time. G r o w t h also affects the

110

R. C. Whitten, O. B. Toon, and R. P. Turco

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//--NO GROWTH

40-

REFERENCE~ MODEL~ ' ~

35-

! /NO COAGULATION

30E tu.25

-

20

-

a 1,-I

,< 15-

NO COAGULATION MODIFIED AITKEN. NUCLEI

i

105

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10 100 1000 TOTAL PARTICLEMIXING RATIO, PARTICLES/mgAIR

10,000

Figure 10a Figure 10 Reference model calculations are compared with model calculations in which growth and coagulation are omitted (a-d).

40 -

NO COAGULATION /MODIFIED AITKEN

35 3O E Jig tu'25 Q D 120

...J

'~15 t,

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OAGULATION

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4 6 8 10 12 14 16 18 20 LARGE PARTICLE(r > 0.15/am) MIXING RATIO, PARTICLES/mgAIR Figure lOb

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22

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Vol. 118, 1980)

Ill

The Stratospheric Sulfate Aerosol Layer

35

E 30

20

REFERENCE

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NO COAGULATION -

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2 4 6 8 10 12 RATIO OF PARTICLES ~> 0.15 ,um RADIUS TO THOSE >~0.25 #m RADIUS Figure 10d

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112

R.C. Whitten, O. B. Toon, and R. P. Turco

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particle size ratio, which, in the absence of growth, is determined by the assumed tropospheric core size distribution, as modified by coagulation and sedimentation. Omission of particle coagulation leads to a sharp increase in the total particle mixing ratio, which, but for sedimentation, would be constant with altitude. Coagulation is clearly the dominant process controlling the total number of particles (particularly small ones). Moreover, coagulation affects the mass-mixing ratio, the largeparticle mixing ratio and the particle size ratio, suggesting that it is an important loss process for particles larger than 0.1/~m as well. Without coagulation the large increase in the total number of particles and the total particle surface area causes a diminishment of the sulfuric acid vapor available to grow individual particles. Because the average particle size is decreased, the sedimentation rate is reduced, enhancing particle mass at high altitudes. Also, the acid mass is redistributed from larger to smaller particles, increasing the particle size ratio. To define the role of coagulation more clearly, another calculation omitting coagulation was performed in which the number of condensation nuclei at the tropopause was reduced by a factor of 10 so that the number of particles at 20 km was comparable to the number in the reference model. Figures 10(b-d) show that in this case, coagulation has much less effect on the massmixing ratio, the large-particle mixing ratio and the particle size ratio, once the total number of particles has been reduced to the observed values.

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aL

Vol. 118, 1980)

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Figure 12: Reference model calculations are compared with calculations in which tropopause height and diffusion profiles are altered (a-d).

~

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R. C. Whitten, O. B. Toon, and R. P. Turco

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9 DICKINSON-CHANG40

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Diffusion coefficient and tropopause height Several eddy diffusion coefficients are shown in Fig. 11. Such diffusivities are usually presumed to represent global average rates of vertical transport. They are based on matches of predicted and measured vertical distributions of various tracers such as methane, nitrous oxide, the chlorofluoromethanes F-11 and F-12, and excess carbon-14 from atmospheric nuclear explosions. The diffusion coefficient used in the reference model being discussed here (TuRCO and WmTTEN, 1977; TURCO et al., 1979a; TOON et al., 1979) is a modification of that proposed by WovsY and MCELROY (1973). Two other frequently used diffusion profiles are also shown in Fig. 11; one was proposed by Hunten (JOHNSTON et al., 1976) and the other is attributed to Dickinson and Chang (NAS, 1976). As illustrated in Fig. 11, the Hunten profile has noticeably smaller diffusion coefficients at high altitudes than the reference model, and the Dickinson-Chang profile is much less abrupt at the tropopause than the reference model profile.

Vol. 1t8, 1980)

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40--

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TO THOSE 1>0.25 ~tm RADIUS Figure 12d Figure 12(a) shows that a calculation using the Hunten profile yields many fewer particles at high altitudes than does the reference model because, with the smaller diffusion coeff• sedimentation dominates vertical diffusion. The DickinsonChang profile yields a total particle mixing ratio similar to that of the reference model at high altitudes, but the mixing ratio falls off less strongly than that of the reference model near the tropopause. The mass and large particle mixing ratios are both decreased with either of the alternative diffusion coefficients, due in part to reduced diffusive supplies of sulfur-bearing gases. The smaller diffusion coefficients of the Hunten profile do not bring as much COS to high altitudes, so fewer larger particles are formed and those that are formed are more rapidly removed by sedimentation. Also, the sulfur supply is decreased because slower diffusion below the tropopause allows less SO2 to reach the stratosphere before it is washed out or chemically converted into H2SO~. The Dickinson-Chang diffusion profile yields a shorter residence time for gases and particles just above the tropopause and a longer residence time in the troposphere. Thus, the particles have less opportunity to grow just above the tropopause, and SO2 transported upward from the troposphere is almost completely

116

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removed before it reaches 14 km. The Dickinson-Chang profile does not substantially suppress the upward transport of COS, however, so the higher altitude portion of the layer closely resembles the reference model. The diffusion coefficients do not affect the particle size ratio very dramatically. The tropopause height varies with latitude, and displays seasonal and random fluctuations at any given location as welL'Figures 12(a-d) illustrate calculations in which the tropopause has been moved from the reference model altitude of 13 km to altitudes of 9 km and 17 km; the change is performed by moving the reference model diffusion profile (Fig. 11) up or down by 4 kin, while altering the nucleation model so that particles below the tropopause are unaffected. The total particle mixing ratio is strongly modified by changing the tropopause height. The calculation corresponding to the higher tropopause yields fewer total particles near the tropopause than the lower tropopause calculation, although the mixing ratios are similar. Nevertheless, coagulation rapidly depletes the particles above the tropopause in each case, despite the variation of residence time with height. As a result, there are fewer particles at each altitude in the lower "r case. The opposite is true for the large-particle and mass-mixing ratios. The lower tropopause case displays higher mixing ratios and a smaller particle size ratio because (1) the aerosol residence time at a fixed height is increased, thus allowing more growth to occur, and (2) the rate of upward diffusion of COS and SO2 is enhanced by increased concentrations at the tropopause level. 5. Model applications - assessments o f anthropogenic effects on the stratospheric aerosol layer

Man-made perturbations to the stratospheric aerosol layer were first considered during the Climatic Impact Assessment Program (CIAP, 1975), which dealt with possible stratospheric and climatic perturbations caused by supersonic transports (SST's). The CIAP assessment was based on a simple residence time model for an aerosol of fixed size dispersion and a rather crude radiative transfer model. POLLACK et al. (1976c), with the aid of more sophisticated radiative transfer techniques, made improved estimates of the temperature changes at the Earth's surface caused by SST aerosol changes. However, Pollack et al. used several approximations in their aerosol model, which lent considerable uncertainty to their results. More recently, the stratospheric models of ROSEN et al. (1978) and of TURCO et al. (1979a) have been applied in studies of global perturbations of the aerosol layer due to anthropogenic activities. Turco et al., for example, have made assessments of the effects of particulate and gaseous pollutants from SST's and Space Shuttle rocket engines and of the effect on the stratospheric sulfate layer of increasing tropospheric levels of carbonyl sulfide. Although detailed papers on these investigations will be published elsewhere, a brief summary of this work is given below. S S T and space shuttle effects

Supersonic transport engines emit gaseous sulfur oxides and carbonaceous particulates as exhaust constituents. Soot particles add directly to the natural aerosol

Vol. t 18, 1980)

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loading of the atmosphere, and sulfur gases add indirectly t h r o u g h condensation on existing particles. F o r the gaseous sulfur, we adopt an emission index o f 1 g o f SO2 per kilogram o f fuel (CIAP, 1975) and assume a fleet of 300 aircraft o f advanced design. Estimating that each SST would consume about 38,000 kg fuel/hr and operate 7 hours per day (e.g., see POPPOFF et al., 1978), the fleet would release about 3 x 107 kg o f SO2 per year worldwide, mostly at an altitude o f 20 km, a likely cruise altitude for future SST's (PoPPOFF et al., 1978). The soot emission of a J79-GE-10B jet engine, under conditions similar to those o f SST cruise, is about 0.3 g per kilogram of fuel (NAVAL ENVIRONMENTALPROTECTION SUPPORT SERVICE, 1977). A l t h o u g h the soot emission rate is much smaller than the SO2 emission rate, some o f the soot particles added to the stratosphere could 40

35

300 SST's WITH SO2 AND SOOT EMISSION (1.18 x 106/era 2 > 14 km)

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Figure 15 Space shuttle effects on large particles. Calculated steady-state large particle (r > 0.15 ~.m) mixing ratios in the stratosphere are shown for nominal space shuttle operations (corresponding to 60 shuttle launches per year), and 10 times the level of activity, assuming the particulate deposition rate profile described in the text. conceivably grow into large aerosol droplets; soot must therefore be carefully considered. Space Shuttle launch vehicles emit large quantities of aluminum oxide (A1203) particles; the emission rate profile determined by HOFMANN et al. (1975b) has been adopted for the work reported here. The average A1203 particle size spectrum measured by wire and tape impactors and a mobility analyzer in several Titan wakes varied as ~ r - ~ ' s between radii of 0.035 and 5 ~m and decreased rapidly for particles with radii smaller than 0.035/xm. The effect of SST emissions on the large-particle mixing ratio is shown in Fig. 13. The main effect is due to sulfur gas rather than soot emission because the small soot particles coagulate rapidly with aerosol droplets of all sizes while the sulfur-bearing gas is absorbed by all of the existing particles as well. Hence, both the soot and SO2 cause existing particles to grow at a rate determined roughly by the relative mass injected. If the sulfur component of aviation fuel were eliminated, the net effect of soot emission alone on large particles would be quite small. In Fig. 14, the total number of soot particles of each size injected during 1 year of SST flight operations, and the ambient and perturbed particle size distributions, are compared. The soot particles are all injected near an altitude of 20 km where fairly large numbers of acid

120

R . C . Whitten, O. B. Toon, and R. P. Turco

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Vol. 118, 1980)

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The effect of planned space shuttle launch traffic on the large aerosol particle concentration in the stratosphere, shown in Fig. 15, would be comparable to that of 300 SST's. It was originally proposed by HOFMANN et al. (1975b) that the small particles emitted by space shuttle engines might act as seeds from which new large particles could be grown in a supersaturated environment. However, Fig. 15 demonstrates the effect to be unimportant because the A12Oa seed particles rapidly coagulate with pre-existing aerosols. Our calculations indicate that the total number of large particles might be increased by only about 20 percent. It is interesting to compare the effects on the aerosol particle Size spectra of SST's and space shuttles (Figs. 14 and 16). The shuttle injects more particles in the range 0.01 to 0.1 ~m, which increases the number of acid droplets near 0.1 t~m by redistributing the available acid mass from larger particles (r > 0.3/~m) to smaller particles (r < 0.3 ~m). This is indicated in Fig. 16 by the crossover of the ambient and perturbed size distributions near 0.3/zm. However, this shift in particle sizes still results in a small net increase in the number of large particles. SST's inject many more very small particles (r < 0.01 t~m) than do space shuttles, but the rate of most of these is coagulation with larger aerosols. To calculate the climatic effects of aerosol layer perturbations, the altitudedependent size spectra predicted by the aerosol model were employed in the 'doubling' routine described by POLLACK et al. (1976c). The doubling calculations are highly accurate multiple scattering computations that explicitly account for solar energy absorption by CO2, Oa, 02, and H20 and absorption and scattering by aerosols in the stratosphere and troposphere. The optical constants of a 75-percent sulfuric acid aqueous solution were used for the droplets and the optical constants of (NH4)2SO4 were used for condensation nuclei. Once the solar energy deposition rate profile is determined, an infrared calculation is performed to achieve radiative-convective equilibrium. This routine uses a numerical approach similar in most respects to that described by POLLACK et al. (1976c) to calculate the infrared radiation emitted and absorbed by H20, CO2, Oa, and aerosols. It differs from that of Pollack et al. in that the routine is iterated until a radiative-convective temperature profile is obtained. Such calculations for a fleet of 300 SST's flying 7 hours per day at an altitude of 20 km suggest a possible temperature decrease of about 3 x 10-3~ The predicted temperature decrease for a space shuttle launch rate of 60 per year is only about 0.1 of that value, or 3 x 10-4~ These estimates, which are to be compared with a rough criterion of temperature change for climate effects of 0.1~ show that likely climatic impact of reasonable-sized fleets of SST's and of planned space shuttle launches are completely negligible. Enhancement o f carbonyl sulfide

In some recent work, TURr et al. (1979b) have estimated that the tropospheric lifetime of COS is ~ 1 yr, and that the present day production rate of COS is about 6 • 106 tonnes yr- t of which approximately half may originate from coal combustion.

122 40

R. C. Whitten, O. B. Toon, and R. P. Turco

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Figure 17 The stratospheric sulfate (SO~.-) mass mixing ratio predicted for ambient and perturbed conditions. A ten-fold enhancement in COS, SO2, and CS2 has been simulated by increasing its surface concentration ten-fold. For several cases treated, the total large particle concentration in the stratosphere (N) and the optical depth of the sulfate layer at 550 nm (T) are given in brackets.

Some important industrial sources of COS whose output may increase substantially in the future are coal gasification and combustion involving the use of more abundant high sulfur coal and petroleum. Figure 17 shows calculations by TURCO et aL (1979b) of the effects of changes in COS, CS2, and SO2 levels in the stratospheric sulfate mixing ratio. The model results indicate a very substantial increase in aerosol mass when COS is increased by a factor of 10. Using the radiative transfer model mentioned above, TURCO et aL (1979b) computed a possible decrease in global average surface temperature of ~0.1~ a change that is on the threshold of climatic significance. It is important to note, however, that COS, like CO2, can also create a 'greenhouse' effect in which the far infrared radiation from Earth is trapped in the lower atmosphere. Such an effect would modify these conclusions by canceling, at least partially, the effect of the increased aerosol loading. In addition, we have not taken into account the effects of emissions of other combustion products such as CO, CO2, and SO2. For example, CO emissions may reduce O H concentrations, leading to a larger build-up of COS. Attempts to suppress SO2 emissions might inadvertently create

4

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The Stratospheric Sulfate Aerosol Layer

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larger COS emissions. On the other hand, CO2 build-up would enhance surface temperatures through the greenhouse mechanism.

6. Conclusion

The stratospheric sulfate aerosol layer, discovered nearly two decades ago by JUNGE et al. (1961), has been the subject of numerous and concerted observational and theoretical studies of its properties and morphology since that time. Furthermore, knowledge of the physics and chemistry of aerosols has evolved sufficiently that with the advent of large computers it is now feasible to construct detailed models of the aerosol layer. As an example, the one-dimensional model developed by the authors and their coworkers has been shown to be in good agreement with m a n y of the observed aerosol characteristics, including mass-mixing ratios and size distributions. Assessments have been made of possible climate effects of space shuttle and supersonic transport operations and the conclusion is that for reasonable levels of operation, the estimated changes in surface temperatures are likely to be negligible. Further applications of such models to possible climatic effects of large volcanic eruptions and to the interpretation of satellite (i.e., SAGE) observations of the aerosol layer await the development of physically realistic two-dimensional aerosol models.

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ACKERMAN,M., Ultraviolet solar radiation related to mesospheric processes, in Mesospheric Models and Related Experiments, G. Fiocco, ed. (Reidel Publ. Co., Dordrecht, Holland, 1971), pp. 149-159. ARNOLD, F. and HENSCHEN,G. (1978), First mass analysis of stratospheric negative ions, Nature 275, 521-522. ATKINSON,R. and PXTTS,J. N. (1974), Rate constants for the reaction of O(3P) atoms with SO2 (M = N2) over the temperature range 299-392 K, Chem. Phys. Lett. 29, 28-30. ATKINSON,R., PERRY,R. A. and PITTS,J. N. (1978), Rate constants for the reaction of OH radicals with COS, CS2, and CH3SCH3 over the temperature range 299-430 K, Chem. Phys. Lett. 54, 14-18. BIGG, E. K., Kviz, Z. and THOMPSON,W. J. (1972), An October influx ofsubmicron particles into the lower stratosphere, J. Geophys. Res. 77, 3916-3923. BRECKINRIDGE,W. H. and TAUBE,H. (1970), Ultraviolet absorption spectrum of carbonyl sulfide, J. Chem. Phys. 52, 1713-1715. BURGMEIER,J. W. and BLIFFORO,I. H. (1975), A reinforced coagulation-sedimentation model for stratospheric aerosols, Water, Air, and Soil Poll. 5, i33-147. CADLE, R. D. and GRAMS,G. W. (1975), Stratospheric aerosolparticles and their opticalproperties, Revs. Geophys. and Space Phys. 15, 475-501. CADLE,R. D. and LANGER,G. (1975), Stratospheric Aitken particles near the tropopause, Geophys. Res. Lett. 2, 329-332. CADLE, R. D., CRUTZEN, P. and EHHALT, D. (1975), Heterogeneous chemical reactions in the stratosphere, J. Geophys. Res. 80, 3381-3385.

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CADLE, R. D., KIANG, C. S. and Louis, J.-F. (1976), The global dispersion of the eruption clouds from major volcanic explosions, J. Geophys. Res. 81, 3125-3132. CADLE, R. D., FERNALD, F. G. and FRUSH, C. L. (1977), Combined use of lidar and numerical diffusion models to estimate the quantity and dispersion of volcanic eruption clouds in the stratosphere: Vulcan Fuego, 1974 and Augustine, 1976, J. Geophys. Res. 82, 1783-1786. CADLE, R. D. and KIANG, C. S. (1977), Stratospheric Aitken particles, Revs. Geophys. and Space Phys. 15, 195-202. CALVERT,J. G. and McQUIGG, R. D. (1975), The computer simulation of the rates and mechanisms of photochemical smog formation, Int. J. Chem. Kin. Symposium 1, 113-154. CALVERT, J. G., SU, F., BOTTENHEIM,J. W. and STRAUSZ,O. P, (1978), Mechanism of the homogeneous oxidation of sulfur dioxide in the troposphere, Atmos. Env. 12, 197-226. CAMPBELL, M. J., SHEPPARD,J. C., Au, B. and MURALIDHAR,V. (1978), Measurement of hydroxyl concentration in Northern and Southern hemisphere boundary layers, Trans. Amer. Geophys. Union (EOS) 59, 1079. CASTLEMAN,A. W., Jr., DAvis, R. E., MUNKELWITZ,H. R., TANG,I. N. and WOOD,W. P. (!975), Kinetics of association reactions pertaining to H2SO4 aerosol formation, Int. J. Chem. Kin. Symposium 1, 629-640. CASTLEMAN,A. W., HOLLAND,P. M. and KEESEE,R. G. (1979), The properties of ion clusters and their relationship to heteromolecular nucleation, J, Chem. Phys. 68, 1760-1767. CHOU, C. C., RuIZ, H. V., MOE, K. and ROWLAND,F. S. (1976), UVubsorption cross sections for OCS, unpublished data, Dept. of Chemistry, University of California, Irvine, California. CIAP, Monograph 2 (1975),Propulsion Effluents in the Stratosphere (ed. by J. M. English), Monograph 3 (1975a), The Stratosphere Perturbed by Propulsion Effluents (ed. by G. D. Robinson, H. Hidalgo and R. Greenstone), and Monograph 5, part 2, Impacts of Climatic Change on the Biosphere (ed. by J. Bartholic), Climatic Impact Assessment Program, U.S. Department of Transportation; NTIS, Springfield, Virginia. CRUTZEN, P. J. (1976), The possible importance of CSO for the sulfate layer of the stratosphere, Geophys. Res. Lett. 3, 73-76. DAVIS, D. D. (1974), Kinetics of atmospheric reactions involving HxOy compounds, Canad. J. Chem. 52, 1405-1414. DAvis, n . D. and KLAUBER, G. (1975), Atmospheric gas phase oxidation mechanisms for the molecule SO2, Int. J. Chem. Kin. Symposium 1, 543-556. DAvis, D. D., KLEMM, R. B. and PILLING, M. (1972), A flush-photolysis resonance-fluorescence kinetic study of ground state sulfur atoms. I, Absolute rate parameters for reaction of S(DP) with 02 (X), Int. J. Chem. Kin. 4, 367-382. FARLOW, N. H., SNETSINGER,K. G., LEM, H. Y., HAYES, D. M. and TROOPER, B. M. (1978), Nitrogen-sulfur compounds in stratospheric aerosols, J. Geophys. Res. 83, 6207-6212. FARLOW, N. H., FERRY, G. V., LEM, H. Y. and HAYES, D. M. (1979), Latitudinal variations of stratospheric aerosols, J. Geophys. Res. 84, 733-744. FERRY, G. V. and LEM, H. Y., Aerosols at 20 km altitude, Second International Conference on the Environmental Impact of Aerospace Operations in the High Atmosphere, July 8-10 (published by the American Meteorological Society, Boston, Mass., 1974), pp. 27-33. FRIEDLANDER, S. K. (1961), Theoretical considerations for the particle size spectrum of the stratospheric aerosol, J. Meteorol. 18, 753-759. FRIEND, J. P. (1966), Properties of the stratospheric aerosol, Tellus 28, 465--473. FRIEND, J. P., The global sulfur cycle, in Chemistry of the Lower Atmosphere, ed. by S. I. Rasool (Plenum Press, N.Y., 1973), pp. 177-201. FRIEND, J. P., LEIFER,R. and TRICHON, M. (1973), On the formation of stratospheric aerosols, J. Atmos. Sci. 30, 465-479. FUCHS, N. A., The Mechanics of Aerosols (Pergamon Press, The Macmillan Co., London, New York, 1964), 408 pp. GOLOMB, D., WATANABE,K. and MARMO,F. F. (1962), Absorption coefficients of sulfur dioxide in the vacuum ultraviolet, J. Chem. Phys. 36, 958-959. GRAEDEL, T. E. (1977), The oxidation of ammonia, hydrogen sulfide, and methane in nonurban tropospheres, J. Geophys. Res. 82, 5917-5922.

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HAMILL, P., KIANG, C. S. and CADLE, R. D. (1977a), The nucleation of H2SO4 solution aerosol particles in the stratosphere, J. Atmos. Sci. 34, 150-162. HAMILL, P., TOON, O. B. and KIANG, C. S. (1977b), Microphysicalprocesses affecting stratosphere aerosol particles, J, Atmos. Sci. 34, 1104-1119. HANSEN, J. E., WANG, W.-C. and LACIS, A. A. (1978), Mount Agung eruption provides test of a global climatic perturbation, Science 199, 1065-1068. HANST, P. L., SPELLER,L. L., WATTS,D. M., SPENCE,J. W. and MILLER, M. F. (1975), Infrared measurements of fluorocarbons, carbon tetrachloride, carbonyl sulfide, and other atmospheric trace gases, J. Air Pollut. Control Assoc. 25, 1220-1226. HARKER, A. ]]. (1975), The formation of sulfate in the stratosphere through gas phase oxidation of sulfur dioxide, J. Geophys. Res. 80, 3399-3401. HARRIES, J. E. (1976), The distribution of water vapor in the stratosphere, Revs. Geophys. and Space Phys. 14, 565-575. HOEMANN, D. G. and ROSEN, J. M. (1977), Balloon observations of the time development of the stratospheric aerosol event of 1974-1975, J. Geophys. Res. 82, 1435-1440. HOFMANN,D. G., ROSEN,J. M. and PEPIN, T. J. (1974), Global measurements of the time variations and morphology of the stratospheric aerosol, Report GM-18 Dept. of Physics and Astronomy, University of Wyoming, Laramie, Wyoming. HOEMANN, D. J., ROSEN, J, M., P~PIN~ T. J. and PINNICK, R. G. (1975a), Stratospheric aerosol measurements. I. Time variations at northern mid-latitudes, J. Atmos. Sci. 32, 1446-1456. HOEMANN, D. J., CARROLL, D. E. and ROSEN, J. M. (1975b), Estimate of the contribution of the space shuttle effluent to the natural stratospheric aerosol, Geophys. Res. Lett. 2, 113116. HOPPEL, W. A. (1976), Growth of condensation nuclei by heteromolecular condensation, J. Rech. Atm. 9, 167-180. INN, E. C. Y. (1975), Absorption coefficients for HCI in the region 1400-2200 A, J. Atmos. Sci. 32, 2375-2377. INN, E. C. Y., VEDDER, J. F., O'HARA, D. and TYSON, B. J. (1979), COS in the stratosphere, Geophys. Res. Lett. 6, 191-193. JAESCHKE, W., SCHMITT, R. and GEORGII, H. W. (1976), Preliminary results of stratospheric SO2 measurements, Geophys. Res. Lett., 3, 517-519. JOHNSTON, H. S., KATTENHORN,D. and WHITTEN, G. (1976), Use of excess carbon 14 data to calibrate models of stratospheric ozone depletion by supersonic transports, J. Geophys. Res., 81, 368-380. JUNGE, C. E., CHAGNON,C. W. and MANSON,J. E. (1961), Stratospheric aerosols, J. Meteorol. 18, 81-108. KASELAU, K. H., FABIAN,P. and ROHRS, H. (1974), Measurements of aerosol concentration up to a height of 27 kin, Pure Appl. Geophys. 112, 877-885. KASTEN, F. (1968), Falling speed of aerosol particles, J. Appl. Meteorol. 7, 944-947. KELLOGG, W. W., CADLE, R. D., ALLEN, E. R., LAZRUS,A. L. and MARTELL,E. A. (1972), The sulfur cycle, Science 175, 587-599. KREZENSKI, D. C., SIMONAITIS,R. and HEICKLEN, J. (1971), The reactions of O(JP) with ozone and carbonyl sulfide, Int. J. Chem. Kin. 3, 467-482. KRITZ, M. A., Formation mechanisms of the stratospheric aerosols, Ph.D. dissertation, Yale University (University Microfilms, 1975a). KRITZ, M. (1975b), An advective hypothesis for the formation of the stratospheric aerosol layer, Journal de Physique, 36, Coll. C8, Suppl. to No. 12, 17-23. KURYLO, M. J. (1978), Flash photolysis resonance fluorescence investigation of the reaction of OH radicals with OCS and CS2, Chem. Phys. Lett. 58, 238-242. LAMB, H. H. (1970), Volcanic dust in the atmosphere, with a chronology and assessment of its meteorological significance, Proc. Roy. Soc. London A, 226, 425-533. LAZRUS, A. L. and GANDRUD, ]]. W. (1974), Stratospheric sulfate aerosol, J. Geophys. Res. 79, 3424-3431. LEVY, H., Photochemistry of the troposphere in Adv. in Photochemistry 9, 372-524, ed. by J. N. Pitts, G. S. Hammond and K. Gollrich (John Wiley and Sons, N.Y., 1974).

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MAROULIS,P. J., TORRES,A. L. and BANDY,A. R. (1977), Atmospheric concentrations ofcarbonyl sulfide in the southwestern and eastern United States, Geophys. Res. Lett. 4, 510-512. MAROULIS, P. J., TORRES, A. L., GOLDBERG,A. B. and BANDY, A. R. (1978), Measurements of tropospheric background levels of SO2 on Project Gametag, Trans. Amer. Geophys. Union (LOS) 59, 1081. MARTELL, E. A. (1966), The size distribution and interaction of radioactive and natural aerosols in the stratosphere, Tellus 18, 486-498. MOORTGAT, G. K. and JUNGE, C. E. (1977), The role of the SO2 oxidation for the background stratospheric sulfate layer in the light of new reaction rate data, Pure Appl. Geophys., 115, 759-774. NATIONALACADEMYOF SCIENCES,Halocarbons: Effects on Stratospheric Ozone (National Academy of Science, Washington, D.C., 1976), p. 106. NAVAL ENVIRONMENTALPROTECTIONSUPPORTSERVICE,Particulate emissions from J79, J52, J57, TF30 and TF41 engines during test cell ferrocene evaluations (Report No. ALSO-111-77, Naval Air Rework Facility, North Island, San Diego, Calif., 1977); also, private communication from L. E. Michalec. PAYNE, W. A., STIEF,L. J. and DAVIS, D. D. (1973), A kinetic study of the reaction of riO2 with SO2 a n d N O , J. Amer. Chem. Soc. 95, 7614-7619. PEPIN, T. J. and MCCORMICK,M. P., Observations of stratospheric aerosols from the Apollo-Soyuz test project (A.S.T.P.), in Proceedings of the Symposium on Radiation in the Atmosphere, ed. by H.-J. Bolle, IAMAP Radiation Symposium; Garmisch-Partenkirchen, West Germany, Aug. 1976 (Science Press, Princeton, N.J., 1976), pp. 151-152. PEYTON, T. O., STEELE, R. V. and MABEY, W. R., Carbon disulfide, carbonyl sulfide: literature review and environmental assessment (Report No. 68-01-2940, Stanford Research Institute, Menlo Park, Calif., 1976), 57 pp. PINNICK, R. G., ROSEN, J. M. and HOFMANN,D. J. (1976), Stratospheric aerosol measurements, Ill. Optical model calculations, J. Atmos. Sci. 33, 304-314. PODZIMEK,J., HABERL,H. J. and SEDLACEK,W. A., Recent measurements of Aitken nuclei in the lower stratosphere, in Proceedings of the Fourth Conference on the Climatic Impact Assessment Program, ed. by T. M. Hard and A. J. Broderick, (U.S. Dept of Transportation DOT-TSCOST-75-38, NTIS, Springfield, Va., 1975), pp. 519-526. POLLACK,J. B., TOON, O. B., SAGAN,C., SUMMERS,A., BALDWIN,B. and VAN CAMP, W. (1976a), Volcanic explosions and climatic change: A theoretical assessment, J. Geophys. Res. 81, 19711983. POLLACK,J. B., TOON, O. B., SUMMERS,A., BALDWIN,B., SAGAN,C. and VAN CAMP, W~ (1976b), Stratospheric aerosols and climatic change, Nature 263, 551-555. POLLACK,J. B., TOON, O. B., SUMMERS,A., VAN CAMP, W. and BALDWIN,B. (1976c), Estimates of the climatic impact of aerosols produced by space shuttles, SST's, and other high flying aircraft, J. Appl. Meteorol. 15, 247-258. POPPOFF, R. C., WHITTEN,R. C., TURCO,R. P. and CAPONE, L. A., An assessment of the effect of supersonic aircraft operations on the stratospheric ozone content (NASA Reference Publ. 1026, NTIS, Springfield, Va., 1978). ROSEN, J. M., HOEMANN,O. J. and LABY, J. (1975), Stratospheric aerosol measurements. H. The worldwide distribution, J. Atmos. Sci. 32, 1457-1462. ROSEN, J. M. and HOEMANN, D. J. (1977), Balloon-borne measurements of condensation nuclei, J. Appl. Meteor. 16, 56-62. ROSEN, J. M., HOFMANN,D. J. and SINGH, S. P. (1978), A steady-state stratospheric aerosol model, J. Atmos. Sci. 35, 1304-1313. RUSSELL, P. B. and HAKE, R. D., Jr. (1977), The post-Fuego stratospheric aerosol: Lidar measurements with radiative and thermal implications, J. Atmos. Sci. 34, 163-177. SANDALLS, F. J. and PENKETT. S. A. (1977), Measurements of carbonyl sulfide and carbon disulfide in the atmosphere, Atmos. Env. 11, 197-199. SCHOFIELD, K. (1973), Evaluated chemical kinetic rate constants for various gas phase reactions, J. Phys. Chem. Ref. Data 2, 25-84.

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SCOTT, W. D., LAMB, D. and DUFFY, D. (1969), The stratospheric aerosol layer and anhydrous reactions between ammonia and sulfur dioxide, J. Atmos. Sci. 26, 727-733. STOIBER, R. E., LEGGETT, D. C., JENKINS, R. F., MURRMANNand RosE, E. I. (1971), Organic compounds in volcanic gas from Santiaguito volcano, Guatemala, Bull. Geolog. Soc. Amer. 82, 2299-2302. TELEGADAS,K. and LIST, R. J. (1969), Are particulate radioactive tracers indicative of stratospheric motions? J. Geophys. Res. 74, 1339-1350. TOON, O. B. and POLLACK,J. B. (1976), A global average model of atmospheric aerosolsfor radiative transfer calculations, J. Appl. Meteorol. 15, 225-246. TOON, O. B., TURCO,R. P., HAMILL,P., KIANG,C. S. and WHITTEN,R. C. (1979), A one-dimensional model describing aerosol formation and evolution in the stratosphere. IL Sensitivity studies and comparison with observations, J. Atmos. Sci. 36, 718-736. TORRES, A. L., MAROULrS, P. J., GOLDBEgG, A. B. and BANDY, A. R. (1978), Measurements of tropospheric OCS on the 1978 GAMETAG flights, Trans. Amer. Geophys. Union (EOS) 59, 1082. TURCO, R. P., HAMILL, P., TOON, O. B. and WmrrEN, R. C. (1976), A model of the stratospheric sulfate aerosol Atmospheric Aerosols: Their Optical Properties and Effects, A topical meeting on atmospheric aerosols, Williamsburg, Virginia, Dec. 1976, Paper WA4, NASA CP-2004. TURCO, R. P. and WI~ITTEN,R. C., The NASA-Ames Research Center one- and two-dimensional stratospheric models. L The one-dimensional model (NASA Tech. Paper 1002, NTIS, Springfield, Va., 1977), 30 pp. TtrRCO, R. P., HAMILL,P., TOON, O. B., WHITTEN,R. C. and KIANG,C. S. (1979a), A one-dimensional model describing aerosol formation and evolution in the stratosphere. L Physical processes and mathematical analogues, J. Atmos. Sci. 36, 699-717; also see NASA Technical Paper 1362 (NTIS, Springfield, Va., 1979) by the same authors. TuRco, R. P., WnITT~N,R. C., Toorq, O. B., POLLACK,J. B. and HAMILL,P. (1979b), Carbonyl sulfide, stratospheric aerosols, and terrestrial climate, Nature (submitted). WARNEClr P., MARMO,F. F. and SULLIVAN,J. O. (1964), Ultraviolet absorption of SOu: Dissociation energies of $02 and SO, J. Chem. Phys. 40, 1132-1137. W~STENBERG, A. A. and DE HAAS, N. (1969), Atom-molecule kinetics using ESR detection. V. Results for 0 + OCS, O + CS2, O + NO2, and H + C2H4, J. Chem. Phys. 50, 707-719. WESTENBERG, A. A., and DE HAAS, N. (1975), Rate of the reaction 0 + SOz + M ~ SOa + M, J. Chem. Phys. 63, 5411-5415. WHITTEN, R. C. and TURCO, R. P., Gas phase chemistry in the Ames stratospheric aerosol model Atmospheric Aerosols: Their Optical Properties and Effects. A topical meeting on atmospheric aerosols, Williamsburg, Virginia, Dec. 1976, Paper WA3, NASA CP-2004. WOFSY, S. C. and MCELROY, M. B. (1973), On vertical mixing in the upper stratosphere and lower mesosphere, J. Geophys. Res. 78, 2619-2624. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birldaiiuser Verlag, Basel

The Importance of Energetic Particle Precipitation on the Chemical Composition of the Middle Atmosphere By RICHARD MANSERGH THORNE x)

Abstract - An assessment is made of the relative contribution of certain classes of energetic particle precipitation to the chemical composition of the middle atmosphere with emphasis placed on the production of odd nitrogen and odd hydrogen species and their subsequent role in the catalytic removal of ozone. Galactic cosmic radiation is an important source of odd nitrogen in the lower stratosphere but since the peak energy deposition occurs below the region where catalytic removal of 03 is most effective, it is questionable whether this mechanism is important in the overall terrestrial ozone budget. The precipitation of energetic solar protons can periodically produce dramatic enhancement in upper stratospheric NO. The long residence time of NO in this region of the atmosphere, where catalytic interaction with 03 is also most effective, mandates that this mechanism be included in future modelling of the global distribution of 03. Throughout the mesosphere the precipitation of energetic electrons from the outer radiation belt (60~ < A < 70~ can sporadically act as a major local source of odd hydrogen and odd nitrogen leading to observable 03 depletion. Future satellite studies should be directed at simultaneously measuring the precipitation flux and the concomitant atmosphere modification, and these results should be employed to develop more sophisticated models of this important coupling.

Key words: Galactic cosmic rays; Solar proton events; Particle precipitation; Chemistry.

1. I n t r o d u c t i o n

As energetic charged particles enter the Earth's atmosphere they are guided in helical orbits by the geomagnetic field until a collision occurs with an ambient atmospheric constituent. This review will consider the importance of three distinct classes o f precipitation which directly deposit energy into the middle atmosphere; namely galactic cosmic radiation, energetic solar protons and relativistic electron precipitation f r o m the Earth's radiation belts. Figure 1 illustrates the general geomagnetic field configuration and classifies three distinct regions for particle precipitation. Over the polar caps (invariant latitudes A ~> 75 ~ the geomagnetic field lines are generally t h o u g h t to be open and connected to the interplanetary medium. This permits direct access for energetic particles o f solar or galactic origin. The auroral zone (70 ~ < A < 75 ~ is a region of continuous and intense precipitation o f low energy (1-10 keV) particles emanating f r o m the Earth's plasmasheet (e.g. EATHER e t al., 1976; LuI et al., 1977; ASHOUR-ABDALLA and THORNZ, 1978). A l t h o u g h the precipitation fluxes in this 1) Department of Atmospheric Sciences, University of California, Los Angeles, USA.

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Figure 1 A schematic view of the Earth's magnetosphere illustrating the dominant zones of particle precipitation. region are considerably enhanced during geomagnetically disturbed periods (termed magnetospheric substorms) the principal energy deposition is confined to altitudes above 100 km and is therefore of little interest to the middle atmosphere. In the subauroral region (A < 70~ however, energetic particles can be stored and accelerated to very high energies (10 keV to several MeV) before eventual precipitation into the middle atmosphere (in the altitude range between 50--100 km). The typical atmospheric penetration altitude (before substantial energy loss occurs) for vertically incident electrons and protons is shown in Fig. 2 as a function of particle energy. Also indicated is the penetration depth for Bremsstrahlung X-rays which are produced during energetic electron precipitation. Most energy loss by the precipitating particles occurs during slowing down collisions with either free or bound electrons. The high energy primary particles themselves are generally inefficient in dissociating or ionizing the ambient atmospheric constituents. But they produce substantial fluxes of secondary electrons (typically between 10-100 eV) which subsequently transfer a major fraction of the incident energy to the atmosphere. The shape of the secondary electron spectrum and the cross sections for their interaction with the atmosphere are therefore of considerable importance (PORTER et al., 1976). Although incoming ions also experience scattering by the Coulomb field of the atmospheric nuclei (and at high energies can undergo nuclear reactions with the scattering nucleus) their overall angular deflection is generally negligible. This greatly simplifies the computation of energy deposition

130

Richard Mansergh Thorne 120

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Energy (kev) Figure 2 The nominal penetration depth of electrons and protons vertically incident at the top of the atmosphere as a function of particle energy. during ion precipitation. On the other hand, in the case of precipitating electrons, angular scattering is of major importance and the energy degradation must be treated by solving an appropriate diffusion equation which takes both energy loss and angular scattering into account (WENTWORTX~et al., 1959; WALT and McDONALD, 1964; WALT et al., 1968). In addition to providing an important and often dominant ionization source for the middle atmosphere, precipitating particles enhance the production of odd nitrogen and odd hydrogen species. Since these are now accepted as a major catalytic sink for middle atmospheric odd oxygen (O or O~) it is important to quantitatively compare the role of particle precipitation with other sources of these catalytic agents. In Section 2 we review the important chemical process, paying particular attention to the relative production rate of odd nitrogen and odd hydrogen species during ionizing particle precipitation. The next three sections separately review recent studies of the role played by galactic cosmic radiation, solar protons and magnetospheric electrons. An overall comparison of these sources is finally made in Section 6 together with an assessment of the status of our understanding and needs for future studies. 2. Chemical considerations during particle precipitation 2.1. Ionization Although the energy deposition by precipitating particles is usually negligible compared to other sources of middle atmospheric (below 100 km) heating it can provide

Vol. 118, 1980)

Energetic Particle Precipitation

131

the dominant source of ionization and dissociation particularly below the altitude (< 80 kin) where solar UV and X-rays are strongly absorbed. Most of the primary ions produced by particle bombardment (N], 0 3 , N § O +) are rapidly converted to O~by the change exchange reactions N+ + O 2 ~ O +

+N2,

0 § + 0~---+0+ + 0 , N + +O2-+O + +N.

(la) (lb) Oc)

A much smaller fraction (~69/oo according to GUNTON et aL, I977) are converted to NO + by the ion-atom interchange reactions O§ +N2~NO

+ +N,

(2a)

N + +O2~NO

+ +O.

(2b)

Ion mass spectrometer observations (e.g. NARCISIand BAILEY, 1965; JOHANNESEN and KRANKOWOSKI,1972) have shown that while O +2 and NO + remain the dominant ions above 85 km the positive ion composition at lower altitudes is complicated by a sequence of clustering reactions which lead to the dominance of multiply hydrated ions of the type H +(H20),, NO +(H20), and H30 +(H20)~. Electron attachment also becomes of major importance below 80 km yielding O~- as the primary negative ion. This subsequently interacts with minor constituents of the middle atmosphere to produce heavier ions such as COy, NOs-, HCO~- and their hydrated clusters. The reader is referred to SECHRIST,(1972), ROWE et al. (1974), THOMAS(1964), FERGUSON(1974), ARNOLD and KRANKOWSKI(1977) and ROBLEand REES (1977) for a comprehensive review of the complex D-region ion chemistry. It is sufficient to note here that the ion chemistry is strongly dependent on the atmospheric temperature and the composition of minor neutral species such as O, O2('A), NO, HO, HO2 and H20. Furthermore, while NO + (produced by solar Ly ~ radiation) is the dominant primary ion in the mesosphere under quiet conditions, O + accounts for 94~ (REAGANet al., 1978) of the ultimate primary ions produced by particle precipitation. This enrichment of 0 + during precipitation events should in turn modify the ultimate composition of cluster ions throughout the lower D-region.

2.2. The importance of catalytic processes involving odd nitrogen and odd hydrogen It is now well established that the direct removal process for odd oxygen species O + 03 -+ 202

(3)

first proposed by CHAPMAN(1930) can account for only about 20~ (e.g. JOHNSTON, 1974, 1975) of the odd oxygen produced by photodissociation of molecular oxygen. The major loss of odd oxygen from the middle atmosphere is thought to occur as a result of catalytic cycles involving trace constituents (e.g. JOHNSTON and PODOLSKE,

132

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Figure 3 Reactions important in odd oxygen loss and the odd oxygen production rate 2/(02) taken from McELRoY et aL (1974). The sum of the recombination reaction rates equals the production rate at every altitude consistent with the assumption of photochemical equilibrium. Odd nitrogen provides the dominant 03 loss below 45 km while odd hydrogen predominates above 55 km. 1978 ; THRUSH, 1979). Although chlorine compounds provide an important contribution to the overall odd oxygen removal process (e.g. Sa'OLARSKIand CICZRONZ, 1974; WovsY and MCELROY, 1974; MOL[NA and ROLAND, 1974; CRUTZEN and HOWARD, 1978) of particular interest here are the cycles involving odd nitrogen and odd hydrogen species since these can be significantly modified during intense particle precipitation. Figure 3, taken from MCELROY et al. (1974), illustrates the altitude range over which these species are of major importance. The catalytic cycle involving odd nitrogen is most important within the stratosphere (below ~45 kin), whereas the reactions involving odd hydrogen species predominate throughout the mesosphere (above ~ 55 km). Although the odd nitrogen and hydrogen species are chemically coupled we shall discuss their roles separately in the following two subsections. 2.3. Odd nitrogen chemistry

The catalytic cycle involving odd nitrogen species first discussed by CRUTZE~ (1970, 1971) and JOHNSTON(1971) NO + 0 3 - + NO2 + O~,

(4a)

NO2 + O --~NO + 02,

(4b)

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Energetic Particle Precipitation

133

results in a net odd oxygen removal equivalent to reaction (3) without any change in the overall concentration of either NO or NO2. Thus even though the odd nitrogen species usually have a very low concentration (in comparison to odd oxygen) they can repeatedly act as a sink of odd oxygen. This catalytic cycle, however, is only effective between 25 and 45 km. In the lower stratosphere the odd nitrogen cycle is shortcircuited by the rapid conversion of NO2 into HNOa. OH + N O 2 + M ~ H N O ~ + M while at higher altitudes (above ~ 45 km) NO2 is dissociated NO2 + hv(h < 3 9 5 0 A ) ~ N O + O at a rate faster than its interaction with atomic oxygen (reaction 4b). Several sources of middle atmospheric odd nitrogen have been proposed. The most important source of stratospheric nitric oxide (MCELROYand MCCONNEL, 1971) is due to the reaction between O(1D) atoms produced during the photolysis of 03 (NrcoLET, 1970) and nitrous oxide which has been transported upward from the Earth's surface (BATES and HAYS, 1967) O(1D) + N20 --~ 2NO.

(5a)

Nitric oxide can also be produced by direct photodissociation N20 + hv(h < 2500 A)-+ NO + N

(5b)

but this is thought to be not nearly as important as (5a) because the competing reaction N20 + hv(A < 3 3 7 0 A ) ~ N 2 + O accounts for more than 99~ of N20 photodissociation (PRESTON and BARR, 1971). Using realistic models for the upward diffusion of terrestrial N20, the peak NO production from (5a) has been estimated to occur in the lower stratosphere typically between 24-32 km (MCELROYand McCONNELL, 1971; NICOLET and PEETERMANS, 1972). Odd nitrogen species are also produced as a result of ionic reactions in the D and E regions of the ionosphere (NICOLET, 1965; NORTON and BARTH, 1970; MEIRA, 1971; NARCISI et al., 1972; ORANet al., 1975). The important ionic reactions lead to excited N(2D) atoms which subsequently react with 02 to yield NO N(2D) + 02-+ NO + O.

(6)

This is the major source of NO in the atmosphere above 100 kin. On the other hand, nitrogen atoms which are produced in the ground N(4S) state act as an important sink for odd nitrogen species in the upper mesosphere (>70 kin) and thermosphere (MCELROY et al., 1974; WoFsY, 1974) via the reactions N(4S) + NO ~ N z + O 7 N2 + 02 N(4S) + NO2--+ N20 + O "~N2 + O + O.

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Richard Mansergh Thorne

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For a quantitative assessment of this thermospheric source it is therefore critically important to know the relative production rate of these two atomic nitrogen species (e.g. ORAN et al., 1975). Theoretical modeling by STROBELet al. (1970) and STROBEL(1971a, b) suggested the need for a substantial downward flux of NO (1 - 5 x 10s cm -2 sec -1) to account for the observed mesospheric concentrations (BARTH, 1966; MEIRA, 1971). However, the rapid dissociation rate of NO throughout the mesosphere (STROBEL, 1971b, 1972; BRASSEURand NICOLET, 1973) compared to the rate of downward transport indicates that there should be little residual NO flux reaching the stratopause. As a consequence the strong thermospheric source of NO should not affect the chemistry of stratospheric ozone. In general only NO produced by in situ sources (below ~ 60 km) can directly influence the removal of ozone from the lower portion of the middle atmosphere. One possible exception to this is the region of polar night mesosphere where the dissociation rate is low and NO concentrations can therefore build up over a long period of time to levels sufficient to permit significant downward transport into the stratosphere. An important in situ source of odd nitrogen species in the middle atmosphere originates from the ionization and dissociation of molecular nitrogen during energetic particle precipitation. The low energy (~ 10-100 eV) secondary electrons produced by incoming primary particles interact efficiently with N~ to produce both ions and free nitrogen atoms; (7a) N 2+ + 2eS N2 + e- --~ 2N + e(7b) "a N + +N+2e(7c) On the basis of the branching ratios given by DALGARNO(1967), WARNECK(1972) initially suggested that cosmic ray impact should produce odd nitrogen species directly in the stratosphere at a rate 1/3 of that for ion-pair formation. However, a more detailed comparison between the cross-sections for total dissociation (WINTERS, 1966) and dissociative ionization (RAPPet al., 1965), led BRASSEURand NICOLET(1973) and NICOLET (1975) to argue that the total primary production of free nitrogen atoms should be more nearly one nitrogen atom for each ion pair. The charge exchange and ion-atom interchange reactions (lc) and (2a) also provide an additional, though relatively small (HEAPS, 1978), contribution to the overall production of free nitrogen. Detailed computations by PORTERet al. (1976) suggest a net value of 1.27 N atoms per ion pair regardless of whether the energetic primary particles are protons or electrons. These authors also show that the average energy required to create an ion pair in air is essentially independent of the primary particle energy; at least for incident energies above a few hundred eV. The numbers quoted are 34.5 and 35.8 eVfion pair for electron and proton bombardment respectively. In the subsequent reactions leading to nitric oxide production N + 02--~ NO + O N + 03--~ NO + 02

(8a) (8b)

Vol. 118, 1980)

Energetic Particle Precipitation

13 5

the rate constant for (8a) depends critically on whether the free nitrogen atoms are produced in the ground state N(~S) or at the excited N(2D) level. Uncertainties in the actual electronic state of middle atmospheric nitrogen atoms has led to a range of computed values, typically between 1.2 to 1.5, for the production of NO molecules[ion pair (e.g. CRUTZEN et al., 1975; FREDERICK, 1976; HEAPS, 1978). The higher values correspond to when the nitrogen atoms exist primarily in the N(2D) state. One further reaction which could augment the net yield of middle atmospheric odd nitrogen species (e.g. NICOLET, 1975; HEAPS, 1978) is O2 + N2 --->NO + + NO.

(9)

The reaction rate, however, is below detectable levels and has been set at less than 10-15 cm 3 see -1 (FERGUSON,1974). Assuming a rate constant of t0 -16, HEAPS (1978) concluded that the reaction (9) is negligible at stratospheric altitudes but that it could become important in the upper mesosphere and thermosphere under quiet or moderately disturbed conditions. Partially supporting this conjecture, FABIAN et al. (1979) have cited rocket measurements of enhanced NO concentrations during auroral precipitation which require an NO production rate between 2 to 2.5 times the ionization rate. However, for our discussions of the middle atmosphere we shall adopt the more

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Figure 4 The ratio of (H + OH) and odd nitrogen production per ion pair for high and low values of the ion-pair production rate Q (HEAPS, 1978).

136

Richard Mansergh Thorne

(Pageoph,

conservative altitude profile of the ratio between odd nitrogen and ion-pair production shown in Fig. 4 (HEAPS, 1978).

2.4. Odd hydrogen chemistry The importance of odd hydrogen species (H, OH, HO2) in the removal of middle atmospheric ozone was first discussed by BATESand NICOLET (1950). The hydrogen chemistry is particularly complex and a number of catalytic cycles have been identified leading to net odd oxygen removal (e.g. JOrrNSTONand PODOLSKE,1978). The following reactions destroy odd oxygen with no net removal of H O , compounds as a group: HO + Oa-+ H02 + Oz,

(10a)

H02 + O~--+ HO + 202,

(lOb)

HO+O-+H+02,

(100 (lOd)

H+Oa-+HO+02, H02 + O - + H O +

02.

(10e)

For example the pair of reactions (10a) and (10b) convert 208 into 302 with no net change in the concentration of either odd hydrogen species while (10c) and (10d) or (10a) and (10e) are simply equivalent to the normal Chapman removal process (3). Because of the catalytic nature of these reactions the only way to terminate this removal process for odd oxygen is by the mutual annihilation of the hydroxyl radicals to reform water vapor or H202 via reactions of the type OH + OH--+ H20 + O, OH + H02--+ H20 + 02, HO2 + HO2-+ H202 + 02, H + H02--+ H20 + O. Odd hydrogen species are produced in the middle atmosphere by photodissociation of water vapor H20 + hv--+ H + OH (11) and by reactions involving O(1D) atoms O(13) + H20 --+ 2OH,

(12a)

O(1D) + H2--+ H + OH,

(12b)

o(13) + CH~-+ OH + CH3.

(120

Under quiet conditions photodissociation is the most important source in the upper mesosphere (>60 km) while (12a) predominates throughout the stratosphere. Odd hydrogen species are also produced during the complex ionic reactions leading to cluster ions formation in the D region of the ionosphere (e.g. ROWE et aL, 1974). SWIDER and KENESHEA(1973) first pointed out that this source can become significant

Vol. 118, 1980)

Energetic Particle Precipitation

137

in the mesosphere during intense precipitation events. Following the dominant production of O~ ions during particle bombardment, one hydroxyl radical is released during the initial reactions leading to the formation of H30 + ; O + +O2 +M~O

g + M,

O~ + H20--~ O~-(H20) + 02, O2+(H20) + H20--~ H30 + + OH + 02. A further odd hydrogen species is released during the subsequent recombination of the cluster ions in reactions such as H30+(H20)~ + e- --~ H + (n + 1)H20. The net result is that two odd hydrogen species can be produced for each ion pair. This, however, represents a strict upper limit since some of the initial and intermediate ions will be lost by recombination or charge exchange before the odd hydrogen production can occur. Figure 4 shows the results of recent chemical modeling by HEAPS(1978) for tWO rates of ion pair production. A lower ratio between odd-hydrogen and ion-pair production occurs during more disturbed (Q = 105) conditions due mainly to increased charge exchange with enhanced NO concentrations. The sharp drop off above 80 km reflects the upper level for cluster ion formation. Finally, one should note that rocket measurements by ARNOLD et al. (1977) indicate a transition from hydronium ion clusters to carbonated species in the stratosphere and this could reduce the production of odd hydrogen below 40 kin. Because of the increasing importance of odd nitrogen species at lower altitudes it is therefore unlikely that odd hydrogen will play a significant role in the removal of stratospheric odd oxygen during precipitation events, although it may modify the odd nitrogen and chlorine catalytic cycles (THRUSH, 1979).

3. Galactic cosmic rays

Energetic ions of extra solar system origin arrive at the Earth essentially isotropically. The primary galactic cosmic radiation (GCR) is composed mainly of protons (~ 83~) and alpha particles (~ 12~). As the ions approach the Earth, their trajectories are deflected by the geomagnetic field. The dipole field geometry permits easier access to the polar regions where the geomagnetic field lines are open (Fig. 1). This produces a latitudinal gradient in the precipitating cosmic ray flux particularly for the less energetic components which are more strongly influenced by the Earth's field. The early balloon observations (e.g. BOWENet al., 1938) demonstrated that galactic cosmic radiation is a major ionization source at low altitudes with a peak production rate near the tropopause. While the rate of ionization is relatively constant it does exhibit a slow variation which is out of phase with the solar active cycle (FoRBUSH, 1958; NEHER and ANDERSON, 1962). This has been explained in terms of larger

138

Richard Mansergh Thorne

(Pageoph,

interplanetary densities which reduce the G C R flux near the Earth during peak solar activity. The first suggestion that galactic cosmic rays might act as a significant source of stratospheric nitric oxide was made by WARNECK (1972). More detailed studies by BRASSEUR and NICOLET (1973) and NICOLET (1975) examined the worldwide contribution and concluded that it was relatively minor in comparison to that from the oxidation of terrestrial N20. Figure 5 shows an update of this comparison obtained by using the more recent estimates (Section 2.3) for the rate of N O production, qNo ~ 1.3 q~on. The two curves for the production of N O from N 2 0 are taken from Table 1 of BRASSEUR and NICOLET (1973) and indicate the large range of uncertainty in this source due to its sensitivity on the rate of vertical eddy diffusion and the production of O(1D) atoms. It is nevertheless clear that while galactic cosmic radiation is important in the lower stratosphere, it becomes a relatively minor source of N O in the main catalytic reaction region above 25 km. As such it can have little effect on the global ozone abundance. Ruderman and Chamberlain (1975) have nevertheless argued that the significant variation in the G C R flux over the solar cycle should provide a time varying source for 50

I

I

t

[

I

I

40 j

~g v

W

0 (ID)+ NzO ~ 2 NO

50 /

I- 2O J

I0 GCR O [

0

[

I

20 NO

I

40 60 80 I00 PRODUCTION RATE,(cc-l, sec -I)

Figure 5 A comparison between the altitude profile of NO production by galactic cosmic radiation and the oxidation of terrestrial N20. The range of GCR production over the solar cycle is shown for both 30~ and 60~ invariant latitudes. The two curves for the N20 source represent the extreme values given by BRASSEURand NICOLET(1963) due to uncertainties in the vertical eddy diffusion coefficient and the production of O(1D) atoms.

Vol. 118, 1980)

Energetic Particle Precipitation

139

stratospheric NO and they have attempted to link this with the small (few percent) long term cyclic variations observed in total ozone content (PAETZOLDet al., 1972; ANGELLand KORSHOVER,1973). However, the more recent estimates of higher mean NO density in the stratosphere (JOHNSTON, 1975) and the acknowledged importance of solar proton events (Section 4), which can be expected to produce more NO during solar maximum rather than solar minimum conditions, raises serious doubts over whether GCR produced NO can indeed explain the solar cycle variation of 03. RUDERMANet al. (1976) have subsequently proposed a different destruction scheme for the cycIic variation of 03 involving negative ion chemistry; but this remains to be tested experimentally.

4. Solar proton events

Intense fluxes of energetic protons (10-300 MeV) are released following flare activity on the Sun (MEYERet al., 1956; Li)sT and SrMPSON, 1957). These particles have more or less direct access to the polar cap regions of the Earth's atmosphere and the more energetic components can also penetrate down to invariant latitudes of about 60~ These solar proton events (SPE), which typically last for several days, were initially called polar cap absorption (PCA) events. This term stemmed from the pronounced disturbance to radio communication due to enhanced ionization throughout the polar D-region (BELROSEet al., 1956; ELLISONand REID, 1956; BAILEY,1959; REID, 196t ; WEBBER,1962). The energy spectrum of the primary precipitating protons has subsequently been measured in considerable detail by rocket or satellite instruments (e.g. SVESTKA, 1970, 1972; KING, 1974; REAGANet al., 1978). In addition to providing the dominant source of ionization in the mesosphere and upper stratosphere (ZMtJDAand POTEMRA, 1972) it has recently been recognized that moderate to large solar proton events can also modify the concentrations of minor neutral constituents leading to a decrease in middle atmospheric ozone. The first observational evidence for such an effect was published by WEEKSet al. (1972) who reported factors of 2 to 4 decrease in mesospheric (,~ 50-70 kin) ozone concentration during the 2 November 1969 solar proton event. These measurements were later interpreted by SWIDERand KENESrtEA(1973) in terms of an enhanced production of OH and HO2 as a biproduct of cluster ion chemistry initiated by increased D-region ionization during the particle precipitation (Section 2.4). A later study by CRtJrZENet al. (1975) examined the production of stratospheric NO during three intense solar proton events (November 1960, September 1966 and August 1972). They concluded that the total NO production (below 60 km) during each event was comparable to or larger than the annual yield by GCR for geomagnetic latitudes above 60~. Also, in contrast to the more energetic galactic cosmic rays, the solar protons yield peak NO production in the altitude range above 25 km, namely in the region where catalytic removal of Oa is most effective. For the August 1972 event, the

140

Richard Mansergh Thorne

(Pageoph,

proton precipitation source was even comparable to the most optimistic estimates for the annual yield of stratospheric N O production from the oxidation of N20. CRUTZEN et al. (1975) therefore suggested that it is important to consider the effects of SPE on the spatial and temporal distribution of stratospheric ozone. This conclusion was quantitatively confirmed by FREDERICK (1976) who modeled the changes in middle atmospheric neutral chemistry during two solar proton events. Because of the long residence time for NO produced directly in the stratosphere (i.e. several months at 50 km increasing to over a year below 40 km) by the more energetic solar protons, Frederick suggested that horizontal winds might transport the odd nitrogen species to middle latitudes from the primary source in the polar regions; in such a case solar proton events could influence O3 on a global scale. In the mesosphere, on the other hand, predissociation should cause the excess odd nitrogen to return to the unperturbed values within a few days. Mesospheric Oa concentrations should, in any event, be primarily controlled by the catalytic reactions with odd hydrogen species, and because the removal time for odd hydrogen is typically on the order of an hour (HEAPS, 1978) the concomitant ozone depletion should rapidly recover, following the cessation of intense precipitation. The August 1972 solar proton events were the most intense ever recorded, comprising about 85~o of the energetic proton flux over the entire period of solar cycle 20 (KING, 1974). As an illustration of the intensity of the precipitation Fig. 6, taken from REAGAN et aL (1978), shows the ion production rate at the peak of the event in comparison to other known sources. The extensive observational data taken during the period of the August 1972 events provides a unique opportunity for a detailed study of a 'controlled' modification of the stratospheric neutral constituents. In fact, the

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, , ,,,,,i M

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PRODUCTION RATE {ION PklrS/cm3-ser

Figure 6 Solar proton induced ion production rates during recent major particle events (from REAGANet al., 1978). Cosmic ray ionization for solar maximum and minimum conditions is shown for comparison.

Vol. t 18, I980)

141

Energetic Particle Precipitation

.021

f

"l .... I .... I .... I ....

| ....

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2H

1972

Figure 7 Zonally averaged total 03 above the 4-mbar pressure surface for equatorial (top), middle (middle), and high latitudes (bottom) during July and August 1972 (HEnTR et al., 1977). The solar proton event occurred on 4 August (day 217).

first observation of a detectable SPE depletion in stratospheric ozone was reported by HEATH et al. (1977), using data from the backscattered ultraviolet experiment on the Nimbus 4 satellite during the August event. Their results are reproduced here in Fig. 7. An abrupt decrease in the zonally averaged concentration of 03 (above the 4-mbar pressure surface) was observed at high latitudes following the solar proton event on 4 August. For latitudes A > 75~ this decrease persisted throughout the month of

142

Richard Mansergh Thorne

(Pageoph,

August while in the intermediate zone between 55-65 ~ the response was apparently complicated by transport processes. HEATH et al. (1977) were able to adequately simulate the observed polar reductions using a two-dimensional, time-dependent model which included the major photochemical reactions and zonally averaged transport processes. In a more recent study FABIAN et aL (1979) have reported that a better fit to the observations can be obtained by assuming an N O production rate approximately 2.5 times the ionization rate. However, in view of the discussion in Section 2.3, it is difficult to imagine how such a high ratio can occur at stratospheric altitudes. The initial results from a more detailed investigation of the August 1972 events have recently been reported by REAGAN et aL (1978). Using preliminary data from the BUV instrument on the Nimbus 4 satellite they report ozone reductions immediately following the main event on 4 August ranging from up to 50~ near 50 km altitude to 970 near 35 km. This corresponds to a net columnar decrease of 27o in total ozone below 55 km altitude. They further conclude that the ozone depletion over the polar regions should cause a net reduction in the heating rate of 2.5~ at 60 km and 1.3~ at 45 km (the altitude of maximum ozone heating). This tends to support the earlier suggestion by ZEREFOSand CRUTZEN (1975) that the solar proton induced O~ reduction should lead to lower temperatures in the upper stratosphere but allow solar UV to penetrate deeper and thus heat the lower stratosphere. Unfortunately, a direct experimental verification is not possible since the selected chopper radiometer flown

~ot-

~

OOON

~~ ~

ao

0

J 3 AUGUST I

t 4 AUGUST

I l

5 AUGUST

l

6 AUGUST

ALASKA STANDARD TIME

Figure 8 A numerical simulation of odd nitrogen, odd hydrogen and odd oxygen changes (plotted on a linear scale in arbitrary units) at 40 km during the August 1972 solar event (from REAGANet al., 1978). The ion production rate Q is shown for comparison. The long term systematic decrease in 03 is primarily controlled by the long lived enhancement in odd nitrogen.

Vol. 118, 1980)

Energetic Particle Precipitation

143

on Nimbus 4 had insufficient sensitivity and height resolution to detect the anticipated temperature changes during the August 1972 event. Preliminary results from the simulation of chemical changes following the event (REAGANet al., 1978) are shown in Fig. 8. Odd nitrogen species were considerably enhanced over the ambient levels at all altitudes above 35 km; near 50 km the enhancement was as much as a factor of 45. The production of odd hydrogen species was also significantly increased during the intense precipitation and this was attributed as the primary cause of the initial rapid ozone depletion above 40 km immediately following the event. However, the excess odd hydrogen rapidly decayed following the ionization peak and the mean concentration of atmospheric ozone was thereafter determined by the long term enhancement in odd nitrogen.

5. Relativistic electron precipitation

Satellite observations of the Earth's radiation belts have shown that the energetic outer zone electron population is significantly enhanced during geomagnetically disturbed periods (e.g. PF[TZER and W[NCKLER, 1968; OWENS and FRANK, 1968; RUSSELLand THORNE, 1970; CORON[TI and THORNE, 1973; WEST et al., 1973; LYONS and W]LUAMS, 1975). The injected electrons subsequently interact with naturally generated magnetospheric plasma waves resulting in pitch-angle scattering loss to the atmosphere (ANDRONOV and TRAKHTENGERTS, 1964; KENNEL and PETSCHEK, 1966; KENNEL, 1969 ; ROBERTS, 1969 ; THORNE and KENNEL, 1971 ; LYONSet al., 1971, 1972; LYONS and THORNE, 1972; THORNE, 1974, 1976). As indicated in Fig. 9, this precipitational removal of energetic outer zone electrons can enhance the rate of ionization throughout the mesosphere by several orders of magnitude over the quiet time values.

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Figure 9 Ionization rates in the middle atmosphere due to several classes of observed electron precipitation (REAGAN, 1977). The sources due to solar radiation and galactic cosmic rays are also shown for comparison.

144

Richard Mansergh Thorne

(Pageoph,

Although the electron precipitation flux is most intense during periods of geomagnetic disturbances (e.g. REAGAN, 1977), significantly enhanced mesospheric ionization can persist at middle latitudes for over a week following the stormtime injection of electrons into the radiation belts (LAUTERand KNUTH, 1967; BELROSEand THOMAS, 1968; SPJELDVIKand THORNE, 1975; LARSENet al., 1976, 1977). Of particular interest to our discussion of middle atmospheric chemistry are the class of sporadic (1-3 hr duration) relativistic electron precipitation (REP) events which were first identified by their pronounced disturbance to D-region radio communication at subauroral (60 ~ ~ A ~< 70 ~ latitudes (BAILEYand POMERANTZ,1965; BAILEY,t968). It was later established that these intense events occur during magnetospheric substorm activity (RoSENBERGet al., 1972; LARSENand THOMAS,1974; THORNE and LARSEN,1976), and are caused by strong diffusion scattering of trapped outer zone electrons (THORNE, 1974, 1977a). Although the primary incoming electrons are unable to penetrate below 50 kin, the); produce copious fluxes of energetic Bremsstrahlung X-rays (BERGERand SELTZER, 1972; BERGER et al., 1974; LUHMANN, 1977) which penetrate deep into the stratosphere (see Fig. 2) before undergoing excitation and ionization collisions with the neutral atmosphere. By comparing the long-term energy deposition with that from GCR or SPE, THORNE(1977a, b) has suggested that REP events could be an important source of NO in the mesosphere and upper stratosphere, and as such should be included in further photochemical modeling of the terrestrial ozone layer. The characteristic energy spectrum of the precipitating relativistic electrons has only recently been measured by satellite borne instruments (e.g. VAMPOLA, 1971; REAGAN, 1977; THORNE, 1978). Using this information, the ionization profile for selected events can be obtained by numerical codes which follow the energy deposition through the atmosphere (e.g. WALT et al., 1968; SPJELDVIKand THORNE, t975). In Fig. 10, the ionization rate during two particularly intense REP events has been combined with the cluster ion chemistry results of Fig. 4 (HEAPS, 1978) to obtain the resulting profiles for mesospheric odd-hydrogen production. When compared to the two major quiet time sources of odd hydrogen it is clear that the electron precipitation can provide an important local contribution over a broad altitude range near 70 km. Since the concentration of ozone near this altitude is controlled by odd hydrogen catalytic cycles (Section 2.4) one can anticipate local changes in mesospheric ozone during the relativistic electron precipitation. A numerical simulation of the atmospheric response at 70 km due to both a daytime and night-time REP event (J. DEVORE,personal communication, 1979) is shown in Fig. 11. In each case the energy spectrum of th e precipitating electrons was modeled after the 12 March 1977 event illustrated in Fig. 10 and the event duration was assumed to be 2 hours. The event near midnight caused an immediate increase (by more than a factor of 10) in OH concentration which remained enhanced throughout the night. Catalytic removal of 03 however did not occur until after sunrise due to the low O concentrations at night. Maximum 03 depletion (~ 15~) occurred soon after sunrise

Vol. 118, 1980)

Energetic Particle Precipitation

I

100

90

145

t

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RELATIVISTICELECTRON--

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ODD HYDROGEN PRODUCTION RATE,(cc-~sec -I) Figure ]0 A comparison between the odd hydrogen production rate during two measured relativistic electron precipitation events and the normal quiet time sources. The REP events can dominate over an extended region near 70 kin.

Figure 11 A numerical simulation of OH and 03 variability at 70 km during relativistic electron precipitation. The shaded areas indicate OH enhancement and 03 depletion relative to normal diurnal variation.

146

Richard Mansergh Thorne

(Pageoph,

80 TO

E

60

"'

50

~-

4o

0

-

~

:~o),

dX2 -dt

= V2(X0) + X1.VVI(X0),

(2.14)

where i in (2.12) stands for the unit vector in the x-direction, and where the fact Vuo = 0 has been used. In the above, V2 consists only of a vertical component given by the last term of (2.10) and the last term on the right-hand side of (2.14) came from the Taylor expansion of V1 about a point Xo, and therefore gradients of velocity components should be evaluated at the point X0. Such a term appears whenever one treats motion of an individual fluid particle to the second order of wave amplitude.

196

Taroh Matsuno

(Pageoph,

Since it is quadratic, it usually contains a non-periodic motion (D.C. component), which is called "Stokes drift" (e.g. LONOUE'r-HiCOINS, 1969) in analogy with the mass transport due to water waves treated by Stokes. For the most general discussion of Stokes drifts, see ANDREWS and MclNTYRE (1978a). We shall now obtain parcel trajectories in the present situation according to (2.12) and (2.14). The zeroth-order velocity is merely a constant flow and a solution of (2.12) is

Xo = (Uot, Yo, Zo),

(2.15)

where Y0 and Z0 are constants and we can make the initial value of the parcel's xcoordinate zero, without loss of generality. The trajectory is just a straight line. Using the first-order velocity fields, i.e., (2.8), (2.9) and the first term of (2.10), we obtain the first-order parcel position as l X1 = f ~ 0 a cos 1Y0 cos 0o,

(2.16)

k Y1 = f~o---~a sin IYo sin 00,

(2.17)

Z1 = - - ~ s a s i n l Y o

mcos0o +

sin0 o ,

(2.18)

where 0o = kuot + mZo. We have set all integration constants zero so that the trajectory approaches the undisturbed one as a0 ~ 0. As can be seen from (2.16) and (2.17) the plan view of this first-order part of the trajectory is an ellipse whose major 9: ..,....;,......,...,.,;r

-.,.......-.-.-,.,,..,

(a)

(b)

C)

()

Y

0 O Figure 1 (a) T h e trajectories o f air parcels on the horizontal (x-y) plane, correct to the first order o f wave a m p l i t u d e . (b) S a m e as (a) but including the second order part. N o t e that the trajectories s h o w Stokes drifts.

Vol. 118, 1 9 8 0 )

Lagrangian Motion of Air Parcels in the Stratosphere

197

Z

-I-Y

~ (b)

Figure 2 (a) Same as Fig. la but as seen on the meridional (y-z) plane. (b) Same as Fig. lb but projection onto the meridional plane. (Motion due to the second order Eulerian-mean velocity is not included.) axis is in the x-direction near both walls and in the y-direction in the middle part of the channel (Fig. la). The sense o f rotation is counter-clockwise in the lower latitude and clockwise in the higher latitudes as shown in Fig. la. Note that these express the parcel trajectories as seen by an observer moving with the zeroth-order motion, u0. What is more important to our problem is the projection o f the trajectory onto the meridional plane. F r o m (2.17) and (2.18) we see that the form of the trajectory is an ellipse on the y - z plane, too. Since the vertical displacement is much smaller than the meridional displacement, the major axis is nearly horizontal and inclined slightly downward towards the pole, as depicted schematically in Fig. 2a. The trajectory can also be viewed as superposition of an ellipse with its major axis in the y direction expressed by the cos 00 term in (2.18), and an inclined straight line (the sin 00 term). Magnitudes of the two components are comparable if we take H = 6 x 103 m and m = 2zr/(6 x 104 m), the latter value being chosen corresponding to the vertical wavelength o f the planetary wave o f zonal wavenumber one. As will be shown later, these two components have different effects on the transport of substances, when the effects are parameterized as eddy diffusion. The inclination ~ o f the straight line as well as that of the major axis of the ellipse is given as c~

f~176

2N2H k

(2.19)

If we take f = 10-4 sec-1, N = 2 x 10-2 sec-1, H = 6 x 103 m , k = (2~/2 x 107m) (zonal wavenumber one along the 60 ~ latitude circle), and u0 = 30 m/sec, we have cz - 5 x 10 -4. This value is (happens to be) very close to those adopted by REED and GERMAN (1965) as the inclination o f parcel trajectories, though the presence of

198

Taroh Matsuno

(Pageoph,

an elliptic component necessitate modification of their theory and the results will lead us to a somewhat different interpretation of their results. Next we shall discuss the second-order part of the trajectory, by calculating the right-hand side of (2.14). The second-order parcel velocity in the x-direction is obtained as

dX2

~ul

d--i- = x l - y ; kl 2

~Ul

7 ~ul

+ rl-Ufy + .~l-yi-z

= fcoo a 2 ( - c~

lYo co s2 0o + sin 2 IY0 sin z 0o) + (small term).

(2.20)

Here two terms in the parentheses of the second line correspond to the respective terms in the first line. The contribution from Z~(Sul/~z) turns out to be smaller than the first two by a factor c%/f, which is identified with the Rossby number and is much smaller than unity in the present problem. In the present investigation we shall confine ourselves to discussions of leading order quantities neglecting those smaller terms, unlike URYU (1979) who treated the Lagrangian-mean motion associated with a growing baroclinic wave retaining higher order terms. Our approximation is consistent with the neglect of ageostrophic components in u and v given by (2.8) and (2.9). The Stokes drift in the x-direction, G which is the non-periodic part of (2.20) is written as

kl 2

G = Xz'~V1 -

-a 2 cos 21Yo. 2fcoo

(2.21)

As readily seen from (2.21), the drift is westerly in the middle of the channel and easterly near the both sides. Thus the Lagrangian-mean velocity of individual air parcels exceeds the Eulerian-mean westerly speed in the vicinity of the region where planetary wave amplitude attains the maximum, while the parcel velocity is slower at other latitude zones. Though we have treated a particular wave structure which can be a solution of (2.3), the present result depends only on its horizontal part, which could be a model of quasi-geostrophic wave disturbances of a wider class. Then we may apply the present result to interpretation of the trajectories of constant pressure balloons 3) reported by MOREL and BANDEEN (1973), in which only a part of the Stokes drift [Xz(4!udbx)] was considered for interpretation of the results (see also WEBSTER and CURTIN, 1974). However, in the real situation the basic westerly is not uniform as assumed here but more jet-like. In this case a contribution to Stokes drift of the form Yg(~,2uo/~y~) may become significant as pointed out by ANDREWS and MCINTYRE (1978a, see also MClNTYRE, 1980) and we need a more careful treatment of the problem. It seems to be instructive to look into the kinematical mechanism which brings about the drift G. From the expression given in (2.20), one can immediately see that the first term causes a negative drift while the second term has a positive contribution. The reason can be explained by use of Fig. 3 (as well as Fig. 1) which depicts the 3) It may be applicable to the problem of tracer transports by eddy dominated ocean currents.

Vol. 118, 1980)

Lagrangian Motion of Air Parcels in the Stratosphere iI

'1I

'

\l

/

199

(

/

Figure 3 Horizontal picture of stream lines (thick arrows) and vertical velocity distribution (thin solid lines) for the explanation of Stokes drift (see text). The vertical motion field including the second order effect is also shown by dashed lines. The average of the latter vertical motion taken over a strip between two stream lines (Lagrangian mean) vanishes, while the usual zonal mean vertical motion at a constant y is upward in the northern half and downward in the southern half.

horizontal stream line pattern in the present situation. The distribution of vertical velocity is also shown for the explanation of vertical Stokes drift given later. A very similar diagram has been presented by WALLACE (1978) for discussion o f the same problem but considering an evanescent baroclinic wave. The phase relationship between vertical and meridional velocities is different for a propagating planetary wave from an evanescent wave so that trajectory slopes are different between the two waves. Now let us consider a mean westerly velocity following an air parcel. The air parcel experiences both faster and slower westerly velocities along a stream line but it spends a longer time where the westerly velocity is weaker because total velocity is also weaker there as understood from Fig. 3. Contrarily it spends a shorter time where the westerly is stronger. This effect corresponds to the first term of (2.20). At the same time the air parcel makes a north-south excursion and if we consider a parcel travelling in the southern half of the channel, it experiences a faster (first-order) westerly velocity when it is displaced to the south and a weaker (first-order) easterly velocity when it is displaced to the north as understood from Fig. la, thus obtaining a net westerly drift velocity as indicated in Fig. lb. It is expressed by the second term in (2.20). Both of the two effects mentioned above are very similar to the origin of mass transport in water waves treated by Stokes (hence called Stokes drift). The second-order correction of the meridional velocity of an air parcel is calculated in a similar way and turns out to vanish except for a higher order term in Rossby number i.e., X l . ~ v l = 0, /~s ~

(2.22)

0.

This result depends crucially on the wave amplitude being steady. The second-order vertical velocity consists of two components, the Eulerian-mean vertical velocity and the correction due to displacement as given by (2.14). The former

200

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has already been obtained as the second term of (2.10). The latter quantity is now calculated as OW1 8W1 ~W1 klm x~ --~- + r~--~-y + z ~ - g 7 = -2fN - 2 a2 sin 21Yo(cos 2 0o + sin 2 00) + (small term).

(2.23) Here three terms on the right-hand side are written to have correspondences to those on the left. Again we see that the two terms due to the horizontal displacements have the same magnitude. They are cooperative in this case, to give only non-periodic part, ~s as klm a2 sin 2l Fo.

(2.24)

The kinematical reasons for the drift can be explained in the same manner as for ~. Namely, if we consider an air parcel travelling in the northern half of the channel it spends more time in the descending regions than in the ascending ones as seen in Fig. 3, and simultaneously it experiences a stronger downward motion when it is displaced to the south but a weaker upward motion when it is displaced to the north, because the wave amplitude decreases with latitudes in this part of the channel (Fig. 2a). Thus both of the two effects cause a net downward drift (see Fig. 2b). Now comparing (2.24) with the second term of (2.10) we see that the two terms are equal in magnitude but opposite in sign so that we have dZ2 --dT-= w2 + ~(l"Vwl = 0.

(2.25)

Thus we understand that individual air parcels do not have a mean motion in the vertical direction, even though they make an up and down motion as given by (2.18). Therefore trajectories of air parcels projected onto the meridional plane remain the same as those shown in Fig. 2a, even if we consider the second-order effects. Since individual air parcels do not make a permanent displacement in the vertical, the mean termperature field is kept unchanged, despite the presence of the Eulerian-mean vertical motion as observed in the real stratosphere. We may say that the cancellation of the eddy heat transport effect and the mean vertical motion effect in the heat budget equation, and hence the Charney-Drazin theorem, appears in the form of (2.25), when viewed from air parcel motion. Since we have demonstrated that parcel trajectories are as depicted in Fig. 2a up to the second order of wave amplitude, it is instructive, conversely, to explain the causes of the eddy heat transport and the Eulerian-mean vertical motions on the basis of these parcels motions. In Fig. 4 the situation is illustrated schematically by drawing parcel trajectories as circles instead of inclined ellipses, for the sake of simplicity. Arrows attached to the circles indicate the direction of parcel motions. The upper semi-circles are drawn as dashed lines to indicate that in these positions

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Lagrangian Motion of Air Parcels in the Stratosphere

201

..,..............~.~

:::::::::::::::::::::::::

w0

iii!i~iii)iii~iii .............,

!iiiiiiiiiiiiiiiiiiiii~:

iiiiiiiiii!iiiiiiiiiii~ .,..........

,....,

\

!

i/

9

9

kl

%

:i:i:i:i:i:!:?i:!:i:;.

iiiilil}ii;i;ili)i;iiii~ .:.:+:.:.:.:.:.:.:.

::::::::::::::::::::: ?:!:??:?)?i:??..

i~iiiii~ii)iiiii)iiii~i

f

.,.......y....,.... :::::::::::::::::::::

..,..............,.,

.....,.......,......,.. ...................,... ..................... .........,...,......... ............. , . . .

i-~.-".:}::!)))i:ii~i ~!i!!i!i!i!i~!!i~i!i!i! ..............._...

:.:.:.:...,........_

Figure 4 Illustrative diagram to show how the zonal mean vertical motions and the meridional heat transport are caused by circular motion of air parcels. Dashed- and solid-lined parts of a circular air trajectory indicate the air parcel is cooler or warmer than its mean surrounding, respectively.

the air parcels have lower potential temperature than the horizontal average. The lower semi-circles drawn as solid lines show higher potential temperature. Then we can readily understand that a northward eddy heat transport should exist because northward moving parcels have higher potential temperature while southward moving ones have lower potential temperature. As understood from the above explanation, the meridional eddy heat transport originates from the vertical gradient of potential temperature so that the flux vector is perpendicular to the gradient vector. This particular feature of transport by planetary waves was recently pointed out by CLARK and ROGERS (1978) from purely Eulerian viewpoint. By treating the perturbation equation for a conservative tracer with a basic concentration gradient together with the perturbation equation for planetary wave propagation, and obtaining fluxes from the solutions they were able to demonstrate the above described property of tracer transports by planetary waves. On the other hand JONES (1969) made a general discussion of transports of energy and entropy by internal waves, without referring to any specific waves, and using the same diagram as Fig. 4 he pointed out that even if individual fluid particles have no mean motion, eddy transport of entropy can take place in the transverse direction to the basic entropy gradient by elliptic motion of fluid particles. In the preceding discussion we have shown that trajectories of air parcels are really elliptical in the case of an upward propagating planetary wave and confimed the Jones' result explicitly9 Neither JONES (1969) nor CLARK and ROGERS (1978), however, considered divergence or convergence of the eddy fluxes. The former erroneously concluded that the transversegradient flux should be non-divergent. In the present problem, the heat transport is

202

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largest at the center of the channel where the wave amplitude attains a maximum, and the transport decreases toward both sides. This meridional variation of heat transport brings about a convergence and a divergence of the heat flux at higher and lower latitudes, respectively. However these effects are offset by the effect of mean vertical motions shown by thin solid lines. The origin of these motions may be attributed to the same meridional variation of the amplitude of planetary wave. Namely, if we consider the Eulerian-mean vertical motion somewhere in the northern half of the region, upward motion is greater than downward motion at the same latitude and height, because the upward motion is a branch of a larger elliptic trajectory whose center is located at a lower latitude while the downward motion is a branch of a smaller ellipse. In this way we can consistently interpret the poleward eddy heat flux, its divergence, the mean vertical motion and the cancellation relation from the knowledge of the parcel trajectories. Viewing things as described above, one may notice that the Eulerian-mean budget consideration is somewhat artificial. It would be more useful if one can devise some way of taking averages which is more closely connected with individual air parcels. This problem will be discussed in the next section. It will also have been realized that the 'eddy heat transport' is not due to random eddies and hence its nature is not diffusive. For parameterizing the effect in terms of eddy diffusion we need a particular care. This problem will be treated in Section 4. 3. Generalized Lagrangian means

So far we have been concerned with 'Lagrangian motion' of air parcels and calculated specifically a mean velocity of an individual air parcel in the Lagrangian sense, i.e., a time mean of V following a parcel. It is clear that in a steady state a time mean following an air parcel can be replaced by a space mean along the path of the air parcel, a stream line. In fact the Stokes drift can be rewritten in the following way.

~(o,

P

Zo)= j

F

0, yo, Zo).VVl(,o,, Y0,Zo)d,/]

dt

In the first line of (3.1), ~1, the displacement of an individual air parcel is a function of time and is labeled by its initial position, while the perturbation velocity V1 is an Eulerian field variable and its gradient at the current position of the parcel is evaluated to calculate correction of the parcel's velocity due to the displacement at t. In contrast to this, in the second line, ~1 can be regarded as an Eulerian field variable as well as V1 and the integration is performed, in effect, with respect to the Eulerian coordinate x. Thus we can calculate the Stokes drift at a given instant only from spatial structure of the wave. The meaning of Xl(x) is the displacement of an air parcel caused by the wave perturbation which was originally at x in the unperturbed state.

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Lagrangian Motion of Air Parcels in the Stratosphere

203

This latter way of calculating Stokes drift, hence Lagrangian-mean velocity, may be applied not only to steady waves but to unsteady waves. This idea leads to the generalized Lagrangian-mean motion considered by ANDREWS and MCINTYRE (1978a). (Their theory covers a wider class of averaging and is applicable to finite amplitude waves.) They developed the theory to describe better the back effect of waves on the mean flow, which has been an object of keen interest among many investigators (e.g. ANDREWS and MCINTYRE, 1978b and references therein) in connection with the 'non-acceleration theorem' first discussed by ELIASSEN and PALM (1961) and CHARNEY and DRAZIN (1961). It should be noted here that the integration given by the second line of (3.1) is a weighted mean of k/1 along a stream line. Namely, the integrand is integrated referring not to the stream line but to the original coordinate. This means that a segment of the stream line is given a weight proportional to the length of the segment at its original position. More physically if we consider a thin material tube with a constant mass per unit length at the unperturbed state, the tube after displacement may have different mass per unit length (being proportional to cross sectional area in the case of an incompressible fluid), which becomes the weight. In the present situation, the weight is proportional to a separation of two neighboring streamlines in Fig. 3. Naturally it is proportional to a time per unit length spent by an air parcel in passing through the streamlines. In short, the generalized Lagrangian mean is a mean over a distorted material tube (ANDREWS and MCINTYRE, 1978a; MCINTVRE, 1979; MA-rSUNO and NAKAMVRA, 1979). Essentially the same averaging procedure was adopted by KIDA (1977) in his numerical model study of Lagrangian general circulation of the atmosphere. A similar but not identical averaging, namely an averaging along a curved jet stream path was considered by RIEHI~ and FULTZ (1957) in their analysis of baroclinic waves in a laboratory model, and their method was applied by MAHLMAN (1969) to an analysis of the vertical motion field in the stratosphere at the time of a sudden warming. He was able to show that the mean vertical motion thus calculated was downward on the pole side and upward on the equator side of the polar night jet, in contrast to the Eulerian-mean (usual zonal mean) vertical velocity field which was directed in just the opposite sense. A qualitatively similar result was obtained by MN theoretically for a simplified model. There is, however, a slight difference between the generalized Lagrangian mean and a simple mean along a stream line. As mentioned previously the former mean is a weighted mean along a stream line. The weight is connected with the longitudinal displacement, as can be understood from the discussion in Section 2. The contribution from this displacement to the Stokes drift, i.e., XI(~V1/?~x), has been shown to be very important in the present problem. The magnitudes of those terms are the same as the magnitudes of the other terms, both in ff~ and ff~. The weight is important because it corresponds to length of time for the individual air parcel to pass through various parts of the path and only by taking this effect into account does the generalized Lagrangian mean become equal (in our case) to a mean following an individual air parcel.

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Taroh Matsuno

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As mentioned previously, originally the generalized Lagrangian-mean description was devised by ANDREWS and MCINTYRE (1978a) in order to describe the evolution of general mean flows in the presence of wave disturbances. The method should also be suited to treating tracer transport problems as pointed out DUNKERTON(1978) and MN (see also MCINTYRE, 1979 for contemporary development), because for any physical quantity x which is advected conservatively, the budget equation does not contain eddy transport terms and is +

~+

~

~ = 0 L,

(3.2)

where .~L denotes the generalized Lagrangian-mean of a quantity A, and Q represents source of A, if any. As discussed in the previous section, ~L and ~L are quite different from their Eulerian-mean counterparts, ~ and ~, because the latters contain a large part whose effect must be compensated by the eddy transport effect. Equation (3.2) is formally identical with the Eulerian-mean equation in the case of no wave disturbances, which was presumed in the earlier studies of BREWER (1949), DOBSON (1956) and MtJRGATROYDand SINGLETON(1961). DUNKERTON(1978) showed that if A is potential temperature and Q is radiational heating rate, the following approximate balance holds in a steady state, i.e., (ITa - F)w L = O~a,

(3.3)

where F is the vertical temperature gradient, f'a is the adiabatic lapse rate, g/c v. The meridional advection of (potential) temperature is neglected against the vertical advection (cf. HOt.TON, 1975). Then he stated that what MURGATROYDand SINGLETON (1961) obtained, and hence the Brewer-Dobson circulation, is .just the Lagrangianmean meridional circulation. He also estimated the residence time of air mass in the stratosphere, using the fact that ff~Lrepresents the mass flow velocity and showed that the estimated value is very close to that inferred from tracer studies. KIDA (1977) also noted that the relation (3.3) holds qualitatively in his numerical model of the Lagrangian general circulation of the atmosphere. In his case, ~" is the observed motion of center of mass of marked air parcels which were distributed initially on a strip of a width of about 7 ~ latitude on an isobaric surface. He found, however, the observed ~L was too large compared with the value expected from the radiational balance (3.3). Examining his results more carefully we notice that the discrepancy is not so large as he claims (a few times), but the magnitude of ~" (negative everywhere in the calculated domain) is at most twice the value deduced from (3.3). The problem will be discussed shortly. Unfortunately Kida's model was not able to produce planetary waves, because the model is confined to a sector of 60 ~ longitude. Though his Eulerian-mean meridional circulation is utterly different from the Lagrangian-mean counterpart, the former was also different from the observed two-cell circulation. Therefore, for the confirmation of (3.3) for a more realistic situation, a rough analysis of the results of

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Lagrangian Motion of Air Parcels in the Stratosphere

205

10 2 e r a g e e -1

30kin t

...... w

//'-",,,

,"

--~/At ......

wl~,,,i :~/r',~

60"',,, -

0~

III

/ f /

:

/

,

-20 km

. .--.

60~ ......

/

.......

\,

~ . ~ 3 ~ ,'/ '

~" I

7

:! i

Figure 5 Three kinds of vertical velocities taken from the HUNT and MANABE(1968) numerical experiment. Solid line: Vertical velocity of a conservative tracer analyzed from the motion of contour lines of equal mixing ratio. Dashed line: Zonal mean vertical velocity. Chain line: Vertical motion required to balance with net radiational heating. HUNT a n d MANABE'S (1968) numerical e x p e r i m e n t was made. The L a g r a n g i a n - m e a n vertical m o t i o n was estimated from the vertical shift o f c o n t o u r s o f equal concentration o f a conservative t r a c e r presented in their Fig. 16. The vertical m o t i o n to balance with the r a d i a t i o n a l heating was also calculated from the d a t a shown in Fig. 12 o f MANAB~ a n d HvN'r (1968). The two vertical velocities as functions o f latitude are shown in Fig. 5 t o g e t h e r with the E u l e r i a n - m e a n vertical velocity taken from their p a p e r . A p p a r e n t l y the L a g r a n g i a n - m e a n vertical velocities agree fairly well with the velocities expected from r a d i a t i o n a l balance, especially at the 30 km level, while the Eulerian m e a n s are quite different from the o t h e r two. Thus we can confirm that (3.3) holds in this case to a g o o d a p p r o x i m a t i o n . In o t h e r words, w h a t governs m o v e m e n t o f tracers is that p a r t o f the vertical m o t i o n that balances with the radiational heating, even t h o u g h the total E u l e r i a n - m e a n vertical m o t i o n is d o m i n a t e d by a c o m p o n e n t forced by e d d y heating due to p l a n e t a r y waves and the f o r m e r c o m p o n e n t is hidden behind the latter. 4) 4) The model did not include topography or continentality. Therefore stationary planetary waves caused by these effects are not present in the model so that the wave-induced Eulerian-mean vertical motions shown in the diagrams are much weaker than the observed counterparts (in the Northern Hemisphere).

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Now comparing the two results for the 30 km level and for the 20 km level, we easily notice that the agreement of two w's is almost perfect for the upper level while for the lower level ~L deduced from tracer motion deviates systematically to the negative side of wR estimated from the radiative imbalance. A similar tendency was found in Kida's results near the tropopause, as already mentioned. This excess downward motion of the Lagrangian-mean circulation in the lowest part of the stratosphere may be attributed to an additional converging motion toward the troposphere. Lagrangian-mean motions are, surprisingly, divergent even if the fluid is incompressible (McINTYRE, 1973, 1979, 1980; ANDREWS and MCINTYRE, 1978a; NAKAMURA, 1979; URYU, 1979). After ANDREWS and MCINTYRE (1978a) and NAKAMURA (1979), we can explain the origin of this divergence in the following way. Consider a situation where a wave disturbance is growing in a uniform flow. If we imagine that straight lines are marked in the fluid in the direction of the uniform flow at the initial time, they will become similar in shape to the stream lines in Fig. 3. Then the center of mass of the fluid contained between one of the side walls and the nearest marker line is likely to shift toward the middle of the channel, thus causing a convergence in the middle (and a divergence near the walls). 5) A converging flow is a dominant feature of the Lagrangian-mean motion associated with a baroclinic unstable wave treated by URVU (1979). On the contrary if a wave decays, the Lagrangian-mean flow must be divergent in the middle of the channel. In both MANABE and HUNT'S (1968) and KIDA'S (1977) numerical experiments, disturbances are thought to be statistically steady and both growing and decaying phases of disturbances must be included for the long periods for which the Lagrangian means were calculated. However, it is also clear that because of the presence of dissipative effects, decay is not a reverse process of growth and after one life cycle of a baroclinic wave a material tube may remain more spread than its initial state. Complicated non-linear processes involving many wave components may also be a source of the irreversible spread. Indeed in KIDA'S (1977) experiment, initially well localized marker particles diffuse with time in the troposphere. In response to this, the Lagrangianmean circulation in the troposphere is dominated by a converging flow toward the center of the troposphere. Bearing these facts in mind the discrepancy between the Lagrangian-mean vertical velocity derived from tracer movements and the vertical velocity estimated from (3.3), found in the lowest stratosphere, may be attributed to the convergent flow toward the troposphere. From the discussions in the present section one may readily understand that it is rational to adopt the Lagrangian-mean meridional circulation (or something like it) as the transport mechanism for a two-dimensional model of the stratospheric chemistry together with a ' t r u e ' eddy diffusion representing the dispersal of material particles on scales smaller than those discussed explicitly. For this purpose one can deduce the circulation directly from the radiative balance, whose approximate form 5) Rhines (1977) noted the same point in discussing the difference between Eulerian and Lagrangian mean flows for a turbulent field.

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Lagrangian Motion of Air Parcels in the Stratosphere

207

is (3.3). It may also be understood that for doing this, especially if the troposphere is included, the phenomenon of convergence and particle dispersion about the mean flow should be dealt with. Investigations on this are now under way (DuNKERTOS, personal communication; MCINTVRE, 1979). It is very interesting that such a method has already been adopted by PRABAKHARA (1963) in his calculations of photochemical-dynamical equilibrium of ozone, made before the discovery of the two-cell Euterian-mean circulation of the stratosphere. He used a meridional circulation derived from MURGATROYD and SINGLETON'S (t961) results but by reducing its magnitude to 20~o of the original. In view of a recent radiation calculation by DOPPLICK (1972), this value seems to be too small but still within an acceptable limit. Prabakhara's procedure may be justified in terms of Lagrangian means, at least qualitatively; and his result, which showed a remarkable agreement with observation, may be taken to indicate that this way of two-dimensional modeling is adequate.

4. A parameter&ation of eddy transports of tracers by planetary waves As mentioned in Section 1, the usual description of transport mechanisms in the stratosphere from an Eulerian viewpoint invokes both mean meridional circulation and eddy transports by planetary waves. In response to this picture of tracer transport mechanism, in two-dimensional modeling of ozone and other chemical substances the transport effects are represented by advection of the tracer by a mean meridional circulation plus eddy diffusion (e.g. HARWOODand PYLE, 1977 ; HIDALGOand CRUTZEN, 1977). In the Eulerian picture the eddy transport is the principal means by which ozone is transported from the subtropics to the polar region, against the counteracting effect of a mean meridional circulation existing in the region; and therefore its representation would appear to have a crucial importance in the problem. The meridional eddy transports are often countergradient, including the ozone transport, though there is no physical basis for supposing that negative diffusion takes place for a passive tracer. In order to parameterize an eddy transport process having such a nature, REED and GERMAN(1965) proposed an eddy diffusion in the meridional plane with an inclined principal axis of diffusion. MURGATROYD (1965) stated that their method would represent well the tracer movements in the stratosphere. Namely, they hypothesized that owing to large-scale disturbances including planetary waves, individual air parcels move along trajectories which are on a plane inclined downward toward the pole. If the slope of this 'mixing surface' is greater than that of equal mixing-ratio surfaces of a tracer in the case where the mixing ratio of the tracer is increasing with height, mixing on this sloped surface would result in a poleward diffusion of the tracer. In this case, the diffusive flux is not parallel to the gradient. They are nearly perpendicular to each other though the flux is still slightly downgradient. The eddy diffusivity connecting the flux and the gradient then becomes a symmetric tensor. Apparently this method represents the eddy transport in the

208

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stratosphere to some extent (cf. CLARK and ROGERS, 1978) and by finding empirically a matched pair of a mean meridional circulation and an eddy diffusivity distribution it is now possible to reproduce the latitudinal distribution and the seasonal variation of ozone fairly well by two-dimensional models (e.g. HARWOOD and PYLE, 1977; HIDALGO and CRUTZEN, 1977). In view of the foregoing discussions in Section 2, however, we note that the Reed-German eddy diffusivity is not satisfactory for representing eddy transport by planetary waves in the following points. Firstly, we have no basis to consider that parcel trajectories are such as assumed by REED and GERMAN (1965). On the contrary we have shown that the trajectory of air parcels associated with a planetary wave is an ellipse when projected onto a meridional plane. Secondly, as argued in Section 2, eddy fluxes of tracers due to planetary waves do not have the physical nature of a diffusion. The eddy fluxes are needed just to offset the effect of mean vertical motions and hence they should have the character of advection. If we were to apply the ReedGerman diffusivity to the problem treated in Section 2, the initial stratification would be smoothed gradually with time, whereas in the circumstances assumed the mean stratification should remain unchanged. The intrinsically unsatisfactory nature of such a wholly diffusive parameterization has also been demonstrated by MAHLMAN (1975) from the results of a numerical experiment using a general circulation model. In what follows we shall attempt to derive a new eddy diffusivity (though it will turn out not to be diffusive in nature) on the basis of a knowledge of the parcel trajectories and applying a mixing-length type assumption. We consider the vertical and the meridional eddy fluxes crossing a constant latitude and height. If we know the velocity of air parcels and the mixing ratio of a tracer carried by them, we can evaluate the eddy fluxes. For this purpose, let us consider a set of air parcels which are all at a given latitude and height at a certain instant. We take the point under consideration as the origin of a coordinate in the meridional plane and also let the time t be zero at the instant considered. Then the parcel trajectories are written referring to (2.17) and (2.18), as

Y(t; 9) = ay[sin (~ot + 9) - sin 9],

(4.1)

Z(t; 9) = -a~[cos (oJt + 9) - cos 9] - b~[sin (~ot + 9) - sin 9],

(4.2)

where au is the amplitude of parcel oscillation in the y-direction, and a~ and b~ are those in the z-direction associated with the elliptic and linear components of a trajectory, respectively. 9 is a parameter designating the initial position of the parcel and may be regarded as the same as kxoo where x00 is the initial position of the parcel in the x-direction. Next, we shall assume that a physical quantity X is carried with the air parcels and it changes according to the following equation

dx

1

&- = 7 (~ - X),

(4.3)

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Lagrangian Motion of Air Parcels in the Stratosphere

209

where 2 is an environmental value of X, which is solely determined by specifying the position (Y, Z ) in the meridional plane, and T is a time constant parameterizing the adjustment of X to its environment. In usual sense of eddy diffusion ~- is a measure of the time needed for a parcel to merge with the surrounding air, hence 9 is a mixing time. F o r chemically active tracers, we m a y interpret ~ as the photochemical equilibrium value and ~- as a photochemical relaxation time. A formal solution of (4.3) is readily obtained as x(t) =

eCt'-t~/~ ~[ Y ( t ' ) , Z ( t ' ) ] dr'.

(4.4)

Here we shall assume that ~ can be approximated by a linear function in the neighborh o o d of the origin, i.e., if(y, z) = ff~y + :~z,

(4.5)

where ~u and 2z are constants. Such an assumption is c o m m o n l y adopted in the mixing-length theory and is justified if mean gradients are nearly constant over particle orbits. It is this assumption that will read to eddy fluxes proportional to mean gradients. The constant term is set zero, because it has nothing to do with the transport. U p o n rewriting ~ in (4.4) in the form given by (4.5) and then substituting Y ( t ) and Z ( t ) into the rewritten expression we can calculate X(0, so), the value of X carried by an air parcel with label So, at t = 0 as cos So + qb2 sin So) - ~za~(- O2 cos So + q~j sin ~o)

x(O, So) = - ~ a y ( 0 1

+ ~b~(qbl cos So + qb2 sin So), where ~1 and qb2 are 9 l(o)r) - - ~

lfO

- ~ sin ~ot e ~/~ dt = 1 +~~

! ~0 qb2(wr) -- --

(4.6)

2'

(4.7)

O)2T2 COS ~ot e t/* dt + 1 = 1 + o927.2.

(4.8)

On the other hand, we readily obtain the velocity components of the air parcel as v(0, So) = ogay cos so, w(0, so) = o)az sin so - ~ob~cos So.

(4.9) (4.10)

Then making products of X(0, 9) and the two velocity components given above and integrating them with respect to q) (equivalent to zonal averages) we obtain eddy fluxes of X as following, --

vx-

oga~ (jp~y + ~oav (a~qb2 + b~q)~)~, 2

-w-X = ~ogav" t-a~

2-

* 2 + bzq)~)~2y - o9 -~ (a~ + b 2 ) O - ~ .

(4. l l) (4.12)

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Taroh Matsuno

(Pageoph,

Since (4.11) and (4.12) represent a linear relation between the flux vector and the gradient vector, they can be expressed as, V X = - D. V;~,

(4.13)

where D is an eddy diffusivity tensor and is written as D = ~3s + D~,

I O)au2 where

D, =

\

60

- ~ a~b~

,o -~ayb~, f(a~ + b~)

(o) 0

D~ =

(4.14)

O)

-~-

1 x qb~(ojr),

(4.15)

~a~ x q)2(o~r).

(4.16)

a~,a~

Evidently the eddy diffusivity tensor consists of both symmetric and antisymmetric components. Since a, and b~ correspond to the first and second terms of (4.2), we see that the symmetric part arises both from the line-shaped component of a parcel motion and from the elliptic component, while the antisymmetric part comes only from the elliptic component of the trajectory. It is important to note that the symmetric part has a common factor qbl, and the antisymmetric part has ~2- As is evident from their expressions (4.7) and (4.8), q51 first increases with the increae of oJ, until it attains a maximum value 89at o~, = 1 and then decreases to approach 0, while qb2 is a monotonically increasing function and approaches 1 asymptotically for a large o r as depicted in Fig. 6. For a small ~or ( 0

and

4 D ~ D ~ > (Du~ + D ~ ) 2,

(4.22)

where equal signs correspond to the case where the quantity (4.21) vanishes. Now we notice that the anti-symmetric part does not enter (4.21) and (4.22); that is to say it does not cause concentration nor diffusion. It leaves (~2> unchanged. This is because an anti-symmetric 'diffusivity' causes a transverse-gradient eddy flux. Letting the yz component be - D , the flux is expressed as

-

Evidently the above flux is orthogonal to V~. Thus we see that, since for a conservative tracer (cot = oo), our eddy diffusivity reduces to an anti-symmetric tensor, the eddy flux becomes perpendicular to the gradient. This is quite reasonable because the anti-symmetric part comes from the elliptic trajectory. JONES (1969) has already shown that for such a trajectory the eddy flux should occur in the transverse-gradient direction, as mentioned previously. CLARK and ROGERS (1978) also showed that eddy transports of conservative tracers by planetary waves are perpendicular to the gradient of the tracers. Their expression for the flux is identical with (4.23). We arrived at the same conclusion via a somewhat different line. The above mentioned works, however, did not deal with spatial variation of diffusivity. As long as the diffusivity is constant, the transverse-gradient flux remains idle without causing any changes of T-field as is evident from inserting (4.23) into

Vol. 118, 1980)

Lagrangian Motion of Air Parcels in the Stratosphere

213

(4.19). Note that even in this case, the flux itself is well defined and observable (JONES, 1969; TmEBAUX, 1975). In the present problem, D is variable because it depends on the amplitude of planetary waves as indicated by (4.16). As can be understood from the arguments in Section 2, this latitudinal variation of eddy diffusivity is of primary importance for causing divergences and convergences of eddy fluxes. These may cause changes of tracer distributions unless they are counter-balanced by the effect of mean circulations. If D is variable we have c~

c~)~

-

cqD c3~

c3D ~

(4.24)

where ~7and 9 are Eulerian-mean meridional and vertical velocities, respectively. The above equation indicates that i is advected by an additional flow which is derived from a stream function D. The if-field can be changed by the effect of the eddy diffusion; but it is not a 'diffusive' process. This is exactly what we wanted for incorporating as an eddy transport into two-dimensional models, in order to compensate the transport by a mean meridional circulation. In fact it can be shown that the flow derived from the stream function D coincides with the Stokes drift in our case, so that the change of i given by the right hand side of (4.24) just cancel with the change caused by the mean vertical velocity, the last two terms on the left. As shown above, following the line taken by REED and GERMAN (1965) but by modifying their formula on the basis of new and correct information about parcel trajectories we obtained an identical result with the one deduced from the consideration of the Lagrangian-mean motion. The method to express transport effects by an Eulerian-mean meridional circulation plus an eddy diffusion, which is currently used in two-dimensional modeling of minor constituents in the stratosphere, could be justified if the eddy diffusion is expressed by an eddy diffusivity which includes a large anti-symmetric component.

5. Summary In the present article we discussed motion of individual air parcels caused by a steady upward propagating planetary wave. It was shown that trajectories of air parcels are elliptical when they are projected onto the meridional plane and they make a cyclic motion in a definite sense along the trajectories. Mean motion following an air parcel is zero both in the meridional and vertical directions. This result is not inconsistent with the presence of Eulerian-mean vertical motion (which is upward on the poleward side and downward on the equatorward side), because mean motion following an individual air parcel differs from mean motion at a fixed latitude and height and the difference, usually called the Stokes drift, is just in the opposite to the mean vertical motion. A mean following an individual air parcel can be replaced by a suitably weighted mean along the stream line in the case of a steady flow. The latter procedure is

214

Taroh Matsuno

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equivalent to calculating a mean for a material tube; in the latter form it can be applied to more general cases. This idea was developed by ANDREWSand MCINTYRE (1978a) for the treatment of the wave-mean flow interaction problems, in the first place, but it now appears to be a useful tool for describing mean meridional circulations. It may be applicable to two-dimensional models of minor constituents in the stratosphere. The theoretical result that the meridional projection of the trajectory of an air parcel in the stratosphere induced by propagating planetary waves is an ellipse rather than an inclined line requires us to reexamine the Reed-German eddy diffusivity which is currently used for two-dimensional models of the stratospheric chemistry. Then we have derived a new eddy diffusivity corresponding to the elliptic parcel motion. The diffusivity tensor is shown to be dominated by an anti-symmetric component in the case of a nearly conservative tracer. The eddy transport derived from this diffusivity is advective rather than diffusive in nature and in effect it approximately represents transports due to the Stokes drift. Thus the two new schemes (Lagrangian and Eulerian) for two-dimensional modeling are approximately equivalent.

Acknowledgements

I am grateful to Dr. M. E. McIntyre who read the original manuscript and offered me a number of valuable comments. For the reference to Plumb (1979) I am indebted to Dr. D. G. Andrews. I also wish to express my appreciation to Mr. T. Dunkerton, Drs. J. R. Holton, J. D. Mahlman, K. Nakamura, M. Uryu and J. M. Wallace for helpful discussions on the present topic. Some part of the work reported in this article was performed while I was visiting U.C.L.A. in the summer of 1972.1 would express my gratitude to Drs. A. Arakawa, Y. Mintz, S. V. Venkateswaran and M. Yanai for their hospitality. I am also grateful to Mrs. K. Kudo for her assistance in preparation of the manuscript.

REFERENCES ANDREWS,D. G. and MCINTYRE,M. E. (1978a), An exact theory o f nonlinear waves on a Lagrangian-mean flow, J. Fluid. Mech. 89, 609-646. ANDREWS,D. G. and MCtNTYRE,M. E. (1978b), On wave action andits relatives, ibid. 89, 647-664. BLAKE, D. and LINDZEN, R. S. (1973), The effect o f photochemical models on calculated equilibria and cooling rates in the stratosphere, Mon. Wea. Rev. 101, 783-802. BREWER, A. W. (1949), Evidence for a worm circulation provided by measurements o f helium and water vapor distribution in the stratosphere, Quart. J. Roy. Meteor. Soc. 75, 351-363. CHARNEY, J. G. and DRAZIN,P. G. (1961), Propagation o f planetary scale disturbances .from the lower into the upper atmosphere, J. Geophys. Res. 66, 83-109. CLARK, J. H. E. (1970), A quasi-geostrophic model o f the winter stratospheric circulation. Mon. Wea. Rev. 98, 443-461. CLARK, J. H. E. and ROGERS,T. G. (1978), The transport o f trace gases by planetary waves, J. Atmos. Sci. 35, 2232-2235.

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CUNNOLD, D., ALYEA, F., PHILLIPS, N. A. and PRINN, R. (1975), A three-dimensional dynamical chemical model of atmospheric ozone, J. Atmos. Sci. 32, 170-194. DOBSON, G. M. B. (1956), Origin and distribution of polyatomic molecules in the atmosphere, Proc. Roy. Soc. London A235, 187-192. DOPPLICK, T. G. (1972), Radiative heating of the global atmosphere, J. Atmos. Sci., 29, 1278-1294. DUNKERTON, T. (1978), On the mean meridional mass motions of the stratosphere and mesosphere, J. Atmos. Sci. 35, 2325-2333. EL1ASSEN,A., and PALM, E. (1961), On the transfer of energy in stationary mountain waves, Geofys. Publ. 22, No. 3, 1-23. HARWOOD, R. S. and PYLE, J. A. (1977), Studies of the ozone budget using a zonal circulation model and linearized photochemistry, Quart. J. Roy. Meteor. Soc. 103, 319-343. HIDALGO, H. and CRUTZEN, P. J. (1977), The tropospheric and stratospheric composition perturbed by NOx emissions of high altitude aircraft, J. Geophys. Res. 82, 5833-5866. HOLTON, J. R. (1975), The dynamic meteorology of the stratosphere and mesosphere, Meteor. Monogr., 15, No. 37, Amer. Meteor. Soc., Boston, 216 pp. HUNT, B. G., and MANABE, S. (1968), Experiments with a stratospheric general circulation model. H. Large-scale diffusion of tracers in the stratosphere, Mon. Wea, Rev. 96, 503-539. JONES, W. L. (1969), The transport of energy by internal waves, Tellus 11, 177-184. JULIAN, P. R. and LABITZKE, K. B. (1965), A study of atmospheric energeties during the JanuaryFebruary 1963 stratospheric warming, J. Atmos. Sci. 22, 597-610. KASAHARA, A., SASAMARI,T. and WASHINGTON, W. M. (1973), Simulation experiments with a 12-layer stratospheric global circulation model. L Dynamical effect of earth's orography and thermal influence of eontinentality, J. Atmos. Sci. 30, 1229-t251. KASAHARA, A. and SASAMORI, T. (1974), Simulation experiments with a 12-layer stratospheric global circulation model II. Momentum balance and energeties in the stratosphere, J. Atmos. Sci. 31, 408-421. KtDA, H. (1977), A numerical investigation of the atmospheric general circulation and stratospherictropospheric mass exchange. 1. Long-term integration of a simplified general circulation model. H. Lagrangian motion of the atmosphere, J. Meteor. Soc. Japan 55, 52-88. LONGUET-HIGGINS, M. S. (1969), On the transport of mass by time-varying ocean currents, Deep Sea Res. 16, 431-447. MCINTYRE, M. E. (1973), Mean motions and impulse of a guided internal gravity wave packet, J. Fluid. Mech. 60, 801-811. MClNTYRE, M. E. (1979), Towards a Lagrangian-mean description of stratospheric circulations and chemical transports, Phil. Trans. Roy. Soc. London (to appear). MCINTYRE, M. E. (1980), An introduction to the generalized Lagrangian-mean description of wave, mean-flow interaction, Pure Appl. Geophys. (in this issue). MAHLMAN, J. D. (1969), Heat balance and mean meridional circulation in the polar stratosphere during the sadden warming of January 1958, Mon. Wea. Rev. 97, 534-540. MAHLMAN, J. D. (1975), Some fundamental limitations of simplified transport models as implied by results from a three-dimensional general circulation/tracer model. Fourth Conference on CIAP, February 1975. ed. T. M. Hard and A. J. Broderick. DOT-TSC-OST-75-38, 132-146. MAHLMAN, J. D. and MOXIM, W. J. (1978), Tracer simulation using a global general circulation model: Results from a mM-latitude instantaneous source experiment. J. Atmos. Sci. 35, 13401374. MAN.ABE, S. and HUNT, B. G. (1964), Experiment with a stratospheric general circulation model. I. Radiative and dynamic aspects, Mon. Wea. Rev. 96, 477-502. MANABE, S. and MAHLMAN,J. D. (1976), Simulation of seasonal and inter-hemispheric variation in the stratospheric circulation, J. Atmos. Sci. 33, 2185-2217. MATSUNO, T. (1970), Vertical propagation of stationary planetary waves in the winter northern hemisphere, J. Atmos. Sci. 27, 871-883. MATSUNO, T. and NAKAMURA,K. (1979), The Eulerian and Lagrangian mean meridional circulations in the stratosphere at the time of a sudden warming, J. Atmos. Sci. 36, 640-654. MIYAKODA, K. (1963), Some characteristic features of winter circulation in the troposphere and the lower stratosphere. Tech. Rep. No. 14, Dept. Geophys. Sci., The University of Chicago, 93 pp. (NTIS PB 174308).

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MOREL, P. and BANDEEN, W. (1973), The EOLE experiment: early results and current objectives, Bull. Amer. Meteor. Soc. 54, 298-306. MURGATROYD, R. J. and GOODY, R. M. (1958), Sources and sinks of radiative energy from 30 to 90 kin, Quart. J. Roy. Meteor. Soc. 84, 225-234. MURGATROYD, R. J. and SINGLETON, F. (1961), Possible meridional circulations in the stratosphere and mesosphere, Quart. J. Roy. Meteor. Soc. 87, 125-135. NAKAMURA, K. (1979), A generalization of 'Eliassen-Palm Relation', J. Meteor. Soc. Japan 57, 215-226. NEWELL, R. E. 0963), Transfer through the tropopause and within the stratosphere, Quart. J. Roy. Meteor. Soc. 89, 167-204. PERRY, J. S. (1967), Long wave energy processes in the 1963 sudden stratospheric warming, J. Atmos. Sci. 24, 537-550. PLUMB, R. A. (1979), Eddy fluxes of conservative quantities by small-amplitude waves, J. Atmos. Sci. (in press). PRABHAKARA,C. (1963), Effects of non-photochemical processes on the meridional distribution and total amount of ozone in the atmosphere, Mon. Wea. Rev. 91, 411-431. REED, R. J. and GERMAN, K. E. (1965), A contribution to the problem of statospheric diffusion by large-scale mixing, Mon. Wea. Rev. 93, 313-321. REED, R. J., WOLFE, J. and NISHIMOTO,H. (1963), A special analysis of the energetics of the stratospheric sadden warming of early 1957, J. Atmos. Sci. 20, 256-275. RHINES, P. B. (1977), The dynamics of unsteady currents. The Sea, Vot. 6, ed. E. D. Goldberg, Wiley, New York, 189-318. SCHLESINGER,M. E. (1976), A numerical simulation of the general circulation of atmospheric ozone. Ph.D. Dissertation, Department of Atmospheric Sciences, University of California, Los Angeles, 376 pp. SIMMONS, A. J. (1974), Planetary scale disturbances in the polar winter stratosphere, Quart. J. Roy. Meteor. Soc. 100, 76-108. THIEBAUX, M. L. (1975), Determination of one-particle effective eddy diffusivity tensor in linearly inhomogeneous turbulent flows, J. Atmos. Sci. 32, 2136-2143. TRENBERTH, K. E. (1973a), Global model of the general circulation of the atmosphere below 75 km with an annual heating cycle, Mon. Wea. Rev. 101, 287-305. TRENBERTH, K. E. (1973b), Dynamical coupling of the stratosphere with the troposphere and sudden stratospheric warmings, Mon. Wea. Rev. 101, 306-322. URYU, M. (1979), Lagrangian-mean motion induced by growing baroclinic wave, J. Meteor. Soc. Japan 57, 1-20. VINCENT, D. G. (1968), Mean meridional circulation in the northern hemisphere lower stratosphere during 1964 and 1965, Quart. J. Roy. Meteor. Soc. 94, 333-349. WALLACE, J. M. (1978), Trajectory slopes, counter-gradient heat fluxes and mixing by lower stratospheric waves, J. Atmos. Sci. 35, 554-558. WEBSTER,P. J. and CURTIN, D. G. (1974), Interpretation of the EOLE experiment 1. Temporal variation of Eulerian quantities, J. Atmos. Sci. 31, 1860-1875. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~user Verlag, Basel

Observational Evidence of the Semiannual Oscillation in the Tropical Middle Atmosphere-A Review By ISAMU HIROTA 1)

Abstract-Observational studies on the semiannual oscillation in the tropical stratosphere and mesosphere are reviewed. Results of many statistics based on rocket and satellite observations reveal that the long-term behavior of the mean zonal wind exhibits two semiannual cycles which have their maximum amplitudes centered at the stratopause level and the mesopause level, each one being associated with the semiannual temperature variations predominating at levels about 10 km lower. Observational evidence obtained from recent studies of the dynamical properties of upper stratospheric waves strongly supports the theoretical consideration that the stratospheric semiannual oscillation is the manifestation of the wave-zonal flow interaction with alternating accelerations of the westerly flow by Kelvin waves and the easterly flow by planetary Rossby waves. Regarding the semiannual variation in the upper mesosphere, however, very little is known about the possible momentum source. Therefore, emphasis is placed on the need for further observations of the structure and behavior of the tropical middle atmosphere. Key words: Semiannual cycles; Kelvin waves; Rossby waves; Wave-zonal flow interaction.

1. Introduction The semiannual oscillation o f the m e a n zonal wind a n d t e m p e r a t u r e in the t r o p i c a l m i d d l e a t m o s p h e r e is certainly one o f the most interesting p r o b l e m s to be solved for the u p p e r a t m o s p h e r i c dynamics. In c o n t r a s t to the studies on the quasibiennial oscillation (QBO) in the tropical lower stratosphere, there seems as yet to be neither a satisfactory mechanistic m o d e l n o r a c o m p e l l i n g t h e o r y for the detailed m e c h a n i s m o f the s e m i a n n u a l oscillation. In the last two decades, however, a great deal o f u p p e r a t m o s p h e r i c s o u n d i n g d a t a have been a c c u m u l a t e d because o f progress in i n s t r u m e n t a t i o n such as m e t e o r o logical rockets a n d satellites, a n d significant d e v e l o p m e n t s in the study on the structure a n d b e h a v i o r o f the s e m i a n n u a l cycle have resulted f r o m these observations. Therefore, at this stage p r i o r to the beginning o f the p e r i o d o f the M i d d l e A t m o sphere P r o g r a m ( M A P ) , it is timely to s u m m a r i z e o u r present knowledge o f the observed features o f the s e m i a n n u a l oscillation in the zonal wind and t e m p e r a t u r e a n d some characteristics o f wave disturbances related to the m e a n zonal wind variation in the e q u a t o r i a l m i d d l e a t m o s p h e r e . ~) Geophysical Institute, Kyoto University, Kyoto 606, Japan.

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Isamu Hirota

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In this review paper, we will be mainly concerned with observations of wind and temperature in the tropical stratosphere and mesosphere extending from 20 to 80 km, while some other important phenomena such as the semiannual cycle in the middle and high latitudes and in the thermospheric ionized atmosphere will be excluded from our discussion. Results of theoretical studies and numerical modelling will of course be referred to interpreting the observational evidence: among them the implications of the theory of the QBO will be very useful for consideration of the semiannual zonal wind oscillation. Preceded by a brief historical review of the upper atmospheric sounding, the climatology of the semiannual oscillation is documented based on the results of many statistics, and some problems to be solved from a dynamical point of view are presented. Next, in order to give an answer to these questions, the characteristic features of large-scale wave disturbances in the tropical middle atmosphere are described on the basis of recent observations and analyses. Finally an attempt will be made to suggest future observational studies needed in order to gain a thorough understanding of the mechanism of the semiannual oscillation.

2. Discovery of the semiannual oscillation Since the period of the International Geophysical Year (1957-58), a considerable amount of wind and temperature data of the stratosphere and mesosphere have been obtained from newly developed rocket observations. By using these data, in the first half of the 1960s, many attempts were made to construct zonal cross sections of mean wind and temperature and to describe their seasonal variations on the basis of the monthly mean statistics (BATTEN, 1961; KOCHANSKI, 1963; KANTOR and COLE, 1964, 1965). However, although these climatological studies represented an improvement over earlier ones (e.g., MURGATROYD, 1957), the reliability of the statistics for the tropical regions was still inadequate, primarily because of the sparsity of data in low latitudes, hence most of their discussions were concerned with the seasonal variation in middle and high latitudes where the annual cycle is predominant with a strong contrast between summer and winter circulations. It should also be noted that, in these climatological studies, the Southern Hemispheric data were incorporated into the Northern Hemispheric data with a tinqe-lag of six months, by assuming hemispheric symmetry. Accordingly, there is no distinction between January and July at the equator. Because of this method of analysis, as was pointed out by REED (1966), such an equatorial time-section must inevitably exhibit a six-month cycle, whether real or not. On the other hand, concerning the long-term variation of zonal wind in the tropical lower stratosphere, the so-called 26-month or quasi-biennial oscillation was found by REED (1960) and EBDON (1960) independently, from balloon observations over several

Vol. 118, 1980)

219

Evidence o f S e m i a n n u a l Oscillation in Tropical M i d d l e A t m o s p h e r e

stations in the tropics. Following the discovery of this remarkable phenomenon, numerous investigations were carried out in the following decade from various points of view: as a result, studies on the structure and dynamics of the mean zonal wind and large-scale equatorial waves have now made it clear that the QBO can be accounted for in the framework of 'wave-zonal flow interaction' (see the text of I-IOLTON (1975), and PLUMB (I977) and PLUMB and McEwAy (1978), for instance). In 1962, while making observational studies on the tropical stratosphere following the discovery of the QBO, Reed found evidence of the existence of a semiannual component in the temperature variation above the 30-rob level (24 kin) at some stations near the equator: the oscillation had its maximum amplitude over the equator and at the highest levels observed, and showed downward phase propagation. However, at that time, he considered the semiannual temperature variation simply as a consequence of the direct absorption of solar ultraviolet radiation by ozone in a region where the heating cycle is semiannual due to the twice-yearly passage of the Sun across the equator. The semiannual oscillation of the zonal wind in the equatorial stratosphere and

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mesosphere was also discovered by REED (1965). Using the rocket observations of wind at Ascension Island (8~ in the region between 28 and 52 km, he found evidence of a six-month cycle which becomes increasingly dominant above 40 km (Fig. 1). In a subsequent study of these topics, REED (1966) confirmed the existence of the semiannual zonal wind oscillation by using the rocket data at Ascension Island and Barking Sands (22~ for two years which was long enough to eliminate the influence of the quasi-biennial cycle. Results of harmonic analysis at the two stations indicate, as in the case of the semiannual temperature variation, that the semiannual wind oscillation is strongest at the equator, with a maximum amplitude of about 30 m/sec near 50 km, and the phase propagates downward. From the foregoing description of the zonal wind behavior, REED (1966) pointed out some interesting problems such as the generation and maintenance of the equatorial westerly flow, the effect of solar radiation in the tropical middle atmosphere, and the dynamical interaction with winter hemispheric circulations. These problems will be discussed later in more detail.

3. Climatology of the semiannual oscillation After the pioneering work on the semiannual oscillation in the equatorial stratosphere by REED (1965, 1966), there have been a large number of statistical studies on the structure and behavior of the mean zonal wind and temperature based on highaltitude observations which were obtained from the Meteorological Rocket Network (QUIROZ and MILLER, 1967; COLE, 1968; ANGELLand KORSHOVER, 1970; BELMONT and DARTT, 1973; BELMONT et al., 1974, 1975; NASTROM and BELMONT, 1975; HOPKINS, 1975; etc.). Despite the variety of years and stations of rocket data used in these studies, results from them all indicate that the semiannual variation of the zonal wind and temperature is global in extent, and now we have the following overall picture of the climatology of the semiannual oscillation in the middle atmosphere: (a) Mean zonal wind Harmonic analyses for each latitude and height level reveal that the semiannual zonal wind oscillation has its maximum amplitude near the stratopause level (45-50 kin) with a value of 25-30 m/sec. In the middle stratosphere (~ 35 kin), the amplitude is almost the same in magnitude (~ 10 m/sec) as that of the QBO at that level. It is interesting to note, however, that the maximum amplitude appears not to be at the equator but in the Southern Hemisphere subtropics (~ 10~ showing equatorial asymmetry (BELMONTand DARTT,1973; HOPKINS, 1975). Regarding the phase of the oscillation, the maximum in the westerlies first appears in the lower mesosphere just after the equinoxes and propagates downward. It is

Vol. 118, 1980) Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

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222

Isamu Hirota

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60 km level is the average of the various estimates, since there seems to be no large difference between them. The amplitude of CIRA (COSPAR International Reference Atmosphere) model (1972), evaluated from the monthly mean values for 0 ~ latitude, is somewhat large below the 60 km level compared with others, while in the upper mesosphere the CIRA model is primarily based on the results of GROVES (1972). In this regard, the CIRA model should be revised in the near future, at least for the tropical middle atmosphere.

(b) Mean temperature The mean temperature also exhibits a substantial semiannual cycle in the equatorial stratosphere (COLE, 1968; ANGELL and KORSHOVER,1970; NASTROM and BELMONT, 1975). Almost all of these statistics reveal that the semiannual temperature component has its maximum at 35-40 km in the tropics, the amplitude being 3-4~ The phase propagates downward from the lower mesosphere to the middle stratosphere. The appearance of this cycle in the equatorial stratosphere with an amplitude of several degrees has also been observed in the Nimbus 3 Satellite Infrared Spectrometer (SIRS) data for 1969-70 (FRITZ, 1974), in the Nimbus 4 Selective Chopper Radiometer (SCR) data for 1970-71 (BARNETT,1974) and in the Nimbus 5 SCR data for 1973-74 (MCGREGORand CHAPMAN,1978). On the other hand, regarding the tropical upper mesosphere, only a little is known about the semiannual temperature variation. In Fig. 3 is presented a rough estimate 100

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Vol. 118, 1980) Evidence of Semianlaual Oscillation in Tropical Middle Atmosphere

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4/2

5/I

6 0 84

t "

*

0 **'o

5o

6o

,os

Figure 4 Latitude-height variation of (a) amplitude (m/sec) and (b) phase (in semimonthly periods) of the semiannual zonal wind oscillation (BELMONTet al., 1974). of amplitude and phase based on a small number of rocket observations at Ascension Island, together with the results of NASTROM and BELMONT (1975) below 60 km and recent observations from the Nimbus 6 Pressure Modulator Radiometer (PMR) over the equator (CRANE, 1979). There seems to appear another maximum of the semiannual temperature oscillation between 70 and 75 km with an amplitude of about 6~ It may be interesting to note that the level of the temperature maximum is about 10 km lower than that of the zonal wind maximum in the upper mesosphere, similar to the case of the vertical distribution of the semiannual variation in the upper stratosphere. This is probably due to thermal wind balance between the mean zonal wind and temperature.

224

Isamu Hirota

(Pageoph,

(c) The semiannual cycle in the extratropical region Global analysis of rocketsonde data indicates another interesting aspect of the semiannual variation appearing in the extratropical middle atmosphere, as was first pointed out by AN6ELL and KORSHOVErt(1970). Further studies by BELMONTand DARTT (1973) and BELMONT et al. (1975) demonstrated that there is maximum amplitude of the semiannual zonal wind oscillation near 60~ in the mesosphere (Fig. 4a), as an extension of the 'half-yearly wave' in the stratosphere shown by van Loon et al. (1972). A similar analysis for temperature (NASTROMand BELMONT,1975) revealed that the maximum amplitude appears at polar latitudes in the middle stratosphere in agreement with van Loon's result. One of the most remarkable differences between the tropical and extratropical semiannual oscillations is the manner of the phase progression: as is clearly seen in Fig. 4b, the phase change occurs almost simultaneously in a deep layer of the polar atmosphere, in contrast to the phase propagation from higher levels to lower levels observed in the tropical region. This fact, together with the separation of amplitude maxima into tropical a n d polar latitudes, strongly suggests that the mechanisms of the two oscillations are quite different from each other. The semiannual cycle observed in the polar region is probably a consequence of mid-winter breakdown of the polar vortex associated with the stratospheric-mesospheric sudden warming. Therefore in this paper we hereafter confine ourselves to the tropical atmosphere.

4. Some theoretical considerations The inspection of observed features of the semiannual oscillation summarized in the previous section gives rise to some interesting problems concerning the driving mechanism of this phenomenon which require plausible theoretical explanations. As was pointed out earlier by REED (1966), there are two classes of forcing mechanisms: one which acts through the heat balance and the other through the momentum budget. Since the zonal wind and temperature fields are considered to be in thermal wind equilibrium for the long-term variation such as the semiannual cycle, the temperature fluctuation due to the seasonal change of heating might be responsible for the production of mean zonal wind variation through mean meridional circulations which maintain the wind and temperature fields in thermal wind equilibrium. In fact, the absorption of solar ultraviolet radiation by ozone in the tropical upper stratosphere must have a considerable semiannual component because of the double passage of the Sun over the equator. However, this possibility seems to have been ruled out as a consequence of a theoretical study of MEYER (1970). By using a diagnostic numerical model for the zonally symmetric flow similar to that of LEOVY (1964), Meyer has demonstrated

Vol. 118, 1980) Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

225

that the response of mean zonal wind to the semiannually varying heat source by solar radiation is negligibly small. As a result, he concluded that a semiannually oscillating momentum flux divergence is required to explain the observed zonal wind variation. Generally speaking; problems of the generation of mean zonal westerlies and easterlies at the equator should be dealt with separately. As regards the equatorial zonal westerlies, we have to explain the mechanism for the production of angular momentum which is greater than the absolute angular momentum of the Earth. Note that the problem of accounting for observed 'equatorial westerly accelerations' arises not only for the Earth's atmosphere but also for other fluids on rotating spheres such as the Jovian atmosphere and the solar photosphere. Since the Coriolis torque due to the mean meridional circulation cannot generate the westerly flow at the equator, an eddy momentum flux convergence must be required, in agreement with Meyer's conclusion. Then an important question arises as to what is the nature of the 'eddies' responsible for the westerly acceleration. In his numerical model, Meyer assumed that the horizontal eddy momentum flux was due to solar diurnal tides. However, HOLTON (1975) pointed out that the possibility of zonal wind acceleration by the tidal wave is doubtful because of the rapid and irregular change of the phase of the flux with height, which is incompatible with the observed uniform acceleration over a deep layer. Instead, Holton hypothesized that vertically propagating Kelvin waves may provide the westerly momentum source for the semiannual oscillation. In view of the fact that the westerly phase of the semiannual oscillation propagates downward as in the case of the quasi-biennial oscillation in the lower stratosphere, it seems reasonable to suppose that the mechanism responsible for the mean zonal westerly acceleration might be similar to that for the QBO. In this connection, let us briefly recall here the QBO theory, especially the role of Kelvin waves as a westerly momentum source, as proposed by LINDZEN and HOLTON (1968) and HOLTON and LINDZEN (1972): Kelvin waves propagate upward more readily when the mean zonal wind is easterly. An upward flux of westerly momentum is associated with the waves. When Kelvin waves reach a westerly shear zone, the Doppler-shifted phase velocity becomes small. Since the damping rate of Newtonian cooling increases with decreasing Doppler-shifted frequency, the waves tend to be absorbed by the mean flow rather rapidly due to radiative damping. As a result, the convergence of westerly momentum occurs there, which in turn gives rise to the downward propagation of the westerly shear zone. On the basis of the consideration for the dynamical properly of Kelvin waves mentioned above, HOLTON (1975) conjectured that only short-period Kelvin waves can penetrate into the upper stratosphere and lower mesosphere with weak absorption, to supply momentum for the westerly phase of the semiannual oscillation. As will be shown later, the existence of such a Kelvin wave at mesospheric levels has been confirmed observationally by HIROTA (1978, 1979).

226

Isamu Hirota

(Pageoph,

On the other hand, as for the zonal easterly acceleration, it is difficult to trace an analogy between the QBO and the semiannual oscillation: the easterly phase of the QBO is considered to be due mainly to the absorption of mixed Rossby-gravity waves and induced mean meridional motions. However, since mixed Rossby-gravity waves are highly susceptible to radiative damping, it is unlikely that they can propagate vertically up to mesospheric levels. Indeed there has been no indication of the existence of mixed Rossby-gravity waves in the equatorial middle atmosphere, either theoretically or observationally. Therefore a different mechanism should be considered. As mentioned earlier, the semiannual easterlies appear simultaneously throughout a deep layer without showing downward phase propagation. Morphologically speaking, the appearance of the easterlies at the equator seems to be merely a consequence of penetration of the summer rnesospheric easterlies into the winter hemisphere. This suggests the possibility of an interhemispheric coupling. In view of the predominance of planetary Rossby waves with long vertical wavelengths in the middle atmosphere of the winter hemisphere and the effect of 'critical line absorption' of the planetary waves shown by the theoretical studies of DmKINSON

TIME CHANGE

FEB17-19,1971

HeW:~(Km)

@

60 50

40

)

30

o

~t

.lo~

'o

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L

10'

10" ~5 Ix

'k;:\ "," /

!

'

'

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\\\\

I

;./+ - - ~+,

V \

.-"-,-.....

I/.,,IIV I 10'

/ 5

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ii 10

15

20

WAVELENGTH (KM)

Figure 5 An example of two-day difference of temperature (T) and zonal (U) and meridional (V) wind component (above) at Ascension Island. Power spectra of each component are shown as a function of vertical wavelength (below) (HIROTA,1978).

Vol. 118, 1980)

Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

227

(1968a,b) and others, it is likely that the horizontal momentum flux divergence due to the planetary waves is responsible for the easterly acceleration in the tropics. Some observational evidence of the hemispheric coupling relevant to the easterly phase of the semiannual oscillation is also shown in the following section.

5. Wave disturbances

During the course of studying the QBO, many efforts have been made to describe the characteristic features of large-scale wave disturbances in the lower stratosphere, with the aid of time-height section analysis and power spectrum analysis of balloon observations at several stations in the tropics. Results of these studies and their significance in relation to the QBO are summarized in a review by WALLACE (1973). However, regarding the equatorial upper stratosphere and mesosphere where daily balloon observations are not available, no attempt was made in those early studies to investigate wave disturbances, primarily because of the sparsity of data. Since the time-scale of the waves under consideration is of the order of a week or so, it is not adequate to apply conventional time-series analysis techniques to rocket data which have a coarse time resolution. More recently, significant evidence has been obtained observationally for the existence of large-scale waves in the tropical middle atmosphere, by using new techniques for analysing rocket and satellite data. Thus in the following we discuss the observed features of these waves in some detail.

POWER (U)

25 v -r

2o laJ

10

MONTH 0

J

F

M

A

M

J

J

A

S

0

N

D

Figure 6 Seasonal variation of power spectral density for the zonal wind component as a function of the vertical wavelength during the period of 1971 and 1972. Units are (m sec-a day-i)2 km (HIROTA, 1978).

228

Isamu Hirota

(Pageoph,

(a) Kelvin waves

In order to test the hypothesis that the vertically propagating Kelvin wave is responsible for the semiannual westerly acceleration, HIROTA (1978) tried to find evidence of Kelvin waves in the equatorial upper stratosphere and lower mesosphere by using rocket data at Ascension Island. Since the Doppler-shifted frequency of Kelvin waves is proportional to the vertical wavelength for a given zonal wavenumber, the short-period Kelvin waves, if they exist, must have a characteristic vertical scale longer than that of lower stratospheric Kelvin waves (6-10 km). On the basis of this consideration, Hirota applied a power spectral analysis, with respect to altitude, to the two-day difference values of wind and temperature for the height region between 25 and 60 km. The making of two-day differences removes the mean field, the long-term trend and the tidal components. An example of the result of such an analysis is shown in Fig. 5, in which a concentration of power spectral density of the zonal wind component and temperature can be seen at vertical wavelengths of 15-20 km. Long-term statistics for the four-year period (1969-72) indicate that the wave has a characteristic vertical scale of about 20 km and is associated with a strong power spectral density in the zonal wind component, with somewhat weaker power in temperature, but with little power in the meridional wind component. Therefore this wave is very likely to be identified as a Kelvin wave. Moreover, it is quite interesting to note that the power Spectral density of this wave shows a significant semiannual variation; as is seen in Fig. 6, the wave activity is stronger in January-February and July-August, corresponding to the easterly phase and the subsequent westerly acceleration in the upper stratosphere. However, it is difficult to obtain direct information about the phase velocity and zonal wavelength, and hence the period, of t h e Kelvin wave from an analysis based on single-station observations. Thus HIROTA (1979) made a further effort to determine the dominant zonal wavenumber and phase velocity of Kelvin waves in the equatorial middle atmosphere directly from global satellite observations by the Nimbus 5 SCR. For the purpose of detecting Kelvin waves from the SCR observations with coarse vertical resolution, a combination of radiances from the upper three channels of the SCR was made to fit a wave with a vertical wavelength of about 20 kin. The height region covered by these data extends from 20 to 60 km. By applying harmonic analysis and power spectral analysis to these data for the two years from 1973 to 1974, it was found that a Kelvin wave with zonal wavenumber one is prominent and moves eastward with a period of 4-9 days (Fig. 7). Note that this period is about a half of that ( ~ 15 days) observed in the lower stratosphere. It is also worth noting that the dominant period of Kelvin waves shows a semiannual cycle with the longest period occurring in January and July so that, because of the semiannual zonal wind variation, the Doppler-shifted phase velocity is almost constant from season to season. Regarding the Kelvin wave amplitude at the stratopause level, an estimate by

Vol. 118, 1980)

Evidence of Semiannual Oscillation in Tropical Middle Atmosphere westward 3 4

6

9

Period (day) 18 co 18

9

6

229

eastward 4

3

~F M i M J 3 i S O N D 3 ~F M A M J J A S 0 N D

-100

-50 0 Velocity (m/sec)

50

100

Figure 7 Seasonal variation of the power spectral density of radiance temperature waves of wavenumber 1 observed by the Nimbus 5 S C R over the equator. Thin dashed line denotes the climatology of the mean zonal wind over the equator at 50 k m h e i g h t (HmOTA, 1979).

HIROTA (1978, 1979) gives values of about 10 m/sec for the zonal wind component and about 5~ for temperature, which are large enough to produce the observed mean zonal wind variation. Quite recently, using the parameters of the Kelvin wave found by Hirota, DUNKERTON (1979) made a numerical model of the westerly accelerations associated with the semiannual zonal wind oscillation and demonstrated that such a Kelvin wave could indeed give rise to the observed accelerations.

230

Isamu Hirota

(Pageoph,

Apart from the detailed mechanism of the excitation of Kelvin waves, the fact that the short-period Kelvin waves have not been observed yet in the lower stratosphere by the conventional time-series analysis of balloon data can be explained by their vertical propagation: as such waves propagate upward with weak absorption, they only need to have a small amplitude in the lower levels. A rough estimate based on kinetic energy conservation between the tropopause (~ 100 mb) and stratopause (~, lmb) yields amplitudes of the order of 1 m/sec for the zonal wind component at the tropopause, which may be masked by longer period Kelvin waves at that level. In conclusion, although there still remain some questions concerning the quantitative reliability of rocket and satellite observations, it can be said without doubt that the Kelvin waves play an essential role in producing the semiannual westerly flow in the upper stratosphere and lower mesosphere.

(b) Planetary Rossby waves The tropical semiannual zonal wind oscillation is not always regular but shows a significant year-to-year variation in strength. Based on the long-term statistics of global rocket data for about 10 years, HOPKINS(1975) found that the variance of the monthly mean zonal wind at the tropical stratopause is a function of season with maximum occurring just after the solstices in the easterly regime of the semiannual cycle. By computing correlation coefficients of zonal wind anomalies between the tropical and other regions, Hopkins further demonstrated that the deviations of the individual monthly mean zonal wind from the mean monthly zonal wind in the easterly regimes of the tropical semiannual cycle are positively correlated with those in the higher latitude winter hemisphere. This evidence suggests coupling between the equatorial stratospheric easterlies and the winter hemispheric circulation. Thus, by taking account of the predominance of planetary Rossby waves in the winter stratosphere and their dynamical properties, Hopkins hypothesized that the tropical semiannual easterlies are a result of the zero-wind line absorption of planetary waves. The observed equatorial asymmetry in the semiannual cycle as denoted earlier also seems to support this hypothesis, because the wave activity in the Northern Hemisphere winter is apparently stronger than that in the Southern Hemisphere winter. Planetary wave propagation from the winter hemisphere into the tropical stratosphere, which was not directly detected in the data from the sparse rocketsonde network, has been convincingly substantiated by the analysis of global satellite observations (BARNETT, 1975; HIROTA, 1976). Using infrared radiation measurements by the Nimbus 5 SCR during the 16-month period from December 1972 to May 1974, BARNETT(1975) studied the structure and behavior of quasi-stationary planetary-scale temperature waves in the upper stratosphere, and found that the zonal wavenumber-one component shows a 6-month cycle

Vol. I 18, 1980) Evidence of Semiannual Oscillation in Tropical Middle Atmosphere - -

WAVE A M P ~ )

___

ZONAL WIND (50km)

231

ZONALWIND

WAVEAMF

(K)

(m/s) +50

I.r

\,, 0.5

//

E /

,, \ \

E

/ -/------

\\ \

~

E N

-50 MONTH--------

Figure 8 Semiannual cycle of monthly root mean square wave amplitude of wavenumber 1 at Nimbus 5 SCR Ch.B12 (averaged for two years), and the mean zonal wind at 50 km height over the equator (HIRoTA, 1976). in the tropical stratosphere with maxima near the equinoxes. HIROTA (1976) made a global analysis of SCR data during the two years 1973 and 1974 for both stationary and transient waves, and confirmed that the 6-month periodicity is observed in the tropical latitudes for wavenumber one (Fig. 8). Another notable feature of this wave is the latitudinal variation of the phase pattern. As is seen in Fig. 9, the phase is continuous from the late winter (Northern Hemisphere) pole across the equator to about 30 degrees in the opposite hemisphere with a north-east to south-west tilt, and after the reversal occurs the phase tilts from south-east to north-west. This result is an extension of the early observational study by HIROTA and SATO 0969) which showed the westward tilt of the planetary wave axes with decreasing latitude in the winter stratosphere. HIROTT (1976) also reconfirmed the seasonal change of phase inclination in both hemispheres throughout the whole stratosphere. The results of the satellite observations mentioned above can be accounted for in the light of the theory of planetary Rossby wave propagation. The wave forced from the mid-latitude troposphere is capable of propagating upward and equatorward when the mean zonal wind is relatively westerly. In this regard the maximum wave activity in April and October is consistent with the fact that the zonal wind in the equatorial upper stratosphere is westerly only near the equinoxes. Conversely, near the times of the solstices, when the mean zonal flow is easterly, the wave activity must be weak at the equator due to the zero-wind line absorption occurring in low latitudes of the winter hemisphere. The wave minima that are indeed observed after the solstices (Fig. 8) are therefore considered to be the manifestation of this process. Moreover, since the westward tilt of phase with decreasing latitudes is indicative of the westerly momentum transport toward the winter pole, the zero-wind line absorption gives rise

232

Isamu Hirota

(Pageoph,

The deviation of Nimbus 5 SCR Ch.B12 equivalent temperature from the zonal mean for (a) 9-23 March 1973, (b) 23 April-7 May 1973 (BARN~T'r,1975).

Vol. 118, 1980)

Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

233

to a momentum flux divergence, which in turn causes the mean zonal easterly acceleration. Therefore, in agreement with Hopkins' argument, we can conclude that the planetary Rossby waves in the winter hemisphere are the most likely source of easterly momentum for the tropical semiannual oscillation.

(c) Upper mesospheric waves Above rocketsonde levels, very little is known about the waves that might be responsible for the semiannual zonal wind oscillation near the equatorial mesopause level, neither has there been any theoretical prediction of the mechanism. However, recent progress in satellite observations makes it possible to investigate the upper mesospheric waves in a global context. From infrared radiation measurements of the Nimbus 6 PMR for a one-month period during the Northern Hemisphere winter, HIROTA and BARNETT (1977) found that planetary waves with zonal wavenumber one and two have significant amplitudes in the mesosphere. HIROTA (1978) made a further analysis of the seasonal variation of planetary wave amplitudes at mesospheric levels. Figure 10 shows a latitude-time section o f zonal wavenumber one in the temperature field based on the 10-day average for the P M R channel 3000 which gives the mean temperature of a layer near the mesopause. It is found that planetary waves at the mesopause level show an apparent semiannual variation in the

PMR

W N " I O1.3000

3

60

4Q 20 Ell.

@.2

20 40

~

2

805

l

A 1975

$

O

N

D

J F ' M 19"/6

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J

Figure 10 Latitude-time diagram of 10-day averaged wave amplitude (K) for wavenumber 1 observed by Nimbus 6 P M R Ch.3000. E and W over the equator denote the phase of maximum easterly and westerly winds of the semiannual component at 80 k m height'(HIRoTA, 1978).

234

Isamu Hirota

(Pageoph,

ZONAL WIND JICAMARCA ( 12.0~

20 r

..

.~-

)

~..o

..;...~_,j

" ~-~,.&:

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r -20 L

20[

- _ _ -

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.

.

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.~y

O. The ' m , ' term represents westward tilt o f the wave. W i t h dissipation there is no value o f h which will p e r m i t p e r m a n e n t free oscillations. However, since we only wish to o b t a i n a feeling for the i m p o r t a n c e o f t h e r m a l d a m p i n g on the vertical structure o f the waves we are discussing, we will assume that when h = ~'H0 we have a free wave in the sense m e n t i o n e d in the beginning o f this section. W e shall limit our discussions to the lower s t r a t o s p h e r e where we have observations o f vertical structure. I f P is the p e r i o d o f the wave then (1/2~)P (a-l) . F o r the 5-day wave c~ ~ 10 -2 so t h a t M - m, cos 89 -

1 and sin 89 0 and c~F/OZ = O. |t is profitable first to consider the following flux relationships derived in B77: p oz (pw'~') = u

V

4 ' 4 ; - (~;)~

~v -4z ~ = f ~1 [F W ' 4 ' + k~4 ' 4~]. '

(30

(32)

In the case where kr = O, (31) gives pW'4' = c~

(33)

where C is independent of Z. In particular, for a trapped wave C is zero. Referring to (32) we then see that, in the absence of radiative damping, the existence of a horizontal heat flux depends on the wind field being such as to allow a vertically p r o p a g a t i n g wave. Similar considerations apply to the vertical heat flux, as can be seen by referring to (28). When kT r 0, however, (31) shows that the d a m p i n g induces a convergence (or divergence) of vertical wave energy flux, so that the wave energy flux cannot be zero t h r o u g h o u t the region, whatever the wind field. Consequently, from (32) and (28), the horizontal or vertical heat fluxes cannot be zero either. Thus, in the case of a trapping wind field, any heat fluxes which occur are entirely radiatively induced. In the simple case where ~: = 0, the influence of d a m p i n g on the vertical heat flux is immediately apparent: the flux is downward and it goes to zero as k~-+ 0, whether the wave be trapped or propagating. Thus we conclude that the mean forcing function (7 resulting from eddy heat fluxes is in general partly induced by radiative d a m p i n g and partly a result of the vertical wave energy propagation, but in the case of a trapping wind field t~ is entirely radiatively induced. Considering the m o m e n t u m fluxes (29) and (30), we see that no information about these fluxes can be obtained without a' knowledge of ~b~.To examine how this quantity is determined we assume perturbation solutions of the form (u', v', W', ~b') = (~, ~, ~, q) e ~/2) e i ~ .

(34)

272

J.R. Bates

(Pageoph,

The perturbation equations (8)--(11) then reduce to a single equation in 0: 0~

-

~20

=

(35)

0

where 1[

tO~ : . 4(tO~ - - tO~)]

n~ = ~, 1 -

,,,(l

-

i~)

1

with tO

--

a cos 0

2Brf~ toe - sin 2 0 ~=

kr mto

From B77 we know that toc is the critical angular velocity for trapping. The 0dependence of this quantity can be expected to play an important role in determining the 0-dependence of ~2, and hence in determining q~0.The damping coefficient enters the governing equation only through the parameter ~. If this parameter approaches unity, the damping can be expected to have a strong influence on the dynamics of the perturbations. For a wind field of 50 m/sec, representative of mean conditions in the upper stratosphere in winter, with kr = (1.5 day) -1 (the maximum value which has been suggested for the radiative damping augmented by the photochemical acceleration) we find that :~ = 0.69/m. In spring and autumn, when the mean circumpolar vortex is weaker, ~ may attain even larger values than this. Thus it is to be expected that radiative damping will indeed play an important role in the dynamics of the perturbations and the consequent interactions with the mean flow.

4. An exact solution for the case o f constant superrotation

In this section we consider an idealized situation where above a given base level (Z = 0) the atmosphere is in constant westerly superrotation (to = const > 0), and kT and I" are constant. The governing equation for the perturbations is then given by (35) with

,[,

t*2 = 5, where

__;,,] ~c

(I

36,

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

273

In addition we assume that the geopotential perturbation at Z = 0 is independent of latitude. U n d e r these conditions the solution for Z > 0 will vary with latitude only through 0-dependence of o)c. Setting

and choosing the positive real part we have

~, = 2-~J~[~ + 012 + ~ ) ~ 1 ~ ~, = - v d ( 2 l z . )

where

89 (46) i.e. unless o5c > 4 (47)

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

275

and > 2/(0% - 4) I/~.

(48)

(v) As N --> 0 the behaviour of the fluxes depends on the nature of the wind field. F o r a ' p r o p a g a t i n g ' wave (~c > 1), W'~', and 6;v tend to zero, but all the other fluxes and forcing functions tend to non-zero values. F o r a ' t r a p p e d ' wave (~c < 1), all the fluxes and forcing functions tend to zero. (vi) As N --->oo all the fluxes and forcing functions tend to zero. In Figs. 1-6, the fluxes and forcing functions are shown as functions of ~ for various values of ~c, taking m = 1, Z = I, 0 = 7r/4. F r o m these figures it is clearly seen that all the fluxes are strongly dependent on ~ , particularly in the region 0 < ~ < 1. In the case of a ' p r o p a g a t i n g ' wave, the effect of increasing ~ is generally to decrease the magnitudes of the heat and m o m e n t u m fluxes, except in the case of the vertical heat flux, whose magnitude increases with ~ for small ~ . In the case of a ' t r a p p e d ' wave, the magnitudes of all the fluxes increase from zero to attain m a x i m u m values for ~ < 1. The forcing functions G and F are likewise strongly dependent on ~ . In the cases shown Ga outweighs Gv, but this need not be so for all values of the parameters. F r o m Fig. 4 it is seen that ffH and -Fv are c o m p a r a b l e in magnitude for small ~ . An interesting feature shown in Fig. 6 is that for certain wind fields, the forcing function F can increase with ~ for small ~ even in the case of a ' p r o p a g a t i n g ' wave. We note that in all cases shown the sign of G is negative, implying by equation (25) a m e a n diabatic cooling. The eddy heat flux divergences thus force a positive

1-0 Solid curves: ~-~0~' v'---Tz Do,shed curves: ~-~T a2~2 w-~'z ,C

~_c x.

=75 _ _g

-.L,~

I

I

o

I

2

3

Figure 1 The horizontal and vertical eddy heat fluxes.

276

J . R . Bates

(Pageoph,

1"0

0

,. . . . _ _ - ~ z _ - ~ = = ~ - = = = ~ : ~ - - - - 2 2 = = - - = = - =

-'S /

/ I

-1~0 -1"5

t I I I

a2~' u~

Solid curves: ~-~2

/

o3~ z

Dashed curveS: - ~

u-~"

-2"0 I 2

1

I 3

Figure 2 The horizontal and vertical eddy momentum fluxes.

0"6

.L~c=t~ __...~-.-__~:~

- - - -

~t= 1'2 = -____-~.

~c = .75 . . . . . .

0

-1-0 So lid curves: r02~ g.

Ooshed curves: ~-~2 o2~ ~,

-2.0

-3.0

I 1

I 2

I 3

Figure 3 The components of the thermal forcing function.

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation 0

-2 -3

- 5 ~F-/ /

1

.Solid . . . . . .curves: . . . . . . ~a3f22 T g .~

-6

Doshed urves:

_7'I 0

I I

I 2

I 3

Figure 4 The components of the momentum forcing function.

0

It..~

-2

-3

I 1

I 2

Figure 5 The thermal forcing function.

I 4

277

278

J. R. Bates

(Pageoph,

-7 -8

I

2 Figure 6 The momentum forcing function.

deviation of the mean zonal temperature from its radiative equilibrium value. With observed values of the perturbation amplitudes in the stratosphere and with a representative value of the thermal forcing function taken from Fig. 5, the eddy-induced cooling rate can be of appreciable magnitude (e.g. taking a geopotential perturbation of amplitude 500 m, implying q~(0) = 4.9 x 103 m2/se@, with a forcing function given by [a2f2/O(0)2]G = - 1 we obtain from (25) a cooling rate of 2.5 K/day for wavenumber one alone). Similarly from Fig. 6 we see that for all cases considered the sign of _Pis negative, implying by equation (21) an equatorward meridional velocity. Again taking q~(0) = 4.9 x 103 m~/sec 2 and with a representative momentum forcing function (from Fig. 6) of [a3f~2/qb(O)2]ff= --3 we find for 0 = ~r/4 that g = - 0 . 5 m/sec.

5. Conclusions

The steady-state forcing of the mean flow in the middle atmosphere by planetary waves has been investigated under the assumptions of quasi-geostrophic motion of Type 2. It has been shown by scaling arguments that under these assumptions the mean zonal flow is geostrophically balanced, a mean meridional circulation is directly forced by the eddy momentum flux divergences and a mean diabatic heating is forced by the thermal forcing function resulting from eddy heat fluxes. The scaling arguments (and some explicit calculations with the scaled equations) indicate that the contribution

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

279

of the vertical eddy fluxes to the forcing of the mean flow can be of the same order as that of the horizontal eddy fluxes. This leads one to question the neglect of vertical eddy fluxes in the numerical models of the middle atmosphere which have been referred to in the Introduction. To gain insight into the fluxes and the resulting forcing functions, an idealized situation has been considered where the atmosphere above a given level is in a state of constant westerly superrotation and has a constant static stability and radiative damping coefficient. W i t h a geopotential perturbation independent of latitude prescribed at the base level, an analytical solution has been obtained which allows all the fluxes and forcing functions to be evaluated. For a given wave amplitude at the base, it has been shown that the eddy fluxes and forcing functions depend critically on the strength of the mean flow - in particular, on whether it is greater or less than the critical value for wave t r a p p i n g - and on the strength of the radiative damping. The influence of the damping is measured by a parameter ~ which is the Newtonian cooling coefficient divided by the product of the wavenumber and the mean superrotation. For a wind field such as to give wave trapping, no eddy fluxes of heat or momentum, and consequently no forcing of the mean flow, occur in the absence of radiative damping. As ~ increases from zero, however, eddy fluxes and forcing functions are generated which reach maximum absolute values for ~ in the interval (0, 1) and decay to zero for large ~ . For a wind field such as to allow wave propagation, eddy fluxes of heat and momentum (though not a vertical eddy heat flux) occur even in the absence of radiative damping; the horizontal eddy heat flux (directed poleward) is a consequence of the upward flux of wave energy, in accordance with the well-known result of ELIASSEN and PALM (1960), while the horizontal and vertical momentum fluxes (the former always directed poleward) are a consequence of the variation with latitude of the critical superrotation for trapping. The consequent (undamped) forcing functions induce a mean meridional circulation and a mean diabatic heating. [The fact that an undamped standing wave propagating through a steady mean flow should force a mean diabatic heating may at first sight appear to contradict the Charney-Drazin Theorem (CHARNEV and DRAZIN, 1961; BOYD, 1976; ANDREWS and MClNTYRE, 1976). That this is not so, however, is shown in Appendix 2.] Radiative damping has been shown to have a very strong influence on the magnitudes of the eddy fluxes and forcing functions for a propagating wave, particularly for .~ in the region (0, I). In general, for small values o f , ~ the effect of the damping is to cause a rapid decrease in the magnitude of the forcing. Under certain circumstances, however, the damping may actually increase the magnitude of the forcing for small values of .N, just as in the case of a trapped wave. This sensitivity of the eddy forcing of the mean flow to the value of.N, considered in conjunction with the balance of terms in the mean thermodynamic equation indicated by the planetary scaling, suggests that the radiative damping coefficient

280

J.R. Bates

(Pageoph,

for the waves is a crucial parameter in determining the mean circulation of the middle atmosphere. Any influence that leads to changes in the ozone concentration in the middle atmosphere will necessarily result in changes in the radiative damping coefficient, both directly through changing the mean temperature and indirectly through modifying the photochemical acceleration. For similar reasons the damping coefficient will be influenced by any changes in the intensity of solarultraviolet radiation, whether due to solar fluctuations or to seasonal changes in the zenith angle. Obviously, to study the full dynamical effects of any such changes it is necessary to consider the total circulation, i.e. the mean flow, the waves and the wave-mean flow interaction. Model calculations described in B77 have suggested that the tropospheric climate may change as a result of changes in the mean wind field in the stratosphere. This suggestion has been corroborated by the more comprehensive model calculations of AVERY (1978) and by calculations referring to the stratosphere alone by SCHOE~ERL and GELLER(1977). In these studies it was found that the sensitivity of the tropospheric planetary waves to changes in the radiative damping coefficient at high levels was of a lesser order than that associated with changes in the mean wind field. The mean wind fields, however, were prescribed independently of the radiative damping, whereas the results of the present paper suggest that the mean wind fields may to a large extent be determined by the wave-mean flow interaction, which in turn, is sensitively dependent on the radiative damping. It is possible, therefore, that the overall climatic sensitivity to changes in the radiative damping rate in the middle atmosphere may be greater than has previously been suggested. All dynamical reasoning about the middle atmosphere and its possible role in the general circulation, whether based on numerical or analytical studies, must remain tentative in the absence of more thorough observational knowledge. There is an urgent need for accurate estimates of the wave fluxes of heat and momentum and the consequent wave interactions with the mean flow.

Appendix I List of Symbols a Earth's radius Burger number (F/a2f22) Br Specific heat of dry air at constant pressure Cp Coriolis parameter (2~2 sin 0) f Radiative damping coefficient k~ 1

L~( )

p c:IZ [P( )]

Lo( )

a cos 0 70 [( ) cos 0]

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation L~( ) m

P Po

Q' 0 R

t

T T* U

t

V'

W' W Z P

8/8x

a c o s 2 0 00 [( ) c ~

0]

Zonal wavenumber Pressure Pressure at base of region of interest (constant) Perturbation heating per unit mass Zonally averaged heating per unit mass Gas constant for dry air Radiative damping parameter (kr/m~o) Time Zonally averaged temperature Radiative equilibrium temperature Perturbation westerly wind component Zonally averaged westerly wind component Dimensionless value of Complex amplitude of u' Perturbation southerly wind component Zonally averaged southerly wind component Complex amplitude of v' Perturbation component of W, dZ/dt Zonally averaged value of W, dZ/dt Complex amplitude of W' - In (P/Po) Static stability parameter [R(?;T'/~Z + KT)] I /~ a cos 0 Oh

0

Dimensionless parameter measuring superrotation Latitude

K

R/C~

h

Longitude Index of refraction divided by i Imaginary part of/z Real part of Perturbation geopotential Zonally averaged geopotential Complex amplitude of r e -z~2 Streamfunction for mean meridional flow Superrotation (9/a cos 0) Critical superrotation for trapping (2Brf2/sin 2 0)

8

F F~ FT

~p x

ose

O)c/r

Earth's rotation rate

281

282

I . R . Bates

(Pageoph,

Appendix 2 The C h a r n e y - D r a z i n theorem states that a simple harmonic wave propagating through a mean flow does not interact with the mean flow in the absence of dissipation, critical levels and thermal forcing. In the present context, where we are considering the particular case of a standing wave in a mean flow which has no critical levels, this theorem implies that setting Q' = ~) = 0 necessarily gives fit = 0, ~zt = 0. If we begin, as here, requiring that in a certain region fit = ~ t = 0 does it not follow that if Q' -- 0 (i.e. ~ = 0) in that region, we must also have Q = 07 Though such a conclusion would certainly be consistent with the C h a r n e y - D r a z i n theorem, we shall show that in general it does not hold. We argue from the primitive equations, using Boyd's (1976) paper. Setting u~ = ~ t = Q' = 0, and also taking ~ = 0 for simplicity, Boyd's equations (2.32) and (2.34) give L~(X) = L~(v'~f'z/r)

(A.1)

Lo(x) = Lo(v'~',/F) - KQ/P.

(A.2)

(Here we have replaced N ~ by I~ and have included Q; it can easily be shown that Boyd's equations will tolerate this degree of generalization.) Integrating (A. 1) gives - -

v'd~'~/r

-

P0

X = 7

[v'C'~/r

-

X]0

(A.3)

where the subscript 0 denotes values at Z = 0. Substituting (A.3) in (A.2) gives = (e~/K)[Lo(v'd?---~'~) -

rLo(X)]o

= (e~'/, 0 for o3C > I (only the case I is of concern here, since only then do we find a non-zero with .# = 0) and thus (25) gives Q = dHl~.

(A.5)

This is consistent with (A.4) if Wo = 0 and GH = e:Gn(0).

(A.6)

We see that (A.6) is indeed satisfied by (42) in the limit ,# -+ 0. We therefore conclude that obtaining a non-zero Q from the scaled equations for steady planetary flow when Q' = 0 is consistent with the properties of the primitive equations and involves no violation of the Charney-Drazin theorem.

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

283

REFERENCES ANDREWS, D. G. and MCINTYRE, M. E. (1976), Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sci. 33, 2031-2048. AVERY, SUSAN K. (1978), The tropospheric forcing and vertical propagation of stationary planetary waves in the atmosphere, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 145 pp. BATES, J. R. 0977), Dynamics of stationary ultra-long waves in middle latitudes, Quart. J. R. Met. Soc. 103, 397-430. BLAKE, D. and LINDZEN, R. S. (1973), Effect of photochemical models on calculated equilibria and cooling rates in the stratosphere, Mort. Weather Rev. 101, 783-802. BOYD, J. P. (1976), The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum, J. Atmos. Sci. 33, 2285-2291. BURGER, A. P. (1958), Scale considerations of planetary motions in the atmosphere, Tellus 10,

195-205.

CHARNEY,J. G. and DRAZIN,P. G. (1961), Propagation of planetary scale disturbances from the lower into the upper atmosphere, J. Geophys. Res. 66, 83-109. CHEN, T-C. and RAMANATHAN, V. (1978), A numeircal simulation of seasonal stratospheric climate. Part H. Energetics, J. Atmos. Sci. 35, 615-633. DICKINSON, R. E. (1969), Vertical propagation of planetary Rossby waves through an atmosphere with Newtonian cooling, J. Geophys. Res. 74, 929-938. DICKINSON, R. E. (1973), Method of parameterization for infrared cooling between altitudes of 30 and 70 kilometres, J. Geophys. Res. 78, 4451-4457. ELIASSEN, A. and PALM, E. (1960), On the transfer of energy in stationary mountain waves, Geofys. Publ. 22, No. 3, 22 pp. HARTMANN~ D. L. (1976a), The structure of the stratosphere in the southern hemisphere during late winter 1973 as observed by satellite, J. Atmos. Sci. 33, 1141-1154. HARTMANN, D. L. (1976b), The dynamieal climatology of the stratosphere in the southern hemisphere during late winter 1973, J. Atmos. Sci. 33, 1789-1802. HOLTON, J. R. (1975), The dynamic meteorology of the stratosphere and mesosphere, Met. Monographs 15, No. 37, American Met. Soc., 218 pp. HOLTON, J. R. and DUNKERTON, T. (1978), On the role of wave transience and dissipation in stratospheric mean flow vacillations, J. Atmos. Sci. 35, 740-744. HOLTON, J. R. and LINDZEN, R. S. (1972), An updated theory for the quasi-biennial cycle of the tropical stratosphere, J. Atmos. Sci. 29, 1076-1080. NEWELL, R. E., KIDSON, J. W., VINCENT, D. G. and BOER, G. J. (1972), The generalcirculation of the tropical atmosphere and interactions with extratropical latitudes, VoI. I, M1T Press, Cambridge, Massachusetts and London, England, 258 pp. NEWELL, R. E., KIDSON, J. W., VINCENT, D. G. and BOER, G. J. (1974), The general circulation of the tropical atmosphere and interaction with extratropical latitudes, Vo[. 2, MIT Press, Cambridge, Massachusetts and London, England, 371 pp. PHILLIPS, N. A. (1963), Geostrophic Motion, Revs. of Geophys. 1, 123-176. PRINN, R. G., ALYEA, F. N. and CONNOLD, D. M. (1978), Photochemistry and dynamics of the ozone layer, Ann. Rev. Earth Planet. Sci. 6, 43-74. RAMANATHAN, V. and GROSE, W. L. (1978), A numerical simulation of seasonal stratospheric climate, Part 1. Zonal temperatures and winds, J. Atmos. Sci. 35, 600-614. SCHOEBERL, M. R. and GELLER, M. A. (1977), A calculation of the structure of stationary planetary waves in winter, J. Atmos. Sci. 34, 1235-1255. SCHOEBERL, M. R. and STROBEL, D. F. (1978), The zonally averaged circulation of the middle atmosphere, J. Atmos. Sci. 35, 577-591. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhhuser Verlag, Basel

A Numerical Model of the Zonal Mean Circulation of the Middle Atmosphere t) By JAMES R. HOLTON a n d WILLIAM M. WEHRBEIN2)

Abstract- The annual cycle of the zonally averaged circulation in the middle atmosphere (16-96 kin) is simulated using a numerical model based on the primitive equations in log pressure coordinates. The circulation is driven radiatively by heating due to solar ultraviolet absorption by ozone and infrared cooling due to carbon dioxide and ozone (parameterized as a Newtonian cooling). Since eddy fluxes due to planetary waves are neglected in the model, the computed mean meridional circulation must be interpreted as the diabatic circulation, not as the total eulerian mean. Rayleigh friction with a short (2-4 day) time constant above 70 km is included to simulate the strong mechanical dissipation which is hypothesized to exist in the vicinity of the mesopause due to turbulence associated with gravity waves and tides near the mesopause. Computed mean winds and temperatures are in general agreement with observations for both equinox and solstice conditions. In particular, the strong mechanical damping specified near the mesopause makes it possible to simulate the cold summer and warm winter mesopause temperatures without generating excessive mean zonal winds. In addition, the model exhibits a strong semiannual cycle in the mean zonal wind at the equator, with both amplitude and vertical structure in agreement with the easterly phase of the observed equatorial semiannual oscillation. Key words: Zonal mean circulation; Diabatic circulation; Rayleigh friction; Equatorial semiannual oscillation.

1. Introduction The general circulation of the middle atmosphere (here taken to be the region of the atmosphere between a b o u t 30-90 km) differs dramatically from that of the lower atmospheric layers. The overall mean circulation of the middle atmosphere is thermally driven by the absorption of solar ultraviolet radiation in the ozone layer. The net radiative heating which arises from the difference between this solar heating and the emission of infrared radiation by water vapor, c a r b o n dioxide, and ozone has strong meridional and seasonal variations. At the solstices there is a m a x i m u m net heating near the s u m m e r pole and a m a x i m u m net cooling near the winter pole. This differential radiative drive has a m a x i m u m amplitude of several degrees per day centered near the stratopause at a b o u t 50 km. The mean meridional circulation driven by this 1) Contribution No. 497, Department of Atmospheric Sciences, University of Washington, Seattle. 2) Department of Atmospheric Sciences, University of Washington, Seattle, Washington 98195, USA.

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

285

8O

80 4

o

*6

3

70

70 l

I

60.

b6o

50-

-50

4400-

.40

7

30

30 90= N JULY

dANUARY

0 LATITUDE

9 0 e S JANUARY I, I.

JULY

7o- r~"

v

/

~._~'~-..~~"'~~

j

90 e S JANUARY 90"

N JULY

I,

I.

~ -

~

- -

/

~

0

I. 9 0 "

--"-:=--~o

L

/ / / -

LATITUDE

\

I, 9 0 ~

-

~'~

,,Io'//

JANUARY JULY

I.

I. 9 0 "

N

9 0 =' $

Figure 1 Latitude-height sections of the observed solstice season mean zonal wind distribution (m s-z, upper frame) and zonally averaged temperature distribution (K, lower frame). After C I R A (1965).

286

James R. Holton and William M. Wehrbein

(Pageoph,

heating distribution consists of a single thermally direct cell with rising motion in the summer hemisphere, sinking in the winter hemisphere, and a compensating meridional flow directed from the summer to the winter hemisphere?) The Coriolis torque associated with this meridional flow generates mean zonal easterlies in the summer hemisphere and mean zonal westerlies in the winter hemisphere as illustrated in Fig. l. The corresponding temperature field, which to a good approximation is in thermal wind balance with the mean zonal winds, is also shown in Fig. 1. Most observational and theoretical studies of the general circulation of the middle atmosphere have emphasized solstice conditions. However, because of the seasonal reversal of both the mean zonal and mean meridional wind fields it is clear that the equinoctial circulation regime must differ substantially from solstice conditions. In fact, the radiatively driven mean meridional circulation at the equinoxes is qualitatively similar to the diabatic mean meridional circulation in the troposphere. That is, there is rising motion in the equatorial zone, poleward meridional drift in both hemispheres, and subsidence near the poles. Thus, the Coriolis torque generates mean westerlies in both hemispheres during this season, as illustrated in Fig. 2. The corresponding mean temperature profile, also shown in Fig. 2, features temperatures decreasing from the equator toward both poles throughout most of the middle atmosphere, as required for thermal wind balance. The first attempt to partially model the general circulation of the middle atmosphere was due to MURGATROYD and S~NGLETON(1961). They used the net radiative heating fields computed earlier by MURGATROYDand GOODY (1958) to diagnostically compute the mean meridional circulation subject to the assumption that adiabatic heating (cooling) by the mean vertical motion exactly balanced the imposed radiative cooling (heating). Their computed mean meridional circulations for solstice and equinox conditions were qualitatively similar to those described above. Their model, however, was based entirely on heat balance considerations. They did not determine whether their derived mean meridional circulations were consistent with the observed zonal momentum field. The momentum budget of the mean zonal flow in the middle atmosphere was first studied theoretically in the classic paper of LEOVV 0964). Leovy divided the radiative heating into two parts: an 'external' heating which was a specified function of location and season, and an 'internal' heating which he assumed was proportional to the deviation of the zonal mean temperature from the standard atmosphere value. Thus, the n e t radiative heating in his model depended indirectly on the computed zonal mean circulation (through the temperature dependent cooling term). Leovy's model employed a linearized version of the zonally averaged dynamical equations. The annual cycle was included by specifying a sinusoidal time dependence with a period of one year. He found that even in the presence of this imposed annual :3) Superposed on this diabatic circulation in the winter hemisphere there may be an oppositely directed eddy driven mean meridional motion. Thus, the total eulerian mean meridiona[ flow may differ from the diabatic circulation described here.

Vol. 118, 1980)

287

A Numerical Model of the Zonal Mean Circulation

\ 60.

1

/

~ 50-

80

t

.70

60

"50

40- ~

94 0

30

, gO" 90 e

$ APRIL I. N OCTOBtR I.

80

30

0 LATITUOE

~zoo-~

'

APRIL I. 90 e OCTOBER I. 90"

'

~.

,

ZlO"

~ 7 0

50

Z70.

t250r 40

80

~210"

70-220-

50 -

~ ]

"~40

30 ~ 90" S APRIL

' I.

90" N OCTOBER I.

%

'

--I

~

250'

i

/"

/-r

0

APRIL

LATITUDE

OCTOBER

13o I

90= N

I 90 ~ S

Figure 2 Latitude-height section of the observed equinox season mean zonal wind distribution (m s-1, upper frame) and zonally averaged temperature distribution (K, lower frame). After C I R A (1965).

288

James R. Holton and William M. Wehrbein

(Pageoph,

cycle, substantial mechanical dissipation was required to prevent the Coriolis torque of the radiatively driven mean meridional circulation from generating excessively strong mean zonal flows. He recognized that at least part of this required damping might be due to eddy momentum fluxes associated with large scale motion systems, and that the same motions would also produce substantial eddy heat fluxes. However, since insufficient data were available to determine the magnitudes and distributions of these fluxes, Leovy parameterized their effects in the simplest possible fashion by including a Rayleigh friction damping term in the zonal momentum equation, and by combining the effects of the eddy heat flux divergence and the temperature dependent radiative cooling into a single Newtonian cooling term in the thermodynamic energy equation. In order to obtain analytic solutions with his linearized model, he specified constant values for the mechanical and thermal damping coefficients. For simplicity, he also assumed that these Rayleigh friction and Newtonian cooling coefficients were equal. He found that in order to produce realistic solstice season mean zonal flow profiles with this model a rather large damping rate (0.743 x 10 -6 s-1) was required. Even with this very short damping time ( ~ 15 days)the computed winter solstice mean zonal flow exceeded 120 m s -1 at 72 km, which is substantially larger than the observed 80 m s -1 given in CIRA (1965). Despite the many simplifications inherent in Leovy's linearized model, he did succeed in qualitatively simulating the essential features of the observed solstice circulation described above. This qualitative agreement between the model and observations suggests that Leovy's simple parameterization of the eddy flux divergences in terms of linear damping may be adequate for simulating the zonally averaged circulation in the upper stratosphere and the mesosphere. Indeed, SCHOEBERL and ST~OBEL(I 978) have shown that with an improved radiative heating formulation and height dependent damping the Leovy model can produce quite realistic mean wind fields. However, simulation of important features of the mean circulation in the lower stratosphere, such as the polar night jet and the quasi-biennial oscillation, probably requires a three-dimensional model in which large scale eddies are computed explicitly. There have been a number of attempts to model various aspects of the general circulation of the middle atmosphere using three-dimensional numerical models. The most sophisticated such models (ile., general circulation models based on the primitive equations) have been limited in vertical extent to the troposphere and lower stratosphere (at least in works published to date). For example, MANABEand MAHLMAN (1976) have used the G F D L model to study the seasonal cycle in the stratosphere below the 10 mb (-~32 kin) level. KASAHARAet al. (1973) have used the NCAR model to simulate the lower stratospheric circulation, but only for perpetual January conditions. The three-dimensional model of most relevance to the present work is the model of CUNNOLD et al. (1975). Their model domain covers the entire globe and extends vertically from the surface to about 72 km. The model is based on the balance equations,

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

289

and has a highly simplified representation of tropospheric processes. Nevertheless, they obtain a fairly realistic annual cycle in the mean zonal winds and temperatures. Their mean meridional circulation does, however, differ from the thermally direct pole to pole circulation found by Leovy for solstice conditions. CU~q~OLDet al. found that in high latitudes during winter the eulerian mean meridional circulation is indirect, with rising motion near the pole and sinking equatorward of 60 ~ latitude. Although CUNNOLD et al., did not attempt to diagnose the cause of this indirect mean meridional flow; there can be little doubt that it is an eddy driven mean flow generated by vertically propagating planetary waves in the winter hemisphere. Since the work of ELlASSEN(1950) it has been known that eddy heat and momentum flux divergences tend to force a compensating mean meridional circulation. Such a compensating mean cell must exist because the eddy fluxes themselves tend to destroy the thermal wind balance in the mean flow (HOLTON, 1972, pages 228-234). The essential consequences of this eddy-mean flow compensation are expressed in the 'noninteraction' theorem (ANDREWS and MCINTYRE 1976; BOYD 1976; and refs.). Specifically, this theorem shows that under suitable conditions nondissipative waves of steady amplitude will induce a mean meridional circulation which exactly cancels the eddy fluxes of the waves. Thus, the waves produce no net mean flow acceleration. The relevance of these theoretical notions to the overall dynamics of the middle atmosphere has been discussed by DUNKERTON(I 978). He has elucidated the difference between the eulerian mean meridional circulation which arises from the combination of adiabaticalIy driven portion and an eddy driven portion, and the [agrangian mean meridional circulation which in the middle atmosphere is nearly identical to the diabatic (i.e., radiatively driven) circulation. As pointed out by Dunkerton, it is the latter flow which is more directly related to the net meridionat mass (tracer) transport in the middle atmosphere. Exact cancellation between the eddy fluxes and the induced mean meridional circulation does not occur when the eddies are transient (varying in amplitude) or subject to dissipation. Nevertheless, for normal stratospheric conditions it is clear from the general circulation model results of MANABE and MAHLMAN (1976) that the net acceleration of the mean zonal flow in the winter stratosphere is due to a small difference between the eddy forcing and the forcing by the mean meridional circulation. Furthermore, this small difference is primarily due to forcing by the diabatic circulation rather than forcing due to eddy transience or dissipation. In summary, it should be permissible in a first approximation to neglect the eddy heat fluxes and the eddy momentum fluxes due to planetary waves provided that the resulting mean meridional circulation is interpreted as the diabatic circulation and not as the total eulerian mean. 2. The dynamical model The model is based on the primitive equations in the log pressure coordinate system as given by HOLTON(1975). In order to avoid the problems inherent in simulat-

290

James R. Holton and William M. Wehrbein

(Pageoph,

ing tropospheric meteorological processes, the lower boundary of the model domain is set at the 100 mb level (i.e., near the tropopause) and the effects of forcing by the zonally symmetric tropospheric flow are included in the lower boundary condition. The upper boundary is at approximately 96 kin, and the latitudinal extent is global. 2.1. Basic equations In setting down the basic equations we will make use of the following symbols: 2, 0 z H R T~ g p Ps u v w To q~o T (1) f~ a J cp dx dy

longitude latitude a measure o f ' h e i g h t ' [-= - H l n (p/p~)] scale height [=RT~/g] gas constant for dry air a constant stratospheric mean temperature gravitational acceleration pressure a constant reference pressure eastward velocity northward velocity a measure of 'vertical velocity' [=dz/dt] a basic state temperature [-= To(z)] a basic state geopotential [~ q)o(z)] departure of local temperature from To(z) departure of local geopotential from q~o(z) angular velocity of earth radius of earth diabatic heating rate per unit mass specific heat at constant pressure ratio of gas constant to specific heat at constant pressure [= R/%] eastward distance increment [=-a cos 0 dA] northward distance increment [ = a dO].

The horizontal momentum equations can then be written in flux form as -

8u 8u 2 1 8 g-y (uv cos 2 0) ~:t + ~ + cos 2 0 -

+--

I ~z ( p o W U ) -

P0

-

8 z

z

o

o o

t~

==

E

rn

E z

9

0

m

_N

z

i f (

"~

I N

No

30Nli IVI

"x::l

I ~

~ No

?OnlllV]

N

t~

Vol. 118, 1980)

Meridional Circulations of Stratosphere and Mesosphere

315

3. Mean meridional circulation calculations from data From the derived data the Eulerian monthly mean meridional circulations can in principle be evaluated using any pair of the zonally averaged zonal momentum, thermodynamic and continuity equations: 8t

v f

a c o s C 8 r ( ~ c ~ 1 6 2 + ~-Zz 1

8

(u'v'c o s 2 r

= a cos 2 r 0-r (u'v'

-

8 IAtW p +

lltW ,

(0

e sT w(RT sT) -7

+ - \ __+

7z

0 %

1 8 (v'T' cos r a cos r 8r 1

8

a cos r 0r (g cos r

8 w'T' + w'T; ( 1 - ~ ) R - ~zz

8u~ + -~z - ~ = 0

(2)

(3)

where z = In (Po/P), P0 = 1000 mb; w = dz/dt; r = latitude; a -- Earth radius; Q = diabatic h e a t i n g ; f = Coriolis parameter; R = gas constant and cp = specific heat of air at constant pressure. A number of studies have shown that, for the observable wave motions, the terms involving eddy vertical motions are usually much smaller than those involving eddy meridional motions and can be neglected without much loss of accuracy. Since the retrievals have yielded ~ and u'v' at specified levels the best choice would appear to be an iterative solution of the momentum and continuity equations (1) and (3) to obtain g and ~, Theoretical calculations of the mean meridional circulation show that ~ changes from typically a few mm s -x in the middle stratosphere to a few cm s-X in the mesosphere. Since the depth of motion is typically several scale heights, H say, then

8if/ _

,--~_/w ~ 1/H

~E

b

~

Vol. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

347

atitudinal distribution of the contribution of vertical ozone advection by the eddies to ozone change is given as an area weighted proportion of the horizontal mean advection. The budget of total ozone is obtained by performing a vertical integration of Figs. 8, 9, and 10. Figure 14 shows that columnar ozone is chemically produced at tropical latitudes of the winter hemisphere and at both tropical and mid-latitudes of the summer hemisphere. It is chemically destroyed at high latitudes, with much of the destruction occurring in the winter hemisphere. Ozone is transported across the equator from the summer to the winter hemisphere by the mean circulation, and thence poleward by the mid-latitude eddies. There is a small poleward transport by the mid-latitude eddies in the summer hemisphere. From Fig. 11, it is seen that the spring maximum in columnar ozone results from ozone variations below 40 mb. At lower altitudes, ozone production in the tropics is offset by only a small chemical loss, while at high latitudes the chemical loss of ozone is counterbalanced by little chemical production. This suggests that at latitudes above 60 ~, the decay of ozone from the spring maximum which occurs over the course of the summer results from chemical and surface destruction of ozone, but is substantially offset by transport of ozone from the lower latitudes. At latitudes below 40 ~, the decay of ozone from the spring maximum is apparently produced by a transport of ozone into the winter hemisphere. The seasonal variations of ozone in the Northern Hemisphere are summarized in Fig. 15. The buildup of ozone occurs over the course of the winter (December, January, and February) and is dissipated over the course of the summer. We note from Fig. 2 that this accumulation of ozone is relatively uniform from month to month in the model. Transient variations having a two to three week period, probably similar to those simulated by HOLTON and MASS (1976), are a prominent feature of the model. However, a substantial breakdown of the polar vortex such as occurs in a sudden stratospheric warming has not been obtained. We suspect it is necessary to more realistically reproduce the observed zonal mean stratospheric temperature gradient, i.e., to increase temperatures in the upper stratosphere in the polar night in order that these transient events may occasionally lead to a breakdown of the polar vortex. The wintertime accumulation of ozone at mid- and high-latitudes occurs through the interhemispheric transfer of ozone from the tropics of the summer hemisphere. During the spring there is also a large transfer of ozone from the spring to the fall hemisphere. However, there is no substantial net gain in spring or loss in fall of ozone in either hemisphere, and this hemispheric interchange of ozone seems to be of importance only for the tropical ozone budget and to be the result of the definition of the model spring being March, April, and May, as opposed to a definition based on the solar declination angle. Returning to Fig. 14, we note that there appears to be a tendency for the maximum contribution of transport to columnar ozone change to occur at approximately 50 ~

348

D.M. Cunnold, F. N. Alyea and R. G. Prinn

(Pageoph,

latitude in the winter hemisphere. It is to be noted that at that location circulation and horizontal eddies are each contributing to the convergence of ozone. It may be significant that this convergence occurs just poleward of the crossover point between mean and eddy contributions to ozone change; this result has previously been noted in the tracer studies of MAHLMANand MOXIM (1978).

4. Mid-latitude transport

Horizontal eddies are responsible for transporting ozone poleward at mid-latitudes. Two pictures of the variation of this horizontal eddy flux of ozone with altitude are shown in Fig. 16. Observations of the transient eddy flux at several mid-latitude sites in the Northern and Southern Hemispheres have been averaged to produce the 'mean-observed' profile. It should, however, be noted that there are an inadequate number of observations to attach great confidence to this mean profile. We believe that the vertical structure given by the model results, which contain both transient and standing eddies, may be more representative of total eddy transport above 50 mb while the observations are likely to be more realistic below 100 mb (where the model contains too little ozone). The observed transient eddy flux above 50 mb is very close to the minimum flux necessary to produce the observed ozone distribution, which has its maximum concentrations at high latitudes. Since the horizontal flux by the mean circulation tends to be equatorward and chemistry is indicated to play a role in the ozone balance above 50 mb with production in the tropics and destruction at high latitudes (cf. Fig. 8), it would appear that planetary waves may be responsible for creating 'a greater than minimum' poleward eddy flux above 50 mb. A schematic picture of the phase relationships responsible for this poleward eddy transport of ozone in the model above 100 mb is given in Fig. 17. In this region, poleward and downward motions are positively correlated and the ozone and temperature perturbations maximize to the east of troughs and the maximum downward motion. Under these phase relationships, air parcels traveling on trajectory $1 tend to sink (due to Stoke's drift) while parcels on trajectory $3 will rise. Since planetary waves also tend to tilt westward with height, air parcels to the north of the trough will also tend to move northward as they sink across the downward sloping isentropes. In the ozone flux balance equation, it is the positive correlation between northward and downward motion which tends to maintain the countergradient northward flux of ozone. The justification for this picture of ozone transport is given in PRINN, CUNNOLD and ALYEA (manuscript in preparation, 1979). We note, however, that analysis of observations by many researchers tend to support this picture. For example, MARTIN and BREWER (1959) found significant correlations between vertical motions, temperature, and vorticity at 100 mb and total ozone. Since ozone mixing ratio and potential temperature increase with height in the lower stratosphere and motions are apparently adiabatic, downward moving air parcels should be rich in ozone and

349

Vol. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

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Figure 16 The calculated annually-averaged eddy flux of ozone at 40~ Shown for comparison is the mean observed transient eddy flux as determined from mid-latitude observations in the Northern and Southern Hemispheres (HuTcmNGS and FARKAS, 1971). All values have been weighted by 360 ~ longitude by approximately 2.8 k m in height and may be converted to gm/cm2/sec by dividing by approximately 9 • 108.

350

D. M. Cunnold, F. N. Alyea and R. G. Prinn

(Pageoph,

(o) NORTH \1 WEST

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~ ,4.J H02 + M HO2 + O--> O i l + O2 H + O s ' - + O H + O2 OH + Oa--> HO2 + 02 H02 + O3--+ OH + 202 CO+ OH-+C02+ H H02 + HOz ~ H202 + 02 H202 + OH--+ H20 + HO2 H20~ + hv-+ 2 0 H O H + HO2--,-H20 + 02 OH + CH4--> H20 + CH3 O i l + OH---> H20 + 0 O('D) + N20 -+ 2NO O('D) + N20--~ N2 + 02 NO + O3--+ NO2 + 02 NO2 + O ~ N O + 02 NO2 + h v ' - > N O + O NO2 + O3---" NO3~ + 02 HO2 + NO--+ NO2 + OH NO2 + OH + M---" HNO3 + M HNO8 + hv--> NO2 + OH HNO3 + OH--+ H20 + NO3 NO + h v - - * N + O N + NO---> N2 + O N + O2-+ N O + O N + O 3 - ' + N O + O2 CFC13 + hv --+ 3C1 CF2C12 + hv -+ 2C1 CFCI, + O('D)--+ C10 + 2CI CF2Clz + O('D) --> C10 + C1 C1 + O3-'+ CIO + O2 C10 + O ~ C 1 + O2 C10 + N O - + C1 + NO2 C10 + NO2 + M--+ C1ONO2 + M C1ONO2 + hv--.'. CIO + NO2 C1ONO2 + O--~ C10 + NOa CH~ + C1--~ CH3 + HCI Ha + C I - + H + HC1 O H + IlC1--+ H20 + C1 HO2 + C1--~ O2 + I-ICI

1.05E(-34) exp (510/T) )t > 3077 A A < 3077 A 1.9E(- 11) exp ( - 2 3 0 0 / T ) 2.0E(-11) exp (108/T) 2.9E(-11) exp (67/T) 2.3E( - 10) 1 . 3 E ( - 10) 1.3E(- 10) 4 . 2 E ( - 11) 2 . 1 E ( - 32) exp (290/T) 3 . 5 E ( - 11) 2 . 6 E ( - 1 I) 1.5E(- 12) exp ( - 1000/T) 3 . 7 E ( - 14) exp ( - 1025/T) (1 + 4.18E(-20)-[M]).2AE(--13) exp ( - - l I 5 / T ) 6.4E(-13) exp (500IT) 1.0E( - 11) exp ( - 750[T) 5 . 1 E ( - 11) 2.36E(-12) exp ( - 1 7 1 0 / T ) 1.0E(-11) exp ( - 5 5 0 / T ) 7 . 0 E ( - 11) 7 . 0 E ( - 11) 9 . 0 E ( - 13) exp ( - 1200/T) 9 . 1 E ( - 12) 1.2E(- 13) exp ( - 2450/T) 1.2E(- 12) ANASTASIet al. (1976) 8 . 0 E ( - 14) Based on CIESLIK and NICOL~T (1973) 8 . 2 E ( - 11) exp (--410/T) 5.5E(-12) exp ( - 3 2 2 0 / T ) 5.0E(-12) exp ( - 6 5 0 [ T ) 2 . 3 E ( - 10) 2 . 0 E ( - 10) 2 . 7 E ( - 11) exp ( - 2 5 7 / T ) 1.07(-- 10) exp ( - 224/T) 8 . 0 E ( - 12) exp (250/T) Based on ZELLNER(1977) and ZAHNISERet aL (1977) 4.5E(-12) exp 7.3E(-- 12) exp 3.5E(-- 11) exp 2.8E(-12) exp 2 . 5 E ( - 11)

(--840/T) ( - 1260/T) (-- 2290/T) (-400/T)

HNO3, H202 and HC1 are removed from the model troposphere with a time constant of 20 days. *) CH3 --->3HO2, instantaneous. t) NO3 --~ (a) NO2 + O and ~ (b) NO + O2 with (a):(b) = 10:4, instantaneous. N . B . 1.0E(-10) =- 1.0 x 10 -1~.

360

J.A. Pyle

(Pageoph,

the odd oxygen family (Oa, O and O('D)), the total rate of change due to photochemical processes, P, is calculated and equation 1 is solved for the family, using the Adams-Bashforth integration scheme. The photochemical steady-state relationships between 03, O and O('D) then determine the relative concentrations of each species within the family. In using a four hour time-step the model does not resolve diurnal variations and the calculated concentrations of the various constituents represent a daily average value. Night time chemistry is not included but the reaction rates are weighted by the fractional number of sunlight hours per day. Consistent with this temporal averaging the photodissociation rates are re-calculated every ten days, finding a daytime average value by Gaussian integration over a number of solar zenith angles. Continuity equations are written for the following species or groups of species: O('D), O and 03; N, NO, NOz and C1ONO2; HNO3; H202; H, OH and HO2; C1, C10, C1ONOa and HC1; CFCla; CF2CIz. The lifetime of the HOx family (H, OH and HO2) is short and transport is ignored in this case. In the upper stratosphere the lifetimes of HNOa and H~O2 become short and these are included in the odd nitrogen and odd hydrogen families respectively, care being taken to ensure conservation. The other species, H20, CH4, Ha, N20 and CO, are assumed to be invariant. Profiles, based on a limited number of measurements, are specified, independent of latitude. The boundary conditions used are presented in Table 2. The model results are not particularly sensitive to the bottom boundary conditions of those species which are rained out in the troposphere. The upper boundary condition for the CFCs ensures that no chlorine is transported through the top level of the model and the calculated ozone depletion will be an upper limit, with the particular chemical scheme used.

Table 2

Boundary conditions

Lower

Upper

03

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NO + NO2 Ha02

Constant volume mixing ratio of 7 x 10-10 Constant volume mixing ratio of 3.2 x 10 -11

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Zero flux into ground

CFC12

Zero flux into ground

CIO~

Constant volume mixing ratio of 0.0

Calculated photochemical equilibrium Constant mixing ratio profile Calculated photochemical equilibrium Calculated photochemical equilibrium Zero flux through upper boundary Zero flux through upper boundary Zero flux through upper boundary

Vol. 118, 1980) Calculation of Possible Depletion of Ozone by Chlorofluorocarbons

361

3. The natural stratosphere While the stratosphere does contain chlorine of natural origin, the discussion in this section is limited to the behaviour of compounds of oxygen, nitrogen and hydrogen. In the following section the behaviour of anthropogenic chlorine compounds is discussed while their effect on the ozone layer is considered in Section 5. Two long integrations have been performed. In R1, the chlorine chemistry was suppressed. Thus R1 represents a control run against which the effects of the chlorine chemistry, included in R2, can be assessed. A comparison of the results of R1 with observational data on atmospheric minor constituents helps to ascertain the degree of confidence which can be placed in the subsequent perturbation studies. Such a comparison is the purpose of this section. Figure 1 shows the latitude-time section of the total ozone from R1. There is a gross resemblance to the behaviour of the atmosphere, although there are differences in detail. There is a maximum in total ozone in the northern hemisphere polar regions in spring with a maximum in the southern hemisphere in mid to high latitudes just over six months later, as observed. Minimum values are found in equatorial latitudes. There is, however, a little too much ozone in low latitudes due, in part, to too great a concentration in the lower stratosphere. PYLE (1976) and H ~ w o o n (1977) have stressed the sensitivity of the ozone distribution to the radiative heating, and hence

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coo is given by the exponent m which lies between - 1 . 5 and - 2 . 2 . These values are close to the exponent - 5 / 3 of the Kolmogorov spectrum (TATARSKII, 1971), respectively to the exponent defining the slope of frequency spectra of step-like fine structure superimposed on the gross vertical profile of temperature in the oceans (GARRETTand MONK, 1971). It has to be checked in further investigations if the shape of the spectra is determined by Fresnel Zone filtering of scattered and reflected components (e.g. ISmMARU, 1978), or represents the inertial and buoyancy subranges of turbulence spectra (e.g. BOLGIANO, 1968; WOODS, 1973). It has to be assumed that in the flow conditions examined in the stratosphere, fluctuating temperatures as well as fluctuating velocities are present. Under the suppositions which are summarized in Section 2.1, estimates of turbulent velocity fluctuations can be obtained from the width of the Doppler spectra of the radar returns. These, however, have to be filtered from the long-term fluctuations due to large-scale spatial variations of sheets advecting through the radar beam. Because meaningful velocities can only be obtained by integrating over time periods of at least several seconds, spectra of short-term velocity fluctuations in the time range of seconds cannot be deduced. When averaging over one minute, the rms vertical velocity fluctuations are typically less than + 0 . 5 m s -~ in the stratosphere. Spectra of vertical velocities at frequencies lower than 0.1 rad/s (T > 1 min) are depicted in the spectrograms of Figs. 6 and 7. Conspicuously, a clear cut-off at the Brunt-V/iisfil~i frequency N (corresponding period Ts) is found. Only during unstable conditions, due to strong wind shear, are higher frequency components significant (Fig. 6). The spectrum at o~ > N (T < TB) is comparable to a white noise spectrum, and does not fall off with co-r~ (m = 5/3). A spectral power slope according to o~-~j3 was not found for co < N which GAGE and CLARK(1978) reported to be existent in horizontal velocity variations. The turbulent fluctuations in vertical velocity w' and the turbulent fluctuations of the temperature T' determine essentially the turbulent transport process of energy and momentum in the atmosphere. It is shown in this section that both these basic quantities can be qualitatively monitored by means of VHF radar. However, to make these observations more quantitative, more detailed investigations of the intimated processes need to be made. 3.3.2. Possible source mechanisms of stratospheric structures In the former section attention was drawn to some similarities between the observed fine structure of the atmosphere and the fine structure of the oceans. When

Vol. 118, 1980) Structure and Dynamicsof the Stratosphere and Mesosphere

515

describing the structure of the ocean, one has to take into account the temperature as well as the salinity. Obviously one cannot be allowed to apply all of these theories (e.g. 'double diffusion' (MoNIN et aL, 1977)) to the atmosphere. There are however still other mechanisms that are applicable to atmospheric structures, and these are briefly described next. The first mechanism envisages the breaking of internal waves (BRETIJERTON, 1969; ORLANS~:Iand B~YAN, 1969). For wave amplitudes larger than a critical value, the particle velocity exceeds the phase velocity, and unstable gradients occur. These unstable gradients lead to convective instability, and energy will be extracted from the wave and transferred into turbulent kinetic energy. It could be suspected that the sheets reflect these regions of turbulence. LUD•AM (I967) developed a similar theory for the characteristics of billow clouds and their relation to clear air turbulence. It was mentioned by GELLZRet al. (1975) that probably another mechanism than breaking of large amplitude waves has to be adopted to explain the thin sheets. Internal waves may also cause turbulence structures and lose energy by shear instability. For this condition to apply, the shear generated by the waves must add to a pre-existing shear so that the local Richardson number becomes less than 0.25. It remains questionable if the large Richardson numbers observed in the stratosphere (e.g. Fig. 2) can be overcome by wave-induced shear to transit into the unstable regime. WOODS and WILEY(1972) pointed out that as an internal wave propagates along a sheet, in the neighborhood of its crests and troughs, the sheet may become unstable and turbulent. Because of entrainment of air, the now turbulent medium becomes thicker. Turbulence will tend to mix the medium and there will be discontinuities in temperature at the top and bottom surfaces so that new sheets form (BOLGIANO, 1968). Repetition of this process creates a whole ensemble of sheets, which incidentally is observed with the VHF radar. We have to check in further investigations if the mechanisms of internal wave-breaking or shear instability apply to explain the stratospheric structures encountered by VHF radar. Another hypothesis for the origin of the stepped microstructure is 'lateral convection' (MoNIN et al., 1977). In this process, horizontal differences between neighboring, differently stratified air masses are equalized by quasi-horizontal displacement of individual layers or lenses of air packets embedded in a laminar flow. Such displacements, for example, may be the result of baroclinic instability and could be produced by sliding layers that are heavier than their horizontal neighbors along isentropic surfaces which lead to the formation of stable stratifications. Pronounced sheets in the tropospheric refractivity pattern during the approach of a frontal system connected with an extratropical cyclone were indeed found (ROTmER, 1979a). Since WOODS (1969) stated that most of the atmosphere is in laminar flow, the hypothesis of lateral convection by means of large, almost horizontally extending eddies or laminae should be followed up in further VHF radar investigations,

516

J. R6ttger

(Pageoph,

4. Investigations of the mesosphere Since BOWLES (1958) and FLOCK and BALSLEY(1967) first reported VHF radar echoes from the ionospheric D-region, a wide-spread interest has grown up in the use of V H F radars to investigate the dynamics of the mesosphere. These echoes received with VHF radars are from fluctuations in electron density which can be very much enhanced over the thermal level in the D-region. This is a consequence of strong collisional coupling between the ionized and the neutral particles which do fluctuate due to turbulence in the neutral atmosphere. Because of this coupling, the fluctuations revealed by VHF radar can be used as tracers of the neutral background in the mesosphere. The mechanism which gives rise to the radar echoes from the mesosphere is not as yet fully understood. It is assumed that under certain conditions, besides pure scattering from turbulence structures at half the radar wavelength, diffuse partial reflection from horizontally stratified laminae of refractive index may occur (FUKAO et al., 1979; R6TTGER et al., 1979). In addition to VHF radars, other radio methods have been successfully applied to investigate mesospheric dynamics such as the partial reflections drifts technique operating at MF (e.g. BRIGGS, 1977), the meteortrail radar technique operating at H F or VHF (e.g. reviews in WEBB, 1972), and the incoherent scatter technique operating at U H F (e.g. MATHEWS,1976). The partial reflection drifts (PRD) technique turned out to be a very potent tool to rather continuously monitor the height range from about 60 to 110 km (e.g. MANSON et al., 1974; VINCENT and STUBBS, 1977). WOODMAN and GUILLEN 0974) introduced a powerful method of coherent data processing to show that non-thermal scattering at VHF is predominant in the mesosphere. In the context of this paper we extend the definition of WOODMAN and GUILLEN (1974) and include diffuse reflection into the term non-thermal scattering. The method of Woodman and Guillen was subsequently used in all VHF radar experiments to improve the sensitivity. In the following sections the results of VHF radar investigations of tides and gravity waves are briefly reviewed and some recent results on turbulence structures in the mesosphere are described.

4.1. Mesoseale phenomena Almost all of the VHF radar results dealing with tides and gravity waves in the mesosphere were obtained with the Jicamarca radar which is located near Lima/Peru in the equatorial region. This radar operates on 50 MHz at a maximum power rating of 4 MW. T h e antenna has a collecting area of 8.4 • 104 m 2, and the beam can be tilted to different zenith directions to measure horizontal as well as vertical velocities. The best height resolution is 2.5 km, which is comparable to the height resolution obtained in PRD experiments. WOODMAN (1974)and WOODMAN and GUILLEN (1974) measured mesospheric velocities with an accuracy of better than 2 m s -1 in the horizontal and better than 0.2 m s-1 in the vertical. The horizontal velocities were

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

517

typically 20-40 m s- 1; in general the instantaneous vertical velocities were found to be less than 2 m s- 1 (RASTOGIand WOODMAN, 1974). WOODMANand GUILLEN(1974), RASTOG~ and BOWmLL (1976a) as well as HARPER and WOODMAN (1977) apparently did not measure such large amplitudes of tides which were expected from theory. Also FUKAO et aL (1979) did not clearly identify a diurnal tide. The sense and the magnitude of the winds measured by FUKAOet at. (1979) are in general agreement with annual and semiannual oscillations. Superimposed on the mean background velocities were periodic velocity fluctuations with a sharp cut-off in the spectra near the BruntV/iis~il/i period of 5-7 min (WOODMAN and GUILLEN, 1974). Further evidence for this cut-off period was given by the experiments of RASTOGI and WOODMAN (1974) and RASTO~I and BOWrIILL(1976a), They interpreted the oscillations to be a manifestation of atmospheric gravity waves in the period range of 4 min to 1 hr. The dominant waves had periods of 10-20 min. It was argued that these waves were vertically evanescent and had a horizontal wavelength of 200-300 km. Possibly also acoustic gravity waves of periods less than 4 rain were observed. There is as yet no clear evidence for possible origins of the mesospheric gravity waves. HARPER and WOODMAN (1977) evaluated vertical velocity oscillations in the period range from about 5-15 rain which were highly correlated at nearby altitudes, while velocities at altitudes separated by more than 5 km showed little or no correlation. The dominant periodicities of the oscillations were observed to change with altitude. A same sort of evidence was reported by FUKAO et al. (1979) who inferred that the velocity oscillations near the Brunt-V/iis/il/i period are largely vertical. Also ROSTER et al. (1979) found a wave with dominant period changing with height. Some similarity between the gravity waves observed in the mesosphere and the stratosphere may be discovered. In Fig. 7b a spectrum of waves with a clear cut-off near the BruntV~iis~it/i period is shown. Like the oscillations of the mesospheric waves, the oscillations of the stratospheric waves seem to be coherent over height ranges of only a few kilometers. It thus appears to be difficult to trace a distinct wave over a larger altitude range. As it was pointed out in Section 3.2, it would be very intriguing to see if a mean profile of the Brunt-V~iis~il/i period can be deduced from the gravity wave spectrum. This profile (if gravity waves are present) could give an indication of the gradient of potential temperature in the mesosphere. Scattering layers at discrete heights, oscillating in intensity with about twice the frequency of a simultaneously occurring velocity oscillation, were found by HARPER and WOODMAN (1977). They pointed out that the turbulent irregularities responsible for the scattering may be at least partially driven by energy from short-period gravity waves. Their assumption was supported by the correlation between velocity and echo power (in some cases). These results were confirmed in recent experiments with the Urbana radar (MILLER et al., 1978) indicating enhanced scattering regions which in many cases corresponded to high-amplitude waves. MILLER et al. (1978) showed waves that were coherent over altitude ranges of up to 10 km. They presented an example interpreted as a wave becoming unstable and generating high-frequency

518

J. R6ttger

(Pageoph,

waves. The mechanism possibly is critical layer interaction or wave-induced shear instability and it is anticipated that gravity waves as well as tides and planetary waves play a role. An example of shear-generated layers due to a tide may be found in the intensity plots obtained with the SOUSY-VHF-Radar by CZECI-tOWSKYet al. (1979), where downward sloping ensembles of layers can be recognized over time periods of hours. It is reported by Rt3TTGERand RASTOGI(1978) and CZECHOWSKYet al. (1979) that an apparent downward motion of a layered structure can be connected with a downward Velocity component, which points to a downward progressing shear layer due to a wave. Depending on the background conditions of electron density, temperature and wind, which vary with season, shears induced by tides and gravity waves may not always be sufficiently large to cause an instability. This could be part of the reason for the seasonal variability in the mesosphere (GREGORY,1961 ; STUBBS, 1976; STENINGet al., 1978; CZECHOWSKYet al., 1979). It appears that radars operating at VHF or at MF (PRD) are appropriate instruments to observe not only mesoscale but also synoptic-scale phenomena in the mesosphere. The PRD technique incidentally seems to be more versatile for these investigations since VHF radars have to be very powerful to provide rather continuous observations of dynamic processes. VHF radars on the other hand can provide better height resolution and therefore are essential instruments to investigate small-scale processes.

4.2. Small-scale phenomena

The echo power from the mesospheric heights varies considerably during the day and from one day to the next (WOODMAN, 1974). Strong variability as function of height is also observed (e.g. HARPER and WOODMAN, 1977). The first experiments did not indicate echoes from the 35-55 km height region (e.g. WOODMANand GUILLEN, 1974), but recently BALSLEY(1978) detected signals in this gap region of the upper stratosphere and lower mesosphere. He used the powerful Jicamarca radar and applied long integration times. It was reported by WOODMAN (1974) that at certain times the echoes between 60 and 85 km in a particularly narrow height range can be 10-15 dB stronger than a mean profile. WOODMAN(1974) suggested that these echoes are caused by the coincidence of a layer of turbulence with a region of strong electron density gradient. It was estimated from the echo power and the spectral width (WOODMANand GUILLEN,1974) that the turbulence in the mesosphere may be confined to layers of the order of 100 m thickness. A first height-time intensity (HTI) diagram of VHF radar echoes from the mesosphere was published by HARPER and WOODMAN (1977). This diagram which was deduced from data taken at 12 altitudes in the height region between 62.5 and 90 km shows regions of enhanced echo power separated by regions from which little or no power was received. HARPERand WOODMAN(1977) pointed out that the appearance of scattering layers (revealed by VHF radar) at discrete heights is similar to partial

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

519

reflection results obtained at M F (GREGORY, 1961). Apart from the spatial (vertical) intermittency, a temporal intermittency is characteristic for the mesospheric echoes (RASTOGI and BOWmLL, 1976b; HarPER and WOODmaN, 1977). In recent high-resolution measurements carried out with the SOUSY-VHF-Radar it was possible to measure the thickness of structures in the mesosphere (CZECHOWSKY et al., 1979; RQTTGER et al., 1979). By means of these measurements, applying a best resolution of 150 m, different types of turbulence structures were identified. Figure 9 shows an example of the life-history of structures in the height range of 66-85 km observed on 20 June 1978. A layer as thick as 2 km was observed from 10.45-10.55 G M T at 70 km height. Another layer of 1.5 km thickness commenced around 11.00 G M T and lasted for more than 30 min. The thinner structure at 80 km, which can be called sheet, shows evidence of a downward progression. This layer descent was accompanied by a downward velocity deduced from the Doppler spectrum (ROTTGER and RASTOGI, 1978). A burst of a short-lived blob of turbulence is discernible at 71 km around 11.25 GMT. In addition stronger echoes due to meteors, which are spread over many contiguous range cells and confined to short time intervals, can often be seen. In Fig. 10 further selected examples of sheets and blobs are shown. The upper heighttime intensity diagram was deduced from data taken with the complementary code system applied by CZEC~OWS[~u et aL (1979), and the lower diagrams were obtained with a different coding system described by WOOD~AN et al. (1979). Both experimental configurations yield a similar impression of turbulence structures in the mesosphere. Intermittent sheets, which have a thickness of less than about 1 km, sporadically may recur at the same height intervals over several minutes. They also may shift down in height during their lifetime. Often sheets may be as thin as the minimum range resolution of 150 m. Blobs of turbulence, also confined to height ranges of

20 JUNE 1978 I---!: ::~:~.:!H~:/;" i"~:-~;--:~!:.-..-:-::."~-;i ~I-i'il'":,': =:I-"i:,'-!::.~:, ~,: ,'I "' :: '~'-:-~ " ~: ~=: ?' '~ ~i-.:'."~:':-'.--::~ :!, - :--w i~." "-:~-!; : ;~ ~ I~ ~ . i~!if:~!:,i~:~i ~ ~_Ii!~"-,:: ~{I::.?l.i:l'-!;.._!-j.w:~!! -:.-~;.: :' ,-i~ ~. ....! , ~:.. ..I:! ~ '.!i!i]:!::::,[':::i{!:.:l~::; /:. li :~,~I:

':

:,!:},;i!~i~i !:ii:::~ili!!i~i/:-:'i/i::~i,I/ii: i:-/!'.if.: :"i:::.;-:-.~:., : . ::.%:~,,;~,.i,'i'..,!://

T

73 ; .::{:::!! ii~:i: : i! !i!i !:. '.i!!ii: !!i~:iii:i:!:'~:!i~a!@,,iii!i~!~!i~ii~lii!t~M~!lli~iiiiiia!!~!!,'i!i;i!!i!

1040

I050

II00

t

= GMT

III0

1120

ii!!!t!!~l,,!.lii!ii.!

1130

L~P = Z+dB

Figure 9 I-ITIplot of mesospheric echoes recorded with the SOUSY-VHF-Radar on 20 June 1978. The difference between blank and dark screen points, Ap is 4 dB.

520

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Figure 10 Examples of sheets and blobs of turbulence observed in the mesosphere. The HTI plot 1 is deduced from data (original range resolution 300 m) taken around noon on 8 May 1978 and published by Cz~crtowsKYet al. (1979). The HTI plots 2, 3 and 4 are from data (original range resolution 150 m) taken around noon on 19 June 1978 (RrTTGERand RASTOOI,1978). The height of the structures is z0 + Az. The gray scales denote the power ratio for plot t, respectively plots 2, 3, 4.

less than about 1 km, can commence within some ten seconds and rise up to large intensity from one range gate to the neighboring. The blobs suddenly decay after living for 1-2 minutes. Assuming that all these structures are advected with the background wind, it was estimated by R6TTGEg et al. (1979) that the blobs can result from bursts of turbulence or even enhanced ionization density gradients generated locally within the radar beam. Their horizontal extent is typically about 1 km. The sheets have horizontal dimensions of several kilometers and the layers of at least 10-50 km. The horizontal size of these turbulence structures is thus much larger than their vertical size. A similar result has been reported from M F partial reflection studies by VINCENT and BELROSE (1978). Reports on aspect sensitivity of structures in the mesosphere below about 70 km (e.g. HARPER and WOODMAN, 1977; R6TTGER and RASTOGI, 1978; FUKAO et al., 1979) allow the assumption that the small-scale structure at half the radar wavelength (~_ 3 m) is also in some way anisotropic. The role of partial reflections from the lower mesosphere is discussed by RSTTGER et al. (1979), who noted the possibility of diffuse partial reflections from heights below 70 km. The velocity spectra of turbulence structures in the mesosphere indicate the typical feature that sheets and blobs, which are thin, exhibit smaller velocity fluctuations (spectral width) than thicker layers. In general, it was found by ROTTGERet al. (1979) that the velocity fluctuations are proportional to the thickness of turbulence structures, which is consistent with turbulence theory. CZECHOWSKY et al. (1979) found that thickness and lifetime are correlated.

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

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Based on considerations of thickness, height of occurrence, duration, and spectral width, RrTTGER and RASTOGI(1978) proposed a classification of these structures, which is summarized in Table 1. It was shown by CZECHOWSKY et al. (1979) that layers, which may occur at heights up to 90 kin, may even be as thick as 10 km so that they proposed a further subdivision into thin and thick layers. They also reported a seasonal variation with thick layers detected only during summer. The high-resolution observations indicate that a boundary altitude exists ( ~ 7 0 km during summer) below which sheets and blobs dominate and above which most of the structures are layers. The maximum duration of sheets and layers may be several hours. It cannot be verified from the current investigations if the structures observed in the mesosphere are similar to those observed in the stratosphere, in spite of the fact that some of their features are similar. A reasonable difference however is established by the diurnal variation of mesospheric echoes caused by the diurnally varying background ionization in the mesosphere. It is also possible that the mesospheric structures are more turbulent than the stratospheric structures, and that the mesospheric structures are closely connected to the background ionization conditions as well as to phenomena in the neutral atmosphere, like gravity waves and tides. The fact that mesoscale phenomena, such as planetary waves, also play a role may be deduced from the day-to-day variability. Varying features of turbulence in the mesosphere from 19 to 20 June 1978 (intermittent sheets were dominant on 19 June, but layers on 20 June) were observed for iflstance with the SOUSY-VHF-Radar when during conditions of geostrophic turbulence rather strong winds in the upper troposphere changed their direction from E over S to NW (ref. Fig. 4). During radar operation on 5 and 7 June 1978, mesospheric structures were rather weak and less obvious. The winds at 300 mb level during that period were constantly blowing from W at a moderate strength. However, much more work has to be carried out to learn about the generation mechanism of these different structures and their connection with lower atmospheric disturbances. Two important parameters inferred from high-resolution VHF radar experiments are the thickness of turbulence structures and the rms velocity fluctuations in these structures. These parameters can be used for estimating the vertical transport or eddy diffusion coefficients K and the dissipation rate e of turbulence (CUNNOLD, Table 1 Blobs

Sheets

Layers

Duration T(min)

< 1-2

Velocity fluctuations

small

60-90 dominant < 70 70

Thickness Az (km)

60-90 dominant < 70 < 0.9

Height z (km)

>0.9 > 5 continuous large

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1975). R6a'a'G~Ret al. (1979) found values of ~ and K which appear in fair agreement with those in use in aeronomic models (e.g. ZIM~tERMANand MtrRPtqu 1977). It should be remarked, however, that the transport coefficients inferred from the radar observations refer to transport in the region within the structures, whereas those used in aeronomic models are transport coefficients averaged over large temporal and spatial scales. Any comparisons naturally require a similar averaging of radar results, and even then it would be necessary to resolve the following objections: (1) In estimating K and ~ from radar data, only turbulence scattering is considered, whereas diffuse partial reflections can also contribute to the signals and influence their correlation time. (2) The scattering has to be from turbulence in the inertial subrange. For a large variation in turbulent energy dissipation the Kolmogorov inner scale is accepted 9 to be at a few meters in the mesosphere (RAsTOGI and BOWHILL, 1976b; GAGE and BALSL~Y,1978). Thus, the Bragg scale of VHF radars is barely marginal in the inertial subrange of mesospheric turbulence. Answering these objections will have an impact on the further understanding of turbulence and the corresponding vertical transport processes in the mesosphere.

5. Summary and conclusion

An attempt was made to summarize existing material and attach recent results to outline the capabilities of VHF radars for atmospheric research, such as the determination of the tropopause level and stratospheric stability, as well as the mutual dependence of winds, waves, laminar structures and turbulence observed in the stratosphere and mesosphere. The investigation of the stratosphere and mesosphere with VHF radars is a rapidly developing research field and innovative processing techniques are being developed. Many questions remain to be solved, which may have impact on the understanding of the structure and dynamics of the middle atmosphere. Some of them were considered in this paper and are summarized below, without laying claim to completeness or importance: (1) How reliable are the tropopause height and stratospheric stability inferred from radar observations? (2) Can gravity wave generation be studied in detail, and can the propagation of wave disturbances from the troposphere into the stratosphere and mesosphere be tracked by VHF radars ? (3) Does a possibility exist to deduce a height profile of the Brunt-V/iis/il/i frequency, i.e. profile of gradient of potential temperature, from internal wave spectra measured with radar? (4) What is the origin of the laminar and turbulence structures in the stratosphere and mesosphere? (5) Can the energy and momentum transport due to wave disturbances be

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estimated from radar observations? How reliable are estimates of eddy diffusivity due to turbulence in the stratosphere and mesosphere ? (6) What are the operational parameters of a V H F radar for continuously monitoring wind velocities and turbulence in the entire middle atmosphere ? It is expected that continuing investigations with V H F radars and supplementary experiments, which are planned to be carried out during the Middle Atmosphere Program, can give answers on some of these questions.

Acknowledgements

The author appreciates the continuous cooperation with his colleagues of the SOUSY project group of the Max-Planck-Institut fiir Aeronomie as well as the stimulating discussions with Prof. K. C. Yeh and Dr. P. K. Rastogi. The provision of meteorological data from the Deutscher Wetterdienst is kindly acknowledged.

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GREEN,J. L., GAGE,K. S. and VANZANDT,T. E. (1978b), Three dimensional wind observations of a jet stream using a VHF Doppler radar, Preprint Vol. 18th Conf. on Radar Meteorology (to be puN., Amer. Meteor. Soc., Boston). GREEN,J. L., WINKLER,R. H., WARNOCK,J. M., CLARK,W. L., GAGE,K. S., and VANZANDT,T. E. (1978c), Observations of enhanced clear air reflectivity associated with convective clouds, Preprint Vol. 18th Conf. on Radar Meteorology (to be publ., Amer. Meteor. Soc., Boston). GREGORY, J. B. (1961), Radio wave reflections from the mesosphere, 1. Heights of occurrence, J. Geophys. Res. 66, 429--445. HARDY, K. R., GLOVER, K. M. and OTTERSTEN,H. (1969), Radar investigations of atmospheric structure and cat in the 3 to 20-kin region, in Clear Air Turbulence and its Detection, ed. Y.-H. Pao and A. Goldburg (Plenum Press, New York), 402--416. HARPER, R. M. and WOODMAN,R. F. (1977), Preliminary multiheight radar observations of waves and winds in the mesosphere over Jicamarca, J. Atmos. Terr. Phys. 39, 959-963. ISHIMARU, A., Wave Propagation and Scattering in Random Media (Academic Press, New York 1978). -KAO, S. K. (1979), Oscillation of inversion layer and pollution pumping, Conf. Preprints 4th Symp. on Turbulence, Diffusion, and Air Pollution, 448--449 (Amer. Meteor, Soc., Boston). KLOSTERMEYER,J. and LIU, C. H. (!978), Indication of gravity wave-meanflow interaction in upper atmospheric radar observations, Geophys. Res. Lett. 5, 507-510. KLOSTERMEYER,J. and ROSTER, R. (1979), Model computation of a jet stream-generated KelvinHelmholtz instability, (submitted to J. Geophys. Res.). KLOSTERMEYER,J., ROSTER,R., CZECHOWSKY,P., ROTTGER,J. and SCHMIDT,G. (1979), Atmospheric research by high power VHF radars, Umschau 79, 514-515. KRAUS, E. B. (Ed.), Modelling and Prediction of the Upper Layers of the Ocean (Pergamon Press, Oxford 1977). Kuo, H. L. and Stm, W. Y. (1976), Convection in the lower atmosphere andits effects, J. Atmos. Sci. 33, 21-40. LUDLAM, F. H. (1967), Characteristics of billow clouds and their relation to clear-air turbulence, Q. J. Roy. Meteor. Soc. 93, 419-435. MANSON,A. H., GREGORY,J. B. and STEI'HENSON,D. G. (1974), Winds andwave motions to 110 km at mid-latitudes, L Partial reftection radiowave soundings, 1972-73, J. Atmos. Sci. 31, 2207-2215. MATHEWS,J. D. (1976), Measurements of diurnal tides in the 80- to lO0-km altitude range at Arecibo, J. Geophys. Res. 81, 4671-4677. MEECHAM, W. C. (1972), Atmospheric turbulence, in Remote Sensing of the Troposphere, ed. V. E. Derr (U.S. Government Printing Office, Washington, D.C.), 4/1-4/22. MILLER, K. L., BOWHILL,S. A., GIBBS,K. P. and COUNTRYMAN,I. D. (1978), First measurements of mesospheric vertical velocities by VHF radar at temperature latitudes, Geophys. Res. Lett. 5, 939-942. MONIN, A. S., KAMENKOVlCH,V. M. and KORT, V. G., Variability of the Oceans (John Wiley and Sons, New York 1977), 43-98. ORLANSKI,I. and BRYAN, K. (1969), Formation of the thermocline step structure by large-amplitude internalgravity waves, J. Geophys. Res. 74, 6975-6983. RASrOGI, P. K. and WOODMAN,R. F. (1974), Mesospheric studies using the dicamarca incoherentscatter radar, J. Atmos. Terr. Phys. 36, 1217-1231. RASTOGI,P. K. and BOWrlILL,S. A. (1975), Remote Sensing of the Mesosphere Using the Jicamarca Incoherent-Scatter Radar, Aeronomy Report No. 68 (Aeronomy Lab., Univ. of Illinois, Urbana). RASTOGI,P. K. and BOWHILL,S. A. (1976a), Gravity waves in the equatorial mesosphere, J. Atmos. Terr. Phys. 38, 51-60. RASTOGI, P. K. and BOWHILL, S. A. (1976b), Scattering of radio waves from the mesosphere- H. Evidence for intermittent mesospheric turbulence, J. Atmos. Terr. Phys. 38, 449-462. R(STTGER, J. (1977), Travelling disturbances in the equatorial ionosphere and their association with penetrative cumulus convection, J. Atmos. Terr. Phys. 39, 987-998. ROTTGER,J. and CZECHOWSKY,P. (1978), VHF-radar echoesfrom the troposphere and stratosphere, Kleinheubacher Berichte 21, 279-290.

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WOODMAN,F. R. and GUILLEN,A. (1974), R adar observations of winds and turbulence in the stratosphere and mesosphere, J. Atmos. Sci. 31, 493-505. WOODMAN,R. F., KUGEL,R. P. and R6TTGER,J. (1979), A coherent integrator-decoderpreprocessor for the SOUSY-VHF-Radar, submitted to Radio Sci. WOODS, J. D. (1968), An investigation of some physical processes associated with the vertical flow of heat through the upper ocean, Meteor. Magazine 97, 65-72. WOODS, J. D. (1969), On Richardson's number as a criterion for laminar-turbulent-laminar transition in the ocean and atmosphere, Radio Sci. 4, 1289-1298. WOODS, J. D. and WILEY, R. L. (1972), Billow turbulence and ocean microstructure, Deep-Sea Research 19, 87-121. WOODS, J. D. (1973), Space-time characteristics of turbulence in the seasonal thermocline, M6m. Soc. Roy. des Sciences de LiSge, 6 e s~ries, tome VI, 109-130. ZIMMERMAN,S. P. and MURPHY,E. A. (1977), Stratosphericandmesosphericturbulence, in Dynamical and Chemical Coupling, ed. B. Grandal and J. A. Holtet (D. Reidel PubL Co., Dordrecht, Holland), 35-47. (Received 15th June 1979)

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Advances in Noctilucent Cloud Research in the Space Era By O. A. AVASTE1), A. V. FEDYNSKy2),G. M. GRECHrZOa), V. I. SEVASTYANOV 3) and CH. I. WILLMANN!)

Abstract - A summary of NLC research in the last two decades is presented. Results of NLC studies from the near-Earth space are discussed. It is shown that NLC can cover much larger territories than those estimated earlier and that there exists asymmetry in the coverage and also in the physical properties of NLC in the Northern and Southern Hemispheres. The mesopause often reveals a compelx multilayered structure. The pilot program of NLC research is discussed as a subprogram of the Middle Atmosphere Program and some vistas in NLC research are discussed. Key words: Noctilucent clouds; Mesosphere.

1. Introduction Noctilucent clouds (abbreviation NLC) have been a challenge to many investigators during the past century. These clouds resemble tenuous cirrus or cirrusstratus clouds except for their extraordinary height which is about 82 km. So they are indicators of the physical processes which take place in the mesopause: i.e. in the top layer of the mesosphere where in summertime the temperature minimum is of the order of 135-145~ Because of their small optical thickness they are visible to the observer on the Earth's surface only in twilight conditions when the Sun's depression angle ranges between 6 to 16~ The nature and origin of these clouds is still under discussion. There exist different hypotheses and contradictive theoretical concepts which try to explain the origin and evolution of N L C as well as their physical and optical parameters. The first recorded observations of N L C were made after the eruption of the volcano at Krakatoa in 1883. In June 1885 N L C were noticed by many observers in different countries. This could be explained by the occurrence of an extraordinarily bright display of NLC. The first well-documented recognition of the observed clouds as being an unusual phenomenon in respect of height was made by BACKHOUSEin 1) Institute of Astrophysics and Atmospheric Physics, Estonian Academy of Sciences, Tartu 202444, Estonia USSR. 2) Central Aerological Observatory, State Committee of Hydrometeorology and Control of Natural Resources, Moscow. a) Pilot-astronaut of the USSR.

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1885 at Kissingen, Germany, on June 8 of that year. On June 10 these clouds were recorded by Laska in Prague (according to JESSE, 1889) and on June 12, 1885 by TSERASKn (1890) in Moscow. Jesse himself observed NLC on June 23, 1885 (see JESSE, 1885). To Jesse we owe the name 'Leuchtende Nactwolken' or noctilucent clouds. The NLC occurrence on June 23, 1885, was recorded by several observers in Europe (see ASTAVOVICIJ, 1939) including Hartwig at the Tartu Observatory, Estonia (HARTWI6, 1893). The first sufficiently accurate NLC height determination (h = 75 km) was carried out by Tseraskii and Belopolskii making use of measurements on June 26, 1885 (see TSERASKII, 1890). The earliest publication of the accurate height measurement belongs to JESSE (1887). He determined the height of NLC which occurred in July 1887 and also obtained the result h = 75 km. Interest in these clouds waned during the period of 1909-24 but picked up again when Astapovich in the USSR began to study them. A summary of those observations was published by ASTAPOVICHin 1961. In the years 1932-34 STORMER (1933) and VESTINE (1934) made the first reported observation in Norway and over North America. The research of NLC intensified around 1948 when Paton in Scotland and Khvostikov in the USSR began their work on NLC. A special effort in NLC research was started during the I.G.Y. A wide network of NLC observation stations was set up over the Northern and Southern Hemispheres between the latitudes of 45-90 ~ and these data were processed and published by specie/1data centers located at College, Alaska; Edinburgh, Scotland and Tartu, Estonia. A NLC observation manual was prepared by Khvostikov, Willmann, Grishin, Fogle and Paton and was published in 1966 under the auspices of the WMO. In the years 1956-76 11 national symposia on NLC were carried out in the USSR. NLC data were discussed at international symposia in Tallinn (1966) (see KHVOSTIKOVand WITT, 1967), Tokyo (1968), Moscow (1971), Koblenz (1973), Berlin (1973), Grenoble (1975), Tallinn (1975), Seattle (1977) and Aberdeen (1978). International cooperation in NLC research is coordinated by the NLC Panel of the International Association of Meteorology and Atmospheric Physics. Bibliographies on NLC research were published in Meteorological and Geoastrophysical Abstracts (Vol. 15, No. 4, 1964) and by KOSIBOVAand PYKA (1969). In the years 1964 to 1974 the Canadian Atmospheric Environment Service published a NLC Newsletter Nos. 1-20 (Editor A. D. Christie). A catalog of NLC occurrences was published by SCHRI~DER(1968) and FAST (1972). In the years 1973-77 the Soviet Geophysical Committee published three topical collections on NLC research: by editors EERME(1973), VASILYEV0975) and AVASTE(1977). Several monographs and review articles on this topic were published (FOGLE, 1967; VASILYEV,1967; WILLMANN (ed.), 1967; WITT, 1969; KHVOSTIKOV, 1970; BRONSHTEN and GRISHIN, 1970; and SCHR()DER, 1975, 1978) where the knowledge of NLC is well documented. Following the excellent summary published by FOGLEand HAURWITZ(1966) the NLC research results from the Earth surface observations in the Northern Hemisphere can be presented as:

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Color: bluish white. Height (average): 82.7 km. Latitude of observations: 45-80 ~, best visible at about 60 ~. Season of observations: March through October, best in June through August. Times of observations: nautical and part of astronomical twilight, while the solar depression angle varies from 6 to 16~ Spatial extent: 10 000 to more than 4 000 000 kmL Duration: several minutes to more than 5 hours. Average velocity: 40 m/sec towards SW; individual bands often move in different directions and at speed differing from the speed of the display as a whole. Thickness (geometrical): 0.5 to 2 km. Vertical wave amplitude: 1.5 to 3 km. Average particle diameter: about 3 • 10 ~5 cm. Number density of particles: 10 -2 to 1 per cm 3. Temperature in the presence of NLC: about 135~ The general properties of NLC, presented in a thorough summary by FOGLE and HAURWlTZ (1966), are valid also at the present time. Nevertheless, the last ten years in NLC research brought some detailization and made several questions more precise. We shall discuss some of these advances in the years 1966 to 1978 and shall pay special attention to the NLC studies carried out from orbital stations.

2. Climatology o f N L C

The subject of NLC climatology covers latitudinal, longitudinal, seasonal and daily regularities of their occurrence and variations as well as their activity characteristics. The data on NLC occurrences prior to 1964 are based on observations of many individuals (see e.g. BRONSHTENand GRISHIN, 1970) randomly distributed (in time and geographical coordinates). Starting from 1964, NLC observations were carried out by a large network of ground stations according to a unified program (see INTERNATIONALNLC OBSERVATIONSMANUAL,1970) in many countries (e.g. Canada, Denmark, England, Federal Republic of Germany, Ireland, Poland, USA, USSR). These observations allow us to investigate some problems of NLC climatology based on statistically sounder data. All earlier observations took into account only the location of the NLC observer on the Earth. A more convenient way of calculating the probability of NLC occurrences and their analyses lies in the determination of their spatial coverage above the points of the Earth's surface where NLC can occur. For every point at an altitude of 82 km above the Earth's surface, the direction towards the point of occurrence can be calculated from many nearby stations and the possibility and probability of discovering NLC at that point can be estimated from the given observation stations. The Bayes' estimate has been suggested by Vasilyev (see WILLMANNand VASILYEV,1973; VASILYEVet al., 1975) for the above calculations.

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The first calculations were carried out on the probability of the presence of NLC at individual points of the Earth's surface and in accordance with the chosen significance level of p r o b a b i l i t y - a r e a s of NLC fields on the Earth's surface undoubtedly show the promising nature of the method suggested by Vasilyev. A probabilistic model of the seasonal and the latitudinal distribution of NLC was elaborated by VASmYEV and MELNIKOVA (1975). They demonstrated that the earliest maximum (in the first decade of June) occurs in the latitude of 45~ later this maximum shifts towards the north and in the first decade of August lies in latitudes of 67~ The problem of variations in NLC activity during the whole observation period (starting from 1885) was investigated by many authors. The summary of the number of nights with NLC is given in Fig. 1. As was pointed out by FAST and FAST (1977) this long muttiyear data set is so inhomogeneous that it is not possible to deduce a statistically sound estimate of the NLC activity in these years (see also DIETZE, 1973). Nevertheless, the number of nights in the given year when NLC occur can serve as a crude characteristic of NLC activity. Figure 2 gives the dependence of the number of nights with NLC (nt) on the number of stations that record these NLC occurrences (mr). Numbers at the circles indicate the year of occurrence. Figure 2 shows that theoretical maximum number of nights with NLC cannot exceed 160, while the maximum observed value nt was 144 (in the year 1966). Figure 3 illustrates the annual variation of NLC activity calculated on the basis of NLC occurrences in ten-day periods all over the globe. The activity is given in tenths: 10 indicates that every night somewhere over the Earth N L C were observed, 0 denotes that in the decade no NLC were observed all over the nt ! T50 ~ 730 I10 90 7O 50 JO lU 1890

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globe. Activity of NLC occurrences increases in summer and has a maximum in July. Figure 4 shows the annual mean activity deviations from the eleven-year mean value (which is taken to be a zero line). In the years 1964-67 the NLC activity was considerably higher than the mean value, in the years 1958, 1959, 1969-72 it was considerably lower. The eleven-year cycle was also clearly observable from the uniform observations carried out in 1957-72 by the observers of the All-Union Society of Astronomy and Geodesy of the USSR. All these observations were carried out in the latitude zone 54 to 59~ Figure 5 gives the number of the NLC occurrences observed in this zone: a maximum occurs in the year 1967 and a minimum in 1971. As pointed out by FAST and FAST (1977), in the year 1976 the NLC activity was rather high. FAST and FAST (1977) drew the following conclusions on the NLC climatological research from the earth surface: (1) the season of NLC occurrences begins in the Northern Hemisphere in the first half of March, the end of the season is less pronounced, ranging from late October to November; (2) 68.7700 of nights and 90.6~ of reports of NLC occurrences fall in summer months, almost a half of the reports, and 28.3700 of nights fall in July;

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(3) in the same latitude belt the frequency of N L C occurrences is the same for any longitudes; (4) the belt of the N L C observation zone is in latitudes 45-71 ~ occasional N L C appearances have been recorded as far as 81-82~ the latitudes 53-57~ are optimal for N L C observations;

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(5) towards the north the period of maximum frequency is gradually shifted to a later time; (6) NLC are observed before midnight only in 37% of the observation time, though NLC occur more often before midnight; (7) NLC are observed during some minutes up to 5 hours and more, bright NLC are observed for 4 hours and more; (8) N L C tend to appear on several successive nights (forming a series of occurrences); (9) in the activity of NLC is revealed an 11-year period with a maximum occurring 2 years after the minimum solar activity. Over the Southern Hemisphere we possess only a limited number of observations from which it is not possible to draw sufficiently reliable long-term climatological conclusions. A summary of NLC observations in the Southern Hemisphere is given by FOGLE and HAURW[TZ (1966). An illustration of the NLC occurrences at 53~ at Punta Arenas, Chile, is given by Fogle in Fig. 6. It appears that the peak of the NLC activity at 53~ occurs some 20-30 days after the austral summer solstice. NLC observations from the Soviet Antarctic stations have been carried out starting from the year 1965 (see e.g. KREEM, 1967, 1968; DOLGIN and VOSKRES~NSKn, 1973), but their maximum occurrence lies in the period of a polar day and therefore only limited data on the transitional months, on autumn and spring are available (see also KILFOYLn, 1968). In the papers by McKAY and THOMAS (1978), COAKLEY and GRAMS (1976), HUMMEL and OLIVERO (1976), HUMMEL (1977) estimates were made of the effect of N L C on the global climate. The analysis of COAKLEYand GRAMS (1976) implies that for ice particles of 10 -5 cm radius in a 10 km thick layer, a density of 12 x 10 -12 g km -3 would produce a drop of 1~ in the global surface temperature. This result is consistent with regional temperature effects present in polar mesospheric ice clouds derived by HUMMEL and

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Percentage of clear nights with NLC at Punta Arenas, Chile, during the austral summer of 1956-66. OLIVERO (1976). MCKAY and THOMAS (1979) pointed out that the solar system in its motion through the galaxy may have suffered a number of encounters with a dense interstellar cloud for which the number density of molecular hydrogen H2 is higher than 10a cm-3 and then the Earth's atmosphere would be subjected to an interstellar H2 flux of 7 x 109 cm-2 sec-1 for periods of l0 s years. This could greatly enhance the water vapor content in the middle atmosphere, reducing the mesospheric ozone concentration and thereby lowering the average temperature and altitude of the mesopause. As a result of this, widespread mesospheric clouds would occur increasing the planetary albedo and the resulting radiative cooling at the surface may have been sufficient to 'trigger off' an ice age. Later on, HUMMEL (1977) showed that ignoring the diffuse nature of the radiation reflected from the Earth-atmosphere system below NLC, as was done in the previous simple models, can result in an overestimation of the climatological impact of aerosols in sign and magnitude by a factor of 4-6, especially when one calculated regional (polar cap) effects. This is consistent with the results of calculations by BRASLAUand DAVE (1973), that an increase of the absorbing aerosol in the atmosphere may lead to cooling or heating depending on the scattering and absorbing characteristics of the aerosol substance and upon the location of dust within the atmosphere. All these calculations include such aerosol parameters as number density, size distribution, refraction index, which have not been determined in the NLC layer with sufficient reliability, and for that reason the climatic effect of N L C needs further investigation.

3. Morphology and dynamics of NLC A specific character of N L C is their extremely diverse, often complicated and filigreed morphological structure. The study of this structure enables one to make

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several conclusions on the physical nature and genesis of NLC as well as upon the processes in the mesopause and its adjacent layers. The morphological classification of NLC was proposed by GRISHIN (1954, 1955a,b). This classification served as a basis for internationally accepted classification (e.g. GRISmN, 1957; INTERNATIONAL NLC OBSERVATIONMANUAL, 1970) and was used as an aid for observers during the I.G.Y. and the I.Q.S.Y. The above papers contained a detailed description of the NLC morphological structure using five main types and seven subtypes. We summarize in the following the description of NLC structural types as it enables one to understand the build-up and genesis of a N L C field. Type L Veils: These are very tenuous, lack well-defined structure and are often present as a background to other forms. They resemble cirrus clouds, occasionally contain faintly fibrous structure, and often exhibit a flickering luminosity. Veils are the simplest form of NLC and often precede (by about half an hour) the appearance of NLC with well-defined structure. Type II. Bands: These are long streaks, often occurring in groups arranged roughly parallel to each other or interwoven at small angles, but occasionally an isolated band is observed. Two groups of this type occur: II.a, are comprised of streaks with diffuse, blurred edges; II.b, have sharply defined edges.

Type IlL Billows: These are arrangements of closely spaced roughly parallel short streaks. The distance separating adjacent billows ranges from about 1 to 10 km. Billows sometimes lie across the long bands, giving the appearance of a comb or feather. At other times they appear alone against the veil background. The billows may change their form and arrangement, or appear and disappear within several minutes or tens of minutes, much more rapidly and frequently than the long bands. This NLC type also may be divided into two groups: III.a, are comprised of short, straight and narrow streaks; Ill.b, exhibit a wave-like structure with undulations.

Type IV. Whirls: These are partial or, on rare occasions, complete rings of cloud with dark centers, and may indicate the presence of turbulence near the mesopause. They are sometimes seen in veil, band and billow forms. Three subgroups may be observed: IV.a, are comprised of whirls of small radius of curvature (0.1 to 0.5~ and may appear as small bright crests looking somewhat like light ripples on a water surface; IV.b, have a form of a simple bend of one or several bands with the radius of curvature of 3-5 ~ IV.c, have a large-scale ring structure.

Type 1I. Amorphous: These are similar to veils in that they have no well-defined structure, bu t they are brighter and more readily visible than the veil type.

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In complex displays, two or more forms may be seen simultaneously, and it is not unusual for two intersecting groups of long bands to occur, and these give rise to bright knots where the waves cross. It is worth noting that the above classification, which was deduced from the observations carried out on the Earth's surface, is applicable also to observations from space. NLC descriptions and sketches in logbooks of the orbital stations 'Salyut-4' and 'Salyut-6' made by the Soviet astronauts V. Sevastyanov, P. Klimuk, G. Grechko and J. Romanenko indicate that the morphological structure of NLC is discernible from space (e.g. WILLMAYN et aL, 1977). The special features of NLC structural forms are evidently connected with their formation mechanism on the one hand and with the dynamic processes in the atmosphere on the other hand. To study these connections the temporal-spatial NLC field parameters and their genesis must be determined. Spatial parameters include the altitude of the NLC field and the geographical coverage, the thickness of the NLC layer and the simultaneous existence of several layers. Genesis is expressed in temporal variations of the NLC field extent as well as in variations of its morphological structure. In the period 1885 to 1967 were published data on 4166 cases of NLC height determinations (e.g. TSERASKII, 1887; JESSE, 1887, 1896; STORMER, 1933; BUROV, 1959, 1966, 1967; WITT, 1962; FOGLE, 1966; DIRIKIS et al., 1966; FRANZMAN and FRANZMAN, 1967; BRONSHTENand GRISHIN, 1970). The weighted mean value of the NLC layer height is 82.97 kin, the maximum and minimum values measured being 95 and 73 kin. It should be mentioned that this result agrees excellently with the mean value obtained from 187 photogrammetric measurements by JESSE (1896), which was 82.08 + 0.009 km. It is remarkable that in some years NLC heights vary in comparatively narrow altitude limits: e.g. in 1958 NLC height varied from 81 to 85 km (598 measurements). Moreover, height determinations by different authors in different geographical locations, made on the same night, differed less than 0.5 km. But there exist years when the height of NLC varies within broad limits: e.g. in 1964 measurements in Estonia and Latvia gave the NLC height range 74-95 kin. Very likely conditions for NLC formation at different moments and locations differ and this is expressed in a large variation of the NLC heights in some years. It was pointed out that the areal coverage of NLC fields varied in a range of 2 • 10~ to 3.6 x 106 km 2 (FOGLE, 1968). The NLC observation data from the surface network processed at the Tartu NLC Center confirmed this estimate. Figure 7 illustrates the areal coverage of NLC fields. Statistical analyses of the data derived from the global surface observations during the I.Q.S.Y. allowed W~LLMANN(1968) to conclude that NLC fields can cover considerable parts of latitudinal belts north of 45~ This was later confirmed by space observations (WILLMANN et al., 1977), and a considerably more complete picture of the coverage and of the specific features in the morphology of NLC was

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Figure 7 Distribution of NLC fields on 24-25 July 1964, deduced from surface observations. obtained. An extract from the notes made by V. Sevastyanov in the log-book of the Orbital Station 'Salyut-4' can serve as an illustration of this: ' . . . i n observations of N L C it struck me that they not only enrapture the observer, but also attract his attention with their unusual picturesqueness. ' I was struck: (1) by their appearance (lustreless, but very intensive color, I called it " m o t h e r of-pearl"-like); (2) by their extension (we observed them over Kamchatka, but on another orbit we saw them extending from the Urals to Kamchatka. Later on the same day we observed them over Canada);

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(3) by their fine azure structure. Their strict upper border (never higher than the "aureole") sometimes reaches its height. Then they (NLC) are visible over the sunlit horizon. Their structure is swan-feather-like, when NLC are observed full in the face; (4) not only by their lateral extension but also their extension in depth. In depth we observed them in different phases...' and further: ' . . . ( I ) are they rotating? Certainly, they are rotating. Together with the Earth's atmosphere but at a speed which is considerably less that of the Earth, i.e. observing them from the Earth surface they must move at a high speed in the direction opposite to the Earth's rotation. (2) They spread over the whole latitudinal belt'. The monitoring of NLC fields from space allows us also to specify the question of the multilayered structure of NLC. GRISmN (1952, 1955b, 1967) deduces from the observations carried out in the years 1950 and 1951 that NLC can occur in twolayered form. He pointed out that as a rule veils occur lower than the wave forms of NLC. The multilayered structure of NLC is distinctly observable from time-lapse cinematography. In some cases different layers of NLC move in different directions. Theoretically the question of the two-layered structure of NLC was discussed by NovozHirov (1962, 1967). He showed that in the mesopause it is possible for two layers to exist with a minimum temperature. Two-layered (even three-layered) NLC fields have also been described from space observations (WmLMANN et al., 1977). There exists no unique theory explaining genesis and distribution of NLC. Several observers (e.g. CHRISTIn, 1969) pointed out that the evidence for a direct relationship between synoptic distributions of NLC and the quasi-geostrophic systems in the tropospheric circulation has been shown to be ill defined. A more indirect coupling mechanism may exist in internal gravity waves originating in the tropospheric jet streams (e.g. HINES, 1959, 1968; AUFF'MORDT and BRODHtJN, 1974). CHRISTm(1969) proposed that the gravity waves, generated sporadically during periods when the mesopause temperature is less than 140~ propagate energy upward, and generate locally increased vertical eddy mixing throughout the upper mesosphere and lower thermosphere. He showed that in the summer mesosphere local supersaturation, in the steady state, could result at the mesopause with an eddy transfer coefficient of about 10 -3 km 2 sec-1. This value is one order of magnitude higher than that given by HESSXVEDr(1969). Thus, NLC may be formed in a region where a local increase in the eddy transfer coefficient has resulted from the gravity wave coupling, and may be advected out of the source region for some considerable distance before evaporating. To prove this it will be necessary to study the effect of the gravity wave source region on NLC, either directly or by means of large-scale parameters found indicative of the gravity wave source.

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HAtn~WITZ and FOGLE (1969), HAURWITZ(1971, 1972) showed also that bands and billows in NLC fields can appear on the ridges of internal gravity waves. REITER and HAtntWITZ (1974) inferred that wave formations observed in NLC regions are most likely generated in situ and not propagated upward from the troposphere. KROPOTKINAand SrIEVOV(1975) also noted that lunar tides, being manifestations of longwave gravity waves, can lead in the summer mesopause to a drop of temperature of 15-20~ and most likely cause the formation of NLC in the form of uniform veils.

4. Characteristics of the mesosphere This section reviews some physical and chemical properties of the Earth's atmosphere relevant to the understanding of the NLC phenomenon.

4.1. Temperature of the mesopause Essential additions to the U.S. Standard Atmosphere 1976 of the Arctic and Subarctic Region, where NLC occur, were prepared by COLE and KANTOR (1977, 1978). Sets of monthly reference atmospheres, which show the seasonal changes in the vertical distribution of the temperature, pressure and density for altitudes up to 90 km, are presented there. Estimates of the magnitude of the diurnal, day-to-day and spatial variability of temperature and density are included. In the lower layers the assumption of the local thermodynamic equilibrium (LTE) enabled Kirchoff's law to be applied so that the Planck black-body function could be employed as a source function in radiative transfer calculations. At high levels in the atmosphere LTE is no longer a good assumption, and the molecular processes involved need to be considered in more detail. However, at the height of the mesopause (80 km) one can yet consider that the rates of excitation and de-excitation by collisions will be sufficiently rapid so as to dominate over radiation processes. This is the situation of local thermodynamic equilibrium. As the temperature in the mesopause appears to be an important parameter for NLC formation, and since NLC seem to form in a thin layer, it would be of great interest to obtain continuous temperature measurements over the height range of 75-90 km. Curves representing the sum of the annual and semiannual cycles of temperature for altitudes between 30 and 80 km are shown in Fig. 8 for Churchill, Fort Greely, Thule and Point Barrow (COLE and KANTOR, 1977). These measurements confirm the deduction of KELLOGand SCHILLING(1951) that the mesopause at high latitudes is warmer in winter than in summer. Latitudinal temperature-height cross-sections of mean monthly temperatures for January and July are shown in Fig. 9 (COLE and KANTOR, 1978). At latitudes 60~ and 75~ the observed day-to-day variations

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Latitudinal temperature-height cross-section of monthly temperature for January and July.

the space observations of NLC on board 'Salyut-6', carried out by Soviet astronauts Yuri Romanenko and Georgii Grechko in the period from December 1977 to March 1978 (see Sections 7 and 8 of this paper), the systematic weekly launches of Soviet meteorological rockets M-100B were performed at the Soviet Antarctic Station 'Molodezhnaya' (68~ 46~ with the aim of determining temperature and wind profiles up to 80 kin. The temperature was measured by using standard rocketresistance thermometers (e.g. IZAKOVet al., 1967). The wind velocity and its direction was detected by tracking the cloud of dipole reflectors (chaff clouds) (PAHOMOV, 1969). The uniform data-set was derived from December i977 to March 1978. The apogee of rocket trajectores was at a height of 85 to 86 kin. A careful critical analysis of the data and an improved data-processing technique allowed Fedynsky to determine mean temperature profiles up to 84 km (see Fig. 10). Average deviation from the mean profile is presented in Table 1. The temporal variation of isotherms above 'Molodezhnaya' is presented in Fig. 11 for altitudes of 78-83 kin. Figure 11 indicates that at a height of 84 km (and higher) there occu r periodically regions with extremely low temperatures (100-120~ The air remains cold also after an adiabatic descent. At heights of 80-79 km these temperature contrasts are considerably smoothed out. Just these periods of a local drop in temperature at an altitude of 80 km are accompanied by the occurrence of intensive

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H~sml

83

82.

81.

80

7g'

78 t00

tt0

120

eO

140

~50

150

Zf*gl

Figure 10 Temperature as a function of altitude according to rocket soundings carried out at the Soviet Antarctic Station ' M o l o d e z h n a y a ' in the period of December 1977 to March 1978. Shaded area indicates variations during different launches.

NLC (see shaded areas in Fig. 11). In the intervening periods of warming NLC disappear. The existence of the general trend of warming in the period studied can be explained by the seasonal variation of the temperature in the mesosphere. The temperature of the mesosphere increases in the austral winter. The maximum decrease of the temperature is reflected in independent wind measurements. A considerable decrease in temperature is connected with the intensification of the eastward zonal flow. An increase in temperature corresponds to the periods of weakening of the eastward zonal flow and to a rise of the meridional flow. Sometimes the eastward flow changes even to a westward one. It should be emphasized that the above local temperature variations are worth more detailed further investigations.

Table 1 Average temperature profile and temperature variation according to rocket soundings at 'Molodezhnaya" (68~ 46~ from December 1977 to March 1978 H(km)

T~ AT~

78

79

80

82

82

83

84

156

151

147

144

147

140

129

7.0

9.3

11.2

9.8

12.1

19.6

26.5

544 Htgt311m

O . A . Avaste e t a l .

f]0

~20#f0

if0 ~

t60

#?/7 ~

r

(Pageoph,

fS0 t50

r

~O #~ ~0

f50

OATE OFLAUI~CH

Figure 1 1 T e m p e r a t u r e variations over the Soviet Antarctic Station ' M o l o d e z h n a y a ' in the altitude interval

of 78 to 83 km in the period of December 1977 to March 1978. At heights of 78, 80 and 82 km, wind velocities and directions are indicated. Shaded areas show NLC existence observed from the Orbital Station 'Salyut-6'. Probably NLC continued their existence on 4 February 1978, but then astronauts did not carry out any observations.

4.2. Chemical composition The chemical composition of the atmosphere is fairly uniform up to 80 km, when we consider the main components N2 and 02. Above this altitude photodissociation produces a marked increase of atomic oxygen. A brilliant review of the neutral composition of the stratosphere and the mesosphere is given by ANDERSON and DONAHUE (1975).

4.3. Ionosphere Ionization of the upper atmosphere depends primarily on the Sun and its activity. The major part of ionization is produced by solar ultraviolet radiation, X-rays and corpuscular radiation from the Sun. As the Earth rotates with respect to the Sun, ionization increases in the sunlit atmosphere and decreases on the night-side. It is reasonable to seek a correlation between N L C parameters and the ionospheric D layer (the part below 90 kin) and the E region (90-160 km). There exists so far no general and overall theory to explain all the peculiarities of the ionization in the D

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region. According to HOUSTON (1958) the electrons in the D region arise from the ionization of NO by Lyman-alpha radiation. HUNTENand MCELRoY (1968) proposed an additional mechanism ionizing the excited molecules O2(1Ag) by the radiation of the wavelengths A = 1027-1118 A. In the night-time the main agent of ions in the D layer seems to be electrons with the energy of n x 10 KeV; GOLDBERGand WtTT (1977) determined from the rocket mass-spectrometric measurements that in the case of NLC occurrences the concentration of ion dusters H30 + • (H20)~,, m = 2-4 and NO + x (H20),, n = 2-3, is in the mesopause by one order of magnitude higher with no NLC. They also noticed that in the layer of 81-86 km are present heavy ion clusters with atomic mass 70 to 128 which contain Fe +, FeD + and FeD +. GOLDBERGand WITT (1977) drew the conclusion that these heavy clusters could act as condensation nuclei where ice crystals grow in the cold mesosphere as a result of the nucleation process. Some theoretical estimates of this kind of NLC formation were discussed by REID (1975) and BURI~E(1977). REID (1975) showed that nonspherical ice particles could fall in the mesopause sufficiently slowly to achieve optically observable sizes in the NLC layer. LAUTER (1974) pointed out that the height distribution of both NO and of the minor constituents involved in water-cluster chemistry will strongly depend on atmospheric dynamical transport processes, like turbulence and advective transport. The thermo-dynamic and circulation regime of the mesosphere has been reviewed in a monograph by RAKIPOVAand YEFIMOVA(1975) and in a recent monograph edited by PORTNYAG~Nand SI'RENGLER(1978). But it should be pointed out that while there exists reasonably good agreement between observations and theory in the mesosphere for odd hydrogen, nitrogen and oxygen systems, serious shortcomings exist in our empirical knowledge of other minor species and of the coupling between dynamics and chemistry in the upper layers. Hopefully the global measurements of the concentration of minor constituents of Nimbus 7 satellite will soon be available and will serve as a basis for a more detailed investigation of the interrelation of the parameters of the mesospheric and ionospheric structure. 4.4. Water vapor concentration

The water vapor concentration in the mesosphere is an important parameter studying the physical processes connected with NLC formation. The available experimental data are rather contradictory. Episodic and sparse measurements of water vapor in the mesosphere show a scatter of data as large as two orders of magnitude. This is partially caused by the use of different methods of measurement. Numerous photochemical models which consider formation and destruction of such minor constituents as H20, CH4, H2 etc. under the influence of solar ultraviolet radiation (HESSTVEDT, 1964; HUNT, 1963, 1973; SHIMAZAKIand LAIRD, 1970; NICOLET, 1970; ANDERSON and DONAHUE, 1975; and others) made use of basic information on the relative water vapor concentration measured in the lower stratosphere: usually the

546

O.A. Avaste e t al.

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value of the mixing ratio equalled 2-3 x 10 -6 g/g. Considering the fact that the atmosphere must be well mixed, this value is inserted into calculations also at the height of the mesopause. However, taking into account that even at a height of 30 km there exist contradictory data on the 'dry' and 'moist' stratosphere models, such an approach needs a critical analysis, the more so as the majority of recent measurements indicate considerably higher values of the water vapor mixing ratios at a height of 30 km compared with the earlier data (e.g. BLrR~ERTet al., 1974; EVANS, 1974; CHALONERet aL, 1975; RADFORDet al., 1977). A more detailed survey of the water vapor concentration in the mesosphere up to I

I

I

I

I

I

I

I

Ht~

50 40 f0q' 30

.20

\ -~40

-f20

-tO0

-NI

-60

-40

-gO

0

*tO

.40 T('l)

Figure 12 Water vapor mixing ratio versus altitude: (1) data generalized by SONNTAG(1974); (2) measurements carried out by FEDYNSKYand YUSHKOV(1974); (3) by EVANS(1974); (4) by ABADIE(1974); (5) by MARTELLand EHHALT(1974); (6) by PEROV and FEDYNSKV(1968); (7) by CHYZHOVand KIM (1970); (8) by ARNOLD and KRANKOVSKV(1977); (9) by MARTVNKEVICH(1972); (10) by QUESSETTE(1968); (11) by MARKOVe t al. (1978); (12) by KONDRATVEVe t aL (1976). Curve T~ gives the mean temperature at 60~ in July (COLE and KANTOR,1978).

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100 km is given by SONNTAG (1974). The data generalized by him are indicated in Fig. 12 as a shaded area (1). Figure 12 illustrates more recent data on the mesospheric water vapor, which were obtained by different methods: curve 3 gives optical rocket measurements (EVANS, 1970); curve 4 shows the results when aluminum oxide sensors were used (ABADIE, 1974); curve 5 denotes the results of cryogen traps of two launchings by MARTELLand EHHALT (1974); curve 6 represents data obtained by means of Pirany gauge type heat recorders (PEROV and FEDYNSKY, 1968); curve 7 displays data derived from absorption in the Lyman-alpha band (CHYzHOVand KIN, 1970); curve 8 gives mass-spectrometric measurements by ARNOLD and KRANKOVSKY (1977); curve 9 illustrates mass-spectrometric measurements by MARTYNKEVICH (1972); curve 10 shows optical measurements by QUESSETTE(1968); curve 11 indicates optical measurements obtained by MARKOV et al. (1978) from the orbital station 'Salyut-5'; asterisk 12 shows an estimate from optical measurements performed aboard 'Salyut-4' (KONDRATYEVet al., 1976). All the data are given in curvilinear coordinates. Thin solid lines indicate isolines of water vapor mixing ratios. In the period of 1977-79 FEDYNSKYand YUSHKOV(1974) carried out measurements of the water vapor mixing ratio using Pirany gauge type heat recorders at Volgograd (46~ and at the station Tumba (8~ These results with the above uniform apparatus and data processing techniques are presented in Fig. 12 as a shaded area (2). The data received by the above method allowed Fedynsky to study the water vapor mixing ratio (in the altitude region of 30 to 80 km) dependence on the season: the results indicated a distinct annual cycle with a maximum in July-August and a minimum in January-February in the Northern Hemisphere. It should be noted that in Fig. 12 solid lines give measurements in tropical regions, and broken lines in middle latitudes. Humidity in the mesopause in middle latitudes always exceeds that in the tropical zone. All soundings indicated that the water vapor mixing ratio increases with height, but nevertheless in tropical regions the atmosphere is closer to the ' d r y ' model up to 50-60 km. In middle latitudes, especially in the summer period, the increase of the mixing ratio is observable starting from the height of 25-30 kin. The quadratic mean error is less than 4 0 ~ ; this value is considerably lower than the mixing ratio variations observed. It should be noted that the differences in the water vapor mixing ratio estimates one based on the data from the orbital station 'Salyut-4' (see KONDRATYEV et al., 1976) and the other from the orbital station 'Salyut-5' (see MARKOV et al., 1978)are explainable as the first estimate was made on the basis of the measurements over the tropical zone, the other over middle latitudes. It follows from the above discussion that the water vapor concentration in the mesosphere depends not only on the season but also on the latitude. Episodical measurements of the water vapor at 80 km using different methods must be systematized and submitted to a critical analysis, taking into account the accuracy of the measuring techniques. The cause of the increase of water vapor mixing ratio with the height and latitude is still under discussion.

548

O.A. Avasteet al.

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Estimates show that the observed increase of the water vapor mixing ratio could be explained by taking into account the velocity of the vertical drift in the atmosphere of 1 mm sec-1; nevertheless the scarce data on the vertical and meridional velocity components measured independently are insufficient for the construction of global models. From the standpoint of the condensation hypothesis the temperature data (given in Section 4.1) show that in the summer period in the mesopause water vapor easily reaches the supersaturation condition. This is illustrated by the curve of the mean temperature at 60~ in July according to COLE and KANTOR (1978) (curve Ts in Fig. 12). Ion clusters (e.g. MARTVNKEVICH,1973; WITT, 1974b)or aerosols of meteor origin (BRoNSHTEN, 1950) can serve as condensation nuclei in the formation of NLC.

5. Aerosols in the mesosphere

The suggestion that NLC particles may be composed of ice belongs to WEGENER (1925, 1926), JARDETSKY0926), HUMPHREYS(1933) and VEGARD (1933). This idea was reviewed and quantitatively examined by HESSTVEDT(1961). This idea has gained general acceptance, as measurements and theoretical estimates of the temperature and the water vapor content in the mesosphere have shown that supersaturation conditions might well be expected to occur in the high-latitude summer mesopause. The idea of the condensation mechanism of NLC particles was in recent years supplemented by the coagulation mechanism proposed by RosINsI~I and PIERRARD (1964), ANDREYEV et al. (1975). They pointed out that considering the lower water vapor concentration in the mesopause the condensation mechanism is insufficient in forming NLC ice particles. So they assumed that spatial-temporal changes in aerosol characteristics are mainly controlled by vertical air currents and the influence of relative humidity on the aerosol structure. In case of low absolute humidity the main mechanism of particle growth must be coagulation of particles. The nonspherical form of particles is typical for crystals formed from hydroscopic materials. The origin and chemical composition of condensation nuclei has been discussed in many papers. A theoretical estimate of the accumulation of cosmic dust in the mesopause was made by DMITRIYEV0959) (see also FOGLE and HAURWITZ, 1966). Rocket samplings by HEMENWAYet al. (1964a,b), W[~rT (1967), Flocco and GRAMS (1971), WlTT et al. (1976) gave a rather good agreement with the theory. Flocco and GRAMS (1971) concluded that in the polar summer mesopause the particles with the radius r = l0 -6 to 5 • 10 -~ cm can be trapped for a period of 1-5 days and they could turn to condensation nuclei in case of the formation of NLC. Later in 1970 (see HEMENWAYet al., 1972; HEMENWAY,1973) nickel and iron nuclei were determined from two rocket experiments carried out at Kiruna, Sweden. HEMENWAY(1973) also put forward a suggestion that particles of La, Tu, Pr, Os, Yt, Ta were present in NLC, but this has not been confirned by other investigators.

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Electron micrographs of NLC particles captured in rocket experiments (e.g. SOBERMANand HEMENWAY, 1965; WITT, 1968; S~:RWANEK, 1969; HEMENWAYet al., 1972; HEMENWAY, 1973) showed that there was usually a halo-like structure around the particles. This structure is impressive only when NLC exist and it has been interpreted as a volatile particle coating, possibly being due to the ice coating on the particles collected from the NLC layer (see Fig. 13). The existence of a permanent layer of light scattering particles in the polar mesopause during the summer months was inferred by DONAHUE et aL (1972). They carried out measurements of the vertical brightness profiles by means of a scanning two-color photometer (~ = 5893 A and 5577 A) on the OGO-6 satellite. DONA~UE and GUENTH~R (1973) showed that the probable thickness of this aerosol layer is less than 5 km and that it is located close to the mesopause having an average height of 84.3 km. They found that the concentration of scattering particles increases by a factor of between 50 and 100 between 65~ and 80~ (see Figs. 14 and 15). They also inferred that this intense scattering layer, whose average vertical optical thickness

Figure 13 Electron micrographs of noctilucent cloud particles collected in a rocket experiment.

550

O . A . Avaste et al.

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2.7 x I0~

i0 3 YELLOW 786 ~ LATIIUDE 175 DAY, 1969 10:27 UT

RAYLEIGH SCATTERING

2.'/x 103

SCA11ERING'LAYER n-

0~

.E

n,,

la

.E

o

2.1x10 zn"

c

._o

E

rr"

t~

21

50

100 Altitude

150

2.1

in km

Figure 14 Slant emission rates observed by OGO-6 airglow photometer at 5890 ~ above the horizon as a function of the altitude of the closest approach of the line of sight for 78.6~

is r = 10 -4, develops over the polar region about 15 days before the solstice and is a permanent feature of the summer polar atmosphere. This scattering layer seems to be a daytime manifestation of N L C ; assuming that the particle radius is r = 10 .5 cm (WITT, 1968, 1974a,b; FARLOW et al., 1970; DONAHUE et al., 1972), the particle concentration must be 15-40 particles per cm 3. This concentration of particles is considerably higher than that estimated in the noctilucent cloud layer (e.g. WITT, 1968). Assuming that particles of the polar aerosol layer are also ice-coated nuclei, ANDERSON and DONAHUE (1975) estimated their total water content. Since each particle with a radius of 1.5 x 10 .5 cm contains 2.7 x 108 H 2 0 molecules, the water amount tied up in these clouds would be between 4 to 13 x 109 cm -3 at about 85 km. According to the model of hydrogen compounds presented by ANDERSON and DONAHUE (1975) the density of H2 at 85 km would normally be 8 x 10 a cm -a, that of H 2 0 about 7 x 107 cm -3 and that of H about 10 a cm -3, making the total 2H only 109 cm -a. This discrepancy could be explained by adding an efficient H~O transport mechanism

Vol. 118, 1980)

Advances in Noctilucent Cloud Research in the Space Era 2.71 I04

551

IOQ(

H SCATTERING

YELLO| 86.9* LATITUDE 64' SOLARZ IT50AY,1969 10:29UT

,,,~'SC~TTERING"LAYER :. ~,,,o~

,~

t

"4 "4 "4 "4

g

-1

g

4

~

~, z,,,o 2 - ~1,

1 "4 "4 -4

"4

27-

ISO ALTiTUOE iN km

Figure 15 Same as Fig. 14 except for 86.9~

to the cold trap in the polar summer mesopause. The above mechanism shows a characteristic build-up time of only about 5 days. On the basis of rocket soundings (e.g. HEMENWAY e t al., 1964a,b) and of optical measurements, WITT (1968) deduces that N L C particles can exist within a large radius range of 2.5 • 10 -6 cm _< r < 10 -4 cm. As a first approximation, the particle distribution is given by the Junge law dn(r)

= c •

r -v

d o n r),

where r is the particle radius. The constant c is a measure of turbidity depending on the number ofpartic/es in a cubic centimeter. The value v occurs in the range 2 < v < 3 (e.g. HEMENWAY e t al., 1964a). As presented above, many papers give an estimate of the mean particle radius r = 10 -5 to 1.3 • 10 -5 cm (e.g. FO6LE and HAURW~TZ, 1966). Three recent papers (TOZER and BEESON, 1974; HUMMEL and OLIVEgO, 1976; HUMMEL, 1977) also suggest that a practical upper limit of particle sizes in the N L C layer can be taken to be 10 -5 to 1.3 • 10 -5 cm. GADSDEN (1978) showed that their analysis is not convincing since cloud particles are non-spherical the deduction of the particle size from measurements of the degree of polarization is rather uncertain, if not erroneous. GADSDEN (1978) also pointed out that the discrepancy in the H 2 0 content estimate (see above) in the aerosol layer over the polar cap in summer derived by ANDERSON and DONAHUE (1975) could be due to assumed unrealistically small sizes of ice particles in the clouds which leads one to postulating impossibly high amounts of the mesopause water vapor.

552

O.A. Avaste et al.

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FRANK et aL (1970), DE BARY and ROSSLER(1974), GADSDEN (1975) inferred that the observations of the NLC gave an indication of 3 x 10 -5 cm as a characteristic radius of cloud particles. GADSDEN (1977a) noted that this could be revised down to 2 x 10-5 cm if particles are rod-like. GADSDEN(1977a,b) pointed out that if measurements show even a small amount of elliptical polarization, this is an indicator that there exist uniformly orientated elongated crystals in NLC; the presence of elliptical polarization indicates clearly that the NLC models involving only spherical scatterers need to be modified. In recent years a number of papers have been published where the optical properties of nonspherical particles are discussed. CHYLEK (1977) proved that the extinction cross-section of a randomly orientated nonspherical particle is always larger than the extinction cross-section of a spherical particle of equal volume. JENNINGS et al. (1978) showed that absorption is generally less dependent on the size distribution than extinction and in general is not linear with the imaginary refractive index, especially in case of broad particle distributions. FAXVOG and ROESSLER(1978) demonstrated that in a highly absorbing particle set the optically most active particles are those whose diameters lie in the range of 0.15 to 0.5L LATIMERet al. (1978) showed that the shape and orientation of particles can strongly influence the measurement of the whole particle size. The effects of the refractive index are also found to be significant but smaller. Results of calculations carried out by GOTTLER(1952) and FENN and OSER (1965) indicate that for compound particles with an absorbing nucleus smaller than about one-tenth of the total diameter of the particle, the optical properties are almost completely determined by the outer shell. The idea of ice-covered particles of NLC was generally accepted; their optical properties were estimated by using data on the complex refractive index of ice (e.g. IRVINE and POLLACK,1968; RAY, 1972). NLC were considered to consist of compounds of ice particles, minerals and metal particles (e.g. HEMENWAYet al., 1964a). It should be noted that if the ice shell is smaller than nine times the absorbing nucleus radius, the optical properties of two-layered particles are essentially different (e.g. R66M, 1974) and these peculiarities must be considered in future research on NLC optical parameters, especially in the first stages of cloud development. A systematic comparison of extinction and absorption efficiencies of nonspherical and spherical particles was carried out by WELCH and Cox 0978). They found that whether the nonspherical correction has any applicability depends on the distribution of particle sizes. Small ice crystals in the solar spectrum can lead to increases in the absorption coefficients of 2 orders of magnitude compared with those resulting from a spherical approximation. No significant difference was found in the extinction coefficients between the distributions of spherical and nonspherical particles. However, the nonspherical distribution led to smaller scattering parameters. It follows from the above that the effects of nonspherical corrections are in need of further research, especially when one tries to make estimates of the radiative

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equilibrium of NLC particles. Since we do not possess such calculations, it will be instructive to estimate the radiative equilibrium for spherical NLC particles. The radiative equilibrium of the spherical particles of different materials was studied by BAmULATOV and IVANIA (1976, 1977) and GRAMS and FIocco (1977). The radiative equilibrium temperature for particles was calculated by taking into account: (1) direct solar radiation, (2) solar radiation scattered in the Earth-atmosphere system, (3) thermal radiation from the Earth, (4) heat released in recombinations of oxygen. BAmULATOV and IVANIA (1976) demonstrated that the radiative equilibrium temperature of particles formed from Cu, Fe, C, SiQ, MgO and ice at a height of 80 km was essentially different. The dependence of the equilibrium temperature on height is given in Fig. 16. This figure demonstrates the difference between strongly absorbing particles (Fe, Cu, C) and dielectric particles of moderate absorption (SiO2, MgO, ice). For the first group the equilibrium temperature increases in the height interval between 80100 km and reaches the value in vacuum. Below 60 km the particle temperature does not differ from the surrounding air temperature. The above-mentioned high temperature gradient in a layer of 80-100 km is probably partially due to the high concentration of atomic oxygen in this layer, partially to an increase in the molecular temperature of the surrounding air as well as due to a decrease in heat conductivity according as the air density decreases. For the dielectric particles in the equilibrium temperature curve there appears a deep minimum near the altitude of 80 km and a maximum is observable in the lower thermosphere. This maximum is more pronounced in case of smaller particles. BAIBULATOV and IVANIA (1976) pointed out that the above-mentioned high gradient in the temperature increase in the 80-100 km layer of strongly absorbing particles leads to intensive evaporation, although the temperature is lower than the melting temperature of these particles. As a result, small condensation nuclei can be formed. Figure 16 (for ice particles) also carries a histogram of NLC heights (see BRONSHTEN and GRISHIN, 1970). The shaded area indicates the region where particle temperatures are lower than the saturation temperature at height of 80 kin. The minimum radiative equilibrium temperature for ice particles coincides with the height of maximum NLC occurrences. Figure 16 illustrates the fact that only in this altitude region can the temperature of ice particles be lower than the water vapor saturation temperature. For particles with r _< 10 -4 cm this condition is fulfilled for a wider height interval. BAmULATOVand IVANIA(1977) also carried out radiative equilibrium calculations of two-layered particles containing an absorbing nucleus (iron) coated with an ice shell. Let the radius of the nucleus be R1 and the particle radius be R2. Figure 17 presents the results for particles with R2 = 5 • 10 -6, 10 -5, 5 • 10 -5 and 10 -4 cm. The ratio R1/R2 increased with a step of 0.1 until the equilibrium temperature exceeded the saturation temperature at a height of 80 km, i.e. calculations were carried out in the temperature interval where ice particles can exist. Figure 17 shows that in the case

554

O.A. Avaste et aL

,+_

(Pageoph,

'+'I

[!l

~'

"~176 t........... "~

il

t "'b \iJ

2ooI ~ ! "do .'o ,Do ,b ,6 ,U

t6zt-

+ ~- r-'--~-Tl

'+t Y

Vi

'+'o ~o ,bo.,7o ,Do ,Do

+~176 ~1

I

+or i/,4"-.... ~1

'~176t l)7'--- .... I '+fElt

'~176

" .... -

'+r-~. ~,, ,,~oo +,1%

++o +co qo0

,so

soo

;;;

.o ,,o t\

~

z,o t

: l

[ 5 x 10 -4 cm) for A = 0.55/~m (BERGSTROM, 1973a; WILLMANN et al., 1973). Polarization properties of NLC models were analyzed in papers by VASILYEV and RADIONOV (1975), ZUEV et al. (1975). All these calculations were made assuming that particles of NLC were small compared with the radiation wavelengths, the effect of their shape was assumed to be small, too. This assumption is not very accurate as it was later shown by GADSDEN (1975, 1977a,b). Nevertheless, the calculated scattering intensities are quite correct. As pointed out by GADSDEN (1977b), the polarization properties of ice crystals are essentially different from those of spherical particles and the NLC models involving only spherical scatterers need to be modified.

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The NLC spectral brightness dependence on the wavelength in the visible and near infrared region was summarized by VESELOVet al. (1976). Figure 19 presents a comparison of the calculated (WILl.MANN and SER6EVEVICH, 1969) and measured (BRoNsnTEN and GRISnIN, 1970; FO6LE and REES, 1972) spectral brightnesses of NLC. Theoretical data show that the optical thickness of NLC can be approximated in the wavelength region of 0.2 to 4/~m by the curve r(A) = r(A0) x 5.5A~ exp (-2A~ where ro(A) is the optical depth of NLC at the wavelength ho = 0.55 tzm. The absolute spectral brightness of NLC according to the data presented in the paper by VESELOV et al. (1976) is shown in Fig. 20. In the above models NLC were assumed to form a uniform spherical layer. Some problems of the variability of NLC optical depth in this layer according to their morphological structure were discussed by AVASTE et al. (1977a). In general the optical depths of NLC can be described as a random function and the radiative

BA REI.ATJVEUNITS 70 ~

\ 10 o

r ..)~.

// ~

7

70 -7

~3

o,5

o,z

~8

7,z

/,s

Figure 19 Spectral brightness of NLC (in relative units) versus wavelength: (1) measurement (VESELOVe t al., 1976); (2) data presented by BRONSHTEN and GRISHIN (1970); (3) FOGLE and REdS (1972); (4) calculations by WILLMANNand SERGEYEVICIt(1969).

558

O.A. Avaste et

(Pageoph,

al.

TO-)

10 -~

~~

~

Figure 20 Brightness of NLC versus wavelength in W cm -2 sr-1/~m-l: (1) by VESELOVet by FOGLEand REES(1972); (3) by HARRISON(1973).

al.

(1976); (2)

transfer can be calculated in a stochastic medium (AvASTEand WILLMANN,1973). Avaste and Willmann determined the distribution function of NLC optical depths from photometric measurements of the NLC brightness. Figure 21 illustrates the optical depths distribution function of different morphological structures. Optical depths of NLC vary within the limits of 10 -5 to 5 • 10 -5. In case of a chaotic structure (e.g. type 'whirls') in the distribution function, secondary maxima are present and the distribution function broadens. The NLC optical depth distribution could be approximated by the ZOLD function (zero order logarithmic distribution) or by the superposition of these functions. In case o f ' w h i r l s ' the distribution function changes in the evolution of clouds; in case of stable 'waves' the distribution function practically does not change.

n(r~}

10-6

5./0-6

lo-S

5./o-S

r0-o

y./O-~rz

Figure 21 Distribution of the optical thickness in different NLC fields.

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7. Observation and photography of NLC from space For the first time the task of observing and photographing mesospheric aerosol layers from space was given to the team of the Soviet spaceship 'Voskhod' in 1964. Observations were carried out in the direction of the twilight aureole as well as in the nadir direction. Observations in twilight aureole conditions were assumed to be most favorable (which was also confirmed afterwards). Observations of the mesospheric aerosol layers in the nadir direction were assumed to be possible due to their structure at a suitable distance from the terminator when the subpoint of the spaceship moved into the Earth's shadow. Unfortunately, the above-mentioned spaceflight was carried out at a time which was quite unfavorable for NLC observations (in autumn in the Northern Hemisphere) when the probability of NLC occurrences is smallest on the planetary scale. Brightness observations revealed the presence of aerosol scattering in the mesospheric layer; however, it was impossible to determine the presence of pronounced aerosol layers which might have been interpreted as NLC (FEoKTISTOV et al., 1965). Later on the possibility of observing and photographing NLC from near-Earth space was studied in several papers (FESEYKOV, 1966 ; ROZENBER6, 1966a,b; JOSEPH, 1967; EERME, 1971, 1973; HOPPE, 1974). The idea of photographing NLC from space in the ultraviolet region at 2550/k was recommended by MARMO et al. (1967). In an intensive ozone absorption band the background emission of the atmosphere from layers lower than 40 km is practically totally absorbed in the ozone layer and calculations show that NLC with the particle concentration of 107 cm -2 in the vertical column can be photographed above the horizon. In the subsequent spaceflights Soviet astronauts continued attempts to observe NLC. For the first time an atmospheric optical phenomenon, which was later identified as an NLC, was observed from space by the Soviet astronaut Aleksei Leonov aboard the spaceship 'Voskhod-2' on 18-19 March 1965, and later by the Soviet astronaut Vitaly Sevastyanov on board the spaceship 'Soyuz-9' on 9 June 1970 (e.g. KONDRATYEV et al., 1971 ; WILLMANN et aI., 1975). Unfortunately, the photographs taken were underexposed. The observed clouds had a rather extended flat filament-cellular structure parallel to the Earth's horizon. The next visual observations of NLC from space were carried out by the pilot of the second Spacelab mission Paul Weitz (see PACKER and PACKZR, 1977) in May and in the first week of July 1973 near 50~ and 10-40~ NLC were observed a total of about four times during that mission. They were always seen at dawn and in the direction of the rising Sun, although clouds and the Sun were never observed together. The clouds were bright, as conjectured, and formed a thin bright line just above the Earth's horizon when first detected. As the spacecraft approached, the thin line appeared to become broken, and finally two or four patchy, thin, stratified clouds were visible. Their lateral angular subtense was of the order of 5 ~, and as the spacecraft drew nearer, the clouds appeared to rise above the Earth's horizon, finally vanishing into the airglow.

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More systematic observations of NLC were carried out aboard the Orbital Stations 'Salyut-4' in the Northern Hemisphere and 'Salyut-6' in the Southern Hemisphere (WmLMANN et al., 1977). Occurrences of NLC were visually determined by the astronauts in several orbits in the period lasting from 1-17 July 1975. An approximate territory over which NLC occurred on 3 and 4 July as well as the subpoint tracks of the OSS are given in Fig. 21. It should be mentioned that for the case illustrated in Fig. 21 only few ground observations were possible from the routine ground network on account of an overcast sky obtaining over the major part of this territory. These few ground observations confirmed that the NLC observed by the astronauts were comparatively bright (on a 5-point scale their brightness was estimated to belong to the numbers 4 and 5, i.e. their optical thickness varied from 10 -5 to 10-~). Visual observations indicated an important fact: certain types of NLC have a multilayered structure, which allows us to judge of a complex build-up of the mesopause. In addition to the above-mentioned visual observations, NLC occurrences were photographed. Considering the fact that the first expedition on the orbital station 'Salyut-6' was carried out from December 1977 to March 1978, it was hoped to discover NLC occurrences in the Southern Hemisphere. According to sparse ground observations, their maximum occurred in January. An unexpectedly large amount of bright NLC occurrences was detected. The number of occurrences was considerably higher than the one expected on the basis of current ideas. The wide spatial-temporaldistribution of a strongly developed NLC field shows that the occurrence of these clouds in the mesopause in the summer period in the Southern or the Northern Hemisphere, respectively, is by far not a rare phenomenon, at least not in the present state of the mesosphere. NLC were observed on 'Salyut-6' in altogether 127 orbits from 23 December 1977 to 2 February 1978, i.e. during 31 days. It should be noted that in this time interval several periods were detected when NLC occurred almost continuously. Thus from 24 December 1977 to 5 January 1978 NLC were observed in all orbits when their viewing conditions were favorable. On 6 January 1978 NLC seemingly abruptly disappeared, making its appearance again on 8 January in the form of a weak veil.

Figure 22 Subpoint tracks of the Orbital Station 'Salyut-4' on 3 and 4 July 1975, when NLC were observed. The sign 9 indicates ground observations.

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Active periods of NLC occurrences were also noted from 14 to 16 January and from 27 January to 2 February. Similar periodic NLC occurrences had been previously detected in the Northern Hemisphere by ground observations (e.g. FAST and FAST, 1977). NLC were always observed at a constant height (at 2 degrees above the horizon) both in the case of a negative and a positive height of the Sun (some degrees above the horizon). Their distance from the orbital station was detected from the geometry (see Fig. 23): when the spacecraft approached NLC, the NLC field seemingly rose from the Earth's horizon and had a pronounced wave structure. On reaching the height of 2 degrees (height of the perigee about 80 km), their brightness increased as their structure seemingly disappeared since they were transformed into a bright thin line above the horizon. Cases were noted when an NLC field extended over the whole southern horizon and it was observed during 7-8 successive orbits. This shows that NLC sometimes completely cover a latitudinal zone, sometimes exceeding a half of the whole latitudinal belt. The above-mentioned fact had been earlier noted for the Northern Hemisphere (WILLMANN et aL, 1977). The observations carried out aboard 'Salyut-6' confirmed this also for the Southern Hemisphere. According to preliminary estimates, NLC in the Southern Hemisphere are situated at latitudes higher than 53-55~ As is known, the wave-like structure is the most frequently observed type of a NLC field. In space observations it is easy to detect medium (20-100 km) and long waves (100-280 kin). It is more difficult to detect short waves (3-12 km). The geometrical effect of the projection of a spherical layer on to the horizon complicates the detection of the fine structure. Therefore a space observer may mistake a projection 8

,/

o Figure 23 The geometry of NLC observations from space.

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of 3-12 km waves for the multilayered structure. This does not mean that multilayered NLC do not exist at all. Both ground observations and photography from space reliably determined the existence of a multilayered structure of some morphological forms of NLC. Altogether 40 black-and-white and 5 colored photographs of NLC were made on board 'Salyut-6' during the first mission. By way of illustration two photographs are presented in Figs. 24 and 25 (one taken when the Sun was above the horizon, another taken when the Sun was below the horizon). A color photograph of NLC from space is given on the frontispiece of this volume. Below will be discussed some preliminary results of the photometric processing of several NLC photonegatives taken on 15 January 1978. Figure 26 shows photometric profiles of the brightness of the Earth's aureole made on 15 January, 17h, 36m MT, when NLC were present. The abscissae indicate angular height above the horizon, the ordinates denote the scaled brightness of the aureole and NLC. Different curves present the change in the azimuth from the Sun. The azimuth step of these brightness profiles was 1 degree. This family of curves shows the morphological structure of this NLC field and illustrates the wave-like structure of this NLC layer, which is projected onto the horizon of the space observer. The decrease of brightness with an increasing azimuth angle is due to the effect of the scattering phase function. The contrast of NLC relative to the aureole was calculated by using the equation K

=

(B,

-

where Br is the absolute brightness of the aureole, Br~Le -- the absolute brightness

Figure 24 A photograph of the Earth's horizon when NLC occurred, taken on board 'Salyut-6'. The Sun is above the horizon. In the lower part of this Figure sunlit tropospheric clouds are visible.

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Figure 25 Same as Fig. 24, except for the Sun being below the horizon.

H

Figure 26 The family of photometric profiles measured ~om a photograph taken aboard 'Salyut-6' on 15 January 1978.

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of NLC. The brightness contrast between NLC and the aureole ranges from 0.38 to 0.78. Figure 27 shows the dependence of NLC brightness upon the azimuth from the Sun's vertical (A - A0) for the height of the perigee h = 82 km. The thick solid line gives the total brightness at the height of NLC, the thin solid line indicates the brightness of the aureole, the dashed line presents the brightness of NLC (measured) and the dot-dashed line shows the calculated brightness according to the NLC model proposed by WILLMANN and SERGEYEVICH(1969). The parts a, b, c give the profiles detected in the three successive photographs (with a time lapse approximately 1 min). From these photometric measurements one can draw the foUowing conclusions: (1) The brightness of the aureole diminishes monotonically with an increasing azimuth. (2) NLC brightness curves have usually a wave-like structure (depending on their optical thickness). (3) The measured brightness of NLC in the Sun's vertical is higher than the one calculated from the model. This points to the fact that in the observed NLC there are more large particles than adopted in the model by WmUaANN and SERGEYEVICH(1969), but these particles must be in the Southern Hemisphere smaller than those detected in the Northern Hemisphere. Summarizing this section on the observations and photography of NLC from space, the following conclusions can be drawn: 1. Photography and visual observations from space enable one to determine the NLC on a global scale. In particular, the investigations performed on board' Salyut-4' revealed that in summer in the Northern Hemisphere NLC often completely covered B

B

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~

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Figure 27 Brightness of NLC and of the Earth's aureole versus solar azimuth. Parts a, b, c give consecutive profiles with a time lapse of 1 minute.

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the latitudinal belt north of 45 ~ Similar observations aboard 'Salyut-6' ascertained that in summer in the Southern Hemisphere there also exist extensive NLC fields, but they are shifted more southward: the NLC belt is south of 53-55~ 2. Photometric investigations as well as visual observations revealed that in both hemispheres the mesopause often has a complex structure (sometimes there exist two- and three-layered NLC fields). 3. These observations allow one to make sound estimates of the spatial-temporal characteristics of NLC fields as well as the morphological features of their evolution. 4. The photometric investigations from space also confirm that in the NLC layer there exist particles whose radius exceeds 10 -5 cm. The NLC in the Southern Hemisphere probably consist of smaller particles than those in the Northern Hemisphere.

8. Radiometric measurements of NLC from space The idea of the possibility of detecting NLC from space photometrically was expressed already in 1962 (see: DEIRMENDJIAN, 1963a), which, however, remained unrealized. The task of optically detecting NLC by using radiometric and spectrometric instruments on board the spaceship was put to all teams of the Orbital Scientific Station (OSS) 'Salyut-4'. It was successfully carried out during the second expedition of 'Salyut-4' in June and July 1975. An illustration of the possible brightness of NLC in the visible region (A = 0.55 /xm) is given in Fig. 28, in case the zenith angle of the Sun equals 96 ~ and the Sun is in the vertical plane. For comparison the brightness of the horizon calculated by the DART method (GRAY et al., 1972) as well as the first-order scattered radiation (SMorcTY, 1969) are given. Figure 28 shows that when the optical thickness of the NLC layer ~ = 10 -5, the brightness of NLC at a height of 80 km is nearly by one order higher than that of the twilight aureole. Moreover, it seems to us that the DART method overestimates the effect of multiple scattering since the Monte-Carlo calculation and the method of characteristics with iterations on the order of scattering (NAZARALIEVand SUSHKEVICH,1975) show that the second-order scattering at A = 0.55/~m constitutes less than 30~ of the horizon brightness in the layer of 0-20 kin. With increasing height the contribution of second-order scattering has a tendency to diminish. The isolines of the brightness of NLC in relative units considering the first-order scattering and extinction in the atmosphere are given in Fig. 29. Compared with the Earth's radius, the vertical scale in Fig. 29 is considerably distorted. The main conclusion resulting from the above data is that in the NLC field the maximum brightness occurs in the vertical plane of the Sun. The brightness decreases rapidly with the increasing azimuth A. Optimum azimuth angles for NLC brightness measurements lie between _+15~ In a summar~y of the airglow VALLANCEJONES(1973) pointed out that the molecular emissions of OH and 02 account for the major part of the emission intensity from the

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3

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k,' #d~ .

d+r ~ '

_,o-t,.

ds

#os! i

i

I

I

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~o 2a 30 4a 50 bO to 80 90#00

H(~m) Figure 28 Brightness of N L C in the vertical plane of the Sun, when the zenith angle of the Sun ~ = 96 ~ for 7 = 10 -~ 10 -5 and 10 -5. The brightness of the horizon for different zenith angles of the Sun (0, 30, 60 and 80 ~ calculated by the D A R T method (GRAY et al., 1972), first-order scattering (SMoKTY, 1969) (dashed line).

3~ ~

\/

~'30~

Figure 29 Isolines of the relative brightness of NLC depending on the line of sight and the azimuth A.

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upper atmosphere in the infrared region. We use the term 'airglow' limited to emissions from the minor constituents which are not in thermal equilibrium (or nearly so) with the atmosphere. An essential feature of O H emissions during N L C occurrences was discovered by SHEFOV (1968). According to his estimates the intensity of O H emissions increased by a factor of 1.5 to 2 during N L C with respect to the mean value, sharply decreasing to a value 2 to 3 times lower than the average intensity of the following day when no N L C were observed. Taking this into consideration, we find that O H emissions increase the brightness of N L C by a measurable amount in the near-infrared region, e.g. Boll, zenith (2, = 2/~m) = 0.5 x 10 -7 [W cm -2 txm -1 sr-1]. The O2(1Ag) dayglow in the zenith direction 1.27/xm band yields Bo2, zenith = 4 x 10-7 [W c m - 2 sr-1] and consequently this emission essentially exceeds the N L C brightness in the direction of the line of sight with the perigee H0 = 80 km. It is concluded from the above that it is important to take into account the emissions of O H and 02 when analyzing N L C brightness measurements (AvASTE et al., 1977b). A four-channel near-infrared radiometer (VALOV et al., 1973) was installed aboard the Orbital Scientific Station (OSS) 'Salyut-4' for measuring N L C brightness. The limb scanning technique was employed by controlling the space orientation of the OSS, with the aim of obtaining the altitude information on the optically observable phenomenon occurring below the spaceship. Spectral bands of the interference filters used had a maximum at the wavelengths of 1.35, 1.9, 2.2 and 2.7 ~m. An example of scanning the twilight segment with N L C at A = 1.9/~m is presented in Fig. 30. It should be noted that all curves of the vertical brightness profile at a wavelength of A = 1.35/zm on lines of sight with a perigee of H0 = 50-70 km had a secondary maximum or a plateau. Figure 31 presents an example of the results of the measurements of the daylight atmospheric aureole in the channels of 1.35 and 1.9/zm. This figure illustrates the case when there are no N L C and the above-mentioned effect ought to be expressed in the most pronounced way. This may be explained as the influence of the wing of the O2(1Ag) emission band centered at A = 1.27 ~m. Over twenty scannings of the N L C field above the Earth's horizon were performed. Depending on the structure and the optical thickness of NLC, the brightness varied within the limits of one order of magnitude. Figure 32 presents an estimate of the spectral brightness of N L C and of the hydroxyl emission in case the line of sight has a perigee of H0 - 81 km. The results of measurements have been entered on the same graph: both average values and maximum deviations from them for channels of 1.35, 1.9 and 2.2/xm. For the channel of 1.35/~m the emission of O~(1Ag) was eliminated. The data at A = 2.7/~m turned out to be insufficiently reliable and were omitted. The N L C spectral brightness was calculated for the optical thickness ~-= 10 -5, 3 x 10 -~, 10 -4 and for a scattering angle of), = 80 ~ since measurements of the N L C brightness were carried out at angles which lay close to 80 ~. The spectral intensities of the hydroxyl emission in the direction of the line of sight with a perigee of Ho = 81 km for 60~ were calculated, taking into consideration the increase of O H when N L C occurred according to Shefov (see FEDOROVA et al., 1974). The solid line

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t98~

\ -1

.=..

-2

9-.

........,-. : 1 i

t -3

,I 2O

80

h (K~)

Figure 30 Brightness measurements of the horizon with N L C at a wavelength of 1.9 t~m.

0 7../- x

.... .....

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Figure 31 Brightness measurement o f the horizon with no N L C : dotted line indicates A = 1.9 t~m, dot-dash line denotes k = 1.35/~m.

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,

I

,

,

,

,

I

I

,

I

5\

0

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Figure 32 Spectra] distribution o f N L C brightness at a scattering angle of 7 = 80~ (1) calculated when T = 10-5; (2) calculated when -r = 3 x 10-~; (3) calculated when ~- --- 10-3; (4) O H emission (SHEFOV, 1968); (5) sum of NLC brightness when ~ = 3 x 10 -s ai~d of OH emission. 9 indicates

mean experimental values, vertical bars denote variation in NLC brightness. characterizes the total effect of both the hydroxyl emission and the radiation scattered by N L C (~- = 3 x 10-5). As can be seen from Fig. 32, the calculated and measured brightnesses have rather close values. The hydroxyl emission at A -- 2.2 t~m is comparable with the radiation scattered by NLC, while at A = 3/~m the former exceeds the latter by one order of magnitude. The following conclusions can be drawn from the above: 1. The consideration of the O2(1Ag) and O H emissions in the near-infrared spectral region shows good agreement between the calculated and measured values of the N L C hrightnesses. This confirms the fact that the model we used in the calculations for the description of the polydisperse ensemble of N L C particles satisfactorily describes the basic optical properties of NLC. 2. The results of the investigations carried out on board the OSS 'Salyut-4' confirm an increase in the O H content in the mesopause at the occurrence of N L C established by H. N. Shefov. 3. F o r the further study of the optical characteristics of N L C from space it is expedient to continue the studies of their spatial distribution and also to carry out measurements in the ultraviolet spectral region as well as in the intensive hydroxyl emission band at h = 3 tzm.

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9. N L C investigations during M A P

As NLC are good indicators of physical and photochemical processes in the mesopause, special attention is paid to this problem in the planning document of MAP (GREGORY et al., 1976). It follows from the previous section that the NLC phenomenon is related to such processes as water vapor transport in the mesopause, temperature variations in the mesopause, the variation of OH, 02 emissions, several photochemical reactions as 03 + H, H20 + M, etc. The occurrence and disappearance of NLC is also related to some problems of solar-terrestrial physics: solar activity, geomagnetic disturbances, characteristics of the Es layer, etc. The wide range of the morphological structure of NLC and its variations allows one to observe various complex dynamic processes in the mesopause (wave-like motions, jet stream, turbulence). It should be mentioned that NLC investigation for the determination of the above parameters of the processes described above has a definite advantage over the other methods as NLC fields cover vast territories (sometimes millions of square kilometers) and are visible from the Earth's surface during several hours. Considering this circumstance and also the fact that the interrelation of the neutral and ionized atmosphere in the mesopause in case of NLC formation has still been insufficiently studied, it is reasonable to start a preparatory MAP project also on NLC research. Such a project was proposed by the Soviet Geophysical Committee for the years 1979-1980. This project included the investigation of the following problems: 1. Climatology of NLC. Investigation of the spatial-temporal characteristics of NLC occurrences with the aim of obtaining uniform and reliable data from ground and space observations both in the Northern and Southern Hemispheres. Special attention must be paid to the existence of breaks in the temporal NLC series. 2. Dynamics and morphology of NLC. Investigation of the morphological and kinematic structure of NLC (different forms of waves, jet streams, whirls, multilayered NLC occurrences). Making use of simultaneous time-lapse cinematography and stereophotogrammetry from the adequately separated ground surface stations, the velocities of horizontal and vertical shifts of different structural forms will be determined as well as the drift of the cloudfield on the whole. 3. Nature of NLC. Investigation of the physical and chemical characteristics of NLC particles, as well as of the optical parameters which characterize the cloud field on the whole. Making use of the optical remote sounding technique and direct rocket soundings, the particle sizes, their physico-chemical properties and the number concentration will be determined. Also optical densities, spectral brightness, etc. will be inferred.

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4. Genesis of NLC; the relation between the meteorological conditions, heliogeophysical phenomena and NLC; the forecast of NLC occurrences. 4.1. Investigation of the conditions which are necessary and sufficient for NLC formation. 4.1.1. Investigation of the water vapor transport and of the temperature variations in the mesosphere. 4.1.2. Investigation of the interrelations between solar acitvity, ozone content in the atmosphere and forms of global atmospheric circulation (the circumpolar vortex). 4.1.3. Investigation of the global distribution of aerosols in the mesosphere. 4.1.4. Modelling physical conditions at the level of the mesopause and investigations of dynamics of the water vapor sedimentation on ice crystals. 4.2. Investigation of interrelations between helio-geophysical phenomena and NLC. 4.2.1. The complex determination of geomagnetic disturbances (index K), emissions (OH, O2), ion concentration and electron density in the mesosphere together with the wind and thermobaric regime. Investigation of the peculiarities in E~ layer in cases of appearance, occurrence and disappearance of NLC. 4.2.2. Investigation of the correlation between NLC occurrences and solar activity, meteor fluxes, ionospheric conditions in D, E and E~ layers, OH emission, 02 emission, meteorological regime in the troposphere and stratosphere. 4.3. Elaboration of methods for forecasting NLC occurrences.

10. Concluding remarks The monitoring of NLC from space demonstrated that: (1) The classification proposed in the International Noctilucent Cloud Observation Manual (1970) is applicable in case of observations from space. (2) NLC fields often cover considerable parts of latitudinal belt north of 45~ (or south of 53~ The NLC coverage in the Northern and Southern Hemispheres are asymmetric, but in both hemispheres the multilayered structure of NLC is observable, indicating the complex structure of the mesopause. (3) In the Southern Hemisphere NLC probably consist of smaller particles than NLC in the Northern Hemisphere. The characteristic radius of cloud particles in the Northern Hemisphere is 2 x 10-5 cm for rod-like crystals, while for spherical particles it is 3 x 10 .5 cm. This exceeds the previous estimates by 1.5 to 2 times. (4) NLC brightness, polarization properties and their particles equilibrium temperatures could be correctly interpreted only when one considers that NLC consist of ice crystals with absorbing nuclei. (5) Ion clusters can play an important role as condensation nuclei. The latitudinal distribution of these electrically charged particles is dependent on the Lorentz forces

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in the Earth's magnetosphere and high particle concentrations were observed over the polar cap. Measurements f r o m space indicate a scattering layer of 15 to 40 particles per c m 8 which seems to be a daytime manifestation o f N L C . (6) In all probability both condensation and coagulation mechanisms play an important role in the growth o f ice crystals in the mesopause. (7) Rocket soundings carried out at the Soviet Antarctic Station ' M o l o d e z h n a y a ' indicate that N L C occurrences are connected with advection and descent o f extremely cold air (110-120~ from the upper layers into the mesopause. The N L C formation is interrelated with m a n y fundamental parameters governing physical processes in the mesopause. Thus visual observations, p h o t o g r a p h y and remote soundings using the satellite technique allow one to monitor data on physical conditions in the mesopause over large territories.

REFERENCES

ABADIE, G. (1974), Mdsure de la teneur en eau de la haute atmosphere par sonde a alumine, La Mdtdorologie, 31/32, 225-236. ANDERSON, J. G. and DONAHUE,T. M. (1975), The neutral composition of the stratosphere and mesosphere, J. Atm. Terr. Phys. 37, 865-884. ANDREYEV,S. D., IVLEV,L. S., SPAZHAKINA,N. K. and YANCHENKO,YE. L. (1975), Space-time variations of atmosphere optical properties caused by interaction between atmospheric aerosol and humidity field (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov. Meteorotogicheskie issledovania, No. 22, pp. 34-49. ARNOLD, F. and KRANKOVSKY,D. (1977), Water vapour concentration at the mesopause, Nature 268, 218-219. ASTAPOWCH, I. S. (1939), Noctilucent clouds (in Russian), in Akademia Nauk SSSR, Izvestia, Geografia i geofizika, No. 2, pp. 183-204. ASTAPOVICH, I. S. (1961), Summary of noctilucent cloud observation in Russia and USSR from 1885 to 1944 (in Russian), in Trudy VI sovechchania po serebristym oblakam, Riga, pp. 49-92. AUFF'M ORDT, N. and BRODHUN, D. (1974), Zur Deutung yon Wellenstrukturen aufLeuchtenden Nachtwolken, Z. Meteorol. 24, 291-298. AVASTE, O. A. (ed.) (1977), Trudy MGK. Meteorologicheskie issledovania, No. 23 (in Russian),

(Publ. House Sovetskoye Radio, Moscow), 87 pp. AVASTE,O. A., VAINIKKO,G. M. and K,~RNER,O. YU. (1977a), Some statistical characteristics of the mesospheric cloud field (in Russian), in Trudy MGK, Meteorologicheskie issledovania, No. 23, 5-11. AVASTE,O. A., VEISMANN,U. K., WILLMANN,CH. ][., GRECHKO,G. M., GUBAREV,A. A., KLIMUK, P. I., LOBANOVA,G. I., POPOV,O. I., SEVASTYANOV,V. l., FEDOROVA,E. O. and EERME,K. A. (1977b), The determination of the daytime and twilight profiles of the O2(1Ag) at 1.27 t~m from measurements aboard the orbital station 'Salyut-4' (in Russian), in Optical Investigation of the Emission of the Atmosphere, Aurorae and Noctilucent Clouds aboard the Orbital Scientific Station "Salyut-4', Tartu, pp. 79-87. AVASTE, O. and WILLMANN,CH. (1973), On the method of determination of the optical depths of noctilucent clouds, in Noctilucent clouds. Optical properties, Tallinn, pp. 80-97. BACKHOUSE,T. W. (I 885), The luminous cirrus clouds" of June and July, Met. Mag. 20, t 33. BAmULATOV,F. KH. and IVA•IVA, S. P. (t976), Numerical studies of aerosol particle temperature in the upper atmosphere (in Russian), Akademia Nauk SSSR, Izvestiia, Fizika atmosfery i okeana 12, 523-530.

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TOZER, W. F. and BEESON,D. E. (1974), Optical model ofnoctilucent clouds based on polarimetric measurements from two rocket sounding campaigns, J. Geophys. Res. 79, 5607-5612. TSERASKII,V. K. (1887), Astronomicalphotometer and its applications (in Russian), Matematicheskii sbornik 13, pp. 76-81. TSERASKII,V. K. (1890), Sur les nuages lumineux, Annales de l'Observatoire de Moscou, II, Ser. 2, 176-180. STANDARDATMOSPHERE,U.S. (1976), NOAA/NASA/US AF, Washington, D.C., 227 pp. VALLANCEJONES, A. (1973), Infrared spectrum of the airglow, Space Sci. Rev. 15, 355--400. VALOV, N. I., VEISMANN,U. K., WILLMANN,CH. J., GANELIN, G. Z. and DEMIDOV, V. V. (1973), Multichannel telephotometer (in Russian), in Izobretenia, promyshlennye obraztsy, tovarnye znaky, No. 37. VASILYEV, O. B. (1967), Astrophysical investigation of noctilucent clouds (in Russian), Akademia Nauk SSSR, Astronomicheskii Sovet, Moscow, 86 pp. VASILYEV, O. B. (ed.) (1975), Trudy MGK, Fizika me2osfery i mezosfernyh oblakov, Meteorologicheskie issledovania No. 22, 149 pp.+Supplement: Materialy issledovania mezosfernyh oblakov, 111 pp. VASILYEV, O. B. and MELNIKOVA,]. N. (1975), Statistical spaeetime model of the appearance of mesospheric clouds (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov, Meteorologicheskie issledovania, No. 22, pp. 125-136. VASILYEV, O. B. and RADIONOV,B. F. (1975), Optics ofmesospheric clouds (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov, meteorologicheskie issledovania, No. 22, pp. 50-64. Supplement in Materialy issledovania mezosfernyh oblakov, VINITI, Moscow, 1975, pp. 5-53. VAStLYEV, O. B., W~LLMANN,CH. I., MELNmOVA,I. N. and CHUBEY, M. S. (1975), Technique of statistical analysis of observations of mesospheric clouds applied by the network of stations of the Hydrometeorological Service (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov. Meteorologicheskie issledovania, No. 22, pp. 110-118. VEGARD, L. (1933), Investigations o f the auroral spectrum based on observations from the auroral observatory, Geophys. Publ. 10, 53 pp. VESELOV, D. P., POVOV, O. I., SEMYENOVA,V. I., SELEZNEV,G. I. and FEDOROVA,YE. O. (1976), Spectral brightness of noctilucent clouds in the visible and the near infrared region of spectrum (in Russian), Akademia Nauk SSSR, Izvestiia, Fizika atmosfery i okeana 12, 1097-1099. VESTINE,E. ILl.(1934), Noctilucent clouds, J. Roy. Astron. Soc., Canada 28, 249-272, 303-317. WEGENER, A. (1925), Die Temperatur der obersten Atmosphiirenschichten, Meteorol. Zeitschr. 42, 402-405. WEGENER,A. (1926), Zusatz zu F. A. Lindemann, G. M. B. Dobson, Die Temperatur der obersten Atmosphiirenschichten, Meteorol. Zeitschr. 43, 102-103. WELCH, R. M. and Cox, S. K. (1978), Nonspherical extinction and absorption efficiencies, Appl. Optics 13, 3159-3168. WILLMANN, CH. I. (ed.) (1967), Observations of Noctilucent Clouds (in Russian) (Publ. House Nauka, Moscow), 136 pp. WILLMANN, CH. I. (1967), Some problems of noctilucent clouds climatology, in Noctilucent Clouds (International Symposium, Tallinn, 1966) (I. A. Khvostikov and G. Witt, eds.) (Publ. House VINITI, Moscow), pp. 19-28. WILLMANN, CH. I. (1968), Statistical data on noctilucent cloud occurrence in the period of the IQS Y (1964-1965) (in Russian), Astronomicheskii Vestnik 1I, 161-170. WILLMANN,CO. I. (1975), Indicatrixes of solar radiation scattering by noctilucent clouds (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov, Meteorologicheskie issleodvania No. 22, pp. 65-77. Supplement in Materialy issledovania mezosfernyh oblakov, (VINITI, Moscow), 1975, pp. 75-111. WILLMANN,CH. I., KLIMUK,P. I., KOKSHAROV,I. I., SEVASTYANOV,V. I., SERGEYEVICH,V. N. and EERME, K. A. (1977), Visual observations and photography of noctilucent clouds aboard orbital station 'Salyut-4" (in Russian), in Optical Investigation of the Emission of the Atmosphere, Aurorae and Noctilucent Clouds aboard the Orbital Scientific Station "Salyut-4', Tartu, pp. 79-87.

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Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

The Structure of the Equatorial Mesosphere at Thumba By B. H. Subbaraya 1 and Shyam LaP

Abstract - The structure of the equatorial mesosphere is being investigated at Thumba by rocket borne ultraviolet absorption photometry as well as by the meteorological M-100 rocket launching programme. Whereas the meteorological M-100 rocket launching programme has been regular, the UV absorption studies have been few in number and sporadic in nature. In this paper an attempt is made to consolidate the results so far obtained from both these investigations.

Key words: Stratosphere; Mesosphere; Ultraviolet absorption; Gravity waves.

Introduction

In spite of the great improvement (brought about by space-borne/n situ techniques) in our understanding of the physical state of the upper atmosphere vis a v i s its structure and composition, the mesosphere and the lower thermosphere remain largely unexplored. Meteorological programmes based on balloons, rockets, and more recently satellites, have contributed a great deal towards the understanding of the structure and circulation at tropospheric and lower stratospheric levels. In the thermosphere, at altitudes above about 200 km satellite drag technique and the satellite borne massspectrometers have contributed towards an understnading of the atmospheric structure and composition as well as their variations. In recent years satellite measurements have been extended to lower heights, down to about 150 km. The intermediate regions, the mesosphere and the lower thermosphere, however, have till recently been dependent mostly on rocket borne techniques, and a significant gap in observational data exists in the upper atmosphere for the altitude range of 60 km to about 150 km. Further, geographically there is much less observational coverage for the equatorial regions than for the other latitude regions and the presently available standard atmospheric models are based to a large extent on mid-latitude data.

The Thumba observational programme

At the equatorial rocket launching station, Thumba (8 ~ 31'N, 76 ~ 52'E), the low latitude mesospheric structure has been explored by rocket borne ultraviolet absorption photometry, a technique which yields molecular oxygen concentration profiles, as well 1) Physical Research Laboratory, Ahmedabad-380009, India.

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B.H. Subbaraya and ShyarnLal

(Pageoph,

as by the Indo-USSR collaborative meteorological rocket programme which involves weekly soundings with the M-100 rocket carrying standard meteorological payload to measure temperatures and winds. Both programmes were initiated in 1970-71. The M-100 meteorological rocket launchings are generally effected every Wednesday around 2000 h local time. Molecular oxygen concentrations in the mesosphere and lower thermosphere have been determined by solar ultraviolet absorption photometry. An ultraviolet ion chamber can be used to measure the solar radiation flux within a selected wavelength band in the extreme ultraviolet (HINTERREGGER, 1969). Molecular oxygen concentrations can be determined from the absorption profile of these radiations in the upper atmosphere since molecular oxygen is the main absorbing constituent in the Earth's atmosphere at these wavelengths (FREIDMAN, 1960). At altitudes below about 90 km the atmosphere is well mixed, and the molecular oxygen concentration measurements can be used to study the atmospheric structure. For these altitudes, a nitric oxide filled ion chamber with MgF2 or LiF window is found to be most convenient since it includes the hydrogen Lyman-Alpha line (1216/~) in its passband 1120-1340A (CARVER and MITCHELL, 1967). The Lyman-Alpha line dominates this wavelength region of the solar spectrum, contributing nearly 90~ to the flux in the total passband that penetrates these altitudes. 02 densities can be estimated by using a single effective absorption cross section at the Lyman-Alpha line and molecular oxygen concentrations can be obtained in the 65-95 km altitude region (HALL, 1972). The instrumentation used at Thumb has been described in the literature (SuBBARAVAet al., 1973). The special features of the instrument are: 1. Use of positive bias to the ion chamber to reduce effects due to photoelectric emission. 2. Use of linear amplifier with gain switching to give a large dynamic range as well as high sensitivity throughout the range. The ion chambers used by the authors at Thumba were fabricated and calibrated indigenously at the Physical Research Laboratory, Ahmedabad.

Stratospheric and mesospheric structure over Thumba

Data from the Indo-USSR collaborative M-100 rocket sounding programme at Thumba for the period 1971-74 has been used to study the behaviour of the stratosphere and mesosphere over Thumba. Data for this period is available in the form of monthly means (mean of four rocket flights) for 2000 h local time, tabulated as a function of altitude up to 80 kin. The data for representative heights in the stratosphere and mesosphere are plotted in Figs. la and lb to show the variations in stratospheric and mesospheric structure. The most striking feature of these figures is a strong semi-annual variation in density and temperature at all heights above 40 km with maxima in the equinoxial months, and minima in the winter and summer months.

Vol. 118, 1980)

The Structure of the Equatorial Mesophere at Thumba

583

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76kin 3.0 2.0 8.0 ~ 7.0 6-O

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The figures also show that the winter minimum is deeper than the summer minimum. Further, the amplitude of the semi-annual feature shows an altitude dependence and there are differences from year to year (SHYAM LAL et al., 1979). Semi-annual variations in the atmospheric densities were first recognized by PAETZOLD and ZSCHORNER (1961) in the satellite drag data for the 300-400 km altitude region. Since then it has been the subject of several studies (JACCHIA, 1965; KING HELE, 1967; JACCHIA et al., 1969; JACCHIA, 1971; MAROV and ALPHEROV, 1971; GROVES, 1972; WALKER, 1978) and the existence of a semi-annual variation in atmospheric densities is well established for the entire thermosphere and exosphere. C o o k (1969) has recognized a semi-annual effect at an altitude of 90 km in phase with the variation at higher altitudes. At lower

584

B.H. Subbaraya and ShyamLal

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Figure lb A t m o s p h e r i c t e m p e r a t u r e s at selected height in t h e 4 0 - 8 0 k m altitude region o b t a i n e d f r o m t h e M - 1 0 0 r o c k e t p r o g r a m m e at T h u m b a f o r t h e period 1971-74.

altitudes, in the stratosphere and mesosphere, seasonal effects have been known in the circulation, especially at tropical and sub-tropical latitudes where the annual oscillation becomes small (COLE, 1975). Studies based on satellite measurements (e.g. HEATH et al., 1974) have shown that the average stratospheric temperatures are lower in December-January than in June-July. However, the semi-annual feature in low latitude stratospheric and mesospheric densities does not seem to have been noticed so far. A comparison of the density behaviour with that of the temperatures shows further interesting results. While there is a semi-annual feature both in densities and temperatures, they go in phase below about 50 kin. A change of phase occurs somewhere in the 50-60 km range and in the mesosphere the temperature and density are opposite in phase. The data of Figs. la and Ib are subjected to a seven point running average and shown in Figs. 2a, b to study features with longer periods. An annual cycle is clearly evident. Further, a long term trend of temperatures decreasing and densities

Vol. 118, 1980)

The Structure of the Equatorial Mesophere at Thumba

585

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Figure 2 Long term trend in (a) atmospheric densities and (b) atmospheric temperatures in the mesosphere over Thumba. Note that the trend is clear at 80 kin, still discernable at 76 km but absent at 70 kin.

586

B.H. Subbaraya and Shyam Lal

(Pageoph,

increasing with decrease in solar activity from 1971 to 1974 is clearly seen at 80 km. The trend persists down to about 75 kin, below which height the trend does not seem to exist.

Molecular oxygen concentrations

A number of Lyman-Alpha absorption profile measurements have been made at Thumba during daytime, mostly within a few hours around noon. The measurements were made sporadically over a period of time, on rockets which were flown for various ionospheric investigations. Some of these results have been reported earlier (SUBBARAYAet al., 1972, 1974). It is not possible to resolve from these occasional measurements the finer aspects of low latitude mesospheric structure such as diurnal variations, variation due to solar and magnetic activity etc. However, an attempt is made to obtain some gross features of mesospheric structure from these measurements. Molecular oxygen concentration profiles from five rocket flights are shown in Fig. 3. Table 1 gives information regarding the flight day and time. Data of Fig. 3 is restricted to the altitude region of 65-85 km even though on some of the rocket flights measurements extend beyond 85 km. It is observed that three of these five profiles shown in Fig. 3a agree within 20~ of one another, while the other two profiles shown in Fig. 3b differ markedly from these three. The O2 concentrations of the first three profiles are less than the standard atmospheric model values such as CIRA 72,

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variability declines with increasing wavelength, from 5~ at 0.174/zm to 1~ near 0.3 ~m (HEATH and THAEKEKERA, 1977). The SME mission will occur during a period of fairly high solar activity, according to predictions of the smoothed sunspot number (Fig. 3). It should be comparable to the maximum of the previous solar cycle (1969-70). Sporadic solar output in the form of either ultraviolet enhancements or energetic proton bombardment will therefore be more likely to occur during the SME time period than during later missions, such as HALOE and UARS. Knowledge of the water-vapor density during times of ozone changes is crucial, since its dissociation products are the primary agents for ozone recombination in the mesosphere. Knowledge of the temperature is also very important, as certain key chemical reactions involving ozone are temperature sensitive. The SME complement of instruments provides essentially all the information necessary to provide a rigorous test of photochemical ozone theories. Such tests have been absent in the past, due to the fact that simultaneous measurements of all the important quantities are seldom available, particularly over a large enough time period to provide confidence that one has isolated the causative agent for the variability. It will also map the various regions where dynamical phenomena are important; for example the high-latitude winter mesosphere is often disturbed by planetary wave activity and changes in ozone density in this region are not expected to be controlled strictly by solar variability.

Vol. 118, 1980)

Scientific Objectives of the Solar Mesosphere Explorer Mission

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Figure 3 Observed (dots) and predicted sunspot number for solar cycle 21, beginning June 1976. The predictions are based on the McNish-Lincoln method (Solar Geophysical Data Report, February 1978). Shown is the time period for the SME mission, along with related middle atmosphere research satellites. NIMBUS G - launched on 25 October 1978; S A G E - Stratospheric Aerosol and Gas Experiment (launched on 18 February 1979); HALOE - Halogen Occultation Experiment - to be launched in 1982; AMPS - the Atmosphere, Magnetosphere and Plasmas in Space program, a Space lab series of missions; and UARS - The Upper Atmosphere Research Satellite. In this p a p e r , we will first describe s o m e o f the p r o b l e m s o f m e s o s p h e r i c ozone t h a t the S M E mission will address. W e will then give s u m m a r i e s o f each o f the S M E experiments, followed by calculated limb radiances for each o f the a t m o s p h e r i c experiments. The d a t a processing a n d analysis p l a n will then be briefly described.

1I. Theoretical background The d o m i n a n t p h o t o c h e m i c a l processes between 30 a n d 80 k m involve ozone. O z o n e is p r o d u c e d as a result o f the p h o t o d i s s o c i a t i o n o f m o l e c u l a r oxygen

02 + hv(h < 0.242 t ~ m ) - + O + O

(1)

followed by the three b o d y reaction O + 02 + M ~ O 3

+ M.

(2)

596

Gary E: Thomas et al.

0 lOs

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(Pageoph,

~--

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The ratio of ozone and atomic oxygen is determined primarily by a photochemical balance between reaction (2) and the following reaction: 03 + hv(,~ < 1.08/zm)--> O + 02.

(3)

It is convenient to define odd oxygen (Ox) to be the sum of ozone and atomic oxygen. Odd oxygen is destroyed by the following reactions O+O+M-~O2+M

(4)

and O + 03 --> 202.

(5)

Reactions (1)-(5) were proposed by Chapman in the 1930s and were believed adequate until the 1960s when measurements showed less ozone than predicted, necessitating modification of the theory involving catalytic ozone-destroying reactions. Odd hydrogen (HOx = H + OH + HO2 + H202) catalytic cycles were first proposed to explain the lower ozone densities observed (HUNT, 1966). The simplified reaction scheme for the mesosphere is illustrated in Fig. 4. The catalytic cycles are H + O 3 - - > O H + 02 O H + O - - > H + 02 Net:

03 + O --> 202

(6)

597

Vol. 118, 1980) Scientific Objectives of the Solar Mesosphere Explorer Mission and O + O H - ~ H + 02 H+O2 + M--~H02 + M HO2 + O - ~ O H + O 2 Net:

O + O --~ 02

(7)

In the stratosphere there is an additional important cycle O H + Oa--> HO2 + 02 HO2 + Oa--~ O H + 202 Net:

2Oa ~ 302.

(8)

In the mesosphere the source of odd hydrogen is mainly photodissociation and O(1D) oxidation of water vapor. The sinks are the reactions O H + HO2 ~ H 2 0 + 02

(9)

H+ HO2->H20 +O H + HO2--> H2 + 02.

(10)

and

Because of their short lifetimes the odd hydrogen species are in photochemical equilibrium with each other and with water vapor. So it is essential to measure the water vapor content. Mesospheric water vapor also is the major source of hydrogen escape flux.

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598

Gary E. Thomas et

al.

(Pageoph,

Figure 5 shows theoretically predicted ozone profiles and the measured midlatitude ozone profile summarized by KRLrE~ER and MINZER (1976). With only the Chapman scheme the predicted ozone is far too high, especially in the upper mesosphere. Including the odd hydrogen catalytic cycles greatly improves the agreement in the mesosphere. Below about 40 km the production of odd hydrogen by photodissociation of H20 drops off due to the increasing opacity of the atmosphere, and it is necessary to include odd-nitrogen (NO2, NO, NOa, HNO3) photochemistry (CRurZEN, 1970, 1971 ; JOHNSTON,1971). Ozone is destroyed by NO and NO2 through NO +. 03--~ NO2 + 02 NO2 + O--~ NO + 02 Net:

O + O8---~ 202

(11)

Inclusion of this catalytic destruction of ozone brings the predicted ozone density in reasonable agreement with observed values. The complete nitrogen chemistry must, however, consider reactions involving N, N2, NO, NO2, HNO3, N205, and N20 (CRuTZEN, 1970 and 1971) and chlorine photochemistry (ROWLANDand MOLINA, 1975; STOLARSKIand CICERONE,1974). The natural source of NO is provided by the oxidation of N20, which is produced by bacteria in the soil. The chlorine catalytic ozone destruction cycle is similar to the nitrogen cycle in equation (11) with NO and NO2 replaced by C1 and C10, respectively. In the lower mesosphere odd oxygen is in photochemical equilibrium, and hence simultaneous measurements of ozone density, ozone photodissociation rate, water vapor density, temperature, and solar ultraviolet irradiance will provide a rigorous test of the above photochemical theory. However there remain uncertainties in the values of several key reaction rates that determine the effectiveness of the odd-hydrogen catalytic cycle (particularly reaction (9)). Thus, if confidence in the basic theory can be established, the SME observations may also provide useful information about reaction rates. The O3-H20 model is expected to break down near the mesopause because of the effects of diffusion on odd oxygen and odd hydrogen, and below about 40 km because of the increasing importance of odd-nitrogen and odd-chlorine species. SME will detect the departures of the measurements from the O3-H20 model predictions and will, therefore, demonstrate and measure the importance of these perturbing influences. In the 30-40 km region the major loss of odd oxygen is due to catalysis by odd nitrogen. The measurement of NO2 and 03 will provide an estimate of the odd oxygen destruction rate in this region. The geographical distribution of NO2 is also of interest because it exhibits an unexpected latitude dependence, marked by a sudden drop in concentration above + 50~ geographic latitude (NOXON, 1979). This marked change is not yet fully understood but appears to be tied to profound changes in stratospheric circulation patterns with latitude. This drop or 'ledge' may be associated with the equatorial edge of the so-called winter circumpolar circulation vortex.

Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

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The SME measurements will also provide information concerning dynamical transport of ozone in regions of the atmosphere where the transport time scale is comparable to the photochemical lifetimes (Fig. 2). It is likely that vertical mixing and horizontal advection are sporadic, that is, much more rapid at some times than at others. This is particularly evident during a winter stratospheric warming event. It is safe to assume that species involving chemical reactions requiring a few days or less will be in chemical equilibrium with each other, and conversely species reacting only on time scales of a year or more will have their distribution largely controlled by transport. In the lower mesosphere, the odd oxygen species depend on fast reactions and so are all in chemical equilibrium. The same is true of the odd hydrogen species. However, molecules, such as H20, are destroyed (or generated) more slowly, and the possible role of transport in determining their distribution must be established. Water vapor has dissociation time scales in the range 10-100 days from 50-70 km. Thus its concentration in the mesosphere is probably not uniformly mixed but controlled jointly by transport and chemistry. Changes in H20 concentration as monitored by the infrared experiment will indicate the action either of transport processes or a changing solar irradiance. Monitoring the temperature field may also indicate possible unusual transport activity, since the radiative time scale (see Fig. 2) may at times be exceeded by the dynamical time scale. There will be additional opportunities to observe changes in the high-latitude mesospheric ozone distribution during solar proton precipitation events (SPE, in the earlier literature called polar cap absorption or PCA phenomena). At geomagnetic latitudes higher than about 60 ~ protons with energies greater than 5 Mev penetrate to altitudes below 75 km, and can produce ionization rates many orders of magnitude greater than quiet-time values. Recombination ultimately results in the destruction of water vapor in the lower mesosphere, with rates comparable to the natural destruction rate. This enhanced production of odd-hydrogen species leads to the greater destruction of mesospheric ozone (SwIDER and KENEASHA, 1973). At lower altitudes the ionization-produced odd-nitrogen species can cause a decreased stratospheric ozone content (HEATH et al., 1977). High-energy electrons at lower latitudes can also produce enhanced ionization in the mesosphere. These so-called REP (Relativistic Electron Precipitation) events are of shorter duration and are on a smaller spatial scale than solar proton events; however, they can cause as much ionization in the lower mesosphere as a PCE and occur more frequently (BAILEY, 1968). In addition to irregular changes in ozone due to changing solar irradiance and energetic particle precipitation, the regular seasonal changes in mesospheric ozone can be readily observed by the SME instruments. Local time variations will not be observable during the nominal mission because of the 3 : 00 AM-3: 00 PM orbit. However, the comparison of ozone data at these two local times at the same longitude will be important in determining the relaxation time scale for ozone recombination at these levels.

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IlL Instrument descriptions In this section we summarize important aspects of each of the five instruments on SME. A more detailed description of the optical and mechanical designs is given in GAUSE and STUART(1979). Three of the instruments, the ultraviolet ozone, the infrared airglow, and the visible NO2, are programmable Ebert-Fastie spectrometers. Their basic design is shown in Fig. 6. The telescope, entrance slits and Ebert mirrors will be the same but the optical coatings, gratings and detectors will be chosen specifically for the desired experiment. The instrument collecting optics will be f/5, 25 cm focal length off-axis parabolic telescopes. These systems demonstrate particularly low off-axis scattered light levels and are easily baffled. The telescope mirrors are 5.0 x 5.0 cm aluminum-coated cervit and will feed f/5, 12.5 cm focal length Ebert-Fastie spectrometers with 0.32 x 3.2 mm entrance slits resulting in a field of view of 0~ x 0~ and a height resolution on the Earth's limb of 3.5 kin. The instruments differ in choice of grating, resolution, and detectors. The main features of all the instruments are summarized in Table 1.

1. Ultraviolet ozone spectrometer. The ultraviolet ozone instrument employs a 3600 grooves/ram grating blazed at 0.24 ~m giving 1.8 nrn/mm dispersion in the focal plane. There are two EMR type 510F photomultiplier tubes behind 0.83 • 3.4 mm exit slits giving 1.5 nm resolution. The exit slits are 19.05 mm apart giving a wavelength separation between the two channels of 30 nm. The sensitivity is 1.1 • I05, 1.2 • 105 and 3.5 • 104 (counts/s)/ kiloRayleigh at 0.22 t~m, 0.26 t~m and 0.3 tzm, respectively.

2. The NO2 visible spectrometer The NO2 visible spectrometer will use a 2000 g/mm grating blazed at 0.4 t~m giving 3.2 nm/mm dispersion in the focal plane. The NO2 measurement will employ dual silicon diode detectors to handle the high photon flux expected near 0.44/zm. The sensitivity expected is 1 x 10 -11 amps/(109 ph/s) at 0.44/~m. The active diode area is 0.32 m m • 3.4 mm giving 0.97 nm resolution in each channel. This instrument will employ an EMR type 510-N photomultiplier in the airglow channel and a 0.64 mm • 3.4 mm exit slit giving 1.96 nm resolution. The airglow channel will cover the wavelength range 0.249 ~m to 0.6 tzm in 0.71 nm steps. The sensitivity at 0.3914 nm is 4 • 105 (counts/s) per kR.

3. Infrared airglow spectrometer The telescope and Ebert mirrors for the infrared airglow instrument will be coated to optimize for the near infrared. The grating will have a ruling density of 150 g/ram

Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

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blazed at 1.8 ~m. The dispersion at the exit stit is 51.4 nm/mm. The exit slits are 0.32 m m wide and give a triangular response function with a full width at half maxim u m of 16.4 nm. This will match the O2(1A~) emission at 1.27/zm. A relay lens behind the exit slit increases the effective speed from f/5 to f/1 and allows the use of small-area lead sulfide detectors. The spectrometer has two exit slits. The wavelength ranges in the two channels are 0.6 to 1.38/Lm and 1.2 to 2.0/~m. Thus there is built-in redundancy for the 1.27/~m measurement. The slit separation of 0.63/~m is chosen so the instrument can measure the 1.27/zm radiance from O2(1Ag) and the (7-5) band of OH(X2~r) at 1.9/zm simultaneously. The signal to noise ratio at 1.27 ~m is expected

SPIN AXIS

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Figure 7 SME Observatory module. The placement of individual instruments is indicated. The spacecraft spin axis is coincident with the axis of the Winston Horn. The Solar UV spectrometer drawing does not show the diffusing screen housing.

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Gary E. Thomas et al.

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to be 7 at 90 km and to increase with decreasing altitude. The signal will be chopped with a frequency of 400 Hz at the entrance slit and synchronously demodulated. 4. Four-channel infrared radiometer Infrared Radiance measurements of thermal emission from CO2, Oa and HzO are achieved with a Mersenne telescope system. The four detectors are radiatively cooled Hg-Cd-Te photoconductors with filters covering the spectral bands 6.1-7.2, 8.6-10.6, 14.7-15.7, and 13.2-17.2/zm. The filters cover thermal emission from the u2 band of H20, the v3 band of 03, the core of the u2 band of CO2, and the entire v2 CO2 band, respectively. Inversion of the CO2 limb scans yields temperature and CO2 density profiles. Knowledge of the temperature profile and emission from H20 and Oa yields H20 and Oa densities. Such procedures have been developed on the LRIR LIMS programs (GILLEet aL, 1978; RUSSELLand GILLE,1978). The Mersenne telescope which employs off-axis confocal paraboloids has a 203 mm aperture and uses gold-nickel plated aluminum optics. The primary mirror ( f = 406 mm) forms the first images at four apertures in a tuning chopper (2400 Hz). The secondary mirror ( f = 76 ram) is followed by a Lyot stop, a third mirror ( f = 57 mm) and the detector package. The overall focal length is 305 mm yielding an f/1.5 beam into the detector. The detectors are passively cooled by radiative loss from a 10 cm diameter disc which is protected from thermal emission from the Earth by a specially shaped horn, coaxial with the roll axis. Since the Earth's limb is 20 ~ from the roll axis, the horn must exhibit ~ 10 -4 rejection of heat inputs past 18~ from the axis. A design that accomplishes this is the Winston horn, or compound parabolic concentrator (Fig. 7). Its cross section consists of parabolas tipped by 18~ and, given a highly polished (~ 2.5 nm rms) interior, exhibits a sharp cutoff of rays entering at angles greater than 18~ The horn has end-diameters of 100 and 328 mm and a length of 660 mm. The expected temperature of the detectors is 105~ With commercially available detectors, the tangent point altitudes at which the signals equal the rms detector noises will be 64, 70, 80, and 86 km for the H20, Oa, CO2 narrow and CO2 wide channels, respectively. If the detector temperature should rise to 140~ these limiting altitudes would decrease by 7 km for the CO2 channels, and 3 km for the H20 and 03 channels. 5. Solar ultraviolet spectrometer The solar ultraviolet spectral irradiance instrument will measure solar radiation in the spectral region 0.16 to 0.31/zm in addition to Lyman-~ at 0.1216/~m. The instrument will be mounted on the side of the Observatory Module with its field of view directed 45 ~ to the spacecraft spin axis (Fig. 7). Data will be taken as the instrument scans through the Sun-satellite line once per spacecraft rotation. The angle between the Sun-satellite vector and the spacecraft spin axis is nominally 45 ~ but, in

Vol. 118, 1980) Scientific Objectives of the Solar Mesosphere Explorer Mission

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fact, it will continually vary due to seasonal effects and possibly due to irregularities in the satellite attitude and orbit. The design incorporating a diffusing screen allows the angle of incident solar radiation to vary + 15~ requiring only a small and calibrated correction. Several screens will be available and by protecting and 'duty cycling' certain calibration screens, long-term degradation of the instrument can be evaluated. The spectrometer will be an f/5 Ebert-Fastie design with a focal length of 12.5 cm. There are two spectral channels using separate exit slits, detectors, and pulse counting electronics. The short wavelength detector will be a 510 G photomultiplier tube (CsI photocathode) with a MgF2 window and will measure solar radiation in the spectral region 0.16/~m to 0.25/zm, and 0.115/zm to 0.125/zm. The long wavelength detector will be a 510 F photomultiplier tube (CsTe photocathode) with a quartz window and will be used in the spectral region 0.22/zm to 0.31 #m.

IV. Simulations In this section we present simulated radiance data for each instrument as it views the Earth's limb. The limb scanning geometry is illustrated in Fig. 8. The instrument views the Earth's limb with the center of its field of view along 1. We first consider the Ultraviolet Ozone and the NO2 instruments which measure Rayleigh scattered sunlight where scattering and/or absorption have depleted the radiance along the line of sight. The Rayleigh-scattered radiance is optically-thin above 20 km and decreases exponentially with altitude, with most of the radiation originating from

/

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Figure 8 Illustration of limb scanning geometry. Light emitted or scattered from a small volume along the line of sight is seen by the satellite instruments. Zo is the minimum ray height.

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within one scale height of the point of closest approach (or minimum ray height), Zo, of the line of sight. In the optically thin approximation, the radiance seen by the satellite instrument when the emitting species exponentially decreases with a constant scale height, H, is 4~rI(Zo) = g

S

n(Zo) e -m dl

(12)

co

where g is the emission rate per atom or molecule, n ( Z ) is the number density of Rayleigh scatterers, and the integral is taken along the path 1. Using the HUNTEN (1954) approximation for the Chapman function at 90 ~, equation (12) becomes 4=I(Z0) = gn(Zo)~V/2~--=RH

(13)

where R is the Earth radius. For pure Rayleigh scattering g = rrF. a-p(tF)

(14)

where rrF is the solar flux, e is the Rayleigh scattering cross section, and p0F) is the Rayleigh phase function for scattering angle ~ . The situation becomes more complicated if a pure absorber is present in the atmosphere. For the ultraviolet ozone experiment measuring Rayleigh scattered sunlight in the 0.2-0.3/xm region, the presence of ozone acts to deplete the incident and scattered sunlight. In this case the contribution to the signal from a small element, P (see Fig. 8), is d(4rrI) dl 9o~

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Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

607

where r~ is the optical depth for ozone between point P and the Sun; and % is the optical depth between point P and the satellite. In the above formulation

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The calculated spectral radiance in Rayleighs/nm as a function of Z0 is plotted in Fig. 9 for three wavelengths at a solar zenith angle of 60 ~ The calculation employed the total atmospheric density and profiles from the U.S. Standard Atmosphere (1976). At each wavelength the emission increases exponentially with decreasing altitude until absorption by ozone becomes important. The maximum radiance occurs when the total optical depth along the line of sight of the ozone is ~ 2. Below this altitude no information is received from the atmosphere near the minimum ray height. For the cases presented, useful information is obtained above 60 km at 0.25/zm, above 57 km at 0.28/zm and above 52 km at 0.29/xm. Thus as the instrument scans in wavelength away from the absorption maximum, the ozone cross-section decreases, and the instrument probes deeper into the atmosphere. The NO2 instrument will monitor Rayleigh scattering at 0.439 ~m and 0.442 txm with 0.97 nm resolution. The technique adopted to determine the NO2 column content along the line of sight is essentially that of NOXON (1975). Although NO2 absorbs light throughout most of the visible region of the spectrum, the two wavelengths were chosen because a relative maximum in the NO2 absorption cross-section occurs at 0.439/xm and a relative minimum occurs at 0.442 ~m. Furthermore an intense signal is required to make the difference between the emission measured in the two wavelength regions statistically meaningful as the total optical depth of NO2 along the line of sight is not normally expected to exceed 0.2. The solar flux when integrated over the two band passes in the two channels is nearly equal and the Rayleigh scattering cross-sections differ by only 2.5%. Any additional difference in the Rayleigh scattered signal is due to absorption by NO2. For the simulation we have adopted an NO2 profile measured by KERR and MCELROY (1976). The calculated spectral radiances are shown in Table 2, where Z is the minimum ray height. In this calculation we

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neglected NO2 absorption along the incident ray path (~-, = 0). The optical depth along the scattered ray path is ,0=~

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In Table 2 the expected radiance in the two channels, the current generated, the difference, the noise and the signal to noise ratio are presented where the signal is the difference between the current in the two channels. The uncertainty in the difference is < 170 at 20 km, 370 at 25 kin, 870 at 30 km and 3570 at 35 km. The statistics may be improved by adding data from two or more spins together to produce one NO~ absorption profile. The excited ~Ag level of 02 results primarily from the photolytic loss of ozone in the sunlit atmosphere. The infrared airglow instrument will monitor the O2(aXAg--> X3E)) emission at 1.27/~m to determine the altitude profile of ozone photolysis between about 50 and 80 km during the daytime. The lower limit will be determined by the observations. The calculated limb radiance of the O2(~Ag) emission is shown in Fig. 10. Here we have assumed that one excited O2(XAg) molecule is formed from each Oa dissociation between 0.2 and 0.3 ~m and that O2(~Ag) molecules are lost to quenching by O2 at a rate of 2 • 10 -~8 cm* s-L The noise level of the detector is equivalent to about 3.5 x 106 R, giving a signal to noise ratio for maximum intensity at 54 ~ solar zenith angle of 330 and at 90 ~ solar zenith angle of 43. The O2(XAg) emission in the nightglow, although much less intense, may be monitored by adding data from two or more spins. The infrared instrument will simultaneously monitor the emission in the 7-5 band of OH(X2~r) at 1.9/~m. The seventh vibrational level of OH is populated directly 90

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Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

611

by the reaction of H and 03 and indirectly by cascade from levels 8 and 9. Thus the interpretation of the 7-5 emission is relatively simple and will provide information on the product of H and 03 in the mesosphere. A simulation of the radiance expected during the night is given in Fig. 11. This model has been shown to be consistent with OH radiance measurements from the AE-E satellite (FREDERICKe t al., 1978). The four-channel infrared radiometer provides radiance measurements in four wavelength channels. The instrument makes temperature measurements by viewing carbon dioxide thermal emission with narrow- and wide-spectral bandwidth channels centered at 15.5 Fm. Thermal emissions from ozone and water vapor are measured at 9.6 t~m and 6.3/~m, respectively. Simulations of expected radiance from the four channels are shown in Fig. 12a-d for mid-latitude winter and for a stratospheric warming. Here NEN denotes the anticipated noise equivalent radiance. For the CO2 channels (Fig. 12a and b) a signal-to-noise ratio greater than one can be expected over the entire region of the experiment. The signal-to-noise ratio for the ozone channel (Fig. 12c) reaches one at about 75 km and occasionally to 70 kin. In most cases the lowest signals occur for cold mesopause situations. The water vapor channel (Fig. 12d) reaches the noise level at about 76 km. The fundamentals of the inversion are described in GILLEand HOUSE (1971) and HOUSE and GILLE (1979), although the implementation for rapid processing will embody the emissivity approach described by BAILEYand GILLE (1978). Accurate results have been demonstrated in the mesosphere and stratosphere (GILLEe t aS., 1979). Ozone densities at high latitudes may be perturbed in the mesosphere and stratosphere during charged particle precipitation (SPE or REP) as discussed earlier. The enhanced ionization produces odd-hydrogen and odd-nitrogen species that catalyzes ozone recombination. The solar proton alarm will signal the occurrence of an SPE above some pre-determined flux threshold. If the spacecraft data system is in the alarm mode it will automatically re-program the observing strategy to concentrate the measurements in high latitudes. Under night-time conditions, the polar particle induced airglow emission in the N + 0.3914 Fm band will be easily measured by the visible light spectrometer. A measurement of the night-time emission profile will directly provide the ionization rate profile in the same volume in which ozone, water vapor and temperature are measured. The ionization rate profile in turn yields the odd-hydrogen and odd-nitrogen production rate profiles. It is important that the SME instruments be able to respond to a particle event in real time, particularly for the mesospheric ozone. This is due to the fast photochemical response time of ozone in this region, for which there is some evidence in the data of HEATH et al. (1977). After-the-fact information on the proton and electron energy spectrum will be obtained from particle measurements on the GOES and TIROS satellites and made available by the NOAA Data Center in Boulder, Colorado. Rocket measurements of the proton spectrum for the 2 November 1969 SPE have been made by SELLERSand HANSER(1972). The ionization profile at the maximum

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IONIZATION RATE (cm-a s-I) 103

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F i g u r e 13 I o n i z a t i o n rate (electrons-cm -a s -1) vs. altitude (km), a n d 0.3914/zm limb r a d i a n c e (R) vs. m i n i m u m r a y h e i g h t p r o d u c e d b y t h e solar p r o t o n event o f 2 N o v e m b e r 1969 at its m a x i m u m intensity. T h e ionization rate values are f r o m LAVERGNAT et aL (1972). T h e 0.3914/~m fluorescent efficiency o f 14.1 i o n pairs per 3914 A p h o t o n was t a k e n f r o m BORST a n d ZIPF 0 9 7 0 ) .

of the event was computed by them and by LAVERGNATet al. (1972) using Explorer 4 charged particle measurements, and were in good agreement. The 0.3914/~m production rate resulting from their ionization profile, and the predicted limb radiance of the 0.3914/zm emission is shown in Fig. 13. The fluorescent efficiency was taken to be 14.1 ion-pairs per 0.3914/zm photon (BORSTand ZU'F, 1970). Using the production efficiency of 10 O2(1Ag) molecules produced per ion pair estimated by SWIDER and GARDNER (1972), the limb radiance in the 1.27/~m band can be inferred from the figure by multiplying the 0.3914/zm profile by 140. Thus a maximum value of 1.27 /zm limb emission of 0.7 megaRayleigh would have resulted from the 2 November 1969 event. However, quenching would greatly reduce this value below about 60 kin.

V. S M E experiment operations

The SME mission has been designed to take advantage of the existing NASA satellite tracking and communications capability. Telemetry, command, and tracking coverage requirements vary from a maximum of two 30-min contacts per orbit for the first three weeks, to 14 contacts per day for the remainder of the mission. The data will be analyzed by the Science Team at LASP as it is processed during the mission.

Vol. 118, 1980) ScientificObjectivesof the Solar Mesosphere Explorer Mission

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The SME Project Operations control center at LASP will be the central facility for the control of the SME satellite and the evaluation and analysis of its data. The commands and data links will also utilize existing facilities at the Goddard Space Flight Center. Tracking data will be linked to Goddard for orbit determination. The real-time and tape recorder playback data will be received and recorded at LASP. Real-time data will be used to monitor the health of satellite subsystems and verify the status of the observatory. Tape recorder playback data will be formatted and available for quick-look scientific evaluation, attitude determination, and scientific analysis. Data from recorded real time and tape recorder playback data will be processed and analyzed using a mini-computer system. A general purpose data reduction language, along with many data reduction programs, has been written for use on other LASP projects and will be available for SME 'quick-look' evaluation and analysis. The Interactive Display language will provide users with easy-to-use, flexible, interactive computing power with no turnaround time. It is display oriented, making use of storage and CRT displays and plots. The language is designed to manipulate and display scalars, vectors (spectral data), and matrices (image data) as any simple variable, allowing a relatively untrained user to reduce and analyze scientific data with desk calculator ease. The interactive nature of the language allows execution of stored or standard routines as well as execution of single statements from the keyboard, where the results of each operation are automatically displayed on the user terminal. Standard data reduction routines will be available for functions such as data smoothing, averaging, contouring, curve fitting and noise removal along with special purpose calibration and inversion routines.

VI. SME personnel and acknowledgements The Principal Investigator of the SME mission is Charles Barth, Director of the Laboratory for Atmospheric and Space Physics. Lowell Dorman is the University of Colorado Project Manager. The SME Project is managed by the Jet Propulsion Laboratory, with John Paulson as JPL Project Manager and James Stuart as Spacecraft Manager. D. W. Rusch has contributed to all phases of preparation of this manuscript, and has also provided the calculations for the simulated radiances for the 03, NO~, O2(1Ag) and OH signals. P. Bailey and J. Gille provided the simulated radiances for the infrared radiometer experiment. S. C. Liu contributed much of the material contained in Section II. The original proposal is described in the unpublished University of Colorado document 'Solar Mesosphere Explorer Experiment Description'. We thank G. P. Anderson for a careful reading of the manuscript and for helpful suggestions. We acknowledge the National Center for Atmospheric Research for

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c o m p u t e r services. N C A R is sponsored by the N a t i o n a l Science F o u n d a t i o n . The S M E Project is supported u n d e r JPL C o n t r a c t n u m b e r 955357.

REFERENCES BAILEY, D. K. (1968), Some quantitative aspects of electron precipitation in and near the auroral zone, Rev. Geophys. 6, 289-346. BAILEY, P. G. and GILLE, J. C. (1978), An approximate method for non-linear inversion of limb radiance observations, in Remote Sensing of the Atmosphere: Inversion Methods and Applications, A. L. Fymat and V. E. Zuev (eds.), Elsevier, Amsterdam, pp. 107-113. BORST, W. L. and ZIPF, E. C. (1970), Cross-section for e- impact excitation of the 0,0 1N N~ band from threshold to 3 Key, Phys. Rev., Sect. A 1, 834-840. CRUTZEN, P. J. (1970), The influence of nitrogen oxides on the atmospheric ozone content, Quart, J. Roy. Meteor. Soc. 96, 320-325. CRUTZEN, P. J. (1971), Ozone production rates in an oxygen-hydrogen-nitrogen oxide atmosphere, J. Geophys. Res. 76, 7311-7327. FREDERICK, J. E., RUSCH, D. W. and LIu, S. C. (1978), Nightglow emissions of OH(X%r): Comparison of theory and measurements in the (9-3) band, J. Geophys. Res. 83, 2441-2443. GAUSE, K. A. and STUART,J. R. (1979), Solar Mesosphere Explorer Optical-Mechanical Systems Engineering, IEEE Region V Annual Conference, April 3-5, E1 Paso, Texas. GILLE, J. C., BAILEY,P., HOUSE,F. B., CRAIG,R. A. and THOMAS,J. R. (1978), in Nimbus 6 Users Guide, J. E. Sissala (ed.), Greenbelt, Maryland, NASA, pp. 141-16t. GILLE, J. C., BAILEY,P. L. and RUSSELL,J. M. III (1979), Temperature and composition measurements from the LRIR and L I M S experiment on Nimbus 6 and 7, Proc. Roy. Soc. (submitted for publication). GILLE, J. C. and HOUSE,F. B. (1971), On the inversion of limb radiance measurements I: Temperature and thickness, J. Atmos. Sci. 28, 1427-1442. HEATH, D. F., KRUEGER,A. J. and CRUTZEN,P. J. (1977), Solar proton event: Influence on stratospheric ozone, Science 197, 886-889. HEATH, D. F. and THEKAEKARA,M. P. (1977), The solar spectrum between 1200 and 3000 A~, in The Solar Output and its Variation, O. R. White (ed.), (Colo. Assoc. Univ. Press, Boulder), pp. 193-212. HOUSE, F. B. and GILLE, J. C. (1979), On the inversion of limb radiance measurements II: Ozone and water vapor, J. Geophys. Res. (submitted for publication). HUNT, B. G. (1966), Photochemistry of ozone in a moist atmosphere, J. Geophys. Res. 71, 1385-1398. HUNTEN, D. M. (1954), A study of sodium twilight. I theory, J. Atmos. Terr. Phys. 5, 44-56. JOHNSTON, H. S. (1971), Reduction of stratospheric ozone by nitrogen oxide, catalysts from supersonic transport exhaust, Science 173, 517-522. KERR, J. B. and MCELROY, C. T. (1976), Measurement of stratospheric nitrogen dioxide from the AES stratospheric balloon program, Atmosphere 14, 166-171. KRUEGER, A. J. and MINZNER, R. A. (1976), A proposed standard mid-latitude ozone model, 1975, Goddard Space Flight Center, NASA, Greenbelt, Maryland. LAVERGNAT,J., BERTHELIER,J. J. and PIRRE, M. (1972), Riometers observations in Antarctica of 2 November 1969 solar proton event, in Proc. of COSPAR Symp. in Solar Particle Event of November 1969, J. C. Ulwick (ed.), AFCRL-72-0474, pp. 181-200. MIEGHAM,VAN J. (1978), Scale analysis of large atmospheric motion systems in all latitudes, Adv. in Geophysics 20, Academic Press, 87-130. MURGATROYD,R. J. (1971), Dynamical modeling of the stratosphere and mesosphere, in Mesosphere Models and Related Experiments, Fiocco, ed., Reidel Publ., 104--121. NATIONAL ACADEMY OF SCIENCES PANEL ON ATMOSPHERIC CHEMISTRY (1971), Halocarbons: Effects on Stratospheric Ozone, Nat'l. Acad. of Sciences, Washington, D.C., p. 107.

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NOXON, J. F. (1975), Nitrogen dioxide in the stratosphere and troposphere measured by ground-based absorption spectroscopy, Science 189, 547-549. NOXON, J. F. (1979), Stratospheric NO2: II. Global behaviour, J. Geophys. Res., in press. PARK, J. H. and LONDON, J. (1974), Ozone photochemistry and radiative heating of the middle atmosphere, J. Atmos. Sci. 31, 1898-1916. ROWLAND,F. S. and MOLINA,M. J. (1975), Chlorofluoromethanes in the environment, Rev. Geophys. Space Phys. 13, 1-35. RtrSSEL, J. M. II and GILLE,J. C. (1978), in Nimbus 7 Users Guide, C. R. Madrid (ed.), Greenbelt, Maryland, NASA, pp. 71-103. SELLERS, B. and HANSER, R. A. (1972), Heavy Particle Ionization Rates, in Proc. of COSPAR Symp. on Solar Particle Event of November 1969, J. C. Ulwick (ed.), AFCRL-72-0474, pp. 181-200. STOLARSKI,R. S., and CICERONE, R. J. (1974), Stratospheric chlorine: a possible sink for ozone, Can. J. Chem. 52, 1610-1615. SWIDER, W. and KENESrIEA,T. J. (1973), Decrease of ozone and atomic oxygen in the lower mesosphere during a PCA event, Planet. Space Sci. 21, 1969-1974. U.S. Standard Atmosphere (Gov. Printing Office, Washington, D.C., 1976), p. 227. VIDAL-MADJAR,A. (1977), The solar spectrum at Lyman-Alpha 1216 A, in The Solar Output and Its Variation, O. R. White (ed.), (Colo. Assoc. Univ. Press, Boulder), pp. 213-236. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh[iuser Verlag, Basel

Satellite Solar Occultation Sounding of the Middle Atmosphere By JAMESM. RUSSELLIII 1)

Abstract- This paper discusses the principles, achievements, and prospects for satellite solar occultation sounding of the middle atmosphere. Advantages, disadvantages, and spatial and temporal coverage capabilities are described. Progress over the past 15 years is reviewed, and results from a recent satellite aerosol experiment are presented. Questions with regard to Doppler shift, atmospheric refraction, instrument pointing, pressure sensing, and measurement of diurnally active species are addressed. Two experiments now orbiting on the Nimbus-7 and AEM-B satellites, and approved experiments under development for future flights on Spacelab and the Earth Radiation Budget Satellite, are also described. In some cases more than one experiment is scheduled to be flown on the same spacecraft, and the advantages and synergistic effects of these applications are discussed. Key words: Solar occultation sounding.

Introduction The middle atmosphere, extending from the tropopause to 100 kin, is an important region of our atmosphere not only from the viewpoint of scientific interest and study, but also because it serves as a buffer zone to shield the Earth surface from extreme ultraviolet rays of the Sun. In addition, it affects the Earth radiation balance, and it is dynamically coupled to the lower atmosphere. It is generally an accommodating region for remote probing since it contains no cloudiness except occasionally at the lower boundary near the tropopause, and this occurs mostly in the Tropics. Noctilucent clouds are also a consideration in this regard but they are not very important since they occur mostly at high altitudes ( ~ 80 km) and latitudes ( < 50~ On the whole, the problems of remote sensing in the middle atmosphere are tractable, and a number of satellite experiments have been conducted including both nadir and limb sounders. Both the thermal emission approach (for sensing of the more abundant gases such as 03, H20, and N20) and solar occultation (for Oa and aerosols) have been used. Early experiments were directed to the nadir and concentrated primarily on measurements of temperature and/or ozone using upwelling thermal emission measurements. These included the Infrared Interferometer Spectrometer - IRIS (PRABHAKARAet al., 1) NASA, Langley Research Center Hampton, VA 23665, USA.

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1976), the Satellite Infrared Spectrometer - SIRS (WARK,1970), the Selective Chopper Radiometer - SCR (ABELet al., 1970), and later the Pressure Modulated Radiometer PMR (CURTISand HOUGHTON, 1974). The Backscatter Ultraviolet (BUV) experiment was also developed and flown on the Nimbus-4 satellite to infer total ozone in a vertical column below the satellite using measurements of solar radiation backscattered by the atmosphere (HEATH et aL, 1973). These experiments provided a wealth of new information on the upper atmosphere. As our knowledge progressed, however, the need for increased vertical resolution became apparent. GILLE (1968) was the first to suggest limb thermal emission sounding for this purpose which he proposed as a means to study diurnal temperature changes. This idea was developed into the Limb Radiance Inversion Radiometer (LRIR) experiment which was later flown on the Nimbus-6 satellite (GILLEet al., 1979). The LRIR experiment relied on measurements of infrared thermal emission coming from the planetary horizon to infer profiles of temperature, ozone, and water vapor concentrations. It was the first satellite experiment to provide temperature and ozone data with high vertical resolution, especially in the mid to lower stratosphere. As model studies of the chemistry in the upper atmosphere became more sophisticated, a number of mechanisms were revealed that could lead to catalytic destruction of stratospheric ozone through reactions with odd-nitrogen, odd-chlorine and oddhydrogen compounds (NOx, CIOx, and HO~). Because of the potentially serious biological and climatic consequences of ozone depletion, a number of experiments were proposed and selected for flight to study the chemistry and dynamics in the upper atmosphere. The Nimbus-7 satellite, launched October 1978, carried several experiments designed to study the first of these chemical chains- the NOx compounds. These experiments included the Limb Infrared Monitor of the Stratosphere (LIMS) (RUSSELL and GILLE, 1978), the Stratosphere and Mesosphere Sounder (SAMS) (DRUMMOND et al., 1978), and the Solar Backscatter Ultraviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) (HEATH et al., 1978). Both LIMS and SAMS are thermal limb sounding experiments. The LIMS measures radiance profiles which are processed to yield the vertical distributions of temperature, 03, NO2, HNO3, and H20 as a function of pressure, while SAMS provides measurements of temperature, CO, N20, NO, CH4, and H20. The SBUV/TOMS measures 03 profiles above the main peak and total ozone in a vertical column. The measurement of chemical species in the chlorine chemistry is more difficult than is the case for NO~. Consequently, no satellite experiments currently exist, although several are under development. The concentrations of important gases are generally less than those in the NOx family by about an order of magnitude, and in some cases (e.g. HC1), the molecular absorption band occurs at a relatively short wavelength (~3/zm) where emission is very weak. These limitations suggest that another approach, namely solar occultation, be used to obtain high signal-to-noise ratios especially at the shorter wavelengths. The use of solar occultation also facilitates the measurement and study of another problem of the middle atmosphere-the

618

James M. Russell III

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aerosol distribution and its effect on the Earth radiation balance. Two solar occultation experiments for this purpose were recently launched on the Nimbus-7 and AEM-B satellites. The Stratospheric Aerosol Monitor II (SAM II) on Nimbus-7 is designed to measure polar region aerosol distributions, and the Stratospheric Aerosol and Gas Experiment (SAGE) on AEM B measures aerosols, ozone, and NO2 profiles (McCoRMICK et aL, 1976). The purpose of this paper is to describe the principles, achievements, and prospects for application of satellite solar occultation sounding in the middle atmosphere. The advantages and disadvantages, geographic and temporal coverage, and past, current, and future approved experiments are described.

Principles of solar occultation sounding The general approach in the solar occultation experiment is to observe the attentuation of the Sun's rays due to absorption by atmospheric constituents (Fig. 1). The general relation for the measured signal, S, at a tangent height, Ho, can be written in terms of the solar intensity and atmospheric absorption by the equation

s=cf~

f~ f~ a.Ns(v, 0, 4)..(0, v, P, r)r(0, 4)e(0 dv

0

v

d~dOdr

(1)

where C is a responsitivity factor that converts radiance to volts, Ns is the solar intensity, A is the instrument aperture area, r is an optical and electronic attenuation factor, % is the transmittance from the Sun along the horizon path to the satellite, ~,(0, r is the instrument spatial response function, F(v) is the instrument spectral response function, Av is the spectral band width, and A0 and A~ define the angular

Figure 1 Solar occultation experiment geometry.

Vol. 118, 1980) Satellite Solar Occultation Sounding of the Middle Atmosphere

619

extent of the field of view. For a spectrometer, Av is small (e.g. _ 20 cm-1). The transmittance for a ray traveling along the instrument optical axis can be written ~-a(v, P, T) = exp

[J0 -

(Kv + ev)n d!

]

(2)

where K~ is the absorption cross-section at wavenumber u, e~ is the scattering crosssection, n is the number density of the absorbing constituent, and L is total path length across the horizon along the ray path. The absorption cross-section cart be a function of both pressure and temperature, depending on the spectral region used. In the infrared, it depends on both parameters. Also, the rather simple Lorentizion expression used in the lower atmosphere must be replaced for the middle atmosphere by the more complicated voight line shape. Equation (1) can be approximated by the expression S ~_ CA~N~-7~F Av

(3)

where the bars denote mean quantities over Av. In this equation S is in units of volts, C is in units of volts per watt, .N~ is in watts/m 2 tLm, Au is in t~m, A in units of m 2, and ~, ~a, and F are unittess. The experiment scenario is to track the solar disk as it rises or sets on the horizon thereby obtaining a profile of signal versus time, t. The transmittance ~ ( t ) can be determined by dividing the signal, S ( t ) , by the signal for an exoatmospheric measurement, S| for which t = 0 and ~ = 1. In principle, time can be converted to tangent altitude using satellite and solar ephemeris data. In practice, effects of atmospheric refraction must be included in the calculations because of the long paths across the limb. This affects the tangent altitude as well as the apparent Sun shape as seen from the spacecraft. PEPIN et al. (1977) show a series of photographs of the setting Sun (Fig. 2) which demonstrate the apparent decreasing

Figure 2 Composite of photographs taken during Apollo-Soyuz mission showing refraction effects on the Sun image (after PEPINet al., 1977).

620

James M. Russell III

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vertical extent of the Sun as it sets. For a field of view locked at a fixed angle relative to the edge of the Sun, this effect causes the center of the field of view to move to successively different points on the solar limb darkening curve at lower tangent altitudes. Thus, it must be taken into account in relating the solar intensity value at any given time, t, to the exoatmospheric value. Refraction also causes the instrument field view to cover a larger area of the Sun for the lower tangent altitudes and must be considered in calculations of spatial averaging. C n u and McCoRMICK (1979) present a method for using the Sun shape at each tangent altitude to accurately account for these factors. The value of N~ at 3 tzm wavelength varies by about 5 ~ due to these effects, and it should be possible to correct for this with little error ( ~ 0.3~o) using climatological temperature-pressure data. If the field of view has infinite spatial resolution, if the instrument pointing capability is perfect, and if other factors such as the atmospheric temperature-pressure profile and Sun spot occurrences are known exactly, it would not be necessary to define the solar limb darkening curve in an occultation experiment. Since these conditions are not met, however, the general approach is to scan the exoatmospheric limb darkening curve on each occultation event to obtain S= versus angle data (relative to one edge of the disk). This procedure will permit determination of Sun spots effects on the signal and any sensitivity the instrument may have to other solar surface features such as granularities. These effects can then be removed later in the data reduction. The scans will also allow effects due to changing field of view area on the disk to be properly considered. Once the limb darkening curve has been defined, the disk can be tracked during occultation either in a continuous scan mode or a mode where the field of view is locked at some fixed angle from one edge or at the disk center. There are advantages and disadvantages to each approach depending upon the instrument and measurement being made. The scanning approach provides more data since each tangent altitude is crossed several times during an occultation, and for certain conditions, when the Sun is not fully occulted by the Earth, a wider altitude range can be covered than in the lock mode. The lock mode, on the other hand, provides a longer measurement integration time, and therefore a given measurement can be made with smaller instrument optics. Thus, it should be possible in principle to sense more tenuous gases with this approach without resorting to data averaging. Effects due to spacecraft motion can be automatically removed with either method by designing the instrument pointing control bandwidth or scan rate to be much greater than 'the frequency of expected spacecraft motions. Sun shape data are obtained automatically in the scan mode and can also be measured with the lock mode approach by proper instrument design. Pressure sensing The use of the transmittance equation (2) at infrared wavelengths to determine number density requires that pressures be determined by some method in order to

Vol. 118, 1980) SatelliteSolar Occultation Sounding of the Middle Atmosphere

621

account for pressure effects on the absorption cross-section. Temperature also affects the cross-section but it is mostly a second order effect, particularly for those lines with a low ground state energy. One approach is to use the tangent altitude calculated from the satellite-Sun ephemeris data along with climatological data to obtain a representative temperature-pressure profile. This places stringent requirements on tracking and pointing stability, and with current systems it can result in substantial errors in number density. PARK et al. (1979) outline a broadband (~100cm -1) method for remotely sensing tangent shell pressure using the occultation technique. The method is based on measurement of limb absorption in the 2.0, 2.7, or 4.3/~m CO2 band and assumes a constant and known CO2 mixing ratio. By proper choice o f spectral regions, lines can be selected which are only weakly temperature dependent, and climatological temperature data may be used with little error. An excellent first guess pressure profile can be obtained by constructing a transmittance versus pressure plot using a climatological temperature-pressure profile. The CO2 ~(t) data can then be used to read pressure directly from the plot. These authors also describe an iterative procedure which carries the initial guess to a final solution. Pressure can be inferred with an RMS accuracy of about 3~o up to 55 km altitude using present instrument systems. A similar approach can be used with high spectral resolution data to determine temperature as well as pressure. A line with low ground state energy and therefore weak temperature dependence is selected for pressure sensing and a line with high energy is used for temperature sensing. Some iteration would be required (ToTH, 1977). Other considerations

Other effects which may need to be considered in applying the occultation approach include Doppler shift, and interpretation of measurements of diurnally active species. With regard to the Doppler shift, the maximum value for 3/zm as an example, is about 0.07 cm-1. This compares with absorption line widths in the upper atmosphere of 0.007 cm-1 or less. Thus large errors result if this is neglected. Since the spacecraft velocity can normally be determined to within a few meters per second, corrections for the Doppler shift do not present a problem in the data analysis. For events where the Sun direction is nearly perpendicular to the orbital velocity vector, the Doppler shift is very small; but the latitude skew, or the latitude range covered during the time required for the occultation to occur, is large. When the latitude skew is minimal, the Doppler shift is maximum. The measurement of diurnally active species (e.g. NO, NO2, CIO, CIONO2, Oa) also adds complexity to the data reduction and interpretation of occultation measurements. Nitric oxide for example is believed to be converted almost entirely to nitrogen dioxide (NO2) during the night. At the occultation solar zenith angle of 90~ the Sun's dissociating potential at the tangent point has been depleted relative to lower zenith angle rays due to the long path. Thus, the vertical distribution of NO with altitude is not the same as for the high noon case. This effect creates a non-spherically

622

James M. Russell III

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symmetric NO distribution along the horizon path (see MURCRAY, 1978). Sunset measurements by RIDLEY et al. (1976) show that the change in NO concentration from the zenith Sun position to 90 ~ is only 207o in the mid-stratosphere. A method for correcting NO occultation measurements and relating these data to daytime values is described by KERR et al. (1977). The diurnal effect is not serious in this instance, but this may not be true for some gases. The effects and errors depend on the magnitude and speed of the diurnal change and must, therefore, be studied on a case by case basis. Advantages and disadvantages

The solar occultation approach has a number of advantages. Because of the experiment geometry and the exponential decrease of density with height, high vertical resolution is obtainable. Most of the absorption occurs in a narrow height range weighted near the tangent point. Also, the limb view provides long optical paths allowing measurements to be made of more tenuous gases than can be measured in a nadir experiment. The Sun provides a very large signal making it possible to perform the measurements using uncooled or, at worst, thermoelectrically cooled detectors. The solar background is a source of nearly constant intensity rather than a highly variable source, as is the case for the nadir experiment. All of these effects simplify data reduction and enhance measurement accuracy. The large solar signal allows use of narrow spectral intervals thereby increasing the potential for measurement of gases in regions spectrally contaminated by interfering species. Solar occultation also covers a much wider spectral range for remote sensing than is the case for emission, thereby allowing measurements of some gases, such as HC1 and HF, which are difficult or impossible to measure by infrared emission techniques. One of the most important advantages of solar occultation is that a relative measurement is made. This self-calibrating feature provides higher accuracy since the instrument is calibrated just before or just after each measurement. Other concerns, such as long term instrument drifts, are also decreased. The only requirement is that the instrument be stable over the time required for an occultation (typically 30 seconds to 3 minutes). All of these factors are important in the design of an experiment for making longterm observations. The solar occultation approach has some disadvantages in that the sampling rate around the globe is less frequent than for a thermal emission experiment which provides data night and day and in any view direction. Also, the geographic coverage is limited. This is not a serious limitation for certain types of experiments such as long-term trend studies, large-scale dynamics, hemispheric differences, or global budgets of chemical constituents. These points are discussed further in the next section of this paper. The horizontal resolution is not as good as in the nadir experiment since the weighted absorption occurs over an effective length of 200-300 km along the path. This should not be a critical factor for study of the middle atmosphere since large horizontal variability is not expected. Finally, the occultation measurements

Vol. 118, 1980)

623

Satellite Solar Occultation Sounding of the Middle Atmosphere

I'q

. 30

285 ~ 6 ~

- -

o

-30 Z -60 -90

0

30

60

90

120 150 180 210 240 270 TIME FROMJANUARY 1 LAUNCH, days

300

330

360

Figure 3 Effect of orbit inclination on the latitude coverage envelope for solar occultation from 600 km altitude (private communication, HARRISON, 1979).

are confined to the 90 ~ solar zenith angle condition which, in some cases already noted, can cause added complexity in data reduction and analysis.

Spatial and temporal coverage considerations A detailed analysis of the spatial and temporal coverage attainable with solar occultation has been presented by HARRISONet al. (1975) and BROOKS(1977). Figure 3 shows the effect of orbit inclinations and seasonal changes on latitude coverage, and Fig. 4 shows the latitude coverage for 1 full year at 56 ~ inclination (HARRISON, 1979). 2) Latitudes of + 45 ~ + 75 ~ and + 90 ~ can be observed for orbital inclinations of 28.5 ~ 56 ~ and 70 ~ respectively. A high noon Sun-synchronous orbit provides only 64-80 ~ coverage in both hemispheres. I f the equatorial crossing time is different than high noon, a different latitude range can be covered but it will still be limited in comparison to the coverage attainable with a non-Sun-synchronous inclination. Note from Fig. 4 that at several times of the year, 100 ~ of latitude is covered in under 1 week time period and that for most of the year, this range is spanned in 2 weeks or less. There are several periods where no occultation occurs due to the satellite-EarthSun geometric relationship created by the orbital precession. The percentage of the year when this condition exists, however, is small. The frequency of coverage for 56 ~ inclination is about twice a month for latitudes of + 45 ~ decreasing to about once a month, on the average, for latitudes greater than + 45 ~ These coverage frequencies will vary with orbital inclination. In a 70 ~ inclined orbit, both poles are covered 2) Private communication, NASA, Langley Research Center, Hampton, VA 23665:

624

James M. Russell :III

(Pageoph,

-u

t~

_2 I- oo. Then, the eddy heat flux is written as follows: e~' ~ ' ~x 8z

=

Ial2.knr

" 2 zr

9s i n

~ y . e ((~m~- 2'~0~,

(3-4) 8)

where nr is the real part of n and the amplitude A is related to the height of the bottom corrugation ho as follows: N' 1 +

1 c~,Uo/~/ o*v n~ + (n~h~-

(3-5) ~-~

Substitution of (3-4) into equation (2-5) gives -

= ~.~.

kn~n~ [A

9sin -L- y" e((1/m- 2,~,~.

(3-6) Hereafter, our concern is focused on the steady solution, i.e., O/Ot = 0. We expand

7) The sign of n, (the real part of n) is determined as follows : n, ~ 0 for Uo ~ UR(-fl/(k 2 + ~r2/L2)). Un is the speed of two-dimensional free Rossby wave. a) It follows from (3-4) that the eddy heat flux is directed southward if Uo is larger than UR (see footnote 7).

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

673

into Fourier cosine series so that the side boundary conditions (mean meridional velocity V vanishes at the walls) are satisfied automatically (cf. URYU, 1974a): ~ = e ~I2n. m:oaa ~" ~mCOS mrr --ff y"

(3-7)

Further, we use the following Fourier expansion: m~-

27r sin-ry=-

8

cos -L-" y m2-4 9

9~

(3-8)

re:odd

Then, equation (3-6) is reduced to the equation for ffm as follows: tZ2m~m=

d2~m dz 2

8 IAI ~ zrkn,n, e(ll2m_2,h,~. ~r m 2 - 4" Lo~*

(3-9)

where I~ =

N2m%r 2 1 f2L-----T - + 4H----~.

The general solution to this equation can be written as ~m = B m "e""z + Cm "e-""~ __8_ [A[ 2 IrknTn~ e((l12H)-2~')~ zr m2 _ 4 L a , ( 1 )2 ~ - B - 2n' - t 4

(3-10)

where A is given by (3-5), and Bm and Cm are determined from the boundary conditions which are assumed as follows; W = u' ~h

v' ~h

e-~ml~ t ~ 0

~y

as z - +

at z = 0, )

(3-11)

~.

We can rewrite (3-11) in terms of ~m by using the thermodynamic equations (including Newtonian cooling) for the wave and the mean flow as follows; + ~-~ = ~r rn~ -- 4 2L--Uo ~ - ~ - n ~ eZlH(am--> 0

at z = 0, t

(3-12)

as z -~> oo.

Substitution of (3-10) into (3-13) gives

B m = 0,

Cm =

s

IA12

rr m 2 - 4

1H _ 2n~ ~ [4--~o ~* + 1 La* 2H tLm

Hrrli

l

674

Michiya Uryu

(Pageoph,

Then, we o b t a i n that m~r

~b= ~

ra:odd

~'k 8

]AI 2

cos--~-y L c ~ . ~ r m ~ 4

(z*

"-

+

(

-;

l'lrn i

e ( ( l / 2 H ) _ t~ra)Z

1 - 2n~

-

1

- i~

nrn~ 2

Thus, it is seen from this solution that the sign of n~ -

. e(am~- 2~,~ 1 .

(3-13)

1/2H is a n i m p o r t a n t factor

for d e t e r m i n i n g the flow structure, a n d the sign is determined by the difference between the amplification effect of density stratification and the d a m p i n g effect of dissipation (cf. DUNKERTON, 1979). F o r inStance, if n~ < 1/2H, i.e., if the wave amplitude increases in spite of the dissipation due to N e w t o n i a n cooling, easterly flows increasing u p w a r d are induced a n d the temperature of the n o r t h e r n region increases relative to that in the southern region. I f the wave amplitude decreases u p w a r d

Uo=20 m/sec 7O

E 50

r121

'~, r

3O

10 S

( m/sec

)

N

Figure 3a Meridional cross section of the mean zonal flow induced by a stationary, dissipating planetary wave applied at 10 km level. Parameter values are as follows. Uo = 20 m/see, ~* = 1.65 x 10- 6/see (= 1/(7 days)), k = 4.42 x 10 -9 cm, L (width of the channel) = ~r/(4.42 x 10 -9) cm, N --= 2 x 10-2/sec, f = 10-4/see,/3 = 1.6 x 10-1Z/sec.cm, H = 7 km, ho = 200 m. In this case, n~ = 1.42 x 10-7[cm, and then n~ < l[2H.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

675

Uo=20 m / s e c 70

/ \ ~50 E

10

-10

/\

7: -~, ~- 30

-1

1 v

/ -

0-1

0.1 V

10 S

? ( deg ) Figure 3b Meridional cross section of the zonal mean temperature anomaly corresponding to Fig. 3a. (n~ > 1/2H), the induced easterly flows also decreases upward and hence a lower temperature appears in the northern side. In Fig. 3a,b, the former example is shown, while the latter is in Fig. 4a,b. In both cases, we assume ~* = (7 days)-1 which m a y be close to the vertically averaged Newtonian cooling rate in the stratosphere and mesosphere (HOLTON, 1975). F r o m the former example, it is likely that dissipating, Uo = 5 m l s e c 70

-0.2 50 E v

"$ r

30

10 S

N ( rn I sec

Figure 4a Same as Fig. 3a but for Uo = 5 m/sec. In this case, n~ = 9.75 x 10-7/cm, and then nj > 1/2H.

676

Michiya Uryu

(Pageoph,

Uo= 5 m I sec

S 50

-•0.04

E

-0.04

r O~

"~, 30

10 S

T (deg)

N

Figure 4b Same as Fig. 3b but for Uo = 5 m/see. stationary planetary waves may contribute to maintaining the higher temperature in the winter polar middle atmosphere. However, to be more convincing, we should calculate the mean flow under more realistic conditions, because ~* and Uo are not constant in the actual atmosphere. In Fig. 6a,b, we show an example obtained for longitudinal wave number 1 by assuming 7O

50

E

z= 30

10 0

20 basic zonal flow

40

60

( rnlsec )

Fig. 5a Vertical distribution of the basic zonal wind.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

20

70

i

677

damping time ( d a y s ) 10 7 5 r

,

5O E

"~ 30

1%

t

2

Newtonian cooling coefficient

( ,o' s-' ) Figure 5b Vertical distribution of the Newtonian cooling rate.

5=1 ~x : c x ( z ) 70 -30 A

5o

i

30

10;

N 0

( ml sec )

Figure 6a Meridional cross section of the mean zonal flow induced by the wave with longitudinal wave number 1 (k = 2.21 x 1 0 - 9 / c m ) when the distributions of the basic zonal wind and the Newtonian cooling are assumed as in Fig. 5a and Fig. 5b, respectively. As to the parameter values used except k, see the legend of Fig. 3a.

678

Michiya Uryu

(Pageoph,

5--1 oc=~(z)

70

"•50 -4

Zr

3O -1 0 10

E

7 (deg)

N

Figure 6b Meridional cross section of the zonal mean temperature anomaly corresponding to Fig. 6a.

the vertical distributions of Uo and c~* shown in Fig. 5a,b. It is seen that the wave reduces the basic westerly wind by about 30 m/sec near z = 70 km in the mid-latitudinal region and causes the meridional temperature difference of about 7~ near the same level. By the numerical simulation with use of the quasi-geostrophic model, MATSUNO (1976) 9) has shown that in a statistically steady state, the temperature of the polar atmosphere near 70 km height becomes higher than that in the equatorial atmosphere by about 15~ and the mean zonal wind decreases by about 20 m/sec from the initial value there. Our results are not so different from Matsuno's.

4. Wave-induced Lagrangian-mean motion As mentioned in the previous sections, a transient wave and a dissipating wave can accelerate mean zonal flow. However, the zonal mean flows obtained in the previous sections do not show the mean motion of air particles, because the averaging procedure employed does not concern any ensemble of air particles, but it is applied merely along a latitudinal line. This averaging procedure is called Eulerian mean. It is interesting, then, to ask how the mean flows obtained so far are related to the mean motion of air particles or how a wave can force air particles to move. This problem is 9) Presented at the autumn meeting of Meteor. Soc. Japan at Nagoya, 23 Oct. 1976.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

679

important not only from the dynamical viewpoint, but also in connection with the transport of minor constituents by planetary waves in the atmosphere. There may be two methods of approaching such a transport problem. One is to evaluate the eddy fluxes and Eulerian-mean circulations due to the waves, while the other is to discuss the mass transport Velocity field. The former is involved in the framework of the Eulerian zonal mean dynamics described in the previous sections, because it concerns an average along a latitudinal line, which is defined independently of the wave disturbance. The latter approach treats an ensemble-mean velocity field of air particles, and is called a Lagrangian mean. As will be shown later, these two methods give different views of the same physical phenomena. The original idea of the Lagrangian-mean approach can be traced back to G. G. Stokes who studied the mass transport by water waves, and particularly in recent years such studies have been developed in connection with m o m e n t u m transport by waves in a material medium. A general theory of Lagrangian-mean dynamics has been formulated by ANDREWS and MClNTYRE (1978b). In what follows, we shall mention briefly the Lagrangian-mean motion associated with the examples described in the previous sections, and in addition the Lagrangianmean motion induced by a growing baroclinic wave. As for the general theory, see ANDREWS and MCINTYRE (1978b) and the article by Dr. McIntyre appearing in this issue and concurrently in Phil. Trans. Roy. Soc. L o n d o n ? ~ Further, Prof. Matsuno will elucidate a detailed mechanism of Stokes drift (see below) in this issue.

(a) Concept of Lagrangian mean Let us consider a latitudinal line (or tube) at a constant height in a fluid layer at rest or flowing in parallel in the zonal direction. In the absence of waves, this line (or tube) is regarded as a material line (or tube). In the presence of waves, however, the latitudinal line does not coincide with a material line, which is now undulating because of the wave. A familiar example similar to this is seen in case of water wave. When the water surface is calm, a line z = H, y = constant in the free surface is identical with a material line, while when a wave is present, z = H cannot specify the free material surface. The equation for the free surface is now given by z = H + ~(x, y, t). Then, in the presence of a wave, we can consider at least two different ways to take a ' m e a n ' value of a physical quantity Q. One is to average Q along a latitudinal line;

QE = Q(x, y, z, t),

(4-1)

where the usual local Cartesian coordinate system is employed and the overbar on the right means the usual zonal mean operation. This is the so-called Eulerian mean and ao) In this paper, Dr. Mclntyre discusses the nonuniqueness and also certain difficulties in using Lagrangian mean on a sphere.

680

Michiya Uryu

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is the one usually employed in meteorology. The discussions in the previous sections are also based on this Eulerian-mean. Another procedure is to average Q with respect to air particles labeled by the fact that they were located on a latitudinal line in the absence of waves. Let (x, y, z) be the'initial' position of an air particle. The particle is now displaced to (x + ~, y + r/, z + ~) because of the wave, where ~:, r/and ~ are the components of the particle displacement vector 1~and they are defined as functions of space (x, y, z) and time t in the Eulerian sense. Thus, the quantity Q belonging to this particle should now be evaluated at the displaced position (x + ~:, y + V, z + ~). We note here that motions of member particles of a material line are identical with each other apart from a phase shift. Conversely, this fact allows us to label particles on a material line by x. In this sense, x plays a dual role as Eulerian coordinate and Lagrangian label. Thus, averaging Q(x + ~, y + ~7, z + ~) with respect to x, we can obtain a different mean value from Q(x, y, z, t). In practice, if we can assume the wave is of small amplitude, we can obtain, to the second order in wave amplitude, by Taylor expansion, that

Q---L= Q(x + ~,y + ~7,z + ~ , t ) -

Q ( x , y , z , t ) + ~ . V Q ' + 89

(4-2)

where Q0 is the basic distribution of Q and Q' is the perturbation. This is the Lagrangian-mean value of Q correct to second order in the small amplitude approximation. It is clearly seen that Qc is different from QE at the second order in wave amplitude. The correction term ~-VQ' + 89 (~-V)VQo is called the Stokes correction (although the second term was first given by ANDREWSand MClNTVRE (1978b)). Particularly, if Q is velocity, the correction term is called the Stokes drift. It is further noted that ~3Ldefined above is equal to a mean value obtained by averaging Q along an undulating material tube with a weight of the cross-sectional area, and hence the Lagrangianmean velocity is the velocity of the center of mass of the tube (MATSUNO, personal communication;ANDREWS and MCINTYRE, 1978b). Since ~ is related to Eulerian perturbation velocity through the following kinematical relationship at the first order in wave amplitude

(c~ ~ 7 + U o ' V ) [ = u' + ~-VUo,

(4-3)

where Uo is the basic velocity vector, we can obtain QL from a solution of the Eulerian equations of motion.

(b) Examples of the wave-induced Lagrangian-mean flow In what follows, we shall illustrate several examples of the Lagrangian-mean flow obtained from the consideration mentioned in the last subsection.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

68 |

(i) Case of a slowly varying wave packet In the case of a slowly varying wave packet, URYU (1974b) showed that the Lagrangian-mean meridional circulation is zero to two orders in the Small parameter E of wave-packet theory (see Section 2). This can be shown as follows without handling the wave-packet solution. For simplicity, we consider a Boussinesq fluid following URYU (ibid.). Under the quasi-geostrophic approximation, the Lagrangian-mean vertical velocity WL is written, from (4-2), as follows; --

~w'

~w'

~w'

~ ~-~

w ~ = w + ~-~x + ~-g)-y + C-Ez - W + F y ~ , -

-

(4-4)

where use has been made of the Boussinesq relation V. g = O(a2) (a is the small amplitude parameter) and the smallness of ~ in quasi-geostrophic flow. W is the Eulerian-mean vertical velocity. Using the adiabatic equation e~ \ az t + -7- w, = 0,

(4-5)

WL is rewritten as Wz = W -

N

-

-

-

v'

,

(4-6)

where v' = O~/~t has been used. Then, in the present case, the first term in square brackets is two orders smaller in the slowly-varying parameter e than the second term (meridional heat flux), because O/Ot = 0(e) and ~ and O~b'/az are in quadrature to leading order. Thus, we can write the Stokes drift W~ as Ws = ~yyr/w' ~ ~-~ ~yy v'

.

(4-7)

On the other hand, the Eulerian-mean vertical velocity W can be obtained from the zonal mean adiabatic equation as follows; W=-N4

~

Fzz +Fyy v'

.

(4-8)

Assuming ~ is a function of slow variables only, the first term on the right of (4-8) becomes two orders smaller in e than the second. That is, -N--~y

+ 0(C).

(4-9)

Then, to this order the Stokes drift W~ just cancels the Eulerian-mean vertical flow W; consequently, Wz = W + W~ = 0(e2). (4-10)

682

Michiya Uryu

(Pageoph,

This result can be obtained also from a somewhat different consideration. Since we are concerned with adiabatic motion, we transform the Eulerian-mean adiabatic equation into its Lagrangian analogue, to obtain that, to the leading order in Rossby number,

e~L d~o e--7 + --~ W~ = 0

(4-11) 1t)

where 17L = P + (O/Oy)vp', in which fi is the Eulerian-mean density anomaly and p' is the perturbation of density (cf. ANDREWS and MClNTYRE, 1978b; NAKAMURA, 1979). This means that the Lagrangian-mean density anomaly tSL is conserved along mean trajectories. Taking into account that 15 =-O~b/3z = 0(E), ~Tp'= 0(E) and 8/8t = 0(~), we can conclude that W~. = 0(42). Then, it is verified that in case of vertically propagating wave packet, the Lagrangian-mean meridional circulation vanishes to two orders in the small parameter E (the slowness of the wave envelope), while the Eulerian-mean circulation is two orders larger. A stronger result holds for a stationary wave; then, WL can be shown to vanish exactly (ANDREWS and MclNTYRE, 1978b; MATSUNO and NAKAMURA, 1979). This means that the C-D theorem is verified on the basis of Lagrangian mean dynamics (cf. ANDREWS and MClNTYRE, ibid.). Also, in case of a wave packet with small damping as discussed in Section 2, WL vanishes approximately because the wave structure in the leading order is same as that of a steady, conservative wave. Further, we note from (4-4) that Ws results from motion of air particles in the x-z plane plus that in the y-z plane; from the assumed form of r to the leading order in E, we have

Ow'

aw'

f%kn

~:-~-x = ~-b--fy = 4 ~

sin

Y'1r176

(4-12)

The Lagrangian-mean zonal flow UL can be written as --

--

8u'

~u '

8

UL = U + ~:-8--/x+ ~/-~y = 8 + ~y-qu

,

(4-13)

again using smallness of the Rossby number. Then, substituting the assumed wave form, we have U~ = ~:"b--xx+ "q ~y -

4or

c~

y1r176 + ~

4~

cos-L- y'1r176

am ~y-[r

2 (4-14)

p

11) Under steady conditions, we can deduce WL = -- Q - (O/Oy)w" where Q is the Eulerianmean heating rate and q' is the perturbation of heating. If ~q' can be neglected, we can obtain WL from a knowledge of Q only. DUNKERTON(1978) has calculated WLfrom this consideration.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

683

It is seen that Stokes drift Us has a jet-like structure in the meridional direction as result of the superposed effects of two terms. As is seen from (2-18), U is proportional to sin2(rr/L)y, and hence a zonal mass transport occurs more strongly in mid-latitudes than in other latitudes. Further, integrating UL in the y-direction, we obtain that

Poo(UL) =

Poo(U) = Eo C"

(4-15)

Then, ' m o m e n t u m ' E/C (more correctly, the pseudomomentum) is equal to the mean momentum of air particles in this particular problem (as to a rigorous consideration on E/C, see ANDREWS and MclNTYRE, 1978C). In the situation considered in Section 2, the origin of the acceleration of the mean zonal flow is the pressure drag force acting on the corrugated bottom. Then, replacing the bottom by an arbitrary undulating material surface in the fluid and calculating the pressure drag on the surface, we obtain

"-~x"5 = C~176

- PYxx/

C "

(4-16)

Thus, we can consider that the acceleration of mean zonal flow by the wave is caused as a result that a fluid below an undulating material surface acts with a pressure drag force -p'(9~/Ox) on a fluid just above the surface. The intuitive discussion in Section 2 is verified within the approximation of wave-packet theory. We note that in the Lagrangian-mean description, the secondary meridional circulation induced by the (Eulerian) eddy heat flux does not appear. In the Eulerian-mean framework, such an effect of the eddy flux does, by contrast, play an important role. The above result can be obtained also from the general theory by ANDREWS and MCINTVRE (1978b). (ii) Case of a stationary, dissipating wave In the case of a stationary, dissipating planetary wave as treated in Section 3, the Lagrangian-mean meridional circulation is induced, as well as the Eulerian-mean one. When the Newtonian cooling rate ~* and the basic westerly wind U0 are constant, the Lagrangian-mean meridional circulation can be easily calculated from the solution mentioned in Section 3 (URYt) and TA~ASHASm, 1979). The results are shown in Figs. 7a and 8a. The former is for n~ < 1/2H, while the latter is for n~ > 1/2H. Figures 7b and 8b show the corresponding Eulerian-mean meridional circulation, respectively. In the case where the wave amplitude decreases upward (n~ > 1/2H), both the Eulerianand the Lagrangian-mean meridional circulations have the upward branch to the north and the downward branch to the south. On the other hand, in the case where the wave amplitude increases upward (n~ < 1/2H), the Lagrangian-mean meridional circulation is completely opposite to the Eulerian-mean one. According to MATSUNO and NAr:AMURA (1979) who have discussed the Lagrangian-mean meridional circulation in the situation in which a stationary planetary wave is incident on a critical level

684

Michiya Uryu

(Pageoph,

Uo= 20 m/sec

2O

/ 1 aO

so

~ 30

1

5

~L ( g cn31/sec )

N

Figure 7a Lagrangian-mean meridional circulation induced by a stationary, dissipating planetary wave applied at 10 k m level. XL is the mass stream function, defined by poVL = -a~L/gz and poWL = a~HOy. The parameter values used are same as those in Fig, 3a. Note that Uo = 20 m/see (n~ < 1/2H).

Uo=20 mlsec 70

~SO E

O~

= 30

10 $

N ~--~ ( g c n ~ l l s e c )

Figure 7b Eulerian-mean meridional circulation corresponding to Fig. 7a. is the mass stream function defined by po F = -8"~E/Sz and poW = a-~JSy.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

Oo= 5 m/sec 70

-0.1

\

E

7_

\

.c 30

S

~L ( g crfil/sec )

N

Figure 8a Same as Fig. 7a but for Uo = 5 m/sec (n~ > 1[2H).

Uo= 5 m/sec

70

A 5O E v

t-

"~ 30 r

,o\

,oS

N

~'E ( gcrfillsec

)

Figure 8b Same as Fig. 7b but for Uo = 5 m/sec.

685

686

Michiya Uryu

(Pageoph,

from below, the Lagrangian-mean meridional circulations below and above the critical level are opposite to each other; the lower one is associated with upward motion to the south, while in the upper one the upward flow appears in the northern side. Since the wave is absorbed at the critical level according to linear theory at the large-time limit, we can consider that the Lagrangian-mean meridional circulations above and below the level correspond to Fig. 8a and Fig. 7a, respectively. According to URYU and TAKAHASHI(1979), if Uo exceeds a certain value, say Urn,12) the Lagrangian-mean meridional circulation shows the so-called 3-cell structure in the meridional direction, consisting of one circulation in the central region of the channel with upward (downward) motion to the north (south) and of two opposite circulations near the side walls. In addition, the central circulation spreads in the meridional direction as U0 increases. By contrast, the Eulerian-mean meridional circulation does not change its pattern substantially so far as Uo changes between Um and URla) (the speed of two dimensional free Rossby wave; > Urn). These results seem due to the assumption that the planetary wave is damped by Newtonian cooling

7~

!

S=I

-10 / E50 -I00 E, '- 30

S

N ~,( gcrff)sec )

Figure 9a Lagrangian-mean meridional circulation induced by the wave with longitudinal wave number 1(k = 2.21 • 10-9/cm) when the distributions of the basic zonal wind and the Newtonian cooling rate are assumed as in Fig. 5a and Fig. 5b, respectively. As to the parameter values used except for k, see the legend of Fig. 3a. ~L is defined in the legend of Fig. 7a. 12) Um- 28 m/see when we adopt the numerical values listed in the legend of Fig. 3a. It is noted that at Uo = U~,, the vertical energy flux po~b'w' becomes maximum when the other parameters are fixed (URYu and TAKAHASHI,1979). 13) UR -- 41 m/sec under the same condition above.

Vol. 118, 1 9 8 0 )

Acceleration of Mean Zonal Flows by Planetary Waves

687

5=1

~=c~[z)

10!/

N ~E ( g crfi1/sec) Figure 9b

Eulerian-mean meridional circulation corresponding to Fig. 9a. ~E is defined in the legend of Fig. 7b.

only (see equation (2-4)). Further, it is noted that if Uo exceeds UR, the directions of both the Eulerian-mean and Lagrangian-mean circulations are reversed to those obtained for U0 below UR (URYu and TAKAHASm, 1979; see also footnote on page 672). When U0 and a* are dependent on height as presented in Fig. 5a,b, the Lagrangianand Eulerian-mean meridional circulations become as shown in Figs. 9a, and 9b, respectively. It is seen that the Eulerian-mean meridional circulation is not so different from that in Fig. 7b, except for the difference in the intensity due to that in the wave amplitude. However, the Lagrangian-mean meridional circulation is completely different from that in Fig. 7a. In the present case, it is split into two parts in the vertical direction; the lower circulation is associated with upward (downward) motion to the south (north), while the upper one is opposite, as a result that the central circulation in the 3-cell structure spreads over the channel (URYU and TArCArlASm, 1979). Although the present circulation pattern happens to be somewhat similar to that obtained by MATSUNO and NAKAMURA(1979), it should be emphasized that while under the present conditions (see the legend of Fig. 3a) the wave amplitude increases upward, it decreases suddenly above the critical level in Matsuno and Nakamura's case. Here, it is emphasized that as is seen from the figures, the Lagrangian-mean mass flux is solenoidal in the meridional plane. This is due to the stationarity of the wave considered (ANDREWS and MCINTYRE, 1978b). In practice, under the stationary wave

688

Michiya Uryu

(Pageoph,

assumption, the meridional and vertical components, Vs and follows; V~ =

Fz - H

W~, are written as

~v

0-W~ = ~y ~/w'

(4-13)

(4-14)

where use has been made of v' = Uo(O~/Ox)and w' = Uo(OUOx),from which v'~ = w'~r = 0 is obtained. Then, considering that the Eulerian-mean mass flux is solenoidal in the meridional plane, i.e.,

-~y p 0 V + ~0 poW = 0, -

-

(4-15)

and that v'C + wq7 = 0 for stationary waves, we can conclude that the Lagrangianmean mass flux is solenoidal in the meridional plane for stationary waves, i.e., m

~

m

-~poV, + ~poWL = o

(4-16)

(cf. A~qDREWSand MclNTYRE, 1978b; MATSUNO and NAICAMURA, 1979). (iii) Case of a growing baroclinic wave In the previous subsections, we have treated waves of almost stationary ((i)) and stationary ((ii)) properties. It is then interesting to ask what mean motion of air particles are caused by a stronger time-dependent behavior of a wave. We shall discuss the recent results of URYU (1979), although it should be noted that one of the relevant effects (divergence of the Lagrangian-mean flow induced by wave transience) was pointed out by MclNTYRE (1973). As is well known, there exists an indirect mean meridional circulation in the troposphere, and this is interpreted as a result of heat transport by cyclone waves. However, this circulation does not show the trajectories of air particles. Figure 10 shows the Lagrangian-mean meridional motion induced by a growing baroclinic wave, which can be regarded as an idealized model of a cyclone. The calculation is done for Eady's model. At first sight, it is quite different from the usual Eulerian-mean picture with an indirect cell in mid-latitudes (cf. RIEHL and FULTZ, 1957; MATSUWO et al., 1977). Air parcels converge toward mid-latitudes almost horizontally, with slow upward motion near the southern wall and downward motion near the northern wall. These vertical motions are thermally direct, showing the process of release of available potential energy. Figure 10 agrees qualitatively well with KIDA'S (1977) numerical experiment as far as the behavior of tropospheric particles is concerned. However, we note that his result was obtained in a statistically

Vol. 118, 1980)

r

~

Acceleration of Mean Zonal Flows by Planetary Waves ,--,9

~

~

4-

~

4"-

689

'-I

I mlsec I cmlser

r

~

7

L

--~

~

,,

-~

4

S

4---

#---

4-

-J

N VL ,Wl

Figure l0 Lagrangian-mean motion in the meridional plane associated with a growing Eady wave. Arrows are drawn by (VL, WL x 500). Parameter values are as follows. Disturbance amplitude measured by maximum meridional disturbance velocity v" = 11 m/sec, growth rate = 0.7/day, wave length (= 27r/k) = 5000 km, width of the channel -- 5000 kin, height of the channel = 10 km, vertical shear of the basic zonal flow = 3 m/sec.km, N = 10-2/sec, f --- 10 -4 sec. Note that the Lagrangian-mean motion is convergent in spite of the Boussinesq assumption, because of disturbance growth (cf. ANDREWSand MCINTYRE,1978b).

steady state, while Fig. 10 is obtained for a growing wave. The reason for the similarity o f two results m a y be attributed to diffusive processes included in Kida's experiment. This point is discussed further in MCINTYRE (1979b). It is noted that the meridional m o t i o n seen in Fig. 10 is largely associated with a balance between the Coriolis force with a force p'(O~/~x) due to a systematic correlation between the disturbance pressure and the zonal gradient o f the meridional displacement of a material surface. A l t h o u g h a small departure flow f r o m such a balance can contribute to changing the Lagrangian-mean zonal flow, the direction o f the contributionfVL to the acceleration is opposite to that in the Eulerian-mean zonal flow, which is accelerated toward west (east) in the upper (lower) layer in the midlatitudinal region by the Coriolis force associated with the Eulerian indirect cell. This difference ( b e t w e e n f V andfVL) is due to the dominance of the Stokes drift U, in that region.

690

Michiya Uryu

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Finally, we note that the converging (or diverging) flow of air parcels is one of the most characteristic properties of the Lagrangian-mean motion induced by a growing wave (cf. MClNT~'RE, 1973; ANDREWS and MclNTYRE, 1978b; MClNTYRE, 1979b).

5. Conclusions In this article, we have mentioned various aspects of planetary-wave-induced mean motions including Eulerian- and Lagrangian-mean motions, which might be helpful towards understanding phenomena occurring in the middle atmosphere. First, we have shown that the acceleration of the mean zonal flow is a transmission process of force acting from the bottom (i.e., is equivalent to a mean stress), and confirmed such an intuitive discussion to be correct, at least in one particular case, by considering a vertically propagating wave packet. On the basis of the foregoing discussion on transient waves, the fact that the so-called C-D theorem concerns a final state in which no further change occurs has been illustrated. At the same time, by including the small damping due to Newtonian cooling and Rayleigh friction, we have illustrated in a compact form the fact that the acceleration of the mean zonal flow is caused by a forcing due to wave transience and one due to wave dissipation. Particularly, when the dissipation of the zonal mean flow itself can be ignored, the induced mean zonal momentum is equal to E/C plus the deposited part during the propagation through the wave dissipation (cf. GRIMSHAW, 1975). In Section 3, we have discussed a steady (Eulerian-mean) flow in the presence of a dissipating planetary wave. For the case where the Newtonian cooling rate and the basic westerly wind are both constant, it is shown that depending on whether or not the effect of density stratification dominates the damping effect, the distribution of the induced easterly flow is quite different (cf. DUNKERTON,1979). When the wave amplitude increases upward in spite of dissipation, the induced easterly wind becomes large with increasing height, and hence the northern region becomes warmer (Fig. 3a,b), while when the amplitude decreases, the northern region becomes cooler (Fig. 4a,b). Thus, the distribution of the damping coefficient and the basic zonal wind, both of which determine the transmissivity of planetary waves, are very important factors for the purpose of discussing how planetary waves can contribute to the flow structure in a statistically steady state of the atmosphere. To be more convincing, we have shown the result (Fig. 6a,b) for the case where the Newtonian cooling rate and the basic westerly wind are both dependent on height (Fig. 5a,b) and the wave with longitudinal wave number 1 is assumed. According to this result, near z = 70 km, the induced easterly wind becomes 30 m/sec in the mid-latitudinal region and the temperature in the northern region increases about 7~ relative to that in the southern region (cf. MATSUNO, 1976). This suggests that the contribution of planetary waves to the structure in a statistically steady state of the upper atmosphere such as the higher temperature observed in the winter polar region (cfl HOLTON, 1975) may be large.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

691

Finally, we have briefly discussed the Lagrangian-mean motion induced by planetary waves. In case of a stationary conservative wave or a slowly varying wave packet, the Lagrangian-mean meridional circulation does not occur, to within certain approximations. Especially, this result for a stationary wave is part of which is involved in the C-D theorem from a Lagrangian-mean dynamical viewpoint (cf. ANDREWS and Mr 1978b). As to the Lagrangian-mean zonal flow, it has been shown that UL has a jet-like structure partly because of the Stokes drift and partly because of the Eulerian-mean zonal flow. We have also shown the Lagrangian-mean meridional circulation induced by stationary, dissipating waves under the assumption that the Newtonian cooling rate and the basic westerly wind are constant. If the wave amplitude decreases upward because of the dominance of damping effect, the Lagrangian-mean meridional circulation is associated with upward motion to the north and downward motion to the south as well as the Eulerian-mean one (Fig. 8a,b). If the wave amplitude increases because of the dominant effect of density stratification, the Lagrangian-mean meridional circulation is associated with upward motion to the south and downward motion to the north, and is opposite to the Eulerian-mean one (Fig. 7a,b). In addition, from the result by URYU and TAKAHASn~(1979), we have noted that the Lagrangianmean meridionaI circulation changes remarkably, depending on the speed of the basic westerly wind: particularly, it is split into 3 cells in the meridional direction when the speed of the basic zonal wind exceeds a certain value. When the Newtonian cooling rate and the basic westerly wind are both dependent on height, the Lagrangian-mean meridional circulation induced by the wave with longitudinal wave number 1 is split into two parts in the vertical (Fig. 9a). The lower circulation is associated with upward (downward) motion to the south (north) and opposite to the Eulerian-mean one. However, the upper circulation is opposite to the lower one, and can be regarded as a result that the central circulation of the 3-cell structure spreads over the channel (URYU and TAKAHASm, 1979). In the case of a growing baroclinic wave, the Lagrangian-mean motion shows convergent flow toward the mid-latitude, with slow upward motion near the southern wall and downward motion near the northern wall (URYU, 1979). These vertical motions are thermally direct. This Lagrangian-mean motion is quite different from the Eulerian-mean picture such as the so-called 3-cell circulation in the troposphere. Further, the convergence of air parcels is one of the most interesting features of the Lagrangian-mean motion induced by a growing wave (cf. ANDREWS and MCINTYRE, 1978b).

Acknowledgements The author wishes to express his hearty thanks to Dr. M. E. Mclntyre, University of Cambridge, for his critical reading of the manuscript and for many valuable comments and suggestions. The author is deeply indebted to Prof. T. Matsuno, who always helpfully criticizes the author's work.

692

Michiya Uryu

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Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

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MCINTYRE, M. E. (1973), Mean motions and impulse of a guided internal gravity wave packet, J. Fluid Mech. 60, 801-811. MCINTvRE, M. E. (1979a), Paper in this issue. MClNTVRE, M. E. (1979b), Towards a Lagrangian-mean description of stratospheric circulations and chemical transports, Phil. Trans. Roy. Soc. London, A (middle atmosphere issue) (to appear). NAKAMURA,K. (1979), A generalization of 'Eliassen-Palm' relation, J. Meteor. Soc. Japan 56, 215-226. RIEHL, H. and FULTZ,D. (1957), Jet stream and long waves in a steady rotating-dishpan experiment: structure of the circulation, Quart. J. Roy. Meteor. Soc. 83, 215-231. URYU, M. (1973), On the transport of energy and momentum in stationary waves in a rotating stratified fluid, J. Meteor. Soc. Japan 51, 86-92. URYU, M. (1974a), Induction and transmission of mean zonal flow by quasi-geostrophic disturbances, J. Meteor. Soc. Japan 52, 341-364. URYIJ, M. (1974b), Mean zonal flows induced by a vertically propagating Rossby wave packet, J. Meteor. Soc. Japan 52, 5481-490. URvu, M. (1979), Lagrangian mean motion induced by a growing baroclinic wave, J. Meteor. Soc. Japan 56, 1-20. URYO, M. and TAKAHASHI,M. (1979), The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves: parts L 11, J. Meteor. Soc. Japan (to be submitted). (Received 15th June 1979)