AERO NOMICA ACTA

Texte intégral

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I N S T I T U T D ' A E R O N O M I E S P A T I A L E D E B E L G I O U E

3 • A v e n u e C i r c u l a i r e B • 1 1 8 0 B R U X E L L E S

A E R O N O M I C A A C T A

A - N° 1 9 9 - 1 9 7 9

C o m p a r i s o n s b e t w e e n v a r i o u s s e m i - e m p i r i c a l t h e r m o s p h e r i c m o d e l s o f t h e t e r r e s t r i a l a t m o s p h e r e

by

F BARLIER, C. BERGER, J . L . F A U N , G- K O C K A R T S a n d G. T H U I L L I E R

B E L G I S C H I N S T I T U U T V O O R R U I M T E - A E R O N O M I E 3 - Ringlaan

B - 1180 B R U S S E L

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FOREWORD

The paper "Comparisons between various semi-empirical thermo spheric models of the terrestrial atmosphere" will be published in Journal of Atmospheric and Terrestrial Physics, 1979.

A V A N T - P R O P O S

L'article "Comparisons between various semi-empirical thermo- spheric models of the terrestrial atmosphere" sera publié dans Journal of Atmospheric and Terrestrial Physics, 41_, 1979.

VOORWOORD

De tekst "Comparisons between various semi-empirical thermo- spheric models of the terrestrial atmosphere" zal in het tijdschrift Journal of Atmospheric and Terrestrial Physics, 41, 1979, verschijnen.

VORWORT

Die Arbeit "Comparisons between various semi-empirical thermospheric models of the terrestrial atmosphere" wird in Journal of Atmospheric and Terrestrial Physics, 41, 1979 herausgegeben werden.

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C O M P A R I S O N S BETWEEN V A R I O U S S E M I - E M P I R I C A L T H E R M O S P H E R I C

MODELS OF T H E T E R R E S T R I A L A T M O S P H E R E

by

F. B A R L I E R ^1\ C. B E R G E R ^1\ J.L. F A L I N ^ \ G. K O C K A R T S ^2 ), and

G. T H U I L L I E R ^3 )

(1) Centre d'Etudes et de Recherches Géodynamiqués et Astronomiques 8 Boulevard Emile-Zola

F - 06130 G R A S S E , France.

(2) Institut d'Aéronomie Spatiale de Belgique 3 Avenue Circulaire

B - 1180 B R U X E L L E S , Belgique.

(3) Service d'Aéronomie du C N R S Boîte Postale n° 3

F - 91370 V E R R I E R E S - L E - B U I S S Ö N , France.

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Abstract

The availability of various global thermospheric models allows intercomparisons to be made for identical geophysical conditions. Solar activity effect, geomagnetic effect, diurnal variation, annual variation and latitudinal-seasonal dependence are analyzed in four semi-empirical models, viz. D T M , M S I S , E S R O 4 and J77. Emphasis is given to the discrepancies between the models, and some direct comparisons are made with satellite d r a g data and micro-accelerometer results. None of the semi-empirical models can represent correctly alj geophysical aspects of the terrestrial thermosphère.

Résumé

L'existence de différents modèles thermosphériques globaux permet d'effectuer des comparaisons pour des conditions g é o p h y s i q u e s identiques. L'effet de l'activité solaire, l'effet géomagnétique, la v a r i a - tion diurne, la variation annuelle et la dépendance saisonnière avec la latitude sont analysés dans quatre modèles semi-empiriques, à savoir D T M , M S I S , E S R O 4 et J77. Les différences entre les modèles sont mises en évidence et des comparaisons directes sont effectuées avec des données de freinage ainsi que des données de micro-accéléromètre.

A u c u n des modèles semi-empiriques est susceptible de représenter correctement tousles aspects géophysiques de la thermosphère terrestre.

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Samenvatting

Het bestaan van verschillende wereldomvattende thermo- sferische modellen maakt vergelijkende studies mogefijk voor identieke geofysische toestanden. Zonnewerkingseffect, geomagnetische be- ïnvloeding, dagelijkse en jaarlijkse schommelingen evenals afhankelijk- heid van jaargetijden en breedteligging worden onderzocht in vier semi-empirische modellen, nl. DTM, MSIS, ESRO 4 en J77. Er wordt nadrukkelijk gewezen op de tegenstrijdigheden bij deze modellen en enkele rechtstreekse vergelijkingen worden gemaakt met gegevens over satellietenwijziging en resultaten van micro-acceleratorënmetingen. Geen enkel van de semi-empirische modellen kan aj de geofysische aspecten van de aardse atmosfeer juist weergeven.

Zusammenfassung

Die Verfügbarkeit verschiedenen kugeligen thermosphärischen Modellen gestattet Vergleichung f ü r gleichbeteutenden geophysikalischen Zustände. Sonnenaktivitätseffekt, geomagnetisches Effekt, tägliche Variation, järhrliche Variation und Breite-Jahreszeitvariationen werden in vier halbempirischen Modellen, d . h . DTM, MSIS, ESRO 4 und J77, analysiert. Die Unterschieden zwischen den Modellen werden klargestellt und Vergleichungen mit Satellitenabbremsungsdaten und Mikrobe- schleunigungsmesser Ergebnissen werden vorgestellt. Keines Model kann alle geophysikalische Effekten in der erdischen Thermosphäre genau vorstellen.

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1. I N T R O D U C T I O N

T h e availability of large data b a s e s r e s u l t i n g from _in__sjtu measurements of v a r i o u s t h e r m o s p h e r i c parameters h a s led to the development of a new generation of three-dimensional models of the terrestrial u p p e r atmosphere ( H e d i n _e_t__aj. 1977a, 1977b; v o n Z a h n

1977.; Jacchia, 1977). In o r d e r to c o n s t r u c t a n y model, it is n e c e s s a r y to determine the t h e r m o p a u s e temperature which is u s u a l l y i n f e r r e d from composition or total d e n s i t y measurements. H o w e v e r , optical measurements of the width of 630 nm line of atomic o x y g e n p r o v i d e a u n i q u e o p p o r t u n i t y to c o n s t r u c t a global temperature model ( T h u i l l i e r _et__aj. 1977a) i n d e p e n d e n t l y of a n y a s s u m p t i o n related to the d i s t r i b u t i o n of atmospheric c o n s t i t u e n t s . T h i s model has recently been combined with satellite d r a g data to c o n s t r u c t a new three-dimensional t h e r m o s p h e r i c model ( B a r l i e r et__aj. 1978b) which we shall r e p r e s e n t b y the a c r o n y m D T M ( D r a g - T e m p e r a t u r e - M o d e l ) . T h e p u r p o s e of the p r e s e n t paper is to compare D T M with o t h e r recent t h e r m o s p h e r i c models.

A f t e r a brief s u m m a r y of the basic p r i n c i p l e s i n v o l v e d in the c o n s t r u c t i o n of D T M , the known g e o p h y s i c a l v a r i a t i o n s of the u p p e r atmosphere are compared in the p r e s e n t l y available models. A l t h o u g h general agreement is u s u a l l y obtained between the v a r i o u s models, specific d i s c r e p a n c i e s still w a r r a n t f u r t h e r i n v e s t i g a t i o n s .

2. T H E D R A G - T E M P E R A T U R E - M O D E L ( D T M )

S i n c e satellite d r a g data lead to total d e n s i t y in the v i c i n i t y of the p e r i g e e , some a s s u m p t i o n s must be i n t r o d u c e d to obtain c o n c e n - trations for each atmospheric constituent. T h e c o n s t r u c t i o n of D T M is b a s e d on the fact that molecular n i t r o g e n , atomic o x y g e n a n d helium are

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successively the major atmospheric constituents above 120 km as a consequence of diffusion separation in the earth's gravitational field.

With a mathematical formalism similar to the approach introduced for the first time by Hedin _e_t__aj. (1974) in thermospheric modeling, Barlier et al_(1978b) used an iterative procedure to represent the three major constituents N^, O and He in terms of spherical harmonics at 120 km altitude. Using the thermopause temperature model of Thuillier _et__aj.

(1977a) and an analytical temperature profile (Walker, 1965) it is then possible to compute concentrations for the major atmospheric constit- uents at a given altitude as a function of local solar time, latitude, day number in the year, solar decimetric flux and geomagnetic index K . The detailed formalism as well as a computer program are given by Barlier _e_t__aj. (1978b) who discussed also several geophysical features of DTM.

Although the distribution of molecular oxygen can be deduced from DTM, it is not given in terms of spherical harmonics since, above 120 km, C>2 is never a major constituent which could account for more than 50% of the total density. DTM gives an O

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distribution in diffusive equilibrium with a constant lower boundary value at 120 km. A similar remark applies to argon. Atomic hydrogen becomes a major constituent above 1000 km for low solar activity (Kockarts and Nicolet, 1963).

There are unfortunately not enough satellite drag data in this height region to allow the construction of a reliable model for H over a wide range of geophysical conditions. In consequence, our comparisons with other models will be restricted to temperature, total density, and the concentrations of O and He.

As an example, Fig. 1 shows a comparison between totaJ densities p

D T M

/ computed with DTM, and observed densities

Q B S

deduced from drag data from Cosmos Rocket 1965-11D. The latitude and altitude of satellite perigee indicate to which location in the atmosphere correspond p

n x M

and

PO R C -

Solar activity and geomagnetic activity

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rT 1 ? U "

5 io a 8

o f 4

1 310

^ 290 Q ID

270 250

a 6

* 3

1 1 1 1 1 C O S M O S R O C K E T

1 9 6 5 - 11 D

i r

+ 1 H 1 h

H H

-L

H h

H 1 1 1 1 1 1 h

H H

H h

1 h

H h 12 0D 10 " U

8 6 A

• 6 0

• 30* >

0 ' -30' g - 6 t f m

250 200 150 100

A M I 3 A S 0 . N D 3 F M

1968 1969

F i g . 1 . - C o m p a r i s o n o f t o t a l d e n s i t i e s p ^ g ^ d e d u c e d f r o m d r a g d a t a o f Cosmos R o c k e t 1965-11D a n d model d e n s i t i e s p ^ - p ^ . L a t i t u d e a n d a l t i t u d e of s a t e l l i t e p e r i g e e a r e g i v e n f r o m A p r i l 1968 t h r o u g h M a r c h

- 2 2

1969. D a i l y s o l a r d e c i m e t r i c f l u x F in 10 W

- 2 - 1

m Hz a n d g e o m a g n t i c i n d e x K .

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l e v e l s a r e c h a r a c t e r i z e d r e s p e c t i v e l y b y t h e d a i l y s o l a r d e c i m e t r i c f l u x

- 2 2 - 2 - 1

F ( i n 10 W m Hz ) a n d t h e K ^ i n d e x f o r t h e c o r r e s p o n d i n g p e r i o d I t a p p e a r s t h a t a r e a s o n a b l e a g r e e m e n t is r e a c h e d b e t w e e n t h e D T M a n d t h e o b s e r v e d d e n s i t i e s , a l t h o u g h t h e l a t t e r r e p r e s e n t o n l y a small f r a c t i o n of t h e 3 6 , 0 0 0 t o t a l d e n s i t i e s e f f e c t i v e l y u s e d f o r c o n s t r u c t i n g D T M . Not all t h e v a l u e s p Q g g s h o w n on F i g . 1 h a v e been u s e d i n D T M , s i n c e t h e p e r i g e e a l t i t u d e o f Cosmos R o c k e t 1965-11D is i n a h e i g h t r a n g e w h e r e atomic o x y g e n p r o g r e s s i v e l y becomes m o r e i m p o r t a n t t h a n m o l e c u l a r n i t r o g e n . O b s e r v e d d e n s i t i e s e f f e c t i v e l y u s e d f o r c o n s t r u c t i n g D T M w e r e s e l e c t e d i n s u c h a w a y t h a t atomic o x y g e n r e p r e s e n t s 70% of t h e t o t a l d e n s i t y , o r t h a t m o l e c u l a r n i t r o g e n leads t o 50% of t h e t o t a l d e n s i t y ( B a r l i e r _et_aj. 1 9 7 8 b ) . T h e r e f o r e , t h e a g r e e m e n t b e t w e e n q bc

a n d d j i v i o n F i g . 1 is n o t o n l y an aJ^ o s t e r i o r j c h e c k o f a n u m e r i c a l f i t t i n g p r o c e d u r e , b u t i t also r e f l e c t s t h e d e g r e e of c a p a b i l i t y t o r e p r o d u c e o b s e r v e d t o t a l d e n s i t i e s . O t h e r c o m p a r i s o n s w i t h d r a g d a t a w i l l be made in s e c t i o n 4 .

3. C O M P A R I S O N W I T H O T H E R MODELS

D T M w i l l e s s e n t i a l l y be c o m p a r e d w i t h t h r e e o t h e r s e m i - e m p i r i c a l m o d e l s , v i z . M S I S , ESRO 4 a n d J 7 7 . T h e m a s s - s p e c t r o m e t e r - i n c o h e r e n t - s c a t t e r model MSIS ( H e d i n _et_aj. 1977a; 1 9 7 7 b ) is c o n s t r u c t e d w i t h d a t a g a t h e r e d f r o m 1966 t o 1976 w h e n t h e mean

— - 2 2 - 2 - 1

s o l a r d e c i m e t r i c f l u x F v a r i e d b e t w e e n 70 x 10 W m Hz a n d 180 x 1 0 "2 2 W m~2 H z "1. T h e ESRO 4 model ( v o n Z a h n _et__a_l. 1977) is b a s e d on mass s p e c t r o m e t e r d a t a o b t a i n e d b e t w e e n D e c e m b e r 1972 a n d

- 2 2 A p r i l 1974 w h e n t h e mean s o l a r d e c i m e t r i c f l u x was b e t w e e n 65 x 10 W m "2 H z "1 a n d 145 x 1 0 ~2 2 W m "2 H z1. T h e J77 model ( J a c c h i a , 1977) is c o n s t r u c t e d w i t h s a t e l l i t e d r a g d a t a e x t e n d i n g f r o m 1958 t o 1975;

h e n c e t h i s m o d e l , as well as D T M ( B a r l i e r _e_t__aj. 1978b) c o v e r s a l m o s t t w o s o l a r c y c l e s . I t s h o u l d be n o t e d , h o w e v e r , t h a t t h e t e m p e r a t u r e model ( T h u i l l i e r e t a l . 1977a) u s e d i n D T M is b a s e d o n d a t a o b t a i n e d

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o n l y b e t w e e n 8 J u n e 1969 a n d 16 A u g u s t 1 9 7 0 . D u r i n g t h i s p e r i o d t h e

- - 2 2

d a i l y solar d e c i m e t r i c f l u x F v a r i e d b e t w e e n 103 a n d 239 x 10

- 2 - 1 — - 2 2

W m Hz a n d t h e mean s o l a r f l u x F r a n g e d f r o m 136 t o 170 x 10 <

- 2 - 1

W m Hz In t h e f o l l o w i n g c o m p a r i s o n s w e . r e f e r e s s e n t i a l l y t o t w o

— - 2 2 - 2 - 1

solar a c t i v i t y l e v e l s , v i z . F = 150 x 10 W m Hz ( h i g h solar-

- 2 2 - 2 - 1

a c t i v i t y ) and F = 92 x 10 W m Hz ( l o w s o l a r a c t i v i t y f o r ESRO 4) p e r i o d ) .

A l t h o u g h t h e models d i s c u s s e d i n t h e p r e s e n t p a p e r a r e c o n s t r u c t e d u s i n g d i f f e r e n t d a t a c o v e r i n g d i f f e r e n t t i m e p e r i o d s and g e o g r a p h i c a r e a s , c o m p a r i s o n s h a v e t o be made u n d e r i d e n t i c a l c o n d i - t i o n s . T h e ESRO 4 model w i l l , t h e r e f o r e , sometimes be u s e d f o r g e o - p h y s i c a l c o n d i t i o n s w h i c h h a v e almost n e v e r been e n c o u n t e r e d b y t h et s a t e l l i t e ESRO 4 , 1972-92A. S i m i l a r s i t u a t i o n s can also o c c u r f o r t h e o t h e r m o d e l s .

3 •1 •_ .Solar. _ac_tiv ity_ _e_f f ect

I n all s e m i - e m p i r i c a l m o d e l s , s o l a r a c t i v i t y is t a k e n i n t o a c c o u n t b y r e l a t i o n s i n v o l v i n g t h e d a i l y 1 0 . 7 cm f l u x F a n d some mean v a l u e F c o m p u t e d o v e r s e v e r a l s o l a r r o t a t i o n s . T h e s o l a r a c t i v i t y e f f e c t / can t h e r e f o r e , be i n v e s t i g a t e d b y c o m p u t i n g d a i l y a v e r a g e d q u a n t i t i e s as a f u n c t i o n o f t h e mean s o l a r d e c i m e t r i c f l u x . F i g . 2 shows d a i l y a v e r a g e d t h e r m o p a u s e t e m p e r a t u r e , t o t a l d e n s i t y and p a r t i a l c o n c e n t r a - ' t i o n s c o m p u t e d on 21 S e p t e m b e r a t t h e g e o g r a p h i c e q u a t o r f o r an a l t i t u d e of 400 km. D a i l y a v e r a g e d q u a n t i t i e s h a v e been o b t a i n e d b y a s s u m i n g t h e d a i l y 10.7 cm f l u x equal t o t h e mean s o l a r d e c i m e t r i c f l u x , a n d b y a d o p t i n g c o n s t a n t g e o m a g n e t i c i n d i c e s K ^ = 2 o r A ^ = 7.

As a g e n e r a l r u l e , t h e b e s t a g r e e m e n t b e t w e e n t h e models is o b t a i n e d f o r mean solar d e c i m e t r i c f l u x e s r a n g i n g f r o m a p p r o x i m a t e l y 100 x 1 0 ~2 2 W m~2 H z "1 t o 150 x 1 0 ~2 2 W m "2 H z "1. T h e l a r g e s t d i s c r e p - ancies o c c u r f o r v e r y low a n d v e r y h i g h f l u x e s as a p r o b a b l e c o n s -

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F i g . 2 . - D a i l y a v e r a g e d t h e r m o p a u s e t e m p e r a t u r e , totall d e n s i t y a n d partial c o n c e n t r a t i o n s at t h e e q u a t o r a s a f u n c t i o n of mean s o l a r d e c i m e t r i c f l u x . C o m p a r i s o n at 400 km between D T M , J 7 7 , M S I S a n d E S R 0 4 o n 21 S e p t e m b e r f o r K = 2 o r A = 7.

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equence of the smaller amount of data available for extreme geophysical conditions. One should, therefore, realize that temperature differences of the order of 100 K and total density ratios of almost a factor of two can be obtained with the various models under extreme conditions.

These differences are also reflected in the partial concentrations. At 400 km the largest differences are seen for Ng which is a minor constit- uent at this altitude. It is evident, however, from Fig. 2 that J77, M S I S , E S R O 4 a n d D T M roughly show a similar solar activity dependence with some noticeable differences depending on the solar activity level.

Perfect agreement between a model and a specific experimental result should not be used at the present time as proof of the complete validity of the model for all geophysical conditions. For instance E S R O 4 model is constructed with data corresponding to rather low solar activ- ity (average F = 92 x 10~2 2 W m~2 H z "1) and extrapolation to high F values should be made with caution.

3.2. Geomagnetic .effect

In all the models, variations associated with geomagnetic activity are expressed in terms of planetary K or A indices. S u c h

r H

indices are used in the spherical harmonic expansions for temperature and partial concentrations in D T M , M S I S and E S R O 4. The situation is slightly different in J77 where the geomagnetic effect is represented by three terms. According to Jacchia _e_t__aj. (1977) the local increase in the thermopause temperature is a function of magnetic latitude and is accom- panied by a variation in the height of the homopause. The geomagnetic perturbation propagates from high to low latitudes and causes an increase in the total density in the equatorial regions a few hours later.

The introduction of magnetic latitude is responsible of a longitudinal effect as shown in Fig. 3 where the temperature increase for Kp = 6 is represented in a geographic coordinate system. Computations are made for a centered-dipole geomagnetic^ field. Since spherical harmonic models

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Geomagnetic effect Kp • 6 N

y^xx^/^/^-J-'——r~

1 [ 270* tcenTer»3 or _

r-yVVi JL1 )

— f—en—-A—^ / /

S

Temperature increase ( K )

Fig. 3 . - Global distribution of the temperature increase ( K ) for Kp = 6 in a geographic coordinate system for J77 model.

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assume an equivalence between geographic longitude and local solar time, it is necessary to specify, in J77, the geographic longitude when comparisons are made with the other models.

Fig. 4 compares the geomagnetic effect in the various models, for equinox conditions (21 September) at 400 km altitude as a function of geographic latitude. The results presented in Fig. 4 are obtained in the following way : each quantity has been daily averaged at 400 km for K = 0 (A = 0) and for K = 5 (A = 4 8 ) , then ratios

p P P P

"disturbed"/"quiet" are computed for concentrations and total density whereas diurnally averaged temperature differences are plotted as a function of geographic latitude. All quantities are computed for F = F =

n n _ fp m i

150 x 10 W m Hz and J77 model is used with a geographic lon- gitude of zero degree.

All the models are characterized by similar trends although noticeable differences in amplitude are observed. Temperature and molecular nitrogen concentrations systematically increase towards polar regions whereas helium decreases in the polar regions for an increase of geomagnetic activity. The decrease of atomic oxygen at the poles is less pronounced at 400 km and this constituent starts moreover to increase towards the poles at higher altitudes. Such features are consistent with a theoretical analysis of magnetic storms (Mayr and Volland, 1973). The small latitudinal variation of the total density p at 400 km, with its weak minima around + 45°, results from the combined effect of O and He variations. Since there is no variation of the N^ homopause with geo- magnetic a c t i v i t y , the small equatorial maximum of Ng in J77 is a con- sequence of the "equatorial wave" (Jacchia _e_t _aj., 1977) which affects

y — — — • all atmospheric constituents by the same amount.

Since the thermospheric energy input responsible for the geomagnetic effect is linked to the auroral oval in such a way that contractions and expansions of the oval lead to variations in the geo-

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F i g . 4 . - Geomagnetic effect for A Kp = 5 ( A Ap = 48) on t e m p e r a t u r e , partial c o n c e n t r a t i o n s ( N2, O, He) and total d e n s i t y p at 400 km on 21 September f o r

— - 2 2 - 2

solar decimetric f l u x e s F = F = 150 x 10 W m H z "1. For J77 longitude is 0°.

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graphical extent of the heating zone ( B a n k s , 1977), it is clear that c h a n g e s in chemical composition s h o u l d d e p e n d not only on g e o g r a p h i c latitude, but also on longitude and local solar time. Realistic compa- r i s o n s are, therefore, difficult in the polar r e g i o n s since t h e y d e p e n d v e r y much on the time a n d g e o g r a p h i c d i s t r i b u t i o n s of the data u s e d in the v a r i o u s models. A s a c o n s e q u e n c e , it is not s u r p r i s i n g that the largest d i s c r e p a n c i e s between the models o c c u r near the poles.

3.3. _Dmrna[_variatjon

When a semi-empirical model is c o n s t r u c t e d with c o n s t a n t values at the lower b o u n d a r y above which d i f f u s i v e equilibrium is a s s u m e d , partial concentrations and total d e n s i t y are in p h a s e with temperature at altitudes above the i s o p y c n i c level, v i z . above a p p r o x - imately 150 km for a lower b o u n d a r y a r o u n d 120 km. For v a r i o u s r e a s o n s , t h i s situation does not o c c u r for a n y of the models u n d e r d i s c u s s i o n . T h e J77 model s t a r t s at 90 km with c o n s t a n t b o u n d a r y v a l u e s , but it allows empirical c o r r e c t i o n s between 90 km and 120 km to simulate d e p a r t u r e s from d i f f u s i v e equilibrium. A t 120 km the s p h e r i c a l harmonic models D T M a n d E S R O 4 adopt variable c o n c e n t r a t i o n s r e s u l t i n g from a spherical harmonic a n a l y s i s performed on data obtained at h i g h e r altitude. In M S I S , c o n c e n t r a t i o n s at 120 km are also v a r i a b l e , but the s h a p e parameter of the vertical temperature profile is g i v e n in terms of spherical harmonics. F u r t h e r m o r e the magnetic term a n d the d i u r n a l terms for O , He and A r are multiplied b y an empirical f u n c t i o n which is indended to r e p r e s e n t h i g h magnetic activities a n d d e p a r t u r e s from d i f f u s i v e equilibrium ( H e d i n _e_t__aj. 1977b). For these r e a s o n s , all models lead, at h i g h altitude, to d i u r n a l maxima o c c u r i n g at d i f f e r e n t times for the different species.

Fig. 5 s h o w s d i u r n a l v a r i a t i o n s at the equator on 21 September for low ( F = F = 92 x 1 0 *2 2 W m "2 H z "1) and h i g h ( F = F = 150 x 1 0 ~2 2 W m~2 H z "1) solar activity at 400 km altitude. It can be

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LOCAL T I M E ( h )

. 5 . - Diurnal variation of N^, O , He and total d e n s i t y at the equator on 21 September. Altitude = 400 km.

_ _p2 - 2 T w o solar activity levels F = F = 92 x 10 W m

H z "1 and F = F = 150 x 1 0- 2 2 W m "2 H z "1. Geo- magnetic index K = 2 or A = 7. For J77

longitude is 0°. P P

15

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seen t h a t t h e h e l i u m maximum o c c u r s a l w a y s i n t h e m o r n i n g , f o l l o w e d in sequence b y t h e atomic o x y g e n a n d t h e m o l e c u l a r n i t r o g e n maxima.

T o t a l d e n s i t y p peaks a r o u n d 15h local s o l a r t i m e . U s i n g a l i n e a r t h e o r y , M a y r a n d H a r r i s (1977) e x p l a i n e d t h e s e f e a t u r e s i n t e r m s o f t h e r m a l e x p a n s i o n and w i n d - i n d u c e d d i f f u s i o n . A l t h o u g h t h e phases g i v e n b y t h e models a g r e e r o u g h l y w i t h t h e o r y a b o v e 200 km, l a r g e r d i s c r e p a n c i e s o c c u r below t h a t h e i g h t w h e r e u n f o r t u n a t e l y f a r f e w e r e x p e r i m e n t a l d a t a a r e a v a i l a b l e . T h e s i t u a t i o n is e v e n w o r s e w i t h r e g a r d t o t h e a m p l i t u d e o f t h e d i u r n a l v a r i a t i o n . For i n s t a n c e , ESRO 4 s h o w s a s e c o n d a r y maximum in atomic o x y g e n a n d t o t a l d e n s i t y , w h e r e a s a v e r y small d i u r n a l v a r i a t i o n of He is seen in J77.

A n i n t e r e s t i n g c o m p a r i s o n can be made f o r atomic o x y g e n s i n c e t h i s c o n s i t u t u e n t can be d e d u c e d f r o m d a t a o b t a i n e d at t h e F r e n c h i n c o h e r e n t s c a t t e r f a c i l i t y at S a i n t - S a n t i n ( 4 4 . 6 ° N ) . A l t h o u g h t h e i n c o h e r e n t s c a t t e r t e c h n i q u e y i e l d s m e a s u r e m e n t s o f t h e e l e c t r o n d e n s i t y a n d of t h e e l e c t r o n and ion t e m p e r a t u r e s at a g i v e n a l t i t u d e a n d a t a g i v e n t i m e , B a u e r _et__aj. ( 1 9 7 0 ) h a v e s h o w n t h a t t h e n e u t r a l atomic o x y g e n c o n c e n t r a t i o n a n d t h e n e u t r a l t h e r m o p a u s e t e m p e r a t u r e can be d e d u c e d f r o m t h e s e m e a s u r e m e n t s . T h e m e t h o d is based o n a b a l a n c e b e t w e e n t h e t h e r m a l loss f r o m e l e c t r o n s t o ions a n d t h e t h e r m a l loss f r o m ions t o n e u t r a l s at a l t i t u d e s r a n g i n g f r o m 220 t o 500 k m . A s i m u l t a n - eous d e t e r m i n a t i o n o f atomic o x y g e n a n d t h e n e u t r a l t e m p e r a t u r e is p o s s i b l e o n l y f o r d a y t i m e c o n d i t i o n s w h e n t h e e l e c t r o n a n d ion t e m p e r a - t u r e s a r e d i f f e r e n t . D u r i n g t h e n i g h t t h e i n c o h e r e n t s c a t t e r d a t a i n t h e

F r e g i o n lead o n l y t o t h e n e u t r a l t e m p e r a t u r e w h i c h is t h e n equal t o t h e ion a n d e l e c t r o n t e m p e r a t u r e s . T h e v a l i d i t y of s u c h an a p p r o a c h has been r e a n a l y z e d i n g r e a t d e t a i l b y A l c a y d e a n d B a u e r ( 1 9 7 7 ) . C o m p a r i s o n s w i t h v a r i o u s models f o r long t e r m v a r i a t i o n s o f atomic o x y g e n a n d of t h e r m o p a u s e t e m p e r a t u r e h a v e been made r e c e n t l y b y A l c a y d e e t a l . ( 1 9 7 8 ) . G e n e r a l l y good a g r e e m e n t has been f o u n d f o r t h e l o n g t e r m v a r i a t i o n s at 4 5 ° N . T h e i n c o h e r e n t s c a t t e r r e s u l t s w i l l n o t be d i s c u s s e d , t h e r e f o r e , in t h e f o l l o w i n g s e c t i o n s d e a l i n g w i t h l o n g t e r m

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variations. We refer the interested, reader to the work of Alcayde et a' 1978.

Up to now no systematic comparison of the diurnal variation of atomic o x y g e n deduced from incoherent scatter data and values

resulting from the presently discussed semi-empirical models is avail- able. F i g . 6 shows, therefore, the diurnal variation at 400 km for

— - 2 2

equinox and solstice conditions assuming F = F = 150 x 10 W

m"2 Hz"1 and K = 2 or A = 7. T h e semi-empirical models discussed in P P

the present paper are compared with the S a i n t - S a n t i n model deduced by Alcayde and Bauer (1977). T h e S a i n t - S a n t i n model presents the largest amplitude for -spring conditions. Furthermore, the afternoon decrease of atomic o x y g e n is always steeper in the incoherent scatter model.

E S R O 4 results are also shown on F i g . 6, although this model should probably not be applied for high mean solar decimetric f l u x e s . In E S R O 4, the secondary maximum present at the equator on 21 September (see F i g . 5) is insignificant at 45°N (see F i g . 6 ) . It is difficult to s a y , at present, wether such a feature is real or not. A similar remark is valid for the secondary maximum g i v e n by the Saint- Santin model on 21 December, since this model is based on data obtained d u r i n g daytime. All the nighttime values in the S a i n t - S a n t i n model actually result from extrapolations. Despite this fact it could be useful to introduce atomic o x y g e n incoherent scatter data in the semi- empirical thermospheric models.

From the comparisons made in this section, it appears that the diurnal variation is probably the less well represented phenomenon in all global thermospheric models. T h i s is not s u r p r i s i n g since, at a specific location, it is usually difficult with satellites to get a good data coverage in local time for a g i v e n set of geophysical parameters.

17

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0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 LOCAL SOLAR TIME (h)

. 6 . - Comparison of atomic o x y g e n incoherent scatter model above S a i n t - Santin ( A l c a y d é and B a u e r , 1977) with J77, M S I S and D T M for equinox and solstice conditions. Solar activity level F = F = 150 x 1 0 ~2 2 W m~2 H z "1. Geomagnetic index Kp = 2 or A p = 7- For J77 longitude is 2.22°E, i.e. longitude of S a i n t - S a n t i n .

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3 . 4 . Annual variation _ of__dL4CQ§'Jy_Y®r^9_e.cL. § § . .tejngeratu re and_ molecu)a r_ njtrogen_ concentration _at _+ _45° J_atitude

Another important variation in t h e u p p e r atmosphere is the annual variation related to changes in illumination according to the position of the e a r t h on its o r b i t around to s u n . We shall f i r s t examine the annual variations of t h e thermopause t e m p e r a t u r e and molecular nitrogen concentration since these two parameters are characterized by a similar behaviour in the course of a y e a r .

All the quantities shown in Figs. 7 and 8 are d i u r n a l l y

— - 2 2

averaged for two levels of solar a c t i v i t y ( F = F = 9 2 x 1 0 W m"2 H z "1 and F = F = 150 x 10"2 W m~2 H z "1) and f o r Kp = 2 or Ap = 7. For J77, the adopted longitude is 2 . 2 2 ° E . Constant solar decimetric f l u x and constant K or A indices never prevail f o r periods as long as P P a y e a r , but t h e hypothesis used in Figs. 7 and 8 eliminates short term variations which could mask t h e characteristics of the annual v a r i a t i o n . T h e overall v a r i a t i o n is dominated by an annual e f f e c t whereas t h e semi-annual effect appears to be small. Marked differences can be seen between the two hemispheres. In t h e n o r t h e r n hemisphere, the tempera- t u r e maximum occurs at t h e end of A p r i l ( e x c e p t f o r J 7 7 ) , whereas in the southern hemisphere the maximum occurs around summer solstice ( e x c e p t for ESRO 4 ) . As a general f e a t u r e the N2 and t e m p e r a t u r e variations are significantly d i f f e r e n t in both hemispheres f o r all models.

In the n o r t h e r n hemisphere the t e m p e r a t u r e and N^ decreases a r e slower a f t e r local spring maximum than a f t e r local summer in t h e southern hemisphere. F u r t h e r m o r e , the t e m p e r a t u r e d i f f e r e n c e between 45°N and 45°S is higher d u r i n g December solstice t h a n d u r i n g June Solstice, and the mean t e m p e r a t u r e around the solstices is higher in t h e southern hemisphere than in the n o r t h e r n hemisphere at these l a t i t u d e s . This fact leads to global p r e s s u r e maps capable of causing, in addition to the normal circulation (Johnson and Gottlieb, 1 9 7 0 ) , a wind compon- ent blowing from south to n o r t h . Such characteristics are related to n o r t h - s o u t h asymmetries discussed by B a r l i e r _e_t__aj. ( 1 9 7 4 ) .

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1000

J F M A M J J A S O N O

MONTH J F M A M J J A S O N D MONTH

Fig. 7.- Diurnally averaged thermopause temperature and moleculer nitrogen concentration at 400 km for + 45° latitude. Geomagnetic index

— - 2 2

K = 2 or A = 7 . Solar decimetric flux F = F = 92 x 10 W 9p .-I P

m Hz . Longitude 2.22°E for J77.

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ro

900

V - F = F = 1 5 0 \

Kp=2

Ap=7

_l I I I I I I I I I L.

J F M A M J j a s o n d M O N T H

F i g . 8 . - Same as F i g . 7, but F = F = 150 x l O " ^2 W m "2 H z "1

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T h e agreement between the v a r i o u s models seems to be better in the n o r t h e r n hemisphere and extrapolation of E S R O 4 to h i g h solar f l u x e s ( F i g . 8) does not appear to be valid.

3.5. A n n u a l variation _of_ _d_iu_r_n_a_l|y _ ay e r a cj ed__a_tom i c_ o_x_^gen_ conc_en_t_r_a_tion at _± .45° _l_a_titude

T h e anuual variation of atomic o x y g e n is shown in F i g . 9 at 400 km for both h e m i s p h e r e s and for two solar activity levels. In all the models the variation is dominated by a semi-annual effect c h a r a c t e r i z e d b y two s i g n i f i c a n t maxima a r o u n d the e q u i n o x e s . S u c h a b e h a v i o u r differs completely from what is seen for N? (see F i g s . 7 and 8) and for He (see F i g . 10). A t h i g h solar f l u x e s the minima a r o u n d J a n u a r y a n d J u l y are comparable in the n o r t h e r n hemisphere whereas in the s o u t h e r n hemisphere the J u l y minimum is deeper t h a n the summer minimum. In c o n s e q u e n c e , the v a r i a b i l i t y of atomic o x y g e n is greater in the s o u t h e r n hemisphere than in the n o r t h e r n hemisphere at 400 km altitude.

For low solar activity the difference between both h e m i s p h e r e s is not so evident a l t h o u g h there e x i s t s a similar t e n d e n c y . T h e minimum d u r i n g local winter solstice is always deeper than the minimum d u r i n g local summer solstice, c o n t r a r y to the situation for h i g h solar a c t i v i t y .

Since atomic o x y g e n is the major constituent at 400 km, the v a r i a t i o n s shown on Fig. 9 can be related to the classical result of the semi-annual variation of the total d e n s i t y ( C I R A , 1972) with an October maximum h i g h e r than the A p r i l v a l u e . From a recent a n a l y s i s of the orbit of Cosmos 462, 1971-106A, Walker (1978) c o n c l u d e s , h o w e v e r , that the A p r i l value near 200 km is h i g h e r than the October v a l u e . S u c h a feature a p p e a r s also in D T M for low solar activity. H o w e v e r , a more detailed a n a l y s i s s h o u l d be made since F i g . 9 indicates different b e h a v - iours for different latitudes and solar activity levels.

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Fig. 9.- Diurnally averaged atomic oxygen concentration at 400 km for + 45°

latitude. Geophysical conditions identical as in Figs. 7 and 8.

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Finally it should be noted t h a t comparisons of various models with atomic oxygen deduced from incoherent scatter data (Alcayde _e_t_ aj.

1978) show a reasonable agreement f o r the annual variation at 400 km.

It has been shown in Fig. 6 t h a t a similar conclusion cannot be made for the diurnal variation.

3.6. Annuaj_var|ation_ o_f_ d j u r n a j _ a v e r a g e d _ h_eNum_ con_centra_tjon_ at

± J . l a t i t u d e

The annual variation of helium is shown in Fig. 10 at 400 km for two solar a c t i v i t y levels. The annual variation of helium is in anti- phase with the annual variation of temperature and molecular nitroger (see Figs. 7 and 8 ) . If an imaginary hemispherical reversal is made m Fig. 10, the similarity between the He and Ng annual variations is v e r y clear. The phase difference of the o r d e r of six months probably results from large scale t r a n s p o r t associated with the helium w i n t e r bulge.

Furthermore, the helium behaviour is similar in both hemispheres. The semi-annual effect is small as f o r N.,. Finally the seasonal v a r i a b i l i t y is higher in the n o r t h e r n hemisphere.

3 . 7 . _L_a_titud|na[ and _seasona| _varjations_ of heUum

In o r d e r to analyze latitudinal and seasonal variations of helium, d i u r n a l l y averaged concentrations are computed at 1000 km f o r w i n t e r and summer solstices. The results obtained f o r various models are shown on Fig. 11, f o r two solar a c t i v i t y levels, as a f u n c t i o n of geographic latitude. The winter helium bulge is clearly present in all models although the w i n t e r to summer ratios v a r y g r e a t l y from one model to another, especially in the polar regions. A t a given pole the discrepancy between the models is larger d u r i n g local summer, i . e . when the helium concentration is small. D u r i n g local summer in the polar regions, models based on mass spectrometer data always give lower values than DTM, which is e n t i r e l y based on d r a g data. This fact

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MONTH MONTH

F i g . 1 0 . - D i u r n a l i y a v e r a g e d helium concentration at 400 km for Geophysical conditions identical as in F i g s . 7 and 8.

+ 45° latitude

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. 1 1 . - L a t i t u d i n a l v a r i a t i o n o f d i u r n a l l y a v e r a g e d h e l i u m c o n c e n t r a t i o n a t

— - 2 2 - 2

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2.0 T ECHO 2 1964 - 0 4 A

Mean ( a l t i t u d e 1150km

0 (& 8 6

2.0

1964 [ 1965 — : L J -

38586 38686 38786

LU O o o ?

CO CO a ?

- O V 3 - 2 fragment 1966-97D - Mean altitude 385km

38866

0 039672 2.0

1967 ! 1968

J L J — _ 39772 39872

T

39972 T

40052

LU Q O a 5

CD

a ?

1.5 -

Transtage 7 1965-108A Mean altitude 210 km

41042 41142 41342 41422

F i g .

41242 M.D. D.

1 2 . - Ratio PQ B S/ P Mo dE L f°r t h r e e s a t e l l i t e s a s a

f u n c t i o n of t h e m o d i f i e d J u l i a n d a y ( M . J . D . ) . Model d e n s i t i e s a r e c o m p u t e d r e s p e c t i v e l y w i t h D T M a n d M S I S .

27

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can be related to the difficulty of measuring low helium abundances by mass spectrometry ( T r i n k s _et_ aj. 1977). Furthermore, model comparisons in the polar regions are perhaps hot v e r y realistic since a large longitud- inal effect could have been omitted in all models. In any case, the large discrepancy between drag data and mass spectrometric data for v e r y low helium abundances remains an unsolved problem at the present time.

4. COMPARISON BETWEEN SPECIFIC DRAG DATA AND MODELS

Since the concentrations given by DTM are entirely based on drag data, it is interesting to make comparisons between total densities PO B e ; deduced from drag data, and total densities p m o d e l computed with the model. Fig. 12 shows such comparisons for three satellites. A general agreement can be seen although the ratio PADc/Pi/mnci c a n b e sometimes greater than two, as in 1968 for OV3-2

O B S M O D E L fragment 1966-97D.

In the same Figure we have also plotted the total densities obtained from MSIS, i . e . a model which is not based on satellite drag data. For OV3-2 fragment and Transtage 7 it should be noted that both models follow almost exactly the same t r e n d . The perigees of these two satellites are in a height range where N2 and O are major atmospheric constituents. The situation slightly changes for ECHO 2 1964-04A which has its perigee around 1150 km where helium is an important atmo- spheric component. It appears in Fig. 12 t h a t , in July 1964 and in January 1965, model densities obtained with MSIS are systematically lower than values deduced from DTM. This effect is clearly seen in F i g . 13 w h i c h s h o w s t h e r a t i o P0 B S/ PM 0D E L F R O M 2 8 J U N E 1 9 6 4 U N T I"

15 January 1965. The results obtained with J77 are also given in this Figure. On 22 July 1964 the perigee of ECHO 2 was in the northern hemisphere at 75° latitude. On 26 December 1964 the perigee of ECHO 2 was in the southern hemisphere at - 75° latitude. On both days the

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T—i i i | 1 — i — r — r E C H O 2 1 9 6 4 - A A H

UJ o o

I/)

o CD

3uly22 e vp =75

December 26

o

DTM 177 MSIS

J I L L i

I l I

1964 .

1'

38575 38675 38775

M. 3. D.

F i g . 13.- Ratio p 4> M OD E L f°r E C H ° 2 3 5 3 °f the modified Julian day ( M . J . D . ) . Model densities

are computed respectively with DTM, MSIS and J77.

Perigee latitude is indicated for 22 J u l y 1964 and 26 December 1964.

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I 1.25

^ I . O O G 0.75 = k

<

u

0.50

360 Ui o

Ü 180 o z

O

-i—i—r 1—n—T 1—I—i—I—I—r~r y

X _ X

• « X

• X

• X

> * • X

• » X

. »

X — _ X

Mean latitude (°) -6.4 -28.1 Mean local time (h) 19.1 22.9 Mean altitude(km) 325

YEAR 1976

F i g . 14.- Comparison between micro-accelerometer densities p and densities obtained from DTM.

0 A G I LJ 2

Longitude of the satellite is indicated as well as K indices.

P

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s a t e l l i t e w a s , t h e r e f o r e , u n d e r local s u m m e r c o n d i t i o n s a t r a t h e r h i g h l a t i t u d e s . A c c o r d i n g t o t h e c h a r a c t e r i s t i c s o f t h e w i n t e r h e l i u m b u l g e , t h e d r a g o f ECHO 2 r e s u l t e d o n t h e s e t w o d a y s f r o m low h e l i u m c o n c e n t r a t i o n s . A s a c o n s e q u e n c e t h e h i g h v a l u e s o f P Q B S ^ M O D E L F O R

MS IS a n d J77 i m p l y t h a t t h e h e l i u m c o n c e n t r a t i o n is t o o samll i n t h e s e m o d e l s f o r h i g h - l a t i t u d e s u m m e r c o n d i t i o n s . I t seems t h a t D T M is t h e o n l y model w h i c h a p p r o p r i a t e l y r e p r e s e n t s t h e h e l i u m s u m m e r d e p r e s s i o n as o b s e r v e d w i t h s a t e l l i t e d r a g .

T h e m i c r o - a c ' c e l e r o m e t e r C A C T U S o n b o a r d o f C A S T O R - D 5 B 1 9 7 5 - 3 9 A o f f e r s t h e p o s s i b i l i t y o f c o m p a r i n g h i g h r e s o l u t i o n d a t a w i t h model r e s u l t s . T h e t o t a l d e n s i t i e s o b t a i n e d w i t h C A C T U S ( B a r l i e r e t a l . , 1977, 1 9 7 8 a ) h a v e a r e l a t i v e a c c u r a c y o f 1% b e t w e e n 300 a n d 400 km a l t i t u d e . F i g . 14 s h o w s a c o m p a r i s o n b e t w e e n p C A C T U S

a n d PD T M f o r f i v e m a g n e t i c a l l y q u i e t d a y s d u r i n g M a y 1976. A l t h o u g h t h e r e is a r e l a t i v e l y g o o d a g r e e m e n t b e t w e e n D T M a n d t h e m i c r o - a c c e l e r o m e t e r r e s u l t s , i t a p p e a r s t h a t D T M d e n s i t i e s a r e a l i t t l e t o o h i g h . S u c h a s y s t e m a t i c d i f f e r e n c e c o u l d b e e x p l a i n e d b y a n o v e r - e s t i m a t i o n o f t h e t e r m o p a u s e t e m p e r a t u r e i n t h e o p t i c a l model o f T h u i l l i e r e t a l . ( 1 9 7 7 a ) d u r i n g M a y 1976. T h i s model a g r e e s , h o w e v e r , w i t h i n c o h e r e n t s c a t t e r d a t a o b t a i n e d i n 1966 f o r low s o l a r a c t i v i t y ( T h u i l l e r e t a l . 1 9 7 7 b ) . B u t d u r i n g t h e 1966 m i n i m u m t h e mean s o l a r d e c i m e t r i c f l u x w a s a r o u n d 100 x 1 0 ~2 2 W m "2 H z "1 w h e r e a s i n M a y 1976 i t r e a c h e d v a l u e s as low as 72 x 1 0 ~2 2 W m "2 H z "1. I n v i e w o f t h e a c c u r a c y o f t h e C A C T U S d a t a , t h e small d i s c r e p a n c i e s o n F i g . 14 c a n n o t be c o n s i d e r e d as r a n d o m n o i s e . T h e y s h o w a c t u a l l y an i n h e r e n t

l i m i t a t i o n o f g l o b a l m o d e l s , n a m e l y t h a t t h e y a r e u n a b l e t o r e p r e s e n t s h o r t - t e r m f l u c t u a t i o n s i n t h e u p p e r a t m o s p h e r e .

F i n a l l y t h e C A C T U S d a t a s h o w t h a t D T M u n d e r e s t i m a t e s t h e g e o m a g n e t i c e f f e c t f o r low l a t i t u d e s a n d low s o l a r a c t i v i t y . T h i s c a n be seen f r o m F i g . 15 w h i c h r e p r e s e n t s t h e d e c i m a l l o g a r i t h m o f

pC A C T U S/ pD T M 3 S 3 f u n c t i o n o f t h e Kp i n d e X f°r a l m o s t a" t h e d a t a

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w ro

er

o>

o

0.20

0.15 -

0 . 1 0 -

K p i n d e x

F i g . 15.- Comparison between micro-accelerometer densities P C A C T U S a n d PD T M as a function of geomagnetic index K . T h e C A C T U S data are e x c l u s i v e l y obtained for low latitudes.

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obtained with the micro-accelerometer. T h i s example indicates that refinements can still be made in global semi-empirical models.

5. C O N C L U S I O N

From the comparisons made in this paper, it would be unfair to conclude that any one of the models is completely inadequate to represent the physical structure of the terrestrial thermosphere. But, it would be pretentious to assert that all the phenomena observed are perfectly well understood and represented.

It is necessary to remember that the solar activity effect is analyzed using data covering at most two solar cycles, and that there can be large differences between different solar cycles. For instance during the very high solar maximum in 1958 only drag data were available, and no _in__sjtu measurements have ever been performed under such conditions.

The global geomagnetic effect is represented by empirical relations involvinq K or A indices deduced from 13 stations which are p p poorly distributed over the world : 11 stations between 63°N and 50°N geomagnetic latitude and 2 stations between 46°S and 48°S ( I A G A , 1970). It is, therefore, not surprising that some difficulties are encountered at high and low latitudes.

The various models indicate different amplitudes in the diurnal variation of the atmospheric constituents and the phases agree only above 200 km.

For the seasonal-latitudinal variation, a specific problem arises with the helium abundance during local summer at high latitude.

The large difference between drag data and mass spectrometric data

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cannot be attributed to g e o p h y s i c a l phenomena. It is conceivable that s u c h a problem could be clarified b y u s i n g extreme ultraviolet optical data for the helium d i s t r i b u t i o n at h i g h altitude.

Except for the geomagnetic effect in J77, in no other model can the mathematical s t r u c t u r e account for longitudinal effects as a c o n s e q u e n c e of the assumed equivalence between longitude and local time. C o m p a r i n g the E S R O 4 data a n d the E S R O 4 model, v o n Z a h n and F r i c k e (1978) have clearly s h o w n the existence a longitudinal pattern for the atmospheric c o n s t i t u e n t s .

Finally d e n s i t y f l u c t u a t i o n s as o b s e r v e d with the micro- accelerometer C A C T U S , are far from being well r e p r e s e n t e d b y global t h e r m o s p h e r i c models.

T h e difficulties e n c o u n t e r e d with the p r e s e n t semi-empirical models of the terrestrial t h e r m o s p h e r e s h o u l d not be r e g a r d e d as g r o u n d s for criticism of the c a r r i e d out w o r k in the past, b u t rather as a stimulation for f u r t h e r r e s e a r c h in a field which is only 20 y e a r s old.

A C K N O W L E D G E M E N T S

We would like to t h a n k Emile Falise ( I A S ) for h i s valuable help in the computations r e q u i r e d for this w o r k .

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