New Static Models of the Thermosphere and Exosphere with Empirical Temperature Profiles

Home , Thermopause

NEW STATIC MODELS OF THE THERMOSPHERE AND EXOSPHERE WITH EMPIRICAL TEMPERATURE PROFILES

L. G..JACCHIA

X 4

Smithsonian Astrophysical Observatory SPECIAL REPORT 313 Research in Space Science

SAO Special Re_ort No. 313

NEW STATIC MODELS OF THE THERMOSPHERE AND

EXOSPHERE WITH EMPIRICAL TEMPERATURE PROFILES

L. G. Jacchia

May 6, 1970

Smithsonian Institution Astrophysical Observatory Cambridge, Massachusetts 021 38

Nn2-f_ TABLE OF CONTENTS

Section

ABSTRACT ...... v

1 INTRODUCTION ...... l

2 COMPOSITION ...... 3

3 COMPUTATION OF DENSITIES AND BOUNDARY CONDITIONS 7

4 TEMPERATURE PROFILES ...... 9 ......

5 VARIATIONS IN THE THERMOSPHERE AND EXOSPHERE . . . 13

6 VARIATIONS WITH SOLAR ACTIVITY ...... 15

7 THE DIURNAL VARIATION ...... 17

8 VARIATIONS WITH GEOMAGNETIC ACTIVITY ...... 21

9 THE SEMIANNUAL VARIATION ...... 23

i0 SEASONAL-LATITUDINAL VARIATIONS OF THE LOWER THERMOSPHERE ...... 25

Ii SEASONAL-LATITUDINAL VARIATIONS OF HELIUM ...... 27

iZ HYDROGEN ...... 29

13 THE TABLES ...... 31

14 COMPARISON WITH OBSERVATIONS ...... 33

15 NUMERICAL EXAMPLES ...... 35

16 ACKNOWLEDGMENT ...... 39

17 REFERENCES ...... 41

iii vm

LIST OF TABLES

Table

Ratio of the local temperature Tf to the global minimum temperature T c as a function of L. S. T. and of latitude (9) 46

Temperature increment as a function of geomagnetic indices ...... 49

Temperature corrections 5T s for the semiannual variation, 50 computed from equation(Z3), for F10 .7 = 100 ...... Tables for the seasonal-latitudinal density variation _log p = SP sin z _ ...... 51

Atmospheric temperature, density, and composition as functions of height and exospheric temperature ...... 5Z

Atmospheric density as a function of height and exospheric temperature (decimal logarithms, g/cmS) ...... 8Z

ILLUST RATION

Figure Pa e

1 Ten-day means of the logarithmic density residuals from the model for five satellites with effective heights between Z70 and 1130 km ...... 34

...... o ..... ABSTRACT

The present models are patterned after similar models published by the author (Jacchia, 1965a). The main differences consist in the lower height

(90 km instead of 120 kin) of the constant-boundary surface and in a higher

ratio of atomic-oxygen to molecular-oxygen density (n(O)/n(Oz) = 1. 5 at 120 km instead of about 1. 0). Mixing is assumed to prevail to a height of

105 kin, diffusion above this height. All the recognized variations that can

be connected with solar, geomagnetic, temporal, and geographic parameters

are represented by empirical equations.

Tables showing temperature, density, and composition as a function of height are given for exospheric temperatures ranging from 600 ° to Z000°K,

at 100°K intervals, and for height= from 90 to 2500 krn. A summary table

at the end gives densities only for the same range of heights and temperatures,

but at 50°K intervals in the exospheric temperature. A set of auxiliary tables

is provided to help in the evaluation of the diurnal, geomagnetic, semiannual,

and seasonal-latitudinal effects.

v R SUM

Les modeles presents sont des copies de modules analogues pu- bli_s par l'auteur (Jacchia, 1965a). Lea differences principales sont la hauteur plus basse (90 km au lieu de 120 Lm) de la surface _ limites constantes et un rapport plus elev_ de la densite de l'oxygene atomique par rapport _ cells de l'oxygene mol_culai- re (n(Ol/n(O 2) _ 1,5 _ 120 km au lieu d'environ 1,O). On suppose qu'un m_lange pr_valoit jusqu'a une hauteur de 105 km, au dessus c'est la diffusion. Des _quations empiriques tiennent compte de routes lea variations connues qui peuvent etre reliees aux pare- metres solaires, geomagnetiques,.._.._emporels et ge.o.graphiques,

Nous donnons des tableaux montrant les variations de la temperature, de la denalte et de la composition en fonction de la hauteur pour des temperatures exospheriques allant de 600 °

2000°K, _ des intervalles de lOO°K, et pour des hauteurs allant' de 90 _ 2500 km. A la fin, un tableau resum_ donne les intensi- t_s seulement pour la m_me gamma de hauteurs et de temperatures mais a des intervalles de 50°K dans la temperature exospherique.

On donne aussi un ensemble de, tableaux auxiliaires pour aider

_valuer lea effets diurnes, lea effets geomagnetlques, semiannuels, et les effets latitudinaux saisonniers.

vi KOHCI-[EKT

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_43MeHeH_491_ !

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_yHKLIM_ BbICOTbI_ ;_aH_ _n_ _M_oc,_ep_ecK_x Te_nepaTyp B _Mana3oHe

OT 600 ° _0 2000°K _epe3 _

2500 EM. CBO_HaH TaO_MHa B KOHLIe BOCI'IpoI48BO/II4T BbICOTS! Id TeMtle- paTyp_ B Tex xe z;zanaaoHax, NO qepe3 _ax_;_,e 50°K _ns a_soc@epx- _ecKzx TeMnepaTyp. ]-[pe_[cTaBneH Ha60p _ononH_nTenBHS[X Ta6n_¢Ll_ noMormo_zx B oueH_e /IHeBHblX, reOMaFHI4THblX, r_onyro;_oB_X _¢ ce3oH-

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vii NEW STATIC MODELS OF THE THERMOSPHERE AND

EXOSPHERE WITH EMPIRICAL TEMPERATURE PROFILES

L. G. Jacchia

I. INTRODUCTION

Static diffusion models of the upper atmosphere with empirical tempera-

ture profiles were published by the author a few years ago (Jacchia, 1965a).

These models have beer., widely used and can also be found incorporated in

the U.S. %tandard Atmosphere Supplements 1966 (COESA, 1966). Their main

drawback is the assumed constancy of the boundary conditions at 120 kin,

shared by other atmospheric models (Nicolet, 1961, 1963; CIRA, 1965).

Actually, both temperature and density undergo considerable variations at

120 krn, and the neglect of this fact makes the models somewhat less reliable

for heights below 200 kin, as was pointed out in the text that accompanied the

tables. The present tables try to remedy that situation as much as possible

by taking constant-boundary conditions at the height of 90 kin, which closely

corresponds to that of the mesopause and also of a layer of minimum varia-

tion inthe global density distribution (Cole, 1961). All _he available obser-

vational material, including the most recent measurements of density and

composition, has been taken into account in the construction of the present tables.

This work was supported in part by Grant NGR 09-015-002 from the National Aeronautics and Space Administration.

- -I ...... I..... I --- -- i ,.... ,. -- . -- t'_'kt_t-£DING PAG& I_LAi',,_K NO_.-I"IL_z_LU.

Z. COMPOSITION

We have assumed that the atmosphere is composed only of nitrogen,

oxygen, argon, helium, and hydrogen, in a condition of mixing up to 1 05 krn,

and in diffusion above this height. We have adopted the sea-level composition

of the U.S. Standard Atmosphere 1962 (COESA, 1962) such as would obtain

after elimination of the minor constituents and of hydrogen (which is intro- duced in our naodels at a height of 500 kin). There is some evidence that for

helium gravitational separation starts at a ]_wer height than for the other

constituents. To eliminate the inconvenience of a separate homopause for

helium, we have had recourse to the artifice of increasing the sea-level

concentration of helium by an an_.ount such that the atmospheric densities at

heights where helium appears as a major constituent be in agreement with

the observed densities. This results in an erroneous helium density below

1 05 kna -- a situation we were willing to tolerate in view of the entirely

negligible contribution of helium to the total density at those heights. Thus the assumed sea-level composition is as follows:

Fraction by volume Molecular weight

q0(i) m.i

Nitrogen (N2) 0. 78110 28. 0134

Oxygen (O2) 0. 20955 31. 9988

Arg_0_n (Ar) 0. 00934 39. 948

Helium (He) 0. 00001289 4. 0026

Sum 1.00000

The resulting sea-level mean molecular mass is M0 = 28. 960.

| I ...... I 1- I ...... " .... • ...... , .... We have assumed that any change in the mean molecular mass M in the

mixing region below 105 km is caused only by oxygen dissociation. There-

fore, the amount of atomic oxygen present in the atmosphere is uniquely

determined by M. From 90 to 105 km we have used an empirical M profile

that had to satisfy certain conditions. Starting from a value not too different

from M0 at 90 kin, we end at 105 km with a value that would-yield a concen-

tration of atomic oxygen such that the ratio n(O)/n(O2) at 120 km would be about 1. 5 and have a gradient dM/dz at 1 05 km roughly equal to that corres-

ponding to the gradient in diffusion immediately above 1 00 km (thus minimiz-

ing the effect on the models of a change in the height of the homopause). The

average observed height of the turbopause is closer to 100 thanto 105 kin, butwe have to allow for a difference of a few kilometers between the turbopause and

the effective homopause. We also constructed a model with the homopause at

1 00 krn, which is virtually identical with the present model above 1 05 kin, but

we chose to publish the present model because it leads to a smoother _ profile across the homopause. The ratio n(O)/n(O2) = 1.5 at 120 km was arrived at after many attempts to construct models with ratios from 0.5 to 4; it seems to fit best the satellite-drag data, particularly near maximum solar activity.

It is larger than the ratio 1. 0 used in the Jacchia 1965 models and the CIRA models, but not quite so large as advocated by VonZahn(1967).

m The adopted M profile can be found in the tables. For computer purposes

we have used a sixth-degree polynomial of the form

M(z) = E cn(z - 100) n (90 < z < 105; z inkm) (1) 1"1=0

to represent it. The coefficients c are given below: n

c = 28. 15204 0

c I = -0. 085586

10 .4 c 2 = +1.2840 X

10 -5 c 3 = -i. 0056 × c 4 = -l. 0210 × lO -5

c 5 = +l. 5044 × lO -6

c6 = +9. 9826 X 10 -8

The number densities of the individual species i in the region from 90 to

105 km are obtained as follows. From the density p the total number of particles N per unit volume is computed by

N = Ap/m , (2) where A is Avogadro's number.

For N2, Ar, and He we have

n([) = q0(i) M N !3) M o

and for 0 and 02, respectively,

n(O) = 2N

(4)

For p in g cm -3 we have usedA= 6. 02257 × 1023 .

t nI'_:CEDING PAGE E_L.ANK NOI" FILMED.

3. COMPUTATION OF DENSITIES AND BOUNDARY CONDITIONS

From 90 to 105 kin, for a given temperature profile T(z), the density p was computed by integrating the barometric equation

dinp = din Mg dz -kT (5)

where g is the acceleration due to gravity, and k = 8. 31432 joules (°1<) -I tool "1, the universal gas constant.

At the height z = 90 km we have assumed the following boundary conditions:

Pl = 3.46 X 10 -9 g cm "3

T = 183°K 1

Above 105 km the number density of each individual species n(i) was computed by integrating the diffusion equation

dn(i) mig dT n(i) = "_ dz - _ (1 + ai) , (6)

where a. is the thermal diffusion coefficient. Following Nicolet, we have 1 used a = -0.38 for helium, and a = 0 for the other constituents.

For hydrogen we have followed Kockarts and Nicolet (1962) and fitted the equation

l°gl0 n(H)500 = 73. 13 - 39.40 log 10 T + 5.5 (lOgl0 Tco)Z (7)

to their concentrations at 500 kin. We have assumed hydrogen to be in diffusion equilibrium above 500 km; n" hydrogen densities were computed below this height. According to equation (7) hydrogen densities decrease when the temperature increases, contrary to the behavior of all other atmospheric constituents. This should be correct in the variations with the ll- year solar cycle. According to Meier (1969), however, the variations of hydrogen in the 27-day oscillations corresponding to solar rotation are in

2hase with those of the other constituents. It would seem, therefore, that at heights where hydrogen is a major constituent, density variations cannot be computed in a simple fashion by just changing the exospheric temperature (see Section 12).

The acceleration due to gravity was computed from the formula

g = 980. 665 (1 + Z/Re)-2 cm sec -2 , (8)

with R = 6 • 356766X 108 cm. This equation (Harrison, 1951" Minzner and e Ripley, 1956) is an excellent approximation to the actual value of g (centrifugal force included) for the latitude of 45 ° 32'40".

8 4. TEMPERATURE PROFILES

All temperature profiles start from a constant value TO = 183"K at the

height z0 = 90 krn, with a gradient G O = (dT/dZ)z=z 0 = 0, rise to an inflection point at a fixed height z x - 125 kin, and become asymptotic to a temperature T (often referred to as the "exospheric" temperature). Both the temperature

Tx and the temperature gradient Gx- (dT/dZ)z_ x- at the inflection point are functions of _; for simplicity we have made G a function of T . X X

The quantity T is defined by the equation X

Tx= a+ bT + c exp (_ To0) , (z x= 125 kin) , (9)

with the constraint that T = T O when T = T (i. e. for the hypothetical case X 00 0 J in which the exospheric temperature is the same as the temperature at

90 kin, namely 183 °, there is no variation of temperature with height). The numerical values of the coefficients are as follows:

a = 444.3807 ,

b = 0.02385 ,

c = -392. 8292 ,

k = -0.0021357

For z < Z< Z the temperature profiles are defined by a fourth-degree 0 X polynomial:

T = Tx + >_ Cn(Z _ Zx )n (10) n= ]

L ...... The coefficients Cl, cz, c3, and c 4 are determined by the following conditions:

T=T 0 when z = z

=z 0

T x -T O = 1.90 Zx - Zo Z = Z _ X =Zx when X 17/dZr -0 z----Z (11) x

These coefficients must be computed separately for every temperature

profile, so their tabulation would be wasteful. The equation for G is justified x in the following manner. The condition for having no inflections in the tem-

perature profile in the interval z 0 < z < Zx is given by

Z - Z 4 0 < x < Z (1Z) T - T Gx x 0

Experiments with gradients within this range have shown that it is quite

feasible to keep the quantity (zx - z0)/(Tx - TO) constant for all temperature profiles; the best value was found to be I. 90.

For z > z the temperature profiles are determined by equations of the X type

T T + A tan-1 t G { x !-X-X (z - Zx) [I + B(Z - Zx)_ , (13)

where

A= 2_ (Too - Tx) ,' B= 4.5 × I0-6 for z inkm ; n= 2.5

L m , As can be seen, continuity is provided in dT/dz when z cr' sses z . The x inverse tangent was selected among several suitable asymptotic functions for its ready availability in tabulated form and in computer libraries. The

presence of the corrective term [1 + B(z - zx)n ] frees the temperature profiles from strict dependence on the selected type of asymptotic function.

- _.L, - d

I,_ftEC_DING PAGE BLANK NOT FILMED,

5. VARIATIONS IN THE THERMOSPHERE AND EXOSPHERE

Several types of variation are recognized in the atmospheric regions covered by the present models. They can be classified as follows:

1 Variations with the solar cycle;

2 Variations with the daily change in activity on the solar disk; 3 The diurnal variation;

4 Variations with geomagnetic activity;

5 The semiannual variation;

6 Seasonal-latitudinal variations of the lower thermosphere;

7. Seasonal-latitudinal variations of helium;

8. Rapid density fluctuations probably connected with gravity way.es:

All these variations, with the exception of the last type, are subject to some amount of regularity and can be predicted with varying degree of accuracy on the basis of ground-based observations. It is obvious that static models cannot represent all the different types of variation equally well.

They should be quite adequate when the characteristic time of the variation is much longer than the time involved in the conduction, convection, and diffusion processes; when, on the other hand, it is comparable or shorter-- as in the diurnal variation and the geomagnetic effect-- we must expect poorer results. By this we mean that, if we try to represent the observed density variations, we may have to introduce temperature variations that are not entirely correct, or vice versa. Since the largest observational material, by far, consists of density measurements, it is the density variations that we have tried to keep correct. We have no direct evidence so far that the resulting temperature variati.ns might actually be incorrect, although it would not be surprising if they turned out to be so, to a certain degree.

Temperatures derived from nitrogen profiles at various times of the day

(Spencer, Taeusch, and Carignan, 1966; Taeusch, Niemann, Carignan, Smith, and BaIiance, 1968) actually are in closer agreement with the J65 static models.

13 An effort was made in the CIRA 1965 tables to treat the diurnal variation apart; unfortunately the inadequacy of present-day theory does not justify the tremendous increase in the size of the tables if one were to cover the diurnal variation over the entire globe, instead of being restricted to one particular latitude as in CIRA 1965. 4

14 6. VARIATIONS WITH SOLAR ACTIVITY

The ultraviolet solar radiation that heats the earth's upper atmosphere actually consists of two components, one related to active regions on the solar disk and the other to the disk itself. The active-region component comes from areas of higher temperature and consists mainly of the spectral lines of highly ionized atoms, such as Fe XIV-XVI, Si IX-X, Mg X, etc. ; the radiation from the clear disk comes from much less ionized atoms, such as He I-II and O IV, and the helium continuum. The active-region component varies rapidly from one day to the next in correspondence with the appearance and disappearance of active areas caused by the rotation of the sun and by spot formation; the disk component presumably varies more slowly in the course of the ll-year solar cycle. Since the radiation in the two components is different, we must expect the atmosphere to react in a different manner to each of them-- and this is actually observed.

The 10.7-cm solar flux (F10" 7) is generally used as a readily available index of solar EUV radiation. It also consists of a disk component and of an active-area component, which can be separated by statistical methods by relating the observed values of the flux integrated over the whole solar disk to the corresponding sunspot numbers (Hachenberg, 1965) or, better, to sunspot areas. Whenthe 10. ?-cm flux increases, there is an increase in the temperature of the thermosphere and exosphere; for a given increase in the disk component, however, the temperature increases three times as much as for the same increase in the active-area component. Separate values of the two components of the solar flux are not readily available; fortunately we have found (Jacchia and Slowey, unpublished) that the disk component is, for all practical purposes, linearly related to the flux averaged, or smoothed,

over approximately three solar rotations (17"20. 7 ). We can, therefore, replace the relation between temperature and disk component with an equivalent

relation between temperature and F--10 ,7. In view of the solar-wind effect on the diurnal variation (see Section 7), it appears quite probable that the varia-

tions of both the solar EUV and the solar wind contribute to this relation.

15 Since the temperature varies with the hour of the day, with geographic location, and with geomagnetic activity, we must specify the parameters of these variations to which the temperature is to be referred. The temperature

T c in the equation that follows is to oe the nighttime minimum of the global exospheric temperature distribution when the planetary geomagnetic index K is zero. We find that P

T = 383" + 3?32 710 . 7 + I?8(FI0. 7 - _I0. 7 ) (for K = 0) ; (14) c p

F 10.7 is expressed in units of 10 -22 watts/mZ/cycles/second bandwidth.

According to Roemer (1968) the temperature variations occur with a time lag of 1. 0 ± 0. 12 days with respect to those of the solar flux.

If we want to compute the average exospheric temperature corresponding to a given phase of the solar cycle, i. e. , to a given value of FS0" 7' we must drop the last term of equation (14), which corresponds to the day-to-day variations of solar activity, and add half of the diurnal temperature range and the difference in temperature between average and quiet geomagnetic conditions. For this purpose, see equation (27) in Section 12.

16 7. THE DIURNAL VARIATION

Densities derived from satellite drag show a maximum around 2 p.m. local solar time(L.S.T.), at a latitude roughly equal to that of the subsolar

point; the minimum occurs around 3 a.rn. at about the same latitude with oppo-

site sign. Thus, if we consider the atmosphere above a particular locality, the

diurnal variation will undergo a seasonal change; this change, however, can

be incorporated in a global description of the phenomenon by a set of suitable

empirical equations (Jacchia, 1965b). The purpose of these equations is to

represent the density variations by use of statlc atmospheric models. To this effect it appears necessary to use the temperature as an auxiliary

parameter, but it must be understood that this "temperature" has no claim to accuracy, since consistency between temperature and density variation

cannot be achieved, on a diurnal time scale, through static models.

We shall assume that the maximum daytime exospheric temperature T M occurs at a latitude $ equal to the sun's declination 5q) , and the minimum temperature T C at a latitude -66). The ratio TM/T C = 1 + R changes with the solar cycle; its variation seems to be in phase with the yearly means of the geomagnetic planetary index K (Jaechia, 1970a) and lags about 400 days P behind those of F10" 7' indicating that there must be a solar-wind component in the heating of the upper atmosphere.

There is also some evidence that the shape of the diurnal density curve changes with height (Jacchia, 1970b) and with solar activity; present data, however, are insufficient to establish the rules of this variation with sufficient assurance, and therefore we have assumed that the parameters that fix the shape of the curve are constant.

We shall assume that the daytime maximum temperature T D and the minimum nighttime temperature T N at a given latitude _ can be represented by the equations

17 T D= Tc(l + R cos m _) ,

T N= Tc(l + R sin m 0) , (15)

where

The temperature T_ at any given point can be expressed as a function of the hour angle H of the sun (the local solar time, counted from upper culmination). Let us write

n T Ti = T N (1 + A cos _) , (16) with

T D - T N m m A- = R cos D - sin (9 TN 1+ R sinm e and

w= H+ _+ p sin(H+ y) (-'IT <_ T < 'IT) ,

where i_, y, and p are constants. It shou]d be remembered that T_, which is derived from T , is referred to K = 0. c p

The constant p determines the lag of the temperature maximm__ '._tth respect to the sun's culmination, while p introduces in the temperature cL.rve an asymmetry, whose location is determined by y. Replacing T D and T N from equation (15), we can write

Tl Tc(1 + R sin m 0) I + R cos _] - sin m O n T _ (17) = 1 + R sinm 0 cos ]

18 Densities derived from satellite drag are best represented by use of the following parameters:

m = 2. 5 _ = -37 °

n =3.0 p=+6 °

y = +43 °

The quantity R varies between 0. 27 and 0.4; a good average is 0. 31. If yearly running means of Kp (which we shall write as _p) are available, R can be computed from the relation

R = 0. 134 + 0. 090 K (18) P

Otherwise, 710. 7 can be used to compute R from the formula

R= -0.'19+ 0.25 log10 F--10.7(t - 400 d) , (19)

where x710. 7 (t - 400 d) indicates the value of 71 0.7 at a rate 400 days before the date for which R is to be computed.

T-a.ble 1 gives the ratio T_/Tc, multipli_.d by the factor 1 000, as a function o£ local solar time (counted from midnight} and of latitude, computed with the above parameters and with R = 0.31. According to this model the houa:_-of-m2mimum and maximum of the daily density variation are inde'pen- dent of latitude and are 2h87 and 14h08 L.S.T., respectively.

A certain degree of smoothing must be expected in the curve of the daily density variation as determined from satellite drag. Neutral temperatures determined :rom Thomson scatter (Carru, Petit, and Waldteufei, 1967;

McClure, 1969) showa rapid increase at sunrise, followed by a much slower increase to a maximum around 16 h, 2 hours later than the 14 h density maximum obtained from drag; the amplitude of the variation, a factor of 1. 5, is much larger than that of our model. By smoothing, this temperature curve ctn be brought closer to the drag density curve, although smoothing

19 alone cannot possibly account for the considerable discrepancy between the two curves. In particular, there is not the slightest indication in the drag density curves of a rapid increase at sunrise (which is a prominent feature of electron temperatures). O,_ the other hand, temperatures derived from nitrogen profiles obtained from six rocket firings from Cape Kennedy on January Z4, 1967 (Taeusch et al., 1968) essentially agree in simplitude and phase with those of the present model. Also in better agreement with the model are the temperature ranges obtained from thermosphere probes (Spencer et el., 1966), from mass-spectrometer data on the Explorer 17 (Reber and NLaolet, 1965) and the Explorer 32 (Ne__zton, 1969), and from EUV absorption (Hall, Chagnon, and Hinteregger, 1967).

Equation (17) should lead to reasonably accurate densities up to the height where hydrogen becomes an important constituent. When hydrogen can no longer be neglected, its density variations, if known, could be represented by using for hydrogen alone a fictitious "temperature" T H different from the temperature T of the other constituents. A formula of the type

R TH= (I - c)(i+2-)T C + * (ZO) could do the trick. With c = 0 the formula gives for hydrogen a constant temperature equal to the arithmetic mean between the daytime maximum and the nighttime minimum, and there is no diurnal density variation of hydrogen. With c = l hydrogen has the same temperature as the other constituents; i. e. , the diurnal density variation of hydrogen is in phase with the one it displays during the 11-year solar cycle. With c = -1 the diurnal variation of hydrogen is reversed and is in phase with that of the other constituents. We can expect c to lie between-1 and +1; on the basis of Meier's (1969) observations there is a definite possibility that it may be negative.

2O 8. VARIATIONS WITH GEOMAGNETIC ACTIVITY

For practical reasons we have assumed that in the temperature changes that accompany variations in geolnagnetic activity the shape of the temperature profiles remains unchanged-- i. e. , we have related changes in an index of geomagnetic activity with changes in the exospheric temperature T and have 0o assumed that at all heights the densities are determined by the model temperature profile ending ._.nT . As in the case of the diurnal variation, this o0 assumption is found to be somewhat in error because of the short character-

istic time of the variations; xnoreover, the distribution in height of the energy dissipation involved in the phenomenon may be different from that of EUV abs o r ption.

The density variations with geomagnetic activity can be represented with a fair degree of approximation by adding to the exospheric temperature a quantity ATg, which is a function of the 3-hourly planetary geomagnetic index I_ or its equivalent a . We can write (Jacchia, Slowey, and Verniani, 1967) P P

ATg = 28 ° Kp + 0.°03 exp (Kp) (21)

ATz = I?0 ap + i00 ° [I - exp (-0. 08 ap)] (22)

The average time lag between the variations in the geomagnetic index and those in the temperature is 6. 7 hours (7.2 hours at low latitudes, less than 6 hours at high latitudes). This means that to compute AT by equation g (21) or (22) for a given time t, K or a must be taken for a tim_: t: minus P P 6. 7 hours. There is some indication that AT is somewhat greatest, possib[_r g by 20% or so, at high geomagnetic latitudes. No appre, ciabh, difference, in

AT has been detected between the night hemisphere and the sunlit ht:'mispht:,r_.,. g Values of AT from equation (21} are given as a function of K and a in g P P Table 2.

21 _':-, _DING PAGE BLAN"_,. NOT I:ILMED.

9. THE SEMIANNUAL VARIATION

As is well known, geomagnetic activity is greater around the equinoxes

than around solstices. This semiannual increase in geomagnetic activity

results, of course, in a cori'esponding increase of atmospheric disturbances,

whic}l is entirely accounted for by equation (21) or (22). This apparent semi-

annual variation must not be confused with a true, global semiannual varia-

tion, which is evident also after the geomagnetic effect has been eliminated.

This semiannual variation, with maxima in April and October and minima

in January and July, has an amplitude that depends on solar activity and is

roughly proportional to the smoothed 10. 7-cm solar flux _10.7" Table 3 gives at 10-day intervals the correction AT s to be applied to the exospheric temperature to account approximately for the semiannual varia-

tion. The table is computed for F-l 0. 7 = 100, so the tabular values must be multiplied by F 10. 7 ]100 to obtain the actual corrections. Table 3 has been

computed by using the formula given by Jacchia, Slowey, and Campbell (i969), which is reproduced below:

m _T s = 2°41' + F 1 0. 7[0. 349 + 0. 206 sin (360°_ - + 226:5)] sin (720°T + 247?6) ,

(23) wh _,r e

d = days since January 1 ;

Y = length of tropical year in days

'['h_, ¢.tat¢:s of it, axima a.r_d n_inhna according to this formula, with their

cc,rl:',-sp_,nel_ng values ,,_ _°[' t'c:_r '_-r = 100, are as follows. " ,_ [ (1. '7

L ..... "...... - .... I ' II I I li III II II la ,ill. "I • Secondary minimum (-16 ° ) : January 15

Secondary maximum (+28 °) : April 3

Primary minimum (-50 ° ) : July 30

Primary maximum (+49 °) : October 28

In reality the semiannual variation is not: a very regular phenomenon.

Both the shape and the amplitude of the variation show erratic changes from

cycle to cycle; sizable residuals must be expected when using equation (23),

which was obtained by fitting the observed density data from 1958 to 1965

(inclusive). ICing-Hele and Walker (1968) think there might be a systematic

modulation of the amplitude with a cycle of about 33 months, but this effect needs confirmation.

Equation (23) seems to give a correct representation of the relative

amplitudes of the density variation at different heights in the interval from

250 to 800 kin. Cook (1967, 1969) found that at If00 km the amplitude is systematically higher. Our data on the Echo 2 satellite confirm this

result, but show that the excess variation that remains after subtracting

equation (23) differs in shape and phase from the semiannual variation in the region 200 to 800 kin. The maxima and minima show no alternation of

primary and secondary, and occur some 25 days earlier, following the

solstices and equinoxes by only 8 days instead of the average 33 of equation (23). We suggest that this residual semiannual variation is a result of the

seasonal migration of helium: if a vertical flux accompanies the helium migration (Kasprzak, 1969), the total mass of helium in any given height

layer may vary in the course of the year.

A semiannual density variation found by Cook (1 969) at 90 kin, which--

if confirmed-- would make equation (23) inapplicable at heights below

200 km, is spurious according to Groves (1969, private co_nmunication),

and caused by an insufficient discrimination between the diurnal and seasonal- latitudinal variations.

11 I I i li a ., , , -- --_ .... 1 0. SEASONAL-LATITUDINAL VARIATIONS OF THE

LOWER THERMOSPHERE

In the present models we have assumed that temperature and density

are constant at 90 km all over the globe. In reality, seasonal-latitudinal

variations are observed at that height-- fairly large in temperature, although relatively small in density. All the variations we have described so far could

be taken into account with a fair degree of approximation by operating on the

exospheric temperature; such a procedure is obviously impossible for the

seasonal-latitudinal variations, for which it is necessary to operate on the

lower boundary conditicns. However reluctantly, the decision to keep the

lower boundary conditions constant had to be taken to prevent the models

from becoming unmanageable in their complexity.

An attempt was made in the U.S. Standard Atn_osphere Supplements t 1966 (COESA, 1966) to effect a smooth junction between the densities of lower-

thermosphere models with seasonal variations and the densities of upper-

atmosphere models computed by use of constant boundary conditions at

120 kin. The models were limited to a fixed, intermediate latitude and to

three seasons (summer, winter, and spring/fall); any greater detail would have entailed a prohibitive proliferation of tables. If we wanted to have models for every month at 15 ° intervals in latitude, the number of models

would increase by a factor of 84:

The amplitude of the seasonal-latitudinal density variation_ incre,;i.._,

very rapidly between 90 and 100 kin; the maximum amplitude is ap_._:!",,,r_tly

reached between 105 and 120 kin; above this height it must decr_,,_st:, b, cnl_:s_,.

above 200 km there seen_ to be no appreciable seasonal-l,,_._,u_i__a[ ,va_'iati.ons

other than those involved in the glohal pattern of the diur_aai varD_D',n. ['L!..s means that the ter_.perature variations, which at 100 t:rr_: .arc,in ph.,_._.,_,_-._i.tr_ the

density variations, must undergo a phase inversio_,_,_._'ound I[O kr_,, and r_.a.ch

a maximum anapiitude, in opposite phase with r,,-:sW:ct t,0. the :t,,,,.r,s_ti..,.'s, sort, e- where• around 150 kin, While it is relatively eas'? to, represent tbe d_,nsity variations in analytical, and even in tabular, form, it would be prohibitively laborious to do the same thing for the temperatures. We thought that the best that could be done was to give formulas for computing the seasonal-latitudinal variations in density, ignoring the temperature variations.

The equation we present here is an attempt to fit the seasonal variations as derived by Champion (1 96 7) and Groves (196 9, private communication). We find that the values of log p given by the models must be corrected by adding a quantity Alog p given by

360 ° _log p = 0.02(z - 90) ._t exp [-0.045(z- 90)] sin2 _ sinT (d + I00) I+I

(Z4) where ¢_ is the geographic latitude, z the height in kilometers, Y the duration of the tropicalyear in days (365 or 366), and d the number of days elapsed since /anuary 1. In Table 4 we have tabulated the maximum amplitude S of the variation as a function of height, the phase P of the variation, and sin z _;

_s log p is obtained as a product of these three quantities.

26 1 1. SEASONAL-LATITUDINAL VARIATIONS OF HELIUM

A strong increase of helium concentration above the winter pole has been revealed by mass-spectrometer measurements (Hartmann et al., 1968;

Kasprzak et al., 1968; Krankowski, Kasprzak, and Nier, 1968; M_lller and

Hartmann, 1969), by observing the intensity of the k I0830 resonance line of helium (Fedorov_a, 1967; Shefov, 1968; Tinsley, 1968) and from satellite- drag data (Jacchia and Slowey, 1968; Keating and Prior, 1968). The amplitude of the variation and its latitudinal depedence are still under investigation; the phase seems to be better established, with the maximum occurring just after the winter solstice. Under this assumption regarding the phase, we find that a flexible and relatively simple expression for the nurr her density n(He) of helium is the following: VfE- '> o<-el + ]-

(zs) where n0(He ) is the value of n(He) given by the models, E the obliquity of the ecliptic, 5 O the declination of the sun at time t - At, and _ the geographic latitude.

As of now it is difficult to give reliable values for all the parameters; we can recommend the following set:

A= 0.5 , B= 2.3 ; p= 2.5 ; r= 4 , _t= 8 days

The value of At was derived indirectly, from the semiannual variation of helium at 1100 km (see Section 9), under the assumption that the ph_.n,.,_r,,4 r_<,n is caused by the seasonal migration of helium. Srm_e <,l'."the num_r_,._al, p<_,"_:_:_ ,- eters, especially p and r, are _n.ly p,ox,rl.y determ_n¢:d and _,r'e ]ik,,_'_ _', I!>,.' considerably improved in the near future. In 'vT_.'w e;,If thes+ ul_<,".t,rta_'_ti:<_,_ i_ appears to be premature to give tables of the heli_r_ varia.tmn

27 As can be easily seen, A and B are, respectively, the maximum :_nd the minimum value that n(He)]n0(He ) can reach. If we assume that the vz.lues we have given for them are correct, we shall have at the winter pole 2.3 ti__es as much helium as in the tabular models, and at the summer pole 0.5 times the tabular value -- a helium variation by a factor of 4.6.

28 12. HYDROGEN

As we mentioned in Section 3, there is some evidence that eq,,ation (7)

can be used only to determine the average amount of hydrogen correspond-

ing to a given phase of the solar cycle, but not the variations of hydrogen on

a shorter time scale. To account for Meier's (1969) observations, we have followed, for our private use, a procedure that we shall briefly outline.

First, we compute the average exospheric temperature'T that corresponds CO to a given value of F I 0. 7 from the formulas

T = 383 ° + 3?32 _ c -l 0.7 '

(Z6)

iT is computed from equation (14) in which the last term has been dropped" T 0o is obtained by adding half of the diurnal temperature range and 56 ° to account for the average heating coming from the geomagnetic effect (K = 2)] . P If we choose to disregard the variations of R and use simply its average value, for which we can take 0. 31, equation (Z6) simplifies and b.ecomes

"To0= 498° + 3?83 _I 0.7 (27)

We compute the hydrogen number density n(H)500 at 500 km from equation (7) using T instead of T . For heights above 500 km we compute O0 OO n(H) by integrating the hydrostatic equation for a temperature T' obtained by taking into account all the short-time-scale variations in which we believe hydrogen behaves in the manner described by Meier (1969). We do not

claim that this procedure is physically justifiable, or even elegant; all we try to do is to prevent hydrogen in our models from varying in a manner contrary to observations.

Z9 I"r'I'!CEDING PAGE gL,.-',hli% NOT t:tLMF.D.

13. THE TABLES

Tables I to 4 are auxiliary tables designed to help in the computation

of the diurnal, geomagnetic, semiannual, and seasona1-1atitudinal effects

when no use is made of an electronic-computer program. No auxiliary table

is provided for the evaluation of the seasonal-latitudinal variation of helium,

for which the parameters are still somewhat uncertain and whose effect on

the total density is too complicated to be accounted for in a simple table.

Table 5 gives temperature, composition, density, and pressure scale

height as a function of height for exospheric temperatures ranging from

600 to 2000°K, at 100°K intervals, and for heights from 90 to 2500 krn. It

should be understood that no good observational data exist above 1100 kin, so

that all tabular data above this height must be considered as unconfirmed

extrapolation.

When only densities are required, Table 6 should be used to greater

advantage. In it, densities only are synoptically assembled for the same

heights as in Table 5, but at 50°I_ intervals in exospheric temperature for

easier inte rpolation.

JR" F'I I .... I-- n _" mIm ...... t'i',ECEDING PAGE BLANII NOT I:ILMt::D.

1 4. COMPARISON WITH OBSERVATIONS

A comparison of the models with atmospheric densities derived from

satellite-drag data obtained at the Smithsonian Astrophysical Observatory is

shown in Figure I. Ten-day means of the residuals in lOgl0 p are plotted for five satellites with effective heights ranging from 270 to 1130 krn (the

"effective" height is the weighted mean of the heights above the geoid in the

satellite's orbit, with the drag taken as weight; for satellites in eccentric orbits

it corresponds roughly to the perigee height augmented by half the density scale height). The scatter in the residuals is due in part to errors in the drag deter- mination and in part to the failure of the models to represent atmospheric den-

sity correctly. As can be seen, the mean systematic error is very close to zero for all satellites. Slowly varying systematic deviations, probably connected with

imperfections in the relation between the exospheric temperature and the

smoothed component of the I0. 7-ca solar flux (equation (14)) can be detected here and there, but they never exceed 0. 05 in log p (12% in the density). The larger, quasi-periodic oscillations in the residuals of Echo 2 and Explorer 19

are the result of our imperfect knowledge of the seasonal migrations of heliunl and the associated semiannual helium variation.

It should be pointed out that the densities were computed from the observed

drag using a drag coefficient variable with the mean molecular mass of the

atmosphere. The constants in the formula for the drag coefficient (Cook,

1966) were adjusted to give C D = 2.2 at heights below 300 km, a value generally used by researchers. This value would correspond to an accommo-

dation coefficient of 0.95 in the case of diffuse reflection from an oxygen-

coated spherical surface. Although C D = Z. 2 at 300 km is well within the

margin of theoretical error, a value C D = 2.4 is, according to Cook, the most probable. If we accept the latter value, all tabular densities should be

decreased by 10%. Such a decrease would bring the densities closer

to the average total densities inferred from mass-spectrometer data (which,

however, show such a wide scatter that the significance of the coincidence

is open to question).

33 1 I I I ] I I I I I I I I I I I I I

'Ibm *_ b'. i . o L,'_. _._.

imoj :,*. II %*:" % b, , *St .

• • S_,**I, ** * r )"¢1 ,/ • ,$' QO_ e' .:2"" "IL %. _,42 ** 'o. % %1 % , .,/.',-,. • , • °i i !, .%. 5

.. :._L'-.. _.* I :°

._,_ _

o_ i ® • _ -; ._" _ _ g4

N @._ t,

°.

• _ _

I: ,.=,.-. I I0 .,_

g_ z " D. ii g° IN _ * X,N IN

I I • I I I [ I I I I I I I II I] II o _. o _. (M 0 {M 0 O I ÷ ! _ ,_ ._ .,_ Q.. 9. 9 9

L -r" - ]-- I I 15. NUMERICAL EXAMPLES

Suppose we want to find the atmospheric density given by the models above a point with the following geographic coordinates:

longitude= 120°W of Greenwich, latitude = +45 ° ,

on January 20, 1969, at 19hll m U.T. = llh0 m L.S.T., for three heights: z = 140 km, z = 350 km, z = 800 km.

We shall first compute T c from equation (14). For that purpose we need

the smoothed solar flux F10" 7 for that date and the actual flux F10" 7 on the day before (to account for the lag of ld0). Consulting solar records we find the following: F10.7 = 155, F10.7 = 136, so Tc = 863.°4. This is the minimum exospheric temperature anywhere on the globe at the desired

instant, for quiet geomagnetic conditions (Kp = 0).

Next we shall use equation (16) or Table 1 to compute the exospheric temperature Tl. Table 1 is computed for R = 0. 31, but the actual R at the date was either 0.33 or 0. 36, according to whether we use equation (18)

with K P = 2. 17 or equation (19) withF10" 7 (t- 400) = 157. Let us take R = 0. 345; this value is i 1% greater than the value of R used for Table i.

The declination of the sun on January 20. 8 was -20. ° 0. For _ = +45" and

L.S.T. = llh0 m, Table 1 gives T_/T = 1. 154. To account for the change C in R,

T_/T c = 1 + 0.154X i. i1 = 1.171

This gives T_ = 1011 ° .

35 We now must evaluate the temperature differentials z_T and _T to be g s added to T1 to account for the geomagnetic and the semiannual effects. For _T we must first look up the value of K at a time 6.h7 before the desired g P date, i.e., on January 20 at 12.h5 U.T. From geomagnetic records we find for that time K p= 2+(ap= 9). From equations (21) or (22)• or from Table 2, we obtain AT = +66 ° . Table 3 yields 5T = -15.4 and _T = -15.4 x 1.55 = g s s -24 °, so the final exospheric temperature is T = 1011 ° + 66 ° - 24 ° = 1053 °. oD

At z = 350 kzn the seasonal-latitudinal densi'_y variations, acc,_rding to

Table 4, are negligible; and helium is a minor constituent, so the helium variations can be neglected• too. We therefore enter Table 6 with an exospheric temperature of 1053 ° and find, for z = 350 kin, logl0 p(g/cm 3) = -14. 011.

For z = 140 km Table 6 gives log p = -i1. 403. To this value• however, we must add a correction for seasonal-latitudinal variations in the lower thermosphere. Table 4 gives S= 0. 105, P= +0.882, sin i _ = 0.500, from which we obtain A log p = SP sin 2 _ = +0. 046, and the final density log p = -II.403 + O. 046 = -ii. 357.

At z = 800 km helium is an important constituent• so we must take into account the seasonal-latitudinal variations of helium. To use equation (25) we must look up the declination of the sun 8 days before Janlary 20.8; for

January 12.8 we find 6(D = -21._6. With the suggested values for A,B•p• and r, we find n(He)/n0(He ) = 1.684. This means that the tabular number density of helium must be increased by afactor 1.684. From Table 5 we find, by interpolation• for T = 1051 °• 00

log n(O) = 5.513 n(O) = 3. 26 X 105

i. e. • log n0(He ) = 5. 998 n0(He) = 9. 95 X 105

36 AI1 otl:_er atmosl;_.l'teric co_at[tu.ents are m_gligible. Applying the correction factor t.684 to n0(H_,t,we obtain n(He) = 1.676 X 1C6. Taking in'_oaccount t:he at_xn.i._cmasses of (_and _:l_,,we find (:hat the relative increase in total

density cau._sed t:_y the }.n:creased I:_._TMlim'rl is

I n(I-te} _2_.. nIOI + ':_ y.'i...... '..g -P-- : + 0.113 1 1.. Z96 ; [°gl 0 P0 P0 n(O) +X n0lHe)

From Table 6, for z = 800 krrl, 'r = 1053°_ we find log p = -16. 815. @3 The final density, corrected for helium variation, i.s therefore

log p = -16.815 + 0.113 = -16.702.

L_ 1 i ...... i i li i i i - , ...... _, i.Ct;[_lr..;G PAG" r_l.Af.:! t NOT FILMED,

16. ACKNOWLEDGMENT

It is a _sure to acknowledge the constant cooperation of Mr. I. G.

Campbell, . was responsible fc,rmost of the laborious programing and computing involved in the preparation of these models.

39 _:"""' :_ N(;' [" _ll MYD,

17. REFERENCES

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the members of COSPAR Working Group IV, North-Holland

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Churchill, Canada. Journ. Geophys. Res., vo]. 66,

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Drag coefficients of spherical satellites. Ann. Ge_qJl,ys., w_l. 22,

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FEDEROVA, N. I.

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A. P. Mitra, L. G. Jacchia, and W. S. Ne_aan,

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. il ...... i - r + -- " ' _ ' " " 11 "i : I

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Investigation of the major constituents of the April=May 1953

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Reaction time of the upper atmosphere within the, 27-day

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l_(mn, 68-08, 29 pp. N. N.

Twilight Ii(,]illlll (,l)_issicm during low and ldgh ,t;em,lagn(.tic

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N_ t.(,lvlp(,ral.tlr(, and d(,nsity data fq)r tl., !50 t() _flf) _m r(,gJ()vx and l.h(,ir ilill)li(:ations. Ann. Cil,_)l)Ixys, , v(')l, 2_., pp. 151-I(,(),

4,1 TAEUSCH, D. R., NIEMANN, H. B., CARIGNAN, G. R., SMITH, R. E., and BALLANCE, J. O. 1968. Diurnal survey of the thermosphere (I) neutral particle results.

In Space Research VIII, ed. by A. P. Mitra, L. G. Jacchia,

and W. S. Newman, pp. 930-939, North-Holland Publ. Co., Am ste rdanL

TINSLEY, B. A. 1968. Measurements of twilight helium 10,830 A emission. Planet.

Space Sci., vol. 16, pp. 91-99. VON ZAHN, U.

1967. Mass spectrometric measurements of atomic oxygen in the upper

atmosphere: A critical review. Journ. Geophys. Res.,

vol. 72, pp. 5933-5937.

45 0 o

,no _'_,_ _._ ,4, _', f_ _.,_ _'_1 ,_v_ _'_ ._..,.., oo o o o o o o o o

.... ooo_ooooo

o _o o

_ _00 _0_

. o

_ _4 _ _-_ _._ _.

r_ r_ om--or---o_r-o_mo

N _0000000000_ _00000000000_

_N_ ,000 _ r_o e_tn 0

_ O0 O0 OO000 _ _000000000_ _0 O0000000_,,-, _

0 ¢'t_ 0 o,I I_" _" $" t" _" e_ 0 ¢'_0

e_ _0000000_

o e_

...... _o

ewt_ N ewe-- _

0.; _t_O_O _ t_ _

• ) r_

.,,t.,rt()(,(_( ()f ( (,,,

t4t_ r4 el

• , ,,, ...... 0,, ,

,, 2':, ;'_:;,;' _,,,,...,'''I';, , , ' t¢ ,,_,

,:_:,:,:_e,r_r) rlr_¢)#_ _ ..<,:. ,,(.¢_r,:,c,,, ,., .o...o ... , • ......

.... ! I I I I # ' 'l I I I I I I I I

L--_ - ...... irll I -- lli _ t O0000000 O0 _ .--_ .-4

r-- m _ ,4. _ .4. u_ ,o coo t_ 000 O00 O00_ _*"_ .-0 _®_.o_o_ 00000000 _' _oo_ _o_ o

,- _.-_,0®o---Zo _

o U

o ' _,v"- ..... 5 .... ,

4_ Table 2. T_,mpcrature increment as a function of geomagn,,tic indices.

AT AT K a (d,' g. ) K a (deg.) P P P P

00 0 0 5- 39 134

O+ 2 9 5 48 145 0 i - 3 1 9 5_ 56 156

+ 4 28 6- 67 167 "' 0 l+ 5 37 6 80 180 0

2 - 6 47 6+ 94 l 94

20 7 56 7- Ill 210

2+ 9 66 70 132 229

3- 12 7!5 7+ 154 251

30 15 85 8- 179 279

3+ 18 94 8 207 313 0

4- 22 l 04 8+ 236 358

4 0 27 114 9- 300 417

4+ 32 124 90 400 495

49 Table 3. Temperature corrections 5T for the semiannual variation, computed from equation (23),Sfor F10" 7 = 100.

Date AT Date AT S s

Jan. 1 --1176 July 9 -43?6

11 -15.6 19 -47.9

21 -15.4 29 -50. I

31 -i I. 9 Aug. 8 -48.8

Feb. 10 - 6. 5 18 -42. 9

20 + 0. I 28 -31.9

March 2 + 7. 8 Sept. 7 -16.4

12 +16.2 17 + 1.7

22 +23.5 27 +19.7

April l +Z7. 5 Oct. 7 +34.9

iI 426. 7 17 +45. 1

Zl +21. l 27 +49. 0

May l +i 2.5 Nov. 6 +46.7

II + 2.7 16 +39.2

21 - 7. 1 26 +Z8.0

31 -16. 0 Dec. 6 +15. l

June 1 0 -Z4. l 16 + 2.5

20 -3]. 3 Z6 - 7.7

30 -37. 8

The actual correction is AT = -- 6T s 100 s"

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I[)_ o. 1.33 160 o. 060 260 O. 001

I IO o. 163 170 0. 044 280 0. 001

II_ 0. 162 18o 0. o31 300 O. 000

120 O. 156 190 O. 022

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Day P Day P Day P Day

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11 t0.048 11 q:0. Z97 July 10 :g0.961 Oct. 8 t o. 255

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_7 BIOGRAPHICAL NOTE

LUIGI G, JACCHIA received his doctorate fr,)m the University of

Bologna in 1932. He continued working with the university as an astronomer at its observatory.

Dr. Jacchia's affiliation with Harvard College Observatory began with his appointment as research associate in 19_. At that time he was studying variable stars. Since joining SAO as a physicist in 1956, most of Dr.

Jacchia's work has been on meteors and upper atmospheric research.