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https://ntrs.nasa.gov/search.jsp?R=19730008785 2018-03-30T17:48:15+00:00Z

X-621-73-37

EMPIRICAL MODEL OF GLOBAL THERMOSPHERIC TEMPERATURE

AND COMPOSITION BASED ON DATA FROM

THE OGO-6 QUADRUPOLE MASS SPECTROMETER

A.E. Hedin

H.G. Mayr

C.A. Reber

N.W. Spencer

Goddard Space Flight Center, Greenbelt, Md.

and

G.R. Carignan

Space Physics Research Laboratory

University of Michigan, Ann Arbor, Michigan

December 1972

Goddard Space Flight CenterGreenbelt, Maryland

f

PCmG PAGE IBLAN NOT FL

EMPIRICAL MODEL OF GLOBAL THERMOSPHERIC TEMPERATURE

AND COMPOSITION BASED ON DATA FROM

THE OGO-6 QUADRUPOLE MASS SPECTROMETER

ABSTRACT

An empirical global model for magnetically quiet conditions has been

derived from longitudinally averaged N2 , O, and He densities by means of

an expansion in spherical harmonics. The data were obtained by the

OGO-6 neutral mass spectrometer and cover'the altitude range 400 to

600 km for the period 27 June 1969 to 13 May 1971. The accuracy of the

analytical description is of the order of the experimental error for He and

O and about three times experimental error for N2, thus providing a reason-

able overall representation of the satellite observations. Two model

schemes are used: one representing densities extrapolated to 450 km and

one representing densities extrapolated to 120 km with exospheric temperatures

inferred from N2 densities. Using the best fit model parameters the global

thermospheric structure is presented in the form of a number of contour plots.

Preceding page blank

iii

EMPIRICAL MODEL OF GLOBAL THERMOSPHERIC TEMPERATURE

AND COMPOSITION BASED ON DATA FROM

THE OGO-6 QUADRUPOLE MASS SPECTROMETER

I. INTRODUCTION

This report presents a global thermosphere model for quiet magnetic con-

ditions based on in situ measurements of N 2 , 0, and He obtained with the neutral

particle quadrupole mass spectrometer [Carignan and Pinkus, 1968] carried

aboard the OGO-6 satellite. The satellite was launched June 5, 1969 into an 820

inclination orbit with a 398 km perigee and 1100 km apogee and was operated until

July, 1971. The reduction of the raw data to ambient densities makes use of the usual

thermal transpiration equation in a moving coordinate system [Schultz et al., 1948;

Horowitz and LaGow, 1957] and further includes corrections to the N2 densities

as a result of CO contributions to the mass 28 peak, and corrections to atomic

oxygen densities as a result of oxygen surface adsorption, recombination, and

desorption [Hedin et al., 1972a]. For each gas species a density value is

determined every 9 seconds.

The uncertainty in N 2 and O densities as a result of noise in the data is

always about 2% to 4%, but for He the uncertainty varies greatly (depending on

the exact conditions) because of the generally low signal to noise ratio. Near

perigee the uncertainty in density due to possible systematic errors in back-

ground subtraction and gas-surface interaction corrections is generally about

2% for N 2 and 6% for O (although it can be several times larger under very low

1

density conditions). These systematic errors increase with altitude, particularly

above 500 km. No densities are used for which the total uncertainty (random

and systematic) is estimated to exceed 25% for N2 and O and 50% for He. In

addition there is a laboratory calibration uncertainty of 10% to 15%.

The model described here is a more recent version of a model presented

byHedin et al. [1972b] at COSPAR. The principal changes are inclusion of: 8

hour local time components in the model formula; data from days with slightly

higher magnetic activity; and data from the second year of satellite operation.

The model is intended to provide in concise form as accurate a representation of

the thousands of measured ambient densities as possible. At the same time, the

model reveals many features, both familiar and novel, in the global distribution

of the various gases which are inherent in the data but would not otherwise be

easily seen.

2

II. DATA SELECTION AND COVERAGE

To eliminate strong magnetic activity effects data are selected

from days which have a daily magnetic index, Ap, of 7 or less and a 3 hour

magnetic index, ap, less than 12 for that day and 6 hours earlier. The quiet days

which have at least 8 orbits of good data reasonably distributed throughout the

day are listed in Table 1. All the data obtained on a given day are grouped into

5° latitude bands (distinguishing also between data taken on north or south bound

passes since these represent drastically different local times) and averaged over

a 24 hour (universal time) period. All averages used in the model are based

upon at least 20 density points. The averaging procedure eliminates

longitudinal/UT effects [Hedin and Reber, 1972] in the data and reduces the

amount of data handled, but does not eliminate local time effects since the orbit

plane changes quite slowly with respect to the sun (2°/day).

For He there is a special data selection problem because it is observed

that data from the second year of operation frequently differ by large factors

from a model using first year data only. Raw data obtained during these periods

are observed to fluctuate erratically in magnitude and the peak shape is not

normal. Thus, an iterative procedure is used in fitting the data in which density

points which differ from the model by more than a factor of two are eliminated

and the remaining points refit.

The latitude and local time coverage of the data can be seen in Figures 1

and 2. In one year the latitude of perigee made three cycles around the globe

3

and (effectively) five diurnal cycles. Values of the mean (taken over three solar

rotations) F 0o 7 flux vary from 108 to 168 with an overall average near 150.

Departures of the daily F 1 0 7 flux from the mean vary from -40 to +60. The

overall average Ap value is 4. The number of days with good data available in the

second year of operation is much less than in the first year because of telemetry

and spacecraft problems.

4

III. MODEL FORMULA AND DATA FITTING

A. 450 km Densities

The composition is described in terms of density variations at 450 kin, with

an altitude dependence which assumes isothermal conditions (above 400 km) at

any given time and location. Using a least squares technique, the average density

data are fit with the following formula based on a spherical harmonic expansion

(in geographic latitude-local time coordinates):

(L) Mg (z - 450) (Re + 450) (1)n (z, L) = n (450) exp G (L) - 1] -exp R T. (L) (Re + z)

where

n = number density of a particular gas species [cm-3]

z = altitude (km)

L = variable representing the geographical and geophysical parameters

on which it is assumed density depends

M = molecular weight (gm/mole)

Re = radius of the earth (6356.77 km)

g = acceleration of gravity (8.5529 x 10 - 3 km/sec2 at 450 km)

R = gas constant (8.314 x 10 - 3 gm-km2 /mole-sec2-deg)

TO = exospheric temperature (°K)

G = spherical harmonic expansion as described in text

5

The function G (L) contains the basic information on the variation of densitywith

selected geographic and solar activity parameters and is given in general as:

co

G (L) = 1 + a ° (td, F1 7 Ap) Pn (0) (2)T. n d' F10.7' Ap) pOn (0)n=1

n

-am (td, F 0 7 ,Ap) P (0) cos (m w T)

1T(dF 0 ,A)P m (0) sin (m 10.7 n

n=1 rnm=1

where

am = parameters of the spherical harmonic expansionn

which are assumed to vary with day of the year

(td), solar flux (F1 0o 7) and magnetic activity (AP)

Pm = Legendre polynomials (not normalized)

0 = colatitude

= angular rate of earth rotation

= local solar time

The merit of an empirical model based on a spherical harmonic analysis

is that these functions form a complete set which can, in principle, represent

any degree of complexity in the data by systematically increasing the number of

coefficients used. Furthermore, the spherical harmonics are approximate

eigenfunctions in the thermosphere so that relatively few terms should be re-

quired, and analysis in terms of these components may aid in understanding the

origin of various thermospheric variations [ Reber, 1971; Mayr and Volland, 1971;

Volland and Mayr, 1972; Reber and Hays, 19721.

6

The specific expansion of Equation 2 used to fit the data for the current model

is as follows:

G= 1

(time independent) + a2 0 P2 0 + a4 0 P4 0

(primary F1 0 7 effect) + F0

(magnetic activity) + (ka + k 0 P20) A A

(symmetrical annual) + (coo + Ck0 P2 0) cos (td- to)

(symmetrical semiannual) +(c + P20 ) cos 2 (td - t2)

(asymmetrical annual) + (c1 Po + c30 P3 0 + c0 Po)(1 +F-1 )cos ( tdtC)

(asymmetrical semiannual)+c2o Plo cos 2 £(td - t c2)

(diurnal) + [a 1 1Pl+ a3 1 P3 1

+ a 5 1P

5 1

+ c1 1 P 1 1 c21 P2 1 ) cOS (td- tl)] (1 + F1 ) cos W

+ [bll Pll + b3 1 P3 1 + b5 1 P5 1

±(d1lP1 1 + + 1 P 2 1) cos £ (td - tCl)] (1 + F1 ) sint

(semidiurnal) + [a222 222 + c 2 P

3 2 cos Q (td - tco)] (1 + F1 ) cos 2WcT

+ [b22 P22 + d2 P32 cos (t d - tco) ] (l + F1) sin2 WT

(terdiurnal) + a3 3 P3 3 (1 +F) cos 3 o'

+ b33 P.3 (1 +F 1 ) sin 3 w 7(3)

7

where

Pm pm (cos.O)nm (COS

F0 fal A F + f 2 (A F)2 + fa A F

F1 = f1 F

AF=F 10. 7 -Flo7

A F = F10.7 - 150.

A = Ap -4.

F1 0

.7 = 10.7 cm flux one day earlier (10-22 watt - m 2 - cps-

)

F10. = 3 solar rotation average of F 10.7

Ap= 24 hour average of magnetic index, ap, with a six hour lag

= 2 77/365 (days- 1)

= 2n /24(hrs-')

td= daycount (days)

= local solar time (hrs)

The significance of the various terms in Equation 3 is indicated briefly in paren-

thesis at the left. The expansion includes local time independent, diurnal, semi-

diurnal, and terdiurnal terms plus terms representing the annual, semiannual,

solar flux, and magnetic activity variations. For convenience, terms higher than the

eight hour local time harmonic are not included. However, it has been shown that the

firstthree harmonics are sufficient to fit incoherent scatter data reasonably well

8

[Salah and Evans, 1972]. The form of the Flo0 7 correlation used is similar to

that of Jacchia [1971] except that allowance is made for a possible non-

linearity in the correlation with the 27 day Flo 7 variation as suggested by in-

coherent scatter data [Waldteufel and Cogger, 1971]. Following Jacchia it is

also assumed that changes in the diurnal and annual temperature amplitudes

resulting from F 107 variations are strictly proportional to the changes in mean

temperature, but the same assumption is not necessarily true for thermospheric

densities which depend strongly and nonlinearly on temperature through the

hydrostatic equation. Thus it is necessary to introduce the parameter fl when

determining the 450 km densities for N2 and O (fl did not differ significantly

fromunityfor He). When determining exospheric temperatures and 120 km den-

sities, as described in the next section, f1 is assumed to equal one. The cor-

relation with Ap is assumed to be linear, as the range of Ap included in this

quiet time model is quite small. While the Ap used in the fitting is a daily

average based on a six hour lag as adopted in the Jacchia models,

the difference in calculating densities using the normal daily Ap is insignificant.

The possibility of a latitude variation of the magnetic activity effect was included.

Combining Equations 1 and 3 there are 37 unknown parameters to be determined

by fitting the data.

The temperature (T.) needed in Equation 1 is determined from the N2 data

in a manner to be described below, but is not critical to determining 450 km

densities since this altitude is near the average altitude of the measurements.

9

Tests were made using both temperatures from Jacchia [19651 and a constant

temperature to verify that the 450 km density determination is relatively in-

sensitive to the exospheric temperature.

B. Inferred Exospheric Temperatures and 120 km Densities

Adopting a method analogous to that employed by Jacchia [19651], the tem-

perature and N2 density are fixed at 120 km and the exospheric temperature

necessary to calculate the measured densities is then determined using analytic

density profiles suggested by Walker [1965] based on a temperature profile

suggested by Bates [1959]:

T (z, L) = To (L) - (Too (L) - T1 2 0 ) exp [- s (z - 120)] (4)

n (z, L) =n (120) D (z, T. (L), s) (5)

1-a . +,+D (z, To (L), s) = { aexp [-o- y (6)

1 - a e-ef

where

- = s + .00015

a=1-T o /T120 (L)

(z - 120) (RE + 120)/(R + )

y = M g /(a-RT. (L))

T, (L) = T G (L)

T120 = temperature at 120 km (3550 K)

10

s = temperature gradient parameter

ge = acceleration of gravity at 120 km (9.44663 x 10-3 km/sec2 )

T. = average exospheric temperature

The temperature calculation is based on the N2 density, rather than O or

He, because this species is probably most nearly in diffusive equilibrium [Reber, 1971;

Mayr and Volland, 1971; Mayr and Volland, 1972a] when dynamical processes

are considered. In addition, variations in the eddy diffusion will have the least

effect on the nitrogen concentration because its molecular weight is approximately

the mean molecular weight at the turbopause. However, the average temperature

(T.) needed to fit the measurements is not arbitrary, because the measurements

are made at different altitudes, and there is an average temperature which will

best fit the density data. The capability of determining an average temperature

independent of the 120 km boundary conditions was maintained by allowing the 's'

parameter to be determined by the least squares fit. Combining Equations 3, 5,

and 6 there are 37 unknown parameters to be determined by fitting the nitrogen

data, including T., s, and the parameters in function G.

It would be possible in principle to determine independently the global

temperature distribution from scale height information alone and a preliminary

attempt indicated that results would be in rough agreement with the temperature

distribution obtained using the diffusive equilibrium model of Equation 5. How-

ever, the uncertainty limits were so large that it was doubtful that useful addi-

tional temperature variation information could be obtained from the scale height.

11

Using the temperatures inferred from the nitrogen data, the average den-

sities and variations at 120 km needed to reproduce the measurements of O and

He are determined by using a slight modification of Equation 5:

n (z, L) = n (120) D (z, T. (L), s) exp [G (L) - 1] (7)

where the density variations are again introduced through the G function of

Equation 3. There are 36 unknown parameters to be determined including

n (120).

It should be noted that the 450 km density model and the diffusive

equilibrium model starting at 120 km can (in principle) represent the measured

densities equally well, as the model parameters are determined independently

by fitting the measured data. However, the inferred exospheric temperature

and absolute densities at 120 km are dependent on the existence of diffusive

equilibrium and the assumed boundary conditions. The variations in com-

position at 120 km are, nevertheless, a convenient way of illustrating departure

from fixed boundary diffusive-equilibrium models; moreover, density ratios

inferred at 120 km are less dependent on errors in exospheric and boundary

temperatures than are the absolute densities at 120 km.

12

IV. MODEL PARAMETER RESULTS AND ACCURACY

The model parameters for N2 , O, and He densities at 450 km are given in

Table 2 and those for O and He densities at 120 km and exospheric temperatures

in Table 3. Also given are the estimated standard deviations for the parameters

and a parameter indicating the overall quality of the fit:

n - ]n 1/2

Qf = '" .(N d - Np) (8)

where

n. = i th measured densitym

ni = th1 calculated densityC

0-i = estimated measurement errorm

Nd = number of data points

Np = number of parameters

The least squares fits are carried out using about 1000 data points randomly

selected from a data base about twice as large.

The temperature at 120 km is fixed at 3550K and the N2 density at 120 km

is chosen to provide an N2 density at 150 km very close to that recommended

by Van Zahn [1970] and used by Jacchia [1971]. The inferred average O to N2

density ratio at 150 km turns out to be about 72% of that recommended by Von

Zahn. However, in light of the errors in the various measurement methods,

the variability of the densities, the assumptions used. in extrapolating the

13

satellite measurements, and the possible error in the assumed 120 km tempera-

ture, this small disagreement in the oxygen to nitrogen ratio is not significant.

A total assessment of various measurements in the lower thermosphere and

their consistency with the upper thermosphere measurements is not attempted

in this model.

The quality of the model fits to the data is examined by using the coefficients

from Table 3 and plotting the measured to calculated density ratios as a function

of time from perigee, latitude, local time, solar flux, Ap, and day-count, as

shown in Figures 3 to 5. In Figures 6 to 8 the residuals are represented by

symbols in a latitude versus local time plot. In general, there are no large syste-

matic differences in the fit. Examination of the plots of measured to calculated

density ratios versus time from perigee indicates that the density data have been

reasonably corrected for gas-surface interactions. The generally good fit does

not necessarily mean that all significant terms have been found, particularly

when interactions between variables are considered. For example, Figures 6

to 8 show that while the overall distribution of points in latitude-local time space

is good, the same is not true at all seasons. The data coverage for N2 and O is

much better during summer than winter and the converse is true for helium.

This will reduce the reliability of the model in winter for N2 and 0, in the

summer for He, and of the seasonal interaction terms.

14

The question of the validity of individual and-combinations of parameters,

and thus the proper decomposition into the various components, is very difficult

to answer completely. In general, one can say that since latitude profiles are

the basic data input to the model, the model should predict latitude profiles with

the most accuracy. While local time variations are basically derived from data

on many different days, the lack of systematic residuals as a function of local

time indicates that these variations should be reasonably well represented on

average but not necessarily in their seasonal variations. The least reliable

coefficients are expected to be those connected with the symmetrical annual and

the symmetrical and asymmetrical semiannual components since the data base

is not long compared to these cycles. There is also the possible confusion of

true annual and semiannual components with these frequencies in the mean F10 7

variation. While the standard deviations calculated for each coefficient give

some guidance, they cannot completely account for a lack of uniform data

sampling in all coordinates.

The possibility of changes in the model coefficients from year to year was

examined by dividing the data into two samples and fitting separately. The re-

sults for the temperature coefficients are given in Table 4. As expected, the

coefficients relating to the semiannual and symmetrical annual components have

changed the most, while the majority are quite stable.

15

The probable accuracy of the inferred average temperature was tested by

arbitrarily changing the average temperature by 500 K and 100°K and refitting

N2 density for the remaining coefficients. The change in Qf (Equation 8) and the

density ratio versus time from perigee plot indicated that a 500 K change would not

be entirely unreasonable, but that a 100°K change produced fairly marked devia-

tions from the best fit. Another consideration is that if the highest altitude den-

sities (about three scale heights above perigee) have a systematic error of 25%,

this would roughly translate to a 800K error. A test fit of oxygen density leav-

ing T. as a free parameter produced a temperature about 500 higher than from

the nitrogen data. Because there is some difference between exo-

spheric temperature and the temperature near 450 km, the inferred exospheric

temperature does depend somewhat on the s parameter. If s were .025,

the inferred exospheric temperature would be 10° lower; and if s were .015, the

inferred exospheric temperature would be 40° higher. The best estimate is that

the average temperature is accurate to ±50 0 K.

The accuracy with which the inferred temperature variations represent real

temperature variations depends on the assumed constancy of the 120 km N2 density

and temperature. This assumption appears, however, to be a reasonable first

approximation that can be modified later to provide better agreement with other

measurements. A 10% variation in 120 km density would result in roughly a

1.5% error in exospheric temperature variations and a 10% variation in 120 km

temperature would result in roughly a 4% error in exospheric temperature

variations. A variation of N2 density during one day at 140 km on the order of

16

30% and temperature on the order of 20% was measured by Spencer et al. [1969]

in a series of rocket flights. Semidiurnal temperature amplitudes at 120 km on

the order of 10% have been reported by Salah and Evans [1972]. Theoretically,

Volland and Mayr 11970] predict a 120 km diurnal temperature amplitude of 5%

and a density amplitude of 10%. Seasonal variations in temperature at 120 km of

about 10%c have been reported by Waldteufel [1970], with a level of relatively

constant density at 130 km. Mayr and Volland [1972b] predict annual amplitudes

at 120 km of 8% in temperature and 20% in N2 density.

The accuracy of the inferred oxygen and helium variations at 120 km depends

on both the accuracy of the inferred temperature variations and the diffusive

equilibrium assumption. Because of mass motions it is expected theoretically

that there will be departures from diffusive equilibrium in the lower thermo-

sphere, particularly for minor constituents like helium.

17

V. GLOBAL THERMOSPHERIC STRUCTURE

The model coefficients given in Tables 2 and 3 can be used to predict at-

mospheric structure for various conditions. Predictions for altitudes, solar

activity conditions, etc., which are beyond the data base used in generating the

model must obviously be used with caution. A set of plots of exospheric temp-

erature, densities at 120 km, and densities at 450 km are presented in Figures

9 through 14. By use of the plots for the individual components of the model a

graphical solution for many situations can be constructed.

The OGO-6 model shows a number of departures from previous empirical

models based on total density measurements obtained from satellite drag [Jacchia,

1965; Jacchia, 1971]. Among these are the morning maximum

for He, the high latitude of the diurnal temperature bulge position for solstice con-

ditions, the seasonal variation of the O to N 2 density ratio with a 400°K summer

to winter temperature difference, and the 1600 hour maximum for N2 with an

extended bulge in latitude. These effects will be discussed in sep-

arate reports. The differences from drag models undoubtedly arise in part be-

cause composition and temperature cannot be uniquely determined from total

density measurements alone [Stein and Walker, 19651 and because of the

smoothing inherent in the method of determining the density from variations in

a satellite's orbit [Jacchia, 1971] .

The total densities predicted by the OGO-6 model are compared with those

of the J71 model [Jacchia, 1971] in Figure 15. The average density is 17%

18

higher than J71, certainly within the overall measurement error and limitations

of model predictions. The shape of the diurnal curve for 45° latitude is in quite

good agreement with J71 and the equatorial curve is in fair agreement, although

the OGO-6 model has a slightly later afternoon maximum. The seasonal vari-

ation compares well with J71, particularly north of -45° latitude.

Measurements of temperature [Salah and Evans, 1972] made during the

same time period as the OGO-6 measurements are compared in Figure 16. The

average OGO-6 inferred temperature is about 7% higher than the incoherent

scatter measurements. The annual variations are in quite good agreement and

are over twice those predicted by J71. The diurnal variations show quite good

agreement except for the early morning hours of winter, which is not too

surprising considering the lack of satellite data in this area (Figure 6).

19

VI. ACKNOWLEDGEMENTS

We are indebted to the many people in the Space Physics Research Labora-

tory of the University of Michigan, particularly W. H. Pinkus and D. R. Taeusch,

and in the Laboratory for Planetary Atmospheres of the Goddard Space Flight

Center, particularly D. N. Harpold and J. E. Cooley, who contributed to the

success of this experiment.

20

REFERENCES

Bates, D. R., Some problems concerning the terrestrial atmosphere above about

the 100 km level, Proc. Roy. Soc. London, A253, 451-462, 1959.

Carignan, G. R. and W. H. Pinkus, OGO-F04 experiment description, University

of Michigan Technical Note 08041-3-T, 1968.

Hedin, A. E., B. B. Hinton, and G. A. Schmitt, Role of Gas Surface Interactions

in the reduction of OGO-6 neutral gas particle mass spectrometer data,

NASA X-621-72-90, 1972a.

Hedin, A. E., H. G. Mayr, C. A. Reber, G. R. Carignan, and N. W. Spencer, A

global empirical model of thermospheric composition based on OGO-6 mass

spectrometer measurements, presented at the XV meeting of COSPAR,

Madrid, Spain, 1972b.

Hedin, A. E. and C. A. Reber, Longitudinal variations of thermospheric compo-

sition indicating magnetic control of polar heat input, J. Geophys. Res., 77,

2871-2879, 1972.

Horowitz, R. and H. E. LaGow, Upper air pressure and density measurements

from 90 to 220 km with the Viking 7 rocket, J. Geophys. Res. 62, 57-78,

1957.

Jacchia, L. G., Static diffusion models of the upper atmosphere with empirical

temperature profiles, Smithson. Contr. Astrophys., 8, 215, 1965.

Jacchia, L. G., Revised static models of the thermosphere and exosphere with

empirical temperature profiles, Smithsonian, Astrophys. Ob. Special

Report 332, 1971.

21

Mayr, H. G. and H. Volland, Semiannual variations in the neutral composition,

Ann. Geophys., 27, 513-522, 1971.

Mayr, H. G. and H. Volland, Diffusion model for the phase delay between

thermospheric density and temperature, J. Geophys. Res., 77, 2359-2367, 1972a.

Mayr, H. G. and H. Volland, Theoretical model for the latitude dependence of

the thermospheric annual and semiannual variations, J. Geophys. Res., 77,

1972b.

Reber, Carl A., Thermospheric wind effects on the global distribution of helium

in the earth's upper atmosphere, NASA X-621-71-480, 1971.

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of minor gases in the earth's upper atmosphere, submitted for publication

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Salah, J. E. and J. V. Evans, Measurements of thermospheric temperature by

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Spain, 1972.

Schultz, F. V., N. W. Spencer and A. Reifman, Atmospheric pressure and

temperature measurements between altitudes of 40 and 110 km, University

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temperature and density variations with increasing solar activity, Space

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22

Stein, J. A. and J. C. G. Walker, Models of the upper atmosphere for a wide

range of boundary conditions, J. Atmos. Sci., 22; 11, 1965.

Volland, H. and H. G. Mayr, A theory of the diurnal variations of the thermosphere,

Ann. Geophys., 26, 907, 1970.

Volland, H. and H. G. Mayr, A three dimensional model of thermospheric dy-

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1768, 1972.

von Zahn, U., Neutral air density and composition at 150 km, J. Geophys. Res.,

75, 5517, 1970.

Waldteufel, P., A study of seasonal changes in the lower thermosphere and their

implications, Planet. Space Sci., 18, 741-748, 1970.

Waldteufel, P. and L. Cogger, Measurements of the neutral temperature at Arecibo,

J. Geophys. Res., 76, 5322-5336, 1971.

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based on Jacchia's static diffusion models, J. Atmos. Scio., 22, 462, 1965.

23

MAR MAY JULY SEPT NOV JAN MAR M1970 1 1971

Figure 1. Geographic latitude coverageof available N2, 0, and Hedensity data as a function ofday.

ilAY

24

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Figure 2. Local time coverage of available N2,

1Y~ 0, and He density data as a function12 of day.

S II I

25

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Figure 3. Ratio of the measured N2 density to the model N2 density as a function of time fromperigee, geographic latitude, local ti me, F10.7 solar flux, magnetic index Apand dayof year.

26

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Figure 4. Ratio of the measured O density to the model O densityplotted in the same format as Figure 3.

27

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28

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30

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OGO-6

Cz 1z 7ll

10 - 91--

-90 -60 -30 0 30 60 90

LATITUDE (deg)

Figure 15a. Diurnally averaged total mass density at 450 km as a function of latitude forsolstice conditions (summer at right) for the Jacchia Model (J71) and the

OGO-6 empirical model.

56

5x10-15"- N Q-"..OGO-6

-LATITUDE 0 °

mode ~ 101.71E" -,-

0

E

5x10-15

LATITUDE 45 OGO-6

0 4 8 12 16 20 24LOCAL TIME (hrs)

Figure 15b. Total mass density at 450 km as a function of local time at equinox forlatitudes 00 and 450 for the Jacchia model (J71) and the OGO-6 empiricalmodel.

57

* INCOHERENT SCATTERxOGO-6 EMPIRICAL MODEL

- 1200 x x x x xr,- XX X

XX XXX· X

1100 -. ' · x x X

* x

900 .

800 I

1969 1970 1971

Figure 16a. Diurnally averaged exospheric temperature as a function ofday for incoherent scatter measurements [Salahand Evans,1972] and the OGO-6 empirical model.1972] and the aGO-6 empirical model°

58

120oo0 ' It28-29 SEPT 1970

/ 1100 -

< 1000a~.

1-

1200a 23-24 MAR 1970

1006 20 24

T 1000

scatter measurements [Salah and Evans, 1972] and the

90 o - .'

0 4 8 12 16 20 24

LOCAL TIME (hrs.)

Figure 16b. Diurnal variation of exospheric temperature for incoherent

scatter measurements ISaiah and Evans, 1972] and theOGO-6 empirical model.

59

I

Table 1. Quiet Days with Available OGO-6 Data

1969 19701.1 1 Il

244245246247255256265269281288289293296302303304305309317318319320321322327328329337342346351352353354355

362363364365

4567

11131415182223242526272829384041424344515254707173747576777879808182

8384

.8592

102103104118127128129130131136138139142146156157160161162163173174175176180181196197200214215216217232

from Jan 1

60

234236280282288294308336343350357

1971

626

1 129

133

178*179180181185186187188189190191192199200201202203204205206210213214218223226227228233234236237240241242243

*Daycount

L

Table 2. Model Coefficients and Errors for450 km Densities

N2 He O

-3.23254E-2 ± 2.4E-22.58195E-1 ± 2.5E-2

9.57068E-3-5.93446E-5

2.59132E-2-1.92310E-1

5.0E-41.6E-51.5E-33.1E-2

2.76819E-2 4.1E-33.32960E-2 6.9E-3

2.15307E-18.45427E-2

-1.19494E+3

2.66389E-12.64229E-17.87142E-1

-1.55170E+0-3.43730E-1

1.67800E-1-5.96942E+0

-9.17841E-22.11428 E+2

-8.06862E-1-7.73657E-2

4.29883E-2-4.91628 E-2-1.62804E-2-8.67463E-1-2.13267E-22.98442E-2

-1.56457E-1-1.52550E-1

1.95106E-22.93628E-21.97074E-21.20904E-2

2.2E-23.1 E-28.OE+0

2.3E-24.1E-21.3E+0

3.9E-23.2E-22.4E-29.1E-1

3.9 E-21.7E+1

3.1E-28.9E-35.7E-34.8E-21.8E-22.5E-29.7E-34.4E-32.4E-21.8 E-2

8.2E-34.6E-37.9E-33.9E-3

1.29388E-2 1.1E-38.06962E-3 1.5E-3

2.16257E+6 5.1E+4

3.14984

4.44944E-2 ±- 3.8E-21.22096E-2 3.4E-2

2.06281 E-4-1.02533E-5-3.22334E-3

1.0

-9.24999E-4-4.90310E-2

3.36485E-1-1.21895E-1

4.16855E+1

4.70517E-1-1.67892E-1

1.02749E+2

1.28528 E+O1.43196E-1

-1.86156 E-1-5.19632E+ 0

2.13583E-1-4.25969E+1

-4.23383E-15.24724E-3

-3.37164E-22.79221E-13.74919E-22.82148E-14.75225E-2

-2.96619E-23.85313E-22.15832E-2

4.30024E-22.70815E-3

-3.75753E-2-2.62367E-3

1.8 E-46.9E-66.9E-4

4.0E-36.9 E-3

2.1E-22.6 E-23.4E +0

2.1E-23.0E-21.1E+0

6.1E-25.3 E-23.8 E-21.1E+O

2.3 E-22.5E+0

2.5E-21.0E-24.0 E-33.8E-22.6 E-22.7E-21.2E-25.8E-34.3E-23.9E-2

8.0E-36.3 E-37.7E-34.6E-3

1.81657E-3 1.2E-32.94319E-3 1.4E-3

3.02168E+6 7.0E+4

0.82871

-1.20421E-1 ± 1.3E-27.53022E-3 1.2E-2

6.42065E-3-4.97163E-51.50364E-21.10527E-1

2.0E-47.5E-66.0E-47.6E-2

1.35510E-2 2.6E-3-7.96150E-3 4.9E-3

7.18792E-2-1.11102E-3

1.55526E+1

2.00090E-16.15261E-28.65226E+1

-2.73134E-1-4.95760E-2-2.06922E-3

1.22284E+1

1.5E-21.7E-28.0E+O

1.2E-21.9E-21.4E+O

1.7E-21.8E-21.6E-23.0E+0

-1.88087E-1 1.4E-22.58183E+1 3.2E+0

-4.44144E-1-2.24184E-26.15071E-3

-1.12828E-1-3.20213E-3-4.15266E-1-9.85268E-3

1.40306 E-3-4.50245E-2

2.97480E-3

1.05858E-21.15912E-29.61430E-37.82691 E-3

1.6E-25.2E-33.3E-32.5E-29.1E-31.2E-25.1 E-33.1E-31.5E-28.8E-3

4.8E-32.6E-34.1 E-32.5E-3

1.92377E-3 6.8E-42.32258E-3 8.OE-4

6.71664E+7 7.0E+5

1.08905

61

a 2 0

a 4 0

f a

00fs2

falfoof

1

k oo2

COO

tal

00

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1 o0

2

Cotcl

Io 10

c2

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a31

as 1

ciiCll11

b11b 31

b 5 l

d11dl

21

a 2 2

C( 1

32b 22dl

32

b33a

33

n(450)

QfNd

Table 3. Model Coefficients and Errors for InferredExospheric Temperatures and 120 km Densities

Temperature He O

1.09746E+3 + 1.1E+1

2o23450E-3 3.2E-32.86450E-2 3.1E-3

1.07969E-3-5.11469E-6

2.67456 E-31.0

5.3E-51.9E-69.8 E-5

4.43908E-3 5.6E-45.82154E-3 9.8E-4

2.09161E-21.82185E-3

-7.90147E+1

2.89788E-21.68314E-28.20221E+1

-1.75059E-1-4.55491E-2

1.78577E-2-7.74545E+0

-7.87872E-34.62196E+1

-1.00212E-1-7.99562E-3

4.12455E-31.01873E-35.84192E-3

-1.04346E-1-3.29270E-3

4.21772E-3-1.87679E-2-1.15860 E-2

-5.41524E-42.58162E-35.70467E-31.04937E-3

2.5E-33.8E-31.OE+1

3.0E-34.7E-32.0E+0

4.8 E-33.8E-33.3E-31.OE +O

5.2E-31.8E+1

3.9E-31.1E-37.4E-46.8E-32.1E-33.0 E-31.2E-36.3E-43.6 E-32.1E-3

1.1E-36.1E-41.0E-35.1 E-4

1.71030E-3 1.5E-41.08499E-3 1.8E-4

2.15093E-23.0 E +113.05984

1.1E-3

3.60004E-2 + 3.8E-2-1.26407E-2 3.5E-2

-2.86349E-4-6.94359E-6

-4.47270E-31.0

-4.98860E-3-5.32688E-2

-3.43574E-11.17012E-1

-1.39608E+2

4.47150E-1-1.85922E-1

1.03883E+2

1.43740 E-01.76714E-1

-2.02116E-1-6.06371E+0

1.7E-46.6 E-67.1 E-4

4.0 E-36.9E-3

2.1 E-22.6E-23.4E +0

2.0E-23.0E-21.1E+O

6.1 E-25.3E-23.8E-21.OE +0

1.98688E-1 2.3E-2-4.18924E+1 2.8E +0

-3.67322E-17.02718E-3

-3.60443E-22.75532E-15.90788E-23.55576E-15.00220E-2

-3.32297E-26.56431E-23.88636E-2

3.73572E-29.67275E-4

-4.09051E-2-2.32445E-3

2.5E-21.0 E-24.0E-33.8E-22.6E-22.7E-21.2E-25.8E-34.3E-23.9E-2

8.1 E-36.4E-37.8E-34.6 E-3

6.91634E-4 1.2E-32.00630E-3 1.4E-3

2.72880E+70.82872

6.3E+5

-9.75916E-2 + 1.2E-2-9.79390E-2 1.2E-2

1.89483E-3-2.58559E-5

3.65676E-31.0

-5.48307E-3-2.50150E-2

1.21477E-15.13802E-25.860 78E+1

8.59177E-2-6.06341 E-2

9.81965E+1

4.91391 E-11.42440 E-1

-1.29622E-1-1.76764E+1

-1.82094E-12.53553E+1

-3.24214E-21.09767E-2

-1.25240E-2-4.67511 E-2

2.00992E-34.65936E-2

-2.49572E-3-2.03136 E-2

2.03699E-27.94588 E- 2

3.29472E-31.03342E-2

-4.27613E-31.63277E-3

-4.84872E-3-8.24512E-4

8.97076 E+ 101.05905

2.1E-47.4E-66.5E-4

2.5E-34.8E-3

1.2E-21.7E-25.4E +0

1.1E-21.7E-23.2E-0

1.9E-21.9E-21.6 E-21.3E+C

1.4E-23.OE+O

1.3E-24.6E-33.2E-32.2E-28.5 E-31.3E-25.2E-33.0 E-31.5E-29.3E-3

4.6 E-33.0 E-33.8E-32.2E-3

6.8 E-47.6E-4

9.OE+8

62

a 2 0

a 4o

fo1'00

fa200

fa100

f,

20

tcl00

Co2oco0

c2

00

CI

30C 10

C210

tC2t0

a

a 3 1

as 1

Cl11C2 1

bl

b5

1

blid,1

a 2 2

c32

b22d 232

b33

a33

Sn(120)

QfNd

Table 4. Model Coefficients for Inferred Exospheric TemperatureBased on Different Time Periods

-1.09877E-3 ± 3.5E-1-1.11568E-3 ± 1.1E-1

n(120) -1.11568E-3 ± 1.1E-1 -1.09877E-3 ± 3.5E-1

27 June 1969 29 June 1970to to

4 Aug 1970 13 May 1971

1.11568E+34.55397E-32.59769E-2

1.12636 E-3-6.14146E-61.81034E-3

± 1.1E+13.5E-32.7E-3

4.3E-51.6 E-64.7E-4

3.67972E-3 5.7E-44.91533E-3 1.1E-3

2.34466E-2 6.0E-36.21293E-3 4.5E-3

-6.97931E+1 1.2E+1

2.65288E-2 3.2E-31.50036E-2 4.3E-39.69683E+1 3.2E+O

-1.63496E-1 5.4E-3-4.62570E-2 3.8E-3

1.68539E+2 3.1E-3-9.81137E+0 1.1E+0

3.84413E-3 1.OE-22.62201E+1 3.8E+3

-1.00840E-1-8.81511E-33.04996 E-3

-4.32113E-31.13675E-2

-9.75982E-2-4.06116E-33.07876F-3

-5.69528E-3-1.22704E-2

1.27142E-42.67250E-35.13250E-31.90120E-3

4.3E-31.0E-36.7E-47.5E-32.1E-33.0E-31.OE-35.5E-43.1 E-32.OE-3

1.2E-37.3 E-49.6E-44.5E-4

1.27724E-3 1.3E-41.09527E-3 1.8E-4

2.05681 E-23.0 E+112.38856

9.7E-4

1.09877E+3 ± 3.5E+1-8.71478E-3 4.1E-22.22340E-2 1.1E-2

1.46310E-3-2.34289E-52.90716 E-3

2.3E-47.6E-67.1E-4

1.64373E-3 6.9E-43.79008E-3 1.2E-3

-1.89772E-3-3.77918 E-2-2.37760E+0

-1.58230E-49.34394E-31.39853E+2

-1.42320E-1-5.52283E-21.38372E-2

-1.78368E+0

2.7E-23.0E-23.7E+1

2.1 E-23.7 E-21.6E+2

2.4E-21.8E-26.2E-33.5E+1

-3.51160E-2 2.5E-2-2.09545E+0 2.8E+1

-1.11487E-1-2.99367E-3

2.89507E-38.98341 E-32.61265E-2

-1.00533E-14.32731E-32.06197E-3

-2.59543E+2-1.46737E-3

1.40907E-34.23722E-35.51530E-32.16673E-3

2.1E-27.8E-31.5E-32.0E-28.1E-33.2E-23.9 E-31.3 E-33.2E-28.6E-3

8.0 E-32.4E-33.5E-32.3E-3

1.61326E-3 7.9E-42.23838E-3 8.6E-4

1.98619E-23.0 E+111.58173

3.8E-3

63

I U.S. GOVERNMENT PRINTING OFFICE: 1972-735-966/492

n(120)

T,a 20

40

f nlfn200

kookoo

kco

C201

cooC

c o20

C00

tC2Coo

C30c o

t cl

2CIO

t22b10

ail

a 3 l

a3SCas

21bi

b31b51dl di

aC2

32b

22

d32

b33

a33

S

n(120)

QfNd