A point of view on semi-empirical thermospheric models

Planet. Space Sri.. Vol. 31, No. 9, pp. 945-966, Printed in Great Britain.

1983

0032A3633/83 $3.00 + 0.00 Pergamon Press Ltd.

A POINT OF VIEW ON SEMI-EMPIRICAL THERMOSPHERIC MODELS F. EARLIER

CERGA/GRGS,

and C.

BERGER

Grasse, France

(Received 2 November

1982)

Abstract-Different types of models of the thermosphere, either with experimental characteristics or with theoretical characteristics, have been elaborated since the Space Age. These models describe the variation of different parameters (temperature, density, pressure, concentrations,. .).A briefdescription of these models is given. As far as theoretical models are concerned, the conservation equations ofenergy, ofmomentum or mass and physico
the other hand, a model can be very useful without being perfect. It has to be a clear conventional reference which gives a satisfactory mean of the behaviour of the thermosphere. It must be easy to use and also be a practical tool to test data or becompared with theoretical models to be developed. Finally,it has to permit one to solve partly some physical problems in assuming some parameters as known. Our opinion is that a new international experimental reference model based upon simplified physical concepts and upon new measured parameters should be very useful if an easily-accessible data bank is created at the same time.

INTRODUCTION

The launching of artificial satellites has made it possible to obtain a great deal of data from the upper atmosphere of the Earth, principally in the altitude range 200-1000 km. The first data gathered were total densities inferred from satellite drag. Other parameters were then measured: temperature, chemic&l composition, winds, turbulence. The variations of thermospheric parameters according to geographic and magnetic coordinates, season, epoch of the year, local time, solar and geomagnetic activity were rapidly identified and analysed. The objective of atmospheric research is to understand the mechanisms which govern the thermosphere and to study the interactions between other parts of the terrestrial environment, such as the mesosphere or the magnetosphere. This leads to the proposal ofphysical models capable ofreproducing the variations in the measured values. Such an objective is extremely ambitious and can only be reached step by Presented at the European Geophysical Society MeetingStructure of the Upper and Middle Atmosphere-Leeds. U.K., 23-27 August 1982, held in honour of Prof. Marcel Nicolet.

step and by successive approximations. The final solution is still distant. While waiting for an ideal model, it is necessary to utilize semi-empirical models based on relatively simplified physical concepts. Their purpose is to represent easily diverse parameters to describe the behaviour of the upper atmosphere before searching for an explanation of the physical processes. One of their applications is to permit the introduction, as known, of the parameters in the partial solution of the physical equations. This philosophy was the basis of the first models, notably those of Nicolet (1961, 1963). These models suppose that temperature and composition are fixed at 120 km(themost reasonable hypothesis possible at that time). Above this altitude, densities vary according to the theory of diffusion except for hydrogen, where equilibrium is obtained at higher altitudts (Kockarts and Nicolet, 1962, 1963). Thermal diffusion is taken into account for helium. The work of Harris and Priester (1962), in which more physical concepts were introduced, should also be mentioned. The hydrostatic equation and the heat conduction equation are integrated simultaneously with a varying heat source with a 24 h cycle. However, it is necessary to adopt a second heat sour& to represent the densities correctly;

946

F. BARLIER and C. BERCER

errors existing in the first models as 565. It became clear that any progress in the empirical representation required the lower boundary conditions to vary at 120 km and that it was necessary to model these variations or to assume conditions fixed at lower altitude (90 km, Jacchia, 1971). Today, in most cases, the temperature and concentration variations at 120 km are represented by expansions in terms of spherical harmonics, as proposed by Hedin et al. (1974). Another approach is the modelling of the variations of the turbopause height (Blum et al., 1978). The basic physics remains simplified (diffusive equilibrium). Some remarks upon more recent semi-empirical models are made in Table 1. Figure 1 presents the monthly mean of the 10.7 cm solar flux and the periods during which different satellites gathered data used in various models. It can be seen that each model is based on a limited set of data and consequently cannot represent with the same accuracy all existing geophysical conditions.

this was at the base of the international reference model (CIRA, 1965). For this reason, in 1965, Jacchia preferred to abandon the theory and to return to a more simplified physical concept. He constructed an empirical temperature profile to represent the measured values, mainly total densities, taking Nicolet’s models as a pattern. Such a semi-empirical model already gave a satisfactory representation of the variations of the parameters with the correct order of magnitude. At that time, the result was remarkable. Space does not permit us to develop the historical record of all the models which followed, nor of all the progresses made in our descriptive knowledge (the winter helium bulge, for example, Keating and Prior, 1968). But considering the large amount of groundbased or in situ satellite data deduced from mass spectrometer, accelerometer, optical techniques, incoherent scatter radar measurements, important progress was made in the descriptive knowledge of diverse parameters and in the elimination of systematic

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As for MSIS model As for M, model OGO

Barlier et al., 1978

Kohnlein,

Blum et al., 1978

Jacchia,

Laux and von Zahn,

Hedin et al., 1979

Thuillier et al., 1979

Stehle et al., 1982

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1980

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Satellite drag-mass

Neutral mass spectrometer on five satellites (AE-B, Ogo 6, San-Marco 3, Aeros A and AE-C) Incoherent scatter at 4 ground stations (Arecibo, Jicamarca, Millstone Hill and St. Santin) Ion mass spectrometer on AE-C satellite OGO 6 Fabry-Perot interferometer OGO 6 Fabry-Perot interferometer Incoherent scatter at 3 ground stations (Arecibo, Millstone Hill and St. Santin) Satellite drag M, Model Neutral and ion mass spectrometer, optical technique on 8 satellites (AE-C, AE-E, Aeros A, Aeros B, Ariel 3, Esro 4, OGO 6 and San Marco) Incoherent scatter at 4 ground stations (Arecibo, Jicamarca, Millstone Hill, St. Santin) OGO 6 and Esro 4 models

*All the models of this table, except 577, have this mathematical

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von Zahn et al., 1977

Data source mass spectrometer

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Authors

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Models

given by the models-remarks

constant

0, density at 120 km

scatter measurements

Long periodic variations of Ar-N,-O-He from T, and turbopause height variations T,-Ar-N,-O,-O-N-He-H Static model and in addition thermospheric variations Longitudinal effect appears by the introduction of magnetic latitude in the formalism of the geomagnetic activity effect Correction function depending on the geographic latitude and longitude Addition of spherical harmonic terms depending on geographic latitude, longitude and universal time Introduction of the magnetic latitude in the formalism of the geomagnetic activity effect O-He T, inferred from N, Analysis in magnetic latitude and magnetic local time coordinates

TW Ar-O,-N,-O-N-He-H

N,-O-He;

TC0 T,

0,-H

T, inferred from N, and incoherent

Expansion in terms of spherical harmonics* N,-O-He Altitude range 40&600 km T, inferred from N, Ar-N,-O-He Altitude range 240-320 km T, inferred from Ar and N2 Ar-N,-O-N-He at 4 and 16 h L.T. Altitude range 220 to 450 km T, inferred from N, N, from five satellites Ar-O-He from four satellites

Parameters

F. BARLIER and C. BERGER

948

Parallel to the development of semi-empirical models, a considerable effort has been made to calculate theoretical models by solving the physical equations which govern the thermosphere (see for example, Fuller-Rowe11 et al., 1980; Fontanari, 1981; Roble et al., 1982). But we shall not approach this subject. The goal of the current study is to inquire into the validity of the empirical representations and into the possibility and interest in considering certain phenomena today well described but not yet included and in improving the quality of the representation. Because this subject is in itself too vast, we have chosen to select a limited number of remarks that are important in reflections on the future of semi-empirical models. COMPARlSON

BETWEEN SEMI-EMPIRICAL

MODELS

AND WITH DATA

Several comparisons have already been made and the majority of authors have taken care to compare their models with others (von Zahn and Fricke, 1978 ; Alcaydir et al., 1978; Barlier et al., 1979; Kockarts, 1981). The temptation is often to search for the best model, but it is necessary to establish beforehand the criteria by which a model is judged to be the best. This is

sometimes omitted. The conclusion remains that of Barlier et al. (1979). It would be unfair to state that among the cited models there are any which are outside of interest, but it would also be incorrect to say that there are no systematic and significant differences between them. Different parameters are chosen to illustrate this point. If we consider the diurnal average of the exospheric temperature in the Northern Hemisphere (Fig. 2), it presents in four models a very broad maximum beginning in April with a slight decrease in the following months. The maximum for the St. Santin model (Fontanari et al., 1983) is flat. For 577 (Jacchia, 1977), the maximum is, on the contrary, much sharper and well-centered in June-July. Since four models agree on this point, the temptation is to doubt the representation predicted by 577 and thus reject this model. If a recent comparison by Hernandez (1982) is now considered, it seems that the 577 model is the best available to represent statistically temperatures deduced from a data set of optical measurements (Fig. 3). Furthermore, a more detailed analysis shows that the quality of the representation largely depends on the level of solar activity. The importance of considering the time period of data collection is evidenced in Fig. 2 where it can be seen that the extrapolation of the 1200

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ESRO 4 to high solar fluxes does not appear to be valid. A recent study (AlcaydC et al., 1982) of exospheric temperatures deduced from the European Incoherent Scatter facility (EISCAT) shows that the temperatures given by different models are fairly close to the observed one but not at the same time (Fig. 4). Therefore it is not easy to find the best model. Atomic oxygen, major constituent around 30&400 km, will also be given as an example (Figs. 5 and 6). The diurnally-averaged concentration, as excerpted from a study of Kockarts (1981), shows in all cases a semiannual oscillation related to the classical result in total density (Fig. 5). But it is surprising to note that at altitudes at which a large amount of data has been used

for the elaboration of each model, deviations of more than a factor of 2 exist in the equatorial regions. For this constituent, it is also interesting to recall the disagreement on the diurnal effect as described by different models (Fig. 6). Models based on satellite data show a diurnal amplitude smaller than shown in the St. Santin model (Alcaydt and Bauer, 1977) and it appears that the diurnal variation is not well represented in all the global thermospheric models. As for helium it is well known (Trinks et al., 1977; Barlier et al., 1979) that, while the winter bulge is clearly present in all models, its amplitude varies, especially in the polar regions. It is similar in models based mainly on mass spectrometer data and smaller in DTM based

950

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FIG. 4. EXOSPHERIC TEMPERATURES DEDUCED FROM EISCAT FACILITIES TO BE COMPARED WITH DIFFERENT MODELS. The data points have been joined for sake of clarity. (Alcaydt et al., 1982.)

-_

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FIG.~. ANNUALVARIATIONSOFATOMICOXYGEN AT 300 km COMPUTED AT 04.00 h L.T. WITHDTM,J~~

AND AEROS. Three latitudes are represented, i.e. North and South Poles and Equator. The daily solar decimetric flux F and the mean flux F correspond to the average conditions covered by AEROS. Geomagnetic indices are A, = 4 or K, = 1 (Kockarts, 1981). MSIS and ESRO 4 in addition.

A point of view on semi-empirical thermospheric models

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FIG. 6. COMPARB~NOFATOMICOXYGENINCOHERENTSCATTERMODELABOVE ST.SANTIN(ALCAYDBANDBAUER, 1977) WITH J77,MSIS AND DTMFOR EQUINOXANDSOLSTICECONDITIONS. Solar activity level F = F = 150 x lo- ‘* W m-2 Hz-‘. Geomagnetic index K, = 2 or A, = 7. For 577 longitude is 2.22”E, i.e. longitude of St. Santin (Barlier et al., 1979).

only on drag data. The discrepancy is larger during local summer when the helium density is low. The problem remains unsolved, more especially as discrepancies between models and airglow-determined densities exist, as shown by Anderson et nl. (1979).

e---------w -

-

These densities are, in general, lower by as much as a factor of 2 than the MSIS and DTM estimates and present relative to them a systematic depletion in the polar regions (Fig. 7). Several inferences can be drawn from these examples.

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LATITUDE (dog) FIG. 7. DENSITY DISTRIBUTIONS ASA FWNCTIONOFLAT~TUDE FOR 16 AUGUST 1973 AND 16 NOVEMBER1972 CALCULATEDWITH DTM, MSIS AND DETERMINED BY THE BESTFIT ~0 THE DATA (AIRGLOW DETERMINED DENSITIES)(ANDERSON et al.,1979).

F. BARLIER and C. BERGER

952

A semi-empirical model represents firstly a limited and particular data set in a statistical manner. In other geophysical conditions, notably during periods for which there are no data, its extrapolation is necessarily uncertain and must be checked. Mathematical formalisms are not obviously appropriate to represent very well all physical phenomena. Therefore the interpolation and the extrapolation of data through this formalism can lead to significant errors. The spat&temporal distribution of data that are needed for computing the empirical coefficients is not also always convenient. So, the diurnal variation is always mixed with seasonal and other long term variations, excepting incoherent scatter data. It is, perhaps, one of the reasons for a disagreement of the diurnal variation in atomic oxygen between global models and local models based on incoherent scatter data. In any case, a single comparison of one feature appears greatly insufficient to judge a model.

EXAMPLES

OF DIFFICULTIES ENCOUNTERED

IN

MODELLING

An open question concerns the semi-annual effect. This effect has been known for a long while, but the analysis of the physical processes put into play (seasonal variation of atmospheric dynamics, turbulence. energy budget) could not be made in a satisfactory manner and could not lead to a precise prediction. In fact, the semi-annual effect seems to be a phenomenon which is susceptible to year-to-year variations in amplitude not correlated with solar activity, as shown in a recent review by Ill (1981), (Fig. 8). Such variations are not modelled. Longitudinal variations were evidenced first in total densities from drag data (De Vries et al., 1967) then in composition mainly from mass spectrometer data (Hedin and Reber, 1972) ; they were confirmed later by several studies under both quiet and disturbed conditions. This leads to improved semi-empirical models by including the observed variations, whose maximum amplitude is of the order of 10%. Thus, Hedin ef al. (1979) have generated a model of longitude/U.T. variations by adding the geographic latitude, longitude and U.T. component to the spherical harmonic expansion of the MSIS model. Laux and von Zahn (1979) have introduced correction functions into the ESRO 4 model depending on geographical latitude and longitude. Universal time effects are ignored because, for their set of data, these are only weakly observed in polar latitudes. But from a comparison of these two models (Kockarts, 1981) it appears that a consistent global representation of the longitudinal variation is not yet entirely available.

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In the 577 model, the increase of the exospheric temperature due to magnetic activity is expressed as a function of the magnetic latitude and ipso facto, a longitude effect is introduced. The importance of the introduction of the magnetic latitude to give a better representation ofthe high latitude effect ofthe magnetic activity is given in Fig. 9 from Thuillier et al. (1980). In case of high activity a significant decrease in the temperature difference between the model Ml and a new formulation using a magnetic latitude parameter is observed. However, it is not true for quiet conditions because the geomagnetic activity effect is introduced as a monotone function converging to zero with the geomagnetic index; but significant longitudinal structures exist for quiet conditions and it appears difficult to represent simply by an empirical formalism both quiet and disturbed conditions, for which the physical reality is different. No completely satisfactory representation yet exists for any geomagnetic conditions in these high latitude regions, also shown in Fig. 10. At other latitudes, even in the equatorial regions, a longitudinal effect has been evidenced for magnetically disturbed periods from the analysis of the Cactus accelerometer total density data. An asymmetrical structure with regard to the geographic hemispheres,

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954

BARLIER and C. BERGER

amplified with magnetic activity, should be noted (Fig. 11). If the two solstices are considered, there exist permanent structures during quiet periods equally amplified with magnetic activity (Berger and Barlier, 1981a). These features are not represented in the existing models. Among the phenomena affecting the thermosphere which cannot be taken into account because of their character and ofthe hypothesis at the base of the models it is necessary also to point out those of tides, gravity waves and of itinerant perturbations. So, it is useful to recall that the total densities measured along the satellite trajectory present quasi-permanent Auctuations, with a wavelength in the range 80&1200 km, attaining several per cent ofthe average value (Villain et al., 1979 ; Villain, 1980). An example during a magnetic storm is given in Fig. 12. Other possibilities for the apparition of itinerant perturbations of this character also exist as described by Villain (1980) but must be studied thoroughly. A final example shows fluctuations in the density scale heights deduced from total density measured by Cactus accelerometer (Ill, 1979). Whereas the reference model predicts a quasi-linear augmen-

i$y$nJg# iii 120

0 Kp~3

Longitude

240

360

FIG. 11. GEOGRAPHIC MAPSOF THE RATIO &,bJ~J71. pobs: Total density measured by the Cactus accelerometer. P,,~: Total density predicted by the Jacchi 1971 model;

different longitude

levels of geomagnetic activity are considered; effects are evidenced for K, 2 5. (Berger and Barlier, 1981a.)

tationin function ofaltitude (on the scale of 100 km), the observations present, in certain cases, non-negligible fluctuations of several km along the track of satellite (Fig. 13). Such profile deformations sometimes occur during several consecutive passes. Because the data are measured along the trajectory, it is not possible to distinguish an altitude effect from a possible longitudinal effect. In return, the fluctuation of this parameter cannot be doubted, because it appears in thousands of passes.

LOWER THERMOSPHERE

It is an established fact that, if we had perfect knowledge of the dynamics, temperature and composition of the lower atmosphere between 90 and 200 km, many of the problems of the upper thermosphere would be resolved. But current semiempirical models are not intended to correctly predict the parameters of the lower atmosphere since too little data were available for this altitude range at the time of their elaboration. This fact is illustrated in Fig. 14, drawn from a study of Philbrick et al. (1982a). In this respect, the contribution of incoherent scatter measurements to the knowledge of this altitude zone is major. A recent study by Alcayde and Bernard (1982) emphasizes this contribution and gives some indication of important remaining problems. Among the various topics described, we note here the analysis and modelling of short- and long-term variations of neutral temperature and composition, as well as their vertical profiles. Some indication of the behaviour of molecular oxygen as a function of the solar cycle is also given. This constituent is not yet well modelled ; either it is taken as a constant at 120 km as in DTM or derived from a chemistry model (to be improved) by using AEC ion concentration measurements as in MSIS. Direct measurements ofthis parameter would be very useful to improve the models. The first direct in situ measurements of 0, obtained by the open source mass spectrometer on board the Atmospheric Explorer satellites have now become available and a comparative study of these data with the MSIS model has been performed by Torr et al. (1982). It indicates differences which can reach 50% for 0, concentrations of about 10” cm-3 but other measurements are yet needed to give confirmation of the accuracy ofthe results. In other respects a study of Philbrick et al. (1982b) concerning the comparison of 577 and MSIS models with measurements of 0, N, N and Ar densities obtained by the ion source mass spectrometer on the S3-1 satellite gives useful results in establishing the lower boundary conditions for modelling of the thermosphere.

A point of view on semi-empirical thermospheric models Another important parameter is the temperature profile which plays an essential role in the vertical distribution of the different constituents. The model formulations are closely based on the Bates (1959) profile: T(z) = T, -(T, - T,) exp (-s(z - z,), where s is the shape parameter and z0 the reference altitude, generally 120 km. The s parameter decreases with increasing solar activity as shown in Fig. 15 (Oliver 1979,1982) but at the moment, the latest models do not consider this variation. If the temperature gradient (dT/dz),,, = 0, - TIzo) at 120 km 1s now considered, it is shown to be nearly invariant during the solar cycle (Alcayde et al., 1979; Fontanari et al., 1983). In Fig. 16, the diurnal mean of the exospheric temperature and of the temperature gradient are plotted as a function ofepoch of the year for a period of

955

low solar flux. The mean value found by Alcayde (1975) for a flux of 125 is also plotted as a comparison. The values deduced from ionospheric data of the F, region are represented by dots and those ofthe E and F, region by triangles. lfthe agreement is satisfactory between the two determinations for T,, a small variation is observed for (dT/dz)rzo. For these reasons, Fontanari et al. (1983) suggest that the choice of a constant s parameter for the entire altitude range must be questioned and that for future thermospheric modelling, it should be preferable to consider the temperature gradient at 120 km as constant. A final remark can be given on the variation of the eddy diffusion coefficient at low altitude, which also acts on the vertical distribution of constituents (Banks and Kockarts, 1973 ; Keneshea et al., 1979). An indirect

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global determination of this quantity resulting from the variation of the turbopause height has been presented by Blum and Schuchardt (1978). Turbopause heights were obtained from mass spectrometer observations of thermospheric constituents as given by the ESRO 4 model (Blum et al., 1978). These results were obtained without including a global circulation and may thus lead to a larger value of the variations than probably exists. But this parameter has not yet been measured on a global scale. There are a few estimates based on

observations of chemical trails (Blamont and Barat, 1967; Zimmerman and Trowbridge, 1973) or using wind data (Zimmerman and Murphy, 1977). Figure 17 (Alcayde et al., 1979) gives an original evaluation of vertical profiles of the eddy diffusion coefficient, using the vertical temperature distributions and the molecular nitrogen concentrations obtained from incoherent scatter dataand theoreticalestimates for the heating and cooling rates. The same computation has been made by using the empirical temperature profile of

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.

.

.

340

I

I

380

.

.

**n:***

40

,,z’*rt::::’

i*t

i 30

I

H

50 .

I

3bo

I;::.*t::****

l +t

*,X*:.0

2.09

1

30 date

I

1

I

300

1

340

1.40

date

I

I

380 altitude

I

300

1

2.02

I

I

340

380 altitudeckm)

(km)

FIG. 13. DENSITY SCALEHEIGHT PROFILES (H)As A FUNCTION OF THE ALTITUDE.

from total density measured by the Cactus accelerometer for successive passes during 1976 (0). Comparison with DTM density scale height (*).

Determination

150

150 Salvo

140

7

B

04472

16 luov.

120 130 i -c Y

March

130 120

J77

MSIS

Salvo A2 00092 1

140

1

llOIOO-

f 5 Q

90 80 70 60 _ 50

I 04

I

I

I

I

0.5 0.6 0.7 0.8 09 Density

FIG. 14. COMPARISON

ratio

I

I

1.0 1.1 12

(mess/model)

501

1

' ' ' 1 1 1 1 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1 1.1

1 1.2

Density ratio (mess/model)

OF THE DENSI~ MEASUREMENTS FROM ACCELEROMETER SPHERE (ENERGY BUDGET cAMPAIGN)WlTHJ77AND MSIS (1977,1979)MODELS.

The density profiles are shown relative to the USSA76 model (Philbrick

et al., 1982a).

.

958

F.

BARLIERand C. BERGER

UT

(hr)

FIG. 15. DIURNAL VARIATIONOF S DETERMINED FROMFl-REGION DATA FORHIGHAND LOW SOLARACTIVITY COMPARED WITH THEMSIS MODELVARIATION.(OLIVER, 1982.) C model from Kiihnlein (1980) in addition.

the J77 model. The comparison shows a good agreement except for equinox periods above 110 km. This fact indicates the importance of the temperature gradient. Therefore its global determination as a good knowledge of the energy production as loss rates are needed to deduce, by this method, the worldwide behaviour of the eddy diffusion coefficient.

ENERGY

INDICATORS-MATHEMATICAL

FORMALISM

It is evident that any physical modelling requires a good knowledge of the energy budget of the atmosphere and that we are still very far from being able to measure its value in a permanent manner. Up to now, the solar radiation effect on the atmosphere and the energy input resulting from Joule heating and particle precipitations have been included in the mathematical algorithm of the models through the daily 10.7 cm solar flux with a time lag of 1 day, the smoothed flux over a few solar rotations and through the planetary index K, or A, with various time lags. A table of the different formula and coefficients is given by Hernandez (1982). It is well known that the 10.7 cm solar flux as well as the K, are only indices that do not necessarily represent the real physical mechanisms. They have the advantage however of having existed for a long time and of continuing to be recorded regularly. More, they are

able to describe the atmospheric variations with a reasonable accuracy. Correlations between solar U.V. and 10.7 cm flux and their significance to aeronomical applications have been the object of numerous studies (among others, Schmidtke, 1979; Hinteregger, 1979, 1981; Torr et al., 1980; Roemer and Framke, 1982; Bossy, 1983). We shall make only a few remarks on this topic and refer to these studies for additional details. Generally speaking there is an acceptable agreement between e.u.v. fluxes and decimetric fluxes. For example, Fig. 18 (Torr et al., 1980) shows that from 1350 to 1750 A the solar flux can be expressed in terms of the 10.7 index to a reasonable approximation. However, the e.u.v. radiation covers a great spectral region and the correlations of the various e.u.v. wavelengths with the decimetric flux are sometimes quite different. Even a classical example of anti-correlation has been given by Hinteregger (1977). Finally a study of the solar e.u.v. variations during several periods of two solar cycles compared with those of the decimetric flux and of their influence on thermospheric parameters points out serious difficulties with attempting to substitute e.u.v. flux indices for the traditionally used indices of F10.7 (Hinteregger, 1979). Long-term determination of u.v.1e.u.v. indices and further investigations of their influence on the atmospheric parameters are needed to give a specific formulation for use in aeronomical

A point of view on semi-empirical

6001

I

I

I

I

I

I

I

thermospheric

I

I

I

I

I

I

models

I

959

I

I

JFMAMJJASOND

(b)

: 5-

I

I

I

.

I

I

I

JFMAMJJASOND

FIG. 16. DIURNAL MEAN OF EXOSPHERICTEMPERATURE(a) AND OF TEMPERATUREGRADIENTS AT 120 km (b) DEDUCEDFROMIONOSPHERICDATA FROM F2-REGION (0) AND FROME AND Fl-REGION (A). (FONTANARI et al., 1983). @ Mean value obtained by Alcaydk (1975) for a mean solar flux of 125.10-22 Wm-’ Hz-‘.

110 ---

t-

T from

Jacchia

T from

incoherent

10’

106

105 Eddy

diffusion

coefficient

(cm*

SC’

5 x 10’

)

FIG. 17. COMPARISON BETWEENEDDY DIFFUSIONCOEFFICIENTSRESPECTIVELYOBTAINED WITH THE INCOHERENT SCATTER TEMPERATUREPROFILES@-ILL CURVES) AND THE 577 TEMPERATUREPROFILES(DASHEDCURVES). The “overhead” heat input above 120 km is 1.5 erg cm-’ s-l. (Alcaydi et al., 1979).

960

F. BARLIER and C. BERGER

.. . .

200190 -

. : . . .e: ..A ‘..& ..a _ . . ..: * ** . . . -.

.

.

.

450.00 “0

.

x’

I

I

I

180-

438.89427.78

.

-

z

.

I

I

T

<‘-

. ‘i Q

I

.

.

,...I . * . c_..&e . *.**. t * . ..*; . . , r :2*.. . . . . ‘.

F10.7 F10.7 F1c.18.PLOTOFTHEINTEGRATEDSOLARFLUXINTHE 14O&t45Oi% REG[ON (a)~~urNTm 1700-1750A~E~10~ fb)VSTHE F 10.7INDEXOVERTHEPERIOD 19761979. The units of F 10.7 are 10mz2 Wm-’ Hz-’ (Torr et al., 1980).

modelling. Thus, at this time, the solar decimetric flux is the more suitable index to be used, but the search for the best formulation is still a problem. Recently, Hernandez (1982) has provided a good description of the observed neutral kinetic temperature data set by using solely the instantaneous solar radio flux (power law as in 577). In the same way, Fontanari et al. (1983) have obtained the best fit of the French incoherent scatter temperature data with such a formalism but by using mean solar radio flux presenting a seasonal variation. The effects of the energy input from the high latitude regions are correctly described with the A, or I(, indices, but observations of higher precision and shorter time resolution show more discrepancies with the models. Figure 19 gives an example of correlation between total density and geomagnetic activity represented by the K, and AE indices. The variations are characterized by a sharp enhancement followed by a relaxation process with oscillations superimposed on the relaxation curve. This complex physical behaviour, implying dynamical prccesses, has been observed in all the cases studied with the Cactus accelerometer data (Berger and Barlier, 1981a, b) but is not taken into account by the model formulae. Berger and Barlier (1981a) have shown that, for the four geomagnetic events for which AE indices were available, the correlation between K, and AE is statistically good. Sometimes, however, the K, index is smooth while the

AE index is oscillating

and the densities reflect such oscillations. The duration of total density variations is more correlated with the duration of the geomagnetic event represented by the AE index. Thus, the aurora1 electrojet index which represents a global measure of the aurora1 zone activity resulting from enhanced ionospheric currents could be introduced with success in atmospheric modelling. Finally, the problem of energy indicators is still largely open as well as the choice of new indices and the new mathematical formalism to use them. ENERGY

SOURCES

AND SINKS

In thermospheric modelling, the effects of energy sources are empirically introduced through different indicators, as has been discussed in the preceding section. However, as has been said, such a situation cannot be entirely satisfactory, either for representing measured data or for providing some insight into the physical reality. A precise energy budget is needed, but we are still very far from being able to quantify it in a permanent manner. For this objective, many recent theoretical studies have been carried out as well as observational campaigns (Energy Budget Campaign, 1980). At high latitudes, computations are performed to estimateboth Jouleheatingandparticleheating(Banks et al., 198 1; Ponthieu, 198 1). An example is given in Fig. 20; by comparison with these sources, input from e.u.v.

961

A point of view on semi-empirical thermospheric models

300 29.5’

1.5-

-

North

1.o-

January FIG. 19.

km

1976

THERMOSPHERIC DENSITY RESPONSE TO A GEOMAGNETIC EVENT, OBTAINED ACCELEROMETER AND BY THE JACCHIA 1971 MODEL. F = &-ac,ur/PJ,I.

solar sources is very small. Analysing polar disturbances, PrGlls (1981) has noted the significant energy coupling between polar and mid-latitude regions even during moderately disturbed conditions from solar wind-magnetospheric energy dissipation. Such a coupling could be studied with the information gathered by two incoherent scatter facilities such as EISCAT and St. Santin. Richmond (1978) has studied gravity wavegeneration in the aurora1 regions as well as their propagation and dissipation in the thermosphere from an analytical point of view. He then (1979) compared other mechanisms with their ability to transport energy from aurora1 regions to low latitudes during magnetic storms. Two examples are given to show how the state of our

BY THE CACTUS

knowledge in this field is changing. In 1980, Torr et al. determined a revision ofthe U.V.heating efficiency of the thermosphere which led to significantly different results from the earlier concerning the magnitude, which must be enhanced from 3&35x to 5&55x and the strong function of the altitude. In 1981, Kockarts showed that nitric oxide plays a major role as a cooling agent in the 120-200 km region (Fig. 21). This fact has been ignored previously. This proves the importance of minor constituents and the need for their introduction in future modelling. Numerical models of the thermal budget in the height range 9&500 km have been developed by Gordiets et al. (1982), including the main sources and sinks of energy and particularly this new result for nitric oxide cooling.

962

BARLIER and C. BERGER

F. 14

04

70

‘1

250 K P=

6

12

\

5

18

24

1001

I

I

bIllI

10-g

I

II1111

1

1o-’

10-8

Energy production

and loss (erg cm-3

s-1

I

FIG. 21. HEIGHTDISTRIBUTION OF THE ENERGY PRODUCTION AND LOSSRATESUSINGTHENO DISTRIBUTION OFTRINKSet al., 1978 (KOCKARTS,1980).

6

A

0 0

12

6

18

24 very

useful to study thoroughly the behaviour of the atmosphere below 100 km and consequently to understand better the coupling between stratosphere, mesosphere and thermosphere (Hauchecorne and Chanin, 1982).

Total 60

IMPORTANCE OF DYNAMICS Some

remarks

importance

thermospheric

6

12

18

24

FIG. 20. HEIGHT INTEGRATEDATMOSPHERIC HEATINGRATES (mW/m2) AT CHATANIKAFOR 14 APRIL 1978. Dashed line represents mean diurnal heating rate resulting from e.u.v. solar radiations (Ponthieu, 1981).

Additional

sources coming from the mesosphere

and

more generally from the lower atmosphere

must also be

taken into account.

in particular

through pation.

tidal The

Energy is transferred

oscillations importance

and

gravity

waves

dissi-

of such sources has been pointed out long ago (Hines, 1965 ; Lindzen and Blake, 1970; Bertel et al., 1978; Garrett and Forbes, 1978). New researches in the low and middle atmosphere (Map Program) could provide new insight into these problems. Such techniques as LIDAR could be

be made

to emphasize

in interpreting

parameters.

idional circulation 0

must

of dynamics

suggested

The

the

and modelling

mechanism

by Johnson

of mer-

and Gottlieb

(1970) modifies the distribution of constituents and tends to accumulate the light ones (as compared to molecular nitrogen) in the regions of converging winds. This fact permits an interpretation of the winter helium bulge. Thedistribution of neutralcompositionduring a magnetic storm as a function of the latitude is also a typical example of the effect of circulation (Fig. 22). The amplitudes of the variations are different between the models, but the trends are similar. At 400 km they are characterized by an increase of the molecular nitrogen concentrations in the polar regions and a decrease of helium and atomic oxygen but less pronounced for the latter. These observations are in agreement with the theoretical model ofmagnetic storm dynamics by Mayr and Volland (1973). From another point of view, the meridional circulation is found to be more important for transferring energy to low latitudes during

A point of view on semi-empirical

thermospheric

’

963

models

z=400 km F=F=150

- 0.2

AKP=5 AA, =48 Day = 21 September 0 -90

-60

-30

0

30

60

Geographic

Jllllllllllllllll 1-60 -30 latitude

0.1 0

30

60

90

1”)

FIG.22. GEOMAGNETICEFFECTSFOR AK, = 5 (AA, = 48) ONTEMPERATURE,PARTIALCONCENTRATIONS(N~,O, He) ANDTOTALDENSITYPAT 400km ON 21 SEPTEMBERFORSOLARDECIMETRICFLIJXESF = F = 150~10-~~ Wm-’ Hz-‘. For 577 longitude is 0”. (Barlier et al., 1979.) DTM is here a new version of the previous model in order to take

into account the under estimation for high geomagnetic activity. magnetically disturbed periods than gravity waves (Richmond, 1979). Winds are also necessary for analysing and interpreting other features. Thus, the tropical longitudinal structure of the emission of the atomic oxygen line (630 nm) needs thermospheric winds to be understood (Thuillier et al., 1976). Differences of intensity of this emission between the Northern and Southern Hemisphere for the same local season can be interpreted by asymmetrical structure of the transequatorial winds (Thuillier, 1973). For reducing incoherent scatter data in the aurora1 regions, Alcayde et al. (1982) have equally shown the efficiency to have direct measurements of ion velocity performed with EISCAT facilities together with neutral velocity measurements with a field-compensated Michelson interferometer (Thuillier et al., 1979).

Theoretical studies are in progress and are supported by experimental data. For example, Roble et al. (1982) have determined a temperature pattern over the pole very similar to that deduced from the Fabry-Perot experiment on the OGO 6 satellite. Finally, many experimental results concerning winds have been gathered by the Dynamics Explorer satellite (Killeen et al., 1982). For example, these measurements indicate that the circulation can be described by the addition of two wind fields, the first one driven by the solar e.u.v. heating, the second one driven by high latitude heating. Perhaps such results could be put together with temperature patterns over the pole for quiet and disturbed conditions as shown in Figs. 9 and 10 in order to predict them. For all these reasons, the inclusion of a theoretical model of thermospheric dynamics in a future reference

964

atmosphere as proposed

F. BARLIERand C. BERGER

must be considered as a very useful effort, by Rees and Fuller-Rowe11 (1983).

CONCLUSION Since the beginning of the space era, the effort to model the thermosphere has followed two principal directions : first a semi-empirical modelling based on very simplified physical concepts of the type of those proposed by Nicolet in 1961, the objective being first and foremost to represent measurements, secondly a theoretical modelling based on the simultaneous resolution of fundamental equations with the objective of analyzing the physical mechanisms put into play. Only the first method ofmodelling was considered here. Its role is multiple. As was noted, the semi-empirical model has the role of representing a large quantity of data measured by various techniques and to describe thermospheric parameter variations. It may be said that this objective has on the whole been reached, but significant differences exist between models up to a factor of 2 in the parameter estimations and sometimes more. One of the reasons for this is that the models which represent values measured by satellite experiments are by definition valuable especially in time and space ofcollection ofdata. Their extrapolation can lead to important divergences if the physical concepts are oversimplified, which is generally the case. Nevertheless, these models have the advantage of being able to predict parameters which may be considered as known in the resolution of the complex physical equation sets, and thus to permit a simplification. These also exhibit the principal phenomena which will require interpretation. They thus contribute in an essential manner to a better knowledge of physical processes. From another point of view, it is necessary to add that the role of a model is to serve as a reference and to permit analysis of discrepancies with respect to observed data sets. It is not necessary that this reference be perfect in order to be useful. But it must be clearly defined and easy to calculate without need of either great computing time or a large computer. The question which is posed today is the future ofthis semi-empirical modelling effort. In reference to the past, new more precise measurements will be obtained. A better knowledge of sources and sinks of energy will be acquired. Finally, theoretical modelling progresses significantly. It is thus necessary to find a compromise as in 1962 between physical concepts permitting a solution which is representative of the reality of today ; that is to say measurements of a new type (winds, turbulence, composition), all while remaining relatively simple and easy to use. This level is not easy to define and a precise proposition is not made in this study. It

remains to be done. It can only be said that dynamics and turbulence cannot be ignored, and indicators of energy budget should be reviewed, as well as the mathematical formalisms of interpolation and extrapolation. One observation seems essential. It will be necessary to use the measurements of the past as well as the measurements of the future. They represent a heritage ofinestimable value. In this sense, the development of a semi-empirical model, of a standard type, even little improved, could be the opportunity to create a data bank which would preserve this heritage.

REFERENCES Alcaydi, D. (1975) Structure et thennodynamique de la thermosph&e a moyenne latitude-tine etude par diffusion incohtrente. These de Doctorat es Sciences, Universitk Paul Sabatier, Toulouse, no. 683. Alcayde, D. and Bauer, P. (1977) Modilisation des concentrations d’oxygene atomique observees par diffusion incohtrente. Ann. Geophys. 33, 305. Alcayde, D., Bauer, P., Hedin, A. and Salah, J. E. (1978) Compatibility of seasonal variations in mid-latitude thermospheric models at solar maximum and low geomagnetic activity J. geophys. Rex 83, 1141. Alcayde, D., Fontanari, J., Kockarts, G., Bauer, P. and Bernard, R. (1979) Temperature, molecular nitrogen concentration and turbulence in the lower thermosphere, inferred from incoherent scatter data. Ann. Geophys. 35,41. Alcayde, D. and Bernard, R. (1982) Modelling of the lower thermosphere: contributions of incoherent scatter observations. J. ammos. ten. Phys. 44,95. Alcaydt, D., Fontanari, J. and Bauer, P. (1982) High latitude neutral atmosphere temperature and composition measurements from the first Eiscat incoherent scatter observations. Ann. Geophys. 38,473. Anderson, D. E., Meier, R. R., Jr. and Weller, C. S. (1979) The seasonal-latitudinal variation of exospheric helium from the He 584-A dayglow emissions. J. geophys. Res. 84, 1914. Banks, P. M. and Kockarts, G. (1973) Aeronomy, Part B.

Academic Press, New York. Banks, P. M., Foster,J. C.and Doupnik,J. R.( 1981)Chatanika radar observations relating to the latitudinal and local time variations of joule heating. J. geophys. Res. 86,6869. Barlier, F., Berger, C., Falin, J. L., Kockarts, G. and Thuillier, G. (1978) A thermospheric model based on satellite drag data. Ann. Geophys. &I, 9. Barlier. F.. Beraer, C.. Falin. J. L., Kockarts, G. and Thuillier, G. (i979) C&parisons ‘between various semi-empirical thermospheric models of the terrestrial atmosphere. J. atmos. terr. Phys. 41, 527. Bates, D. R. (1959) Some problems concerning the terrestrial atmosphere above about the 100 km level. Proc. R. Sot., Lond. h 253,451. Bereer. C. and Barlier. F. (1981a) Response of the equatorial thermosphere to magnetic activity analysed with accelerometer total density data. Asymmetrical structure. J. atmos. terr. Phys. 43, 121. Berger, C. and Barlier, F. (1981b) Asymmetrical structure in the thermosphere during magnetic storms as deduced from the CACTUS accelerometer data. Ado. Space Rex 1,231.

A point of view on semi-empirical Bertel, L., Bertin, F., Testud, J. and Vidal-Madjar, D. (1978) Evaluation of the vertical flux of energy into the thermosphere from medium scale gravity waves generated by the jet stream. J. atmos. terr. Phys. 40,691. Blamont, J. E. and Barat, J. (1967) Introduction d’un modile pour la structure des mouvements de I’atmosphtre entre 85 et 110 km d’altitude. Ann. Geophys. 23, 173. Blum, P. W., Schuchardt, K. G. H. and von Zahn, U. (1978) Semi-empirical models of the neutral atmosphere based on turbopause height and exospheric temperature variations. J. atmos. terr. Phys. 40, 113 1. Blum, P. W. and Schuchardt, K. G. H. (1978) Semi-theoretical global models of the eddy diffusion coefficient based on satellite data. J. atmos. terr. Phys. 40, 1137. Bossy, L. (1983) Solar activity indices and comparison with solar UV and X-rays. EGS, Leeds, August 1982. Planet. Space Sci. 31,977O. CIRA (1965) Cospar International Reference Atmosphere. Akademie; Berlin. De Vries. L. L.. Fridav. E. W. and Jones. L.C. (1967) Analvsis of densit; data reduced from low-aliitude,~ high resolution satellite tracking data. Space Res. 7, 1173. Energy Budget Campaign, November 1980. Fontanari, J. (1981) Modeles tridimensionnels de la thermosphere : contribution exptrimentale par diffusion incohtrente et analyse thiorique. Thise de Doctorat es Sciences, Universitk Paul Sabatier, Toulouse. Fontanari, J., Alcaydk, D. and Bauer, P. (1983) An incoherent scatter study of short- and long-term temperature and atomic oxygen variations in the thermosphere. Ann. Geophys. 1,81. Fuller-Rowell, T. J. and Rees, D. (1980) A three-dimensional time-dependent global model of the thermosphere. J. Atmos. Sci. 37, 2545. Garrett, H. B. and Forbes, J. M. (1978) Tidal structure of the thermosphere at equinox. J. atmos. terr. Phys. 40, 657. Gordiets, B. F., Kulikov, Yu. N., Markov, M. N. and Marov, M. Ya. (1982) Numerical modelling of the thermospheric heat budget. J. geophys. Res. 87,4504. Harris, I. and Priester, W. (1962) Theoretical models for the solar cycle variations of the upper atmosphere. G.S.F.C., NASA. Hauchecorne, A. and Chanin, M. L. (1982) Mid-latitude ground-based Lidar study of stratospheric warmings and planetary waves propagaiion. .I. atm&. terr. Phys. 44, 577. Hedin,A. E.and Reber,C.A.( 1972)Longitudinal variationsof thermospheric composition indicating magnetic control of polar heat input. J. geophys. Res. 77,2871: Hedin, A. E., Mayr, H. G., Reber, C. A., Spencer, N. W. and Carignan, G. R. (1974) Empirical model of global thermospheric temperature and composition based on data from the Ogo 6 quadrupole mass spectrometer. 1. geophys. Res. 79, 2 15. Hedin, A. E., Salah, J. E., Evans, J. V., Reber, C. A., Newton, G. P., Spencer, N. W., Kayser, D. C., Alcaydk, D., Bauer, P., Cogger, L. and McClure, J. P. (1977a) A global thermospheric model based on mass spectrometer and incoherent scatter data, MSIS 1, N, density and temperature. J. geophys. Res. 82,2139. Hedin, A. E. Reber, C. A., Newton, G. P., Spencer, N. W., Brinton, H. C., Mayr, H. G. and Potter, W. E. (1977b) A global thermospheric model based on mass spectrometer and incoherent scatter data. MSIS 2, Composition. J. geophys. Res. 82,2148. Hedin, A. E., Reber, C. A., Spencer, N. W., Brinton, H. C. and Kayser, D. C. (1979) Global model of longitude/UT

thermospheric

models

965

variations in thermospheric composition and temperature based on mass spectrometer data. J. geophys. Res. 84, 1. Hernandez, G. (1982) Mid-latitude thermospheric neutral kinetic temperatures 1. Solar, geomagnetic, and long-term, effects. J. geophys. Res. 87, 1623. Hines, C. 0. (1965) Dynamical heating of the upper atmosphere. J. geophys. Res. 70, 177. Hinteregger, H. E. (1977) EUV flux variation during end of solar cycle 20 and beginning cycle 21, observed from AE-C satellitk. Geophys. R&. Letty 4; 231. Hinteregger, H. E. (1979) Development of solar cycle 21 observed in EUV spectrum and atmospheric absorption. J. geophys. Res. 84, 1933. Hinteregger,H. E.(1981) Representationsofsolar EUVfluxes for aeronomical applications. A&J. Space Res. 1,39. Ill, M. (1979) Determination of density scale height profiles. Spuce Res. 19,235. Ill, M. (1981) A review of the semi-annual effect. 2nd Intercosmos seminar on upper atmospheric research. Baja (Hungary), September 1981. Jacchia, L. G. (1965) Static diffusion models of the upper atmosphere with empirical temperature profiles. Special Report 170, Smithson. Astrophys. Observ., Cambridge, Massachusetts. Jacchia, L. G. (1971) Revised static models of the thermosphere and exosphere with empirical temperature profiles. Special Report 332, Smithson. Astrophys. Observ., Cambridge, Massachuserts. Jacchia, L. G. (1977) Thermospheric temperature, density, and composition: new models. Special Report 375, Smithson. Astrophys. Observ., Cambridge, Massachusetts. Johnson, F. S. and Gottlieb, B. (1970) Eddy mixing and circulation at ionospheric levels. Planet. Space Sci. 18,1707. Keating,G. M. and Prior, E. J. (1968)The winter helium bulge. Space Res. 8, 982. Kelly, J. D.and Wickwar,V. B.(1977) Trans. Am. Geophys. Un. 58, 1197. Keneshea, T. J., Zimmerman, S. P. and Philbrick, C. R. (1979) A dynamic model of the mesosphere and lower thermosphere. Planet. Space Sri. 27, 385. Killeen, T. L., Hays, P. B., Spencer, N. W. and Wharton, L. E. (1982) Neutral winds in the polar thermosphere as measured from Dynamics Explorer. COSPAR, Ottawa, May-June 1982. Kockarts, G. and Nicolet, M. (1962) Le probltme akronomique de l’htlium et de l’hydrogene neutres. Ann. Geophys. 18,269. Kockarts, G. and Nicolet, M. (1963) L’h&lium et l’hydrog8ne atomique au tours d’un minimum d’activitk solaire. Ann. Geophys. 19, 370. Kockarts, G. (1980) Nitric oxide cooling in the terrestrial atmosphere. Geophys. Rex Left. 7, 137. Kockarts, G. (1981) Some recent advances in thermospheric models. Adv. Space Rex 1, 197. Kiihnlein, W., Krankowsky, D.,LBmmerzahl, P.,Joos, W. and Volland, H. (1979) A thermospheric model of the annual variations of He, N, O,N, and Ar from theAeros Nims data. J. geophys. Res. 84,4355. Kiihnlein, W. (1980) A model of thermospheric temperature and composition. Planet. Space Sci. 28, 225. Laux, U. and von Zahn, U. (1979) Longitudinal variations in thermospheric composition under geomagnetically quiet conditions. J. geophys. Res. 84, 1942. Lindzen, R. S. and Blake, D. (1970) Mean heating of the thermosphere by tides. J. geophys. Res. 75,6868. Mayr, H. G. and Volland, H. (1973) Magnetic storm

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