changes in thermospheric density caused by turbulence variations

8
Adv. Space Res. Vol. 7, No. 10, pp. (10)247—(10)254, 1987 0273—1177/87 $0.00 + .50 Printed in Great Britain. All rights reserved. Copyright © 1987 COSPAR CHANGES IN THERMOSPHERIC DENSITY CAUSED BY TURBULENCE VARIATIONS P. Blum and G. W. Prölss Institut für Astrophysik und Extraterrestrische Forschung, Universitat Bonn, Auf dem Hugel 71, D-5300 Bonn 1, F.R.G. ABSTRACT Seasonal and geomagnetic density variations in the thermosphere can be explained either by a system of thermally driven winds or, equally well, by changes in the turbulence structure. Observations show that both processes take place, but their relative importance has not yet been established. In this paper, a model incorporating both mechanisms is presented. Whereas seasonal changes may be generated by changes in the turbopause height, geomagnetic perturbations may be associated with a turbulent layer above the homopause region. INTRODUCTION Observations of thermospheric densities have shown that in the winter hemisphere the relative density of lighter gases, like helium, is increased, while heavier gases, like argon, are depleted as compared to the yearly average densities. In the summer hemisphere, the opposite situation is found. These observations have been incorporated into all empirical models of the thermosphere. A situation like in the summer hemisphere also exists during increased geomagnetic activity: the relative density of light gases decreases, while the density of heavier constituents increases. These changes are observed not only in the polar regions, where the energy is injected into the thermosphere, but also at subauroral latitudes. A theoretical explanation of these observations is derived from the diffusion equation. For a binary gas mixture consisting of a major and a minor component, the difference between the vertical transport velocities is given approximately by /e.g. 1/ = —D [±.~a + (I) —K [I do + I + I dT Lndz RH Tdz with n = density of minor constituent T = temperature H = scale height of minor constituent HH = homospheric scale height of gas mixture D = diffusion coefficient K = eddy diffusion coefficient aT = thermal diffusion coefficient This equation can be solved for the vertical distribution of the minor constituent n(z). A qualitative discussion of the result is facilitated by introducing a sharp boundary the turbopause between the region where turbulent mixing is perfect (homosphere, D=O) and the (10)247

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Page 1: Changes in thermospheric density caused by turbulence variations

Adv. Space Res. Vol. 7, No. 10, pp. (10)247—(10)254, 1987 0273—1177/87 $0.00 + .50Printedin GreatBritain. All rightsreserved. Copyright© 1987COSPAR

CHANGES IN THERMOSPHERIC DENSITY

CAUSED BY TURBULENCE VARIATIONS

P. Blum andG. W. Prölss

Institutfür Astrophysikund ExtraterrestrischeForschung,UniversitatBonn,AufdemHugel 71, D-5300Bonn1, F.R.G.

ABSTRACT

Seasonal and geomagnetic density variations in the thermosphere can be explained either bya system of thermally driven winds or, equally well, by changes in the turbulencestructure. Observations show that both processes take place, but their relative importancehas not yet been established. In this paper, a model incorporating both mechanisms is

presented. Whereas seasonal changes may be generated by changes in the turbopause height,geomagnetic perturbations may be associated with a turbulent layer above the homopauseregion.

INTRODUCTION

Observations of thermospheric densities have shown that in the winter hemisphere therelative density of lighter gases, like helium, is increased, while heavier gases, likeargon, are depleted as compared to the yearly average densities. In the summer hemisphere,

the opposite situation is found. These observations have been incorporated into allempirical models of the thermosphere.

A situation like in the summer hemisphere also exists during increased geomagnetic

activity: the relative density of light gases decreases, while the density of heavierconstituents increases. These changes are observed not only in the polar regions, where theenergy is injected into the thermosphere, but also at subauroral latitudes.

A theoretical explanation of these observations is derived from the diffusion equation. Fora binary gas mixture consisting of a major and a minor component, the difference betweenthe vertical transport velocities is given approximately by /e.g. 1/

= —D [±.~a+± +

(I)

—K [I do + I + I dTLndz RH Tdz

with

n = density of minor constituent

T = temperature

H = scale height of minor constituent

HH = homospheric scale height of gas mixture

D = diffusion coefficient

K = eddy diffusion coefficient

aT = thermal diffusion coefficient

This equation can be solved for the vertical distribution of the minor constituent n(z). Aqualitative discussion of the result is facilitated by introducing a sharp boundary — theturbopause — between the region where turbulent mixing is perfect (homosphere, D=O) and the

(10)247

Page 2: Changes in thermospheric density caused by turbulence variations

(10)248 P. Blum and 0. W. Prölss

region where molecular diffusion is perfect (heterosphere, K=O). Neglecting thermal diffu-sion effects and integrating atepwise from a lower boundary z

0 to the turbopause height ZTand from there to some higher altitude z, we obtain

z T z zT(z) d d

0(z) = n(z) exp — ZT ~+ J0 K+D dz (2)

As can be seen, the vertical density profile of a minor species is determined by thedensity at a certain base level z , by the temperature profile, by the molecular and eddydiffusion coefficients D and K, b~the turbopause height ZT~ and by the relative velocitydifference between the minor constituent and the main gas.

Both the density at z0 and the temperature profile need not be considered here as they areassumed to be known. Their contribution to the observed seasonal changes is clear andrequires no further explanation.

Seasonal changes of the density above those caused by temperature variations therefore canbe explained only by changes in the turbopause height ZT (Fig. 1) and the associatedchanges in the diffusion coefficients or by changes in the diffusion velocity heightprofile. In particular, it should be pointed out that the horizontal wind motion does notdirectly influence the vertical distribution of a species. The effect a horizontal windsystem has on the vertical density profile is only indirect. It is governed by the equationof continuity, which connects the divergences of the horizontal and vertical motions. Thisindirect effect may be considerable.

In the following, models of the seasonal or magnetic—activity—associated thermosphericdensity changes based on turbopause height variations or turbulent layers will be called“turbulence models”, models based on global wind systems “wind models”.

SEASONAL VARIATIONS

It has been suggested /e.g. 2/ that the seasonal variation of the thermospheric density iscaused by a seasonal change in the turbopause height. While models based on this assumptionprovide an explanation for the characteristic changes observed, they also suffer from someshortcomings. These deficiencies may be summarized as follows:

(1) The required changes in the turbopause height appear to be rather large (up to 2.5scale heights).

(2) The observations presently available /e.g. 3,4,5,6/ do riot provide a firm basis for thepostulated turbopause height variations.

(3) Competing mechanisms (like wind—induced diffusion) are neglected.

He N2I-

0uJI

120 ‘L~ UPWARDS L,l SHIFT OF

\ HOMOPAUSE

100 *

Fig. 1 Density changes of aminor constituent (helium)

__________________________________________________ caused by changes in the tur—

LOG (DENSITY) bopause height.

Page 3: Changes in thermospheric density caused by turbulence variations

ThermosphericDensityChanges (10)249

An alternate explanation for the observed seasonal variations is offered by globalcirculation models /e.g. 7,8,9/. This explanation is based on the divergence of horizontalwind systems and the associated vertical diffusion effects. These models also suffer fromsome difficulties:

(1) Three—dimensional calculations of thermospheric wind cells pose serious computationaldifficulties which may affect the validity of the results obtained. Also, many of therequired input parameters are not well known at the present.

(2) Firm observational support for the predicted and required wind system is not yetavailable, especially in the all important height region below, say, 200 km /e.g. 10/.

(3) As was the case for the turbulence models, competing mechanisms (like turbopause heightchanges) are neglected.

To overcome some of these difficulties, a new model has been constructed which considersboth seasonal changes introduced by turbopause height variations and seasonal changescaused by global wind circulation /11,12/. In this “wind—turbulence” model, the respective

UPPER BOUNDARYCONDITIONS ‘KFOBSERVEDDENSITIES OF HELIUM AND ARGON

300 -: :A I

——---—-— ___I

WIND-TURBULENCEMODEL

AZIMUTHAL AVERAGES

E 8Oto300kmI-I

(-I,

I— .~ ~‘1m(0

w ‘i(I,

-I

0 • ~

U(ze) I

150W(z~e)

100 K(z~e)

WINTER SUMMERPOLE LATITUDE POLE

80LOWER BOUNDARYCONDITIONS

LARGE- AND SMALL-SCALE DYNAMICMIXED ATMOSPHERE I

L

Fi4~ Basic processes included in the wind—turbulence model. Model parameters and

boundary conditions are indicated in a meridional cross section of the atmosphere.

Page 4: Changes in thermospheric density caused by turbulence variations

(10)250 P. Blum and G. W. Prölss

seasonal variations of the turbopause height are assused, and the wind system, which inaddition is required to explain the observations, is calculated. The advantages of thismodel as compared to the previous ones are the following:

(1) Both seasonal changes in turbulence and in the global wind system, which are certain toexist, are included in the model.

(2) The required height variation of the turbopause is much smaller than in the pureturbulence models.

(3) Even a turbulence lower in summer than in winter could be accommodated by the model. Itwould require a stronger wind system than is presently predicted by the wind models.

Of course, this model cannot establish the relative importance of the two processesconsidered. This would require conclusive observational evidence on either the magnitude ofthe wind system or the magnitude of the turbulence variation. However, it does indicatewhich combination of the two is compatible with the data.

A detailed discussion of the wind—turbulence model of the thermosphere has been presentedby Schuchardt /13/. The principal processes underlying the wind—turbulence model are shownin Fig. 2. It is assumed that the horizontal wind system in the height region between 100and 150 km transports a mixture of gases present at these heights. This horizontal flowtakes place from the summer to the winter pole. A vertical transport of gases at highlatitudes and a return flow at altitudes lower than the turbopause closes the circuit.While it is assumed that the horizontal velocities of all constituents are equal, thiscannot be the case for the vertical velocities, because above the turbopause the densityratios of the constituents are height—dependent. A downward excess velocity at the winterpole is calculated for helium. According to equation (2), this means a higher helium

300

I : Hw = 165 km, S~=

II : Hw = 145 km,5W = 2 III

III :H~ 95km, S~1

~ 200 - /I II III’

100 -

1MM 1CM 1DM 1M

VERTICAL VELOCITY

~g~3 Height profiles of the vertical velocity used in the wind—turbulencemodel. Hw (wind scale height) and SW (form factor) are parameters whichdetermine the profile shape. Velocity profiles inferred from theoreticalconsiderations by Johnson and Gottlieb ((J+G, /14/) and Reber and Hays (R+H,/15/) are indicated by dashed lines.

Page 5: Changes in thermospheric density caused by turbulence variations

ThermosphericDensityChanges (10)251

WINTER- SUMMERDIFFERENCE ~

OF TURBOPAUSEHEIGHT AT THE POLES (km).-I •0 :1.0

0.-I ~)

0 00 0 0 ‘—4 C’.,C’., .—I ~5 (5

I + o______________________________________________________ .0I I_I _I

cC—’ ‘0~ ~u,0 cC 0-.~.

‘—‘9 00

— US I— -. —. .—4 ‘.1 .,~ LO~ S ~

WE W9 W0 GJQ)

0 0 00 C’.) a)C’.) ‘-4 0 0.05>

- 0 55 0.0>0.-I

vS 550W~

LL6T [9 ~e NOSNI)1310 C-’

0

LL6I •I~~~ 31~O~1 - ~ ~ ~

1,1 1861 ~ I~ NOSNDI3I~ ~ ..-.

I.’.I> I...) 4~,

S I— 0

S ~S ‘, ~ 0011)

S ‘.~P.0 U

S vsS - 0~

S ~°

E

U0

11I__i .\ W )j.-~’..~O5 0 ‘00 •H

V) S. ~ 05.~-’Li_ 0 ~_, e0 ~ 0 o

~ ::::::::::::~~~.“‘. ~ — ~~ LU 00 ..J ~ S ~— ~ S. \I— ~ ‘. .0 ,-j 0)

cC 0 *. •.,~

~ ~I~0 ~ ...,

I 0.4.’ 0 a

o 0 —, ‘—‘ ‘‘

o ‘.‘ • 0-‘ 0

—J 4~,Q)~W

LU vs0 .U ...J ‘0 ~ ‘0

LU 0 (I) LU CI) ~ 0 0‘-4

LU 0~.-. I— 0) <I~

C-) 0 I— cC ‘0 ~ ‘.4C-) LU .Op b8~

‘0 LU ~— ‘~ (I) C.) ‘.4_j ~ ‘0 -4.~

.1-( ~ — .~ I~— LU Li 0

0) ~.. ~_•~ ‘.4 >, ‘.4~ I~— LU ‘0~ I— U

0 ~ 0 ~ LU ~-‘ ‘0 ~

LU cC c.~ I ~ .~ sLU I.,.4 ~) “ (5

0 — .iso~cC .,_ e~o.-4~

0- .‘.4Q5 ~

L~0 0 (5 ~

IN3IDIJJ3O3 NOISflJJIO A003 ~iV1Od JO OI1V~I ~J3WWflS-~31NIM

Page 6: Changes in thermospheric density caused by turbulence variations

(10)252 P. Blum and G. W. Prdlss

density than for the diffusive equilibrium situation obtained from equation (2) by assumingAW= 0. The turbopause acts like a barrier to this dynamic process and causes the differingvelocities of the various constituents to becomeequal below the turbopause.

Together with this dynamic process, there exists a periodic seasonal up and down movementof the turbopause. Both processes are responsible for the strong increase of the heliumdensities in winter and the correlated decrease of the argon densities. Of course, themodel critically depends on the height profile of the vertical diffusion velocities of theminor constituents. In the wind—turbulence model, no attempt has been made to calculatethese height profiles, as they depend on various parameters whose accuracy is not wellknown. To overcome this difficulty, a parametric approach has been chosen, and severalmodels for the height profile of the diffusion velocities have been assumed. This procedureis really not less reliable than calculating these velocities, except that in theparametric approach the assumptions made are more evident than in theoretical models, where

the diffusion velocities are calculated, but the unknown factors are not really eliminated.In Fig. 3, three models for the vertical diffusion velocities are shown and compared to

theoretical estimates by Johnson and Gottlieb /14/ and Reber and Hays /15/.

Results of the wind—turbulence model are presented in Fig. 4 and are compared to seasonalwinds as proposed in various theoretical models. The figure shows the combination of

turbopause height variation and wind system necessary to explain the observed seasonaldensity changes of helium and argon. The required amplitudes of the meridional winds at 300and 130 km and of the vertical wind at 130 km are given by the curves. The conditions arerepresentative for the winter solstice. The turbopause models would correspond to points onthe curves with a zero wind amplitude, while the wind models are represented by thehorizontal line corresponding to a vanishing winter—summer turbopause height difference.Results for winds obtained by four theoretical models have been marked on the curves.Observations of meridional daily winds at 300 km are also shown in the figure to indicatewhich combinations of winds and turbulence would have some observational support.

GEOMAGNETIC ACTIVITY EFFECT

Increased turbulence may also play an important role during thermospheric storms. Forexample, at middle latitudes significant composition changes are maintained for extendedperiods of time and presumably long after the actual disturbance process has ceased tooperate /16/. A possible explanation for this long recovery phase are deviations fromdiffusive equilibrium in the lower thermosphere generated -by increased turbulence. Thisincreased turbulence is not necessarily associated with changes in the turbopause height,but may occur in a transient layer above the homopauseregion. The effect such a layer willhave on the upper thermospheric composition is illustrated in Fig. 5 for the minorconstituent helium. If temperature effects are included, these effects would be consistentwith the observations /17/.

Thereby, it is not important whether the mixing initially took place in a restrictedaltitude region or in the whole upper thermosphere. What is essential is that the mixing

extended to the lower thermosphere where the recovery—time constants are large. Whereasthe

\ UPPERTHERMOSPHERE

— i~—I -I~ He N

2

TURBULENTLY140 KM MIXED

LAYER

HOMO Fig. 5 Density perturbations

100 KM •~“•~‘..‘••.‘~•‘~ “~,.,‘.,-“,‘.,-,-“,-,.--,.-.“---‘..,..*-,.“‘....-,‘., of a minor gas (helium)HOMOSPHERE caused by a turbulently mixed

- - ---~- >>-x--~---->~-. ~ - ~ layer above the homopause

LOGIDENSITY) region.

Page 7: Changes in thermospheric density caused by turbulence variations

ThermosphericDensityChanges (10)253

upper thermosphere will always quickly return to a diffusive equilibrium situation (r <lhat 250 km altitude), the lower thermosphere will remain disturbed (TD>6h at 148 kmaltitude).

There are several possibilities how this initial mixing could have been affected. Forexample, dissipation of large—scale traveling atmospheric disturbances (TADs) may thorough-ly mix the upper atmosphere /18/. Also, convective transport from high to middle latitudesmay contribute to the observed mid—latitude perturbation. This latter mechanism, however,is not supported by numerical simulations /19/.

CONCLUSION

In most of the recently published theoretical models of the seasonal and storm—timevariations of the thermosphere, the observations have been explained by global wind cellsand a resulting wind—induced diffusion. Variations of turbulence as an additional causehave been excluded. The authors suggest that presently available observations of turbulenceand winds are not sufficient to justify such an approach to thermospheric modeling. Bothturbulence variations and dynamic processes exist side by side. Most probably, both play arole in thermospheric behavior and should be included in the models.

REFERENCES

1. P.M. Banks and G. Kockarts, Aeronomy, Academic Press, New York and London, 1973

2. P.W. Blum and K.G.H. Schuchardt, The role of eddy turbulence for long periodicvariations of upper atmospheric density, Space Research XVIII, 191 (1978)

3. S.P. Zimmerman, Meteor trails and atmospheric turbulence, J. Geophys. Res. 78, 3927(1973)

4. D. Alcayde, J. Fontanari, G. Kockarts, P. Bauer and B. Bernard, Temperature, molecularnitrogen concentration and turbulence in the lower thermosphere inferred from incoher-ent scatter data, Ann. Geophys. 35, 41 (1979)

5. A.D. Danilov, U.A. Kalgin and A.A. Pokhunkov, Variation of the turbopause level atpolar region, Space Research XIX, 173 (1979)

6. W.K. Hocking, Turbulence in the altitude region 80—120 km, MAP—Handbook 16, 290 (1986)

7. H. Volland and H.G. Mayr, Theoretical aspects of tidal and planetary wave propagationat thermospheric heights, Rev. Geophys. Space Phys. 15, 203 (1977)

8. R.E. Dickinson, E.C. Ridley and R.G. Roble, A three—dimensional general circulation

model of the thermosphere, J. Geophys. Res. 86, 1499 (1981)

9. D. Bees, Theoretical thermospheric models, Adv. Space Res. 5, No. 7, 215 (1985)

10. D. Dartt, G. Nastrom and A. Belmont, Seasonal and solar cycle wind variations,80—100 km, J. Atmos. Terr. Phys. 45, 707 (1983)

11. P.W. Blum and K.G.H. Schuchardt, Principles of a global wind—turbulence model of thelatitudinal—seasonal variation of the thermosphere as deduced from satellite data,Space Research XX, 97 (1980)

12. K.G.H. Schuchardt and P.W. Blum, A global wind—turbulence model deduced from satellitedata — discussion of results, Space Research XX, 101 (1980)

13. K.G.H. Schuchardt, Modelle zur zonal gemittelten Dynamik der ThermosphWre, disserta-tion, UniversitWt Bonn (1982)

14. F.S. Johnson and B. Gottlieb, Eddy mixing and circulation at ionospheric levels,Planet. Space Sci. 18, 1707 (1970)

15. C.A. Reber and P.8. Hays, Thermospheric wind effects on the distribution of helium andargon in the earth’s upper atmosphere, J. Geophys. Res. 78, 2977 (1973)

16. G.W. Prblss, Local time dependence of magnetic storm effects on the atmosphere atmiddle latitudes, Ann. Geophys. 2, 481 (1984)

Page 8: Changes in thermospheric density caused by turbulence variations

(10)254 P. Blumand G. W. PrOiss

17. P.W. Blum, C. Wulf—Mathies und H. Trinks, Interpretation of local thermosphericdisturbances of composition observed by ESRO4 in the polar region, Space Research XV,209 (1975)

18. G.A.M. King, The ionospheric disturbance and atmospheric waves, J. Atmos. Terr. Phys.28, 957 (1966)

19. H. Rishbeth, B. Gordon, D. Bees and T.J. Fuller—Rowell, Modelling of thermosphericcomposition changes caused by a severe magnetic storm, Planet. Space Sci. 33, 1238(1985)

20. J.F. Kasting and R.G. Roble, A zonally averaged chemical—dynamical model of the lowerthermosphere, J. Geophys. Rea. 86, 9641 (1981)

21. R.E. Dickinson, E.C. Ridley and R.G. Roble, Meridional circulation in the thermosphere.II. Solstice conditions, J• Atmos. Sci. 34, 178 (1977)

22. R.G. Roble, R.E. Dickinson and E.C. Ridley, Seasonaland solar cycle variations of thezonal mean circulation in the thermosphet’e, J. Geophys. Res. 82, 5493 (1977)