Seasonal and latitudinal variations of eddy diffusion coefficient in the mesosphere and lower thermosphere

Journal of Atmospheric and Terrestrial Physics, Vol. 54, No. 11/12, pp. 1481-1489, 1992.

0021-9169/92 $5.00+ .00 (f3 1992 Pergamon Press Ltd

Printed in Great Britain.

Seasonal and latitudinal variations of eddy diffusion coefficient in the mesosphere and lower thermosphere A. D. DANILOV and U. A. KALGIN Institute of Applied Geophysics, Glebovskaya 20, Moscow 107258, Russia

(Received in final form 24 January 1992 ; accepted 27 March 1992) Abstract--Two approaches to turbulence parameter determination around the turbopause are discussed. It is shown that there is a contradiction in the results concerning seasonal variations of the eddy diffusion coefficient between direct measurements and estimations based on minor constituents. Taking account of the vertical mean transport in the continuity equations for the above constituents might eliminate that contradiction. Results of the re-examination of the authors' data on the Ar to N 2 ratio published earlier are presented. The results show stronger turbulence in winter than in summer, the amplitude of the effect increasing towards higher latitudes.

l. INTRODUCTION Various experimental data, as well as theoretical studies, show that the terrestrial atmosphere is turbulent up to heights around 100 kin. It is widely known that turbulence to an essential degree determines atmospheric properties and the distribution of its parameters. First of all, it is true for the vertical distribution of atmospheric constituents. In the transport of heat, induced in the upper part of the atmosphere, through the lower thermosphere and mesosphere, turbulence also plays a determining role. Important, but still not solved, is the question of the competition between the heating in the lower thermosphere due to the dissipation of turbulent energy and the cooling by the turbulent transport of heat down into the mesosphere. Thus, one needs a parameterization of turbulent processes to describe atmospheric properties. However, we do not have enough knowledge about turbulence in the whole atmosphere to meet these needs. A classical hydrodynamic description of turbulence is faced with the problem of 'closing' the system of equations and, in the case of the free atmosphere, also with the problem of boundary conditions. It is impossible at present to calculate with acceptable accuracy the value of the eddy diffusion coefficient starting from the theoretical characteristics in the same way as the coefficients of molecular diffusion are calculated in molecular-kinetic theory. Experimental data on turbulence parameters are still poor and, as we will see below, contradictory in such an important aspect as seasonal variations of the turbulence. The aim of this paper is to compare two principal

approaches to turbulence determination around the turbopause, and to show that a proper account of vertical mean motions can eliminate the contradiction between the results of direct and indirect measurements concerning seasonal variations of turbulence parameters. The results of mass-spectrometer determinations of the turbopause height h, are re-examined and, based on these results, a model of the eddy diffusion coefficient K is constructed.

2, TWO APPROACHES TO DETERMINE TURBULENCE PARAMETERS

Direct methods of turbulence parameter measurements in the lower thermosphere allow us to determine the eddy diffusion coefficient K, the energy dissipation rate ca, and the intensity of turbulence W 2 defined as the mean square of turbulent velocity fluctuations. Simultaneous measurements of winds and temperature give the vertical profile of the local Richardson number Ri. There is a great, up to an order of magnitude, scatter of the measured parameters, but even with such scatter and the relatively small number of measurements there seems to be some tendency in the variations of K, ed and W 2. ZlMMERMAN and MURPHY (1977) have published results of direct measurements of turbulence parameters in a series of rocket experiments at various latitudes. Observing the evolution of explosioninduced smoke they obtained vertical profiles of K, ea and W z in the altitude range 40-90 km. They discovered that the probability of the appearance of a layer of turbulence was determined by the condition

148!

1482

A. D. DANILOVand U. A. KALGIN

Ri(h) < 0.25 increased exponentially with altitude.

Lg Kzz (cm-as -1)

This fact agrees with the idea that the turbulence is generated as a result of internal gravity wave dissipation. It was also revealed (ZIMMERMAN and MURPHY, 1977) that, on the average, below 90 km the winter values of turbulence parameters were higher than the summer ones at middle and high latitudes. This is shown in Fig. 1 from HOCKING (1987). An important complex of interrelated problems was reviewed by EaEL (1980). He used a zonally averaged approximation and obtained a seasonal and latitudinal distribution of the tensor components for the eddy diffusion coefficient based on the archive of measured fluctuations of the wind velocity. Statistical theory of the turbulence gives :

\',\

/,,

', ,0o\\ ,'\, \ . . o\ ,, ',// "2

~

~

-90 °

/ /,i

_

"'. : ~ & . J , :

-30

30

Summer

90

Winter

Geogrophical Iotitude

(1)

Fig. 2. Seasonal and latitudinal variations of the vertical eddy diffusion coefficient Kzz (EB~L, 1980).

where v' is the meridional wind velocity fluctuations, z is an integral time scale, ~0 is the latitude, h is the altitude, Kyy is the meridional component of the diffusion tensor (K). The shortage in experimental data led EaEL (1980) to introduce some simplifications to the relation between Kyy and Kz~. The shape of the vertical profile of K.~ was assumed to be independent of both latitude and season. The vertical profile of the tensor components was determined only up to 110 km ; K~ was permanently increasing, and not supposed to describe the turbulence around the turbopause. The map of altitude-latitude variations ofK:~ according to EBEL (1980) is presented in Fig. 2, showing higher K= for the winter hemisphere than for the summer one. An analysis of all the data on turbulence obtained with artificial clouds and smoke trails above 100 km does not allow us to find any systematic seasonal effect. The scatter of results amounts to two orders of

magnitude, as shown in Fig. 3 from HOCKIr~G(1987). This is probably the reason why no conclusion has been made on the basis of these measurements as to the seasonal and latitudinal variations of turbulence parameters by HOCraNG (1987). To the direct measurements of turbulence parameters we would like to mention determinations of the turbopause height h, based on mass-spectrometer data. DANILOVet al. (1979) and DANILOV(1984) have analyzed a set of data of rocket mass-spectrometer measurements of the Ar to N 2 ratio R (R = [Ar(h)]/[N2(h)]). The flights were made in various seasons and geographical locations. Values of the

K.(~, h) = v'~(~o,h)- ~(~o,h)

/ 1 --Summer

"N

110

2 - - Winter

110

w

90

90

-

I -3

~

I -1

Ig ca ( m 2 s "5)

Fig. 1. Seasonal variations of the energy dissipation rate ea (ZIMM/~RrCtAr~and MuRI'I-IV, 1977) for summer(l) and winter(2), taken from HOCKt~rG(1987).

I I

2

I 3

I 4

Ig K (m z s-1)

Fig. 3. Limits of the observed and calculated values of eddy diffusion coefficient (dashed area), from HOCKING(1987).

1483

Eddy diffusion coefficient turbopause height h, were derived from these data. This height ht was suggested to be the altitude where R starts to deviate from its ground value Ro = 1.2" 10 -2. The results of the above works have led the authors to the conclusion that the turbulence around the turbopause is more strongly developed in winter than in summer. More sophisticated analysis of the same data confirms this conclusion (see below in this paper). Thus, direct measurements of the turbulence parameters show stronger turbulence (higher value of K and h,) in winter. There are other, indirect, methods to determine turbulence parameters. These methods, in contrast to those described above, are purely phenomenological and the parameters derived are mean values. One of the first parameters obtained in this way was the K(h) profile derived from the analysis of the heat transfer processes (JOHNSON and WlLKINS, 1965 ; JOHNSON and GOTTLXEB, 1970). To explain the observed temperature profile, in addition to molecular heat transfer, they had to introduce some other mechanism which was supposed to be turbulent conductivity in the mesosphere and lower thermosphere. Turbulent diffusion was introduced also to explain the values of [0]/[02] observed at 120km (COLEGROVE et al., 1966; SmMAZAKI, 1971), COLEGROVE et al. (1966) suggested that K(h)= constant, whereas SHIMAZAKI (1971) not only accounted for the observed values of [0]/[02] but also suggested the following parameterization of K(h), which do not contradict the experiments : [Kmexp {-S~(h-h.,)2}, h ~ h,. / K(h) = ~ ( K , . - K I ) exp { - S2(h-h.,) 2 /

t

+K~exp{-S3(h-hm)},

(2)

h
where Km and h,. are the maximum value and the altitude of the K(h) maximum, S~, $2, $3 are the shape parameters for the top side and bottom side of the profile. Shimazaki suggested the following values for these parameters: Km = 10 7 cm 2 S -I, h,. = 100 km, $ 1 = $ 2 = 0 . 0 5 km 2, Ki = 106 cm 2 s 1 and $ 3 = 0.07 k m - i. The lower part of the profile corresponds to the increase of K(h) with altitude often observed in the experiments (see, for example JOHNSON and WILKINS, 1965; JOHNSON and GOTTL1EB, 1970). The sharp decrease above the maximum (the upper part of the K(h)-profile) agrees with the observed disappearance of turbulence above the turbopause height h,. The analytical approximation (2) is widely used in aeronomical studies of the mesosphere and lower thermosphere.

The above-mentioned papers (JOHNSON and WILKINS, 1965; JOHNSONand GOTTLIEB, 1970; COLEGP,OVE et al., 1966 ; SHIMAZAKI, 1971) used a universal approach to the problem of turbulence. The approach suggested the existence of passive minor constituents having no effect on gas movement (in the particular cases above O and O2), whose distribution might be described by the one-dimensional continuity equation : 0n ~ t +V-4) = P - L

(3)

where n is the concentration of the given minor constituent, q) is its flux, and P and L production and loss rates for the constituent. For the turbulent and molecular flux the following phenomenological expression is quite often used in aeronomical studies :

dp = - Kn

ffh + ~ N + ~

-Dn

~ + ~ h - +/4

(4)

where H and H,~, are the scale heights for the minor and the principal components, K and D are the molecular and eddy diffusion coefficients, and T is the temperature. The general approach based on equation (3) and expression (4) has been used by many authors to derive K(h) from the observed vertical profiles of various atmospheric constituents (see, e.g., ALLEN et al., 1981; WOFSY and MCELROY, 1973; HUNTEN and STROBEL, 1974). In these works various atoms and molecules (Ar, O, 03, CH4, N, N20) were used as a passive minor constituent with different altitude ranges studied and initial sets of data corresponding to various seasons and latitudes. The works by JOHNSON and GOTTLIEB (1970), JOHNSON and WILKINS (1965), COLEGROVE et al. (1966) and SHIMAZAKI (1971) became a foundation for many determinations of seasonal-latitudinal variations of K(h) based on an interpretation of the mesospheric and lower thermospheric composition (see, e.g., SINHA and CHANDRA, 1974; IVELSKAYAand KATIUSHINA, 1978; ANTONOVA and KATIUSHINA, 1976, 1980; ZADOROZHNY and GINZBURG, 1977). In all these papers, based on the solution of the one-dimensional continuity equation, the observed values of atomic oxygen lead to a summer increase of K(h) in the vicinity of its maximum. BLUM and SCHUCHARDT (1978, 1980), using the same approach to analyze satellite data on the neutral

1484

A . D . DANILOV and U. A. KALG1N

composition, claimed that both K and h, are higher in summer than in winter. Thus, there is clear contradiction between the two groups of turbulence parameter determinations concerning seasonal variations of its principal parameters (hi and K). Figure 4, taken from BLUM and SCHUCHARDT (1980), presents a good illustration of that contradiction. Recently a series of papers appeared (THRANE et el., 1985; BLIX et al., 1990; LUBKEN et al., 1987) in which turbulence parameters in the mesosphere and lower thermosphere were derived from rocket measurements of the vertical fine structure of neutral or ionized atmospheric constituents. In our opinion the above works, giving an essential input to the general problem of turbulence, cannot help in eliminating the above contradiction because of two reasons. First, measurements of that kind give us a 'snapshot'--an instantaneous picture of the turbulence layers. At another moment the picture of those layers may be quite different. For aeronomical purposes (minor constituent distribution, heat balance, etc.) we need some net effect of many such pictures, averaged for a period of at least a few days. Secondly, there are still not enough measurements to make conclusions on the seasonal variations of the turbulence parameters. 3. THE ROLE OF THE VERTICAL MEAN MOTIONS

BRASSEUR and SOLOMON (1984) were the first to suggest that the results of the K(h) determination from minor constituent profiles may be, in some cases, erroneous, because the divergence of constituent fluxes was not taken into account. The divergence is produced by atmospheric winds and should, to a greater or lesser extent, influence the distribution of minor constituents with various lifetimes and various altitude profiles. In fact the above explanation of seasonal and latitudinal variations of oxygen constituents by the effects

of turbulent transport is not the only possible explanation. The rival explanation takes the global thermospheric circulation into account. Even in the scope of one-dimensional models taking the vertical mean velocity of the gas into account allowed an explanation of the seasonal variation of oxygen constituents by seasonal variations of the vertical velocity (AKMAEVand SHVED, 1980; KOSHELEVet al., 1979) without suggesting a summer increase in K(h). Mass-spectrometer measurements on board the OGO-5 (HEDIN, 1974) and ESRO-4 (YONZAHN, 1977) satellites at altitudes 300-500 km have revealed typical peculiarities of the seasonal and latitudinal distribution of thermospheric neutral components--a winter bulge in the atomic oxygen and helium concentrations, and a summer increase of argon. These features of the neutral composition variations were explained in terms of zonally averaged models of the meridional circulation (REBERand HAYS, 1973). Both relatively simple (JOHNSONand GOTTLIEB, 1970 ; REaER and HAYS, 1973) and more sophisticated models (DICKINSON et al., 1975, 1977) give qualitatively the same picture of the meridional circulation, with upwelling at the summer pole, horizontal transport to the winter pole through the equator and downwelling over the winter pole. The velocity field obtained by the above models provides at least a possibility to eliminate the contradiction between the direct measurements of K(h) and estimates based on the phenomenological approach. A detailed consideration requires the use of three dimensional spherical coordinates z, 0 and 2, z being the distance from the centre of the Earth, 0 the colatitude, and 2 the longitude. In spherical coordinates the continuity equation for a minor constituent in a zonally averaged approximation may be written in the form

On O 2nv~ + - -1 ~ + ~ z (nv')+ z z'sin0 0 • ~ (sin O" n" Vo) = P - L.

Alcoyde

"--

--

/

I ~ "~- -~. "~.

'Blum

]

"

(5)

The vertical nv~ and horizontal nvo fluxes of the component are defined by

nv~ = n V ~ - D n

~ +~ ~

+

100 -o~ I.- 90

-_-/ I Winter

(1 On

\Donilov 19"/9 I Spring

-- Kn

1 OI

\ n az + T ~zz + ~

1) (6)

I

Summer

Foil

Fig. 4. Comparison of different concepts of h, seasonal variations (BLuMand SCHUCHARDT,1980).

nvo = n Vo

(7)

where V, and Vo are the velocity components of the

1485

Eddy diffusion coefficient principal gas. In (7) the meridional diffusive flux of the minor constituent is neglected. In the same way as (5) the continuity equation for the principal component can be written 3N (3 2NV~ ~ "~ - dt + (NV~) T

- -

1 t sin 0

"Jc -

O • ~0 (sin O" N" Vo) = 0.

(8)

constituent to the temporal and spatial derivatives of its relative concentration n/N. We emphasize that (9) and (10) relate height and latitudinal distributions of constituents with diffusion coefficients K, D and velocities of the mean motion V~ and Vo. If we do not take into account the meridional circulation, the same distribution is described by c)n

Formulae (5)-(8) allow us to write the continuity equation for a minor constituent in the form

ot=~

[1On

+/(olin

N+~+

°'~

0 '

+-

+Kn N + ~ N + ~

1 OT

l'

7)

N +r N +

Dn

(:0. l . D +

+

clO,~+ T,-O- -t + ,)}

+ K,•n \ n OT + t

Dn

0

+

~ + ~

, \n00

N00) + P-L'

(9)

+P-L.

(11)

As was already mentioned above, in the latter case the observed seasonal variations of atomic oxygen concentrations may be explained by a decrease of Ko, from summer to winter. As far as both (10) and (11) describe the same atmospheric situation, let us try to find a relation between K and K,~. For the sake of simplicity let us consider the situation for solstice at the geographic pole where it is possible to neglect the horizontal component of the transport. Subtracting (11) from (10) we obtain

The latter leads to 0

+ K~ +

,~t + ? ~t + 14<,11

,{ t

+Kn

{K(t) - Kerr(T)}+ {K(t) - K, rr(z) }

Dn

?.t

+

,,..)

This equation is of the form

0f(O

T~r +

~t

Here the functions K(z) and K~n(r) are determined in the interval (rE, to), where vE is the radius of the Earth and To the distance from the centre of the Earth corresponding to the lowest height where K(zo) = Ko~ (to) = 0. Equation (12) has the general solution :

< 7 ~ + T ~ z +H,,7

- v,,, L- <~T j

+f(~)Q(z) = P(t).

- ~;,n

C

, F"n l #7

"~L

~0

j+p-L

(10)

K(,)-K~rr(t)

nx2~

1

In

n'r

x

Formula (10) relates diffusive fluxes of a minor

V~nzz g

o~tln~) In

d~.

(13)

A. D. I)ANILOVand U. A. KALGIN

1486

The above boundary condition allows us to find the constant C in the following way. For the upper boundary condition: K(zo)-Kerr(Zo) =

1 2 ~ /`

n'~ nz ~ ~ln ~/)

•0 20 n x ( C q - f ~ E g~nz ~ ( l n ~ ) d z ) = 0

(14,

and thus ,0

C=-

20/'

n•

V~nz ~ t l n ~ ? ~ d ' r .

variations of K taking the vertical mean motion into account were made by GRIDCmN et al. (1982). They transformed the one-dimensional continuity equation to a form, describing the vertical distribution of atmospheric constituents and considered a three-component atmospheric model, including N2, 02 and O. Numerical solution of the system (continuity, hydrostatic and energy equations) showed that, taking into account vertical mean motions, it was possible to describe the experimental data on temperature and concentration only if the K(h) values in the winter hemisphere were higher than in the summer hemisphere. Their results are shown in Fig. 5.

(15)

E

Now we have the solution in the final form

4. M A S S - S P E C T R O M E T E R DATA A N D T H E M O D E L O F

/t'(h)

1 r(~)-gor,(0

=

×

;~o

20/'

nk

V, nz ~ l n ~ ) d z .

(16)

It is also worth mentioning that from equations (9) and (10) it is possible to obtain the equations used by JOHNSON and G O T T L I E B (1970), A K M A E V a n d SHVED (1980), REBER and HAYS (1973), GRIDCHIN et aL (1982) as particular cases to account for the influence of the vertical mean transport on the vertical distribution of neutral constituents. If we rewrite (16) as follows K(z) = K~rr(z) + A

(17)

As mentioned above the mass-spectrometer measurements of the neutral composition around the turbopause were used to determine its height h, (DANILOV et al., 1979, 1980; DANtLOV, 1984). Re-examination of this approach to h, determination as the height where the Ar to N2 ratio achieves its tropospheric value of 1.2 × 10-2 confirmed (DANILOVet al., 1989, 1990) the earlier conclusions on the seasonal variations of hr. Because some rocket Ar to N2 vertical profiles have a wave-like structure (for details see DANILOVet al., 1989, 1990) it was impossible to use these profiles for the direct determination of h,. To use all the rocket measurements available an additional analysis was made in terms of the total amount of argon in a column between 105 and 135 km :

where

A

=

-

-

•

n

(18) 6 --

01n~ nz 2 - -

120

x 10 6

dz we see that seasonal variations of the 'real' eddy diffusion coefficient K depend on seasonal variations of both Kar (obtained without taking vertical mean motions into account) and A. Seasonal variations of A have the opposite phase to those of Kcjr for both light (mi < n~) and heavy (mi > ~h) atmospheric constituents. Thus, qualitatively the above difference between the seasonal variations of K obtained in two approaches can be accounted for by the value A in (17) if it is large enough to change the sign of the seasonal variations of the sum (K~fr+A). Numerical estimates of seasonal and latitudinal

i

u

4

2

115

i

105

Summer I

-30 °

0° GeogrophicoI

30" Iotitude

Fig. 5. Seasonal and latitudinal variations of the parameters Kmand hmfrom GPaDcms et al. (1982).

Eddy diffusion coefficient I =

Ii 35

1487 Table 1.

R(h) dh

(19)

05

Season

in the same way as OFFERMANN et al. (1981). The lower integration limit is determined by the dynamic range of the mass-spectrometer, the upper one by its sensitivity. It is worth mentioning that the relaxation time of R(h) to new conditions z (z ~ H2/K, H2/D) is about one month. Thus, only those parameters which are obtained from the neutral composition data averaged for a period longer than one month are correct. Only seasonally averaged values satisfy this criterion. Keeping the latter in mind, all the data on I were divided into five groups according to the season and latitude of the flight. For each group an average value and its standard deviation were calculated. The results are shown in Fig. 6. The value of[might be considered as an indicator of turbulence intensity around the turbopause. The stronger the turbulence is, the higher should be the value of T Thus, Fig. 6 shows that the turbulence is stronger in winter than in summer, and that the amplitude of the seasonal variation increases towards higher latitudes. To obtain the turbulence parameters h, and K from the above data on [ one has to assume that the averaged values •correspond (in contrast to the individual ones) to a condition of diffusive equilibrium. With this assumption I does not depend on K and can easily be related to/~,. A neutral atmosphere model (CIRA72, 1972) and the above values of [ were used to calculate the turbopause height. The results are shown in Table 1. It is necessary to mention that in this paper we define the turbopause height as the height where

h-, (km)

Latitude

Winter Winter Tropics Summer Summer

= = Iwl < = =

80°N 48°N 23° 48°N 80°N

109 112 107-110 102 104 100~103 98 101

K = D (see, for example, BLUM and SCHUCHARDT, 1978). In fact, what we obtained from the neutral composition data is the homopause height, hh. However. we assume that these two values are equal (hh = h~) if h, is defined as above. One can easily see from Table 1 that the behaviour of/~, demonstrates the same tendency in its seasonal variation for all latitudes except the tropics : the winter /7, is higher than in the summer. It is worth mentioning that in deriving/7t we have not taken the vertical mean motion into account because its velocity is poorly known. If we did that we would obtain only the lower limit for the amplitude of the seasonal variation of/~t, because vertical mean motions would lift ,q, in winter and lower it during summer. Using the K(h) profile (equation 2) suggested by SHXMAZAKI(1971) it is possible to obtain the following expression for fixed ]~, and [ (keeping in mind that for any reasonable shape of the K(h) profile/7, > hm always) : INK(/;,) =

lnK,.-S,(~,-h.,) 2.

(20)

This formula gives a relation, between the maximum value of the eddy diffusion coefficient Km and the altitude of its maximum h,, for given fixed/7, and I. Figure 7 shows an example of various K(h) profiles

/

Winter 0.20

//

11o

/

h~

--

iI i I

"E 105-

b_-" 0.15

l I

0

--e_ _

{

1 I

50

GeogrophicQI Iotitude

T --~-Summer I 80

ii

.I:

I

~'--~-._

DI I / I 100

i I i I 6

I 7

Ig D,K (cm 2s -1)

Fig. 7. Two different kinds of K-profiles (solid lines) satisfyFig. 6, Seasonal and latitudinal variations of the parameter ing the condition of constant/~, and _LThe dotted line denotes Ifrom DANILOVet al. (1989) (points) and from OFFERMANN the geometrical place of maximum for any profile satisfying (1974) (circles). this condition.

1488

A . D . DANILOVand U. A. KALGIN

110

,< 123"1 "~

70

. .. t j i l l

70

I

I

6

7

Ig K,D (ern z s-1)

Fig. 8. Eddy (thick lines) and molecular (thin lines) diffusion coefficientsfor summer (dashed lines) and winter (solid lines) at high latitudes.

(solid lines) and all the possible positions of h,, (dashed line). To choose between all the profiles described above for each particular fit a n d / w e combined those profiles with the model by EBEL (1980), which presents the best, in our opinion, description of the seasonal variation of the lower part of the K(h) profile. The vertical eddy diffusion profiles obtained by this method for five seasonal and latitudinal conditions are presented in Figs 8-10. These figures present some sort of model for the seasonal and latitudinal variations of K(h). We realize that our model describes some average condition. The above K(h) profiles should differ from any instantaneous K(h)-profile obtained in 'snapshot' measurements of atmospheric irregularities (THRANE et al., 1985; B u x et al., 1990; LUBKEN et al., 1987) but we hope that they can be useful for aeronomical

~,~~ 1 1 0' 9 0 .~ .c

// 70

.

~" /

48 N

~/

I~ I 6 7 Ig K,D (cm2 s-ll Fig. 9. Eddy (thick lines) and molecular (thin lines) diffusion coefficientsfor summer (dashed lines) and winter (solid lines) at middle latitudes. "t"

5

90

5

I

I

6

7

Ig K , D ( c m ~s -1)

Fig. 10. Eddy (thick line) and molecular (thin line) diffusion coefficients at low latitudes.

tasks in which the net effect of the eddy diffusion has to be taken into account. 5. CONCLUSIONS There exists a contradiction between the results of seasonal variations of the eddy diffusion parameters K and h,. The determinations of these parameters based on direct atmospheric measurements give a picture of better developed turbulence in winter, as compared with the summer. Estimates derived from minor constituent distributions lead to the opposite conclusion that the turbulence is stronger in summer, but these estimates disregard the mean vertical motion of the gas due to the horizontal circulation. Taking the mean vertical motion into account our estimates are in agreement with the measurements. Thus, our considerations may help to eliminate the differences in the seasonal variations of turbulence obtained by different methods. Re-examination of earlier results on the turbopause height h, based on measurements of the argon to nitrogen ratio confirms our conclusion that in winter h, is higher than in summer. Using the amount of Ar between 105 and 135 km as an indicator of turbulence activity, the seasonal effect is shown to increase towards high latitudes. Combining the experimental data on fi, and [ w i t h the eddy diffusion vertical profile by SmMAZAKI(1971) and the data collected by EBEL (1980), the vertical profile of K for two seasons and three latitudinal zones has been obtained. This exercise gives higher values of eddy diffusion for winter than for summer; the amplitude of the effect increases towards high latitudes.

Eddy diffusion coefficient

1489

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