Thermospheric winds and the F-region: A review

Journul of Atmospheric and Terrestrial Phyaica,

1972, Vol. 34. pp. l-47.

Thermospheric winds and the F-region: A review H. RISHBETH Radio and Space Research Station, Ditton Park, Slough SL3 9JX, England (Received 19 July

1971)

Abstract-This

review deals with the neutral-air winds that blow in the upper atmosphere at heights above about 150 km. Starting from a discussion of the forces acting on the air, the equations of motion are set up and solved, enabling various properties of the wind systems to be deduced. The effects of the winds on the ionospheric PB-layer are considered in some detail. 1. 1NTRo~ucT10N 1.1

Some background ideas

years ago very little was known about neutral air winds at heights above 200 km. It was however known, from studies of the orbits of artificial satellites, that large daily variations of air density exist at such heights (JACCHIA, 1959). The variations are primarily due to heating by solar XW radiation. By day this radiation is mainly absorbed between 100 and 200 km, producing heating and ionization ; at night much of the heat is conducted away to the denser, cooler atmosphere below 100 km. This article is mainly concerned with the upper thermosphere, at heights above about 200 km, where the daily variation of temperature amounts to 20-30 per cent in middle and low latitudes. Figure 1 is a map of the isotherms in the upper thermosphere, according to the idealized model of JACCHIA ONLY

10

(1965).

The thermal expansion of the atmosphere by day forms the so-called ‘diurnal bulge’ which, in Fig. 1, is centred on the Equator at about 14 00 LT. This ‘bulging’ of the atmosphere gives rise to horizontal gradients of air pressure which can drive horizontal winds. Since the mid 1960’s, when these winds were first discussed in the literature (KINO and KOHL, 1965; LINDZEN, 1966), much consideration has been given to the questions of how the winds blow and what forces control their speed and direction. Like the winds in the lower atmosphere, the thermospheric winds are influenced by the Coriolis force due to the Earth’s rotation. In addition they are influenced, even more strongly, by frictional forces due to the viscosity of the air and to collisions between the neutral air particles and the positive ions. The ions exert a drag on the air because their motion is strongly impeded by the Earth’s magnetic field, so they cannot be freely blown along by the wind. This frictional force, or ‘ion-drag’, is generally the major factor limiting the wind speed in the thermosphere. Figure 2 shows the form of the global wind system at heights above about 250 km, according to the computations of KOHL and KINQ (1967). The winds blow away from the hottest part of the thermosphere, which is in the afternoon sector, and towards the coldest part in the early morning sector. They therefore blow across the polar regions and zonally around the Earth in low latitudes. This behaviour is quite different from that of winds in the lower atmosphere, which are strongly controlled by Coriolis force and which circulate around 1

H. RI~FSB~E

2

‘highs’ and ‘lows’ of pressure, and the difference is attributed to the great importance of frictional forces-viscosity and ion-drag-in the thermosphere. The winds can move the F-region ions and electrons in the direction of the geomagnetic field. If the field lines are inclined, this ion motion has a vertical component which can affect the ion and electron concentration, mainly because the The effect of the wind depends on its loss coefficient is very height-dependent. orientation with respect to the geomagnetic field; poleward wind (which mainly

L

I

04

I

,

08

12 LOCAL. ME411 FiME

16

___--_L-L___ 20

P

Fig. 1. Exospheric temperature distribution according to the model of JACCHIA (1965) for moderate solar activity at equinox (solar 10 cm flux approx 155 units). In this model the isotherms are also the isobars of the pressure distribution.

by day ; see Fig. 2) causes downward drift and tends to reduce the ion concentration, while equatorward wind (which occurs mainly at night) causes upward drift and tends to increase the ion concentration. These effects, being dependent on the geometry of the magnetic field, vary with latitude and with magnetic declination. Many of the phenomena of the F2-layer, such as the diurnal variation of the height of the peak (k,F2) and the peak electron concentration (N,,,F2) are well explained in terms of winds. Wind effects are particularly striking in high latitudes. Other phenomena, such as the seasonal anomaly, cannot be properly accounted for in terms of winds and require different explanations. Although F-layer storm phenomena are not yet fully explained, winds probably play a significant part in producing them. 1.11 T?te layout of this review. Although this article does not purport to describe the experimental data on winds in any detail, the sources of data should be mentioned occurs

Thermospheric winds and the F-region

3

(Section 1.2). Then, since so many wind calculations are based on empirical models of the diurnal bulge, one such model-that of Jacchia-is briefly described in Section 1.3. Part 2 presents the basic equations from which the winds are computed (Section 2.1). The equations have to take account of the pressure gradients that drive the wind; the inertia and viscosity of the air; gravity; the Coriolis and centripetal accelerations due to the Earth’s rotation ; and ion-drag (Sections 2.21-2.23).

0500

0700

I

40 mbrc

h -300km

H=BOkm

N,=10%-3

2. Northern hemisphere wind system at 300km height (KOHLand KINQ, 1967). The North Pole is at the centre of the diagram and the perimeter represents

Fig.

the geographic equator. The vertical ion distribution is everywhere assumed to be a Chapman layer with scale height 80 km and peak electronconcentration101sm-s.

Since the ion-drag force is proportional to the difference between the wind velocity

and the ion drift velocity, the various forces that cause ion motion must also be reviewed (Sections 2.31-2.34). When all these factors have been considered, one can set out the equations of motion of the air in greater detail and discuss the appropriate boundary conditions (Sections 2.41-2.45). In Part 3 the equations of motion of the air are solved in various ways, in order to study the importance of the different forces mentioned above and establish the general features of the wind system (Section 3.1). From Fig. 2 it will be seen that, at any particular latitude, the wind direction varies continually with local time. This variation, discussed in Sections 3.21-3.23, largely determines how winds affect the behaviour of the F2-layer (Sections 3.25, 4.2). The extent to which the wind speed and direction vary with height, at any given place and time, is strongly

4

H.

RISHBETH

influenced by viscosity (Se&ion 3.3). But the calculations of wind patterns raise some more basic questions. It is clear from Fig. 2 that air flows from the day side of the Earth to the night side; what sort of average circulation exists, how is the continuity of the flow maintained, and how much energy is expended in driving the winds? These questions are touched upon in Sections 3.41-3.44. In discussing the effeots of winds on the FZ-layer it is useful to develop some theoretical formulas relating to the behaviour of the FL? peak (Section 4.1). The F2 layer phenomena which are, or might be, influenced by winds are reviewed in Sections 4.21-4.27. Special factors apply at high latitudes and at low latitudes, so these are discussed separately (Sections 4.3, 4.4). Table Vectors (components

1. Principal

in geographic

used in this article

east, north, upward

u v

u,, I’,,

F

P,, F,, F,

a

B

0, R cos v, Q sin q BsinDcosI, BcosDcosI,

: S

0, 0, --9 0, 0, R &!, s,, 8,

Common@

symbols

u,, u, Vy, T’,

-BsinI

directions) neutral air wmd velocity ion drift velocity ( = - p-*pp) force per unit mass due to pressure gradient Eerth’s angular velocity geomagnetic induction acceleration due to gravity radius vector from Earth’s centre acceleration of air due to ion drag

used subscripts relating to electrons, ions, neutral particles components in directions parallel to, perpendicular

e, i, n II’ 1.

to B

Scalar quantities U F e

Y

D I

9

t h ;I N T P P

m f 11 &

horizontal component of U( = ( Uz2 + U,2)k) horizontal component of F( = (Fs2 + Fv2)$ azimuth of U( = arc tan (U,/ U,)) azimuth of F( = mc tan (FE/F,)) magnetic declination magnetic dip (.r = sin I) geographic latitude locrd time height (h,FZ refers to peak of F2-layer, etc.) reduced height scale height ion or electron concentmtion (N,FZ refers to peak of FZ-layer, etc.) temperature gas pressure density particle mass (mi,* = reduced mass of ion and neutral particle) charge of singly-charged positive ion Boltzmann’s constent coefficient of molecular viscosity momentum transfer collision frequency ( = Y,,~unless otherwise stated) pararr~t.erfor ion-neutral collisions ( = K,,i unless otherwise etated) Sun’s declination Coriolis parameter ( = 2R sin (p)

!lThermospheric win& and the

F-region

5

A recapitulation of the principal conclusions, and of some problems requiring further &ention, is given in Part 6. 1.12 Winds, tides and cErij’L9.Certain terms that are used in this article ought to be cl&rifled. ‘Winds’ here mean large scale motions of the neutral sir. Although the thermospheric wind system could be regarded as a ‘diurnal tide’, it is simpler to discuss it in terms of an equation of motion without using the concepts of potential functions and tidal modes which occur in tidal theory. Therefore, in this article, ‘tidal’ motions mean those that are driven by solar energy absorbed in the ozone layer and troposphere, and by lunar and solar gravitational effects; see the review by LINDZEN and CHAPMAN (1969). These tides may certainly be expected to influence the thermosphere. Indeed VOLLAND (1969) considers that their contribution to the diurnal density variation may be appreciable as high as 300 km. So any proper study of the thermospheric energy balance must certainly consider both the ‘tidal’ and XUV energy inputs. But many calculations of thermospheric winds, such as are described in this article are based on empirical models (like that of Fig. 1) ; so long as these models provide a reasonably good representation of the thermosphere, the wind calculations need not be particularly concerned with details of the energy sources. The ‘tidal’ motions certainly predominate at around 100 km, where they drive the E-layer dynamo (e.g. MATSUSHITA, 1969). The dynamo electric fields cause drift motions of FZ-layer ionization by the ‘motor’ effect (MARTYN,1953). In the present article, ‘drift’ refers to a bulk motion of the ions end electrons, due to either winds or electric fields. The term ‘drift’ has often been applied to the apparent motions of small-scale ionospheric irregularities, but these motions are not necessarily related to the large scale motion of even the ionization in the F-region, much less to the neutral-air winds. 1.13 Termhology and notation. The terminology used in this review is generally that of ionospheric physics: for example an ‘eastward’ wind means west-to-east. In calculating winds at a particular point most workers express their equations in Cartesian rather than spherical coordinates, and the present article uses the x = eastward, y = northward convention of meteorology, though many published papers take 5 = southward, y = eastward. Cartesian components of vectors are indicated by subscripts, x, y, z (the z-direction being upwards, not downwards as in geomagnetism) ; the convention that subscripts denote derivatives, used in some meteorological works, is not followed here. Table 1 lists principal symbols, but omits some that are used only within one section of this article. 1.2 Sources of experhmtal

data on Wind8

Before the advent of ertiflcial satellites, detailed theoretical and experimental knowledge of wind systems did not extend above the meteor region at 80-110 km. But in recent years experimental data on thermospheric winds have begun to accumulate. KENT (1970) has reviewed some available techniques. Winds can be measured by releasing chemicals from rockets, though in the upper thermosphere difficulties are caused by the rapid diffusion of the chemical clouds. Either the neutral wind velocity or the ion drift velocity is measured, depending on the substance released. Measurements have been reported for example by

H. RISHBETH

6

HAEBENDAL et d. (1967), and KOHL(1970) has found the measurements of Haerendal and Rieger to be reasonably consistent with wind calculations of the type described in this article. The doppler shift of the 630 nm airglow, emitted by atomic oxygen at 200-400 km altitude, can be used to measure winds at night (ARMBTRONO, 1969; NAQY et al., 1971). Indirect information has come from measurements of the ion drift velocity by the incoherent scatter technique (VASSEUR,1969; EVANSet d., 1970) and from the analysis of F&layer variations caused by winds (HANSONand PATTERSON, 1964 ; KIN@ et al., 1967). The motions of artificial satellites are slightly perturbed by winds, and it was by this means that the eastward rotation of the atmosphere was discovered by KING-HELE(1964). Large-scale waves in the thermosphere are observable as ‘travelling ionospheric disturbances’ but these phenomena are outside the scope of this article. As already mentioned, the motions of small-scale irregularities in the F-region are not considered to bear a close relation to the neutral-air winds. 1.3 Jac&a’s

nz0de.lof the diurnal

bulge

To calculate winds one needs to know the horizontal gradients of pressure and density, so a model giving the latitude and local-time variations of these quantities is required. Such a model is that of JACCHIA(1965), which is based on extensive data obtained from observations of satellite motions, and comprises: (i) A set of tables giving the vertical distribution of density, gas concentrations, scale height, and mean molecular weight for different assumed temperature profiles T(h). At the lower boundary, 120 km, all gas concentrations are assumed fixed with a fixed temperature T(120) = 366’K. The temperature profile is assumed to be of a fixed mathematical form in which the gradient dT/dh is positive at 120 km and decreases upwards as T approaches a limiting value T o3at great heights. T, is called the ‘exospheric temperature’ and the individual tables correspond to T m = 660(56)2100°K. Given T(h) and assumed lower boundary conditions, the other parameters are calculated from the barometric equation and the perfect gas law. Using BATHIS’(1969) temperature function, WALKER (1966) has constructed analytic formulas to represent the vertical distributions of gas concentrations, which are useful for computational purposes. Some numerical data on pressure gradients are given in Section 2.22 of the present article. (ii) A formula giving T,, the minimum global value of T,, in terms of solar activity (as measured by the solar deuimetric flux density), magnetic activity, and the semi-annual and 27-day variations. (iii) Formulas giving the global distribution of T,/T, as a function of geographic latitude, local time, and solar declination 6 (which introduces a seasonal variation). The formulas contain various disposable constants; using Jaechia’s recommended values of these, the maximum global value of exospheric temperature, T,, is found in latitude B at 14 13 LT and the minimum value, T,, in latitude --B at 03 47; the ratio T,}T, = 1.3.

7

Thermospheric winda and the F-region

All the parameters involved in (ii) and (iii) are chosen to give the best possible agreement between model densities and satellite drag data (JAC~EIAand SLOWEY, 1968) ; subsequent modifications do not greatly alter the form of the diurnal bulge as shown in Fig. 1. The CIRA (1966) model uses rather similar lower boundary conditions to those of Jacchia’s model but it does not give latitude variations. Its local-time variations are computed by solving the time-varying heat balance equation for the thermosphere, for 10 different values of solar activity. 1.31 Then&&ion of globd mod& to o&r data. The satellite drag data have the advantage of global coverage, as compared to data obtained from rockets ; however a good deal of averaging has to be done, so the models obtained from satellite data do not show any localized features. Essentially the satellite drag data give values of density, and other information has to be used to obtain the distributions of pressure, temperature and gas concentrations. The model values of these derived parameters are generally less reliable than those of density and do not always agree well with other kinds of data. For example : (i) Although in Fig. 1 the global temperature minimum is situated in low latitudes, incoherent scatter data (WALDTEUFEL and MCCLURE,1969) and rocket data (REEK, 1971) suggest that it is in high latitudes. (ii) Incoherent scatter measurements locate the diurnal maximum at around 16 00-17 00 LT, while the CIRA and Jacchia models place it at about 14 00 LT. (iii) The models necessarily use rather arbitrary lower boundary conditions, so they cannot be expected to be very accurate at lower heights. Should the current models be found in need of amendment, the wind systems computed from them will of course be inaccurate in detail. However, most of the general principles described in this review should nevertheless hold. 2. THE EQUATIONSOF MOTION

2.1 Introduction In the thermosphere the molecules collide so frequently that the air may be regarded as a fluid which is subject to hydrodynamic equations of motion. At 300 km the interval between collisions (about 1 a) and the mean free path (about 1 km) of a neutral particle are small compared to the time and distance scales that characterize the wind systems. The air can be treated as a single fluid because any differential motion of the various constituents (except perhaps hydrogen) is very much less than the overall wind speed. Only in the exosphere above about 600 km, where the air molecules move in ballistic orbits and suffer few collisions, does the validity of the fluid equation of motion become questionable. It is convenient to set out here the important terms in the equations of motion, 6rst in words and then in symbols: (Acceleration) + (Coriolis term) = (Pressure-gradient force) - (Ion drag) + (Viscous drag) + (Gravity) dU/dt + 28 x U = F - %tnJ - V) + (p/pPU

+ 8.

(1)

8

H.

RISHBETH

Here U is the wind velocity, V the ion drift velocity, Q the Earth’s angular velocity (Section 2.21), F the driving force per unit mass due to pressure gradients (Section 2.22), Y,~ the appropriate neutral-ion collision frequency (Section 2.31), (p/p) the kinematic viscosity (Section 2.23) and g the acceleration due to gravity. Since equation (1) contains the ion velocity V and the collision frequency Y,,, which is proportional to the ion concentration N, it is necessary to take into consideration the equation of motion and continuity equation for the ions (Section 2.3). The discussion then returns, in Section 2.4, to consider the equation (1) ; its components, the size of its terms, and the appropriate boundary conditions. 2.2 Forces acting on the neutral air 2.21 Acceleration of the air. Normally one wishes to find the wind velocity U(t) in a coordinate frame fixed with respect to the Earth, which is rotating with angular velocity8. The Coriolis and centripetal accelerations due to the rotation have then to be included in the equation of motion, which then gives the acceleration ‘following the motion’ of the air, i.e. the total derivative dU/dt. At any given point the derivative au/at differs from this because the flow of air transports momentum past the given point. According to the equations of hydrodynamics (d/dt) = (a/&) + when this identity is applied to the velocity U it results in a nonlineal 0J.V); ‘advection’ term in the equation of motion. If ZF’ stands for the entire right-hand side of (1) one can rewrite the equation in two ways: dU/dt+2PxU+I(Zx(QxR)=~l?

(2)

au/at+(n.v)u-t_2s2~u+sz~(fi~x)=t;F

(3)

in which R is the radius vector from the centre of the Earth to the point where the equations are applied. The Coriolis acceleration 2S2 x U must be included in accurate wind calculations. The centripetal acceleration 51 x (SL x R) is usually neglected even though its magnitude is comparable to that of the Coriolis term ; it is unimportant because at a given place it is constant in magnitude and direction, and may be regarded as a small fixed perturbation (less than # per cent in size) of the gravitational acceleration g. The nonlinear term (U .V)U is small if the wind speed is very much smaller than the Earth’s rotational speed (U Q RQ), but when U is large and has large spatial gradients, aa might be expected near sunrise and sunset, the term might be sign&ant (Section 3.24). It is usually neglected, however, in order to make the equations more tractable. 2.22 Pre88we-gradient force. Owing to the presence of the diurnal bulge the air pressure gradient Vz, is not precisely vertical. Its horizontal components provide the driving force for the winds. This will be called the ‘pressure-gradient force’ (it is actually the force per unit mass), and its zonal (eastward) and meridional (northward) components are respectively F* =

-p-lapjax;

p, = -P-lap/ay

where p is the air density. Naturally the vertical component of

(4) Vp is

by far the

Thermoapheric winds and the P-region

9

largest but, since it is almost exactly balanced by gravity, it gives rise to very little

air motion. Since the JACCHIA(1965) model gives T,

a8 a function of latitude and local time, it is useful to have numerical values of the quantity p-Vp/aT, for the purpose of calculating winds. The following formulas hold (to within a few per cent) for T, between 800 and 1400°K: p-lJp/i?T,

=

1530 - O-92 T,

(h = 200 km)

3550 - 2-00 T,

(k = 300 km)

( 5400 - 2-95 T,

mS8-2(“K)-1.

(5)

(h = 400 km) 1

2.23 viscosity. If there exist wind shears, i.e. spatial gradient8 of u, viscous expression for the viscous force per unit forces will be set up. The mathematical volume is fairly complicated but, on neglecting certain terms that are probably small, it reduce8 to pVTJ where p ia the coefficient of molecular vi8coRity (e.g. SUTTON,1953). Normally only the vertical wind shear matters 80 the force per unit ma88 become8 simply (P/p)i32U/i3h? This term gives the equation of motion the form of a diffusion equation ; the momentum of the air tend8 to ‘diffuse’ in such a way as to smooth out the velocity-height profile. As will be seen in Section 2.44, this tendency is particularly important at great heights where p is small and the ratio p/p, known a8 the ‘kinematic viscosity’, correspondingly large. From the calculation8 oxygen is given by

of DAL~ARNO and SMITH (1962) the value of p for atomic

,u = 4.6 x 10-6(T/1000)o’71

kg m-l 8-l.

(9)

At height8 where viscosity is important, the atmosphere consists largely of atomic oxygen and the gradient8 of temperature are small, 80 p may be treated a8 a constant. Equation (6) is adopted for the numerical values of y employed in this article.

2.3 Motion of the positive ions 2.31 ColEisionsbetween ions and neutral particles. The ion-drag force per unit mass acting on the neutral air (velocity U) due to collision8 with ion8 (velocity V) may be written 8 = Y,,(V -

II).

(7)

The parameter Y,( L called a ‘frictional frequency’ or ‘collision frequency for momentum tranefer’. It is comparable to the average frequency with which any one neutral particle experiences collisions with ions. By Newton’s Third Law it is related to the ion-neutral collision frequency ytn by the equation pnvnc = pIvl+,, pn, pi are the densities of neutrals and ions. In the daytime PZ-layer at 300 km, where about 1 part in 1000 of the air is ionized, vin N 1 s-l and Y,~E 1O-J s-1. The reciprocal of Y,< may be regarded as a time constant (about 1000 8) within which the ions, if set into motion by an electric field, communicate their motion to the neutral air (DOUGHERTY,1961). Let Y,( = K,,N, where N, is the ion concentration. The coefficient K,, depend8 on the species involved. For 0+ ions in atomic oxygen, the most important ca8e where

H. RISHBETH

10

aa regards the Fe-layer, the following values may be obtained from data given in the literature : K,,

= 7.3 x 10-1e(T/1000)0’4 m3 s-l (DALOARRO,1964)

Kni = 9.3 x 10-1s(T/1000)0~37 m3 s-l (STUBBE,1968).

(8)

Here T is the temperature of the neutral particles and ions; if the ion temperature T, difFeraappreciably from T, a certain combination of T and T, replaces T in these equations (STUBBE,1968) though near the F2 peak this correction is generally not very important. In calculating K,, for like ions and neutrals, such as 0+ and 0, the occurrence of charge exchange must be taken into account. If the ions and neutrals are unlike, as is mainly the case in the FI-layer, K,, is generally smaller and less temperature-dependent; some values for T -h lOOO”K, derived from STUBBE(1908), are as follows (in unite of lo--l6 m3 s-i) : 3.9 for N, and 0+ ;

4.9 for 0 and NO+ ;

4.7 for N, and NO+ .

The corresponding values for O,+ are nearly the same as for NO+. As discussed by Stubbe, many authors use a rather different definition of collision frequency which makes use of the reduced mass mm* of the ions and neutrals. Let K,i*, vni* be the collision parameter and collision frequency defined in terms of so that v,,~*= Kni*Ni. Then, if m,,,m, are the ionic and neutral particle masses: mi,* m,K,,

= mrKin -N 1-9 x lO-“l kg m3 s-l

= m,,*Ki,*

(9)

in which the numerical value applies to 0+ and 0 at lOOO%, and K,, is the coefficient, analogous to K,i, for ion-neutral collisions. The formulation in terms of reduced mass has the property that Kin* = K,,*, and if m, = m, then Ki, = K,, = iK,,*. 2.32 Causes of ion motion. The four principal causes of ion motion in the Flayer, and the orders of magnitude of their contributions to 0 in midlatitudes at around 300 km, are as follows : plasma diffusion, 10 m s-l; neutral horizontal air winds, 100 m s-l at night, 30 m s-l by day; vertical thermal expansion and contraction of the atmosphere, 3 m s-l ; and drifts due to electric fields generated by dynamo action in the E-layer, 30 m s-l. If the ion gyrofrequency oi greatly exceeds the collision frequency vi,, with neutral particles, as is the case for ions and electrons throughout the F&layer, the first three kinds of motion are essentially parallel to the geomagnetic induction B,but the drift due to electric fields is normal to B. (F-region winds do produce a very slow ion drift normal to B (RISHBETH, 1971) but this effect may be ignored for the purposes of this article.) Many published calculations only take into account the ion motion due to winds. In this approximation the ion velocity equals the field-aligned component U,, of wind velocity ; in vector terms v = (U . BpyB?

(10)

The ion-drag acceleration $ then depends on the orientation but not the magnitude of the magnetic field; it is a function of the magnetic dip f and de&nation D. If D = 0 then V7, = 0 and VU = U, co@ I so that in the ion-drag expression (7) (cf. GEISLER,1966) : x, = -v,,u,;

S, = -VALUEain=I.

(11)

!I’hermosphericwinds end the P-region

11

More generally when D # 0:

S, = ~,~U,(sin~D cos2I - 1) + v,~U,, sin D cos D coszI S, = v,JJ&os~D

COGI -

1) + v,JJz sin

(12)

D cos D COGI.

(13)

More accurate expressions have been given by ROSTER (1971). The drifts due to electric fields should be taken into account in accurate wind calculations (BRAMLEY, 1967). As is well known, the electric field E in the F-region is very nearly perpendicular to B and the drift is perpendicular to both, being given bY

V, = E x B/F.

(14)

The components of V, can be expressed in terms of the horizontal E,, E, of the electric field: V,,

= -(&,/B)

sin D cos D cos I cot 1 -

(E,/B)(sin

components

I + cos”D cos I cot I) (15)

I + sin2D cos I cot I) + (E,/B) sin D cos D cos I cot I

V Iv = (E,/B)(sin

(16) V,,

= (EJB)

cos D COBI - (E,/B) sin D cos I.

(17)

When D = 0 these reduce to (cf. MAEDA and KATO, 1966):

V 12 = -(E,/B)

cosec I;

V,,

= (E,/B) sin I;

V,,

= (E,/B) cos I.

(18)

The velocity V, is then included in the ion-drag term of equation (1). In practice it is often neglected, largely for simplicity but partly because the electric fields E,, E, are not accurately known. CHALLINOR (1970s) has shown that the inclusion of electric fields makes a perceptible difference to the calculated wind velocity, at any rate in low latitudes. Nevertheless the effect of electric fields on the calculated variations of N,F2 and h,F2 at midlatitudes is quite small (STUBBE and CHANDRA, 1970; BRAMLEY and ROSTER, 1971). In considering plasma diffusion the presence of the electrons must be taken into account because of the electrostatic force between them and the ions. It can be shown that the ion diffusion velocity depends on the sum of the electron and ion partial pressures, p6 = NkT,, pi = NET, respectively, where T,, Ti are the electron and ion temperatures and k is Boltzmann’s constant. The collisional force between electrons and ions has very little effect on the ion drift velocity snd the effect of electron-neutral collisions on the air motion is entirely negligible. The remaining kind of ion motion, that due to vertical expansion or contraction of the atmosphere, is accounted for by including the appropriate vertical air velocity U, in the ion equation of motion. 2.33 The equation of motion for the ions. All the motions discussed above are included in the equation for the ion motion:

dV/dt = g -

N+i V@e+ pi) -

vi,(V - U) + i, (E + V x B) N 0 t

(19)

H.

12

RISHBETH

where mi, e are the ionic mass and charge. If more than one ion species is present a separate equation is required for each. The Coriolis term has been omitted because Q Q v,,, and dV/dt may also be neglected because of the very short time constant rinl (about 1 8) within which the ions attain their steady-state drift velocity. As mentioned in Section 2.32 the velocity normal to B is just E x B/B2. The equation for the ion velocity parallel to B is obtained by resolving (19). Using the 8UbBCript,, to denote components of vectors parallel to B, and putting dY,,/dt = 0: 0 = g sinI - +g

Vf,(P,+

Pi)

-

vin(v[[

-

U,,)

1

where U,, = U, sin D cos I + U, cos D cos I -

U, sin I.

(21)

2.34 The continuity equation for the ions. In any complete theoretical inveatigation of F-region winds it is necessary to take account of the variations of the electron and ion concentration N, since the ion-drag force is proportional to N. If q and 1 are the production and loss rates, the continuity equation is i?N/i3t = q -

Z(N) -

V. (NV)

(22)

where V is obtained by solving the equation of motion (19). A separate equation is required for each ion species if there is more than one, a8 is the case below about 200 km. But in the FZ-layer most of the ions are Of and the equation with a linear loss coefficient #l 8N/i3t = q -

,!?N -

V . (NV)

(23)

applies quite well to ions and electrons alike. Often for simplicity this equation is applied at all height8 in the computation of F-region winds ; below 200 km its use leads to an underestimate of N and hence an underestimate of the ion-drag force. 2.4 The equation of motion of the air and its boundary condtkns 2.41 Equations for the wind components. On combining the expressions given in Sections 2.21, 2.22, 2.23 and 2.31 but neglecting centripetal force, the equation of motion (1) can be written in a slightly modified form : dU/dt = F + (,u/~)~~U/~P - KN(U - V) - 251 x U f g.

(24)

For purposes of computation this equation ha8 to be resolved into equation8 for the components of U. At geographic latitude v: dU,/dt = F, + (p/p)Z12U,/i3h2- NK(U,

-

V,) + 2ft(U, sin ‘p -

dU,/dt = F, + (p/p)i32U,/i3h2 - NK(U,

-

V,) -

dU,/dt = F, + (,+)a2U,/ah2

-

NK(U,

-

U, co8 v,)

2f2U, sin Q‘

v,) + 2fiU, ~0s y.~-

(25)

(26) g.

(27)

It is convenient to denote by F and U the magnitudes of the horimatal components of the vectors F and U: thus F = (FE2 + Fy2)1/2;

u = (U,2 + uy2p2.

(28)

13

Thermospheric winds and the F-region

2.42 The set of equations governing air motion. Equations (25) and (26) are the basic equations used to compute the horizontal winds. They are complicated to solve for several reasons: they are coupled by the Coriolis terms (though the term in U, may be omitted from (25)) ; they contain height derivatives in the viscosity terms; they contain nonlinear acceleration terms such as U,i?U,/ax (Section 2.21); and they contain the ion parameters N and V which must be obtained from other considerations. Neglecting electric fields, there are six equations governing the motions of the air and the ions : three equations of motion for the air (25-27) ; one equation for the field-aligned ion velocity (20); the continuity equation (23) for the ions; and the continuity equation for the neutral air, viz:

an/at = 3.

(nU).

(29)

These six equations connect six variables, namely U,, U,, U,, I’,,, N and n (or p)., However the equation (27) is not useful in practice because it virtually reduces to the hydrostatic equation .F# = g; the Coriolis term is of order 1O-s g and the other terms are smaller still (RISHBETE et al., 1969). Most calculations ignore equation (27) and therefore require additional information ; generally this is obtained by adopting a model atmosphere so that n (or p) is treated as known. If ion motion normal to B is taken into account there are two extra equations of motion for the ions, so that two extra parameters (such as E, and E,) have to be specified. Some published calculations reduce the number of equations by further assumptions, e.g. by taking N as known, which dispenses with the ion continuity equation, or by assuming U,, = V,,, which dispenses with the ion equation of motion. As will be discussed in Section 3.2, these simplifications can be most useful if it is only desired to compute horizontal winds. If on the other hand a more fundamental calculation is intended, in which the air distribution is not assumed to be known, it is necessary to include the thermal balance (energy) equations in the analysis. 2.43 The magnitudes of the terms. In order to understand the properties of the winds it is useful to have some idea of the relative magnitudes of the terms inequation (24). These are demonstrated in Table 2, in which part (a) shows data for 300 km Table 2. Typical values of parameters at midlatitudes PlW8metM Unit

T

H

N

OK

10-l~Pkgmva

km

(a) 300 km height Sunspot min., midnight Sunspot min., midday Sunspot max., midnight Sunspot max., midday

720 1010 1170 1590

8 15 32 45

39 52 60 72

1.3 3.1 2.0 14

0.8 2.3 l-6 12

30 12 5.1 2-7

230 300 200 180

280 130 130 16

(b) Sunspot min., midday 15Okm 200 km 250 km 300km 400km 500 km

590 850 900 1010 1040 1050

2100 213 48 15 2.2 o-4

21 35 44 52 61 70

l-7 2-6 4-o 3.1 1.3 o-5

O-8 l-8 2.9 2.3 1.0 0.4

o-1 l-6 4.6 12 56 225

30 120 210 300 480 650

40 70 70 130 480 1600

Coriolis parameter at latitude 45’:

10”

f = 2n sin Q = 1.03 x lo-’

s-1

H. RISEBETH

14

midnight and noon, sunspot minimum and sunspot maximum ; part (b) shows data for several heights, for noon at sunspot minimum only (see Fig. 3). The neutral atmosphere data ere taken from CIRA (1966), models 2 and 7 for solar 10 cm flux v&lues of 76 and 200 units respectively. Since the CIRA models do not give latitude variations the horizontal pressure gradient force F has been computed from Jacchia models for latitude 45’, using the same values of T, a,s are at

E(m SK-*)

03

.06

.09

’ /’

./

./’

./F /

I!

p?Tr/’

./

/,

,

/ ,/

/ //

//

I

//

/ //

//

/ //

/

I

Fig. 3. Graphs of quantities shown in Table 2 for mlddey at sunspot minimum. The upper scale applies to the acceleration due to the pressure grcldient, P (- . - . - e). The lower scale refers to the ion-drag parameter, vni(); the Coriolis parameter for latitude 45’, f(. . . . .); and the normalized kinematic viscosity parameter, ,u/pH2(- - - -).

given by the CIRA models. The electron concentrations are for Watheroo, W. Australia, for September 1954 (sunspot minimum) and September 1948 (sunspot maximum), taken from Tables of Ionospheric Electron Density (Cavendish Laboratory, Cambridge) by S. A. CROOM, A. R. ROBBINS and J. 0. THOMAS; reasonable extrapolations are made for heights above h,F2. Values of ,u and v,,~are computed from equations (6) and (8). The ratio F/v,~ is the steady-state wind speed if ion-drag alone is assumed to control the wind. The relstive importance of ion-drag and Coriolis force may be seen in Table 2 by comparing vmi with the Coriolis parameter f = 2Q sin 45’ = 1.03 x 10-O 8-l. At 300 km Coriolis force is not particularly important during the day, but it will be dominant at night in winter when N,F? becomes very small. Figure 3 shows that

Thermoapheric winds and the P-region

16

f > vml,( below about 150 km, so that Coriolis force becomes an important factor in but at such heights the lower thermosphere. Above about 400 km, too, f > Y,,~ neither Coriolis force nor ion-drag is as important as viscosity, the effects of which are now considered. 2.44 Vi.mkty and tire upper botmdary condition. To estimate the size of the viscous term in the equation of .motion, some particular height variation of U must be assumed because the term depends on the derivative aaU/aha. Since both F and v,,( are height-varying on a scale comparable to the atmospheric scale height H it is reasonable to suppose that U might vary similarly. Thus if for example U cc exp ( hh/IZ), the vi scous term is (p/Hpa)U. The quantity p/pH*, which serves as a rough measure of the importance of viscosity, exceeds the ion-drag parameter Y,~at 300 km (Table 2(a)), except for sunspot maximum midday when ion-drag is very strong. For the conditions of Table 2(b), ,u/pHa > vnht at heights above 220 km (Fig. 3). The rapid upward increase of p/pHa, which is due to the upward decrease of density p, suggests that the viscous term might dominate the equation of motion of the air at great heights. In contrast the pressure-gradient force F increases only approximately linearly with height (Fig. 3), whereas the Coriolis parameter f remains constant and Y,*decreases above the FL?peak. Therefore, if the viscosity term is not to be overwhelmingly large at great heights, a8U/ahs must become small so that au/ah -+ constant. In fact au/ah + 0 at great heights as otherwise, to maintain a gradient of U, there would have to exist a shearing force which neither the pressure gradients nor Coriolis force nor ion-drag can provide. Hence at great heights U must become height-independent, which is the upper boundary condition for the equation of motion. 2.45 The lower boundary. The CIRA and Jacchia models of the thermosphere assume unvarying temperature and density at the lower boundary, 120 km, so there the horizontal pressure gradient is zero. It is therefore often assumed that at this height 27, = U, = 0, viscosity being too weak in this region to transmit any significant velocity from greater heights. LINDZEN (1967) has shown that even if non-zero values of U, and U, are imposed at 120 km they have virtually no effect on the values computed above about 160 km. However, the vertical velocity does not necessarily vanish at the lower boundary (RISEBETRet al., 1969), though it is likely to be small there. The assumption of unvarying conditions at 120 km, though convenient for the construction of thermospheric models, cannot be expected to be realistic. Unfortunately not many data are available on atmospheric variations at this level. HABRIS and PBIESTER(1966), VOIGND (1969) and CEWDRA and STUBBE(1970) have considered the effect of variations of temperature or density or composition at the lower boundary, but did not consider in detail how they might affect the thermospheric wind pattern. 3. THE COMPUTED WINDS 3.1 Idr0dwti0n

The equations of motion can now be used to discuss the main features of the wind system, the general form of which was described in Section 1.1 and illustrated in Fig. 2. The factors that control the wind direction, as a function of local time, 2

H. RI@-

16

are dealt with in Section 3.3, while Section 3.3 considers how viscosity influences the variation of wind velocity with height. Some other aspects of the winds, euch as the net transport of air and energy considerations, are dealt with in Section 3.4. 3.11 RWcr’e mk%&ude wind cok~ions. To i&&rate various features of the winds, use will be made of detailed caluulations kindly provided by Dr. R. Rtister.

LT

00

06

I2

18 LOCAL TIME

24

06

(hr)

Fig. 4. Locel time varietion 8t 300 km of the total wind speed U(), ZOn81 wind speed U,, positive tx&war&e(- - - -), and meridiomslwind speed CT,,positive northw8rde (.**.* *), from R&t&e c&ulstione for latitude 81% st equinox. The computed variation of N,F2 is shown below (- 3- * - m).

The calculations are for Lindau (bl”N, lO”E, I = 66’, D = -4’) for equinox at moderate solar activity (solar 10 cm flux 160 units) and are based on Jacchia’s atmospheric model (Section 1.3) for magneticaby quiet conditions. The ion, electron and neutral gas temperatures are assumed equal and no electric fields are included. Continuity equations for four ion species (0 +, 09+, NO+, Na+) and electrons are solved in the course of the calculations. Further details mregiven by R~ETER(197l). Figure 4 shows the diurnal variation of the wind components U, (eastward) and U, (northward) and the total wind speed U at 300 km. The big day-to-night difference in U is mainly due to the difference in ion-drag, as may be seen by comparing U with the curve of N,,,F2 plotted below. As discussed later in Sections 3.41-3.42, the diurnal averages of U, and U, are not zero, there being a prevailing (mean) westward and equatorward wind.

Thermoepherio winds and the F-region

17

Calculations for other levels of solar activity are not given here, but as solar activity decreases the wind speeds increase (at least by day) because the ion-drag decrease8 more rapidly than the pressure-gradient force (CEO and YEE, 1970). Though the position of the diurnal bulge varies with season, the general form of the wind pattern does not change much. 3.2 Wind direction and how it varks with

local time

The factors that control the wind direction may first be studied with the aid of simplified equations of motion in which viscosity is neglected and the ion motion is assumed to be solely due to winds. Then U,, = VI, so that, with V, = 0 and zero magnetic declination, V= = 0 and I’, = U, co& (Section 2.32)and (25),(26)' reduce to dU,/dt = F, - KNU,

+ fU,

dU,,/dt = F, - KNU#’

(30)

- fU,

(31)

where f = 2f2sin v is the Coriolis parameter and s = sin I. 3.21 Steady-state conditions with Coriolie force and ion-drag. For steady-state conditions with d/dt = 0 the solutions of (30),(31)are (cf. GEISLER, 1966)

u, = KNFa3

KaNW

jiJ

Y

=

+fF, +$

(32)

KNF,

-fFal KaNaes’ +$

(33)

’

Let 8, y be the azimuths of the wind and pressure-gradient force respectively, measured clockwise from geographic north so that tan y = FJF,.

tan 8 = U,IU,;

(34)

From (32)and (33)it can then be deduced that tan(c)

=KN-vJ

+f

KN -ftany

(35)

.

If Coriolis force dominates so that If 1 > KN then 0, = F,lf;

U, = -Pelf

(36)

and the speed and direction of the wind are given by U = F/lfl:

tan 8 = -cot

y.

(37)

This is the ‘geostrophic’ wind of meteorology, parallel to the isobars and therefore perpendicular to the pressure-gradient force, with 8 = y f 90“ (+ sign in the northern hemisphere, - sign in the southern). Alternatively if ion-drag dominates so that If I < KNea then U, = FJKN;

U, = F,,/KNs=

tane=a*tany

(33)

(99)

18

H. RISEBETH

and the wind speed is (Fez + B,*/s4)‘Iz/gN. Equation (39) shows that the wind is precisely parallel to the pressure-gradient force, and therefore ‘cross-isobaric’, if either s = 1 (i.e. at the magnetic pole) or if y = O”, f QO”, or 180’ (i.e. the isobars run north-south or east-west). Otherwise the ion-drag acts in such a way as to twist the wind slightly towards the meridian. The twist is greatest if y G f46’ or f135’, in which case it amounts to only about 6” of arc at latitude 45’ where 52fs O-8. The same considerations apply, but with 0 and y referred to the magnetic meridian, if the declination D is not zero. More generally the azimuths of the wind and the driving force are inclined at an acute angle which can be calculated from (35). It is given approximately (and exactly if either 8 = 1 or tan y = 0) by the equation tan (0 - y) = f/KN.

(40)

Thus 16 - 1yI= 45” if KN = Ifl, i.e. if ion-drag and Coriolis force are equally important (and under these conditions (6 - y) is most sensitive to variations of ion-drag). Using Dalgarno’s value of the collision parameter in equation (8), with T = lOOO”K,the condition KN = IfI occurs if: N = l-00 x loll m-3 (plasma frequency 2.8 MHz) at latitude 30” N = l-41 x 10” m-3 (plasma frequency 3.4 MHz) at latitude 45” N = 1.99 x loll m-3 (plasma frequency 4-OMHz) at latitude 90’. 3.22 Thelocal-time variation of wind direction. At any given place the azimuth of the pressure-gradient force is constantly changing. It rotates through 360’ every 24 h, but even with the highly idealized Jacchia model (Fig. 1) the rate of rotation is not uniform except at the poles. The broken curve in Fig. 5, which applies to equinox at latitude Sl”N, shows the variation of azimuth of the pressure-gradient force, which is poleward (y = 0’) at the diurnal maximum of pressure, 14 13 h, and equatorward (y = 180’) at the pressure minimum, 03 47 h. The dot-dashed curve in Fig. 5, displaced 90” from the curve of y, shows the direction of the geostrophic wind. The wind azimuth 13at 360 km, given by Riister’s calculations, is shown by the full curve; it is close to y by day, when ion-drag is strong, but not so close at night when ion-drag is weaker and Coriolis force becomes important. At no time do 8 and y differ by more than 45’, so the wind is never geostrophic. The other curves in Fig. 5 represent two approximations to the wind azimuth 8. The + signs at 2-h intervals are steady-state values given by equation (35), taking account only of Coriolis force and ion-drag (using Rtister’s computed values of N,,,FZ for N and Dalgarno’s value of K for 1000’K). The full curve, which takes account of inertia and viscosity, lags behind the steady-state values at night and does not respond quickly to the increased ion-drag at dawn (06 00), when the + signs rapidly approach the direction of the pressure-gradient force (broken curve). The dotted curve is obtained by solving the simplified equations (30, 31), again taking N = N,,,FZ, and using (34) to compute 8. This curve therefore takes account of inertia but neglects viscosity. Except between 04 00 and 08 00 it lies within about 10” of the Rtister (full) curve, and may be regarded as an acceptable approximation.

Thermospheric

winde and the F-region

19

To sum up: during the day (12 00-18 00 h) all three calculations of 8 give almost the same result, ion-drag being so important that the wind is virtually parallel to the pressure-gradient force. At night Coriolis force and inertia influence the wind direction to some extent. GEISLER (1967)finds that an appreciable latitude variation of fl results from the

I

06

I

I

I

I8 I2 LOCAL TIME (hr)

24

06

Fig. 6. Wind direction versus local time at 300 km for latitude 61’N at equinox. Curve -, Riister’s comput&iona (Section 3.11), taking sccount of ion-drag, Coriolis force, viscosity and inertis. Curve * * - * - , approximate calculations neglecting viscosity, baged on equations (30, 31). Points + + +, steady-state approximation from equation (36). Curve ---, direction of pressure-gradient force according to Jecchie’s model; this is 90” from curve . - * - * which shows the geostrophic wind direction. (Azimuth OOO” is south-to-north, 090° is westto-east, etc.)

variation of Coriolis parameter and meridional ion-drag, this variation being most pronounced in the morning. It is interesting to treat the thermos3.23 The winds as an oscillatory system. pheric winds as an oscillatory motion driven by a periodic force. To a first approximation the pressure-gradient force, in high and medium northern latitudes, can be represented as a vector of constant magnitude F rotating with angular velocity Q (for the southern hemisphere, replace fi by -a). From equations (30, 31),putting sin I = .s = 1 and neglecting the nonlinear acceleration term:

aU,/&!+ VU, - fU, =

F sin (Qt + E)

(41)

au,lat + YU, + fU, =

F co9 (Lit + E)

(42)

where E is a phase angle determined by the position of the diurnal bulge and for

H. RISHBETH

20

simplicity V(= ynf = KN) is assumed independent of time. second-order differential equation for U, is obtained : 2

+ 2v z

By eliminating

+ (f” + v2)U, = vF sin (fit + E) + cf + 0)P

The general solutions of (43) and the corresponding

~0s (Qt + 8).

U, a

(43)

equation for U, are

U, = (Xi sin ft + X, cos P)e-VL + @,F sin (tit + E + @J

(44)

U, = (Y, sin,/? + Y, co8 fE)e-v’ + @,,B cos (Qt + E + 0,)

(45)

in which the X’s and Y’s are arbitrary constants and the Q’s are algebraic functions off, v and Q. It is found that if v > f then a1 -rr v-l, QD,s‘ 0 but if v < f then 0 1 zz (f - Q-1, Qz e &r. Equations (44, 45) may be interpreted as follows. The wind velocity vector may be regarded as the sum of a ‘complementary function’, which oscillates with angular frequency f( = 2Q sin v) and decays in amplitude like e-‘l, and a ‘forced oscillation’ which rotates with angular velocity rR. If ion-drag is dominant (v > f), as by day, then the ‘complementary function’ is heavily damped and the ‘forced oscillation’ is in phase with the driving force since then OD,fi 0. Now suppose that at sunset the electron concentration deereases rapidly to a value for which v < f: this can happen in winter at high and middle latitudes. Then the nighttime wind velocity oscillates in accordance with equations (44, 45), the coefficients of the ‘complementary function’ (the X’s and Y’s) being determined by the starting values of U, and U, at sunset. The ‘complementary function’ decays quite slowly (e.g. for a plasma frequency of 2 MHz, the decay time v-l fi 8 h) and therefore persists throughout the night. Since the phase Qz c in, the ‘forced oscillation’ is in quadrature with the driving force; i.e. the wind is geostrophic. The analysis could be extended to include higher harmonics of the pressure-gradient force. At first sight it might appear that, since the amplitude Cp, z= (f - Q)-l, a ‘resonance’ occurs at latitude 30” where sin q = 4 so that f = il. There is a corresponding feature in the tidal equations for the lower atmosphere (e.g. LINDZEN and CHAPMAN, 1969) but this causes no singularity in the wind velocity (BEILLOUIN, 1932), so the ‘resonance’ cannot be considered real. 3.24 The nonlinear acceleration term. The wind equations are very difficult to solve if the nonlinear term in equation (3) is included. Consequently the term is generally neglected, and it is necessary to consider whether this is justifiable. Neglecting all vertical velocity and vertical derivatives, the nonlinear term is

As discussed by GEISLER (1967), this term may be comparable to the linear acceleration term W/i% if the wind speed is a significant fraction of the peripheral speed !CiR cos CJJ of the Earth’s rotation, which is 485 COBq m s-l at 300 km. If longitude and local-time variations are assumed to be equivalent, a/ax can be replaced by a time derivative (QR cos q$-la/at, except at the poles.

Thermospheric winds and the P-region

21

Some workers (e.g. KOHL and KING, 1967; BAILEY et al., 1969; STROBELand MCELROY, 1970) have solved the equations of motion with only the linear term, and calculated the nonlinear term retrospectively. It is small by day, but it can be significant with the larger wind speeds that occur at night. Since the linear inertial term only affects the wind azimuth by about 20’ at night, and even less by day (Fig. 6), the nonlinear term would not be expected to be very important at most times. CEALLINOR(1968) included all the terms of (46) in his global wind calculations, though he neglected viscosity. He stated that little difference was made by neglecting the nonlinear term (CHAUJNOR, 1969) but he did not make detailed comparisons of wind velocities computed with and without the nonlinear term. ROSTERand DTJDENEY (1972) included parts of the term (46) in their calculations and found that the phase of the meridional wind was then more advanced near sunrise than if only the linear term was used. They were unable to include the complete term. RISEBETH (1971) made calculations for the Equator, with U, assumed zero, and found that at night the inclusion of the nonlinear term reduced U, by 15 per cent and delayed its phase by <$ h. 3.25 The p?uw of the wind. From the point of view of the F&layer effects (to be discussed in Part 4) the important parameter is the wind component in the magnetic meridian, which is closely related to the ion drift velocity (equation (10)). The phwe of its local-time variation depends on various factors :

(1) The local-time variation of ry, the azimuth of the pressure-gradient force, which in the present work has been derived from an empirical model atmosphere based on observational data. This azimuth depends on the location and shape of the diurnal bulge, which is determined by all the processes that contribute to the energy balance of the thermosphere ; it may be expected to vary from day to day, with season and with the solar cycle. Current models show only the gross features of these variations and cannot be expected to provide much detail. Uncertainties in p may be aa much as 30°, corresponding to an uncertainty of 2 h in the phase of the drift. (2) The difference between v and the wind azimuth 8 has been discussed in detail in Sections 3.21-3.23. It largely depends on the ion-drag/Coriolis force ratio; in a steady state, (0 - y) varies from 0’ to 90’ as this ratio increases from 0 to co (equation (40)). Inertia can modify the steady-state value of 6 by up to 20°, but viscosity does not affect 8 much at heights near the F2 peak. (3) Viscosity does however influence the wind azimuth at heights well above and below the F2 peak, as discussed shortly in Section 3.31. (4) The nonlinear acceleration term may affect the phase slightly around sunrise (Section 3.24). (5) At some places in midlatitudes the declination is as large as -&45’. Since the wind component in the magnetic meridian is U cos (0 - D), its phase clearly depends on D, and this leads to detectable effects in the F2-layer (Section 4.25). (Bemuse the ion-drag depends on D, as shown by equations (12, 13), there is in addition a weak dependence of U and 8 on declination but this is comparatively unimportant. See CEAILCNOR and ECCLES(1971).)

H. R~smnmi

22 3.3

Viecoeity and the variation of wind velocity with height

3.3 1 The height variation of wind dire&on. In Section 3.2 the discussion was limited to heights in the P2-layer around 300 km. The present section describes how viscosity causes the computed wind velocities & gre&er and lower heights to conform to the velocity at heights around the P2 peak (cf. &ISLER, 1966). The effect of viscosity on wind direction is dealt with first. 400

1

500 _; r I3 is 200

fy I 20

150

180

210 AZIMUTH

240 (DtQ.

300

NOON ,

i 330

360

E of N)

Fig. 6. Wind direction versus height for midnight and noon for equinox at latitude Sl*N, oompared to the direction of the driving fame due to pressure gradients. Curve -, from Rtister’s calculations, taking account of ion-drag, Coriolis force, viscosity and inertia. Arrows, approximate dire&ions at the F2 peak (near 300 km at noon, 400 km at midnight) computed by solving equations (30, 31), which neglect viscosity. Curves - - - -, steady-state approximations from equation (36), using the same N(h) distribution as given by Riister’s calculations. (Azimuth 180’ is north-tosouth, etc.)

Figure 6 compares the wind direction, computed both accurately and approximately, to the azimuth p of the driving force due to pressure gradients. According to the Jacchia model, y is height-independent and is 126’ at midnight, 311” at noon for the conditions used in the figure. The broken curves show the steady-state azimuth 0 given by equation (35), taking account of ion-drag and Coriolis force only. At midnight ion-drag is so small below 300 km that the geostrophic approximation (37) holds, with 0 - y = 90’. But at 400 km, near the midnight 272 peak, ion-drag is almost as important as Coriolis force and 8 is 40’ from the geostropbic direction. When instead the wind is computed from equations (30, 311, so that inertia is included, the resulting value of 6 (shown by the arrow) is even further from the geostrophic direction. When viscosity is included, as in Rtister’s calculations (full curves), the wind

Themospheric winds and the

23

F-region

azimuth varies much less with height. Coriolia force produce8 & slight twist at lower height8 but, both at noon and midnight, the azimuth only varies by about 25’ over the whole range from 160 to 400 km. At noon h,F2 is about 300 km end at this height RiiBter’B calculation (including viscosity) agree8 with the two that neglect viscosity (broken curve and arrow): viscosity tend8 to smooth out the variation of azimuth with height, though to a lesser extent than at midnight. 3.32 The height variation of wind speed in a steady-state model. To investigate how viscosity influence8 the wind speed, it is simplest to start with a BtE%%dy-state model in which only ion-drag and viscosity are acting and Coriolis force is negligible, 80 the wind U is parallel to the pressure-gradient force F. If the ions are stationary (V = 0) the equation of motion (24) reduce8 to the scalar equation (~/p)dBU/dh2 = KNU

- F.

(47)

In order to simplify the analysis an isothermal model atmosphere is assumed, with K and p con&ant; ‘reduced height’ z is measured in units of the constant neutral gas scale height H, the level z = 0 being taken a8 the F2 peak, real height h,. Above z = 0 the ion distribution N(z) is taken to be a so-called alpha-Chapman layer, but below z = 0 a different function G(z) is used, a8 explained below. F is assumed to increase linearly with height from a base level h,, which is below h, RO that zI, the ‘reduced height’ of h,, is negative. Then: z = (h - h,)/H

(46)

d”/dzz = IPd2/dhs

(‘3

p = p,e-” F = F,# N=

N,

(50) (51)

+ Z/G) exp i( 1. - z - e-6)

N,G(z)

for

z>o

for

z < 0.

(52)

Inserting these function8 into (47) give8 A d2U/dz2 = y,(z)U(z) - m(z)U, where A = j.i/KH2pmNm;

U,, = FJKN,.

(53) (54)

The dimensionleae function8 y,(z) cc Np and r2(z) cc Fp are easily derived from equation8 (50-52). They are normalized 80 that y1 = y2 = 1 at z = 0; U, is the wind speed at this level in the absence of viscosity. The parameter A is a mea8ure of the relative importance of viscosity and ion-drag at the F2 peak, z = 0. Figurea 7 and 8 ahow numerically computed solutions of (53) for variou8 values of A, for the two different ion distributions shown by open circles. The full curve8 (A = 0) show the wind speed in the absence of viscosity, given by y2(z)/~1(z)which is proportional to F/N. The winds are normalized to U, and the ion distributions to N,,,. In Fig. 7 the ion distribution G(z) is made to fall off elowly below z = 0 80 that the full curve is monotonically increasing with height; this is done by arbitrarily

H. RISHBETH

24

f

3

2

0

-3

-5

I

0

I 2

I I

I 3

N/N,,U/U,

Fig. 7. Verietion of steady-state wind speed with ‘reduoed height’ z for different valuea of the viscosity/ion-drag retie, epeaifiedby the pararnek A defined in equation (84). The wind ape& U ia normdimd to its value U, at the F2 peak (Z = 0) for no visooeity, A = 0. The aa& eimlm show the aeeumed ion dietribution N(z), normal&d to its value at z = 0.

taking Q(z) = [( 1 + +z)* + +I’“. The four curves for A = 0.1, 0.3, 1, 3 show how viscosity limits U and makes the gradient dU/dz small at pt heights. As A is increseed from O-1to 3, the in&aence of v&co&y extenda to lower heighta, but in no case is it sign&ant much below z = 0. Figure 8 is included to ahow that a more complex curve U(z) can be produced if the ion distribution N(z) is changed only slightly. In this case the alpha-Chapman function is used down to z = -1 but then iV is assumed constant (about O-0,) below 2 = -2 (which prevents U from becoming unduly large at low heights). With no viscosity (full curve), U htw a minimum near z = -0.4 and a maximum nearz= -143. When viscosity is included, not only is U limited at great heights, but also the maximum snd minkurn tend to be emoothed out : for A = 1 they are reduced to a alight ledge’ in the V(z) curve.

Thermoepherio winda and the F-region

25

3-

2

O-

-3 -

1

I

1

2 N/N,, U/U,

I

3

Fig. 8. Ae Fig. 7, but ueiug e different normalized ion distribution (small circles) which demore rapidly with decmaaing height below the peak at z = 0.

It is interesting to note that in the sunspot minimum noon data given in Table 2 the value of A is about 1.6 at the P2 peak, just below 250 km. But for noon at sunspot maximum when 7Q’2 * 300 km, A is only 0.25 and viscous control is then weaker. 3.33 Effect of viscosity in a time-varying model. Figure 9 shows how the wind speed varies with height in Rtister’s wind calculations for equinox at latitude 61°, at four local times. Three of the curves show a ‘ledge’ at 200-260 km, muoh aa in Fig. 8. In the fourth curve, that for midnight, this ‘ledge’ does not exist because viscous control is particularly strong. This happens mainly because ion-drag is weaker at night, so that A (given by (54)) is larger than by day. 3.4 Air j&m in the thermoephere In diaouaaing the transport of air, it must be remembered that the density decreases rapidly upwards, so the relatively slow winds in the lower thermosphere carry a much greater mm of air than the faster winds higher up. Since the wind

26

H. RISEBETH

calculations described in this article are not reliable in the lower thermosphere, they can give only tentative information about any general thermospheric circulation. 3.41 The prevailing equatorward wind ad its consequences. Many published calculations of winds give a prevailing equatorward wind, which in the case of Riister’s model (Section 3.11) amounts to 27 m s-l at 200 km and 54 m s-l at 300 km, latitude 51’. This prevailing wind arises because, in a model atmosphere

1

I

I

200

100 WIND

SPEED,

ii00

m ICC-~

Fig. 9. Height variation of wind speed at four local times, from Riister’s caiculations for latitude 51’ at equinox.

such as is shown in Fig. 1, the equatorward pressure-gradient force at night is similar in magnitude to the poleward force by day, whereas the ion-drag is much smaller at night. Hence the poleward daytime wind fails to balance the faster equatorward wind at night. In principle this equatorward flow of air could be balanced by a slow return motion in the dense lower atmosphere. But to complete the circulation there would have to be upward air motion (which causes adiabatic cooling) at high latitudes and downward air motion (which causes adiabatic heating) at low latitudes. This transport of energy from poles to tropics seems implausible on thermodynamic grounds (DICKINSON and GEI~LBB, 1968), and is almost opposite in sense to the circulation pattern, derived from energy-balance considerations by JOENSON and GOTTLIEB (1970), which gives a mean transport from the summer to the winter hemisphere. The prevailing equatorward motion given by the wind calculations can be suppressed if the atmospheric model is so mod&d as to reduce the mean temperature at high latitudes, which would incidentally agree better with certain data, such as

Thermospheric winds and the F-region

27

the incoherent scatter temperature data of WALXITEUFEL and MCCLURE (1969). Nevertheless there is some experimental evidence that fast equatorward winds blow at night, such as the airglow doppler observations (hMS!CIZONG, 1969), the artificial-cloud experiments of HAERENDALand RIE~ER (cited by KOHL, 1970), besides the fact that such winds are consistent with F2-layer behaviour (Section 4.21). 3.42

The prevailing zonal wind. In published wind calculations the prevailing zonal wind is generally fairly small ; e.g. in those of Riister (Section 3.11) it is -25 m s-l at 200 km and -14 m s-l at 300 km. The negative sign indicates a westward wind, which agrees with other midlatitude calculations but disagrees with the observation (e.g. KINGHELE, 1964) that the thermosphere has a net eastward. motion or ‘superrotation’. The calculations of -OR (1969) do give a prevailing eastward wind at low latitudes, but the superrotation problem has now become quite complex and will not be further discussed here. 3.43 Continuity of air motion. The thermospheric winds have a natural tendency to reduce the pressure inequalities that drive them, by transporting air horizontally. This transport may well influence the global distribution of air, and its importance can be studied with the aid of the continuity equation, as was done by DICKINSON and QEISLER(1968) for a global model and in more detail for latitude 45’ by RISHBETHet al. (1969). In these papers two components of the vertical air velocity U, are distinguished. The first component is the ‘barometric velocity’ FV,, the vertical velocity of the isobaric surfaces, which is upwards (positive) when the atmosphere is thermally expanding and downwards when it is contracting. It is computed on the assumption that perfect hydrostatic equilibrium prevails, which is justified because the vertical accelerations associated with vertical air motions, and other factors such as Coriolis force, are at least three orders of magnitude smaller than g (cf. Section 2.42). In models such as those of H-IS and PRIESTER(1962), CIRA (1965) and JACXHIA (1966) the total column content of air above the lower base level (120 km) is constant, horizontal motion is ignored, and only the barometric velocity is present. The continuity equation (29) for these models is then merely an/at = -a(nw,)/ah.

(65)

If horizontal winds exist another component of U, must exist to offset any resulting horizontal divergence of air. This is the ‘divergence velocity’ WD. If a purely barometric model is used to compute the winds, an/& must still conform to (55) so the flux of air carried by WD must exactly balance the horizontal outflow of air produced by the horizontal wind components U,, 27,. Thus: & (nUz) + % (nU,) = - i

(nWD).

Integrating with respect to height to find WD at any given height h (and making the reasonable assumption that no air flows into or out of the exosphere): (57)

28

H. RISHBETH

Unlike the barometric velocity W,, which must be zero at the lower base level if the pressure is kept constant there, the divergence velocity W,o at the base level does not normally vanish. If Wno is positive (upward), the atmosphere below the base level acts as a source of air for the thermospheric winds; if Wno is downward, it acts as a sink of air. Obviously the lower atmosphere contains sufficient air to fulfil these functions but there are difficulties regarding the energy input. The calculations of DICKINSONand GEISLER(1968) and RISHBETHet aI. (1969) show that the horizontal divergence of air at midlatitudes is sufficient to remove most of the air above 120 km during the day, and that an upward velocity WD * 2 m s--l (which is similar in magnitude to W,) is needed above 150 km to replace this air. To support this upward motion an energy input of a few mW m-2, comparable to the solar XUV input, is needed. This energy is liberated as heat at night when WD is downward, so the wind divergence influences the daily temperature variation. At any latitude, the daily average of the vertical air flux may not be zero. In that event there is a net gain or loss of air, which must be balanced by a general meridional circulation. Vertical motion, though very slow in comparison to the horizontal winds, is therefore important to the energy balance and to the general circulation (cf. Section 3.41). If the air removed by horizontal winds above 120 km, in the course of a day, is not fully replaced by an upward WD, this might produce a phase difference between the daily density and temperature variations at greater heights, as is observed (RISHBETH,1969). These would probably be accompanied by variations of the boundary conditions at 120 km ; but the whole question of the phase of diurnal variations is a complex one. See CHANDRAand STUBBE(1970) and VOLLANI)(1969, 1970). 3.44 The energy required to drive the winds. It is of interest to estimate how much of the solar energy absorbed in the thermosphere is actually consumed in driving the winds. The rough numerical values quoted below refer to a 1 m* vertical column with its base at 120 km; they have been computed from Riister’s model for moderate solar activity, described in Section 3.11. The energy flux of solar XUV radiation above the atmosphere is 25 mW m-2, and the diurnal average of power absorbed at latitude 51” at equinox is O-5mW m-2 (which is of the order of one-millionth of the solar constant, I.4 kW m-2). The XUV energy heats the gas, causing the thermal expansion which sets up the horizontal pressure gradients ; most of the energy is eventually conducted via the neutral and ionized gas to the heat sink at the base of the thermosphere, though some is lost by radiation. One per cent of this energy is dissipated in the thermospberic winds, by the action of molecular viscosity (roughly 4 PW m-s at noon and 30 PW m-z at midnight) and ion-drag (roughly 40 PW m-z at noon and 3 ,uW m-2 at midnight). STUBBEand CHANDRA(1971) calculate that at night the ion temperature may exceed the neutral gas and electron temperatures by lOOoK or so, as a result of the dissipation of energy. Finally it is of interest to note that the total kinetic energy density, per unit vertical column above 120 km, associated with the winds is 0.1 J m-z at noon, 0.6 J m-2 at midnight, as compared to a total thermal energy density of order 50 J m-2.

Thermospheriowinds and the F-region

29

4. THE EFFECTSOF WINDS ON TEE F-LAYER

4.1 Introduction: Some theoretical ideas In their first basic paper on the subject of winds, KING and KOHL(1965) suggested that the winds could play an important part in controlling the behaviour of the FZ-layer, end this idea has been amply confirmed by subsequent work. At lower levels in the ionosphere, where production and loss processes are relatively more important, winds produce only small perturbations. ZENITH

t

-TRUE

NORTH

Fig. 10. Perspective diagram showing the geographic and magnetic meridian planes at a point P in the northern hemisphere. A horizontal wind, speed U, geographic azimuth 0, has a component U’ = U COB(f3 - D) in the magnetic meridian. The resulting drift velocity of the ionization in the direction of the magnetic field is VII = U’ COBI and the vertical component of this drift is W = - U’ cos I sin I. As shown here, W is negative (downward).

In this Section some theoretical matters are first considered; then the effects of winds at midlatitudes, in polar regions, and near the magnetic equator are considered in turn in Sections 4.2, 4.3 and 4.4. 4.11 Borne formulae relating to the F2 peak. In the midlatitude FB-layer, a~ a rule, the vertical gradient of N greatly exceeds the horizontal gradient (except, of course, just at the F2 peak). It follows from the properties of the continuity equation (22) that vertical ion drift is much more effective than horizontal ion drift in causing changes of N, so only vertical drift is considered here. From equation (10) it can be deduced that the vertical ion drift W produced by a. horizontal wind U blowing at azimuth 8 is (see Fig. 10):

w=

-ucos(e

- D)cosIsinI.

(53)

30

H. RIEERETH

At midlatitudes cos I sin I -N O-4 so that a typical daytime wind of 70 m s-l (poleward) gives W N -30 m s-l and a typical nighttime wind of -250 m s-l (equatorward) gives W N + 100 m s-l (cf. Fig. 4). In contrast the vertical air velocity U, is usually only of order 3 m 8-l so its contribution to W, namely U, sin*1, is usually quite unimportant. MARTYN (1966), DUNCAN (1956), DUNGEY (1956) and YONEZAWA (1956) showed that the height of the F2 peak is largely determined by plasma ditEusion. According to RISHBETH and BARRON (1960) and RISHBETH (1966) the equilibrium peak (height h,,) in the absence of vertical drift occurs where the loss coefficient B is comparable to the ‘diffusion rate’ d = (0,/Hi2) sin21 where D, is the plasma diffusion coefficient and Hi the scale height of the ionizable gas, taken to be atomic oxygen. For a reasonable model in which ,$ is proportional to the molecular nitrogen concentration, and decreases upward with scale height +H,, the equilibrium height k,, is where p/d ‘u O-6 (day);

/I/d N 0.13 (night).

(59)

A vertical drift W shifts the peak by a vertical distance Ah,,, ‘u O+aW/d(h,,) N

@55WW,,) (day) O*lZW//?(h,,) (night).

By day, the effect of the displacement Ah, on the peak electron concentration ;VR1 can be estimated by noting that the ‘photochemical equilibrium’ electron concentraVery roughly, a displacement tion, namely Q//3, increases upwards as exp (fh/Hi). Ah,,, in the height of the peak may be expected to produce a change in N, given by A(ln N,) N dAh,/H,.

(61)

Using (60) (for day) it follows that A(ln N,) N 0.4W/H,/I(h,,).

(62)

Incidentally HI/3(h,J is comparable to the diffusion velocity at -height h,. To put numerical values into these formulas one has to compute hnu from a With the CIRA Model 2 for sunspot minimum (cf. suitable model atmosphere. RISHBETH, 1966) it is found that h,, = 293 km, Hi = 60 km, #t(h,,,J = 6 x 1O-4s-l and d(hm) = 1 x 1O-3s-l by day. Then if W = -30 m s-l, as suggested above, it is deduced from (60) and (62) that Ah, ‘v 0.9W N -30

km;

A(ln N,) N 0.01 W cr( -0.3.

(63)

At night the analysis becomes even less accurate, but the displacement of the peak due to the upward drift can be very roughly deduced from (60). This displacement results in a reduction of the effective loss coefficient /?‘; assuming the scale height of @ to be 25 km at night, and taking W = +lOO m s-l as given above, it is found that Ah,1-0.2W~2Okm;

A(ln @‘) N -0.008

W -N -0G3.

(64)

Equations (59-64) should only be used as rough guides to PB-layer behaviour, because they apply to steady-state conditions and to fairly small displacements.

Thermoepheric winds and the P-region

31

The coefficients in (63) and (64) are quite sensitive to the atmospheric model used ; they are for example about 24 times greater for the model of NORTGK et al. (1963) than for CIRA (1965), the models being different in chemical composition. 4.12 Sensitivity of the F2 peak to changes of wind speed. The equations just presented show theoretically how the F2 peak is affected by vertical drift. The amount by which the layer is perturbed when the wind changes by a given amount depends on ion-drag and on geometrical factors. For simplicity it is assumed that ion-drag is dominant (KN > Ifl) and that steady-state conditions apply. Let F”, U’ denote the components of F, U in the magnetic meridian (positive northwards; hence F’ = F,, U’ = U, if the declination D = 0). Then, applying equation (38) at the level of the F2 peak : U’ = (F’/KN,)

cosec21.

(65)

Suppose that a change in the air pressure distribution alters the meridional pressurcgradient force by 6F’, causing changes 6U’ in U’ and 8N in N,. Differentiating (65) :

W’ = (6F’/KN,)

cosec21 - U’(GN/N,).

W)

The first term on the right is the change of U’ caused directly by the alteration of F: The second term represents a ‘feedback’ effect; the change of wind affects the ion concentration, and thus modifies the ion-drag and further affects the wind. This ‘feedback’ effect can be studied by using equation (62). Since the change 6U’ in the wind alters the vertical drift by --6U’ 00s I sin I, the resulting perturbation of N, is given by (6N/N,)

N -(6U’/w,)

where for brevity w,,, = 2*5H,/3(h,,). (66) :

cos I sin I

Using (67) to eliminate in turn 6N, 6U’ from

(BF’/KN,) cosec2_l 6u’ = 1 - (U’/w,) co8 I sin I dN/N, = -

(67)

@F’/KN,,,) cot I wm - U’ 00s I sin I ’

(68) (69)

If U’ is zero or very small, the perturbation SN/N, produced by a given SF’ is just proportional to (cot 1)/N, which may be regarded as a ‘sensitivity factor’ (JONESand RISHRETH, 1971). But if U’ is not so small (i.e. if (U’ 00s I sin I) is an appreciable fraction of w,,,, which is of order 30-100 m s-l by day) the ‘sensitivity’ is modified, being reduced if U’ is equatorward and increased if U’ is poleward. This ‘feedback’ might produce some interesting consequences, though the approximations used above fail if the perturbations become large, and moreover Coriolis force (here neglected) will control the wind if N, should become small. 4.13 The jield-aligned ion drift velocity. In many published papers, and in some earlier parts of the present article, it is assumed that the ion drift velocity V is simply equal to the field-aligned component U ,, of the wind speed (equation (10) of Section 2.32). This assumption is good enough for the purpose of computing approximate wind speeds and directions (Section 3.2) and for roughly estimating the F2layer perturbations caused by the wind (Section 4.11). However, as shown by 3

32

H. RISEBETH

equation (19), plasma diffusion, gravity and electric fields also affect V, and have to be taken into account when deductions about winds are made from experimental determinations of V, like those obtained from incoherent scatter experiments (VA~~EUR,1969). If there are no electric fields then the ion velocity is field-aligned and the relevant equation of motion is (20). Consider the point on a. given field line where @, + pi) is greatest so that the pressure gradient term vanishes; this is st (or very close to) the F2 peak. The equation then reduces to (70) Note that field-aligned velocities are reckoned positive in the direction of B, i.e. northward and downward in the northern hemisphere, northward and upward in the southern. Since vtn decreases exponentially upwards the last term in (70) is very heightdependent; at 300 km it is typically 20 m s-l. By day the poleward wind (U,, positive in the northern hemisphere, negative in the southern) pushes the F2 peak down to a level where g/Yin < IV,,1so that V,, N U,, and the field-aligned ion velocity does give a measure of the wind. But at night the equatorward wind pushes the FZ peak up to a level where (g/vi,,) sin I is comparable to U,,, and opposite in sign, so that V,, is small. Detailed calculations show that (provided no ionization escapes through the top of the layer) the resultant V,,is small and downward ; thus ionization flows from great heights, where loss is negligible, down to lower levels where loss occurs. In fact the flux of ionization is related to the value of p at the peak (e.g. HANSON and PATTERSON, 1964). Theoretical calculations of BAILEY and MOFFETT (1970) show that VI,is downwards throughout the day at midlatitudes, except for a transient period near sunrise. Qualitatively, these results agree with the observational data of VASSEUR(1969). 4.14 Field-aligned drift due to an electric Jield. The ions and electrons also drift if theresxists en electric field normal to B; if E,’ is its component in the magnetic eastward direction, the drift has a vertical component (E,‘/B) cos 1. But in an equilibrium situation the ions and electrons will simultaneously drift parallel to B at a speed (E,‘/B) cot I, of which the vertical component is -(E,‘/B) cos I, just such as to give a zero resultant vertical drift (STUBBEand CHANDRA,1970). In a more complex situation in which both wind and electric field are present, Stubbe and Char&a show that the total vertical ion velocity is still nearly zero. But, as mentioned above, some downward flow of ionization takes place with velocity of order H,#?(F,,), or a few m s- l, to offset loss occurring at lower heights. 4.2 Wind effects in tL midla&&de F&layer 4.21 The diurnal variationa of h,,,FZ and N,F2. By day the poleward winds at midlatitudes reduce h,,,FZ; at night the equatorward winds increase h,FZ. KINK et al. (1967) showed that the diurnal variations of hmF2 observed at several stations can be well explained in these terms. The changes of Ic,,J@ strongly influence the diurnal variation of N,,,FZ according to the principles set out in Section 4.1. Because of the interaction of wind speed and electron concentration, these quantities have to be computed simultaneously, as has been done in several investigations

Thermoepheriowinda and the F-region

2ud ” 04

m

’

’

12

”

16

’

Loco1llme

”

20

’

00

’

”

OQ

33

1

08

(hr)

Pig. Il. Loeel time v&&&me of N,F2 and B,F2, wlcnl&ed by S-BE.L end MoEIaoY (1970) for sunspot minimum, April 1964, st latitude 43’N, Curves (s) inoludewinda cmdthermal non-eqnilibrinm; cnrves (b) include winds but sseume thermal equilibrium; carves (c) include thermal non-equilibrium but negleot winds. Points X are Evans’ observational date from Millstone Hill.

(KOHL eta2-,, 1968; BAILBY et&., 1969; STUBBE, 1970; STROBEL and MoEnno~, 1970 ; R@STER,1971). Since ebtric field8 are thought to have only a minor influence on the behaviour of the JG! peak at midlatitudes (STUBBEand CHAHD~A,1970; BRAMLEYand ROSTER,1971), they are ignored in most caloulations. Figure 11 shows the diurnal variation8 of N&2 and &$‘Z computed by Strobe1 and McElroy, The cro88e8 represent the incoherent scatter data of EVANS(1967), obt&ned at Mi%tone IElI (43’N) in April 1964. In the computed curve8 (a) and (e) the difference between ion and eleafron temperature8 ha8 been taken into account in computing the ion d@usion velocity (cf. eqruttion (20)), the adopted values of T, and T, being ba8ed on Evans’ data. Curves (b) assume thermal equilibrium (T, = T. = T,,). In curves (0) wind8 are negleoted and there is little difference between

34

H. RISHB~ET~

the daytime and nighttime values of h,FZ, apart from transient effects in the morning. But in cases (a) and (b), in which are included winds computed from an atmospheric model resembling Jacohia’s, &,F2 varies diurnally by about 60 km. The winds produce a slight daytime minimum in N,,,F2, such as is often seen at midlatitudes in summer and at equinox. At night the raising of the layer by winds reduces the effective loss coefficient in case (a) to about 30 per cent of its value in case (c), so the winds contribute substantially to the maintenance of the layer. Except near sunrise and sunset, there is no great difference between curves (a) and (b), so the lack of thermal equilibrium does not a&& the behaviour of N,,,F2 and h,,,P2 very much. The evening maximum of N,F2 in curves (a) and (c) is largely caused by thermal contra&ion resulting from the rapid cooling at sunset. However, winds also tend to produce an evening maximum in iV,F2 (Koa~ et al., 1968), which can be large, and depends on the phase of the meridional wind. The relative importance of winds and thermal contraction at sunset probably varies from place to place. 4.22 Tlw problem of the.&we of the winds. Both KOHLet al. { 1968) and STROB~L and MCELROY(1970) show that the agreement between calculated and observed values of N,F2 and B,F2 is improved if the phase of the meridional wind variation is advanced by 1+2 h. This increases the evening maximum of N,F2 and reduces the morning maximum, giving a more realistic diurnal variation. This result might imply that the pressure maximum in the diurnal bulge occurs at 12 00-13 00 LT, instead of at 14 13 LT as in Jacchia’s model. The earlier maximum does not agree with satellite density data, and even less with incoherent scatter data on the diurnal temperature variation (NISBET, 1967; CARRUet al., 1967). Note however that Strobe1 and MoElroy used data from Millstone Bill, where D 2 - 13’ and the diurnal drift variation, given by (58), is advanced in phase by almost an hour as compared to their aalculations, which took D = 0’. This reduces the shift of bulge phase needed to obtain good agreement between the observations and their calculations. The phase shift also increases the nighttime values of N,F2 because it advances the time at which W (equation (58)) changes from downward to upward. If this time p&es sunset the ionixation produced just before sunset is preserved by the upward drift. But if production oeaseswhile the drift is still downward the ionization is rapidly lost, and the F2-layer cannot recover till sunrise unless there is a nocturnal souroe of ionization. The survival of the F24ayer at night does not entirely depend on the phase of the wind, however, because some input of ionixation probably does ooour at night. In the presence of the upward drift due to winds, only a weak source (0.1-l per cent of the daytime produdion) su&es to maintain the F2-layer. This aould be provided by influx from the protonosphere (TITEE~U~~E, 1968; RBHBXT~Z,1968) or by corpuscular ionization (TORRand TORR, 1970). 4.23 &uuonal vayiatiorcs. Pigure 12 shows Strobe1 and McEhoy’s computed variations of N,F2 and ?4,,F2 for three seasons. There is obviously a strong seasonal variation in the shape of the N,F2 curvea and this is essentially due to the varying length of the day. In winter the wind is poleward throughout the hours of daylight ;

Thermoepheric winds and the F-region

2001”“““““’ 04 08 12

16

20

00

04

36

I

06

Local Time (hr) Fig. 12. Local time variations of N,F2 and h,F2, calculated by STROBELand MCELROY (1970) for sunspot minimum at latitude 43ON, including the effects of winds and thermal non-equilibrium. Curves (a)--equinox; curves (c)-winter. Seasonal variations of composition

curves (b)-summer; have been assumed

(see text).

it causes a rapid afternoon decrease of N,F2 and there is no tendency for evening or morning maxima of N,F2 to occur. Contrary to what might be thought at first glance, the seasonal anomaly in noon N,F2 that appears in Fig. 1% is not produced by the winds. The anomaly has been introduced by altering the atmospheric composition so as to vary the ratio of production and loss ; the O/O, concentration ratio at 120 km has been assumed to be O-8 in summer, l-25 at equinox and 2.9 in winter, though the aggregate oxygen mass is kept constant. If the composition were kept constant the calculated noon N,F2 would decrease from summer through equinox to winter, as would be expected. Thus winds are not the direct cause of the seasonal anomaly (RISHBETH, 1968).

36

H. RIEHBETH

Nevertheless, Strobe1 and McElroy show that winds could account for some observed seasonal variation in the shape of the F24ayer. Except at sunspot maximum the semi-annual 4.24 Semi-annual variations. variation of N,F2 is more conspicuous than the seasonal variation (BURKARD, 1951; YONEZAWA, 1959; KING and SMITH, 1968). This variation is in phase with the semi-annual variation of thermospheric temperature (JACCHIA, 1965) which would be expected to influence h,F2 by the ordinary processes of thermal expansion and contraction. ECCLES et al. (1971~) indeed show that the semi-annual variations of h,F2 can be accounted for in this way, but the semi-annual variations of N,F2 cannot. Since N,F2is not particularly sensitive to temperature variations (THOMAS, 1906), this last result is not surprising. It remains to be seen whether the semiannual atmospheric variations can produce significant changes in the wind patterns or in other factors that might influence N,F2. 4.25 Effects depending on magnetic declination. In current models of the thermosphere, such as Jacchia’s model shown in Fig. 1, it is assumed that the temperature, density and pressure vary with latitude and with local time, and that these variations are identical at all longitudes. This assumption is not necessarily correct, but the present state of knowledge does not enable any substantially better assumption to be used. Consequently, in the equation of air motion (24), the pressure-gradient force The ion-drag term depends somewhat on F(v, t) is the same at all longitudes. longitude, because it depends on the direction of B; however, as remarked in Section 3.25, the resulting longitude variation of wind velocity is small. On the other hand, the vertical ion velocity W can vary markedly from one place to another (CHALLINOR and ECCLES, 1971). By equation (58), Section 4.11, W cc cos (0 - D) and so the phase of the diurnal variation of W depends on U. Moreover W cc cos I sin I, so the amplitude of the diurnal variation of W depends on I. Figure 13 shows how D and cos I sin I vary with longitude at two particular latitudes, 45”N and 45’5. In the northern hemisphere the wind vector rotates clockwise as local time advances (see right of diagram) so that the phase of W at place A, which has the greatest westerly declination at 46”N, is in advance of that at B, which has the greatest easterly declination ; there are subsidiary extreme values at A’ and B’. In the southern hemisphere the wind vector rotates anticlockwise and the phase of W at Q (greatest easterly declination) leads that at P (greatest westerly declination). Easterly declination is always reckoned positive. The difference in Fe-layer behaviour at places of similar latitude but opposite declination is illustrated by Fig. 14. KOHL et al. ( 1969) have carried out similar calculations for other pairs of stations, and conclude that wind effects can account for the dependence of the diurnal F2-layer variations on declination that was suggested by EYFRIG ( 1963). 4.26 Longitude vam’ations at Jixed local times. The longitude variations are to some extent connected with the declination effects just described. If (at fixed latitude and local time) the vertical drift velocity W varies with longitude then, from the analysis of Section 4.11, one might expect the electron concentration to be greatest where W is algebraically greatest, and smallest where W is algebraically smallest. The situation for latitudes 45”N and S may be discussed with the aid of Fig. 13.

Thermospheric

MAGNETIC I 100

I ISSW

I 9ow

FIELD

winda and the F-region

37

GEOMETRY

I I 45w 0 Ceo9raphic latitude

I 4x (de91

LOCAL TIME 1 90E

I 13X

1 I80

OS

VARIATION OF klND DIRCCTION

t

Fig. 13. Magnetic field geometry at latitudes 45’N and 45%. The polewardpointing arrows show the direction of the magnetic meridian at 46’ intervals of longitude, the length of the arrows being proportionalto COB I sin I. The extreme values of declination are found at the longitudes marked A, B, A’, B’ at 45’N and P, Q at 46%. The diagrams at the right give the approximate local times (h) at which the wind blows in the four cardinaldirections.

When the wind is meridional, as at 03 00 or 14 00 LT, declination effects are not large because the angle between the wind and the magnetic meridian is fairly small (being less than 25” everywhere except in the S. Atlantic and S. Indian Ocean sectors, where its maximum value is 46” at P). Hence I cos (f3 - D) I > 0.7 everywhere, but significant longitude variations arise from the (cos I sin 1) factor, notably in the southern hemisphere where 1cos I sin I 1 is twice as great in the S. Atlantic sector as in Australasia. At 03 00 the drifts are upward everywhere; at 14 00 the drifts are downward everywhere but are smaller than at 03 00 because the wind speeds U are smaller by day. When the wind is zonal, the effect of declination is more marked. For instance, in the southern hemisphere at 2 1 00 LT, (8 - D) ranges from 65’ at & to 135’ at P, so the value of cos (6 - D) ranges from +0*42 at & to -0.71 at P ; maximum upward drift is at &, so the greatest electron concentrations may be expected there. A detailed investigation shows that, as local time varies, the locations of maximum and minimum W (at a given latitude) progressively change. They tend to be at places where D has an extreme value, such as P, Q in the southern hemisphere and A, B, A’, B’ in the northern. This is illustrated by the broken curves in Fig. 15 which are obtained from detailed calculations by ECCLESet al. (1971a). The longitudes at which the curves pause correspond approximately to A, B, A’, B’ in Fig. 13 even though that figure refers to a slightly different latitude. In the southern hemisphere

H. RISHBETH

-

VICTORIA (0

---__

ST JOHNS( 0 I 47’N,

I =

= 4B’N.

71’. D = 23=‘E)

I =71°, D = 27’W)

I

SEPTEMBER 01 00

I 04

I 08

I 12

I 16

I 20 LOCAL

MAG#TK;

-TloN

I 24

1958 I 08

04

/ 12

I 16

I 20

I 24

MEAN TIME

EFFECT AT VICTORIA AND ST. JOHNS

Fig. 14. Mean local-time variations of fe_8’2 for two &a&ions with opposite declination, for September 1968. After KOHL et ail. (laS9).

J

IflO

90’ WEST

OD

90”

IfJO

EAST

GEOGRAPHIC LONGITUDE

Fig. 16. For any given local time, the electron concentration at 65“N, 660 km height, is greatest at the two longitudeashown by the broken curves (calculations by EaoLEs et al. (19718) for June 1964) and by the dota (A&l III satellite obaervations (PIMOTT, 1970) during aStryto December 1907). From EO~LESet al. (1871a).

Thermospheric winda and the P-region

39

the geomagnetic field is simpler in form, and a diagram similar to Fig. 15 would have only one maximum at any local time. Evidence for the reality of these longitude effects is provided by measurements of the worldwide distribution of electron concentration at 500-600 km, made by the Birmingham University experiment on the Ariel III satellite (SAYERSet aZ., 1969; PKWOTT, 1970). On a given day the satellite observes at two local times 12 h apart ; these local times change gradually from day to day and a complete diurnal coverage is obtained in 80 days. The points in Fig. 15 show the positions at which electron concentration maxima with respect to longitude were actually observed. The calculated ratio of maximum to minimum N at 500-600 km, roughly 3 : 1, is similar to that measured by Ariel III. At the F2 peak the ratio should be smaller, perhaps I.5 : 1. Although reasonable agreement between theory and observation is found in Fig. 15, not all the data can be so well accounted for. PIGQOTT (1970) has described ‘fingers’, or regions of enhanced electron concentration, which probably have to be explained in terms of smaller-scale variations of atmospheric parameters. 4.27 Storm effects. KOHLand KING (1967) pointed out that the altered temperature distribution during storms, described by JACCHIAand SLOWEY(1964), must influence the thermospheric wind system. The most obvious possibility is that aurora1 zone heating, known to be intense (COLE, 1962), could cause equatorward winds which have been observed (NAVY et aZ., 1971). JONESand RISHBETH(1971) suggested that these winds could cause some observed ‘positive storm effects’ in the midlatitude F&layer (though MENDILLOet al. (1970) attribute the increases to magnetospheric compression). Other possible wind effects in storms have yet to be studied in detail. 4.3 Wind effects at high latitudes The wind system shown in Fig. 2 blows across the polar regions, giving rise to vertical ion drifts which vary diurnally. In principle these drifts affect the diurnal variation of h,F2 in much the same way as at midlatitudes (Section 4.21), and produce conspicuous variations of N,,,F2. Since at high latitudes the diurnal variation of the photoionization rate is rather small, particularly in summer, the variations of N,F2 caused by drifts are relatively more important than at midlatitudes. KING et al. (1968, 1971) have shown that winds can account for observed variations in some detail. It may be remarked, in passing, that winds cannot be responsible for maintaining the F2-layer in the polar winter, because the bringing of ionization from sunlit parts of the ionosphere would necessitate transport across field lines, which winds could not cause. Particle ionization may of course produce important effects in the highlatitude F2-layer. 4.31 Universal Time eflects. The wind effects naturally depend on the geometry of the magnetic field. The southern dip pole lies near 67’S, l4O”E on the edge of the Antarctic continent. The centre of the diurnal bulge passes the 140”E meridian at about 05 00-06 00 UT, at which time the wind blows from the dip pole towards the south geographic pole (Fig. 16). Most Antarctic and South Atlantic observatories

H. RIS~BETH

40

are so situated as to experience upward drifts at this time, with the wind blowing away from the dip pole, so maxima of h,F2 and N,F2 tend to occur around 06 00 UT, as observed (D~cAN, 1962; PI~GOTTand SHAPLEY,1962). This explanation of the ‘UT effect’ in the Antarctic has been controversial but now seems quite well established (ECCLESet al., 1971b). But even if winds can account for the diurnal variations of N,F2, the geographic distribution of N,F2 in the Antarctic is not, according to DUNCAN(1969b), explained by wind theory. Thus other factors must be important, such as geographic variations of production and loss rates or particle ionization.

Fig. 16.

The positionsof the north and south dip poles in geographic coordinates, in relation to the wind directions at 06 00 UT and 20 00 UT (J. W. RINU).

In the Arctic the wind blows across the dip pole towards the geographic pole at 20 00 UT (Fig. 16), but the distribution of ionospheric observatories is such that maximum upward drift can occur at a wide range of Universal Times at different stationa; some minor maxima of N,F2 may be attributable to winds, but no strong ‘UT effect’ exists (CHALLINOR, 1970b). 4.32 The polar wind and the F24ayer. The polar wind (BANKSand HOLZER, 1969) removes F2-layer ionization upward along ‘open’ magnetic field lines. It is not obviously related to the thermospheric winds, but a study of whether the two phenomena interact in any way might be interesting. Owing to the nature of the magnetospheric circulation, the polar wind affects the FS-layer at latitudes poleward of the plasmapause boundary. An alternative explanation of the ‘trough’-poleward of the plasmapausg-is that of BRACEet aE. (1970), who attribute it to downward drift caused by thermospheric winds. The latitudinal variation of N due to winds is fairly gentle, however, unlike the sharp gradients that actually occur near the plasmapause.

Thtxmosphericwinds end the P-region 4.4

41

Wind efsects in the equatorial Fblayer

The F24ayer equatorial anomaly is generally considered to be produced by tidal electric fields, acting in conjunction with diffusion along field lines (e.g. DUNCAN, 1960). Zonal electric fields are effective in low latitudes because they produce vertical ion drift. Some calculations have been made of how horizontal winds might affect the equatorial F2-layer, though somewhat arbitrary assumptions have had to be used, owing to the lack of information on low-latitude wind patterns.

TYPE A TRANSEQUATORIAL WIND

*-----.

TYPE B DIVERGING WIND (day1

t

*---:--*

:

\

---*

/CT-l .

TYPE C CONVERGING WIND (night 1

*--_ WIND

*---

.. .. *----:. . . .. . .. .. .

l%RIFT

MAGNETIC EQUATOR

Fig. 17. Three types of meridional wind, and the malting drifta of ions along equatorial magnetic field lines.

Winds blowing in the magnetic meridian can readily move the ionization along the magnetic field lines. The simplest types of meridional wind are sketched in Fig. 17; they include a wind blowing across the dip equator, producing upward drift on the upwind side of the Equator and downward drift on the downwind side (A), and a latitude-varying wind, zero at the dip equator and blowing either poleward in both hemispheres, producing downward drift (B), or equatorward in both hemispheres, producing upward drift (C). In order to maintain continuity of air motion, a wind of type ‘B’ or ‘C’ must be accompanied by zonal or vertical winds, but these will have smaller effects on the ion drift and will be ignored for present purposes. A type ‘A’ wind is not necessarily accompanied by zonal or vertical winds in low latitudes, so long as the transport of air across the Equator is balanced by return winds somewhere else. According to the daytime equilibrium calculations of BRAMLEY and Yonaa (1968), which include the electromagnetic drift required to produce the equatorial

42

H. RISHBETH

anomaly, a type ‘A’ wind reduces N,F2 at both. ‘crests’ of the anomaly (Fig. 18). At the upwind crest the height of the peak (expressed in ‘reduced height’, z,) is increased, which reduces the value of the loss coefficient at the peak, pm, but evidently this effect fails to compensate for the removal of ionization across the Equator to the other hemisphere. At the downwind crest, the influx of ionization W-1 Nm

(a)

L

6

30.

200

100

S

(b)

I

30’

0 LATITUDE

10’

/

2o”

30’ N

o) \ I-

20’

S

10.

0

LATITUDE

IO0

20°

I

30’

N

Fig. 18. Equilibrium values of peak electron concentration, Xm (above), and reduced height of F2 peak, z,,, (below), plotted against magnetic latitudo. The assumed vertical electromagneticdrift velocity at the Equator is 4.1 m s-1; the curves 0, 10, 20 respectively assume north-to-south wind speeds of 0, 41, 82 m s-l (BRAMLJXY and YOUNQ, 1968).

across the Equator is outweighed by the effect of the reduction of z,, and consequent increase of pm, caused by the downward drift. The distribution of N,F2 becomes asymmetrical, the downwind crest being the greater. Observational data (cf. LYON and THOMAS, 1963) are consistent with the existence of ,a wind blowing from the summer to the winter hemisphere by day, as would be produced by a ‘diurnal bulge’ centred in the summer hemisphere. From a time-varying calculation ABURROBB and WINDLE (1969) showed that after sunset the asymmetry becomes reversed; the downwind crest decays more rapidly on account of the inmeased &,, and greater values of N,,, are then found in the upwind hemisphere. If the diurnal bulge is centred in low latitudes, as in Fig. 1, a ‘diverging’ wind of type ‘B’ would be expected to blow by day and a ‘converging’ wind of type ‘C

Thermospheric winds and the P-region

43

at night. ABIJR-ROBB(1969) and STERLINGet al. (1969) have computed theoretical electron distributions in the presence of such winds, taking account also of tidal electric fields. The converging type ‘C’ wind at night helps to maintain the layer which, without it, would probably decay too quickly. By day the diverging type ‘B’ wind may help to enhance the so-called ‘noon biteout’-the midday minimum in the local-time variation of N,FZ-but as shown by BAXTER and KENDALL(1968) a ‘biteout’ can be produced at low latitudes by electromagnetic drift without winds. So far it has not been possible to explain the differences in behaviour of the equatorial F2-layer observed at different longitudes (THOMAS,1968); this would require much more detailed knowledge of the distribution of atmospheric pressure and electric fields than is now available. 5. CONCLUSION 5.1 Sunmry

of main conclusions

(1) Theoretical calculations, based on an empirical model atmosphere derived from satellite density data (Jacchia’s), imply that there exists a global wind system blowing across the poles and around the Equator (Fig. 2). There is some experimental evidence for the reality of the wind system ; perhaps the most detailed direct evidence comes from vapour trail experiments (KOHL, 1970). (2) The pressure-gradient force that drives the winds rotates 360’ in azimuth every 24 h. At any time the wind direction is determined by ion-drag and Coriolis force, with some modification due to inertia. At heights near the F2 peak viscosity has not a very great effect on the wind direction (Fig. 5). (3) Because of the effects of viscosity, the wind direction at levels above the F2 peak, and to a lesser extent below the F2 peak, does not differ greatly from the wind direction at the F2 peak (Fig. 6). (4) Viscosity also smooths out the height variation of wind speed, particularly at levels above the F2 peak (Figs. 7-9). (5) In order to study the general form of the wind system at FB-layer heights, simplified calculations neglecting viscosity may be adequate, particularly when the limitations of current atmospheric models are borne in mind. By day, inertia may sometimes be neglected too (Sections 3.21, 3.22). (6) The nonlinear acceleration term in equation (3), which for simplicity is usually neglected, does not normally have an unduly large effect on the wind direction. It may be important at certain times, e.g. before sunrise, when wind velocities are large and possess appreciable spatial gradients (Section 3.24). (7) The wind component in the magnetic meridian produces interesting effects in the F2-layer. The phase of the local-time variation of this component controls the shape of the diurnal variations of h,F2 and N,,,F2; in particular, the LT at which this component changes from poleward to equatorward affects the F2-layer sunset phenomena and the preservation of the layer at night. (8) This phase is controlled by (i) the phase of the diurnal bulge, which depends on the numerous factors involved in the thermospheric energy balance (not discussed in detail here); (ii) the relation between the pressure-gradient force and wind direction (see item 2 above); (iii) the magnetic declination (Section 3.25). (9) The shape of the diurnal variations of N,,,F2 and h,,,F2 are well explained

44

H.

EISHBETII

in terms of wind effects (Section 4.21; Fig. 11). Geographical variations at a given season have not been fully investigated. (10) The seasonal, annual and semi-annual anomalies in iV,F2 are not readily explained in terms of winds, and require other explanations (Sections 4.23, 4.24; Fig. 12), possibly changes of atmospheric structure. (11) When the geometry of the Earth’s magnetic field is taken into account, many longitude and declination variations in the Fklayer can be explained (Figs. 14, 15). (Variations of wind velocity with longitude and declination are, on current models, quite minor). (12) Winds can account for many features of F2-layer behaviour in high latitudes, including the ‘UT effect’ seen in the Antarctic. They are not particularly relevant to the question of the maintenance of the FB-layer during the polar winter (Section 4.3). (13) Winds can influence the form of the FB-layer equatorial

anomaly produced by electromagnetic drift. A meridional wind blowing across the dip equator produces an asymmetrical N,F2 distribution. A wind converging towards the EquaWind velocities at low latitudes tor at night can help to maintain the Fe-layer. are however not well known (Section 4.4 ; Fig. 18). (14) Atmospheric heating during storms alters the global pressure distribution this must alter the wind pattern and affect the F2-layer. in the thermosphere; In particular, equatorward winds due to aurora1 zone heating could produce increases of N,F2 at midlatitudes (Section 4.27). 5.2 Some outstanding problems

The explanation of many FB-layer phenomena in terms of wind effects has reached quite a satisfactory state ; the outstanding problems are largely concerned with the properties of the neutral atmosphere. Not enough is known about the temporal and spatial variations of thermospheric pressure, density and temperature, or about how these parameters are related to the sources and sinks of energy. Current atmospheric models, though extremely useful, are too idealized and too highly averaged. In these models the lower boundary conditions are a major source of uncertainty. The setting of fixed boundary conditions at, say, 120 km has been a computational necessity. It may partly be justified on the grounds that the wind velocities computed at 150 km and above are virtually independent of the wind velocities assumed at the lower boundary (LINDZEN, 1907). But the computed winds may not be insensitive to the variations of other parameters at the lower boundary. Indeed CHANDRA and STUBBE (1970) have shown that diurnal density and temperature changes at the lower boundary could influence the phase of the density and temperature variations at greater heights (contrary to the deductions of EIAXBIS and PRIESTER (1965) which were based on more restricted calculations). VOLLAND (1969) has shown that the tidal motions in the lower atmosphere (below 100 km) influence the density.and temperature variations and the wind velocities at heights up to 300 km. Clearly more work is needed to see how these fsotors might inauence (a) the winds themselves and (b) the FB-layer variations; this necessitates computing the winds with more realistic boundary assumptions.

Thermospheric

46

winds aud the F-region

Questions of the energy balance; the large-scale transport of air; superrotation ; and continuity of air motion require further investigation. They are difficult to study with present atmospheric models because the winds in the lower thermosphere (which are most important as regards mass transport, on account of the variation of density with height) are very poorly known. Again this trouble is largely due to the practical necessity of setting arbitrary boundary conditions in the lower thermosphere. Some FZ-layer phenomena, such as seasonal changes and some storm effects, are probably not due to winds but to changes of atmospheric composition. These changes might result from a general circulation, of the type described by DUNCAN (1969a) and JOHNSONand GOTTLIEB(1970), which must bear some relation to the thermospheric wind pattern. To conclude: the importance of winds in the Ftlayer is well established. But while great uncertainties exist in the parameters of the neutral atmosphere, it seems prudent not to attach too much weight to fine details of FB-layer behaviour in relation to winds. Acknozuledgenaetu%-The author is grateful to many people for valuable discussions, particularly Dr. E. N. BRA-Y, Mr. J. R. DUDENEY, Mr. D. ECCLES, Dr. J. W. KING, Mr. W. R. Pmaon and Dr. L. THOMAEZ. Dr. R. RUSTER kindly made available his detailed calculatious, which were used to illustrate several features of the wind system. Thanks are due to those who supplied diagrams. This paper is published by permission of the Director of the Radio and Space Research Station in the Science Research Council. REFERENCES ABIJR-ROBB M. F. K. ABUR-ROBB M. F. K. and WINDLE D. W. ARYSTRONo E. B. BAILEY G. J. and MOFFETT R. J. BAILEY G. J., MOFIXTT R. J. and RISHBETH H. B~KS P. M. and HOLZER T. E. BATES D. R. B-R R. G. aud KENDALL P. C. BRACE L. H., MAYR H. G. and MAHAJAN K.K. BRAMLEY E. N. BRAMLEY E. N. and YOUNo M. BRAMLXY E. N. and RUSTER R. BRILLOUIN M. BURKhaD 0. CARRU H., PETIT M. and WALDTICUYEL P. CHALLINOR R. A. CFIALLINOR R. A. CHALLINOR R. A. CHALLINOR R. A. CHALLINOR R. A. and ECCLES D. CEANDRA 8. and STIJBBE P. CEO H. R. and YEH K. C.

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46

H. RISHBETH

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1966

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1963 1956 1969 1970

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306.

Pmoom W. R.

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THOBUS L. TITHERID~EJ. E. TORR D. G. and Torts M. R. VASSEURG. VOLUND H. VOLLAND H. WALDTEUFELP. and MCCLUREJ. P. WALKER J. C. G. YONEZAWA T. YONEZAWA T.

4

1967 1903

1966 1968 1968 1970 1969 1969 1970 1969 1965 1966 1969