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Some effects of neutral air winds on the ionospheric F-layer
Journal of Atmospheric and Terrestrial Phyeics,
1966, Vol. 39, pp. 1733-1744.
Pergamon Press.
Printed in Northern Ireland
Some effects of neutral air winds on the ionospheric F-layer H. KOHL,* J. W. KING and D. ECCLES S.R.C., Radio and Space Research Station, Ditton Park, Slough, Bucks. (Received
12 April 1968)
Abstract-The ionospheric continuity equation for the F2-layer and the equation of motion of the neutral atmosphere have been solved simultaneously to calculate diurnal variations of FZ-layer critical frequency and height at different latitudes for summer, equinox and winter conditions. The agreement between the calculated and observed f,,FZ variations is reasonable for daytime conditions, but the night-time calculated values are generally too small. The anomalous Fe-layer behaviour observed at high latitudes in summer, and also the variation of the height of the layer peak at middle latitudes, appear to be satisfactorily explained by neutral air winds. These winds are also shown to be responsible for the evening enhancements observed at middle latitudes in summer. Relatively slight changes in the atmospheric model used in the calculations can result in very different diurnal variations of calculated critical frequency.
1. I~TR~Du~TI~N IT IS well known from satellite measurements that above 120 km the atmospheric density and temperature vary over the Earth; there are, consequently, horizontal pressure gradients in the atmosphere, and these gradients result in neutral air winds. KING-HELE (1964) concluded from observed distortions of satellite orbits that strong atmospheric winds blow in a predominantly eastward direction, and HINES (1965) emphasized that such winds will be strongly controlled by drag forces between the neutral air and the ionization. KING and KOHL (1965) made an approximate calculation of the atmospheric wind velocities at F-layer heights and found that they are at least of the same order of magnitude as the ionization drifts produced by electric fields (MAEDA, 1963). King and Kohl concluded, therefore, that the effects of neutral air winds must be taken into account in theoretical studies of F-layer behaviour. Wind velocities have since been calculated from atmospheric models by GEISLER (1966 and 1967), KOHL and KING (1967) LINDZEN (1967) and VOLLAND (1967) using different assumptions. RISHBETH (1967 and 1968) has used an approximate method, which included wind velocities derived by GEISLER (1966 and 1967), to estimate the diurnal behaviour of f,F2 and h,F2 at middle latitudes for summer and winter conditions. KOHL and KING (1967) described the global atmospheric wind system existing at F-layer heights and used appropriate wind velocities to calculate the diurnal variations of f,,FZ in summer for Port Lockroy (65’S, 64”W) and Lindau (51°N, 10”E) ; these calculations gave results in good agreement with observed data. KOHL and KING (1967) and RISHBETH (1967 and 1968) used, in their solutions of the ionospheric continuity equation, wind velocities which had been obtained * Max-Planck-Institut fiir Aeronomie, Institut fiir Ionosphiirenphysik, 3411 Lindau/Harz, Germany. 1733
1734
H. KOHL, J. W. KING and D. ECCLES
from entirely separate solutions of the atmospheric equation of motion. This is not a satisfactory procedure because, just as the ion concentration depends on the winds, so the wind velocity also depends on the ion concentration; it is thus desirable to solve the continuity equation for the ionization and the equation of motion for the neutral air wind simultaneously. Such calculations have been performed by the present authors and will be presented in this paper. 2. THE
THEORETICAL CALCULATIONS
2.1.The equations to be solved The .&?-layer continuity equation was written in a form, used by STUBBE (1968), which includes a vertical temperature gradient :
aiv
2.6i3T
x=q-PN+D
+r%-
+N
(
G2+
0.30+p H
1aT T ah
--
)I-T,
(1)
where p = [n(O) + 2.5n(N2)]/[n(0) + 1*4n(N,)] and the other symbols have their usual meanings. The temperatures of the electrons, ions and neutral particles are assumed to be equal. The term a(Nw)/ah represents the effects of vertical ionization drifts. In the present paper these have been assumed to be caused entirely by horizontal neutral air winds; drifts which may have been caused by electric fields have been ignored. The magnitude of w is thus simply related to the velocity u of the neutral air wind. Since charged particles are constrained to move along magnetic lines of force, they will not move with the wind velocity u, but with the component v = (u . B)B/@ which is the projection of u along the line of force; B is the magnetic induction. The velocity v has a vertical component w = (u . B) sin I/ IBI, where I is the magnetic dip angle, and this component has to be used in equation (1). In order to obtain w, the horizontal wind velocity u must be calculated by solving the equation of motion of the neutral air:
au at
-
(ct;;
+ 2(0 x u) + 2
II
(u -
(u. B)B/B2)
= -
1 Op. P
The terms on the left-hand side represent the inertial force, the viscous force, Coriolis force and the ion-drag (which is proportional to the difference between the velocities of the neutral air and the ionization) per unit mass respectively. The term on the right-hand side gives the driving force which produces the wind. The equation of motion should also contain a nonlinear term (u . V)u, but this has been omitted from equation (2) for reasons of simplicity. In order to test whether it is justifiable to neglect this term, the authors have made approximate calculations taking it into account. It appears from these that at middle and higher latitudes its importance is, fortunately, not very great.
Some effects of neutral air winds on the ionospheric P-layer
1735
2.2. The values of the parameters used The parameters below : (a) Electron-ion
invoIved in solving the two differential equations production
a(% X) = aS,n(O)
are discussed
was assumed to be given by
exp, C-~~(0)~(O)~~o(~)
-
aU(NMN&&z(~)],
where (Tis the absorption cross-section, assumed to be lo-l7 cm2 for both 0 and N,; X, is the flux of ionizing photons at the top of the atmosphere, and n, II and Ck denote the concentration, scale height and Chapman function respectively. The above expression implies that, while nitrogen molecules absorb solar U.V. radiation, the contribution of nitrogen to the production rate q is unimportant; this assumption (hTICoLET and will be valid only if the N,+ ions disappear quickly by recombination. SWIDER(1963) have discussed this problem in detail.) The Chapman functions were calculated using approximate formulae given by NICOLIW (1945) for x > QO’, and by GREEN and BARNUM (1963)for x G 90”. For x > 105",q was taken to be zero at all heights. The ionizing flux was assumed to be 8,
= 4 x 10sP10.7em-3sec-1,
where P,,., is the intensity of the 10.7cm radiation from the Sun in units of 1O-22W m-2Hz-1. This value agrees reasonably well with the measurements made by HINTEREGGER and WATANABE (1962)for sunspot minimum conditions. (b) The recombination coefficient was assumed to be given by /? = t%n(N,) = 2 x lo-l2 n(N,) see-l, and to be dependent on the reaction O+ _t N, 3 NO+ + N. FEHSENFELD et aE.(1965)have reported a value of lc of (3 -& I) x IO-l2 cm3 see-I,
and the value used in the present paper thus represents a lower limit. The nitrogen concentration values used in the calculations were 40 per cent less than those derived from Jacchia’s atmospheric model; this reduction was introduced in order to make the value at 120 km agree with that measured by HEDIN and NIER (1966).Finally,
recombinatioxl of 0+ ions by means of the reaction o+ + 0, -+ o,+ + 0’ has been ignored although this reaction may be about as efficient as the N, one assumed. It is possible, in view of the assumptions described immediately above, that the loss rate used in the present paper may be too low; the authors desired, however, for reasons which will be discussed below, to use the smallest loss rate which could reasonably be accepted. (c) The coefficient of ambipolar diffusion was assumed to be given by II = 2.2 x 101’To*” sin2 l/[n(O)
+ l&(N,)]
cm2 set+.
This expression gives good agreement between the laboratory measurements made by KNOF et al. (1964) and the theoretical results Of DALGARNO (1964).The factor 1.4 in the denominator arises from the different cross-section and reduced mass for 0+ - N, collisions (STUBBE, 1968).
1736
H. KOHL,J. W.
KING
and
D. ECCLES
(d) The kinematic coefficient of viscosity was calculated from the expression p = 3.34 x 10-6To’71/p cm2 se&
given by DAL~AFLNO and SMITH(1962). (e) DAL~ARNO(1964) has derived values of yi/Nn, for collisions between 0+ ions and 0 atoms, which can be approximated by the expression Y~/N~& = 4.6 x 10-11To*4see-l cm3. If other constituents are involved the ion drag term cannot be written in the simple form used in equation (2), but it is believed that for F-region heights this expression is sufficiently accurate. (f) The pressure gradient term, -VP/P, was derived from Jacchia’s atmospheric model, and takes into account diurnal, seasonal and solar activity variations. It should be noted that the values of all parameters such as concentration and temperature (except the nitrogen concentration which was discussed in Section 2.2b above) required for the calculation of q, D and ~1were also derived from the same atmospheric model (JACCRIA,1965 and JACCHIAand SLOWEY,1968). 2.3 The method of solution Before solving the equations (1) and (2) a transformation of variables N = xy, 2 = exp
(-X0$)
was applied where H is the scale height of neutral atomic oxygen. In the resulting equations x is the height variable and u and y have to be calculated as functions of x. The boundary conditions used for the new set of equations were:
du dy -_=__= dx dx
0
for
x = 0,
for
2=1.
and u=O,y=O
(4)
The heights corresponding to x = 0 and x = 1 are h = co and h. = 120 km respectively. Condition (3) means that with increasing height the diffusive flux of ionization vanishes (see RISHBETHand BARRON,1960), and that u approaches a constant value. This latter point has been discussed by KOHL and KING (1967). Condition (4) implies that at 120 km the wind velocity and the electron concentration are zero; this condition does not, of course, describe the observed situation, but it represents the behaviour of the desired solution at that height. Jacchia’s model assumes that no horizontal pressure gradients exist at 120 km and, on the basis of this assumption, any winds at 120 km will be caused by viscous drag produced by the winds above 120 km, and they will therefore be very small. Furthermore, since we are only dealing with the F-layer, it is reasonable to assume that the electron concentration is zero at 120 km.
Some effects of neutral air winds on the ionospheric P-layer
1737
The solution of the equations was obtained by means of a finite difference method (see COLUTZ, 1959). Each of the two differential equations was replaced by a system of algebraic equations linear in y and u respectively. Stepwidths of Az = 0.002 and At = 20 min were used.
00
04
’
’ 08
’
t-
’ 12
’
’ 16
’
’ 20
’
2L
L.T.
Fig. 1. Diurnal variations off,,B’Z at Canberra.
Dots: Thick line: Thin line: Dashed line:
Observed monthly medians Calculated variation, including the effects of neutral air winds Calculated variation, excluding the effects of neutral air winds Calculated variation, allowing for a l)-hr phase shift of the neutral air winds.
3. RESULTS
OF THE CALCULATIONS
Diurnal variations of f,,F2 have been calculated for three different stations: Canberra (35’S, 149”E, I = -66*), Lindau (51°M, lO”E, I = 67’) and Port Lockroy (65’S, 64*W, I = -58’). Figures l-3 show the c~culat~ critical frequencies (thick lines) compared with the observed monthly medians (dots) for equinox, summer and winter conditions during 1964 at the three stations respectively.
H. KOHL, J. IV. KING and D. ECCLES
1738
In order to study the effect of the neutral air winds on the FZ-layer, the calculations were repeated without including the vertical drift term ; these results are drawn as thin lines in Figs. l-3. Diurnal variations which are very similar to these no-drift results have been derived by RISHBETH (1964) and GLIDD& and KENDALL (1962).
June 196L
MHz c
foF2
September
December
t ----+
196&
1964
L.T.
Fig. 2. Diurnal variationsoffOF& at Lindau. (For furtherexplanation see caption to Fig. I.)
Several conclusions may be reached by studying Figs. 1-3; the following are the most important : (a) The values calculated by including the effects of winds (thick lines) agree better with the observed data than do the values calcula~d without including the winds (thin lines). (b) The form of the diurnal variation calculated for Port Lockroy (Fig. 3) in summer does not resemble the observed values unless the effects of winds are included. (c) At Canberra and Lindau the calculated summer variations do not exhibit an evening enhancement unless the effects of winds are included; the evening enhancements caused by the winds agree quite well with the observations.
Some effects of neutral air winds on the ionospheric F-layer
1739
(d) The calculated night-time f,,F2 values are generally too small whether the effects of winds are included or not. The values calculated by including the effects of winds are, however, much closer to the observed values, especially at Canberra and Lindau in summer and at Port Lockroy in September. (e) The diurnal variations calculated by including the effects of winds show pronounced morning maxima at Canberra and Lindau in summer; these are not
L-
____
_.____-
_._l__---.~,
. ..-
/---
I
I
/
toF2
r----------
~._______..
t-
.._~/
L.T.
Fig. 3. Diurnal variations of f,,F2 at Port Lockroy. caption to Fig. 1.)
(For further explanation see
evident on the monthly median data, but they are fr~quelltly observed on diurnal f,,P2 variations for individual days (see Fig. 5). The wind velocities used in the calculations described thus far were derived from Jacchia’s atmospheric model. In an attempt to improve the agreement between the cal~ula~d and the observed data, further calculations were performed in which the phase of the ionization drift was advanced by 1+ hr ; the results of these calculations sre also shown in Figs. l-3 (dashed lines). The results obtained for Canberra and Lindau are generally in even better agreement with the observations; in
H. KOHL, J. W. KING and D. ECCLES
1740
particular, the very large morning maxima have been reduced and the night-time values increased. (There are obvious physical reasons for these two effects, but they need not be discussed here.) It is possible to suggest reasons why the phase change described above may be genuine ; the atmospheric model may be slightly erroneous, or electric fields may produce additional drifts which have to be superimposed on those produced by the winds. The authors do not wish to suggest, however, that either of these possibilities 100
-
--
I
t-
L.T.
Fig. 4. Upper Section: Diurnal variationsof the calculatedvertical drift velocities produced at the peak of the FZ-layer by neutral air winds. The thick line shows the drifts produced if Jacchia’s model atmosphere is used, and the dashed line shows those producedif the phase of the diurnalwind variation is advanced l& hr. Lower Section: Diurnal variations of h,F2 at Lindau, September, 1964. The dots show mean values derived from ionograms recorded on five magnetically quiet days; the thick, thin and dashed lines refer to different calculations as described in the caption to Fig. 1.
does in fact occur; the main purpose of the trial was to demonstrate that the resulting electron concentration variations are very sensitive to the phase of the ionization drifts, and that relatively minor errors in the atmospheric model used will lead to appreciable differences in the calculated behaviour. Figure 4 shows the mean P&peak height, h,FZ, derived from ionograms recorded at Lindau on five magnetically quiet days in September 1964, compared with the corresponding calculated h, values. The thick, thin and dashed lines represent
Some effects of neutral sir winds on the ionospheric F-layer
1741
the same cases as before. The data agree reasonably well with the calculations in which the effects of winds have been included, but not with the no-wind calculations. 4. DISCUSSION Horizontal neutral air winds move the F-layer ionization along the magnetic lines of force and thus produce vertical movements of the layer. It may be seen from the upper part of Fig. 4, which shows the diurnal variation of vertical drift at the layer peak, that there is a downward movement during the day and an upward movement at night. The effect of the downward drift is to move the layer into a region of greater loss rate and thus decrease the critical frequency. An upward drift, on the other hand, moves the layer into a region of smaller loss rate, and the critical frequency will thus be greater than it would otherwise have been; BECKER (1961) has in fact, shown that the rate at which f,,F2 decays during the night is closely related to the height of the layer peak. A comparison of the critical frequencies calculated by including and excluding the winds (Figs. l-3) shows to what extent the winds cause a reduction of the critical frequency during the day (this is the wellknown ‘midday bite-out’, most pronounced in summer) and an enhancement at night. As indicated in Section 3, the calculated daytime f,F2 values agree in many respects fairly well with observed values off,,FZ; this agreement cannot, however, be used by itself as a convincing argument for the importance of neutral air winds, because results which are almost as good could be achieved for daytime conditions without assuming vertical drifts, but by using different values of q and /I. Calculations made using these alternative assumptions result, however, in variations of h, similar in form to that shown in Fig. 4 (thin line) and which are thus quite different from those observed. The agreement between the calculated and observed h,F2 data constitutes strong support for the suggestion, made by KING et al. (1967), that vertical drifts caused by winds largely determine the variations of the layer height and thus exert an important influence on f,,FZ. The night-time critical frequencies calculated for each of the three stations agree fairly, well with observed data for the summer months, and also for equinox conditions This good agreement thus only occurs in the cases in which at Port Lockroy. ionization is produced during an important part of the night, viz. after sunset and before sunrise, and there are only a few hours during which the layer is not controlled by production ; in such cases the problem of the maintenance of the night-time ionization is not serious. The equinox and winter behaviour at Canberra and Lindau, and the winter data from Port Lockroy, indicate that in these cases the maintenance of the night-time F-layer is not fully explained in terms of atmospheric winds, although Figs. 1-3 show that very much worse theoretical results are obtained if the effects of winds are neglected. The agreement between the calculated and observed critical frequency data could be made much better by assuming that additional upward drifts, caused by electric fields, occur during the evening hours. Such additional drifts would, however, result in much greater layer peak heights than those observed (see Fig. 4). It appears, therefore, that one or more of the other mechanisms suggested by various
H. KOHL, J. W. KINU and D. ECCLES
1742
workers (including EVANS, 1965, and YONEZAWA, 1965) for maintaining the nighttime ionosphere must be important. The calculated diurnal variations of f,,FZ shown in Figs. 1 and 2 exhibit midlatitude evening enhancements ; these increased critical frequencies are produced when the layer is moved upwards at times near ground sunset when there is still electron production at F-region heights. This explanation of the evening enhancements was suggested by KOHL and KING (1967). It is interesting that BECKER (private communication) has found an example of a pronounced evening rise in h,,FZ on a day which showed an extremely large evening maximum in f,,FZ. 8:
MHz
t
T __---__
2 June
1963
’
’
3 June
1963
2? 0 8
’
I
’
’
’
I ___~
)
I
-L_L~_! I _~ _.
fok2 ifyyp+J 6 June 1964
0
4
8
12
16
20 t -
Fig. 5. Diurnal variations off@‘2
24
LI-11 4 8
1
L-L.--J
7 June 1964
12
1
16
I
20
I
I 1
2L
L.M.T observed at Linda
on four summer days.
The pronounced morning maxima which appear on the calculated diurnal variations of f,,FZ in summer (Figs. 1 and 2, thick lines) are not observed in the corresponding monthly median data. Such maxima do, however, exist on many individual days; Fig. 5 shows diurnal variations of f,,FZ observed at Lindau on four summer days all of which exhibit pronounced morning maxima. The diurnal variation of critical frequency at Port Lockroy in summer is very peculiar ; minimum values occur near midday and maximum values just after midnight. The reason is that, at latitudes as high as that of Port Lockroy (65”S), ionization is produced throughout all 24 hr of the day and the major variations in critical frequency are caused by the downward drift by day, which reduces f,,FZ, and the upward drift at night which not only maintains the ionization, but actually leads to increased f,F2 values. This behaviour may be inferred from a comparison of the calculations (Fig. 3) which were made using zero drift velocity (thin line) and those which included the effect of winds (thick line). There seems little doubt that the diurnal variation at Port Lockroy is produced, as KOHL and KING (1967) suggested, by vertical drifts of ionization.
Some effects of neutral air winds on the ionospheric F-layer
1743
In this paper neutral air winds have been considered as the sole cause of vertical ionization drifts. It is possible that an appropriate electric field, whose existence would have to be assumed, could produce similar drifts and thus bring about the same ionospheric behaviour. The maintenance of the night-time F-layer has in fact been attributed to electric fields by many authors including GARRIOTT and THOMAS (1962), HANSON and PATTERSON (1964), BECKER (1965), EISEMANN (1966) and STUBBE (1968). The present authors, however, believe that at middle latitudes atmospheric winds are very important (particularly as far as the evening enhancements are concerned) because winds having very nearly the desired phase and magnitude will exist if the current atmospheric models a,re correct. Knowledge of electric fields, on the other hand, is such that it is not known whether the appropriate fields exist for producing the desired drifts. 5. CONCLUSIONS
It has been shown that neutral air winds exert an important influence on the ~stribution of ionization in the FZ-layer by moving the ionization up or down magnetic field lines. During daytime conditions the critical frequency is reduced by a downward drift, while in the evening the layer is moved upwards and the loss rate consequently decreases. The critical frequency is enhanced at latitudes and seasons where the upward movement of the layer occurs at a time when there is still electron production; this mechanism explains the peculiar variation of f,,FZ at Port Lockroy, and also the evening maxima of f,FZ observed at middle latitudes, in summer. The upward drifts caused by the winds also provide a partial explanation of the night-time maintenance of the F-layer. Aclcnowledgements-The work described in this paper forms part of a cooperative project undertaken by the Max-Planck-Institut fiir Aeronomie, Lindau, and the Radio and Space Research &ation, Slough, and is published by permission of the Directors of these laboratories.
REFERENCES
1965
J. Atmosph. Terr. Phye. 22, 275. Klein. Ber. 10, 151. The Numerical Treatment of Diffepent,ial ~~~ut~~~, p. 184, Scriber-VerIag, Berlin. J. Atmo8ph. Terr. Phys. 26, 939. Planet. Space Sci. 9, 1. Klein. Ber. 11, 17. J. Geophys. Res. 70, 4331. PEanet. Spare 2%. 13, 219.
1962 1966 1967 1962 1964 1966 1965
J. Geophys. Res. 67, 4211. J. Atmosph. Terr. Phys. 28, 703. J. Atmosph. Terr. Phys. 29, 1469. J. Atmoapk Terr. Phys. %, 1073. PEanet. Space Sci. 12, 979. J. Geophye. Res. 71, 4121. Planet. Space Sci. 13, 169.
BECKER W. BECKERW. COLLATZ L.
1961 1965 1959
DALGARNO A. DALGARNO A.and SMITHF.S. EI~EMANNE.
1964 1962 1966
EVANS
J.V.
FEHSEN~ELD F.C.,SCHMELTEEOPF A.L. ~~~FERGusoNE.E. G~RRIOTT O.K.andT~o~ss J.O. GEISLER J.E. GEISLERJ. E. GMDDO~ J.E.C.~~~KENDALLP.C. H~NsoNW.B.~II~PATTERSONT.N.L. HEDIN A.E.and NIER A.O. HINES C. 0.
1965
1744
H. KOHL, J. W. KINU and D. ECCLES
HINTIEREUGERH. E. and WATANABE K. JACCHIA L. G.
1962 1965
J. Geophys. Rea. 87, 3373. Space Research V (Edited KING-HELE, RIGHINI) p, Amsterdam.
by D. G. P. MULLER and G. 1152, North-Holland,
Planet. Space Sci. IS, 509.
JACCHIA L. G. and SLOWEY J. W. KING J. W. and KOHL H. KINQ J. W., KOHL H. and PRATT R. KING-HBLE D. G. KNOF H., MASON E. A. and VANDERSLICE J. T. KOHL H. and KING J. W. LINDZEN R. S. MAEDA H.
1968 1965 1967 1964 1964
J. Atmoeph. Tern. Phys. 20, 1529. Planet. Space Sci. 12, 835. J. Chem. Phys. 40, 3548.
1967 1967 1963
J. Atmosph. Terr. Phya. QQ, 1045. J. Beophy8. Res. 72,1591. Proc. Int. Conf. Ionosph., p. 187, Inst.
NICOLET M. NICOLET M. and SWIDER W., JR. RISHBETH H. RISHBETH H. RISBBETH H. RISEBETH H. and BARRON D. W. STUBBE P. VOLLAND H. YONEZAWA T.
1945 1963 1964 1967 1968 1960 1968 1967 1965
Inst. Roy. Met. Belg. Mem. 10,74. Planet. Space Sci. 11,1459. J. Atmosph. Terr. Phys. 26, 657. J. Atmosph. Terr. Phys. 20, 225. J. Atmosph. Terr. Phye. SO, 63. J. Atmosph. Terr. Phya. 18, 234. J. Atmoeph. Terr. Phya. 30, 243. J. Geophy8. Rea. 12, 2831. Space Research V (Edited by D.
LVature, Lond. 206, 699.
Phys. and Phys. Sot., London.
G. King-Hele, P. Muller and G. Righini) p. 49, North-Holland, Amsterdam.
Reference is ako w&e to the following unpublkhed material GREEN A. E. S. and BARNUM L.
1963
“Note on a simple approximation to the Chapman function” Rep. Space Sci. Lab., General Dynamics/Astronautics, San Diego, California.
1966, Vol. 39, pp. 1733-1744.
Pergamon Press.
Printed in Northern Ireland
Some effects of neutral air winds on the ionospheric F-layer H. KOHL,* J. W. KING and D. ECCLES S.R.C., Radio and Space Research Station, Ditton Park, Slough, Bucks. (Received
12 April 1968)
Abstract-The ionospheric continuity equation for the F2-layer and the equation of motion of the neutral atmosphere have been solved simultaneously to calculate diurnal variations of FZ-layer critical frequency and height at different latitudes for summer, equinox and winter conditions. The agreement between the calculated and observed f,,FZ variations is reasonable for daytime conditions, but the night-time calculated values are generally too small. The anomalous Fe-layer behaviour observed at high latitudes in summer, and also the variation of the height of the layer peak at middle latitudes, appear to be satisfactorily explained by neutral air winds. These winds are also shown to be responsible for the evening enhancements observed at middle latitudes in summer. Relatively slight changes in the atmospheric model used in the calculations can result in very different diurnal variations of calculated critical frequency.
1. I~TR~Du~TI~N IT IS well known from satellite measurements that above 120 km the atmospheric density and temperature vary over the Earth; there are, consequently, horizontal pressure gradients in the atmosphere, and these gradients result in neutral air winds. KING-HELE (1964) concluded from observed distortions of satellite orbits that strong atmospheric winds blow in a predominantly eastward direction, and HINES (1965) emphasized that such winds will be strongly controlled by drag forces between the neutral air and the ionization. KING and KOHL (1965) made an approximate calculation of the atmospheric wind velocities at F-layer heights and found that they are at least of the same order of magnitude as the ionization drifts produced by electric fields (MAEDA, 1963). King and Kohl concluded, therefore, that the effects of neutral air winds must be taken into account in theoretical studies of F-layer behaviour. Wind velocities have since been calculated from atmospheric models by GEISLER (1966 and 1967), KOHL and KING (1967) LINDZEN (1967) and VOLLAND (1967) using different assumptions. RISHBETH (1967 and 1968) has used an approximate method, which included wind velocities derived by GEISLER (1966 and 1967), to estimate the diurnal behaviour of f,F2 and h,F2 at middle latitudes for summer and winter conditions. KOHL and KING (1967) described the global atmospheric wind system existing at F-layer heights and used appropriate wind velocities to calculate the diurnal variations of f,,FZ in summer for Port Lockroy (65’S, 64”W) and Lindau (51°N, 10”E) ; these calculations gave results in good agreement with observed data. KOHL and KING (1967) and RISHBETH (1967 and 1968) used, in their solutions of the ionospheric continuity equation, wind velocities which had been obtained * Max-Planck-Institut fiir Aeronomie, Institut fiir Ionosphiirenphysik, 3411 Lindau/Harz, Germany. 1733
1734
H. KOHL, J. W. KING and D. ECCLES
from entirely separate solutions of the atmospheric equation of motion. This is not a satisfactory procedure because, just as the ion concentration depends on the winds, so the wind velocity also depends on the ion concentration; it is thus desirable to solve the continuity equation for the ionization and the equation of motion for the neutral air wind simultaneously. Such calculations have been performed by the present authors and will be presented in this paper. 2. THE
THEORETICAL CALCULATIONS
2.1.The equations to be solved The .&?-layer continuity equation was written in a form, used by STUBBE (1968), which includes a vertical temperature gradient :
aiv
2.6i3T
x=q-PN+D
+r%-
+N
(
G2+
0.30+p H
1aT T ah
--
)I-T,
(1)
where p = [n(O) + 2.5n(N2)]/[n(0) + 1*4n(N,)] and the other symbols have their usual meanings. The temperatures of the electrons, ions and neutral particles are assumed to be equal. The term a(Nw)/ah represents the effects of vertical ionization drifts. In the present paper these have been assumed to be caused entirely by horizontal neutral air winds; drifts which may have been caused by electric fields have been ignored. The magnitude of w is thus simply related to the velocity u of the neutral air wind. Since charged particles are constrained to move along magnetic lines of force, they will not move with the wind velocity u, but with the component v = (u . B)B/@ which is the projection of u along the line of force; B is the magnetic induction. The velocity v has a vertical component w = (u . B) sin I/ IBI, where I is the magnetic dip angle, and this component has to be used in equation (1). In order to obtain w, the horizontal wind velocity u must be calculated by solving the equation of motion of the neutral air:
au at
-
(ct;;
+ 2(0 x u) + 2
II
(u -
(u. B)B/B2)
= -
1 Op. P
The terms on the left-hand side represent the inertial force, the viscous force, Coriolis force and the ion-drag (which is proportional to the difference between the velocities of the neutral air and the ionization) per unit mass respectively. The term on the right-hand side gives the driving force which produces the wind. The equation of motion should also contain a nonlinear term (u . V)u, but this has been omitted from equation (2) for reasons of simplicity. In order to test whether it is justifiable to neglect this term, the authors have made approximate calculations taking it into account. It appears from these that at middle and higher latitudes its importance is, fortunately, not very great.
Some effects of neutral air winds on the ionospheric P-layer
1735
2.2. The values of the parameters used The parameters below : (a) Electron-ion
invoIved in solving the two differential equations production
a(% X) = aS,n(O)
are discussed
was assumed to be given by
exp, C-~~(0)~(O)~~o(~)
-
aU(NMN&&z(~)],
where (Tis the absorption cross-section, assumed to be lo-l7 cm2 for both 0 and N,; X, is the flux of ionizing photons at the top of the atmosphere, and n, II and Ck denote the concentration, scale height and Chapman function respectively. The above expression implies that, while nitrogen molecules absorb solar U.V. radiation, the contribution of nitrogen to the production rate q is unimportant; this assumption (hTICoLET and will be valid only if the N,+ ions disappear quickly by recombination. SWIDER(1963) have discussed this problem in detail.) The Chapman functions were calculated using approximate formulae given by NICOLIW (1945) for x > QO’, and by GREEN and BARNUM (1963)for x G 90”. For x > 105",q was taken to be zero at all heights. The ionizing flux was assumed to be 8,
= 4 x 10sP10.7em-3sec-1,
where P,,., is the intensity of the 10.7cm radiation from the Sun in units of 1O-22W m-2Hz-1. This value agrees reasonably well with the measurements made by HINTEREGGER and WATANABE (1962)for sunspot minimum conditions. (b) The recombination coefficient was assumed to be given by /? = t%n(N,) = 2 x lo-l2 n(N,) see-l, and to be dependent on the reaction O+ _t N, 3 NO+ + N. FEHSENFELD et aE.(1965)have reported a value of lc of (3 -& I) x IO-l2 cm3 see-I,
and the value used in the present paper thus represents a lower limit. The nitrogen concentration values used in the calculations were 40 per cent less than those derived from Jacchia’s atmospheric model; this reduction was introduced in order to make the value at 120 km agree with that measured by HEDIN and NIER (1966).Finally,
recombinatioxl of 0+ ions by means of the reaction o+ + 0, -+ o,+ + 0’ has been ignored although this reaction may be about as efficient as the N, one assumed. It is possible, in view of the assumptions described immediately above, that the loss rate used in the present paper may be too low; the authors desired, however, for reasons which will be discussed below, to use the smallest loss rate which could reasonably be accepted. (c) The coefficient of ambipolar diffusion was assumed to be given by II = 2.2 x 101’To*” sin2 l/[n(O)
+ l&(N,)]
cm2 set+.
This expression gives good agreement between the laboratory measurements made by KNOF et al. (1964) and the theoretical results Of DALGARNO (1964).The factor 1.4 in the denominator arises from the different cross-section and reduced mass for 0+ - N, collisions (STUBBE, 1968).
1736
H. KOHL,J. W.
KING
and
D. ECCLES
(d) The kinematic coefficient of viscosity was calculated from the expression p = 3.34 x 10-6To’71/p cm2 se&
given by DAL~AFLNO and SMITH(1962). (e) DAL~ARNO(1964) has derived values of yi/Nn, for collisions between 0+ ions and 0 atoms, which can be approximated by the expression Y~/N~& = 4.6 x 10-11To*4see-l cm3. If other constituents are involved the ion drag term cannot be written in the simple form used in equation (2), but it is believed that for F-region heights this expression is sufficiently accurate. (f) The pressure gradient term, -VP/P, was derived from Jacchia’s atmospheric model, and takes into account diurnal, seasonal and solar activity variations. It should be noted that the values of all parameters such as concentration and temperature (except the nitrogen concentration which was discussed in Section 2.2b above) required for the calculation of q, D and ~1were also derived from the same atmospheric model (JACCRIA,1965 and JACCHIAand SLOWEY,1968). 2.3 The method of solution Before solving the equations (1) and (2) a transformation of variables N = xy, 2 = exp
(-X0$)
was applied where H is the scale height of neutral atomic oxygen. In the resulting equations x is the height variable and u and y have to be calculated as functions of x. The boundary conditions used for the new set of equations were:
du dy -_=__= dx dx
0
for
x = 0,
for
2=1.
and u=O,y=O
(4)
The heights corresponding to x = 0 and x = 1 are h = co and h. = 120 km respectively. Condition (3) means that with increasing height the diffusive flux of ionization vanishes (see RISHBETHand BARRON,1960), and that u approaches a constant value. This latter point has been discussed by KOHL and KING (1967). Condition (4) implies that at 120 km the wind velocity and the electron concentration are zero; this condition does not, of course, describe the observed situation, but it represents the behaviour of the desired solution at that height. Jacchia’s model assumes that no horizontal pressure gradients exist at 120 km and, on the basis of this assumption, any winds at 120 km will be caused by viscous drag produced by the winds above 120 km, and they will therefore be very small. Furthermore, since we are only dealing with the F-layer, it is reasonable to assume that the electron concentration is zero at 120 km.
Some effects of neutral air winds on the ionospheric P-layer
1737
The solution of the equations was obtained by means of a finite difference method (see COLUTZ, 1959). Each of the two differential equations was replaced by a system of algebraic equations linear in y and u respectively. Stepwidths of Az = 0.002 and At = 20 min were used.
00
04
’
’ 08
’
t-
’ 12
’
’ 16
’
’ 20
’
2L
L.T.
Fig. 1. Diurnal variations off,,B’Z at Canberra.
Dots: Thick line: Thin line: Dashed line:
Observed monthly medians Calculated variation, including the effects of neutral air winds Calculated variation, excluding the effects of neutral air winds Calculated variation, allowing for a l)-hr phase shift of the neutral air winds.
3. RESULTS
OF THE CALCULATIONS
Diurnal variations of f,,F2 have been calculated for three different stations: Canberra (35’S, 149”E, I = -66*), Lindau (51°M, lO”E, I = 67’) and Port Lockroy (65’S, 64*W, I = -58’). Figures l-3 show the c~culat~ critical frequencies (thick lines) compared with the observed monthly medians (dots) for equinox, summer and winter conditions during 1964 at the three stations respectively.
H. KOHL, J. IV. KING and D. ECCLES
1738
In order to study the effect of the neutral air winds on the FZ-layer, the calculations were repeated without including the vertical drift term ; these results are drawn as thin lines in Figs. l-3. Diurnal variations which are very similar to these no-drift results have been derived by RISHBETH (1964) and GLIDD& and KENDALL (1962).
June 196L
MHz c
foF2
September
December
t ----+
196&
1964
L.T.
Fig. 2. Diurnal variationsoffOF& at Lindau. (For furtherexplanation see caption to Fig. I.)
Several conclusions may be reached by studying Figs. 1-3; the following are the most important : (a) The values calculated by including the effects of winds (thick lines) agree better with the observed data than do the values calcula~d without including the winds (thin lines). (b) The form of the diurnal variation calculated for Port Lockroy (Fig. 3) in summer does not resemble the observed values unless the effects of winds are included. (c) At Canberra and Lindau the calculated summer variations do not exhibit an evening enhancement unless the effects of winds are included; the evening enhancements caused by the winds agree quite well with the observations.
Some effects of neutral air winds on the ionospheric F-layer
1739
(d) The calculated night-time f,,F2 values are generally too small whether the effects of winds are included or not. The values calculated by including the effects of winds are, however, much closer to the observed values, especially at Canberra and Lindau in summer and at Port Lockroy in September. (e) The diurnal variations calculated by including the effects of winds show pronounced morning maxima at Canberra and Lindau in summer; these are not
L-
____
_.____-
_._l__---.~,
. ..-
/---
I
I
/
toF2
r----------
~._______..
t-
.._~/
L.T.
Fig. 3. Diurnal variations of f,,F2 at Port Lockroy. caption to Fig. 1.)
(For further explanation see
evident on the monthly median data, but they are fr~quelltly observed on diurnal f,,P2 variations for individual days (see Fig. 5). The wind velocities used in the calculations described thus far were derived from Jacchia’s atmospheric model. In an attempt to improve the agreement between the cal~ula~d and the observed data, further calculations were performed in which the phase of the ionization drift was advanced by 1+ hr ; the results of these calculations sre also shown in Figs. l-3 (dashed lines). The results obtained for Canberra and Lindau are generally in even better agreement with the observations; in
H. KOHL, J. W. KING and D. ECCLES
1740
particular, the very large morning maxima have been reduced and the night-time values increased. (There are obvious physical reasons for these two effects, but they need not be discussed here.) It is possible to suggest reasons why the phase change described above may be genuine ; the atmospheric model may be slightly erroneous, or electric fields may produce additional drifts which have to be superimposed on those produced by the winds. The authors do not wish to suggest, however, that either of these possibilities 100
-
--
I
t-
L.T.
Fig. 4. Upper Section: Diurnal variationsof the calculatedvertical drift velocities produced at the peak of the FZ-layer by neutral air winds. The thick line shows the drifts produced if Jacchia’s model atmosphere is used, and the dashed line shows those producedif the phase of the diurnalwind variation is advanced l& hr. Lower Section: Diurnal variations of h,F2 at Lindau, September, 1964. The dots show mean values derived from ionograms recorded on five magnetically quiet days; the thick, thin and dashed lines refer to different calculations as described in the caption to Fig. 1.
does in fact occur; the main purpose of the trial was to demonstrate that the resulting electron concentration variations are very sensitive to the phase of the ionization drifts, and that relatively minor errors in the atmospheric model used will lead to appreciable differences in the calculated behaviour. Figure 4 shows the mean P&peak height, h,FZ, derived from ionograms recorded at Lindau on five magnetically quiet days in September 1964, compared with the corresponding calculated h, values. The thick, thin and dashed lines represent
Some effects of neutral sir winds on the ionospheric F-layer
1741
the same cases as before. The data agree reasonably well with the calculations in which the effects of winds have been included, but not with the no-wind calculations. 4. DISCUSSION Horizontal neutral air winds move the F-layer ionization along the magnetic lines of force and thus produce vertical movements of the layer. It may be seen from the upper part of Fig. 4, which shows the diurnal variation of vertical drift at the layer peak, that there is a downward movement during the day and an upward movement at night. The effect of the downward drift is to move the layer into a region of greater loss rate and thus decrease the critical frequency. An upward drift, on the other hand, moves the layer into a region of smaller loss rate, and the critical frequency will thus be greater than it would otherwise have been; BECKER (1961) has in fact, shown that the rate at which f,,F2 decays during the night is closely related to the height of the layer peak. A comparison of the critical frequencies calculated by including and excluding the winds (Figs. l-3) shows to what extent the winds cause a reduction of the critical frequency during the day (this is the wellknown ‘midday bite-out’, most pronounced in summer) and an enhancement at night. As indicated in Section 3, the calculated daytime f,F2 values agree in many respects fairly well with observed values off,,FZ; this agreement cannot, however, be used by itself as a convincing argument for the importance of neutral air winds, because results which are almost as good could be achieved for daytime conditions without assuming vertical drifts, but by using different values of q and /I. Calculations made using these alternative assumptions result, however, in variations of h, similar in form to that shown in Fig. 4 (thin line) and which are thus quite different from those observed. The agreement between the calculated and observed h,F2 data constitutes strong support for the suggestion, made by KING et al. (1967), that vertical drifts caused by winds largely determine the variations of the layer height and thus exert an important influence on f,,FZ. The night-time critical frequencies calculated for each of the three stations agree fairly, well with observed data for the summer months, and also for equinox conditions This good agreement thus only occurs in the cases in which at Port Lockroy. ionization is produced during an important part of the night, viz. after sunset and before sunrise, and there are only a few hours during which the layer is not controlled by production ; in such cases the problem of the maintenance of the night-time ionization is not serious. The equinox and winter behaviour at Canberra and Lindau, and the winter data from Port Lockroy, indicate that in these cases the maintenance of the night-time F-layer is not fully explained in terms of atmospheric winds, although Figs. 1-3 show that very much worse theoretical results are obtained if the effects of winds are neglected. The agreement between the calculated and observed critical frequency data could be made much better by assuming that additional upward drifts, caused by electric fields, occur during the evening hours. Such additional drifts would, however, result in much greater layer peak heights than those observed (see Fig. 4). It appears, therefore, that one or more of the other mechanisms suggested by various
H. KOHL, J. W. KINU and D. ECCLES
1742
workers (including EVANS, 1965, and YONEZAWA, 1965) for maintaining the nighttime ionosphere must be important. The calculated diurnal variations of f,,FZ shown in Figs. 1 and 2 exhibit midlatitude evening enhancements ; these increased critical frequencies are produced when the layer is moved upwards at times near ground sunset when there is still electron production at F-region heights. This explanation of the evening enhancements was suggested by KOHL and KING (1967). It is interesting that BECKER (private communication) has found an example of a pronounced evening rise in h,,FZ on a day which showed an extremely large evening maximum in f,,FZ. 8:
MHz
t
T __---__
2 June
1963
’
’
3 June
1963
2? 0 8
’
I
’
’
’
I ___~
)
I
-L_L~_! I _~ _.
fok2 ifyyp+J 6 June 1964
0
4
8
12
16
20 t -
Fig. 5. Diurnal variations off@‘2
24
LI-11 4 8
1
L-L.--J
7 June 1964
12
1
16
I
20
I
I 1
2L
L.M.T observed at Linda
on four summer days.
The pronounced morning maxima which appear on the calculated diurnal variations of f,,FZ in summer (Figs. 1 and 2, thick lines) are not observed in the corresponding monthly median data. Such maxima do, however, exist on many individual days; Fig. 5 shows diurnal variations of f,,FZ observed at Lindau on four summer days all of which exhibit pronounced morning maxima. The diurnal variation of critical frequency at Port Lockroy in summer is very peculiar ; minimum values occur near midday and maximum values just after midnight. The reason is that, at latitudes as high as that of Port Lockroy (65”S), ionization is produced throughout all 24 hr of the day and the major variations in critical frequency are caused by the downward drift by day, which reduces f,,FZ, and the upward drift at night which not only maintains the ionization, but actually leads to increased f,F2 values. This behaviour may be inferred from a comparison of the calculations (Fig. 3) which were made using zero drift velocity (thin line) and those which included the effect of winds (thick line). There seems little doubt that the diurnal variation at Port Lockroy is produced, as KOHL and KING (1967) suggested, by vertical drifts of ionization.
Some effects of neutral air winds on the ionospheric F-layer
1743
In this paper neutral air winds have been considered as the sole cause of vertical ionization drifts. It is possible that an appropriate electric field, whose existence would have to be assumed, could produce similar drifts and thus bring about the same ionospheric behaviour. The maintenance of the night-time F-layer has in fact been attributed to electric fields by many authors including GARRIOTT and THOMAS (1962), HANSON and PATTERSON (1964), BECKER (1965), EISEMANN (1966) and STUBBE (1968). The present authors, however, believe that at middle latitudes atmospheric winds are very important (particularly as far as the evening enhancements are concerned) because winds having very nearly the desired phase and magnitude will exist if the current atmospheric models a,re correct. Knowledge of electric fields, on the other hand, is such that it is not known whether the appropriate fields exist for producing the desired drifts. 5. CONCLUSIONS
It has been shown that neutral air winds exert an important influence on the ~stribution of ionization in the FZ-layer by moving the ionization up or down magnetic field lines. During daytime conditions the critical frequency is reduced by a downward drift, while in the evening the layer is moved upwards and the loss rate consequently decreases. The critical frequency is enhanced at latitudes and seasons where the upward movement of the layer occurs at a time when there is still electron production; this mechanism explains the peculiar variation of f,,FZ at Port Lockroy, and also the evening maxima of f,FZ observed at middle latitudes, in summer. The upward drifts caused by the winds also provide a partial explanation of the night-time maintenance of the F-layer. Aclcnowledgements-The work described in this paper forms part of a cooperative project undertaken by the Max-Planck-Institut fiir Aeronomie, Lindau, and the Radio and Space Research &ation, Slough, and is published by permission of the Directors of these laboratories.
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1965
J. Atmosph. Terr. Phye. 22, 275. Klein. Ber. 10, 151. The Numerical Treatment of Diffepent,ial ~~~ut~~~, p. 184, Scriber-VerIag, Berlin. J. Atmo8ph. Terr. Phys. 26, 939. Planet. Space Sci. 9, 1. Klein. Ber. 11, 17. J. Geophys. Res. 70, 4331. PEanet. Spare 2%. 13, 219.
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J. Geophys. Res. 67, 4211. J. Atmosph. Terr. Phys. 28, 703. J. Atmosph. Terr. Phys. 29, 1469. J. Atmoapk Terr. Phys. %, 1073. PEanet. Space Sci. 12, 979. J. Geophye. Res. 71, 4121. Planet. Space Sci. 13, 169.
BECKER W. BECKERW. COLLATZ L.
1961 1965 1959
DALGARNO A. DALGARNO A.and SMITHF.S. EI~EMANNE.
1964 1962 1966
EVANS
J.V.
FEHSEN~ELD F.C.,SCHMELTEEOPF A.L. ~~~FERGusoNE.E. G~RRIOTT O.K.andT~o~ss J.O. GEISLER J.E. GEISLERJ. E. GMDDO~ J.E.C.~~~KENDALLP.C. H~NsoNW.B.~II~PATTERSONT.N.L. HEDIN A.E.and NIER A.O. HINES C. 0.
1965
1744
H. KOHL, J. W. KINU and D. ECCLES
HINTIEREUGERH. E. and WATANABE K. JACCHIA L. G.
1962 1965
J. Geophys. Rea. 87, 3373. Space Research V (Edited KING-HELE, RIGHINI) p, Amsterdam.
by D. G. P. MULLER and G. 1152, North-Holland,
Planet. Space Sci. IS, 509.
JACCHIA L. G. and SLOWEY J. W. KING J. W. and KOHL H. KINQ J. W., KOHL H. and PRATT R. KING-HBLE D. G. KNOF H., MASON E. A. and VANDERSLICE J. T. KOHL H. and KING J. W. LINDZEN R. S. MAEDA H.
1968 1965 1967 1964 1964
J. Atmoeph. Tern. Phys. 20, 1529. Planet. Space Sci. 12, 835. J. Chem. Phys. 40, 3548.
1967 1967 1963
J. Atmosph. Terr. Phya. QQ, 1045. J. Beophy8. Res. 72,1591. Proc. Int. Conf. Ionosph., p. 187, Inst.
NICOLET M. NICOLET M. and SWIDER W., JR. RISHBETH H. RISHBETH H. RISBBETH H. RISEBETH H. and BARRON D. W. STUBBE P. VOLLAND H. YONEZAWA T.
1945 1963 1964 1967 1968 1960 1968 1967 1965
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LVature, Lond. 206, 699.
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G. King-Hele, P. Muller and G. Righini) p. 49, North-Holland, Amsterdam.
Reference is ako w&e to the following unpublkhed material GREEN A. E. S. and BARNUM L.
1963
“Note on a simple approximation to the Chapman function” Rep. Space Sci. Lab., General Dynamics/Astronautics, San Diego, California.