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Lunar variations of the F2 layer at Ibadan
,Journal of .ktnl,~sl~h(~ric and Terrestrial Physi(~s, 1!156, Vol. 9 pp. 144 to 154. PergamonPress Lt,l., LolMon
Lunar variations o~ the F2 layer at Ibadan R. A. B ~ o w x Physics Depai'tmenl. University College, I b a d a l b Nigeria
(Ret'eired 1 3larch 1!156) Abstract--l~egular readings of F2-1ayer p a r a m e t e r s taken at I b a d a n from D e c e m b e r 1!151 to April 1954 have been analysed for lunar and hmi-solar variations. H a r m o n i c analysis shows t h a t the l u n a r variations of ]~., F2, y.~F2, foF2, and h'F2 arc semidiurnal and of considerable amplitude. These variations are presented as h a r m o n i c dials. The}' s h o w m a r k e d seasonal variation of amplitude mM phase. The hmi-solar eff~,ets are also large; the phase of the lunar oscillations changing b y particularly large a m o u n t s during the course of a solar day. Values of the r e c o m b i n a t i o n coefficient a,t various heights in t~ho F2 region are deduced from the hmi-solar variations, and s h o w n to be consistent, with ml exponential decrease with height. 1.
INTRODUCTION
ALTHOUC,It the tidal variations of the equatoriM ionosphere are known to be large in amplitude, and to differ considerably in t)hase from the tides observed at higher latitudes, they have been studied in detail for one station only. MARTYI~" (1947) has made a s t u d y of the lunar and hmi-solar variations of height and critical frequency of the F2-1ayer at Huancayo, and his results are largely supported by McNIs~ and GAUTIER (1949) tbr noon values offoF2 only at Huaneayo, and OSBORS~E (1952) for noon values offoF2 only at Singapore. McNISH and ( ~ A U T I E R , however, lind no evidence of any luni-solar effects at Huancayo, and it seemed desirable therefore to make a detailed analysis of these effects for a second equatorial station. The analysis for Ibadan given below is based on the routine measurements of F2-1ayer parameters made from December 1951 to April 1954, using an automatic ionospheric recorder lent by the Radio Research Station of D.S.I.R. From the photographic record, the values of h'F2 are read directly with an accuracy of about 2=5 kin, and those offoF2 to =~0.1 Me/see. The values of h,,~F2 and ymF2 are found either by the method of APgLETON and BE:t'NO~" (1940), or by the use of transparent sliders of the type described bs, "PIG¢OT " ~ W (1953), and are accurate to about ~10 km and =-15 km respectively. There are considerable gaps in the records, caused mainly by failures of the power supply, and after removing months for which no records or very few records were obtained, there remain twenty-four months for which it is possible to investigate the variation of h,,,F2, y,,F2, and foF2, and twenty-five months for h/F2. (For most. of February 1954 the recorder was not working on frequencies t~bove 7 Me/see.) '2. A N A L Y S I S OF THE
DATa
The data were analysed by what is essentially the method of ( mtP,lAN and BAR'rELS (1940). The mean solar diurnal variation was subtracted from the readings for each month, and the data rearranged according to hmar time. In this way the mean lunar diurnal variation of the parameter was obtained for each month, with readings at intervals of one-twenty-fifth of a lunar day (approximately one solar hour). 144
Lunar variations of the F2 layer at. Ibadan i n o r d e r to reduce t h e a m o u n t of c o m p u t a t i o n n e c e s s a r y to decide which c o m p o n e n t s of t h e l u n a r v a r i a t i o n are significant, t h e full analysis of CHAP51AX a n d BA~TELS was n o t a p p l i e d to t h e i n d i v i d u a l m o n t h l y v a r i a t i o n s . I n s t e a d , a w e i g h t e d m e a n was f o u n d for each c a l e n d a r m o n t h for all t h e y e a r s in which readings were available. I n all, t h e l u n a r v a r i a t i o n s for eleven " m e a n m o n t h s " were f o u n d in this w a y . (There were no readings for O c t o b e r of a n y year.) 10
,,'
/
/v
11
O0
10
01
11
O0
/z/h-ca
09
,,01
' ', "° \ cY-3 G ', ) <
08 .9(
'
'~o'A.
07 11
O0
01
•
:i'.0 2
g
I
-
06
08 02
11
07 O0
06
01
10 10
02
O3
og
09
\
03
06
04 08
07
06 05 07 06 05 Fig. I. Harmonic dials shouing mean hmar semidiun,al tides in F2-layer parameters at [badan. • Months of soulhern solstice. (-) ]~3quinoetia.l months. ") Months of norlhern solstice.
T h e first % u r h a r m o n i c c o m p o n e n t s of t h e l u n a r diurnal v a r i a t i o n of t h e p a r a m e t e r s for each " m e a n m o n t h " were t h e n e v a l u a t e d a n d p l o t t e d on h a r m o n i c dials. W h e n p r o b a b l e e r r o r ellipses were c o n s t r u c t e d oi1 these d i a g r a m s , it was f o u n d t h a t , ill each case, o n l y the s e c o n d . h a r m o n i c c o m p o n e n t was significant. T h e i n d i v i d u a l m o n t h l y l u n a r d i u r n a l v a r i a t i o n s of the four F2-1ayer p a r a m e t e r s were t h e n s u b j e c t e d to h a r m o n i c analysis tbr the second c o m p o n e n t only. Tile results of this analysis are s h o w n in the h a r m o n i c dials of Fig. 1. T h e m e a n v a l u e a n d its p r o b a b l e error ellipse are also shown. T h e a m p l i t u d e (P2) a n d t i m e of m a x i m u m (t,,) in h m a r h o u r s a f t e r local l u n a r t r a n s i t , of the m e a n tide are given in 'Fable 1. T h r e e s y m b o l s h a v e b e e n used in p l o t t i n g t h e points on t h e h a r m o n i c dials 145
04
R. A. BRow>z Table 1. A m p l i t u d e a n d p h a s e of t h e l u n a r s e m i d i u r n a l tides in t h e F2-1ayer p a r a m e t e r s a t I b a d a n , w i t h t h e m e a n results for t t u a n c a y o
h.~F2
y.~F2
foF2
1~2
t2
I)2
t2
P2
t2
(kin)
(hmar hours)
(kin)
(lunar hours)
(Mc/see)
(hmar hours)!
N o r t h e r n solstice ; Equinoxes S o u t h e r n solstice
9-47 7.49 7-30
8"4 8"6 7"3
5'96 4"90 9"82
9"1 9"4 8'5
0"169 0"129 0'095
Mean
7-74
8.1
6.96
8.9
Huancayo mean (MARTYN)
5"20
8"43
--
--
10
11 O 0
/!
i
1)2
t2
(kin)
(lunar hours)
4"5 3"8 2"6
l'22 1'80 3"89
6"0 8"2 8"7
0.119
3.8
2.16
8.2
0"10
4"33
2"32
9"23
10
11
O0
08
O~
06
//
,!
09
h'F2
J
og
O8 07 O0
01
06 10
02
11
O0
01
0.1Mc/s I
foF~
03
Og
(~,
03
08 /
06
05
O4 07 . 06 Fig. 2. Harmonic dials showing seasonal variation of the tides in the F2-1ayer parameters at Ibadan. 146
05
Lunar variations of the T'2 layer at Ibadan
of Fig. 1: • for the months around the southern solstice (November, December, J a n u a r y , F e b r u a r y (S)), O for the equinoctial months (March, April, September (E)), and o for the months around the northern solstice (May, June, July. August (N)). These three symbols are distributed over the diagrams in very different ways, and when the mean for each group was calculated, three well separated points were found. The amplitudes and phases of these seasonal means are also given in Table 1. Probable error ellipses were drawn from the distribution of each group of points on the harmonic dials. The seasonal means and their probable error ellipses are shown in Fig. 2. The seasonal effects are well marked in all four parameters. "Fable 2. Lunar tidal components for groups of three solar hours hmF2
Solar time
P2
(km)
Ym F 2
t2
~
t)2
(hmar (kin) hours) ,
i
fo F 2
t2
1'2
(hmar hours)
(Me/see)
4.22
0.248
h'F2
t2
P2
t.,
(hmar ' hours)
(krn)
i (hmar hours)
10.41
2-32
6.95
I
2300 ] 0000 0100
3"08
0200 J 0300 0400
5-86
7.77
3.67
8-92
0.091
11'47
5.29
8.34
0500 } 0600 0700
7-88
8.23
4.22
8.18
0-131
9"07
1'60
7'39
0800 } 0900 1000
10.72
8.27
13-83
8.93
0-202
2"49
4"91
7'83
llO0 } 1200 1300
8.50
7-00
8-86
7.84
0'333
3"28
6'62
8'34
1400 } 1500 1600
8.84
7.95
7.95
9.37
0"286
4-03
5-03
9.14
1700 1800 1900 J
8.08
9"17
6"97
9"68
0"186
4"81
0"51
7.89
2000 } 2100 2200
8-57
1'48
8-54
0.51
0.073
6"92
3'90
1.53
8.92
2.54
i
147
it. A. BROWN One o t h e r analysis of the d a t a was m a d e - - t o d e t e r m i n e the luni-solar variations. I f the response of the ionosphere to e x t e r n a l forces is not a linear flmetion o f height, the solar and l u n a r tidal forces m a y be e x p e c t e d to interact, a n d the h m a r coefficients of the v a r i a t i o n of the layer p a r a m e t e r s will d e p e n d on solar time. ] f the available d a t a are split into t w e n t y - f o u r groups, in order to d e t e r m i n e the lunar tide s e p a r a t e l y for each h o u r of the solar day, the p r o b a b l e errors in the final a m p l i t u d e s and phases are increased at least, five times over those for the m e a n tide. F o r this reason it would seem necessary to p a y p a r t i c u l a r a t t e n t i o n 11
10
O0
01
O0
11
'
02
10
/.
01
/ , 5k.m, ( k
02
03 03
O9
o L\
/ / 07
1oi 11
04
05
06 O0
O4
01
08 10
06
07 11
O0
O5 01
foF2 ~1
L\q
02
/
03
09
O3 04
08 ~
:
cs
,ikrn/
O4 07
06
07
05
06
05
Fig. 3. Htu'monic dials showing luni-sola.r efl'eets ~t lbadan. to the significance of the results of such a luni-solar analysis, t h o u g h this seems not to h a v e been done previously. The a p p a r e n t discrepancies between the results of MARTYN, and MoNIsK and (IAUTIER for H u a n e a y o m a y be due to insufficient a c c u r a c y in the determinations. I t was felt t h a t the d a t a available for I b a d a n were i n a d e q u a t e to d e t e r m i n e s e p a r a t e l y the lunar variations for each solar hour. I n s t e a d , the readings (after the r e m o v a l of the m o n t h l y m e a n solar variation) were split into eight groups, each containing readings for three solar hours c e n t r e d on one of the t.imes: 0000, 0300, 0600. 0900, 1200, 1500, 1800, or 2100 GMT. The l u n a r coefficients were t h e n e v a l u a t e d s e p a r a t e l y tbr each of these groups. The results of this analysis are given in '.Fable 2, and are illustrated on h a r m o n i c dials in Fig. 3. T h e m e t h o d of calculation used p r e v e n t e d the c o n s t r u c t i o n of p r o b a b l e error ellipses as on 14S
Lunar w~riationsof' the _F2layer at Ibadan the other harmonic dials, but an estimate of the errors involved was made. The error in the co-ordinates of a representative point on the dial was assumed to be inversely proportional to the number of individual readings of the parameter used in deriving the point. A circle can then be drawn round each point with radius V/(A/rr)(no/nl), where A is the area of the appropriate probable error ellipse in Fig. 1, n 0 the total number of readings of the parameter, and n~ the number of readings used in deriving the point concerned. These circles give a rough idea of the "reliability" of the points shown in Fig. 3. The luni-solar variations appear to be significant in all cases except t h a t of h'F2, and are most clearly marked in the case offoF2. 3. T~E Lu~:an VAR~ATIO~:S The mean lunar semi-diurnal tides in the F2-1ayer at Ibadan are very similar in magnitude to those found at Huancayo by MARTY?¢ (1947), but are slightly advanced in phase. MARTYN'S results are included in Table 1 for comparison. The tide in h,, has an amplitude of 7.7 kin, the m a x i m u m upward displacement occurring S. 1 lunar hours after the local lunar transit. The seasonal effects consist principally of a considerable increase in amplitude during the months around northern solstice, and an advance of about one hour in phase in the months around southern solstice. The semidiurnal variation of y,~ has an amplitude of 7-0 km, and its m a x i m u m 8.9 hmar hours after transit. The most remarkable characteristic of the y,, variation is its regular lag behind the variation of h,,. Despite the scatter of the points on the harmonic dials of Fig. l, the month-to-month variation of the y,~ tide follows t h a t of h m closely, so that, in all but three months out of the twentyfour, its phase is retarded on t h a t of h,,. Consequently, the seasonal change of phase is also very similar for the two parameters, although the Ym tide has its greatest amplitude in the months around southern solstice. The phase-lag of the Ym tide on t h a t of ]~, is difficult to explain except in terms of a gradual retardation of the phase of the tidal drift of ionization with height. This is not, however, supported by any significant difference in phase between the h,,, and h'F2 variations, nor by the latest drift theory of MAnTYX (1955). No other results for the hmar semidiurnal variation of the F2-layer semithiekness y,,, are available for comparison with those for Ibadan. A very similar lag is, however, noticeable in the mean solar (tiurnal variations of h,~ and y,,,. A rapid increase in )~,,, begins immediately after sunrise at 0600 GMT, whereas y,,~ decreases gradually till 0700 GMT, and then increases rapidly. Again, the maximum value of ]~,,, is attained between 1000 and 1100 GMT, while the m a x i m u m of y,,,, occurs between 1100 and 1200 GMT. The phase of the hmar semidiurnM variation offoF2 is the most striking difference between equatorial stations such as Ibadan and Huaneayo, and the rest ~f the worl(I. At Ibadan the foF2 variation has an amplitude of 0.12 Me/s, with the m a x i m u m at 3.8 hnmr hours after local transit, in marked contrast to the average 10 hours of higher-latitude stations. The seasonal change in this tide is very regular. At southern solstice the amplitude is nmch smaller than at northern solstice, and the phase advanced by about two hours. At the equinoxes, amplitude and phase have intermediate values. 149
R. A. Buow~¢
The tide in h'F2, although much smaller, is in phase with t h a t in hmF2. (Amplitude 2.2 km, m a x i m u m at 8.2 lunar hours after transit.) The only significant seasonal variation of this tide is the increase in the amplitude in the months of southern solstice, h i this respect it resembles the tide in ym. While the mean tides at I ba da n and H u a n c a y o are very similar, their seasonal effects are quite different. The phase changes in the height variations at I b a d a n are like those found by DELOBEAU (1.955) at Dakar, the nearest station to I b a d a n for which results are available. This similarity does not extend to the variations of critical frequency, however, and since DELOBEAU gives no assessment of his errors from which the reality of his seasonal effects can be judged, no importance can be attached to this similarity. The seasonal change of the aniplitu
tan 1 ((O/~Nm)
(1)
where 2<,) is the pulsatance of the lunar semidiurnal tide. From Fig. l, the mean value of ~ for I badan is 231 °, from which, using the mean value offoF2 for the period concerned, 7.05 Mc/sec, a value of the apparent recombination coefficient can be calculated: z -- 0.92 ~( 10 -l° cm -3 sec -1 at an average height (h,,) of 340 km. values of ~ found by other methods.
This is ill reasonable agreement with the
4. THE I~UNI-SOLAR VARIATIONS ANI) TtIE ])~ECOMBINATION COEFFICIENT
The lunar tides in the F2 l a y e r over I b adan show large changes in both amplitude and phase in the course of the solar day. For all parameters the amplitude tends to be a m a x i m u m at about midday, i.e. when the height of the layer is 150
L u n a r variations of the
F2 layer at I b a d a n
g r e a t e s t . I n fact, t h e a m p l i t u d e is r o u g h l y p r o p o r t i o n a l to h m. I n this respect, the luni-solar v a r i a t i o n s are similar to those f o u n d for H u a n c a y o b y 1V[ARTYIq(1947). T h e r e is no simple r e l a t i o n s h i p b e t w e e n the p h a s e s of the tides a n d a n y o t h e r p a r a m e t e r of t h e layer. T h e p h a s e t e n d s to be g r a d u a l l y r e t a r d e d t h r o u g h o u t t h e d a y , a f t e r a n initial a d v a n c e in s o m e cases. T h e r e a p p e a r to be large alterations during t h e night, a l t h o u g h t h e a c c u r a c y of the results is u s u a l l y insufficient to be certain of t h e i r n a t u r e . T h e m o s t regular change of p h a s e is s h o w n b y t h e tide in foF2, which, a f t e r a r a p i d change soon a f t e r sunrise, undergoes a s t e a d y p h a s e r e t a r d a t i o n of a b o u t one h a l f l u n a r h o u r per solar h o u r t h r o u g h o u t the rest of the d a y a n d night. This is of the s a m e n a t u r e as t h e change a t H u a n c a y o flmnd b y MARTYY, a l t h o u g h of c o n s i d e r a b l y smaller m a g n i t u d e . The p h a s e difference b e t w e e n the tides in h,,y2 a n d foF2 shows a regular height v a r i a t i o n . (lonsequently, values of the r e c o m b i n a t i o n coefficient c a l c u l a t e d f r o m t h e p h a s e differences a t different times also show a regular height v a r i a t i o n . T a b l e 3 gives values of y a n d ~ at various times. The values of ~. h a v e beeu o b t a i n e d "l'¢tble 3. Values of the r(,combinati(m c(~eflicient and attachment coefficient from tho hmi-sob~v variations ('M T
~,
00()0 ()30!P 060[) 090o 120o 150o IS()() 2 100
225 291 205 lS7 248 242 229 163
i
foF2
tan ;,
(Mc/s~c)
1.00 negative 0-466 0.122 2.47 1"88 1.15 negative
~ :: 1011 (cm-3 see-1)
6.15 4.30 5.15 8.02 7.59 8.66 8"64 7"56
~" : 10 5 (s~,c-1)
14 13 . . . . . 47 : 31 75 12o 3.7 5.8 4.1 7.7 6.8 13 . . . . . . .
]lm (kin)
']
301 277 275 373 401 394 374 331:
f r o m e q u a t i o n (1), using the m e a n values of foF2 for the various intervals, which are also g i v e n in T a b l e 3. A g r a p h of lOglo e a g a i n s t the c o r r e s p o n d i n g m e a n values of h,, is s h o w n in Fig. 4, which is consistent with the suggestion t h a t the v a l u e of ~ decreases e x p o n e n t i a l l y w i t h height. (The p o i n t in the circle is t h e v a l u e p r e v i o u s l y calculated f r o m the m e a n tide.) I f the e q u a t i o n of the s t r a i g h t line d r a w n t h r o u g h t h e points of Fig. 4 is w r i t t e n ~ %e Kz, this gives: l°glo e = l°gl0 ~0 -- K(hm -- h0)/(2"303 Ho) w h e r e H 0 is t h e "scale h e i g h t " of the layer. The slope of the line is --K/2.303Ho, a n d the m e a s u r e d v a l u e is --1/140, which c o r r e s p o n d s to K = 1 if H o = 60 kin. I t is also possible to i n t e r p r e t the p h a s e difference b e t w e e n the l u n a r tides in h,, F2 andfoF2 in t e r m s of an a t t a c h m e n t coefficient :¢' i n s t e a d of a r e c o m b i n a t i o n coefficient. I n this case, an a r g u m e n t v e r y similar to t h a t of MAI~TYS'S (1955) gives: 7 = t a n - * (2(o/~'). 151
(2)
R. A . BROWN
Values of e' calculated from this expression are also given in Table 3. A graph of values of :¢' against h~ is also shown in Fig. 4. The scatter of the points from the straight line is r a t h e r worse t h a n in the corresponding graph for ~. In deducing these values for ~ and :¢', the effects of solar drift divergence, ion production, and diffusion have been ignored. This is also true of other m e t h o d s -9
-3
x
[]
o -4 g'
o
_l
_1
-11
250
300
bin
350
400 km
-5
F i g . 4. V M u e s o f t h e r e c o m b i n a t i o n a n d att, a c h m e n t c o e f f i c i e n t s d e r i v e d f r o m t h e h m i - s o l a r effects at Ibadan. ~ R e c o m b i n a t i o n c o e f f i c i e n t . ~ A t t a c h m e n t c o e f f i c i e n t . V M u e s in circles are obtained from the mean tide.
giving similar results. The values of ~ obtained are "effective ~'s." and include the effects of divergence and diffusion. Some estimate of the size of these effects can, however, be made. Following FEnRARO (1945) and MARTYN (1955), we can write the rate of change of ionization density at the m a x i m u m of the F2layer as:
ON 1 Ot ]z m = q - ~ N m 2
N.flo ex @ 213~ p(z,~)sin 2I(13 ~ -- 1) - - N m d i v v
(3)
where d o is a diffusion constant, fi -- y,,/2H o, and v is the drift velocity of the ionization. Normally, fi ----- 1, and the direct effect of the diffusion t e r m m a y be 152
L u n a r v a r i a t i o n s of t h e F 2 layer at I b a d a n
neglected. If, following MARTYN, we assume t h a t there is a lunar perturbation of the height A z , , ~ z 1 cos 2~ot, which produces a perturbation of the electron density N1, we have from equation (3):
~z=v~ (tt v~ (2gN,,~ q- div
t')N 1 ~
( ~Xm2
-~
0~ t Z1 COS 2~ot ~Z!
(4)
The term involving d2v/dz ~ has been neglected, as it can be shown to be much smaller t h a n the others. (v.i.) If we wish to consider the solution to this equation for one given solar time aq only, we may, as a first approximation, consider div v and 0z to be constants. I f this is so, the solution to equation (4) becomes:
N~
=
~=,
~/( ~ ~,rith
. c o s (2~ot -
m -~ div v) 2 -r 4e~ 2
~ - - t a u -1 lc~0¢~7m
/'"
~)
(~) (6)
Thus, the ion-production term affects only the amplitude of the lunar variation of critical frequency, while the phase difference ~ is affected by div v only. In a separate analysis of the solar diurnal variations of the F2-1ayer (to be published) I have calculated values of 2~N~, and estimated (following MARTYN) values of div v and d 2 v / d z 2 throughout the day. From these it appears t h a t at all times other t h a n noon, 2~N,, is at least five times as great as div v. At noon, the ratio 2~N,,/div v m a y be as low as 2. The effect of neglecting the solar-drift divergence is thus to make the deduced daytime values of ~ too high, and the night-time values too low. The error (except at noon) should never be greater than 20%. This is also true of the values deduced for ~'. 5. C O N C L U S I O N
The agreement between the mean hmar tides at Ibadan and Huancayo provides confirmation of the large differences between the hmar ionospheric tides in the equatorial regions and those in other parts of the world. The lack of similarity in the seasonal effects is, however, disappointing, although there does not in fact seem to be any regular pattern in the worldwide seasonal variations of the lunar ionospheric tide. It is probable t h a t they are influenced largely by relatively local peculiarities of the earth's magnetic field. In this connection it should be noted that, although the latitude of Ibadau is 7.5 ° N and its geomagnetic latitude is about 10 ° N, the magnetic dip is 5 + S. It is, therefore, not to be expected t h a t any simple theory of lunar tides, based on latitude (or more probably on geomagnetic latitude), could explain their detailed variations. The luni-solar effects seem to decrease rapidly with increasing latitude. The effects found at Huancayo by MARTYN (1947) are large; those described here for Ibadan are considerably smaller; while those found by MARTY_X=(1948) at Canberra are much smaller still. 153
R. A. Br~()w.x: Lurmv variations of the F2 layer ~xt I|)~(t~m A l t h o u g h the t h e o r y of MARTYr" (1955) a c c o u n t s satisfactorily {br the difference in phase b e t w e e n the tides in h,,~F2 a n d f o F 2 , there is as y e t no e x p l a n a t i o n of the individual effects. The earlier t h e o r y of MARTYN (1947) relied on a r e g u l a r c h a n g e of drift phase with height, and h a d to be discarded whe,~ the revise(l dym~mo t h e o r y of BAKER a n d MAwrY:,- (1953) was publishe(t. Nevertheless, such a height v a r i a t i o n of phase seems at present to be the only w~y of accom~ti.lg for the hmi-solar effects a n d the difference in phase between the tides iH h,,,F2 and y,,F2. A c k n o w l e d g e m e n t s - - I am i n d e b t e d to m y colleagues at i b a d a n , a n d to Mr. W. R. PIG(~OTT O:[' the R a d i o Research St,~tio~, Slough, for m a n y hell)f(fl discussions ou this work. REFERENCES APPLETON 1~]. V. a n d BEYNON V~-. G. J , BAKER ~,~(. (I. a n d MARTYN D. F . CItAPMAN ~. &l~(] BARTELS ,)', ~)ELOBEA1; F .
FERRARO V. (!. A. MARTYN ]). F. McNls~ A. (**.and GAUTIERq]. N. OSBORNE B. ~V. DI(~GOTT~V. R.
1940 1!}53 ] 94() 1955 1945 1947 1948 1955 ]949 ] 952 1953
154
Proc. Phys. Noc. 52, 518. Phil. Traz~s. A246, 281. (;eom(~gnetism, Oxford. C.R. Ac,d. Sci. Paris 240, 222. Terr. 3lrtg. Arm. Elcc. 50, 215. t'roc. Roy. Noc. A190, 273. t'r~w. Roy. Soc. A194, 429. }>roe.Phys. Soc. Cambridg~ ('(mr'. 1). 254. d. Geophys. Res. 54, 303. N(zture 169, 661. Paper RD/25 D.S.I.R. Slough.
Lunar variations o~ the F2 layer at Ibadan R. A. B ~ o w x Physics Depai'tmenl. University College, I b a d a l b Nigeria
(Ret'eired 1 3larch 1!156) Abstract--l~egular readings of F2-1ayer p a r a m e t e r s taken at I b a d a n from D e c e m b e r 1!151 to April 1954 have been analysed for lunar and hmi-solar variations. H a r m o n i c analysis shows t h a t the l u n a r variations of ]~., F2, y.~F2, foF2, and h'F2 arc semidiurnal and of considerable amplitude. These variations are presented as h a r m o n i c dials. The}' s h o w m a r k e d seasonal variation of amplitude mM phase. The hmi-solar eff~,ets are also large; the phase of the lunar oscillations changing b y particularly large a m o u n t s during the course of a solar day. Values of the r e c o m b i n a t i o n coefficient a,t various heights in t~ho F2 region are deduced from the hmi-solar variations, and s h o w n to be consistent, with ml exponential decrease with height. 1.
INTRODUCTION
ALTHOUC,It the tidal variations of the equatoriM ionosphere are known to be large in amplitude, and to differ considerably in t)hase from the tides observed at higher latitudes, they have been studied in detail for one station only. MARTYI~" (1947) has made a s t u d y of the lunar and hmi-solar variations of height and critical frequency of the F2-1ayer at Huancayo, and his results are largely supported by McNIs~ and GAUTIER (1949) tbr noon values offoF2 only at Huaneayo, and OSBORS~E (1952) for noon values offoF2 only at Singapore. McNISH and ( ~ A U T I E R , however, lind no evidence of any luni-solar effects at Huancayo, and it seemed desirable therefore to make a detailed analysis of these effects for a second equatorial station. The analysis for Ibadan given below is based on the routine measurements of F2-1ayer parameters made from December 1951 to April 1954, using an automatic ionospheric recorder lent by the Radio Research Station of D.S.I.R. From the photographic record, the values of h'F2 are read directly with an accuracy of about 2=5 kin, and those offoF2 to =~0.1 Me/see. The values of h,,~F2 and ymF2 are found either by the method of APgLETON and BE:t'NO~" (1940), or by the use of transparent sliders of the type described bs, "PIG¢OT " ~ W (1953), and are accurate to about ~10 km and =-15 km respectively. There are considerable gaps in the records, caused mainly by failures of the power supply, and after removing months for which no records or very few records were obtained, there remain twenty-four months for which it is possible to investigate the variation of h,,,F2, y,,F2, and foF2, and twenty-five months for h/F2. (For most. of February 1954 the recorder was not working on frequencies t~bove 7 Me/see.) '2. A N A L Y S I S OF THE
DATa
The data were analysed by what is essentially the method of ( mtP,lAN and BAR'rELS (1940). The mean solar diurnal variation was subtracted from the readings for each month, and the data rearranged according to hmar time. In this way the mean lunar diurnal variation of the parameter was obtained for each month, with readings at intervals of one-twenty-fifth of a lunar day (approximately one solar hour). 144
Lunar variations of the F2 layer at. Ibadan i n o r d e r to reduce t h e a m o u n t of c o m p u t a t i o n n e c e s s a r y to decide which c o m p o n e n t s of t h e l u n a r v a r i a t i o n are significant, t h e full analysis of CHAP51AX a n d BA~TELS was n o t a p p l i e d to t h e i n d i v i d u a l m o n t h l y v a r i a t i o n s . I n s t e a d , a w e i g h t e d m e a n was f o u n d for each c a l e n d a r m o n t h for all t h e y e a r s in which readings were available. I n all, t h e l u n a r v a r i a t i o n s for eleven " m e a n m o n t h s " were f o u n d in this w a y . (There were no readings for O c t o b e r of a n y year.) 10
,,'
/
/v
11
O0
10
01
11
O0
/z/h-ca
09
,,01
' ', "° \ cY-3 G ', ) <
08 .9(
'
'~o'A.
07 11
O0
01
•
:i'.0 2
g
I
-
06
08 02
11
07 O0
06
01
10 10
02
O3
og
09
\
03
06
04 08
07
06 05 07 06 05 Fig. I. Harmonic dials shouing mean hmar semidiun,al tides in F2-layer parameters at [badan. • Months of soulhern solstice. (-) ]~3quinoetia.l months. ") Months of norlhern solstice.
T h e first % u r h a r m o n i c c o m p o n e n t s of t h e l u n a r diurnal v a r i a t i o n of t h e p a r a m e t e r s for each " m e a n m o n t h " were t h e n e v a l u a t e d a n d p l o t t e d on h a r m o n i c dials. W h e n p r o b a b l e e r r o r ellipses were c o n s t r u c t e d oi1 these d i a g r a m s , it was f o u n d t h a t , ill each case, o n l y the s e c o n d . h a r m o n i c c o m p o n e n t was significant. T h e i n d i v i d u a l m o n t h l y l u n a r d i u r n a l v a r i a t i o n s of the four F2-1ayer p a r a m e t e r s were t h e n s u b j e c t e d to h a r m o n i c analysis tbr the second c o m p o n e n t only. Tile results of this analysis are s h o w n in the h a r m o n i c dials of Fig. 1. T h e m e a n v a l u e a n d its p r o b a b l e error ellipse are also shown. T h e a m p l i t u d e (P2) a n d t i m e of m a x i m u m (t,,) in h m a r h o u r s a f t e r local l u n a r t r a n s i t , of the m e a n tide are given in 'Fable 1. T h r e e s y m b o l s h a v e b e e n used in p l o t t i n g t h e points on t h e h a r m o n i c dials 145
04
R. A. BRow>z Table 1. A m p l i t u d e a n d p h a s e of t h e l u n a r s e m i d i u r n a l tides in t h e F2-1ayer p a r a m e t e r s a t I b a d a n , w i t h t h e m e a n results for t t u a n c a y o
h.~F2
y.~F2
foF2
1~2
t2
I)2
t2
P2
t2
(kin)
(hmar hours)
(kin)
(lunar hours)
(Mc/see)
(hmar hours)!
N o r t h e r n solstice ; Equinoxes S o u t h e r n solstice
9-47 7.49 7-30
8"4 8"6 7"3
5'96 4"90 9"82
9"1 9"4 8'5
0"169 0"129 0'095
Mean
7-74
8.1
6.96
8.9
Huancayo mean (MARTYN)
5"20
8"43
--
--
10
11 O 0
/!
i
1)2
t2
(kin)
(lunar hours)
4"5 3"8 2"6
l'22 1'80 3"89
6"0 8"2 8"7
0.119
3.8
2.16
8.2
0"10
4"33
2"32
9"23
10
11
O0
08
O~
06
//
,!
09
h'F2
J
og
O8 07 O0
01
06 10
02
11
O0
01
0.1Mc/s I
foF~
03
Og
(~,
03
08 /
06
05
O4 07 . 06 Fig. 2. Harmonic dials showing seasonal variation of the tides in the F2-1ayer parameters at Ibadan. 146
05
Lunar variations of the T'2 layer at Ibadan
of Fig. 1: • for the months around the southern solstice (November, December, J a n u a r y , F e b r u a r y (S)), O for the equinoctial months (March, April, September (E)), and o for the months around the northern solstice (May, June, July. August (N)). These three symbols are distributed over the diagrams in very different ways, and when the mean for each group was calculated, three well separated points were found. The amplitudes and phases of these seasonal means are also given in Table 1. Probable error ellipses were drawn from the distribution of each group of points on the harmonic dials. The seasonal means and their probable error ellipses are shown in Fig. 2. The seasonal effects are well marked in all four parameters. "Fable 2. Lunar tidal components for groups of three solar hours hmF2
Solar time
P2
(km)
Ym F 2
t2
~
t)2
(hmar (kin) hours) ,
i
fo F 2
t2
1'2
(hmar hours)
(Me/see)
4.22
0.248
h'F2
t2
P2
t.,
(hmar ' hours)
(krn)
i (hmar hours)
10.41
2-32
6.95
I
2300 ] 0000 0100
3"08
0200 J 0300 0400
5-86
7.77
3.67
8-92
0.091
11'47
5.29
8.34
0500 } 0600 0700
7-88
8.23
4.22
8.18
0-131
9"07
1'60
7'39
0800 } 0900 1000
10.72
8.27
13-83
8.93
0-202
2"49
4"91
7'83
llO0 } 1200 1300
8.50
7-00
8-86
7.84
0'333
3"28
6'62
8'34
1400 } 1500 1600
8.84
7.95
7.95
9.37
0"286
4-03
5-03
9.14
1700 1800 1900 J
8.08
9"17
6"97
9"68
0"186
4"81
0"51
7.89
2000 } 2100 2200
8-57
1'48
8-54
0.51
0.073
6"92
3'90
1.53
8.92
2.54
i
147
it. A. BROWN One o t h e r analysis of the d a t a was m a d e - - t o d e t e r m i n e the luni-solar variations. I f the response of the ionosphere to e x t e r n a l forces is not a linear flmetion o f height, the solar and l u n a r tidal forces m a y be e x p e c t e d to interact, a n d the h m a r coefficients of the v a r i a t i o n of the layer p a r a m e t e r s will d e p e n d on solar time. ] f the available d a t a are split into t w e n t y - f o u r groups, in order to d e t e r m i n e the lunar tide s e p a r a t e l y for each h o u r of the solar day, the p r o b a b l e errors in the final a m p l i t u d e s and phases are increased at least, five times over those for the m e a n tide. F o r this reason it would seem necessary to p a y p a r t i c u l a r a t t e n t i o n 11
10
O0
01
O0
11
'
02
10
/.
01
/ , 5k.m, ( k
02
03 03
O9
o L\
/ / 07
1oi 11
04
05
06 O0
O4
01
08 10
06
07 11
O0
O5 01
foF2 ~1
L\q
02
/
03
09
O3 04
08 ~
:
cs
,ikrn/
O4 07
06
07
05
06
05
Fig. 3. Htu'monic dials showing luni-sola.r efl'eets ~t lbadan. to the significance of the results of such a luni-solar analysis, t h o u g h this seems not to h a v e been done previously. The a p p a r e n t discrepancies between the results of MARTYN, and MoNIsK and (IAUTIER for H u a n e a y o m a y be due to insufficient a c c u r a c y in the determinations. I t was felt t h a t the d a t a available for I b a d a n were i n a d e q u a t e to d e t e r m i n e s e p a r a t e l y the lunar variations for each solar hour. I n s t e a d , the readings (after the r e m o v a l of the m o n t h l y m e a n solar variation) were split into eight groups, each containing readings for three solar hours c e n t r e d on one of the t.imes: 0000, 0300, 0600. 0900, 1200, 1500, 1800, or 2100 GMT. The l u n a r coefficients were t h e n e v a l u a t e d s e p a r a t e l y tbr each of these groups. The results of this analysis are given in '.Fable 2, and are illustrated on h a r m o n i c dials in Fig. 3. T h e m e t h o d of calculation used p r e v e n t e d the c o n s t r u c t i o n of p r o b a b l e error ellipses as on 14S
Lunar w~riationsof' the _F2layer at Ibadan the other harmonic dials, but an estimate of the errors involved was made. The error in the co-ordinates of a representative point on the dial was assumed to be inversely proportional to the number of individual readings of the parameter used in deriving the point. A circle can then be drawn round each point with radius V/(A/rr)(no/nl), where A is the area of the appropriate probable error ellipse in Fig. 1, n 0 the total number of readings of the parameter, and n~ the number of readings used in deriving the point concerned. These circles give a rough idea of the "reliability" of the points shown in Fig. 3. The luni-solar variations appear to be significant in all cases except t h a t of h'F2, and are most clearly marked in the case offoF2. 3. T~E Lu~:an VAR~ATIO~:S The mean lunar semi-diurnal tides in the F2-1ayer at Ibadan are very similar in magnitude to those found at Huancayo by MARTY?¢ (1947), but are slightly advanced in phase. MARTYN'S results are included in Table 1 for comparison. The tide in h,, has an amplitude of 7.7 kin, the m a x i m u m upward displacement occurring S. 1 lunar hours after the local lunar transit. The seasonal effects consist principally of a considerable increase in amplitude during the months around northern solstice, and an advance of about one hour in phase in the months around southern solstice. The semidiurnal variation of y,~ has an amplitude of 7-0 km, and its m a x i m u m 8.9 hmar hours after transit. The most remarkable characteristic of the y,, variation is its regular lag behind the variation of h,,. Despite the scatter of the points on the harmonic dials of Fig. l, the month-to-month variation of the y,~ tide follows t h a t of h m closely, so that, in all but three months out of the twentyfour, its phase is retarded on t h a t of h,,. Consequently, the seasonal change of phase is also very similar for the two parameters, although the Ym tide has its greatest amplitude in the months around southern solstice. The phase-lag of the Ym tide on t h a t of ]~, is difficult to explain except in terms of a gradual retardation of the phase of the tidal drift of ionization with height. This is not, however, supported by any significant difference in phase between the h,,, and h'F2 variations, nor by the latest drift theory of MAnTYX (1955). No other results for the hmar semidiurnal variation of the F2-layer semithiekness y,,, are available for comparison with those for Ibadan. A very similar lag is, however, noticeable in the mean solar (tiurnal variations of h,~ and y,,,. A rapid increase in )~,,, begins immediately after sunrise at 0600 GMT, whereas y,,~ decreases gradually till 0700 GMT, and then increases rapidly. Again, the maximum value of ]~,,, is attained between 1000 and 1100 GMT, while the m a x i m u m of y,,,, occurs between 1100 and 1200 GMT. The phase of the hmar semidiurnM variation offoF2 is the most striking difference between equatorial stations such as Ibadan and Huaneayo, and the rest ~f the worl(I. At Ibadan the foF2 variation has an amplitude of 0.12 Me/s, with the m a x i m u m at 3.8 hnmr hours after local transit, in marked contrast to the average 10 hours of higher-latitude stations. The seasonal change in this tide is very regular. At southern solstice the amplitude is nmch smaller than at northern solstice, and the phase advanced by about two hours. At the equinoxes, amplitude and phase have intermediate values. 149
R. A. Buow~¢
The tide in h'F2, although much smaller, is in phase with t h a t in hmF2. (Amplitude 2.2 km, m a x i m u m at 8.2 lunar hours after transit.) The only significant seasonal variation of this tide is the increase in the amplitude in the months of southern solstice, h i this respect it resembles the tide in ym. While the mean tides at I ba da n and H u a n c a y o are very similar, their seasonal effects are quite different. The phase changes in the height variations at I b a d a n are like those found by DELOBEAU (1.955) at Dakar, the nearest station to I b a d a n for which results are available. This similarity does not extend to the variations of critical frequency, however, and since DELOBEAU gives no assessment of his errors from which the reality of his seasonal effects can be judged, no importance can be attached to this similarity. The seasonal change of the aniplitu
tan 1 ((O/~Nm)
(1)
where 2<,) is the pulsatance of the lunar semidiurnal tide. From Fig. l, the mean value of ~ for I badan is 231 °, from which, using the mean value offoF2 for the period concerned, 7.05 Mc/sec, a value of the apparent recombination coefficient can be calculated: z -- 0.92 ~( 10 -l° cm -3 sec -1 at an average height (h,,) of 340 km. values of ~ found by other methods.
This is ill reasonable agreement with the
4. THE I~UNI-SOLAR VARIATIONS ANI) TtIE ])~ECOMBINATION COEFFICIENT
The lunar tides in the F2 l a y e r over I b adan show large changes in both amplitude and phase in the course of the solar day. For all parameters the amplitude tends to be a m a x i m u m at about midday, i.e. when the height of the layer is 150
L u n a r variations of the
F2 layer at I b a d a n
g r e a t e s t . I n fact, t h e a m p l i t u d e is r o u g h l y p r o p o r t i o n a l to h m. I n this respect, the luni-solar v a r i a t i o n s are similar to those f o u n d for H u a n c a y o b y 1V[ARTYIq(1947). T h e r e is no simple r e l a t i o n s h i p b e t w e e n the p h a s e s of the tides a n d a n y o t h e r p a r a m e t e r of t h e layer. T h e p h a s e t e n d s to be g r a d u a l l y r e t a r d e d t h r o u g h o u t t h e d a y , a f t e r a n initial a d v a n c e in s o m e cases. T h e r e a p p e a r to be large alterations during t h e night, a l t h o u g h t h e a c c u r a c y of the results is u s u a l l y insufficient to be certain of t h e i r n a t u r e . T h e m o s t regular change of p h a s e is s h o w n b y t h e tide in foF2, which, a f t e r a r a p i d change soon a f t e r sunrise, undergoes a s t e a d y p h a s e r e t a r d a t i o n of a b o u t one h a l f l u n a r h o u r per solar h o u r t h r o u g h o u t the rest of the d a y a n d night. This is of the s a m e n a t u r e as t h e change a t H u a n c a y o flmnd b y MARTYY, a l t h o u g h of c o n s i d e r a b l y smaller m a g n i t u d e . The p h a s e difference b e t w e e n the tides in h,,y2 a n d foF2 shows a regular height v a r i a t i o n . (lonsequently, values of the r e c o m b i n a t i o n coefficient c a l c u l a t e d f r o m t h e p h a s e differences a t different times also show a regular height v a r i a t i o n . T a b l e 3 gives values of y a n d ~ at various times. The values of ~. h a v e beeu o b t a i n e d "l'¢tble 3. Values of the r(,combinati(m c(~eflicient and attachment coefficient from tho hmi-sob~v variations ('M T
~,
00()0 ()30!P 060[) 090o 120o 150o IS()() 2 100
225 291 205 lS7 248 242 229 163
i
foF2
tan ;,
(Mc/s~c)
1.00 negative 0-466 0.122 2.47 1"88 1.15 negative
~ :: 1011 (cm-3 see-1)
6.15 4.30 5.15 8.02 7.59 8.66 8"64 7"56
~" : 10 5 (s~,c-1)
14 13 . . . . . 47 : 31 75 12o 3.7 5.8 4.1 7.7 6.8 13 . . . . . . .
]lm (kin)
']
301 277 275 373 401 394 374 331:
f r o m e q u a t i o n (1), using the m e a n values of foF2 for the various intervals, which are also g i v e n in T a b l e 3. A g r a p h of lOglo e a g a i n s t the c o r r e s p o n d i n g m e a n values of h,, is s h o w n in Fig. 4, which is consistent with the suggestion t h a t the v a l u e of ~ decreases e x p o n e n t i a l l y w i t h height. (The p o i n t in the circle is t h e v a l u e p r e v i o u s l y calculated f r o m the m e a n tide.) I f the e q u a t i o n of the s t r a i g h t line d r a w n t h r o u g h t h e points of Fig. 4 is w r i t t e n ~ %e Kz, this gives: l°glo e = l°gl0 ~0 -- K(hm -- h0)/(2"303 Ho) w h e r e H 0 is t h e "scale h e i g h t " of the layer. The slope of the line is --K/2.303Ho, a n d the m e a s u r e d v a l u e is --1/140, which c o r r e s p o n d s to K = 1 if H o = 60 kin. I t is also possible to i n t e r p r e t the p h a s e difference b e t w e e n the l u n a r tides in h,, F2 andfoF2 in t e r m s of an a t t a c h m e n t coefficient :¢' i n s t e a d of a r e c o m b i n a t i o n coefficient. I n this case, an a r g u m e n t v e r y similar to t h a t of MAI~TYS'S (1955) gives: 7 = t a n - * (2(o/~'). 151
(2)
R. A . BROWN
Values of e' calculated from this expression are also given in Table 3. A graph of values of :¢' against h~ is also shown in Fig. 4. The scatter of the points from the straight line is r a t h e r worse t h a n in the corresponding graph for ~. In deducing these values for ~ and :¢', the effects of solar drift divergence, ion production, and diffusion have been ignored. This is also true of other m e t h o d s -9
-3
x
[]
o -4 g'
o
_l
_1
-11
250
300
bin
350
400 km
-5
F i g . 4. V M u e s o f t h e r e c o m b i n a t i o n a n d att, a c h m e n t c o e f f i c i e n t s d e r i v e d f r o m t h e h m i - s o l a r effects at Ibadan. ~ R e c o m b i n a t i o n c o e f f i c i e n t . ~ A t t a c h m e n t c o e f f i c i e n t . V M u e s in circles are obtained from the mean tide.
giving similar results. The values of ~ obtained are "effective ~'s." and include the effects of divergence and diffusion. Some estimate of the size of these effects can, however, be made. Following FEnRARO (1945) and MARTYN (1955), we can write the rate of change of ionization density at the m a x i m u m of the F2layer as:
ON 1 Ot ]z m = q - ~ N m 2
N.flo ex @ 213~ p(z,~)sin 2I(13 ~ -- 1) - - N m d i v v
(3)
where d o is a diffusion constant, fi -- y,,/2H o, and v is the drift velocity of the ionization. Normally, fi ----- 1, and the direct effect of the diffusion t e r m m a y be 152
L u n a r v a r i a t i o n s of t h e F 2 layer at I b a d a n
neglected. If, following MARTYN, we assume t h a t there is a lunar perturbation of the height A z , , ~ z 1 cos 2~ot, which produces a perturbation of the electron density N1, we have from equation (3):
~z=v~ (tt v~ (2gN,,~ q- div
t')N 1 ~
( ~Xm2
-~
0~ t Z1 COS 2~ot ~Z!
(4)
The term involving d2v/dz ~ has been neglected, as it can be shown to be much smaller t h a n the others. (v.i.) If we wish to consider the solution to this equation for one given solar time aq only, we may, as a first approximation, consider div v and 0z to be constants. I f this is so, the solution to equation (4) becomes:
N~
=
~=,
~/( ~ ~,rith
. c o s (2~ot -
m -~ div v) 2 -r 4e~ 2
~ - - t a u -1 lc~0¢~7m
/'"
~)
(~) (6)
Thus, the ion-production term affects only the amplitude of the lunar variation of critical frequency, while the phase difference ~ is affected by div v only. In a separate analysis of the solar diurnal variations of the F2-1ayer (to be published) I have calculated values of 2~N~, and estimated (following MARTYN) values of div v and d 2 v / d z 2 throughout the day. From these it appears t h a t at all times other t h a n noon, 2~N,, is at least five times as great as div v. At noon, the ratio 2~N,,/div v m a y be as low as 2. The effect of neglecting the solar-drift divergence is thus to make the deduced daytime values of ~ too high, and the night-time values too low. The error (except at noon) should never be greater than 20%. This is also true of the values deduced for ~'. 5. C O N C L U S I O N
The agreement between the mean hmar tides at Ibadan and Huancayo provides confirmation of the large differences between the hmar ionospheric tides in the equatorial regions and those in other parts of the world. The lack of similarity in the seasonal effects is, however, disappointing, although there does not in fact seem to be any regular pattern in the worldwide seasonal variations of the lunar ionospheric tide. It is probable t h a t they are influenced largely by relatively local peculiarities of the earth's magnetic field. In this connection it should be noted that, although the latitude of Ibadau is 7.5 ° N and its geomagnetic latitude is about 10 ° N, the magnetic dip is 5 + S. It is, therefore, not to be expected t h a t any simple theory of lunar tides, based on latitude (or more probably on geomagnetic latitude), could explain their detailed variations. The luni-solar effects seem to decrease rapidly with increasing latitude. The effects found at Huancayo by MARTYN (1947) are large; those described here for Ibadan are considerably smaller; while those found by MARTY_X=(1948) at Canberra are much smaller still. 153
R. A. Br~()w.x: Lurmv variations of the F2 layer ~xt I|)~(t~m A l t h o u g h the t h e o r y of MARTYr" (1955) a c c o u n t s satisfactorily {br the difference in phase b e t w e e n the tides in h,,~F2 a n d f o F 2 , there is as y e t no e x p l a n a t i o n of the individual effects. The earlier t h e o r y of MARTYN (1947) relied on a r e g u l a r c h a n g e of drift phase with height, and h a d to be discarded whe,~ the revise(l dym~mo t h e o r y of BAKER a n d MAwrY:,- (1953) was publishe(t. Nevertheless, such a height v a r i a t i o n of phase seems at present to be the only w~y of accom~ti.lg for the hmi-solar effects a n d the difference in phase between the tides iH h,,,F2 and y,,F2. A c k n o w l e d g e m e n t s - - I am i n d e b t e d to m y colleagues at i b a d a n , a n d to Mr. W. R. PIG(~OTT O:[' the R a d i o Research St,~tio~, Slough, for m a n y hell)f(fl discussions ou this work. REFERENCES APPLETON 1~]. V. a n d BEYNON V~-. G. J , BAKER ~,~(. (I. a n d MARTYN D. F . CItAPMAN ~. &l~(] BARTELS ,)', ~)ELOBEA1; F .
FERRARO V. (!. A. MARTYN ]). F. McNls~ A. (**.and GAUTIERq]. N. OSBORNE B. ~V. DI(~GOTT~V. R.
1940 1!}53 ] 94() 1955 1945 1947 1948 1955 ]949 ] 952 1953
154
Proc. Phys. Noc. 52, 518. Phil. Traz~s. A246, 281. (;eom(~gnetism, Oxford. C.R. Ac,d. Sci. Paris 240, 222. Terr. 3lrtg. Arm. Elcc. 50, 215. t'roc. Roy. Noc. A190, 273. t'r~w. Roy. Soc. A194, 429. }>roe.Phys. Soc. Cambridg~ ('(mr'. 1). 254. d. Geophys. Res. 54, 303. N(zture 169, 661. Paper RD/25 D.S.I.R. Slough.