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Solar-cycle modifications of the effects of thermospheric winds on the height of the F2-layer over Antarctica
Journal of Atmospheric and Terrestrial Physics, Vol. 38, pp. 291 to 294. PergamonPress, 197{}. Printed in ~orthern Ireland
Solar-cycle modifications oi the effects o~ thermospheric winds on the height o~ the F2-1ayer over Antarctica J . R . DUDE~-EX* British Antarctic Survey, 2 All Saints Passage, Cambridge, CB2 3LS, England
(Received 28 July 1975) Abstract--Results of analysis of the diurnal variations of hm2'2 for Argentine Islands (65°15'S, 64~16'W) and Halley Bay (75°30'S, 26°40"W) are presented. It is shown that, for summer months, the diurnal variations can be approximated by simple sinusoidal functions, the phases of which vary smoothly with solar activity. This behaviour can be explained in terms of the effects of thermospheric winds; it results partly from a change in the relative importance of 'ion drag' and Coriolis force, and partly from changes in the chemistry which controls the characteristic time required for the layer to respond to the wind. A comparison of observations and theory suggests that the local solar time at which the thermospheric pressure maximum occurs does not vary with solar activity.
1. INTRODUCTION A number of analyses (KING et al. 1967; I~NG et al. 1971; STROBEL and McELRoY, 1970) have
and November 1965. These examples suggest t h a t a reasonable approximation of the diurnal variatiou is a simple sinusoidal function of the form
suggested t h a t the observed diurnal variations of
h m F 2 -~ a o + aj cos ~(t' + a2);
hm.F2 at middle and high latitudes are a result of horizontal thermospheric winds. This hypothesis will be tested here by comparing the results of calculations involving winds with hm)F2 data derived from ionospheric measurements at two Antarctic
where ~( = 2~/24) is the mean angular velocity of the Earth, and t' is local zone time in hours.
observatories through a solar cycle, 2. ANALYSIS OF OBSERVATIONAL D A T A
(1)
Other similar plots, not shown, for different epochs confirm this suggestion. I t is possible (DunE~rEX, 1973) to fit this type of function to the data using the principle of least squares, which allows considerable simplification in analysis since each set of data is described in terms of the coefficients a 0 (mean value), al, (amplitude) and a s (phase). The smooth curves in Fig. 1 are fitted in this manner.
DUDEN-EY (1974) has described a m e t h o d by which h m F 2 can be determined to better than 5% using only the routinely scaled ionospheric charaeteristics ] o F 2 , JoE and M ( 3 0 0 0 ) F 2 . This m e t h o d
This paper is limited to a discussion of the phase parameter a s and its variation with solar activity. Figure 2 shows values of this parameter, plotted as funetions of the mean exospherie temperature T ~ , where the latter is a diurnal average value deduced
has been employed to obtain representative monthly median values of h m F 2 , at each hour for the four summer months (November, December, J a n u a r y and February), using data selected from the period 1957-1969 from Argentine Islands (65°15'S; 64°16'W) and Halley B a y (75°30'S; 26°40'W). I t can be shown t h a t perturbations due to magnetic activity appear negligible in such data
from the JACCHXA(1965) J65 model using m o n t h l y mean values of solar 10.7 cm flux. The r.m.s. uncertainty in the mean phase is shown by the
provided the average m o n t h l y value of the magnetic index 'a' is less t h a n or equal to 13. Only data which obey this limit have been included here and hence the results are representative of magnetically quiet conditions. Figure 1 shows samples of the results obtained using Argentine Islands data for N o v e m b e r 1958
error bars. I t is apparent from this figure that, at both locations, the phase retards smoothly as T ~ increases. Also, the rate at which a s changes with T ~ is approximately the same a t both locations. Notice however, t h a t there is a uniform displacemerit of about 1 h between the Halley Bay and Argentine Islands groups, with the former being t h e more retarded. A small sample of values are included in the figure which were deduced from
* At the S.R.C. Appleton Laboratory during the course of this work.
analysis of data for individual magnetically quiet days from Argentine Islands during N o v e m b e r
291
292
J . R . DUDE~TEY 500
~
I
L
400
~
~ • 3oo~
1 .
200
oo
.
" ,2
.
.
24
" I ~2
z4 LZT (hours) Fig. 1. Monthly median diurnal variations of h m F 2 for Argentine Islands for November 1958 and November 1965 ( l ) . Also shown are the best fit curves of the form of equation (1). 1969. These give an indication of the day-to-day variability on quiet days, which is shown to be significantly smaller t h a n the solar-cycle trend understudy. 3. THEORY OF WIND-PRODUCED VARIATIONS OF hmF2
in ~ from the value given b y equation (2), b u t this perturbation is only a few degrees and is here neglected. The Coriolis parameter is constant for a particular latitude, whilst ~ varies diurnally, seasonally and with solar activity as/V and Too vary. I n the limit ~f(~-~/2, whereas if v > ~ f ~ - ~ 0 . Thus, changes in v can alter ~ within the limits (--~/2) ~ ~ 0, resulting, for example, in a solar cycle change in the azimuth of the wind, relative to that of the driving force. I t follows from a resolution of vectors (RISHBETH and KELLEY, 1971) that a horizontal neutral wind will produce a vertical ion motion of velocity V, which, for the southern hemisphere, is given b y V = U cos I sin I cos (0 -- D -}- (~).
I n this equation, 0 is the instantaneous azimuth of the driving force (measured positive east of north, thus negative in the southern hemisphere), U is the magnitude of the wind, a n d D is the declination of the geomagnetic field (also positive east of north). RISHBET]t and B ~ R O ~ (1960) demonstrated empirically t h a t a n imposed vertical drift would displace the peak of the layer from its reference height (z0) to a new level (zz), where
I n this section an analytical expression for a S will be derived using theory which incorporates the effects of thermospheric winds in a simplified form. Values of a~ computed from this expression will be compared with those observed. B y assuming a steady state a n d neglecting viscosity, RISHBETH (1972) demonstrated t h a t for a particular location the instantaneous azimuth of
(5)
(6)
z l - - z o = az V H / ~ ,
in which ze and z1 are reduced heights, 2 is the ambipolar plasma diffusion coefficient, H is the scale height of monatomie oxygen, and ~1 is an empirical constant of order unity. I f it is assumed that the layer approaches z1 exponentially with a
the wind differs from t h a t of the driving force b y a n angle given approximately by I
= arctan(f/v)
(2)
f = 2El sin ~,
(3)
i
J
where
l
(taken as negative in the southern hemisphere). The parameter f is a coefficient representing the effect of Coriolis force, whilst v is a frictional coefficient representing the 'drag' exerted b y the ions upon the wind. I t will be assumed (after DALGAZ~TO, 1964) that
++ ~, '
~f!
+
~x!~: ~x
6oo
1~5 ~ ~ I eco
I ,ooo T~f=g
--0"4 S--1 v = 4"6 × 10--17 1VTo~
(4)
where N is the ion concentration (m-S). E q u a t i o n (2) is strictly valid only if the angle of inclination (I) of the E a r t h ' s magnetic field is 90°. However ]:)UD]~rEY (1973) has shown t h a t if I :/: 90° there is a small semi-diurnal perturbation
?
)
] ,20o
,4oo
Fig. 2. Values of a 2 for Argentine Islands (O) and Halley Bay (@) plotted agains~ ~ (see text), using all available data for the months November, December, January and February during the period 1957-1969. A sample of values for magnetically quiet days from Argentine Islands during November 1969 are also given (X).
Effects of thermospheric winds on the height of the F2-1ayer over Antarctica characteristic t i m e /-/-z]2 (I=~ISHBETI:r, 1967), t h e n
293
Table 1. Parameters computed using sample data from Argentine Islands and the J65 model
dz dt
°:s~
(zl
z),
(7)
where % is a f u r t h e r empirical c o n s t a n t of order unity. C o m b i n i n g (5), (6) a n d (7) gives the differential e q u a t i o n of t h e f o r m
Parameter
Nov 1958
FlU~ (t622w~~ H~q)
B 2i- C c o s
(0
D -~ ~).
(8)
dt
207
153
77
1090
755
1'213
0"928
0'469
9-9
7.0
5-L
--0"5l
-0"71
--l'54
a v e c t o r of c o n s t a n t a m p l i t u d e r o t a t i n g a t c o n s t a n t speed. T h e a z i m u t h of this v e c t o r is t h e n 0 = - f 2 ( t + e), w h e r e t is t h e local solar t i m e in hours a n d E represents t h e lag of t h e diurnal pressure bulge w i t h respect to t h e subsolar p o i n t ; (b) t h a t v (equation 2) can be r e p r e s e n t e d b y a diurnal m e a n v a l u e (~). I n general ul a n d ~s v a r y diurnally, b u t in s u m m e r at high latitudes, d a y - t i m e conditions prevail for all hours and it is t h u s acceptable to use t h e d a y t i m e values ~z = 0.9 a n d us = 0.5 q u o t e d b y I~ISHBETH (1967). I t t h e n follows t h a t z = z0 q- A cos (~t 4- f2e 4- D -- ($ -- ~w) (9) where ~w = a r c t a n (~2HZ/~s~),
(10)
a n d A is a n a n a l y t i c a l constant. E q u a t i o u (9) is of t h e s a m e f o r m as e q u a t i o n (1) a n d so b y c o m p a r i s o n a 2 = E + (D -- ~ -- 8w)/~2 + (t - - t ' ) .
(11)
I n this e q u a t i o n , (t -- t') is t h e difference b e t w e e n local solar a n d local zone time, (D -- 5) represents t h e t i m e lag b e t w e e n t h e driving force a n d t h e r e s u l t a n t drift v e l o c i t y i m p o s e d on t h e lv2-1ayer ionization, a n d 8w gives t h e d e l a y in the response o f t h e l a y e r t o this i m p o s e d drift. The p a r a m e t e r a 2 varies w i t h position as a result of t h e declination t e r m a n d because (~ depends on f (equation 3) w h i c h is a f u n c t i o n of latitude. For a p a r t i c u l a r location, a 2 will v a r y w i t h solar a c t i v i t y because b o t h 6 a n d ~w are c o m p l e x functions of t h e latter. The
~--(1°-43a~1) 6
This e q u a t i o n can b e solved a n a l y t i c a l l y for certain simplified conditions. These are: (a) t h a t t h e driving force can be r e p r e s e n t e d b y
table shows
the diurnal
average
values
of
(~ a n d dw c o m p u t e d for t h e case of A r g e n t i n e Islands for t h r e e m o n t h s spaced t h r o u g h t h e solar cycle. These values were o b t a i n e d f r o m e q u a t i o n s (2), (4) a n d (10) using t h e J 6 5 m o d e l w i t h a n expression for 2 g i v e n b y Ko/~r, et al. {1968). The values of -hz r e q u i r e d in e q u a t i o n (4) to e v a l u a t e were o b t a i n e d b y a v e r a g i n g t h e m e d i a n h o u r l y
(hours)
Nov 1965
13z7
~(°K) (10t2 m-3 )
dz + Az
Nov 1969
Gw(ho.rs)
147
L30
i
,00
i
values of N m z V 2 o b s e r v e d at A r g e n t i n e Islands for t h e m o n t h s in question. T h e d a t a indicate t h a t b o t h ~ a n d 8w change in t h e same sense t h r o u g h t h e solar cycle, p r o d u c i n g a t o t a l change in a s of a p p r o x i m a t e l y 1"5 h for a t e m p e r a t u r e v a r i a t i o n of 770 ° to 1330°K. Of this, a b o u t 1 h results f r o m a change in (5 a n d t h e r e m a i n d e r f r o m ~w. These results are illustrated graphically in Fig. 3, in w h i c h e is t a k e n as --3.0 h (in r o u g h a g r e e m e n t w i t h J a c c h i a ' s model) a n d D is t a k e n as 16-6°E. Also shown are t h e results o b t a i n e d using t h e J a c c h i a (1971) model, a n d those o b t a i n e d using t h e m o r e c o m p l e t e theoretical t e c h n i q u e s d e v e l o p e d b y Ko]~_L et al. (1968). The l a t t e r i n v o l v e s a simultaneous t i m e - v a r y i n g solution of t h e e q u a t i o n of m o t i o n of t h e n e u t r a l air a n d t h e c o n t i n u i t y e q u a t i o n . I t utilizes t h e J 6 5 m o d e l a t m o s p h e r e , b u t w i t h t h e c o n c e n t r a t i o n s of molecular n i t r o g e n r e d u c e d b y 40~o. All t h r e e sets of results are p l o t t e d w i t h respect to a t e m p e r a t u r e scale d e r i v e d f r o m J65. The a g r e e m e n t b e t w e e n o b s e r v a t i o n a n d t h e o r y is good (compare Fig. 2 a n d Fig. 3), b u t c a u t i o n should be used in drawing detailed conclusions because of t h e u n c e r t a i n t i e s in t h e a t m o s p h e r i c models a n d because o f t h e v a r i o u s simplifying assumptions used in t h e theory. ~i 4~i 3~ ~ ~ 2I
'
T
, ----~
~ ~
/
~ ~ f / ~ /
?,
©
I
~,~ /
01I ~oo
o
, see
oJ ~ 10oo ~ IoK)~oo
L ~4oo
i ~
Fig. 3. The variation of as as a function of ~¢o as deduced from theory. The solid curve is deduced from equation (11) using J65; the dashed curve using J71; the circles from KoH~ et al. (1968) theory. All calculations are for Argentine Islands.
294
J. 1~. I)UDElqEY
E q u a t i o n (11) m a y b e r e a r r a n g e d so t h a t t h e o b s e r v e d v a l u e s o f a S ( e x p r e s s e d n o w i n t e r m s of local solar t i m e ) , t o g e t h e r w i t h t h e c o r r e s p o n d i n g t h e o r e t i c a l v a l u e s o f ~ a n d ~w give e s t i m a t e s o f ~. The results of such an analysis are presented in Fig. 4 for t h e case o f t h e J 6 5 m o d e l . T h e m e a n v a l u e for t h e A r g e n t i n e I s l a n d s d a t a i s - - 2 . 2 5 w i t h a s t a n d a r d d e v i a t i o n o f 0.3 (21 v a l u e s ) , w h i l s t t h e c o r r e s p o n d i n g v a l u e s for H a l l e y B a y a r o - - 2 - 7 5 a n d 0.3 (9 values). B o t h t h e s e v a l u e s a r e i n r e a s o n a b l e agreement with the position of the pressure bulge g i v e n b y J a c c h i a ' s models. T h e y a r e h o w e v e r n o t e n t i r e l y c o n s i s t e n t w i t h e a c h o t h e r , t h o u g h consist e n c y is p r o b a b l y n o t t o b e e x p e c t e d i n v i e w o f t h e very simple model used and the small data samples a v a i l a b l e . I t is n e v e r t h e l e s s p o s s i b l e t o i n f e r t h a t t h e d i f f e r e n t b e h a v i o u r o b s e r v e d a t t h e t w o sites, a n d i l l u s t r a t e d b y Fig. 2, is m a i n l y a r e s u l t o f t h e v a r i a t i o n i n m a g n e t i c d e c l i n a t i o n (see e q u a t i o n 11), I
,
=
"~d~ oo
-
• oo
1
• o8~ o o - - o°
o •o
O
~V
w i t h a s m a l l c o n t r i b u t i o n d u e to t h e c h a n g e o f Coriolis force w i t h l a t i t u d e . Also, f r o m Fig. 4, i t is apparent that the variation in the mean position of t h e p r e s s u r e b u l g e as a f u n c t i o n o f s o l a r a c t i v i t y c a n o n l y b e slight, a n d is p r o b a b l y less t h a n 10 r a i n t h r o u g h t h e solar cycle. T h e noise i n t h e s a m p l e s i n Fig. 4 a p p e a r s to r e s u l t p a r t l y f r o m a s y s t e m a t i c variation with month, the highest values occurring i n J a n u a r y a n d t h e l o w e s t i n :November. M o r e a n a l y s i s is r e q u i r e d t o c o n f i r m this. 4. CONCLUSIONS I t h a s b e e n d e m o n s t r a t e d t h a t for t w o A n t a r c t i c o b s e r v a t o r i e s t h e d i u r n a l v a r i a t i o n s of h m F 2 i n s u m m e r are a p p r o x i m a t e l y s i n u s o i d a l . T h e p h a s e s of these variations have been shown to retard s m o o t h l y w i t h i n c r e a s i n g solar a c t i v i t y i n a m a n n e r consistent with that expected from the interaction between thermospheric winds and the ionization p r e s e n t i n t h e _F-layer, I t is c o n c l u d e d f r o m comparing observation with theory that the position of t h e d i u r n a l p r e s s u r e b u l g e does n o t v a r y w i t h r e s p e c t t o t h e s u b - s o l a r p o i n t as a f u n c t i o n o f solar a c t i v i t y . Acknowledgements--The author acknowledges helpful
_
.
I
soo
1
~ooo Tee/°K)
I
~2oo
14oo
Fig. 4. Values of e computed from e q u a t i o n (11) using the observed values of a~ (normalized to local solar time) for Halley B a y (@) a n d Argentine Islands ( © ).
discussions with Mr. W. R. PmOOTT a n d Dr. J. W. K I l o , a n d is grateful for constructive criticisms of ~he manuscript made b y Dr. H. RISHBETH. The author also t h a n k s Dr. J. W. KINO a n d Mr. D. EccL]~s for making available their computer program. Use of the facilities of the Appleton Laboratory during the course of this work is gratefullyacknowledged. The paper is published b y permission of the Director of the British Antarctic
Survey.
REFERENCES
DAr.G~R~O A. DUDENEY J. 1:~. J'ACOtIIA L . G . JAcc~IA L . G . ~.INO J. W., ECCLES D. and KOHL H. KING J. W., KOHL H. a n d PRATT R. K o ~ , H., KrN(~ J. W. a n d Ecc~Es D. RIS:HBETH H. RIS]~BETn H. I~IS:HBETtI I~. a n d B~t~RO~ D . W . : R I S ~ B ~ H. and K E L l e y D . M . S~OBEL D. F. and McELRo~~ M. ]3.
1964 1974 1965 1971 1971 1967 1968 1967 1972 1960 1971 1970
J . atmos, terr. Phys. 26, 939. Brit. Antarct. Surv. Sci. Rept. 88. Smithson. Contr. Astrophys. 8, 215. Smithson. Spec. Rept. 332. J . atmos, terr. Phys. 33, 1067. J. atmos, terr. Phys. 29, 1529. J. atmos, terr. Phys. 30, 1733. J. atmos, terr. Phys. 29, 225. J . atmos, terr. Phys. 84, 1. J. atmos, terr. Phys. 18, 234. J. atmos, terr. Phys. 33, 539. Planet. Space Sci. 18, 1181.
~eference is also made to the following unpublished material:
DU])ENEY J'. l~.
1973
Ph.D. Thesis Univ. London.
Solar-cycle modifications oi the effects o~ thermospheric winds on the height o~ the F2-1ayer over Antarctica J . R . DUDE~-EX* British Antarctic Survey, 2 All Saints Passage, Cambridge, CB2 3LS, England
(Received 28 July 1975) Abstract--Results of analysis of the diurnal variations of hm2'2 for Argentine Islands (65°15'S, 64~16'W) and Halley Bay (75°30'S, 26°40"W) are presented. It is shown that, for summer months, the diurnal variations can be approximated by simple sinusoidal functions, the phases of which vary smoothly with solar activity. This behaviour can be explained in terms of the effects of thermospheric winds; it results partly from a change in the relative importance of 'ion drag' and Coriolis force, and partly from changes in the chemistry which controls the characteristic time required for the layer to respond to the wind. A comparison of observations and theory suggests that the local solar time at which the thermospheric pressure maximum occurs does not vary with solar activity.
1. INTRODUCTION A number of analyses (KING et al. 1967; I~NG et al. 1971; STROBEL and McELRoY, 1970) have
and November 1965. These examples suggest t h a t a reasonable approximation of the diurnal variatiou is a simple sinusoidal function of the form
suggested t h a t the observed diurnal variations of
h m F 2 -~ a o + aj cos ~(t' + a2);
hm.F2 at middle and high latitudes are a result of horizontal thermospheric winds. This hypothesis will be tested here by comparing the results of calculations involving winds with hm)F2 data derived from ionospheric measurements at two Antarctic
where ~( = 2~/24) is the mean angular velocity of the Earth, and t' is local zone time in hours.
observatories through a solar cycle, 2. ANALYSIS OF OBSERVATIONAL D A T A
(1)
Other similar plots, not shown, for different epochs confirm this suggestion. I t is possible (DunE~rEX, 1973) to fit this type of function to the data using the principle of least squares, which allows considerable simplification in analysis since each set of data is described in terms of the coefficients a 0 (mean value), al, (amplitude) and a s (phase). The smooth curves in Fig. 1 are fitted in this manner.
DUDEN-EY (1974) has described a m e t h o d by which h m F 2 can be determined to better than 5% using only the routinely scaled ionospheric charaeteristics ] o F 2 , JoE and M ( 3 0 0 0 ) F 2 . This m e t h o d
This paper is limited to a discussion of the phase parameter a s and its variation with solar activity. Figure 2 shows values of this parameter, plotted as funetions of the mean exospherie temperature T ~ , where the latter is a diurnal average value deduced
has been employed to obtain representative monthly median values of h m F 2 , at each hour for the four summer months (November, December, J a n u a r y and February), using data selected from the period 1957-1969 from Argentine Islands (65°15'S; 64°16'W) and Halley B a y (75°30'S; 26°40'W). I t can be shown t h a t perturbations due to magnetic activity appear negligible in such data
from the JACCHXA(1965) J65 model using m o n t h l y mean values of solar 10.7 cm flux. The r.m.s. uncertainty in the mean phase is shown by the
provided the average m o n t h l y value of the magnetic index 'a' is less t h a n or equal to 13. Only data which obey this limit have been included here and hence the results are representative of magnetically quiet conditions. Figure 1 shows samples of the results obtained using Argentine Islands data for N o v e m b e r 1958
error bars. I t is apparent from this figure that, at both locations, the phase retards smoothly as T ~ increases. Also, the rate at which a s changes with T ~ is approximately the same a t both locations. Notice however, t h a t there is a uniform displacemerit of about 1 h between the Halley Bay and Argentine Islands groups, with the former being t h e more retarded. A small sample of values are included in the figure which were deduced from
* At the S.R.C. Appleton Laboratory during the course of this work.
analysis of data for individual magnetically quiet days from Argentine Islands during N o v e m b e r
291
292
J . R . DUDE~TEY 500
~
I
L
400
~
~ • 3oo~
1 .
200
oo
.
" ,2
.
.
24
" I ~2
z4 LZT (hours) Fig. 1. Monthly median diurnal variations of h m F 2 for Argentine Islands for November 1958 and November 1965 ( l ) . Also shown are the best fit curves of the form of equation (1). 1969. These give an indication of the day-to-day variability on quiet days, which is shown to be significantly smaller t h a n the solar-cycle trend understudy. 3. THEORY OF WIND-PRODUCED VARIATIONS OF hmF2
in ~ from the value given b y equation (2), b u t this perturbation is only a few degrees and is here neglected. The Coriolis parameter is constant for a particular latitude, whilst ~ varies diurnally, seasonally and with solar activity as/V and Too vary. I n the limit ~f(~-~/2, whereas if v > ~ f ~ - ~ 0 . Thus, changes in v can alter ~ within the limits (--~/2) ~ ~ 0, resulting, for example, in a solar cycle change in the azimuth of the wind, relative to that of the driving force. I t follows from a resolution of vectors (RISHBETH and KELLEY, 1971) that a horizontal neutral wind will produce a vertical ion motion of velocity V, which, for the southern hemisphere, is given b y V = U cos I sin I cos (0 -- D -}- (~).
I n this equation, 0 is the instantaneous azimuth of the driving force (measured positive east of north, thus negative in the southern hemisphere), U is the magnitude of the wind, a n d D is the declination of the geomagnetic field (also positive east of north). RISHBET]t and B ~ R O ~ (1960) demonstrated empirically t h a t a n imposed vertical drift would displace the peak of the layer from its reference height (z0) to a new level (zz), where
I n this section an analytical expression for a S will be derived using theory which incorporates the effects of thermospheric winds in a simplified form. Values of a~ computed from this expression will be compared with those observed. B y assuming a steady state a n d neglecting viscosity, RISHBETH (1972) demonstrated t h a t for a particular location the instantaneous azimuth of
(5)
(6)
z l - - z o = az V H / ~ ,
in which ze and z1 are reduced heights, 2 is the ambipolar plasma diffusion coefficient, H is the scale height of monatomie oxygen, and ~1 is an empirical constant of order unity. I f it is assumed that the layer approaches z1 exponentially with a
the wind differs from t h a t of the driving force b y a n angle given approximately by I
= arctan(f/v)
(2)
f = 2El sin ~,
(3)
i
J
where
l
(taken as negative in the southern hemisphere). The parameter f is a coefficient representing the effect of Coriolis force, whilst v is a frictional coefficient representing the 'drag' exerted b y the ions upon the wind. I t will be assumed (after DALGAZ~TO, 1964) that
++ ~, '
~f!
+
~x!~: ~x
6oo
1~5 ~ ~ I eco
I ,ooo T~f=g
--0"4 S--1 v = 4"6 × 10--17 1VTo~
(4)
where N is the ion concentration (m-S). E q u a t i o n (2) is strictly valid only if the angle of inclination (I) of the E a r t h ' s magnetic field is 90°. However ]:)UD]~rEY (1973) has shown t h a t if I :/: 90° there is a small semi-diurnal perturbation
?
)
] ,20o
,4oo
Fig. 2. Values of a 2 for Argentine Islands (O) and Halley Bay (@) plotted agains~ ~ (see text), using all available data for the months November, December, January and February during the period 1957-1969. A sample of values for magnetically quiet days from Argentine Islands during November 1969 are also given (X).
Effects of thermospheric winds on the height of the F2-1ayer over Antarctica characteristic t i m e /-/-z]2 (I=~ISHBETI:r, 1967), t h e n
293
Table 1. Parameters computed using sample data from Argentine Islands and the J65 model
dz dt
°:s~
(zl
z),
(7)
where % is a f u r t h e r empirical c o n s t a n t of order unity. C o m b i n i n g (5), (6) a n d (7) gives the differential e q u a t i o n of t h e f o r m
Parameter
Nov 1958
FlU~ (t622w~~ H~q)
B 2i- C c o s
(0
D -~ ~).
(8)
dt
207
153
77
1090
755
1'213
0"928
0'469
9-9
7.0
5-L
--0"5l
-0"71
--l'54
a v e c t o r of c o n s t a n t a m p l i t u d e r o t a t i n g a t c o n s t a n t speed. T h e a z i m u t h of this v e c t o r is t h e n 0 = - f 2 ( t + e), w h e r e t is t h e local solar t i m e in hours a n d E represents t h e lag of t h e diurnal pressure bulge w i t h respect to t h e subsolar p o i n t ; (b) t h a t v (equation 2) can be r e p r e s e n t e d b y a diurnal m e a n v a l u e (~). I n general ul a n d ~s v a r y diurnally, b u t in s u m m e r at high latitudes, d a y - t i m e conditions prevail for all hours and it is t h u s acceptable to use t h e d a y t i m e values ~z = 0.9 a n d us = 0.5 q u o t e d b y I~ISHBETH (1967). I t t h e n follows t h a t z = z0 q- A cos (~t 4- f2e 4- D -- ($ -- ~w) (9) where ~w = a r c t a n (~2HZ/~s~),
(10)
a n d A is a n a n a l y t i c a l constant. E q u a t i o u (9) is of t h e s a m e f o r m as e q u a t i o n (1) a n d so b y c o m p a r i s o n a 2 = E + (D -- ~ -- 8w)/~2 + (t - - t ' ) .
(11)
I n this e q u a t i o n , (t -- t') is t h e difference b e t w e e n local solar a n d local zone time, (D -- 5) represents t h e t i m e lag b e t w e e n t h e driving force a n d t h e r e s u l t a n t drift v e l o c i t y i m p o s e d on t h e lv2-1ayer ionization, a n d 8w gives t h e d e l a y in the response o f t h e l a y e r t o this i m p o s e d drift. The p a r a m e t e r a 2 varies w i t h position as a result of t h e declination t e r m a n d because (~ depends on f (equation 3) w h i c h is a f u n c t i o n of latitude. For a p a r t i c u l a r location, a 2 will v a r y w i t h solar a c t i v i t y because b o t h 6 a n d ~w are c o m p l e x functions of t h e latter. The
~--(1°-43a~1) 6
This e q u a t i o n can b e solved a n a l y t i c a l l y for certain simplified conditions. These are: (a) t h a t t h e driving force can be r e p r e s e n t e d b y
table shows
the diurnal
average
values
of
(~ a n d dw c o m p u t e d for t h e case of A r g e n t i n e Islands for t h r e e m o n t h s spaced t h r o u g h t h e solar cycle. These values were o b t a i n e d f r o m e q u a t i o n s (2), (4) a n d (10) using t h e J 6 5 m o d e l w i t h a n expression for 2 g i v e n b y Ko/~r, et al. {1968). The values of -hz r e q u i r e d in e q u a t i o n (4) to e v a l u a t e were o b t a i n e d b y a v e r a g i n g t h e m e d i a n h o u r l y
(hours)
Nov 1965
13z7
~(°K) (10t2 m-3 )
dz + Az
Nov 1969
Gw(ho.rs)
147
L30
i
,00
i
values of N m z V 2 o b s e r v e d at A r g e n t i n e Islands for t h e m o n t h s in question. T h e d a t a indicate t h a t b o t h ~ a n d 8w change in t h e same sense t h r o u g h t h e solar cycle, p r o d u c i n g a t o t a l change in a s of a p p r o x i m a t e l y 1"5 h for a t e m p e r a t u r e v a r i a t i o n of 770 ° to 1330°K. Of this, a b o u t 1 h results f r o m a change in (5 a n d t h e r e m a i n d e r f r o m ~w. These results are illustrated graphically in Fig. 3, in w h i c h e is t a k e n as --3.0 h (in r o u g h a g r e e m e n t w i t h J a c c h i a ' s model) a n d D is t a k e n as 16-6°E. Also shown are t h e results o b t a i n e d using t h e J a c c h i a (1971) model, a n d those o b t a i n e d using t h e m o r e c o m p l e t e theoretical t e c h n i q u e s d e v e l o p e d b y Ko]~_L et al. (1968). The l a t t e r i n v o l v e s a simultaneous t i m e - v a r y i n g solution of t h e e q u a t i o n of m o t i o n of t h e n e u t r a l air a n d t h e c o n t i n u i t y e q u a t i o n . I t utilizes t h e J 6 5 m o d e l a t m o s p h e r e , b u t w i t h t h e c o n c e n t r a t i o n s of molecular n i t r o g e n r e d u c e d b y 40~o. All t h r e e sets of results are p l o t t e d w i t h respect to a t e m p e r a t u r e scale d e r i v e d f r o m J65. The a g r e e m e n t b e t w e e n o b s e r v a t i o n a n d t h e o r y is good (compare Fig. 2 a n d Fig. 3), b u t c a u t i o n should be used in drawing detailed conclusions because of t h e u n c e r t a i n t i e s in t h e a t m o s p h e r i c models a n d because o f t h e v a r i o u s simplifying assumptions used in t h e theory. ~i 4~i 3~ ~ ~ 2I
'
T
, ----~
~ ~
/
~ ~ f / ~ /
?,
©
I
~,~ /
01I ~oo
o
, see
oJ ~ 10oo ~ IoK)~oo
L ~4oo
i ~
Fig. 3. The variation of as as a function of ~¢o as deduced from theory. The solid curve is deduced from equation (11) using J65; the dashed curve using J71; the circles from KoH~ et al. (1968) theory. All calculations are for Argentine Islands.
294
J. 1~. I)UDElqEY
E q u a t i o n (11) m a y b e r e a r r a n g e d so t h a t t h e o b s e r v e d v a l u e s o f a S ( e x p r e s s e d n o w i n t e r m s of local solar t i m e ) , t o g e t h e r w i t h t h e c o r r e s p o n d i n g t h e o r e t i c a l v a l u e s o f ~ a n d ~w give e s t i m a t e s o f ~. The results of such an analysis are presented in Fig. 4 for t h e case o f t h e J 6 5 m o d e l . T h e m e a n v a l u e for t h e A r g e n t i n e I s l a n d s d a t a i s - - 2 . 2 5 w i t h a s t a n d a r d d e v i a t i o n o f 0.3 (21 v a l u e s ) , w h i l s t t h e c o r r e s p o n d i n g v a l u e s for H a l l e y B a y a r o - - 2 - 7 5 a n d 0.3 (9 values). B o t h t h e s e v a l u e s a r e i n r e a s o n a b l e agreement with the position of the pressure bulge g i v e n b y J a c c h i a ' s models. T h e y a r e h o w e v e r n o t e n t i r e l y c o n s i s t e n t w i t h e a c h o t h e r , t h o u g h consist e n c y is p r o b a b l y n o t t o b e e x p e c t e d i n v i e w o f t h e very simple model used and the small data samples a v a i l a b l e . I t is n e v e r t h e l e s s p o s s i b l e t o i n f e r t h a t t h e d i f f e r e n t b e h a v i o u r o b s e r v e d a t t h e t w o sites, a n d i l l u s t r a t e d b y Fig. 2, is m a i n l y a r e s u l t o f t h e v a r i a t i o n i n m a g n e t i c d e c l i n a t i o n (see e q u a t i o n 11), I
,
=
"~d~ oo
-
• oo
1
• o8~ o o - - o°
o •o
O
~V
w i t h a s m a l l c o n t r i b u t i o n d u e to t h e c h a n g e o f Coriolis force w i t h l a t i t u d e . Also, f r o m Fig. 4, i t is apparent that the variation in the mean position of t h e p r e s s u r e b u l g e as a f u n c t i o n o f s o l a r a c t i v i t y c a n o n l y b e slight, a n d is p r o b a b l y less t h a n 10 r a i n t h r o u g h t h e solar cycle. T h e noise i n t h e s a m p l e s i n Fig. 4 a p p e a r s to r e s u l t p a r t l y f r o m a s y s t e m a t i c variation with month, the highest values occurring i n J a n u a r y a n d t h e l o w e s t i n :November. M o r e a n a l y s i s is r e q u i r e d t o c o n f i r m this. 4. CONCLUSIONS I t h a s b e e n d e m o n s t r a t e d t h a t for t w o A n t a r c t i c o b s e r v a t o r i e s t h e d i u r n a l v a r i a t i o n s of h m F 2 i n s u m m e r are a p p r o x i m a t e l y s i n u s o i d a l . T h e p h a s e s of these variations have been shown to retard s m o o t h l y w i t h i n c r e a s i n g solar a c t i v i t y i n a m a n n e r consistent with that expected from the interaction between thermospheric winds and the ionization p r e s e n t i n t h e _F-layer, I t is c o n c l u d e d f r o m comparing observation with theory that the position of t h e d i u r n a l p r e s s u r e b u l g e does n o t v a r y w i t h r e s p e c t t o t h e s u b - s o l a r p o i n t as a f u n c t i o n o f solar a c t i v i t y . Acknowledgements--The author acknowledges helpful
_
.
I
soo
1
~ooo Tee/°K)
I
~2oo
14oo
Fig. 4. Values of e computed from e q u a t i o n (11) using the observed values of a~ (normalized to local solar time) for Halley B a y (@) a n d Argentine Islands ( © ).
discussions with Mr. W. R. PmOOTT a n d Dr. J. W. K I l o , a n d is grateful for constructive criticisms of ~he manuscript made b y Dr. H. RISHBETH. The author also t h a n k s Dr. J. W. KINO a n d Mr. D. EccL]~s for making available their computer program. Use of the facilities of the Appleton Laboratory during the course of this work is gratefullyacknowledged. The paper is published b y permission of the Director of the British Antarctic
Survey.
REFERENCES
DAr.G~R~O A. DUDENEY J. 1:~. J'ACOtIIA L . G . JAcc~IA L . G . ~.INO J. W., ECCLES D. and KOHL H. KING J. W., KOHL H. a n d PRATT R. K o ~ , H., KrN(~ J. W. a n d Ecc~Es D. RIS:HBETH H. RIS]~BETn H. I~IS:HBETtI I~. a n d B~t~RO~ D . W . : R I S ~ B ~ H. and K E L l e y D . M . S~OBEL D. F. and McELRo~~ M. ]3.
1964 1974 1965 1971 1971 1967 1968 1967 1972 1960 1971 1970
J . atmos, terr. Phys. 26, 939. Brit. Antarct. Surv. Sci. Rept. 88. Smithson. Contr. Astrophys. 8, 215. Smithson. Spec. Rept. 332. J . atmos, terr. Phys. 33, 1067. J. atmos, terr. Phys. 29, 1529. J. atmos, terr. Phys. 30, 1733. J. atmos, terr. Phys. 29, 225. J . atmos, terr. Phys. 84, 1. J. atmos, terr. Phys. 18, 234. J. atmos, terr. Phys. 33, 539. Planet. Space Sci. 18, 1181.
~eference is also made to the following unpublished material:
DU])ENEY J'. l~.
1973
Ph.D. Thesis Univ. London.