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A new analysis of eclipse effects in the equatorial F-region
Jonmal of Atmospheric an13Terrestrial Physics, 19SS, Vol. 31, pp. 1333 to 1344. Pergsmon Press. Prl&ad in Northern Ireland
A new analysis of eclipse effects in the equatorial Fagion N. J. SKINNER Department of Physics, Ahmadu Be110University, Z&a, Nigeria, Africa
(Received 23 October 1908; ila rev&&form 21 April 1989) Ah&r&-P-region electron density measurements obtained during the solar eclipse of 2 October, 1959 at Ibadan and ~a~dn~i are re-examined. A method haa been developed to analyse the datain which the transport term in the electron density continuity equation is retained, and its effect is found to be important. The variations of &Mron density at the two stations can be explained in terms of essentially the same ionosphericmodel in which there is downward vertical drift with velocities in the range 5-60 msec-l at the time of the eclipse, together with a vertical velocity gradient whioh decreasesupwards. ‘.l!bevalues of the photoionization rate q and the linear loss coefficient/I?obtained from this analysis are consistent with those of other workers, and the scale heights of the atmospheric constituents predicted from the height variations of q and /I are shown to imply reasonable exosphexictemperatures.
1. bE&ODOCTION
IN AN earlier paper (SEIIWER, 1967) an attempt wss made to determine the photochemical rates in the equ~to~~l P-region from an sn@sis of eclipse observations at ~~~d~~~ in northern Nigeria using the method described by VAX ZANDT, NOBTOX and STONEHOCICER(1960). 51 this method it was aasnmed that changes in electron density during a solar eclipse could be accounted for entirely in terms of changes in the rate of electron production caused by progressive obscuration of the solar disc, together with either a quadratic or linear loss process depending on the altitude under consideration. The effect of vertical transport of ionization was not oonsidered. Values of the electron production rate r~and the linear loss coefficient p obtained by this method were found to vary with height h as @(fi) = 2.46 . IO-4
&A) = 330 exp
exp
-(h [
i
-(W - 300) 84
1
3
set-1
- 300) cm_s sea-f 109
where fi is in km. These expressions predict reascmable values of 4 and /? at 300 km, but the logarithmic decrements 109 and 84 km sre too large if they are to be interpreted as the scale heights of the ionizable constituent 0, and the molecular constituent which takes part in the atom-ion exchange process N, (or O,), respectively. These scale heights would imply exospheric temperatures of 1850 and 2500% (or 2850°K) compared to an expected value of about 1400°K based on the solar 10 cm flux index ;tt the time of the eclipse. XXIan at~mpt to resolve this d&&y a new approach to the problem has been made in that the vertical transport term has been retained in the electron density 3
1333
1334
?rr’.tr. SKINSER
continuity equation. An estimate has been made at five fixed heights of the electron density that would have been expected in the absence of a solar eclipse, and an analysis is made of the departures from these predicted values using the actual eclipse data. This clearly involves some subjective judgement in the estimation of the control data but it is felt that this is probably a more sound procedure than the original method in which vertical transport is neglected completely. For the solar eclipse of 2 October 1959, data are now analysed for two stations, Tbadan and Maiduguri, whose positions and eclipse circumstances are given in Table 1. Figures l(a) and (b) show (thick lines) the variations with time of the electron Table
I
At 300 km ahtutlc Max. Geog. Locatloll
Ibadan Maiduguri
Co-ords.
(NJ
7’26.5’, 11’50.6’,
@I
Magnetic dip
3’54.5 13’04.6’
-6’ -t4O
First contact (G.M.T.) 11.25 11.43
Time of’ max. Last contact, obscuration (G.M.T.) (G.M.T.) (%) _____________~. 13.04 13.19
14.31 14.41
~~.
73.6 100
density IV at fixed heights 260, 300, 340, 380 and 420 km, for the t’wo stations on the eclipse day. The thinner lines indicate the ‘non-eclipse’ values assumed for the purposes of this analysis, based on the values of the electron density before and after the eclipse. It will be shown that a single ionospheric model can account satisfactorily for the electron density variations at both stations in the height range 260-420 km. 2. METHOD UF ANALYSIS (a) 5% original method In the method used by VAN ZANDT et aE. (1960) and by SKINNER (1967) it was assumed that the continuity equation at large heights during the solar eclipse is given by
where E is the unobscured fraction of the solar disc at any instant. (At lower heights it was assumed that cLV replaces @iV, where CL is a recombination coefficient. A fuller discussion of the relevant photochemical reactions is given in the earlier papers). Plots of (1 /N)( W/at) vs. (E/N) for various fixed heights were found to bereasonably linear so that 4 and fl could be determined from the slopes and intercepts. (Similarly at lower heights q and tc could be obtained from suitable plots). (b) The new method The vertical transport term is now retained so tha,t the basic continuity in the absence of an eclipse becomes &!V -= at
q -
&V -
div (NV)
equation
(2)
A new analysis of eclipse effects in the equatorial ET-region
24
Donsltv
-3
CRI
8
4
(4 0
06
08
IO
12
14
16
18
-I
G.M.T.
20
Electron Oenslty
I2 cm-3 8
4
0
(b)
06
08
IO
I2
14
16
18
G.M.T.
Fig. 1. (a) The variation with time of the electron density at fixed heights, 260, 300,340, 380 and 420 km for the eclipse day at Maiduguri. (b) The variation with time of the electron density at 260, 300, 340 and 380 km for the eclipse day at Ibadan. In eaoh ease the thin lines represent the predicted variations in the absence of an eclipse.
1336
1336
S.
J. SIUNNEIS
where v is the transport velocity. Assuming that only the vertical velocity Q (measured positive upwards) contributes appreciably to the transport term, equation (2) b ecomes
ai
an;zq-pn;-~
(N(f))
at
$I _ q _
01
N
tlil +
During a solar eclipse the corresponding
aLv, - = at
.!!;j _ !$i. o
equation will be
qE -- N,
where 8, represents the measured values of electron during the eclipse. Subtracting (4) from (3) for the same fixed height
For an appreciable
(4) density at a fixed height h
part of the eclipse, the term
is small compared with the other terms in the equation, When this condition is satisfied a plot of
and can be neglected.
should be linear, and q and /I’ can be obtained from the slope and intercept respectively. Furthermore, tllc values of (I and /I’ so obtained for various levels can bc substituted back into equation (4) to obtain o( &V,/ah). Since &YE/ah can be measured at these fixed heights, w can then be obtained as a function of height. This in turn yields &o/ah at various levels, and /? can be calculat,cd from the measured values of /3’. Thus, in principle, all the quantities in (4) can bc determined, including both the vertical drift velocity and the velociby gradient, for any height in the F-region for which electron density measurements are available. For the range of heights considered, 260-420km, the variatioll of’ ‘1 with solar zenith angle during the eclipse period is extremely small, since these levels are all two or more scale heights above the height of maximum electron production, and uo correction for this effect has been made. It should be noted that there are several assumptions inherent in the above* analysis.
A new analysis of eclipse effects in the equatorial F-region
1337
(1) It has been assumed that during the relatively short period of the eclipse there are no significant changes in the neutral atmosphere (which would in turn affect p and ,!l at fixed heights) caused either by the eclipse or by normal daily variations. NORTON and VAN ZANDT (1964) have shown that such changes in the neutral atmosphere due to thermal expansion and contraction can cause significant changes in electron density on a diurnal time scale. (2) As stated earlier, it has also been assumed that horizontal drift does not contribute to the transport term in equation (2). This is probably justified at lower heights but at greater heights, North-South horizontal diffusion along the geomagnetic field lines may start to become important. (3) Finally, it has been assumed that the vertical drift velocity cois unchanged by the eclipse. This is reasonable if this drift has an electrodynamic origin since the magnitudes of the controlling electrostatic and magnetic fields should not change appreciably during the eclipse.
3. EXPERIMENTAL RESULTS Some typical examples of plots of (8 - B,)/AN vs. (1 - @/AN are shown in Figs. 2(a) and (b) for heights of 260 and 300 km for the two stations. Extremely good linear fit,s are obtained for the middle portion of the eclipse period, Near the beginning and end of the eclipse, when the values of AN and (a - i+$J are small and very sensitive to small errors in estimating the non-eclipse variation, the fit is not always so good. However, in general, much beffer linear fits are obtained by this method than in the original method. An important conclusion from this work is that a linear loss process is now found to occur at, all levels down to 260 km whereas the earlier analysis indicated a transition from a linear to a quadratic loss process at an altitude of about 300 km. The values of the production rate p determined from fhe slopes of the above plots are shown in Fig. 3 for Maiduguri (crosses) and Ibadan (circles). They can be represented as functions of height by the following equations: I#) = 490 exp Q(h) = 555 exp
1 1
-(F, - 300) cm-3 se& 77 -(h
- 300) cm-3 set-l 100
Maiduguri Ibadan.
Similarly the intercepts /?’ obtained from plots of the type illustrated in Fig. 2 have been plotted as a function of height in Figs. 4 and 5 for Maiduguri and Ibadan respectively. The vertical bars in Figs. 3, 4 and 5 give an estimate of the range of each value of p and @’ based on the closeness of fit,of fhe straight line used to determine each value. Using these values of p and fl’ at each fixed height the corresponding values of w( aN,/ ak) have been calculated using equation (4) for a series of times spaced about the centre of the eclipse effect. These are found to be reasonably constant with time and the mean values for each height are plotted in Fig. 6. Average values of (aN,/ah) for the same time interval for each height have been measured from the N-h profiles and the calculated values of o are shown in Fig. 7 for the two stations.
1338
I-E
cm 3
AN
-4 XI0
I-E AN
Fig.
2. Examplus
of plots
cm3
of the function
(.% .- .&)/M
vs.
(1 -
((t) h = 360 km at Ibadan, and (h) h = 300 km at Maidugwi.
&J/AS f’or
The drift velocity is negative, indicating downward drift, and decreases from about msec-l at 260 km to about 5-10 msec-l at 420 km. Values of &0/S obtained from the gradients of the curve8 in :Fig. 7 have been used to calculate the loss coeiiicient /3 f?om the measured values of /?’ at each height, and these are shown as the lower curves in Figs. 4 and 5. The calculated values of o(aN,/S) and CO depend critically on the assumed values of q and /I’ at each height, and these are subject to some uncertainty, as shown by the vertical range bars in Figs. 3, 4 and 5. 40-50
A MW analysis
t
of eclipse effects in the equatorial F-region I
I
I
,
IOOO-
IO0 -
260
300
340 HEtGHT,
380
420
km
Fig. 3. The variation with height of the photoionization rates p calculated from the slopes of plots similar to those shown in Fig. 2 for Maiduguri (crosses) and Ibadan (ciroles). The straight lines represent the functions
104s’ and
IO+
WEIGHT,
km
Fig. 4. The variation with height of the intercept 8’ and the loss cosEioient /? caloulated from the Maiduguri data.
1339
7
104Fj’ and
4
m48’ 2
tbadan
The values of CO( &YE/&) and w shown in Figs. 6 mtl 5 must therefore bc regarded as being less precisely known than the corresponding values of q and ,3’ on which t.hcy are based. However, the consistency of t,hc values and of their height. variations at the tu,o widely separated observing stations supports t.he view that these quantities are being determined with reasonable accuracy. Table 2 summarises values of OJ,&oi% and #I for the two st,ations at, t.he reference heights. Q, p’, o(as,~ah),
1341
A new analysis of eclipse c&k&s in the equatorial P-region
,
I
,
1
260
300
340
3eO
HEIGHT,
Fig. 7,
I
420
km
The vertical driit velocity o (measured positive upwards) as a function of height, for Meiduguri (orosses) and Ibadan (circles). Table 2
Station
Maiduguri
Ibadan
The
260 300 340 380 420 260 300 340 380
860 470 275 197 87 780 540 405 235
13 6.0 3.0 1.66 0.75 12 6.4 3.9 2.0
-194 -166 -120 -65 -25.5 -243 -175 -137 -85
-40 -20 -12.5 -7.8 -4.2 -52.5 -31 -22 - 14.7
6.0 3.0 l-5 1.0 0.5 6.8 3.45 2.0 1.45
7.0 3-o 1.5 0.65 0.25 5.2 2.95 1.9 0.55
height variations of ,f?can be represented by p(h) = 3-l X
and
10V4 exp
-@
5.
300)
b(Tb)= 2.85 x 10-Q exp
for the two stations. 4. DXWUSSIONOF (a)
4.9 8.2 9.6 8.3 6.1 4-64 5.62 6.24 5.8
1 1
sec_’
Set-1
Maiduguri Ibadan
RESULTS
The photochemical rates
has summarised evidence which suggests that the loss coefficient &ot is temperature dependent. Using the procedure outlined by JACGRIA (1965), the exospheric ~mperature at the time of the eclipse has been calculated from the solar 10 cm flux data to be 137CPK and the corresponding measured value of j&, of 3 x 1O-4se& is consistent with this earlier evidence. It should be pointed out that values of p obtained by other workers will be inaccurate SKINNER (1967)
B at 3ookm,
S. ,J. SKINNER
1342
if a vertical drift gradient existed at the time measurements were taken. In t11cse cases it is p that is measured (=/? -+ a~/&) and not ,$. If the loss process consists of atom-ion exchange with the molecular constituent N, (or 0,) followed by dissociative recombination, the denominator of the exponential term in the expression for /3(h) should represent the scale height of the molecular constituent. The value of 50 km obtained from the Maiduguri results corresponds to an exospheric temperature of 1500’K if the molecular constituent is N, and 1720°K if it is 0,. The corresponding temperatures based on t,he Ibadan data are 1770’K and 2030°K respectively. The electron production rates a,t both stations are found to be about 820 cm-3 set--i at a height of 260 km. However, the decrease in q(h) with increasing altitude is slower at Ibadan where the scale height H, is 100 km than at Maiduguri where lY, is 77 km. Interpreting H, as the scale height of the ionisable constituent, atomic oxygen, temperatures of 1330°K and 1720°K are obtained for Maiduguri and Ibadan respectively. Thus, to summarize, the exospheric temperatures calculated from q(h) and /3(h) at Maiduguri are 1330°K and 1500°K and are in excellent agreement with an expected value of about 1370°K. The values obtained for Ibadan, 1770°K and 1720°K are rather high, and the discrepancy may be due to the greater uncertainty in estimating the non-eclipse electron densities at Ibadan where the variations in N just before the commencement of the eclipse were rather complex at the larger heights. In Table 3 the value of 4 at 260 km obtained from this analysis is compared with The values for values at the same height obtained from other eclipse investigations Canton Is. and Danger Is. were quoted by NORTON and VAN ZANDT (1965), and the Tablc 3 qZ60
Observing station
(cm-3 set-l)
5’
L?
Danger Is. Maiduguri/Ibadan Tamanrasset C’aut0u Is.
1080 820 320 200
219 149 113 100
221 182 94 !lX
value for Tamanrasset for the eclipse of 20 May, 1966 has been calculated by the author using data from BOUSQUET et al. (1967). In each case the solar 10 cm flux index for the eclipse day, S, and the mean flux index for the 27-day period preceding the eclipse, 8, are given and it is seen that there is a consistent trend such that y increases with increasing solar activity. Until reliable figures are available for the variation of the ionizing flux and of the number density of atomic oxygen during the solar cycle it is difficult to take this comparison any further. HINTEREOGERet al. (1965) have calculated photoionization rates using rocket data on Nuxes of solar XUV radiation at sunspot minimum and their graphs indicate a value of qaso of about 400 cm-3 set-l with maximum photoionization rates of about 6000 cm-3 set-l at 140 km. Other workers, ALLEN (1965), NORTCN et al. (1963) from similar investigations, have quoted rather smaller values of 3700 and 4400 cm-~-3see-l at 150 km for a mean sunspot number of about 55. dllowing for the height difference the values of qztio quoted in Table 3 thus seem reasonable in the light of present knowledge.
A new analysis of eolipse effeots in the equatorial F-region (b) The vertical
drift
1343
velocity
Many processes have been suggested whereby vertical transport of ionization could take place in the F-region, contributing to the div (No) term in the continuity equation. These include ambipolar plasma diffuaion under the influence of gravity, electromagnetic drifta due to electric fields originating by ‘dynamo’ action in the lower ionosphere, thermal expansion and contraction of the atmosphere and plasma, exchange of plasma between the ionosphere and the outer atmosphere (the protonosphere) and by the action of horizontal winds in the neutral atmosphere driving the plasma up or down geomagnetic field lines. An excellent summary of these is given by RISHBETH(1968). However, very little quantitative work has been done and there are virtually no measurements of vertical drift velocities and velocity gradients during the daytime with which to compare the present results. It seems surprising at first sight that the present work points to a downward drift velocity during the early afternoon at equatorial stations. The wellknown equatorial geomagnetic anomaly, whereby there exists a trough in electron density centred on the magnetic equator with crests X-20’ north and south, has been explained (e.g. by MARTYN,1955) by assuming that plasma is lifted upwards at the equator by electrodynamic action and then diffuses north and south along the geomagnetic field lines. LYONand THOMAS(1963) have shown that near sunspot maximum the anomaly is moat pronounced in the late evening hours and poesibly connected with the sharp rise near the equator in the height of the F-layer at about 18.00 hr. It thus seems possible that upward vertical drift affecting the whole of the F-region is most effective later in the day than had been earlier supposed. The appearance of the geomagnetic anomaly in the late morning could be produced by upward drift in the topside F-region. The downward drift velocities reported in this paper are decreasing upwards and it can be seen that extrapolation of the curves in Fig. 7 could lead to upward drifts above the height of maximum ionization. Downward vertical drift in the period 11-14 hr is not inconsistent with the normal diurnal variation of the maximum electron density iV,F2 in the F-region which frequently shows a pronounced minimum at this time of day. A shallow midday minimum in iV,F2 can be explained in terms of thermal expansion due to diurnal temperature changes in the neutral atmosphere (e.g. NORTONand VAN ZANDT, 1964), but by itself this explanation is probably inadequate to account for the magnitude of the observed effect. It seems probable that both processes, downward vertical drift and thermal expansion, contribute to the observed midday minimum. 5. CoNCLusIoNs Although with so many variables this cannot claim to be a unique interpretation of the data, the eclipse variations in the F-region at two equatorial stationa for the same eclipse are consistent with the following conclusions. (a) The continuity equation at a fixed height during the eclipse is -ah
at
= pE - /?Nx - div (N~o).
1344
N. ST. SKINNER
(6) in the height range 260-420 q(h) = 490 oxp
i
km,
--th --y--
P(h) = 3.1 X 1Wexp
3W
cm.” se(3 _I 1
--(k ^ 300) ---
set .-I
~~aidugur~ Maiduguri
I The col~esponding scate heights from Ibadan data are 100 and 59 km respectiveIy. (c) The scale heights at ~aidugu~ imply exospheric temperature of 133O’K and 1500°K compared to an expected value of l370”K deduced from the 10 cm solar flux. The temperatures based on Ibadan data are rather higher. (d) The values of qzaoand /?,, are consistent with measurement of other workers, and with present ideas of ionizing flux intensity. (e) A &YE loss process is obeyed throughout the height range considered. (f) The vertical drift velocity co is downward and takes values in the range 40 msec-1 at 260 km decreasing to 4 msec-l at 420 km at Maiduguri. The drifts at Ibadan are similar, decreasing from 52 msec-l at 260 km to 15 msec-L at 380 km. (g) B vertical velocity gradient &u/S exists which decreases upwards from about 6 x IO-& set-1 at 260 km to 0.5 x lo-” s~c-~ at 420 km. (h) Earlier eclipse analyses measure #Yrather than a true p. It is seen that when velocity gradients exist corrections for &~/ah may be large. (i) The eclipse variations at two st&ions separated by a distance of 1150 km are consistent with essentially the same ionospheric model. REFERENCES
1965
A. S. snd THOMAS L. MARTYN t). F.
LYON
SORTON
and
H. S., UENISON
ZaNr>r
vAtiN j.
‘t‘. .E.
s.
SORTON I<. Ls. ltlld VAN XANDT ‘I‘. E;. NORTON R. W. and VAN ZANDT T. E.
1964 1965
i 968 1067 1060
A new analysis of eclipse effects in the equatorial Fagion N. J. SKINNER Department of Physics, Ahmadu Be110University, Z&a, Nigeria, Africa
(Received 23 October 1908; ila rev&&form 21 April 1989) Ah&r&-P-region electron density measurements obtained during the solar eclipse of 2 October, 1959 at Ibadan and ~a~dn~i are re-examined. A method haa been developed to analyse the datain which the transport term in the electron density continuity equation is retained, and its effect is found to be important. The variations of &Mron density at the two stations can be explained in terms of essentially the same ionosphericmodel in which there is downward vertical drift with velocities in the range 5-60 msec-l at the time of the eclipse, together with a vertical velocity gradient whioh decreasesupwards. ‘.l!bevalues of the photoionization rate q and the linear loss coefficient/I?obtained from this analysis are consistent with those of other workers, and the scale heights of the atmospheric constituents predicted from the height variations of q and /I are shown to imply reasonable exosphexictemperatures.
1. bE&ODOCTION
IN AN earlier paper (SEIIWER, 1967) an attempt wss made to determine the photochemical rates in the equ~to~~l P-region from an sn@sis of eclipse observations at ~~~d~~~ in northern Nigeria using the method described by VAX ZANDT, NOBTOX and STONEHOCICER(1960). 51 this method it was aasnmed that changes in electron density during a solar eclipse could be accounted for entirely in terms of changes in the rate of electron production caused by progressive obscuration of the solar disc, together with either a quadratic or linear loss process depending on the altitude under consideration. The effect of vertical transport of ionization was not oonsidered. Values of the electron production rate r~and the linear loss coefficient p obtained by this method were found to vary with height h as @(fi) = 2.46 . IO-4
&A) = 330 exp
exp
-(h [
i
-(W - 300) 84
1
3
set-1
- 300) cm_s sea-f 109
where fi is in km. These expressions predict reascmable values of 4 and /? at 300 km, but the logarithmic decrements 109 and 84 km sre too large if they are to be interpreted as the scale heights of the ionizable constituent 0, and the molecular constituent which takes part in the atom-ion exchange process N, (or O,), respectively. These scale heights would imply exospheric temperatures of 1850 and 2500% (or 2850°K) compared to an expected value of about 1400°K based on the solar 10 cm flux index ;tt the time of the eclipse. XXIan at~mpt to resolve this d&&y a new approach to the problem has been made in that the vertical transport term has been retained in the electron density 3
1333
1334
?rr’.tr. SKINSER
continuity equation. An estimate has been made at five fixed heights of the electron density that would have been expected in the absence of a solar eclipse, and an analysis is made of the departures from these predicted values using the actual eclipse data. This clearly involves some subjective judgement in the estimation of the control data but it is felt that this is probably a more sound procedure than the original method in which vertical transport is neglected completely. For the solar eclipse of 2 October 1959, data are now analysed for two stations, Tbadan and Maiduguri, whose positions and eclipse circumstances are given in Table 1. Figures l(a) and (b) show (thick lines) the variations with time of the electron Table
I
At 300 km ahtutlc Max. Geog. Locatloll
Ibadan Maiduguri
Co-ords.
(NJ
7’26.5’, 11’50.6’,
@I
Magnetic dip
3’54.5 13’04.6’
-6’ -t4O
First contact (G.M.T.) 11.25 11.43
Time of’ max. Last contact, obscuration (G.M.T.) (G.M.T.) (%) _____________~. 13.04 13.19
14.31 14.41
~~.
73.6 100
density IV at fixed heights 260, 300, 340, 380 and 420 km, for the t’wo stations on the eclipse day. The thinner lines indicate the ‘non-eclipse’ values assumed for the purposes of this analysis, based on the values of the electron density before and after the eclipse. It will be shown that a single ionospheric model can account satisfactorily for the electron density variations at both stations in the height range 260-420 km. 2. METHOD UF ANALYSIS (a) 5% original method In the method used by VAN ZANDT et aE. (1960) and by SKINNER (1967) it was assumed that the continuity equation at large heights during the solar eclipse is given by
where E is the unobscured fraction of the solar disc at any instant. (At lower heights it was assumed that cLV replaces @iV, where CL is a recombination coefficient. A fuller discussion of the relevant photochemical reactions is given in the earlier papers). Plots of (1 /N)( W/at) vs. (E/N) for various fixed heights were found to bereasonably linear so that 4 and fl could be determined from the slopes and intercepts. (Similarly at lower heights q and tc could be obtained from suitable plots). (b) The new method The vertical transport term is now retained so tha,t the basic continuity in the absence of an eclipse becomes &!V -= at
q -
&V -
div (NV)
equation
(2)
A new analysis of eclipse effects in the equatorial ET-region
24
Donsltv
-3
CRI
8
4
(4 0
06
08
IO
12
14
16
18
-I
G.M.T.
20
Electron Oenslty
I2 cm-3 8
4
0
(b)
06
08
IO
I2
14
16
18
G.M.T.
Fig. 1. (a) The variation with time of the electron density at fixed heights, 260, 300,340, 380 and 420 km for the eclipse day at Maiduguri. (b) The variation with time of the electron density at 260, 300, 340 and 380 km for the eclipse day at Ibadan. In eaoh ease the thin lines represent the predicted variations in the absence of an eclipse.
1336
1336
S.
J. SIUNNEIS
where v is the transport velocity. Assuming that only the vertical velocity Q (measured positive upwards) contributes appreciably to the transport term, equation (2) b ecomes
ai
an;zq-pn;-~
(N(f))
at
$I _ q _
01
N
tlil +
During a solar eclipse the corresponding
aLv, - = at
.!!;j _ !$i. o
equation will be
qE -- N,
where 8, represents the measured values of electron during the eclipse. Subtracting (4) from (3) for the same fixed height
For an appreciable
(4) density at a fixed height h
part of the eclipse, the term
is small compared with the other terms in the equation, When this condition is satisfied a plot of
and can be neglected.
should be linear, and q and /I’ can be obtained from the slope and intercept respectively. Furthermore, tllc values of (I and /I’ so obtained for various levels can bc substituted back into equation (4) to obtain o( &V,/ah). Since &YE/ah can be measured at these fixed heights, w can then be obtained as a function of height. This in turn yields &o/ah at various levels, and /? can be calculat,cd from the measured values of /3’. Thus, in principle, all the quantities in (4) can bc determined, including both the vertical drift velocity and the velociby gradient, for any height in the F-region for which electron density measurements are available. For the range of heights considered, 260-420km, the variatioll of’ ‘1 with solar zenith angle during the eclipse period is extremely small, since these levels are all two or more scale heights above the height of maximum electron production, and uo correction for this effect has been made. It should be noted that there are several assumptions inherent in the above* analysis.
A new analysis of eclipse effects in the equatorial F-region
1337
(1) It has been assumed that during the relatively short period of the eclipse there are no significant changes in the neutral atmosphere (which would in turn affect p and ,!l at fixed heights) caused either by the eclipse or by normal daily variations. NORTON and VAN ZANDT (1964) have shown that such changes in the neutral atmosphere due to thermal expansion and contraction can cause significant changes in electron density on a diurnal time scale. (2) As stated earlier, it has also been assumed that horizontal drift does not contribute to the transport term in equation (2). This is probably justified at lower heights but at greater heights, North-South horizontal diffusion along the geomagnetic field lines may start to become important. (3) Finally, it has been assumed that the vertical drift velocity cois unchanged by the eclipse. This is reasonable if this drift has an electrodynamic origin since the magnitudes of the controlling electrostatic and magnetic fields should not change appreciably during the eclipse.
3. EXPERIMENTAL RESULTS Some typical examples of plots of (8 - B,)/AN vs. (1 - @/AN are shown in Figs. 2(a) and (b) for heights of 260 and 300 km for the two stations. Extremely good linear fit,s are obtained for the middle portion of the eclipse period, Near the beginning and end of the eclipse, when the values of AN and (a - i+$J are small and very sensitive to small errors in estimating the non-eclipse variation, the fit is not always so good. However, in general, much beffer linear fits are obtained by this method than in the original method. An important conclusion from this work is that a linear loss process is now found to occur at, all levels down to 260 km whereas the earlier analysis indicated a transition from a linear to a quadratic loss process at an altitude of about 300 km. The values of the production rate p determined from fhe slopes of the above plots are shown in Fig. 3 for Maiduguri (crosses) and Ibadan (circles). They can be represented as functions of height by the following equations: I#) = 490 exp Q(h) = 555 exp
1 1
-(F, - 300) cm-3 se& 77 -(h
- 300) cm-3 set-l 100
Maiduguri Ibadan.
Similarly the intercepts /?’ obtained from plots of the type illustrated in Fig. 2 have been plotted as a function of height in Figs. 4 and 5 for Maiduguri and Ibadan respectively. The vertical bars in Figs. 3, 4 and 5 give an estimate of the range of each value of p and @’ based on the closeness of fit,of fhe straight line used to determine each value. Using these values of p and fl’ at each fixed height the corresponding values of w( aN,/ ak) have been calculated using equation (4) for a series of times spaced about the centre of the eclipse effect. These are found to be reasonably constant with time and the mean values for each height are plotted in Fig. 6. Average values of (aN,/ah) for the same time interval for each height have been measured from the N-h profiles and the calculated values of o are shown in Fig. 7 for the two stations.
1338
I-E
cm 3
AN
-4 XI0
I-E AN
Fig.
2. Examplus
of plots
cm3
of the function
(.% .- .&)/M
vs.
(1 -
((t) h = 360 km at Ibadan, and (h) h = 300 km at Maidugwi.
&J/AS f’or
The drift velocity is negative, indicating downward drift, and decreases from about msec-l at 260 km to about 5-10 msec-l at 420 km. Values of &0/S obtained from the gradients of the curve8 in :Fig. 7 have been used to calculate the loss coeiiicient /3 f?om the measured values of /?’ at each height, and these are shown as the lower curves in Figs. 4 and 5. The calculated values of o(aN,/S) and CO depend critically on the assumed values of q and /I’ at each height, and these are subject to some uncertainty, as shown by the vertical range bars in Figs. 3, 4 and 5. 40-50
A MW analysis
t
of eclipse effects in the equatorial F-region I
I
I
,
IOOO-
IO0 -
260
300
340 HEtGHT,
380
420
km
Fig. 3. The variation with height of the photoionization rates p calculated from the slopes of plots similar to those shown in Fig. 2 for Maiduguri (crosses) and Ibadan (ciroles). The straight lines represent the functions
104s’ and
IO+
WEIGHT,
km
Fig. 4. The variation with height of the intercept 8’ and the loss cosEioient /? caloulated from the Maiduguri data.
1339
7
104Fj’ and
4
m48’ 2
tbadan
The values of CO( &YE/&) and w shown in Figs. 6 mtl 5 must therefore bc regarded as being less precisely known than the corresponding values of q and ,3’ on which t.hcy are based. However, the consistency of t,hc values and of their height. variations at the tu,o widely separated observing stations supports t.he view that these quantities are being determined with reasonable accuracy. Table 2 summarises values of OJ,&oi% and #I for the two st,ations at, t.he reference heights. Q, p’, o(as,~ah),
1341
A new analysis of eclipse c&k&s in the equatorial P-region
,
I
,
1
260
300
340
3eO
HEIGHT,
Fig. 7,
I
420
km
The vertical driit velocity o (measured positive upwards) as a function of height, for Meiduguri (orosses) and Ibadan (circles). Table 2
Station
Maiduguri
Ibadan
The
260 300 340 380 420 260 300 340 380
860 470 275 197 87 780 540 405 235
13 6.0 3.0 1.66 0.75 12 6.4 3.9 2.0
-194 -166 -120 -65 -25.5 -243 -175 -137 -85
-40 -20 -12.5 -7.8 -4.2 -52.5 -31 -22 - 14.7
6.0 3.0 l-5 1.0 0.5 6.8 3.45 2.0 1.45
7.0 3-o 1.5 0.65 0.25 5.2 2.95 1.9 0.55
height variations of ,f?can be represented by p(h) = 3-l X
and
10V4 exp
-@
5.
300)
b(Tb)= 2.85 x 10-Q exp
for the two stations. 4. DXWUSSIONOF (a)
4.9 8.2 9.6 8.3 6.1 4-64 5.62 6.24 5.8
1 1
sec_’
Set-1
Maiduguri Ibadan
RESULTS
The photochemical rates
has summarised evidence which suggests that the loss coefficient &ot is temperature dependent. Using the procedure outlined by JACGRIA (1965), the exospheric ~mperature at the time of the eclipse has been calculated from the solar 10 cm flux data to be 137CPK and the corresponding measured value of j&, of 3 x 1O-4se& is consistent with this earlier evidence. It should be pointed out that values of p obtained by other workers will be inaccurate SKINNER (1967)
B at 3ookm,
S. ,J. SKINNER
1342
if a vertical drift gradient existed at the time measurements were taken. In t11cse cases it is p that is measured (=/? -+ a~/&) and not ,$. If the loss process consists of atom-ion exchange with the molecular constituent N, (or 0,) followed by dissociative recombination, the denominator of the exponential term in the expression for /3(h) should represent the scale height of the molecular constituent. The value of 50 km obtained from the Maiduguri results corresponds to an exospheric temperature of 1500’K if the molecular constituent is N, and 1720°K if it is 0,. The corresponding temperatures based on t,he Ibadan data are 1770’K and 2030°K respectively. The electron production rates a,t both stations are found to be about 820 cm-3 set--i at a height of 260 km. However, the decrease in q(h) with increasing altitude is slower at Ibadan where the scale height H, is 100 km than at Maiduguri where lY, is 77 km. Interpreting H, as the scale height of the ionisable constituent, atomic oxygen, temperatures of 1330°K and 1720°K are obtained for Maiduguri and Ibadan respectively. Thus, to summarize, the exospheric temperatures calculated from q(h) and /3(h) at Maiduguri are 1330°K and 1500°K and are in excellent agreement with an expected value of about 1370°K. The values obtained for Ibadan, 1770°K and 1720°K are rather high, and the discrepancy may be due to the greater uncertainty in estimating the non-eclipse electron densities at Ibadan where the variations in N just before the commencement of the eclipse were rather complex at the larger heights. In Table 3 the value of 4 at 260 km obtained from this analysis is compared with The values for values at the same height obtained from other eclipse investigations Canton Is. and Danger Is. were quoted by NORTON and VAN ZANDT (1965), and the Tablc 3 qZ60
Observing station
(cm-3 set-l)
5’
L?
Danger Is. Maiduguri/Ibadan Tamanrasset C’aut0u Is.
1080 820 320 200
219 149 113 100
221 182 94 !lX
value for Tamanrasset for the eclipse of 20 May, 1966 has been calculated by the author using data from BOUSQUET et al. (1967). In each case the solar 10 cm flux index for the eclipse day, S, and the mean flux index for the 27-day period preceding the eclipse, 8, are given and it is seen that there is a consistent trend such that y increases with increasing solar activity. Until reliable figures are available for the variation of the ionizing flux and of the number density of atomic oxygen during the solar cycle it is difficult to take this comparison any further. HINTEREOGERet al. (1965) have calculated photoionization rates using rocket data on Nuxes of solar XUV radiation at sunspot minimum and their graphs indicate a value of qaso of about 400 cm-3 set-l with maximum photoionization rates of about 6000 cm-3 set-l at 140 km. Other workers, ALLEN (1965), NORTCN et al. (1963) from similar investigations, have quoted rather smaller values of 3700 and 4400 cm-~-3see-l at 150 km for a mean sunspot number of about 55. dllowing for the height difference the values of qztio quoted in Table 3 thus seem reasonable in the light of present knowledge.
A new analysis of eolipse effeots in the equatorial F-region (b) The vertical
drift
1343
velocity
Many processes have been suggested whereby vertical transport of ionization could take place in the F-region, contributing to the div (No) term in the continuity equation. These include ambipolar plasma diffuaion under the influence of gravity, electromagnetic drifta due to electric fields originating by ‘dynamo’ action in the lower ionosphere, thermal expansion and contraction of the atmosphere and plasma, exchange of plasma between the ionosphere and the outer atmosphere (the protonosphere) and by the action of horizontal winds in the neutral atmosphere driving the plasma up or down geomagnetic field lines. An excellent summary of these is given by RISHBETH(1968). However, very little quantitative work has been done and there are virtually no measurements of vertical drift velocities and velocity gradients during the daytime with which to compare the present results. It seems surprising at first sight that the present work points to a downward drift velocity during the early afternoon at equatorial stations. The wellknown equatorial geomagnetic anomaly, whereby there exists a trough in electron density centred on the magnetic equator with crests X-20’ north and south, has been explained (e.g. by MARTYN,1955) by assuming that plasma is lifted upwards at the equator by electrodynamic action and then diffuses north and south along the geomagnetic field lines. LYONand THOMAS(1963) have shown that near sunspot maximum the anomaly is moat pronounced in the late evening hours and poesibly connected with the sharp rise near the equator in the height of the F-layer at about 18.00 hr. It thus seems possible that upward vertical drift affecting the whole of the F-region is most effective later in the day than had been earlier supposed. The appearance of the geomagnetic anomaly in the late morning could be produced by upward drift in the topside F-region. The downward drift velocities reported in this paper are decreasing upwards and it can be seen that extrapolation of the curves in Fig. 7 could lead to upward drifts above the height of maximum ionization. Downward vertical drift in the period 11-14 hr is not inconsistent with the normal diurnal variation of the maximum electron density iV,F2 in the F-region which frequently shows a pronounced minimum at this time of day. A shallow midday minimum in iV,F2 can be explained in terms of thermal expansion due to diurnal temperature changes in the neutral atmosphere (e.g. NORTONand VAN ZANDT, 1964), but by itself this explanation is probably inadequate to account for the magnitude of the observed effect. It seems probable that both processes, downward vertical drift and thermal expansion, contribute to the observed midday minimum. 5. CoNCLusIoNs Although with so many variables this cannot claim to be a unique interpretation of the data, the eclipse variations in the F-region at two equatorial stationa for the same eclipse are consistent with the following conclusions. (a) The continuity equation at a fixed height during the eclipse is -ah
at
= pE - /?Nx - div (N~o).
1344
N. ST. SKINNER
(6) in the height range 260-420 q(h) = 490 oxp
i
km,
--th --y--
P(h) = 3.1 X 1Wexp
3W
cm.” se(3 _I 1
--(k ^ 300) ---
set .-I
~~aidugur~ Maiduguri
I The col~esponding scate heights from Ibadan data are 100 and 59 km respectiveIy. (c) The scale heights at ~aidugu~ imply exospheric temperature of 133O’K and 1500°K compared to an expected value of l370”K deduced from the 10 cm solar flux. The temperatures based on Ibadan data are rather higher. (d) The values of qzaoand /?,, are consistent with measurement of other workers, and with present ideas of ionizing flux intensity. (e) A &YE loss process is obeyed throughout the height range considered. (f) The vertical drift velocity co is downward and takes values in the range 40 msec-1 at 260 km decreasing to 4 msec-l at 420 km at Maiduguri. The drifts at Ibadan are similar, decreasing from 52 msec-l at 260 km to 15 msec-L at 380 km. (g) B vertical velocity gradient &u/S exists which decreases upwards from about 6 x IO-& set-1 at 260 km to 0.5 x lo-” s~c-~ at 420 km. (h) Earlier eclipse analyses measure #Yrather than a true p. It is seen that when velocity gradients exist corrections for &~/ah may be large. (i) The eclipse variations at two st&ions separated by a distance of 1150 km are consistent with essentially the same ionospheric model. REFERENCES
1965
A. S. snd THOMAS L. MARTYN t). F.
LYON
SORTON
and
H. S., UENISON
ZaNr>r
vAtiN j.
‘t‘. .E.
s.
SORTON I<. Ls. ltlld VAN XANDT ‘I‘. E;. NORTON R. W. and VAN ZANDT T. E.
1964 1965
i 968 1067 1060