Sunrise effects in the equatorial F-layer

Journal qf Amospherrr

Pergamon

and Solar-Terresrrral

Phyrrcs, Vol.

PII: SOO21-9169(96)00093-l

All rlghtr

59, No I I, pp. 1287 -1297. 1997 SQ 1997 Elsevm Science Ltd reserved. Prmted ,n Great Bnta~n 13646826197 $17.00+0.00

Sunrise effects in the equatorial F-layer 0. P. Kolomiitsev,’

B. M. Reddy’ and V. A. Surotkin’

‘Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences (IZMIRAN), Troitsk, Moscow Region, 142092 Russia; ‘Radio Science Division, National Physical Laboratory, New Delhi 110012, India; ‘Kahningrad Observatory IZMIRAN, Kaliningrad 236017, Russia (Received infinaiform

10 June 1996; accepted 14 June 1996)

Abstract-In the sunrise period, under certain conditions, a cavity of a low electron density arises in the equatorial ionosphere at altitudes between the peaks of the night F-layer and the morning F-layer. The dependence of the cavity parameters on the initial conditions, solar activity, season, photochemistry, geomagnetic disturbance, diffusion, and vertical drift of the ionospheric plasma is studied theoretically. It is shown that temporal variations of the electron density, as well as of the cavity parameters, depend mainly on the initial profile parameters, ionizing solar radiation flux, ion formation rate, diffusion, and geomagnetic activity. It is concluded that reduced diffusion can be one of the major physical mechanisms which can assist the preservation, at large heights in the pre-sunrise F-layer, of the electron density at the day-time level. 0 1997 Elsevier Science Ltd

INTRODUCTION

Figure 1 shows a number of plasma frequency altitude profilesf, (h) that describe a typical situation of the sunrise effect in the equatorial ionosphere F-region which are plotted according to vertical sounding data obtained at the Indian observatory in Kodaikanal (geographic latitude cp = 10.2”N, longitude 3. = 77.5”E, geomagnetic latitude C#I= 0.54”, dip angle I = 1.41’). The typical pre-history of the effect observed is that a large value of the electron density 600 I

2001 2

I 3

, 4

, 5

1 6

, 7

1 8

/ 9

, 10

fp (MHz) Fig. 1. Profiles.&(h) deduced from the ionograms of Kodaikanal observatory, India, on 23 October 1958.

remains after the night at high altitudes. A special feature of the vertical structure of the F-layer evolution is the appearance at sunrise of a new F-layer at altitudes below the night-time height. Within the time interval 05.45507.00 LT this layer gradually transforms to the main layer, and in this case the value of the electron density and the height of the low edge of the night layer vary slightly with time. The effect described represents an example of the stratification of the electron density in the equatorial ionospheric F-region at sunrise. Although the physical nature of the effect observed is evident, it is not clear how the temporal evolution of the F-region altitude structure depends on the competing actions of photochemical and transport processes at different heights under various solar and geophysical conditions. These processes, in particular, determine the rate of the night layer spreading, the depth of the electron density cavity between the day-time and night-time F-layers, the rate of the cavity filling, etc. This article presents the method of numerical-analytical description of the equatorial ionospheric Fregion vertical structure variations which occur in the sunrise period under various solar-geophysical conditions. It also gives the solution of the continuity equation for the electron density, details of the model calculations, and the result of the calculations for various initial conditions and solar-geophysical conditions. In the present article we use the continuity equation 1287

1288

0. P. Kolomiitsev et al.

for the electron density due to Sterling et a/. (1969) as it successfully represents most of the conditions observed in the equatorial ionosphere. However, the solution used in this article is that of Cauchy (Korn and Korn, 1968), but not the solution of Sterling et al. (1969). Figure 1 shows the qualitative characteristics of the ionosphere. The inverse problem, i.e. fitting the modelled results to the observations, was not the main aim of the present work.

SOLUTION

OF CONTINUITY

EQUATION

The continuity equation for the electron density N, in spherical polar coordinates (r, 9, I) can be written in the form (Sterling et al., 1969)

a”,_

a2 -

P - pNe - N,D, - N,D,

DaD,,-DcDA)](

z

+Q)’

(1)

On the right-hand side of equation (1), D,, DA, D,,, of Dw and DA are vertical and horizontal components electromagnetic drift divergence, derivative operators of diffusion, horizontal and vertical neutral air winds, respectively. For equatorial conditions (9 - 900):

D

=

A

Equation

-’

D,=O.

(1) may be written in the form:

%_

an -

NZ, cm’, respectively; T is the optical thickness of the atmosphere; Ch(r/H, Z,) is the Chapman function (Chapman, 193 1), Z, is the zenith angle of the Sun; B=

is the effective recombination coefficient; are the rate coefficients of ion-molecular cm’ss’; 71 O++N,+NO++N;

p =

PI is J,4Wxp[-

~W~lff,+Jl,

where [0] and [NJ are the density of atomic oxygen and molecular nitrogen, in cm-j, respectively; J, is the flux of ionizing short-wave solar radiation incident on the upper ionosphere, cm-‘s-l; xjo denotes the summing of the radiation over the whole wavelength range from the ultra-violet part of the spectrum to the X-ray region (1037-I A); A(0) and A(N,) are the cross-sections of ionization and absorption for 0 and

(3) y, and y2 reactions,

Y2 O++O,+O:+O;

y, = 1.5 x lo-‘* (300/T); y* = 2.5 x lo-” (300/T) of (Hanson and Cohen, 1968); T is the temperature the neutral atmosphere, K; V,” is the velocity of the vertical plasma drift V, above the equator, m s-‘; V, is the velocity of the plasma drift with respect to the Earth in the east-west direction; Y is the geocentric distance, h is the altitude, r0 is the Earth’s radius, Y, is the value of r above the equator, km; r = h + r,; B is the co-latitude, /z is the longitude, degrees; D, = [O]-’ x 1.38 x lOI (T,/lOOO) Ii* is the ambipolar diffusion coefficient (Dalgarno, 1964) cm* s-‘; c( = (T,+ T,)/T,, where T, and T, are the electron and ion temperatures, respectively; His the scale height of the homogeneous atmosphere, H(0) is the scale height of atomic oxygen, H(N,) is the scale height of molecular nitrogen, km; R-7.29 x lo-’ is the angular velocity of the Earth’s rotation, radss’; T, is the temperature of the exosphere; ho = 120 km is the altitude where the pressure is supposed constant; the third and fourth terms describe the vertical plasma drift; the fifth term describes the horizontal plasma drift; the sixth term describes the ambipolar diffusion; the seventh term describes the vertical neutral wind (temporal dynamics of the atmosphere expansion and compression). On the left-hand side (2) aN,/aI is the Lagrange derivative with respect to time related to aN,/& by the relation (Sterling et al., 1969; Surotkin et al., 1985):

ahqat = On the right-hand side of equation (2), P and /3Ne are the rates of production and loss of electrons (in cmd3 ss’)

YINI+YPzI

( fQre +

n)alv,jan,

t is the time, in s. The solution of equation (2) is based on the onestep method of solving Cauchy’s problem (Korn and Korn, 1968). According to Korn and Korn (1968), the solution to equation (2) can be represented in the form: N,, = N,,i-F,Ai

(4)

N,, = N,, -t F,M

(5)

N,, = N, + F,An

(6)

up to the completion of the diurnal cycle (O,l,. , j) by the constant and sufficiently small time step; N, is the

1289

Equatorial F-layer at sunrise initial profile (a known function); F, is the right-hand side of (2); N,, is the unknown function. Let us rewrite (2) in the form aNJan = F and aN, = Fal,, where F = (P-M NJ/K, K = V’$re+Q; M is the expression within the square brackets in equation (2). As an example, the unknown function can be calcu/ated for some time, for example, for equation (5) 1 aNe = ‘{ Fal the integral trap:zium

is approximated

by a

ofarea:

hi-4

NC,-N,, = AI-----

2 A1. pz =-(

Let us introduce

2

Ic2 -

MzN,x

P,

lC2 +x,

MJ’G, -

--)

K,

6 = AJ.121~;then

After the regrouping of the left and right sides for the known and unknown functions N,, we have

(7) DETAILS

OF MODEL

CALCULATIONS

The set of solutions (4) (5) (6) in the form (7) permits us to reproduce the variations of the F-layer vertical structure as a whole, as well as to evaluate the contributions of some photochemical or transport processes in the ionospheric structure near the electron density peak at sunrise. As the initial profile N, (h), we can use an experimentally measured profile or the profile constructed analytically. In the present article, as the basis for the initial profile we use the profile obtained in Kodaikanal at 05.45 LT (see Fig. 1). The plasma frequency f, is related to the electron density by the relation

f, = (N,e2/na0m)“* andN,=l.24x

104fi

(8) (9)

where e and m are the electron charge and mass, respectively, a0 is the permittivity of free space, and,f, in (9) is in MHz. To obtain the profile for a selected ,f, (h), the extrapolation from the bottom to the top was carried out: at the bottom, at altitudes 12s 140 km, the electron density was put from lo2 to lo4 electrons cm-+ at the top, from the F-region peak and higher the electron density profile obeys the diffusive equilibrium distribution. The extrapolations adopted seem to be correct because they do not contradict accepted results of experimental and theoretical investigations of the equatorial ionosphere under night-

time conditions (see, for example, Bauer, 1969; Ossakow, 1981; Anderson et al., 1987). Concerning boundary conditions, in the altitude range 120
v_E’ I

as -1 v;_ =a2IBl,r,; arPI.

where S = - 120 r, ($” sin i + $” cos 1) is the electrostatic field potential (in CGS units); I/? = 0.7 - 2.95 cos(3.2 0); $” = -6.4+3.8 cos(3.2 0); 1B1, = 0.35r&/r: is the geomagnetic field at the equator, G. The numerical values V, and VI from Sterling et al. (1969) used in the present article are given in Table 1 and Appendix A. Time variations of Vl and V, can be substantial (Fejer, 1981). At the same time, in accordance with experimental measurements (McClure and Peterson, 1972) VL and Vi are independent of altitude. This condition is assumed in the present article for theoretical investigations of equatorial ionosphere (see, for example, Anderson et al., 1987). The numerical calculations were based on parameters of the neutral atmosphere using the MSIS model (Hedin et al., 1977a, 1977b), so P, p, D,, H, T,, aT,/ai, T, [0], [O,], [N,] are calculated, the spectrum of solar radiation, and cross-sections of ionization and absorption (Ivanov-Kholodny and Nickolsky, 1969). Here, as well as in Sterling et al.

1290

0. P. Kolomiitsev Table 1. Rates of vertical

LT, h V,, m ss’ V,,, m s - I

00 -20 40

02 -10 60

Table 2. Calculated

04 -5 80

et al.

VL and horizontal

V, plasma

08 10 80

12 20 -10

06 0 100

10 15 10

drifts (Sterling 14 20 -80

et al., 1969)

16 10 -100

values of some daytime parameters of the neutral atmosphere for the equator: night-time values in brackets

18 20 -100

20 0 -80

22 -5 -10

24

- 10 10

under quiet conditions

Solar activity Parameter Solar 10.7 cm flux density Incident EUV photon flux Temperature at h = 120 km h = 300 km h = 1OOOkm Density at h = 120 km [Ol

P*l WI Density [Ol

High

Low

150 14.0 391 (391) 1229 (912) 1239 (914)

80 5.4 391 (391) 926 (735) 932 (736)

9.2 (9.2) 3.6 (2.7) 3.0 (3.1)

7.9 (7.9) 3.6 (2.7) 3.0 (3.1)

9.9 (6.8) 0.13 (0.038) 2.9 (1.2)

4.9 (3.3) 0.032 (0.01) 0.87 (0.32)

Units 10m22w me2 (Hz))’

10’“cm~Zs-’ “K “K “K

at h = 300 km

(1969) it is supposed that r, = r, = T. As is seen from (2) the influence of temperature variations on the numerical calculations can be taken into account. According to long-term experimental measurements of the plasma drift in the equatorial ionosphere F-layer with the aid of the incoherent radar at Jicamarca Peru (cp = 12’S, i = 74”W, @ = -0.57”, I = 0.29”) near the sunrise at 06.00 LT, reversal of the vertical V1 drift direction is usually observed (Fejer, 1981) (see Table 1 of the present article). In this connection, to reveal the possible influence of the electrodynamic drift regime, two sunrise effects in the Flayer were additionally calculated. In the first case, the diurnal variation VL was taken with the maximum of f40m s-‘, and in the second case with the minimum -40 m ss’ at 06.00 LT (see Appendix A).

Table 3. Production,

Table 2 shows calculated values of some parameters of the neutral atmosphere under quiet conditions (on the basis of a 3 h index of geomagnetic activity, with ap in gammas). In Table 3, the rates of electron formation, recombination and diffusion at h = 300 km are given.

RESULTS OF CALCULATIONS

The results of the calculations carried out are given in Tables 4 and 5, and Figs 2-6. In Tables 4 and 5 and Appendix B, 1. C is the normalizing factor of the initial profile f, (h) x C (as an example, the expression ,& x 0.5 signifies that for the calculation of the plasma fre-

loss and diffusion rates at h = 300 km = night-time in brackets

Solar activity Noon production rate, P Loss coefficient, b Diffusion coefficient, Da

High 890 1.85 (0.91) 1.54 (1.85)

Low 160 0.68 (0.3) 2.5 (3.08)

values

Units cm~3s~l 10m4sm’ 101”cmZs~

Equatorial Table 4. The dependence

F-layer

at sunrise

of the sunrise effect on the initial conditions

1291 (the initial profile parameters)

Conditions Decrease hmfp, km; equinox, F,07 = 150; a.. = 3.9 loo? 200 Fig. 4(b) Fig. 4(c)

Decrease&(h) C; equinox, F 10,= 150; ap = 3.9 c = 1.0 Fig. 2(b)

c = 0.5 Fig. 3(a)

c= 0.2 Fig. 4(a)

2 At, 3 YInI 4 Ah

5.0 35 215 200

2.7 10 195 230

0.5 5 150 290

0.5 10 190 130

5 (C?Ne/&), 6 (8Ne/at), 7 (aNe/at),

498 166 304

517 102 71

508 140 15

508 450 70

Parameters

1 Af,

, (4

Units

-

MHz min km

185

km cmm3 s-’ cm-3 smI cm-3 smI

440 -

, (b)

fp(MHz) Fig. 2. Calculated

profiles

5 fp (MHz) for: (a) high; (b) moderately high; (c) low solar activities: 150; (c) 80; C = 1 .O; ap = 3.9; equinox; 06.004)7.00 LT.

quency in the F-region the plasma frequency was halved. 2 Af, = C& -&,) characterizes the cavity depth, in MHz; fb, is the maximum plasma frequency of the

fp (MHz) F,07 = (a) 226; (b)

morning layer, f,, is the quency in the cavity between layers; Af, corresponds to 20.2 MHz, when f,, -A,

minimum plasma frethe morning and night the observation period i.e. from the vertical

0. P. Kolomiitsev et al. sounding the stratification can be observed from below, where&, is the night layer frequency. At, is the lifetime of the cavity, in min. Ah = h,-h, characterizes the linear cavity dimensions, km; h, is the altitude of the night F-region peak, h, is the altitude of the morning layer maximum (for the same conditions as A& Arc). Y,,,/2 is the half-width of the F-layer, km, at 07.00 LT at the level with& = 3.2 MHz (or where N,- 105cm~3) above and below the electron density maximum. 6. f,/‘&, is the relative plasma frequency at 07.00 LT, f, is the maximum plasma frequency for any case described in Table 5, f&, is the maximum plasma frequency of the profile shown in the Fig. 3(a). are time changes of the F-layer vertical 7. (anklw,,,,, structure, cm-3s-’ (the mean value for the time interval 06.OCO7.00 LT); (aNe/&), characterizes the rate of electron density increase in the morning layer maximum; (aNe/LJt), characterizes the rate of cavity filling; (dNe/&), characterizes t,he rate of electron density spreading at the altitude h = (h,+ 100) km above the night layer maximum. Figures 226 show profilesf, (h) for the period 06.OtS 07.00 LT at 5 min intervals, except in Fig. 4(a) where the profiles are at 15 min intervals with the addition of one at 06.05 LT; in Fig. 4(c) thef, (h) profiles in the interval 06.OCO6.15 are at 5 min intervals, the others being at 15 min intervals and, in Fig. 6(b), where in the interval 06.0&06.30LT profiles are shown each 5 min, the others being at 15 min intervals. The bold curves describef,(h) whose parameters AfP, Ah, At,, YnJ2, (aNJW, 2.3 are given in Tables 4 and 5. For comparison with the experimental data (see Fig. I), Fig. 2(a) shows calculated& (h) profiles for the conditions under which the observations were carried out. The f, (h)profile series in Fig. 2(a) show that the described model representation of the sunrise effect in the F-region of the equatorial ionosphere is similar to that observed experimentally; the f, (h) calculated show common characteristic features of the ionospheric vertical structure observed at sunrise. However, at 07.00 LT the maximum plasma frequency fpm of the model layer (14.1 MHz) is 1.5 times the experimental value (9.5 MHz). The discrepancy is probably because the calculations were carried out with too high values of the ionizing solar radiation flux. Indeed, Ivanov-Kholodny and Firsov (1974) concluded that the J, in Ivanov-Kholodny and Nickolsky (1969) must be decreased by a factor of two. Then, for conditions close to the photochemical equilibrium we could write as N,, -f pm-q/pJ, and, hence, the J, decreasing by a factor of two gives the

Equatorial

F-layer

at sunrise

, (4

1293

, @I

800

Fig. 3. The same as in Fig. 2 for (a) moderately equinox;

high, and (b) low solar activities 06.OCkO7.00 LT.

fpm model profile value close to the experimental one. It is necessary to take this remark into account for all the profiles& (h) calculated, as discussed below. The diminished J,, value corresponds to J, that were used in other theoretical investigations of the equatorial ionosphere (see, for example, Anderson et al., 1987) where a good agreement between the model calculations and the experimental data have also been obtained. Further discussions of the problem of the choice of J, is beyond the scope of the present article. Let us consider the influence of various conditions on the development of the sunrise effect. (a) Initial conditions

(Table 4).

1. For the plasma frequency of the initial nighttime profile f, (h) x 1.O; f, (h) x 0.5 and f, (h) x 0.2. 2. For the altitude of the night-time (initial) profile maximum h, decreased by 100 km and by 200 km. The computer results show that the initial condition influences all the parameters of f,(h). For example, a decrease off, (h) by a factor

at C = 0.5; ap = 3.9;

of 0.5 leads to the cavity lifetime decreasing by nearly a factor of four, being 35 and IOmin, respectively; strong modifications occur in the rate of cavity filling, the rate decreasing by nearly a factor of three, and in the rate of the nighttime layer spreading which slows down by nearly a factor of four. The layer becomes thinner, the half-width of the layer decreasing by about 100km; the rate of the morning (new) layer increase drops. The effect can still be observed if fP (h) is only a fifth of the initial value, but in this case the cavity lifetime is I5 min. The 100 km decrease of the night layer maximum altitude in comparison, for example, withf, (h) x 0.5 leads to an increase in the rate of the cavity filling by almost a factor of four, though its lifetime practically does not change. At 200 km, a decrease in the sunrise effect does not manifest itself. (b) Solar-geophysical conditions (Table 5): variations of solar activity, season, photochemistry, geomagnetic disturbance, diffusion regime, and vertical

1294

0. P. Kolomiitsev

600

et al.

600

fp (MHz)

fp (MHz)

Fig. 4. Profile_& (h) for moderately high solar activity: (a) at C = 0.2; (b) the altitude of the night-time layer peak is 100 km lower than the observed one at C = 0.5; (c) the altitude of the night layer maximum h, is 200 km lower than the observed one at C = 0.5; ap = 3.9; equinox; 06.00-07.00 LT.

drift regime. As the basic profile with respect to which the degree of influence of one or other condition is determined, the profile f, (h) given in Fig. 3(a) (F,,,, = 150, equinox, day 90; up = 3.9; C = 0.5) has been taken. Rapid diffusion means that D, is increased by a factor of 10; slow diffusion means that D, - 0. We consider briefly the calculation results for each parameter: A& the depth of the cavity decreases by 30%, 1. with geomagnetic activity increasing, 2. with the diffusion increasing, and 3. when V, is directed downward Af, = 2.7 MHz 2.0 MHz at up = respectively; At,, reduced ionizing observed at solar At, = IOmin at F ,. 7 = 80, winter, The half-width

at aP = 3.9 and A& = 2.0; 1.8; 94, fast diffusion, VL downward, the cavity lifetime increases for solar radiation flux that is activity minimum and at winter, F,o.7 = 150 and At,= 15min at J,/2, respectively. of the layer decreases by almost

a factor of two at the solar activity minimum and for rapid diffusion; for slow diffusion it increases by a factor of two; (aNJat), the growth rate of the morning layer, decreases by almost a factor of three for solar activity minimum; this depends also on the season in summer and winter it is smaller than at the equinoxes, (aNJat),: the rate of cavity filling has a minimum for solar activity minimum and is inversely proportional to the diffusion, velocity and drift direction, it decreases for rapid diffusion and for V, directed downwards, and grows for slow diffusion and V, directed upwards, (aN,/at),: the night layer spreading is practically absent for a slow diffusion, fp/fbm: the relative plasma frequency grows for geomagnetic disturbance and at VI directed downwards; in all the other cases, it decreases and has minimum values for solar activity minimum. The total lifetime of the stratification (the sunrise effect), by observation from above and from below, is

1295

Equatorial F-layer at sunrise

800

800

600

600

_c 500

-is 3 c 500

I

I

5

10

fp (MHz) f,,WW Fig. 5. The same as in Fig. 3 for moderately high solar activity: (a) the flux of ionizing solar radiation is decreased by a factor of 1.6;(b) the geomagnetic disturbance, aP = 94 at C = 0.5; equinox; 06.00-07.00 LT.

equal to C At, 2 120 min (see, for example, curve in Fig. 3(b)).

the dashed-

CONCLUSIONS

1. In the ionospheric equatorial F-layer near sunrise, for certain conditions a cavity of lower electron density N, can arise, which is situated between the F-layer surviving after the night and the new morning F-layer. By ionospheric sounding from below, the cavity manifests itself as the stratification of the F-layer. The theoretical investigations carried out revealed the dependence of the cavity parameters on initial conditions, on the solar activity level, on season, photochemistry, geomagnetic disturbance, diffusion regime, and the ionospheric plasma vertical drift. The total cavity lifetime can vary from several minutes up to 2 h or more; the lowest N, value in the cavity can reach less than half the N, morning layer maximum;

the difference between the altitudes of the N, night and morning layer peaks can be about 100-300 km. It has been found that, for equatorial conditions, the relation

ahhlat=fWe,,F,, ,,P,Da, VL,a,) is valid, i.e. temporal variations of the electron density depend most strongly on parameters of the initial profile, the ionizing solar radiation flux, electron production rate, diffusion, drift, and geomagnetic activity. This result supplements essentially the early result that aNJat= P for mid-latitude conditions (see, for example, Rishbeth, 1964). One of principal physical mechanisms that can contribute to the conservation at large altitudes of the Flayer electron density at night (pre-sunrise) at daytime values can be slow diffusion. 2. The numerical-analytical method discussed in the present article permits us to reproduce changes of the F-layer vertical structure in other transition periods

1296

0. P. Kolomiitsev

et al.

, (4

(b)

600

600

Fig. 6. The same as in Fig. 3 for moderately high solar activity: (a) rapid diffusion; a, = 3.9; C = 0.5; equinox; 06.00-07.00 LT.

such as a solar eclipse, or the response to the influence of an artificial source, etc. In Kolomiitsev et al. (199 la, 1991b) for example, the time evolution results of the vertical structure of the artificially modified equatorial ionosphere F-layer obtained with the aid of this method have been described. The method can be used to calculate any parameter appearing in equation (2). Ivanov-Kholodny and Kolomiitsev (1967) used the method for estimating the ionizing source supporting the electron density in the F-region during the long polar night in the near-polar

(b) slow diffusion,

ionosphere. As the initial case, a profile N, constructed analytically was taken. 3. Numerical calculations obtained in the present article are specific: they are based on certain theoretical representations and experimental data. Under other conditions, for example, at other values of operating parameters in equation (l), such as J,, ap, IQ, yz, D,,

vl,

VI, T, a, A(O),

WI, Nl, they can be

different. Acknowledgements-The authors rov and Yu. Kopylov for fruitful

are grateful discussions.

REFERENCES

Anderson D. N., Mendillo M. and Herniter B. Bauer S. J. Chapman S. Dalgarno A. Fejer B. G. Hanson W. B. and Cohen R. Hedin A. E., Salah J. E., Evans J. V., Reber C. A., Newton G. P., Spencer N. W. et al.

at

1987 1969 1931 1964 1981 1968 1977

Radio Sci. 22, 292-306. Proceed. IEEE57, 1114-1118. London, Proc. Phys. Sot. 43,2645 J. atmos. terr. Phys. 26,939. J. atmos. terr. Phys. 43, 377-386. J. geophys. Res. 73,83 I-840. J. geophys. Res. 82,2139%2147.

to Drs I. Ego-

Equatorial

F-layer

at sunrise

1297

Hedin A. E., Reber C. A., Newton G. P., Spencer N. W., Brinton H. C. et al. Ivanov-Kholodny G. S. and Kolomiitsev 0. P. Ivanov-Kholodny G. S. and Nickolsky G. M. Ivanov-Kholodny G. S. and Firsov V. V. Kolomiitsev 0. P., Surotkin V. A. and Reddy B. M.

1977

J. geophys. Res. 82,2148-2156.

1967 1969 1974 1991a

Kolomiitsev 0. P., Migulin V. V., Surotkin V. A. and Reddy B. M. Korn G. A. and Kom T. M. McClure J. P. and Peterson V. L. Ossakow S. L. Rishbeth H. Sterling D. L., Hanson W. B., Moffett R. J. and Baxter R. J. Surotkin V. A., Namgaladze A. A. and Kolomiitsev 0. P.

1991

Geomagn. Aeronom. I, 731-733. Sun and Ionosphere, Nauka, pp. 455. Geomagn. Aeronom. 14,393-398. Proc. of the III Suzdal URSI Symp. on Modification of the Ionosphere by Powerful Radio Waves, pp. 196 197. DAN 319, 1353-1356.

1968 1972 1981 1964 1969

Mathematical Handbook, McGraw-Hill, Radio Sci. 7, 539-547. J. atmos. terr. Phys. 43,437452. J. atmos. terr. Phys. 26,657485. Radio Sci. 4, 1005-1023.

1985

Geomagn. Aeronom. 25,39&399.

pp. 701

APPENDIX B APPENDIX A A$

loo80 ~

,’ /’

/‘\

‘\

-v ---_

\,

Ate> y,,,G

(aNkdt),.*,,

1 V A

At, fp,,,>

for profile

f,b(h)

at tb LT (thick line). Af = fb-fb P

PI

P2

Ate = t;- t; Ah = hi- hi @N@)t

g (AN/At),=

(aN

g

N,“,-“,“, - ,<_-; I I b

/at)

e

2

/At)

(AN

e

1

2

a

-!?-!,2 b a t2-t2

-60 -

\, \

-80 -100 00

I 04

I 08

I 12

\

\

‘.___* I 18

,’ ,’ #’

400

(aNdat),

I 20

g (ANkAt),=

The initial profile LT (thin line).

Local time (hours) (see Table 1)

0

5 $ (MHz)

(see Tables 4 and 5)

10

f;(h)

N,“-Nea, -

- isi<

at ta