Electron density distributions in the lower ionospheric regions from multi-frequency A1-absorption data

Journal of Atmospheric and Terre&&lPhysics, 1971, Vol.23,pp.221-227. Pergamon Press.Printed in Northern Ireland

Electron density ~~butio~ in the lower ion~phe~c regions from mxiiti-frequencyAl-absorptiondata Department

S. GANWJLY * of Physics, Bose Institute,

Calcutta-9,

India

Abs&&---Attempts have been made to derive the height-distribution of electron-density in the D- and the E-region of the ionosphere, from the multifrequency AI-absorption data. Available cross-modulationprofiles for moderately low latitudes have been used to fix the lower bound of ionization distribution. The method of deriving the prof2es is essentially a process of trial and error, where the observed experimental values are matched with those derived from the proposed models. MULTIFREQUENCY A,-absorption measurements can in principle be employed to yield reliable information regarding the electron density distribution around D- and lower E-regions (PICWOT and THRANE, 1967). The technique consists essentially in calculating theoretically the absorption suffered by various frequencies for a proposed model and in comparing the theo~tieal and experimental values (FEJER and VEX, 1959; PIGGOT and THRANE, 1967). The lowermost portions of the proposed models are usually based on the results obtained by cross-modulation and partial reflection, whereas for the upper E-regions theoretical models (e.g. Chapman-type parabola) are used. In the present paper are presented the electron density distribution for three solar zenith angles (x = O”, 30” and 50”) for Calcutta which is a low-latitude station. These profiles are based on the multifrequency A,-absorption data collected by the author during the period of 1967-68. The E-layer is assumed to be parabolic with a half-thickness of 2H = 15 km (W, being the scale-height) down to a scale-height from the peak given by h, = 105 + 7.6 In (set x) km (ROBINSON, 1959), where x is the solar zenith angle. The collision frequency profile is obtained from the relationship (THEANE and PIGIUOT, 1966) :

yrn = a.4 x 1O’p

(I)

where v, is the collision frequency for monoenergetic electrons and p is the pressure in mm of Hg (the pressure variations with height are taken from the U.S. Standard Atmosphere Supplement 1966). The effective collision frequency fv& which takes into account the Sen-Wyller (1960) genera~zation of the Appleton-Hartree equation is obtained from the relations V $$f

=

2.5 v,;

V
V eff

=

l-5 vm;

Y>U

where w is the angular frequency of the exploring wave. The above asymptotic approximations have been used to derive the profile by varying the veit smoothly * Presentaddress: Radio ScienceDi&ion,

National Phpical 221

Laboratory, New Delhi-12.

222

S. GAN~ULY

from one asymptote to another. Appropriate electron-density profiles up to a height of about 8&--85 km and the (f,,E) values for the three chosen solar zenith angles are taken from the different sources as shown in the following table. x = 3o”

,y = 0”

x = 50°

N-h Data upto about 75km

Armidale data (SMITH et al., 1967) for x = 155’ suitably modified

Tsumeb

(geographic

foE

Haringhata (23’N) data, average of May to July 1967 (noon values) f,,E = 3.87 MC/S Rz = 78

Haringhata data, average of March 1968, p.m. values for x = 30’ f,,E = 3.6 MC/S

Average of x = 50’ profile for various stations, published by THRANE et al., (1968).

latitude 19+2’s) and Crete (35%) data (TITRANE, 1967) for March 1965 p,m. values slightly changed for appropriate R,

R, = 92

Haringhata data. Twelve month average for the period 1967-68 for x = 50’ (a.m. and p.m. values) foE = 3.35 MC/S R, = 98

The author’s absorption data have been lumped in a way exactly similar to that shown in the above table for (fp). The averaging periods for (f,,E) for different values though look arbitrary, are dictated by the limited availability of the N-h data for lower height ranges. Having thus fixed the lower and upper portions of the profile for any particular x, the two portions are joined by a smooth curve as shown by the curve marked Trial 1 in Fig. l(a) for x = 50'. Next the amounts of absorption

w.5

I IO

I.0 x=500

loo

[

MC/s /

2

t lo’

I

N ,cm3

lo4

I

IO5

Fig. l(a). Electron density models derived for x = 50°, R, = 98. The thick lines show the models determined by wave interaction and E-layer data. Trial 1 and Trial 2 indicate models with too large and too little losses, and Trial 3 shows the adopted model. The plasma frequencies corresponding to the electron densities are shown on the subsidiary scale.

Electron distribution in the low ionosphere

223

(L) suffered by various frequencies are calculated by integrating the absorption index k as follows: h

L = 2 x

8.7

s

kdh

indb.

(2)

The net absorption suffered bi any frequency is calculated by using the full Appleton-Hartree equation in the height range of 65 km to a few km down the height of reflection and by using the approximation given by Whitehead (1956) for the rest of the height range. Whitehead’s expression for k (with the approximation v/w < (1 - X) has been shown to yield extremely accurate results when the integration is carried up to the classical height of reflection given by X = 1 (TITHERIDGE, 1961, 1967). It has also been shown by TITHERIDGE (1961, 1967) that the virtual heights calculated by neglecting collisions and by integrating the real part of the complex refractive index up to X = 1, are more accurate, than those obtained by the phaseintegral method. Thus the total absorption is calculated from (2) by using the 16point Gaussian integration in two steps, the upper limit being either the height of reflection (for waves reflected from E) or the peak of the E-layer (for waves penetrating E). These theoretically calculated values of absorption are then compared with the experimental values and the entire process is repeated (Trial 2 and Trial 3 in Fig. l(a)) until a reasonably good agreement is obtained. The virtual heights are calculated by using the tables given by SHINN and WHALE (1952). This process of trial-and-error for x = 50” is shown in Figs. I(a) and (b) which clearly indicate that Trial 3 gives the best fit between the experimental and the theoretical values of absorption.

x=50”

R, = 9s” 1967-196s

2.0

4.0

30

5-O

5.5

f , MC/S Fig. 1 (b). Comparison between computed and observed (circles) values of absorption for x = 50°, R, = 98, for the profiles marked Trials 1, 2 and 3 in Fig. 1 (a). The inset shows the comparison of calculated and measured virtual heights (solid circles) for the adopted model.

224

S. GANGIJLY I IO

r

60

r

I

I

I

I

I

I05

lo4

IO3

id

Kl6

N ,cm3 Fig. 2. Electron density profiles. (a) Derived for x = O”, R, = 78; (b) Derived with March afternoon data for x = 30°, R, = 92; (c) Rocket observation by Kane on 8 March 1968 over Thumba, 2 = 14’; (d) Cross modulation observation by Smith et al. on 4 November 1963 over Armidale, x = ~5’. SO

x =o” May, June , July 1967

70

L

60

0

50

B

0

"0 ; 40

30

20

I

I

I

I

20

30

4.0

5.0

I

5.5

f , MC/S Fig. 3. The observed and computed values of absorption and virtual heights for x = O“, R, = 78. Median values of observed absorption are shown by circles. Whereas the crosses indicate the absorption values for above conditions, when the reflections are from blanketing E,.

Electron distribution in the low ionosphere

225

kg f 0,3

0.4

0.5 i

I

0.6 t

0.7 I

4

5

0.9 /

I

I

3

2

‘0.8 k

6

Frequency

7

8

I.0

1

I

3

IO

I I

1.2

I

f

I

12

14

16

3

I

18

, MC/S

Fig. 4. The ionogram over ~&r~g~t~ and the true height profile, for 15 January f968, at 1330 IST. The inset shows the calculated absorption for the above profile along with the observed values at that time. 90-

80

-

E s c

NY x IO-* 6. The product NV (where N is the electron density in cnz‘-9and v the collision

frequency in c/s) plotted against height (h) in km.

226

S. GANGULY

The results thus obtained for the zenith angles of 0" and 30"are shown in Fig. 2, along with the results of a rocket flight (KANE, 1969)of 8 March, 1968 for a x = 14” over Thumba and a cross modulation profile (SMITH et al., 1967) for 4 November 1963 for a x = 15.5” over Armidale. The comparison between the theoretical and experimental values of absorption and the virtual heights for x = 0” is shown in Fig. 3. It is, however, evident from Figs. l(b) and 3 that the agreement between the theoretically and the experimentally observed values of absorption for waves penetrating the E-region is poor. This is perhaps due to the losses incurred between the E and F-regions. This conclusion is supported by the fact that when reflections are from blanketing E,, the agreement is improved as shown in the Fig. 3, where the crosses ( x ) indicate E, reflections. The absorption calculated for the N-h profiles derived from ionogram data, using Mitra-Mathur (1960) model of collision frequency also show quite significant absorption to be occurring above the E-region level. In Fig. 4 is shown an ionogram along with the true height profile derived there from using the method of Ventrice and Schmerling. The calculated values of absorption suffered by waves penetrating the E-region, at and above the E-region are higher than the observed values at that time (shown in the inset). To determine the region of maximum contribution of absorption, the NV product (which is proportional to the absorption to a first approximation) for the proposed model of x = O”, is shown in Fig. 5. The region of maximum contribution is around 83.0 km, signifying the sensitivity of A,-absorption around that height. It must, however, be mentioned that the profiles presented above cannot be claimed as unique ; on the other hand they can be considered as representative as they explain the measured A,-absorption over Calcutta. Acknowledgements-The author is thankful to Professor S. R. KHASTGIRfor his guidance and and to Dr A. P. MITRAfor his creative suggestions. He is also indebted to Dr. MANORANJAN RAO for his help. Thanks sre also due to the computer section, I. I. T., Kharagpur. The financial support for this work came from the C.S.I.R., New Delhi. FEJER J. A. and VICE R. W. KANE J. A.

MITRA A. P. and MATHURS. B.

PIGGOTW. R. and TEEANE E. V.

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p. 607. ROBINSONB. J. SEN K. H. and WYLLER A. A. SRINN D. A. and WHALE H. A. SMITE R. A., COYNE T. N. R., Loca R. G. and BOUREE I. A.

1959

1960 1952 1967

Rep. Prog. Phys. 22, 241. J. geophys. Ree. 65, 3931. J. Atmosph. Terr. Phys. 2, 85. Conf. Proc. on Growno? Based Radio Waves Propagation Studies of the Lower Ionosphere, Ottawa, Canada,

Vol. 2, p. 336.

Electron

distribution

in the low ionosphere

227

1966

J. Atmosph.

1968

J. Atmosph.

1967

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1961 1967 1956

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