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VERTICAL IONOGRAMS AS A TOOL IN HF PULSE PROPAGATION ANALYSIS

Davorka P. Grubor and Zivko V. Jelic

Geomagnetic Institute, 11306 Grocka, Belgrade, Serbia, Yugoslavia

Abstract

The dispersive bandwidth, or the reciprocal parameter, ie. the rise time, is calculated for oblique propagation using vertical ionograms. A number of ionograms taken at equinox, noon and high solar activity conditions are chosen and used to estimate the first total derivatives of group path with respect to frequency. To this purpose the slopes dh'/dfv of the tangents drawn at the selected points of h'(fv) curves, corresponding to the E, F1 and F2 traces, are used. These points are selected so that the equivalent frequency of the oblique propagation over the great circle distance D=300 km is fo=5 MHz for both the 1E and the 1F1 wave and fo=11 MHz for the 1F2 wave. The obtained values for rise times are about 5 µs for the 1E wave, about 9 µs for the 1F1 wave and 10-15 µs for the 1F2 wave. The results are in fair agreement with the corresponding values obtained by the simulation method, based on the application of the raytracing program to the same propagation path.

Introduction

Recent aspects of HF communications have given rise to interest in the analysis of vertical ionograms in order to obtain some additional information apart from the commonly scaled parameters. One useful parameter characteristic of oblique HF pulse propagation, which can be obtained from vertical ionograms, is the value of the

dispersive bandwidth. The procedure explained in [1] is applied here to nine quiet condition ionograms, taken in October 1988 at Grocka ionospheric observatory (44o 38' N, 20o 47' E, I=61o), where an IPS-42 ionosonde is operating.The relationship between the first total derivative of the group path with respect to frequency and the first total derivative of the virtual height with respect to frequency, as obtained in [1], is given by:

where P' is the group path, fv is the frequency of a vertically incident wave reflected at the virtual height h', and fo is the equivalent frequency of the wave propagating obliquely with the angle of incidence io. The expression is valid for mirror type reflections. Since the ionograms selected for the present analysis show continuous and unambiguous traces, the values of dh'/dfv are determined by simply drawing the tangents at the points of interest, instead of applying the computational process described in [1]. According to the theory developed in [1] and [2], the distortion of the obliquely propagating pulse through a stratified ionosphere, in the quadratic phase approximation, can be described by the dispersive bandwidth, given in the following form:

where

tis so called pulse rise time andcis the velocity of the electromagnetic wave in vacuum. From (1) and (2), the rise times can be determined.The rise times were calculated previously by simulation of the multipath pulse propagation as proposed in [2]. To this purpose, the Jones-Stephenson raytracing program [3] was used, considering the 1E, 1F1 and 1F2 ray paths over the range of 300 km, with frequencies 5 MHz, 5 MHz and the 11 MHz, respectively. The procedure for numerical evaluation of dP'/dfo was developed and the values thus obtained were subsequently used in (2) for the determination of rise times. The IRI electron density profile data were inserted in the raytracing program in the form of an analytic function, applying Booker's method [4]. The results of this numerical simulation and the ones obtained by the analysis of the ionograms are compared in this paper.

An Analysis of Ionograms

The IPS-42 ionosonde range of sounding frequencies is 1-22 MHz and the maximum registered virtual height is 800 km. Ionograms taken in October 1988, starting with October 1 (day 275 of the year) are used in the analysis. As all ionograms are taken around noon hours, the average values of scaled parameters are: h'E=115 km, foE=3.6 MHz, h'F=206 km, foF1=5.5 (UL), foF2=12.4 MHz. Only the ordinary ray traces are considered. The transmission curves are drawn assuming the distance D = 300 km with the equivalent frequency fo = 5MHz for 1E and 1F1 fo=11 MHz for 1F2 propagation. The vertical frequencies are determined from the intersections of the transmission curves with the ionogram traces, related to the low ray. The values are spread within an interval 0.5 MHz wide around fv = 2.99 MHz (E trace), 0.17 MHz around fv = 4.27 MHz (F1 trace) and 0.35 MHz around fv = 10.4 MHz (F2 trace). The tangents are drawn at the points of the h'(fv) curves, corresponding to these average fv values and the slopes of the tangents are estimated. In Table 1 the vertical propagation frequencies, the corresponding virtual heights and the slopes dh'/dfv, at the selected points (fv, h'), are given for each ionogram.

The values of group path derivatives calculated from (1) using the slopes estimated from the ionograms (Table 1), along with corresponding rise times calculated from (2), are given in Table 2. It can be seen from Tables 1 and 2 that both the variations in the virtual heights scaled at a given frequency and the dispersion of rise times values are the greatest for the E trace. The average values of group path derivatives and rise times for each of the three traces considered are also given in Table 2, in order to provide comparison with the results presented in Table 3 obtained using the simulation method.

A Simulation of Multipath Propagation

By this simulation method the rise times are determined for three cases of propagation considered, using the 3D Jones-Stephenson raytracing program. The ionospheric profile inserted in the program is constructed on the basis of IRI data for equinox, 1200 LT, R=100, applying the fitting method [4]. For all three cases the great circle distance was D=300 km. In the case of 1E propagation, D=300 km is obtained with fo=5 MHz and with the elevation angle 35.50o. The proper 1F1 propagation could not be obtained with the IRI profile, since this does not include the F1 layer. Nevertheless, the wave with frequency fo=5 MHz and elevation angle 58.52o reflected at the base of the F region will be here named as "1F1" wave. In the case of 1F2 propagation, D=300 km is obtained for fo=11 MHz and with the elevation angle 70.35o. The azimuth angle providing the north-south propagation direction is chosen to be a=180o for all the three cases considered. The ray tracing calculations are performed by slightly varying the initial

Table 1. Estimations from ionograms: fv (MHz),h' (km) and dh'/dfv (km/MHz).

Ionogram

1E

fv=2.99

1F1

fv=4.27

1F2

fv=10.40

day

time LT

h'

dh'/dfv

h'

dh'/dfv

h'

dh'/dfv;275

1130

112

10.4

212

14.7

359

29.4

276

1200

100

5.6

200

16.4

300

32.0

279

1000

124

0.7

212

20.0

324

27.1

279

1215

121

10.6

224

13.9

329

25.7

280

1200

100

6.2

209

33.4

335

26.0

286

1245

118

3.9

224

10.2

312

26.0

288

1000

129

14.3

215

12.1

347

38.1

290

1400

127

19.1

227

16.4

335

30.7

301

1000

112

28.9

206

18.6

268

18.3

Table 2. The group path derivatives and rise times; dP'/dfo (m/Hz) t

(m s).

Ionogram

day, time LT

1E dP'/dfo

t

1F1 dP'/dfo

t

1F2 dP'/dfo

t275, 1130

0.0074

5.0

0.0196

8.1

0.0501

12.9

276, 1200

0.0034

3.4

0.0210

8.4

0.0512

13.1

279, 1000

0.0006

1.4

0.0267

9.4

0.0446

12.2

279, 1215

0.0084

5.3

0.0192

8.0

0.0425

11.9

280, 1200

0.0038

3.6

0.0441

12.1

0.0433

12.0

286, 1245

0.0029

3.9

0.0141

6.9

0.0422

11.9

288, 1000

0.0122

6.4

0.0163

7.4

0.0642

14.6

290, 1400

0.0159

7.3

0.0228

8.7

0.0511

13.1

301, 1000

0.0207

8.3

0.0243

9.0

0.0279

9.6

Average :0.0084

4.9

0.0230

8.7

0.0463

12.4

parameters. Consequently, the small variations in the distance, group path and azimuth of the received ray are produced. From the series of calculations, the dependence of the distance, the group path and the azimuth on the initial ray parameters is established, enabling the evaluation of the total derivative of group path with respect to frequency. The values of the total group path derivatives and the rise times calculated from (2) are given in Table 3.

Table 3. Total group path derivatives corresponding and rise times; dP'/dfo (m/Hz), t (µs).

1E

1F1

1F2dP'/dfo

t

dP'/dfo

t

dP'/dfo

t

0.0144

6.93

0.039

11.40

0.164

23.3

By comparing the values from Table 3 and Table 2, it can be seen that the rise time values obtained from vertical ionograms and the ones following the numerical simulation are in reasonable agreement. The difference is most evident for 1F2 propagation, as shown in Figure 2. In that case, the ray path calculated using the IRI profile, which assumes layer penetration, significantly differs from the ray path corresponding to a mirror type reflection.

In order to estimate the discrepancy between IRI profile and the real ionospheric profile corresponding to the ionograms, the real height of the F region base and the real height of the maximum electron density of the F2 layer are determined, following the procedure given in [5]. As can be seen from Table 4, the obtained real heights of the F region base, hb, the real height of the F2 layer electron density maximum hm with the corresponding scale height H, significantly vary from ionogram to ionogram.

Fig. 2. The ray paths for 1F1 and 1F2 propagation: mirror type reflection - dotted line, reflection in the ionosphere described by IRI model - solid line.

Table 4. The real heights obtained using the parameters scaled from the ionograms.

ionogram

scale height

base height

maximum F2 height

day, time LT

H (km)

hb (km)

hm (km)275, 1130

86.7

197.5

429.1

276, 1200

72.1

187.6

393.9

279, 1000

56.1

190.2

334.1

279, 1215

43.2

225.8

341.3

280, 1200

57.4

219.2

373.6

286, 1245

40.7

212.7

325.3

290, 1400

70.5

194.7

395.8

301, 1000

46.6

179.3

323.1

average values:

60.2

197.7

363.5

Conclusion

The average values of hb and hm following from Table 4 differ from the corresponding values described by the IRI model by about 30 km. Table 4 shows that some of the ionograms could be described by the IRI model, while other indicate large deviations from it. Therefore, the comparison of the rise times values as determined from ionograms, with the ones obtained by the simulation method, is adequate only in cases where the real height analysis suggests the ionospheric profile close to the one described by the IRI model.

Further improvement in the determination of the rise times (or dispersive bandwidth) from vertical ionograms might be achieved by adopting a more realistic expression for the group path than the one describing the mirror type reflection, from which the group path derivative with respect to frequency could be estimated.

References

[1] Lin, K. H., Yeh, K. C., Soicher, H., Reinisch B. W. and Gamache, R. R., Vertical ionograms and dispersive bandwidths for an oblique path,

Radio Sci. vol 24, No 4, pp. 521-526, 1989.[2] Lundborg, B.,Pulse propagation through a plane stratified ionosphere,

J. atmos. terr. Phys. vol 52, No 9, pp. 759-790, 1990.[3] Jones, R. M. and Stephenson, J. J. A versatile three-dimensional ray tracing computer program for radio waves in the ionosphere, U. S. Department of Commerce,

OT Report75-76, 1975.[4] Booker H., Fitting of multi-region ionospheric profiles of electron density by a single analytic function of height,

J. atmos. terr. Phys., vol 39, pp. 619-693, 1977.[5] Krinberg, I. A., Vyborov, V. I., Koshelev, V. V., Popov, V. V., and Sutyrin, N. A.,

Adaptive model of the ionosphere, (in Russian), Nauka, Moscow, 1986.