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Alexander Eliseyev, Nikolay Zaalov

Radiophysics Division, Research Institute of Physics, St. Petersburg State University, 198904 Petrodvoretz, RUSSIA


Antenna Besprozvannaya

Arctic & Antarctic Research Institute, Beringa 38, 199397 St. Petersburg, RUSSIA


An empirical model is proposed for the interpretation of experimental ionospheric data. The model represents the major large-scale characteristics of the sub auroral and auroral F2 layer as well as the temporal variations during the transition from quiet to disturbed conditions. The model is in FORTRAN code and the correction of predicted foF2 values is possible using satellite and vertical sounding data.


A global network of ionospheric observatories provides the possibility of determining ionospheric "weather" at a given time. Ionospheric modelling is used for ionospheric forecasting and for the calculation of ionospheric parameters along a radio path. The data from ionospheric observatories as well as in-situ satellite measurements can be used for the correction of the model parameters. In this paper, an empirical model is proposed for ionospheric weather monitoring. The first part of the paper gives the outline of the model. In the second the results of calculations for quiet and disturbed conditions are presented and briefly discussed, and finally an example of a comparison with experimental HF doppler sounding data is presented.

The Main Principles of the Model

The idea of plasma tubes connecting the ionosphere with the conjugate region is proposed as the basis for computation of the level of noon ionisation. The latitude variations of foF2 are approximated by a product of two functions. One is determined by the solar zenith angle and the other by magnetic field geometry (for the model under consideration the inclined dipole approximation is suitable).

(1) foF2 12=A.cosnc 12 . M

where foF2 12 and c 12 are dependent on the noon values of the critical frequency and solar zenith angle and M is the factor of conjugation, dependent on the geographical latitude difference at the ends of the tube and hence on their illumination conditions.

Following Rothwell (1962): M = (cos c c/cos c g)1/4, where c g and c c are values of the solar zenith angle at the given (g) and magnetically conjugate (c) points. The solar cycle variations of A and n are:

(2) A = a. [1 + b . (log(F10.7) - 1.812)]

n = c + d . R

where F10.7 and R are radio emission flux and sunspots number (3-month average) respectively; a, b, c, d are coefficients of the model (Besprozvannaya, 1991). Experience has shown that both indices of solar activity are to be employed in modelling solar activity effects in the ionosphere. Introducing their interdependence (eg. in the IRI model) generally worsens the results.

The relation (1) for an analysed period (December 1988, F10.7 = 108, R = 152, A = 13.3, n = 0.34) is presented in Figure 1. In the same figure the noon values of F2 divided by the M-factor for 24 ionospheric observatories are shown (black dots). One can see that the experimental data agree closely with the model. Equation (1) gives the noon F2-layer critical frequency corresponding to an average undisturbed ionosphere for the invariant latitude belt from 35 to 75 , for any given solar activity level. This value is basic for further model calculations. Critical frequencies for other times are related with the noon values by the simple dependence:

(3) F2 = Ki.foF2 12

Factor Ki shows how F2-layer ionisation varies with changes in magnetic activity and with the local time. The model incorporates a set of Ki -tables for four fixed UT periods; for three levels of magnetic activity (Kp = 0, 3, 5); for high F10.7 > 150) and low (F10.7 < 100) solar activity; in winter, spring, summer and autumn. [A set of tables on diskette is available from the authors (A. E.) ].

The Ki-value for a particular point at a given UT is obtained by interpolation between two tables of coefficients for the nearest fixed UT times. The longitude value, for which the coefficients are taken from the table, corresponds to the local time of the point under consideration at the given UT. Thus the interpolation is being made practically in longitude. The transition from one level of magnetic activity to another is made assuming that the Kohlein and Raitt (1977) formula describes the movement of the mid-latitude trough:

(4) F = 65.2 - 2.1 .Kp - 0.5 .t

where F is invariant latitude and t is the number of hours counted from local midnight.

To show the potential of the model for ionospheric reconstruction it is instructive to look at the calculated distribution of foF2 for selected universal times. This is done in this section.

Maps of F2 in the Northern Hemisphere are shown in Figure 2 for two values of universal time (UT = 6 and UT = 18) for moderately disturbed (Kp = 3) conditions. One can see the dynamics of the high-latitude distribution of plasma density in F layer. During disturbed conditions the maximum change takes place in the night sector which is connected with the main trough movement (Eq.4). The comparison of the maps for UT = 6 and UT = 18 shows notable longitudinal dependence.

Considerable computation efforts are required to incorporate longitudinal dependence into the ionospheric model (Sojka et al., 1979). But HF propagation forecasting needs a simple code that can be realised in real time. Our model was developed as FORTRAN code for IBM PC. Only a few minutes are required for the map calculation. Testing of the model (Besprozvannaya and Eliseyev 1992, Besprozvannaya et al., 1990) shows good agreement with experimental measurements.

Ionosphere Reconstruction and Data Interpretation

In the light of the above, it seems that for practical modelling some additional information about the input parameters of the model are needed.

First, for the noon value calculation we have to know A and n in Eq.1. One can use F10.7 and R indices of solar activity and Eq.2. Another way possible is that the analysis of the noon data from an ionospheric network for the preceding period (as in Figure 1) can give us the parameters of the regression line: gradient n and A. For further calculations we can also use the observed noon foF2 value.

During the night auroral and sub auroral stations fall into different regimes of large-scale ionospheric structures. The time of transition from one structure to another is a complicated function of latitude, local time and geomagnetic activity level. In Figure 3, data (versus modelled values) for two ionospheric disturbances (December 6, 1988; December 10, 1988) are presented for 8 observatories of the Northern Hemisphere. One can see that for disturbed conditions a great difference occurs between observed and calculated foF2 (Figure 3a). Analysis of the ionospheric network data showed that in one case (December 6) the ionospheric trough was 2 southward from the model position and in the second case (December 10) it was about 3 northward (Besprozvannaya et al., 1990). Using formula (4) we can calculate an "effective" Kp value. Results of this correction are presented in Figure 3b. The fitting was improved considerably.


For probing regular and rapid changes in the ionosphere we used the oblique HF Doppler technique. An observational multichannel receiver is situated at the St. Petersburg University (60 N, 30 E) where it is a useful tool for investigations of solar flares effects, ionospheric gravity waves and natural and man-made ionospheric distortions. Doppler shift spectra (DS) can be obtained from the computer processing of the measurements on the ray paths between St. Petersburg and a network of broadcasting stations all over the world. DS usually show the frequency displacement of the signals reflected by different ionospheric structures.

The left side of Fig. 4 illustrates such DS spectra of the signal at the frequencies 9.519, 9.625, 11.884 MHz received on June 30, 1992 from transmitter situated in Germany (52 N, 10 E). For 9.519 and 9.625 MHz, an additional mode appeared at 10.47 UT and 10.49 respectively. No effect was observed for 11.884 MHz. In the right side of the figure the results of raytracing for 9, 10 and 12 MHz calculations are presented. From these results we can conclude that the new mode at 1580 km was a two-hope F2 mode for 9 and 10 MHz while only E mode could be observed for 12 MHz. Observed results agree well with the model calculations and show the transition of skip distance for 9.519 and 9.625 MHz in succession.


The purpose of this paper is to demonstrate the capability of the empirical model to calculate and interpret foF2 and Doppler spectra. The model adequately describes the main features of foF2 distribution at auroral and sub auroral latitudes both for quiet and disturbed conditions. However, because the commonly used Kp-index is a poor quantitative measure of the ionospheric disturbance intensity, a real time data input is needed. As a replacement, an effective Kp value can be used which is estimated from the known position of the main trough.

Cambou and Galperin (1982) showed the possibility of monitoring the trough wall location. They used oblique incidence sounding at a chain of ionospheric observatories. The polar wall of the trough created by electron precipitation coincides with the equatorward diffuse auroral boundary. Monitoring of that boundary is possible from satellites (Gussenhoven et al., 1983, Gdalevich et al, 1986). To correct the model the measurements of interplanetary magnetic field are also desirable (Grib et al., 1985, Benkova et al., 1989).

The other way is to make a choice of Kp so that the model foF2 value equals the observed one at an ionospheric observatory in the trough region. It is necessary to allow for the operator experience because the direction of foF2 gradient depends on the location of the observatory (polar or equatorial wall of the trough). The effective Kp value found by either method (time resolution better than 3 hours is desirable) will be the main input parameter of the model.

In the future, we intend to propose our model as a FORTRAN subroutine for IRI to enable further comparison with experimental data as well as with other models. With ray-tracing calculations, the model can be used for near real-time interpretation of Doppler spectra observations and could be used for ionospheric weather monitoring over a wide region by passively receiving signals from broadcasting transmitters.

Acknowledgments. The staff of HF Propagation Laboratory of St. Petersburg University operated and maintained the DS multichannel receiver, which obtained the data, described in this report. Irshat Nasyrov (Ukraine) supplied us with the HF ray path code for computer. This research was partially supported by the "Geocosmos"program grant.


Benkova, N.P., A.S. Besprozvannaya, E.F. Kozlov, and S.A. Pullinets - IMF Influence on the Main Ionospheric Trough Position as Deduced from "Intercosmos-19" Satellite Data, Geomagnetism i Aeronomiya, 29, 863, 1989.

Besprozvannaya, A.S. - Empirical Modelling of the F2 Peak Density at 50x-70x Invariant Latitude Using Magnetic Conjugacy, Adv. Space Res., 11, 23, 1991.

Besprozvannaya, A.S., A. Yu. Eliseyev - Empirical Model for foF2 Forescasting. Proc. Solar-Terrestrial Predictions IV, 3, 403, 1993 .

Besprozvannaya, A.S., P.N. Kishcha, E.V. Nepomniashchaya, S.A. Pulinets and T.I. Shchuka - Estimates of Accuracy and Correction of the Empirical Reference Ionosphere Model for Isolated Periods, XXIII General Assembly URSI Abstracts, Prague, 1, 163, 1990.

Cambou, F., and Yu. I. Galperin - Main Results of the Joint French-Soviet Space Project ARCAD-1 and ARCAD-2 for Magnetospheric, Auroral and Ionospheric Physics, Ann. Geophys., 38, 83, 1982.

Gdalevich, G.L., A. Yu.Eliseyev, O.P. Kolomiytsev, V.V. Afonin, V.D. Ozerov, T.N. Soboleva - Ionospheric Plasma Density Variations at the Main Ionospheric Trough Zone Connected with IMF Changes for Magnetic Storm 18-19.12.1978, Kosmicheskie Issledovaniyua, 24, 79, 1986.

Grib, S.A., A. Yu. Eliseyev, O.P. Kolomiytsev - Ionosphere at the Main Ionospheric Trough Zone During Magnetic Storms, Geomagnetism i Aeronomiya, 25, 211, 1985.

Gussenhoven, M.S., D.A. Hardy and N. Heineman - Systematic of the Equatorward Diffuse Auroral Boundary, J. Geophys. Res., 88, 5692, 1983.

Kohlein, W., W.J. Raitt - Position of the Midlatitude Trough in the Topside Ionosphere as Deduced from ESRO-4 Observation, Planet. Space Sci., 25, 600, 1977.

Rothwell, P. - Charged Particles in the Earth's Magnetic Field and the Ionospheric F2 Layer, J. Phys. Soc. of Japan, 17, 263, 1962.

Sojka, J.J., W.J. Raitt and R.W. Schunk - Effect of Displaced Geomagnetic and Geographic Poles on High-Latitude Plasma Convection and Ionospheric Depletions, J. Geophys. Res., 84, 9943, 1979.

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