Linear Modeling of Ionospheric Electrodynamics

Brief Description and References

The LiMIE is a Web-based interface to the IZMIRAN Electrodynamic Model (IZMEM) which utilizes a linear regression relationship between the interplanetary magnetic field (IMF) strength and ground-based geomagnetic disturbances. The IZMEM model was developed at the end of 1970's at the Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation (IZMIRAN, Troitsk, Moscow Region, Russia) [see Papitashvili et al., 1994, and references therein]. Such an approach provides a better parameterization of observed geomagnetic variations by the IMF components magnitude and direction. Then ionospheric electrodynamics can be mapped over both the northern and southern polar regions using a given model of the ionospheric conductivity. The IZMEM does not require collection of in situ ground-based geomagnetic data for the event under investigation or selection of a magnetically quiet period to calculate geomagnetic disturbances. These distinguish the IZMEM from other similar algorithms such as the ''magnetogram inversion technique'' (TIM) developed at SibIZMIR, Irkutsk [Mishin et al., 1980], the well-known KRM method [Kamide et al., 1981], and the AMIE technique [Richmond and Kamide, 1988].

The IZMEM model postulates that the magnetosphere-ionosphere coupling link can be considered as "a black box", which accepts changes in the IMF and solar wind plasma (SW) parameters (Bx, By, Bz, velocity V, and density n) as an input signal, and induced ground-based geomagnetic perturbations as an output signal. This approach has already been used by others, in particular, those employing the linear prediction analysis [e.g., Clauer, 1986, and references therein]. A number of interplanetary parameters are known to be associated with the solar wind and magnetosphere interaction. For example, there is much evidence in the literature showing impact of the IMF By and Bz components on the magnetic field at the Earth's surface. The division of Bz into negative and positive values may represent disturbed and quiet geomagnetic conditions, respectively, though a northward Bz can induce a strong polar cap currents as well.

The IMF Bx component has been found to show little correlation with geomagnetic variations [Maezawa, 1976; Levitin et al., 1982; Troshichev, 1982]. Therefore we can compute the regression coefficients K but may disregard their contribution to the model. A number of SW parameters (velocity V, density n, temperature T, and some of their combinations) are tried to find a better correlation with ground-based data and it was concluded that V and nV show significant correlations. The V term may, in part, represent "quasi-viscous'' interaction of the solar wind plasma with Earth's magnetosphere; the nV is proportional to dynamic pressure of the solar wind.


We use a regression model where regression coefficients relate any ground-based geomagnetic field component, for example, H, to changes of the corresponding IMF parameter:


The free term of equation (1) can be expanded for the solar wind parameters:


Here K are regression coefficients for i=1,...,24, where i is universal time (UT) hour; H0 is a residual part of (1) for the average conditions of solar wind (n=4 cm,V=450 km/s); H00 represents geomagnetic variations which are free of the IMF and SW impact (we shall omit index i further). In the current model we utilize parameterization by the IMF only and refer the reader to the papers by Levitin et al. [1982] and Papitashvili et al. [1990] where the solar wind parameters are considered.

The total hourly mean values of the IMF and ground-based geomagnetic data for each season of the year (summer, winter, and equinox) and both northern and southern polar regions above = +/- 57 degrees corrected geomagnetic (CGM) latitude have been used in the regression analyses. The arrays of the IMF and geomagnetic data were subjected to regression analyses for each of 24 UT hours of each day over the entire season of the year (120 days). The resultant magnetic local time (MLT) daily variation of regression coefficients K and H0 around daily mean value were obtained. These results have been compared for the same hourly mean values of the IMF and geomagnetic data, and IMF values one hour ahead of the ground-based data. A better correlation was obtained when the same hourly mean values were compared.

With this model we assume that ground-based geomagnetic disturbances are proportional to variations of the IMF components and there are a variety of physical mechanisms that provide links that transfer energy from the solar wind plasma to the high-latitude magnetosphere and ionosphere. The assumed linearity was studied and confirmed for the Bz component [Papitashvili et al., 1981; Troshichev, 1982]. The solar cycle effect on the IMF/magnetosphere interaction processes has been studied by Papitashvili [1982]. No significant changes are found with a half of solar cycle.

The "regression modeling'' approach has several advantages: (1) total values of geomagnetic field components are used in the analysis, and there is no subjective selection of a perturbation baseline; (2) the technique uses many measurements made by a limited amount of magnetic observatories at different local times due to the Earth's rotation, therefore, 24 values of K are found for each observatory; (3) only an interpolation of K along meridians is required, instead of spherical harmonic expansion; (4) only the IMF values are required to model geomagnetic variations, and then electrodynamic parameters can be obtained using the IZMEM during all three seasons of the year in both northern and southern polar regions.

This regression model of geomagnetic variations is used as an input for numerical solution of the second-order partial differential equation [Faermark, 1977]:


Here is electrostatic potential ( = 0 at = +/- 57 degrees, is a tensor of nonuniform ionospheric conductivity, n is a unit radial vector, and is an equivalent current function, uniquely related to geomagnetic perturbations on the Earth's surface. A definition of the current function in the IZMEM method is similar to that in the work by Kamide et al. [1981].

equation (3) may be rewritten in spherical coordinates (colatitude) and (east longitude) [Feldstein and Levitin, 1986]:


where and are height-integrated Hall and Pedersen ionospheric conductivities specified on a grid of one degree corrected geomagnetic latitude and one MLT hour. Since no ionospheric conductivity models exist specifically for the southern polar region, the statistical particle precipitation ionospheric conductivity model of Wallis and Budzinski [1981] and the solar UV conductivity model of Robinson and Vondrak [1984] are used for both polar regions..

The distributions of electric potential can be determined and parameterized as a superposition of the IMF related terms:


Here is a corrected geomagnetic latitude; MLT is magnetic local time; may represent electric potential, as well as electric and magnetic fields, ionospheric (Hall and Pedersen) and field-aligned currents, or Joule heating rate; A{Bz} and A{By} are dimensionless amplitudes of the IMF components for a given MLT hour; z and y are the solutions of (5) for each set of regression coefficients and correspond to changes of a given parameter (electric potential, ionospheric currents, etc.) on the IMF 1-nT step; o is the solution of (5) for the free terms in (1) during different conditions in the IMF (e.g., negative or positive Bz and By).

The o term in (5) represents the "background'' potential, which exists in the ionosphere during average conditions in the solar wind, that is, "viscous'' convection according to Reiff et al. [1981]. The other terms of (5) represent the "elementary convection cells'' at high latitudes caused by the corresponding IMF components. A combination of these elementary cells for given conditions in the IMF reproduces a typical convection pattern observed by satellites and radars over the polar regions Papitashvili et al., 1995]. Therefore, as equation (1) describes a basic structure of the high-latitude geomagnetic variations, equation (5) allows one to construct a quantitative model of the ionospheric electrodynamics based on the linear regression model.


Clauer, C. R., The technique of linear prediction filters applied to studies of solar wind-magnetosphere coupling, in Solar Wind-Magnetosphere Coupling, edited by Y. Kamide and J. A. Slavin, p. 39, Terra Sci., Tokyo, 1986.

Faermark, D. S., A restoration of 3-dimensional current systems in high-latitudes by the use of ground-based geomagnetic observations, Geomagn. Aeron., Engl. Transl., 17, 114, 1977.

Feldstein, Ya. I., and A. E. Levitin, Solar wind control of electric fields and currents in the ionosphere, J. Geomagn. Geoelectr., 38, 1143, 1986.

Kamide, Y., A. D. Richmond, and S. Matsushita, Estimation of ionospheric electric fields, ionospheric currents and field-aligned currents from ground magnetic records, J. Geophys. Res., 86, 801, 1981.

Levitin, A. E., R. G. Afonina, B. A. Belov, and Ya. I. Feldstein, Geomagnetic variations and field-aligned currents at northern high-latitudes and their relations to solar wind parameters, Phil. Trans. R. Soc. London Ser. A, 304, 253, 1982.

Maezawa, K., Magnetospheric convection induced by the interplanetary magnetic field: Quantitative analysis using polar cap magnetic records, J. Geophys. Res., 81, 2289, 1976.

Mishin, V. M., A. D. Bazarzhapov, and G. B. Shpynev, Electric fields and currents in the Earth's magnetosphere, in: Dynamics of the Magnetosphere, edited by S.-I. Akasofu, pp. 249-268, D. Reidel, Norwell, Mass., 1980.

Papitashvili, V. O., Relationship between geomagnetic variations in the polar cap and the interplanetary magnetic field during the solar activity cycle, Geomagn. Aeron., Engl. Transl., 22, 130, 1982.

Papitashvili, V. O., O. A. Troshichev, and A. N. Zaitzev, Linear dependence of the intensity of geomagnetic variations in the polar region on the magnitudes of the southern and northern components of the interplanetary magnetic field, Geomagn. Aeron., Engl. Transl., 21, 565, 1981.

Papitashvili, V. O., Ya. I. Feldstein, A. E. Levitin, B. A. Belov, L. I. Gromova, and T. E. Valchuk, equivalent ionospheric currents above Antarctica during the austral summer, Antarct. Sci., 2, 67, 1990.

Papitashvili, V. O., B. A. Belov, D. S. Faermark, Ya. I. Feldstein, S. A. Golyshev, L. I. Gromova, and A. E. Levitin, Electric potential patterns in the Northern and Southern polar regions parameterized by the interplanetary magnetic field, J. Geophys. Res., 99, 13,251, 1994.

Papitashvili, V. O., C. R. Clauer, A. E. Levitin, and B. A. Belov, Relationship between the observed and modeled modulation of the dayside ionospheric convection by the IMF By component, J. Geophys. Res., 100, 7715, 1995.

Reiff, P. H., R. W. Spiro, and T. W. Hill, Dependence of polar cap potential drop on interplanetary parameters, J. Geophys. Res., 86, 7639, 1981.

Richmond, A. D., and Y. Kamide, Mapping electrodynamic features of the high-latitude ionosphere from localized observations: Technique, J. Geophys. Res., 93, 5741, 1988.

Robinson, R. M., and R. R. Vondrak, Measurement of E region ionization and conductivity produced by solar illumination at high latitudes, J. Geophys. Res., 89, 3951, 1984.

Troshichev, O. A., Polar magnetic disturbances and field-aligned currents, Space Sci. Rev., 32, 275, 1982.

Wallis, D. D., and E. E. Budzinski, Empirical models of height-integrated conductivities, J. Geophys. Res., 86, 125, 1981.

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