*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 *B*z
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:

**(1)**

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

**(2)**

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 *B*z 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]:

**(3)**

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]:

**(4)
**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

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

**(5)
**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;

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.