A Mathematical Model of the Ionospheric Part of the Global Electric Circuit

Valery Denisenko1, Michael Rycroft2, Giles Harrison3

1Institute of Computational Modelling, Russian Academy of Science, 660036, Krasnoyarsk, Russia
2CAESAR Consultancy, 35 Millington Road, Cambridge CB3 9HW, U.K.
3Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, U.K.

Electric currents flowing in the global electric circuit (GEC) are closed by ionospheric currents. A model for the distribution of the ionospheric potential which drives these currents is constructed. Only the internal electric fields and currents generated by thunderstorms are studied, and without any magnetospheric current sources or generators. The atmospheric conductivity profiles with altitude are empirically determined, and the topography of the Earth’s surface is taken into account. A two-dimensional approximation of the ionospheric conductor is based on high conductivities along the geomagnetic field; the Pedersen and Hall conductivity distributions are calculated using empirical models. The values of the potential in the E- and F-layers of the ionosphere are not varied along a magnetic field line in such a model. Under typical conditions for July, under high solar activity, at the considered point in time, 19:00 UT, the calculated maximum potential difference in the ionosphere is 42 V. The voltage increases to 55 V at 23:00 UT and up to 72 V at 06:00 UT, when local midnight comes, respectively, for the African and Central American thunderstorm areas. These voltages are about twice as large at solar minimum. With our more realistic ionospheric model, the electric fields are an order of magnitude smaller than those found in the well-known model of Roble and Hays (J Geophys Res 84(A12):7247–7256, 1979). The designed model contains the equatorial electrojets. These electrojets appear in any global current system because of the equatorial singularity of the ionospheric conductivity. The positions and the directions of the electrojets are defined by the global distribution of the main thunderstorm areas, as well as of the ionospheric conductivity, and so they strongly vary with Universal Time. There are day-time electrojets, the strength of which may be up to 175 A, and night-time ones (of up to 60 A), while the total current of the GEC is not larger than 1400 A in our model. The equatorial electrojets of the GEC produce magnetic perturbations on the ground, which are in the 0.1 nT range. In principle, these magnetic perturbations could be measured, especially at the night-time geomagnetic equator where they are not so disguised by other ionospheric currents, which are concentrated mainly in the day-time equatorial electrojets.