### Abstract

We have developed a time-dependent model of global electric circuit (GEC) in spherical coordinates. The model solves time-dependent charge continuity equation coupled with Poisson's equation. An implicit time stepping is used to avoid a strict dielectric relaxation time step condition, and boundary conditions for Poisson's equation are implemented to allow accurate description of time evolution of the ionospheric potential. The concept of impulse response of GEC is introduced that allows effective representation of complex time dynamics of various physical quantities in the circuit using model results obtained for instantaneous deposition of a point charge. The more complex problems are then reconstructed using convolution and linearity principles. For a point charge instantaneously deposited at a typical thundercloud altitude the impulse response of the charge density shows induction of the same value and polarity charge at the ionospheric boundary, while charge of the same value but opposite sign is moving down logarithmically with time and neutralizes the source point charge on time scale corresponding to the dielectric relaxation time at altitude of the source point charge. The ionospheric potential is modified immediately with input of the source point charge based on free space solution of Poisson's equation. Then the ionospheric potential relaxes. It is shown that during formation of two main charge centers of the thundercloud, typically represented by a current dipole, the ionospheric potential can be determined from the difference of time integrals of two ionospheric potential impulse responses corresponding to charge locations at the opposite ends of the current dipole. For latitude- and longitude-independent conductivity model, the total charge on the Earth is exactly zero at all times. During cloud-to-ground lightning discharge, the ionospheric potential changes instantaneously by a value proportional to the charge moment change produced by lightning and then relaxes to zero. For a typical charge moment change of 35Ckm and lightning frequency 10s^{-1}, the ionospheric potential changes by 9.3kV; this value agrees well with the results presented by Rycroft et al. (2007) and Rycroft and Odzimek (2010).

Original language | English (US) |
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Pages (from-to) | 10,184-10,203 |

Journal | Journal of Geophysical Research: Space Physics |

Volume | 119 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2014 |

### All Science Journal Classification (ASJC) codes

- Geophysics
- Forestry
- Oceanography
- Aquatic Science
- Ecology
- Water Science and Technology
- Soil Science
- Geochemistry and Petrology
- Earth-Surface Processes
- Atmospheric Science
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science
- Palaeontology