Stationary and nonstationary models of the global electric circuit: Well-posedness,analytical relations,and numerical implementation

We analyze the formulation of the problem of global atmospheric electric circuit modeling. It was shown that under some relatively simple and widely used simplifying assumptions this problem can be reduced to finding the temporal and spatial dependencies of the electric potential on the specified generators, which are determined by the external electric current density. They correspond to thunderclouds in the real atmosphere. The ionospheric potential (the potential difference between the upper and lower atmospheric boundaries) is not specified explicitly but can be uniquely determined from the solution. The formulations of the stationary and nonstationary problems are given in terms of the potential and their well-posedness is discussed. We obtained a number of analytical relations under some restrictions on the distribution of conductivity. They include the formulas which explicitly express the ionospheric potential in terms of the problem parameters. The examples of numerical calculations using the software developed on the basis of general formulations of the stationary and nonstationary problems are demonstrated.