A Global Time-Dependent Model of Thunderstorm Electricity. Part I: Mathematical Properties of the Physical and Numerical Models

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Abstract
A time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, displacement, and source currents. Lightning phenomena are neglected and the electric field is assumed to be curl free. Corona, convection, and precipitation currents are not considered in this initial study and their contribution to the source function is not specified explicitly. As a preliminary test of the model we assume that the storm is axially symmetric in spherical geometry, the conductivity depends only on the vertical coordinate, the ground is equipotential, and far from the thunderstorm region the horizontal electric field is zero. These assumptions are for computational efficiency only and can be relaxed in more realistic studies. The mathematical energy method is applied to the continuity equation to determine boundary conditions that are sufficient to form a well-posed... Abstract A time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, displacement, and source currents. Lightning phenomena are neglected and the electric field is assumed to be curl free. Corona, convection, and precipitation currents are not considered in this initial study and their contribution to the source function is not specified explicitly. As a preliminary test of the model we assume that the storm is axially symmetric in spherical geometry, the conductivity depends only on the vertical coordinate, the ground is equipotential, and far from the thunderstorm region the horizontal electric field is zero. These assumptions are for computational efficiency only and can be relaxed in more realistic studies. The mathematical energy method is applied to the continuity equation to determine boundary conditions that are sufficient to form a well-posed...

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