Model of Electric Field Discontinuities Occurred above Thunderclouds

A simple numerical model of the vertical electric field discontinuities triggered by positive lightning discharge, as was observed above thunderstorm clouds by Marshall et al. [1], is presented. Layers of a stratiform cloud are modeled with three thin parallel coaxial uniformly charged disks. Thickness and radii of the disks and the lowest disk altitude were free parameters, whereas remaining disk altitudes and charge densities were calculated. Electrostatic field and field discontinuities along the cloud axis after positive lightning discharge were calculated for disk radii 5, 7 and 10 km, and for the lowest disk altitude 2, 3, 4 and 5 km. It was adopted that before lightning the field magnitudes are equal to -1 kV/m (at 16 km altitude above the cloud) and +10 kV/m (at 1 km altitude under the cloud). Besides it was adopted that at two mostly strengthened points inside the cloud under the middle and the upper disks there is achieved critical field intensity for relativistic runaway electron avalanche in accordance with mechanism of Gurevich, Roussel-Dupre et al. [2] Absolute values of the charge density in the disks were calculated to vary from 0.8 up to 4.5 nC/m³ for disk thickness 500 m. The maximum magnitude of the vertical electric field discontinuity -16.3 kV/m at 16 km altitude was calculated for 10 km radius and 5 km altitude of the lowest disk that is very close to the observed values [1]. Our results have demonstrated that electric field discontinuity above stratiform thundercloud regions of the mesoscale convective systems after intra-cloud or cloud-to-ground positive lightning discharges may be higher than relativistic electron avalanche threshold above 30 km, and higher than ordinary dielectric breakdown threshold above 60 km. These results support the idea that optical atmospheric phenomenon, so called ‘Red Sprites’, may be initiated by dielectric breakdown at 60-80 km altitude and/or runaway electron breakdown [2] at 30-80 km altitude due to above-cloud quasi-static field changes caused by intra-cloud or cloud-to-ground positive lightning discharges.