Effect of self-absorption on attenuation of lightning and transmitter signals in the lower ionosphere

The attenuation of VLF signals from lightning and ground-based VLF transmitters during transionospheric propagation has been the subject of recent interest, as discrepancies have been found between satellite data and model calculations. Previous modeling efforts, however, have not considered the self-absorption effect due to nonlinear heating and ionization in the lower ionosphere. A self-consistent model of ionospheric heating is presented here using a time-domain model of VLF wave propagation through the ionosphere. The model is able to estimate the attenuation of signals due to heating below ∼100 km altitude. In this model, the ionospheric state is updated as the fields propagate, leading to changes in collision frequency and electron density, which in turn affect the wave propagation. We use this model for ground-based VLF transmitters at different frequencies, amplitudes, and latitudes (i.e., magnetic dip angle), and for lightning-generated sferics with different amplitudes, at different latitudes, and using a variety of ionospheric density profiles. We find that the inclusion of self-consistent heating causes a change in the transionospherically propagating wave amplitude that varies considerably with the source amplitude and other parameters. Typical values for the heating contribution to wave attenuation are 1−2 dB for VLF transmitters, but greater than 10 dB for large amplitude lightning discharges. An interesting effect is observed for VLF transmitters and low-amplitude lightning, where the signal is actually enhanced due to heating, rather than attenuated, in the direction propagating across the Earth’s magnetic field.