Variable phase propagation velocity for long-range lightning location   system
  The electromagnetic wave propagation velocity at low radio frequencies is an important input parameter for lightning location systems that use time of arrival (TOA) method. This velocity is normally fixed at or near the speed of light. However, this study finds that the radio waves from two submarine communication transmitters at 20.9 kHz and 23.4 kHz exhibit phase propagation velocities that are $\sim$0.51% slower and $\sim$0.64% faster than the speed of light as a result of sky wave contributions and ground effects. Therefore, a novel technique with a variable phase propagation velocity is implemented for the first time in the TOA method and applied to electric field recordings with a long-baseline lightning location system that consists of four radio receivers in western Europe. The lightning locations inferred from variable velocities improve the accuracy of locations inferred from a fixed velocity by $\sim$0.89-1.06 km when compared to the lightning locations reported by the UK MetOffice. The normal distributions of the observed phase propagation velocities in small geographic areas are not centered at the speed of light. Consequently, representative velocities can be calculated for many small geographic areas to produce a velocity map over central France where numerous lightning discharges occurred. This map reflects the impact of sky waves and ground effects on the calculation of lightning locations as a result of the network configuration. It is concluded that the use of variable phase propagation velocities mitigates the influence of sky waves and ground effects in long-range lightning location networks. 
Zhongjian Liu, Kuang Liang Koh, Andrew Mezentsev, Sven-Erik Enno,   Jacqueline Sugier, and Martin F\"ullekrug
physics.space-ph physics.ao-ph