  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.
