Empirical modeling of nighttime easterly and westerly VLF propagation in the Earth-ionosphere waveguide

It has been known for many years that easterly and westerly propagation of VLF in the Earth-ionosphere waveguide is nonreciprocal with the mean attenuation rate to the west being greater than to the east for ground to ground transmissions. It is also true that nighttime propagation to the west is more difficult to accurately predict than is propagation to the east. For example, a simple exponential β = 0.5 km^–1, h’ = 87 km (notation of Wait and Spies (1964)) profile does an excellent job of predicting nocturnal in-flight measurements over the Hawaii-San Diego path but does not accurately predict nighttime propagation over the Hawaii-Wake path. This is partly because propagation to the west is less stable than propagation to the east. In this study, full wave solutions will be used to show that propagation to the west is more sensitive to upper levels of the ionosphere than is propagation to the east. It therefore seems reasonable that propagation to the west is more sensitive to variable regions of the ionosphere than is propagation to the east and that this, at least in part, is responsible for the difficulty of accurately predicting westerly propagation. Comparisons are made between calculations based on empirical electron density profiles and in-flight measurements between Hawaii and San Diego, and Hawaii and Wake.