Statistical model for low‐frequency propagation

Abstract

Prediction of LF signal strengths is usually done by using a single “average” model of the ionosphere. However, this approach suffers from the fact that signal strength is a nonlinear function of ionospheric parameters. Hence the “average” ionosphere does not always give the correct average signal strength. In addition, the standard deviation of signal strength varies considerably with position, in general being larger in the vicinity of modal interference nulls. A model where the daytime ionosphere is treated statistically is presented. The propagation model used is an earth ionosphere wave‐guide. The ionospheric electron density profile is specified by a reference height h′ and slope β. These parameters are assumed to be distributed in a jointly normal distribution. Best fit values for this model are obtained using measurements made at two points on either side of a deep modal interference null located about 1000 km from a 59‐kHz transmitter. The measured signal strength mean, and standard deviation were used to obtain a best fit mean, standard deviation and correlation coefficient for the β and h′ distribution. The resulting ionospheric parameters give signal statistics that fit the measured mean and standard deviation at both monitoring points within 1 dB.

Ionospheric model validation at VLF and LF

“…This waveguide model has been detailed in a series of documents which describe the initial model and its subsequent development [Gessard et al, 1966;Pappert et al, 1967Pappert et al, , 1970Sheddy et al, 1968a, b;Pappert and Smith, 1971;Sheckey, 1972, 1974;Merritt and Shellman, 1976;Pappert and Ferguson, 1986;Shellman, 1986;Ferguson and Snyder, 1987;Pappert and Hitney, 1988]. Although the model can use profiles of particle density and collision frequency specified as arbitrary functions of height, in practice, exponential profiles of ionospheric electron conductivity (which is essentially the scaled ratio of electron density to collision frequency) are used with positive ions assumed for charge neutrality [Bickel et al, 1970;Merritt, 1977;Ferguson, 1980;Ferguson et al, 1985;Merritt et al, 1981; In the past we have found data collected aboard in-flight aircraft to be most useful for selecting ionospheric profiles. These data reveal a characteristic pattern of signal interference minima and maxima with distance from the transmitter that provide clues to guide the choice of profile.…”