The Nature of D-region Scattering of Vertical Incidence Radio Waves. I. Generalized Statistical Theory of Diversity Effects Between Spaced Receiving Antennas

Abstract

A theoretical basis for studying the nature of ionospherically reflected radio waves is described. The expected statistical properties of the amplitude and phase variations of the radio wave ground pattern sampled at a pair of spaced receiving antennas are derived for general correlation conditions, assuming different models of the angular spectrum of reflected radio waves. The results provide a basis for experimental measurements of the angular spread and coherence ratio of the angular spectrum of reflected waves.

Measuring the Electron Density Roughness of the D‐Region Ionosphere

“…A paper by Bramley (1951), similar to the paper by Briggs et al (1950), summarizes the use of a cross-correlation analysis technique on the reception of radio waves from the ionosphere for two closely spaced aerial antennas, such as two antennas on an airplane, for various conditions, such as whether there is a steady signal present or not. This work was expanded on by Lindner (1975aLindner ( , 1975b, using the partial reflection technique, to understand the angular spread of downcoming reflected waves, the coherence ratio, and the scale/size of reflecting ionospheric irregularities. The work by Wernik et al (1983) used spaced receivers to study turbulent ionospheric irregularities, specifically the mean drift velocity and direction, the characteristic random velocity, the spatial scales of the irregularities, and the orientation of the irregularities.…”

“…The normalization gives a reference for how rough the D‐region is given the wavelength and, in general, the correlation length scale can serve as a proxy for the scale of the perturbation (e.g. Bowles et al, 1963; Bramley, 1951; Lindner, 1975a). In the case of Figure 10, the major axis correlation length scale measured using the NDGPS transmitter is about 8× larger than that measured by the VLF transmitter when normalized by the wavenumber, 3.8× for the minor axis.…”

“…The work done by Spetzler and Sneider (2001a, 2001b) and Spetzler et al (2002) investigated when it was appropriate to use ray theory versus scattering theory based on this ratio, which can be used to provide a sense of scale of roughness. The correlation length scale can be thought of as a proxy for the scale of the perturbation (Bowles et al, 1963) or rather the resulting angular spreading of the signal (Bramley, 1951; Lindner, 1975a). If the primary scattering mechanism is attributed to some number of small irregularities, then the correlation length scale is expected to be smaller than the Fresnel zone (Doviak & Zrnic, 1983).…”

Evidence for viscosity, thermal conduction and diffusion waves in the Earth’s atmosphere (invited)

“…Less direct studies had been performed many years earlier as well. 8,9 Indirect evidence for such specular reflections in the troposphere may, with hindsight, have even been seen as early as 1939. 1,10 It should also be noted, however, that turbulence itself can be anisotropic, and care needs to be taken to differentiate specular reflectors from anisotropic turbulence.…”