Knowledge of the refractive index profile at radio frequencies in the surface layer of the atmosphere is required to predict the performance of terrestrial radio systems, and although a constant gradient of refractivity with height is often assumed, both measurements and theory suggest that gradients in the lowest 20 m of the atmosphere may often be greater than those above this level. For the special case of evaporation ducts over water in a neutral atmosphere, a logarithmic refractivity profile is normally assumed, but a general model that includes both this case and the linear profile as special cases is proposed, which may also be used to approximately model stable and unstable surface atmospheres. This new model may be particularly suited to predicting sub-refractive fading.
Reliable information about the cumulative distribution of surface refractivity gradient is often required in the design of radio systems. Strong negative gradients, or super-refraction, may lead to interference between terrestrial stations, both terrestrial links and satellite earth stations. Predicted positive or sub-refractive gradients are taken into account in determining the minimum antenna heights, to ensure terrestrial links achieve their required availability. This paper reviews sources of refractivity gradient data, and considers how refractivity gradient at a point may relate to an effective value over a terrestrial path.
Modelling of point-to-point radio propagation over terrain is of interest in the design of radio systems working over obstructed radio paths, or which may be subject to sub-refractive fading, or in estimating the visibility of radar targets close to terrain. Practical implementation of Fourier split-step PEM to provide accurate prediction of field-strength deep into the terrain diffraction region, over a wide frequency range, faces significant challenges. At high frequencies a large transform size is required, and at low frequencies the artificial upper boundary must be sufficiently high and the absorber layer sufficiently thick, to prevent spurious reflections from the upper boundary interfering with the weak terrain diffracted field. An adaptation to the PE method is described, and tested for the canonical problems of wedge and smooth-Earth diffraction over the frequency range of 10 MHz to 100 GHz, and compared with path measurements from 150 MHz to 1.5 GHz.
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