Methods for evaluating the effects of conduits at the surface of the sea
Abstract
The propagation of radio waves in the atmosphere is determined by the index of refraction which is sensitive to the pressure, temperature and moisture of the air. In the vicinity of the surface of the sea, there is a strong gradient of moisture related to the evaporation of water; it gives rise to a fast decrease of the index of the air creating a conduit of propagation in vicinity of surface. A source located in the interior of the conduit (i.e., at an altitude ranging between that of the minimum of the modified index and sea surface) sees most of its energy remaining captive inside this conduit. This has as an operational consequence  a considerable increase in the range of the radio hardware working in the vicinity of the surface of the sea. In addition, the propagation inside the conduit is characterized by the presence of multipaths related to the successive reflection of the electromagnetic wave on the surface of the sea and the boundary of the conduit. What results is a series of reinforcements and attenuations of the field being propagated in the conduit. Taking into account the practical importance of these effects it is advisable to have suitable methods of evaluation. In this talk three methods are examined: (1) parabolic equation method, (2) method of modes, and (3) method of geometrical optics. The parabolic equation method consists of making an approximation of the wave equation by supposing that the field is propagated around a primary direction. Under these conditions one reduces the equation of propagation to a partial derivative equation of parabolic type which leads to an easy algorithm to work with. The method of modes makes it possible to carry out calculations in an entirely analytical way by supposing that the profile of the index follows a simple law. This method constitutes an analytical reference with respect to the two other methods which are numerical. The method of geometric optics is an asymptotic method. It consists of considering the trajectory of the rays resulting from the source by solving the eikonal equation. The intensity of the electromagnetic field can be given in conjunction with the equation of the trajectories; the calculation of the divergence of the wave vector tangent to the ray passing by the point where the field is evaluated. One thus obtains a system of ordinary differential equations which can be solved numerically by the method of RungeKutta. Each one of these methods is analyzed and a comparison between them is carried out on a number of concrete examples. In each case the theoretical limits, the advantages, and the limits of use of the three methods are highlighted.
 Publication:

In AGARD
 Pub Date:
 July 1994
 Bibcode:
 1994mmpp.agarQ....F
 Keywords:

 Atmospheric Effects;
 Atmospheric Moisture;
 Ocean Surface;
 Propagation Modes;
 Radio Transmission;
 Transmission Efficiency;
 Algorithms;
 Geometrical Optics;
 Parabolic Differential Equations;
 Refractivity;
 Wave Equations;
 Communications and Radar