Modeling electromagnetic wave propagation in the troposphere using the parabolic equation

Brief review on PE method application to propagation channel modeling in sea environment

“…Both verification and validation refer to different inhomogeneous environments and a broad range of frequencies and propagation scenarios. A quite good agreement between the simulation results obtained with wide-angle SSF PE and GTD (Geometrical Theory of Diffraction) for propagation in standard troposphere over irregular terrain is reported in Barrios [45]; an excellent agreement is found in Dockery [67] comparing the PE and the rigorous normal-mode method for surface duct conditions; a favorable comparison for surface duct over a rough surface (with Miller-Brown RRF) between the SSF PE solution and normal-mode based solution is reported in Dockery and Kuttler [69]. A recent work, Apaydin and Sevgi [65], reports canonical test cases and systematic comparisons between the SSF-based and FE-based solutions to PE (1) as well as calibration of both solutions against analytically exact solutions.…”

“…During the last two decades the numerical implementation of the PE solutions has been repeatedly verified through comparisons to other propagation models [33,34,45,65,67,69]. The adequacy of the PE method in modeling the radio wave propagation has been also extensively validated by means of comparisons to measured data [27,31,32,[89][90][91][92][93].…”

“…Also, (7) requires knowledge of the field above and below = 0. For smooth, perfectly conducting earth/sea surface, the boundary conditions for horizontal polarization and vertical polarization are satisfied if U( ) is odd or even, respectively, about = 0; in Dockery [67] this symmetry has been extended to impedance-type boundary condition for smooth finitely conducting surfaces. The symmetry means that only the field for ≥ 0 is to be considered in the real calculations.…”

“…The start of the computation procedure for the PE requires knowledge of the initial field U(0 ). It is obtained using the relation between the far-field antenna pattern F(p), which is normally a known function, and the aperture field distribution A( ): F ( ) and A( ) form a Fourier transform pair [33,45,67] (see also [38] and [87] for the 3D case). The application of the boundary condition for perfectly conducting surface and image theory allow expressing U(0 ) through A( − ) and A * ( + ), where is the antenna height and the asterisk denotes the complex conjugate.…”

Coastal effects on radar propagation in atmospheric ducting conditions

“…The internal propagation model for AREPS is a hybrid called the Advanced Propagation Model, which solves a parabolic approximation to the wave equation through use of split-step Fourier transforms (Dockery 1988). Factors such as range-dependent refractivity environments, variable terrain, range-varying dielectric ground constants for finite conductivity and vertical polarization calculations, troposcatter and gaseous absorption are taken into account in this model.…”