V.V. Akhiyarov, S.V. Chernavsky

In this work the numerical methods for field strength prediction above terrestrial surface are considered. These methods have replaced the well-known analytical formulas, which were obtained by solving the model diffraction problems for the smooth and spherical earth-s surface, refractive index linear model, etc. Numerical methods are free of such restrictions, and the foundation problem is the realization of efficient computational algorithms. Most often, for the field strength prediction above any terrain profile, the numerical solutions of integral and parabolic equations are used. The integral equations method is the rigorous and for its realization one needs to produce the numerical solution of Fredholm integral equations of the first or second kind. It was shown for wedge diffraction, that in the illuminated region these equations provide the same accuracy, and in the shadow the integral equation of the first kind is preferable. Attenuation factor above the real terrain profile is presented. Parabolic equation method is based on replacing the Helmholtz equation with parabolic equation, which is correct in paraxial approximation. However, when the radio waves propagate above the Earth surface, such assumption is satisfied automatically: the maximum transverse size usually is no more than several kilometers, while the longitudinal distance above the Earth is much greater. The field strength prediction results for spherical earth, linear atmosphere model and tropospheric waveguide are presented. The obtained results correspond with the known analytical solution.