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Theoretical description of the parabolic approximation/Fourier split‐step method of representing electromagnetic propagation in the troposphere
Author(s) -
Kuttler James R.,
Dockery G. Daniel
Publication year - 1991
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/91rs00109
Subject(s) - helmholtz equation , fourier transform , mathematical analysis , wave equation , scalar (mathematics) , troposphere , wave propagation , parabolic partial differential equation , electromagnetic wave equation , mathematics , computation , boundary value problem , partial differential equation , physics , geometry , algorithm , optics , electromagnetic field , meteorology , quantum mechanics , optical field
A theoretical foundation for the use of the parabolic wave equation/Fourier split‐step method for modeling electromagnetic tropospheric propagation is presented. New procedures are used to derive a scalar Helmholtz equation and to subsequently transform to a rectangular coordinate system without requiring approximations. The assumptions associated with reducing the resulting exact Helmholtz equation to the parabolic wave equation that is used for computations are then described. A similar discussion of the error sources associated with the Fourier split‐step solution technique is provided as well. These discussions provide an important indication of the applicability of the parabolic equation/split‐step method to electromagnetic tropospheric propagation problems. A rigorous method of incorporating an impedance boundary at the Earth's surface in the split‐step algorithm is also presented for the first time. Finally, a few example calculations which demonstrate agreement with other propagation models are provided.