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Normal Mode Analysis of Three-Dimensional Propagation Over a Small-Slope Cosine Shaped Hill

Megan S. Ballard

Applied Research Laboratories, University of Texas at Austin, Austin, Texas 78758, USA

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Benjamin M. Goldsberry

Applied Research Laboratories, University of Texas at Austin, Austin, Texas 78758, USA

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, and

Marcia J. Isakson

Applied Research Laboratories, University of Texas at Austin, Austin, Texas 78758, USA

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https://doi.org/10.1142/S0218396X15500058Cited by:13 (Source: Crossref)

Abstract

Three-dimensional propagation over an infinitely long cosine shaped hill is examined using an approximate normal mode/parabolic equation hybrid model that includes mode coupling in the out-going direction. The slope of the hill is relatively shallow, but it is significant enough to produce both mode-coupling and horizontal refraction effects. In the first part of the paper, the modeling approach is described, and the solution is compared to results obtained with a finite element method to evaluate the accuracy of the solution in light of assumptions made in formulating the model. Then the calculated transmission loss is interpreted in terms of a modal decomposition of the field, and the solution from the hybrid model is compared to adiabatic and N × 2D solutions to assess the relative importance of horizontal refraction and mode-coupling effects. An analysis using a horizontal ray trace is presented to explain differences in the modal interference pattern observed between the 3D and N × 2D solutions. The detailed discussion provides a thorough explanation of the observed 3D propagation effects and demonstrates the usefulness of the approximate normal mode/parabolic equation hybrid model as a tool to understand measured transmission loss in complex environments.

Keywords:

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