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Terrain and Sea Surface Truth: Profile Distributions

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The surface truth of particular interest in this paper is the surface profile distributions of height, slope, and base random variables averaged over the same or similar ensemble of paths above a terrain or sea surface from which coherent and incoherent scatter measurements are averaged. One theoretical scattering model, in which the surface height is assumed to be exponentially distributed, was recently shown in ESD-TR-81-147 to be superior to other height distributions and to be at least as good as the Longley-Rice semi-empirical model in fitting three sets of measurement data for microwave and acoustical coherent forward scatter from smooth and moderately rough surfaces. The question arises as to how well the assumed exponential distribution agrees with the actual distribution of surface heights. This paper reviews the empirical data of surface profile distributions reported in the literature and particularly those associated with the above three sets of scattering data. Surface profile distribution data was found to be sparce and inconclusive. A surface profile data base and additional methods for hypothesizing theoretical fits to the data base need to be developed. Existing digital elevation maps of the U.S. Geological Survey offer a particularly promising data base with sufficient accuracy for determining height, slope, and base distributions of terrain profiles. In the absence of surface truth or scattering data to the contrary and for situations in which surface shadowing and multiple scattering are neglibible, an exponential distribution is recommended for the probability density function of the height random variable in statistical scattering models.

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  • Physical and Dynamic Oceanography

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