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Geophysical media are very often mixtures of different types of particles which can be characterized by many parameters. They can be described by their physical parameters, such as size, concentration or fractional volume, shape, and orientation. They also can be described by the dielectric property which determines the wave | Scattering of Electromagnetic Waves Theories and Applications Leung Tsang Jin Au Kong Kung-Hau Ding Copyright 2000 John Wiley Sons Inc. ISBNs 0-471-38799-1 Hardback 0-471-22428-6 Electronic Chapter 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES 1 Ice 168 2 Snow 170 3 Vegetation 171 4 Atmosphere 172 5 Correlation Function and Pair Distribution Function 173 5.1 Correlation Function 174 5.2 Pair Distribution Function 176 6 Gaussian Rough Surface and Spectral Density 179 7 Soil and Rocky Surfaces 184 8 Ocean Surface 185 References and Additional Readings 195 - 167 - 168 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES Geophysical media are very often mixtures of different types of particles which can be characterized by many parameters. They can be described by their physical parameters such as size concentration or fractional volume shape and orientation. They also can be described by the dielectric property which determines the wave propagation velocity and loss in the medium. The presence of a rough surface is ubiquitous as wave propagation in geophysical terrain such as the ocean-atmosphere interface and the soil surface within a vegetation canopy. The physical characteristics of a random rough surface is generally described by its statistical properties like the height distribution function and height correlation function. The dielectric properties of the two different media will determine the reflectance and absorption of the interface. Because of the applications of microwave remote sensing to earth terrain extensive theoretical and experimental studies have been made on the characterization of earth terrain physical parameters and their dielectric properties at microwave frequencies Ulaby et al. 1982 1986 Tsang et al. 1985 Fung 1994 . Along with these studies a variety of theoretical terrain models have been derived. As we know a terrain model is an abstraction from the often very complex geophysical media. For example a layered medium .