Ocean Surface in .NET

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8 Ocean Surface
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show differences for soils with different textures. These differences persist whether the moisture content is determined in percent by dry weight or by volume basis. Because of irrigation, the surfaces of the soils are generally not flat. The surfaces can be classified as smooth, medium rough, and rough [Newton, 1976; Newton et al. 1982]. The surface can also have row structures [Wang et al. 1980]. Thus, study of scattering by periodic surfaces and random rough surfaces are important problems in microwave remote sensing of soils.
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Ocean Surface
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The ocean surface consists of irregularly spatial and temporal variations as a result of extremely complex local and non-local interactions [Phillips, 1977]. Ocean waves can exist over a range of scales, from swell to capillary waves. Interactions between different scales of roughness, the presence of non-locally generated waves which propagate into the region of observation, and the forces of wind stress and surface tension combine to make ocean surfaces difficult to characterize. Ocean wave spectra provide some general information about the ocean surfaces, and they are important in understanding how ocean waves interact with electromagnetic waves for practical remote sensing applications, such as the detection of wind speed and direction over the ocean surface using electromagnetic sensors. An ocean directional spectrum may be viewed as the distribution of ocean wave energy density with respect to frequency and direction. Measurements of ocean spectra are pursued basically in two methods: (1) direct measurements through the use of wave height recording buoys within the ocean wave field or in indoor wave tanks [Wetzel, 1990] and (2) remote measurements based on the photogrammetric or optical techniques and radiowave backscatter techniques. The direct measurements usually record time series of sea surface displacements, which can be processed to provide a temporal frequency spectrum W (w) of the ocean. The temporal frequency spectrum can be converted to a spatial frequency, or wavenumber, spectrum W(k) by making use of a particular dispersion relation between wand k for ocean waves. The wavenumber spectrum is a function of two components of the surface wave vector k, kx and ky in cartesian coordinates, or k and in polar coordinates. Another convenient assumption is made of the separation of wavenumber and directional spectra such that
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W(k, )
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where W represents the spectrum amplitude, k =
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tan- (ky/k x ).
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4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES
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If the wind direction is chosen to be in the x-direction, then is also the azimuthal angle relative to the wind. Thus, with this assumption, the effects on amplitude and direction may be looked at separately. A number of analytical representations for ocean spectra have been proposed, based either on ocean or wave tank measurements or on empirical fits to radar backscatter data through the composite rough surface scattering model [Valenzuela, 1978; Wetzel, 1990; Apel, 1994]. A brief description of several commonly used ocean spectral models available in the literature follows. It is common practice to truncate (bandlimit) the spectrum between kdl and k du ' Given the bandlimited spectrum between k d and k u , the rms height and rms slope can be calculated:
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The rms slope squared, s~, in the x direction is
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while the rms slope squared in the y direction is
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fa27r d k 2 cos 2 W(k, )
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dk k
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(4.8.4)
(4.8.5)
Power Law Spectrum
The power law ocean spectrum is an isotropic wavenumber spectrum given by [Valenzuela, 1978; Wetzel, 1990]
W(k, ) = aok- 4
(4.8.6)
where ao is known as the spectral constant. The k- dependence for the ocean spectrum has been proposed based on purely physical requirements [Apel, 1994]. Because of the singularity at k = 0, the power law spectrum is only valid for a specified portion of the ocean wavenumber given by k dl ::; k ::; kdu' Although variations with wind speed and azimuth angle are not included in this simplified model, measured ocean spectra are well-fitted qualitatively by a truncated k- 4 spectrum near the Bragg scattering portion for microwave frequencies.