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Figure 8.2.7 Brightness temperature for vertical polarization as a function of observation angle for Elm. = 1.8(1 + iO.0005)E o , frequency = 10 GHz, lz = 2 mm, T = 300 K, and 6 = 0.002.
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where f3 = v, h and = 2k~m' In the following, we illustrate brightness temperature of a layer of random medium overlying a homogeneous dielectric half-space (Fig. 8.2.6). In Fig. 8.2.7, the vertically polarized brightness temperature for a half-space random medium as a function of viewing angle is plotted for different lp values. We note that as lp increases, the brightness temperature decreases because the albedo increases with lp and scattering induces darkening for a half-space medium. We also note that for small lp, scattering is diffuse while for lp = 00, results reduce to that of laminar structure where there is coupling only between the specularly related upward and downward directions. This is evident from Fig. 8.2.7, because the brightness temperature for medium with the large lp exhibits stronger angular dependence. In Fig. 8.2.8, the brightness temperature as a function of frequency is illustrated for a half-space random medium. We note that there is a broad minimum caused by resonant scattering analogous to the case of the laminar structure of Section 2.1. The minimum cannot be uncovered by Rayleigh approximations or point scatterers. In Fig. 8.2.9, we plot the brightness temperature for a two-layer medium as a function of frequency. The presence of a subsurface boundary introduces
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Frequency (GHz)
Figure 8.2.8 Brightness temperature as a function of frequency for Elm = 1.8(I+iO.0005)E o , lz = 2 mm, T = 300 K, 6 = 0.002, and observation at nadir.
260 ,--.--,---,----,-.---.--,--,----,-.---.---,--,r----r-..--, 250 240 \
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Frequency (GHz)
Figure 8.2.9 Brightness temperature as a function of frequency for Elm = 3.2(1 +iO.0009)E o , lz = 1 mm, lp = 2 em, T = 273 K, 6 = 0.02, and a subsurface layer at the depth of 2 m with permittivity 1"2 = 77.2(1 + iO.17)E o .
a maximum at the low-frequency side. At very low frequencies, the received emission at the radiometer originates primarily from the subsurface dielectric E2 which has a small emissivity. As frequency increases, brightness temperature increases since the medium Elm, which has a higher emissivity, begins to contribute to the received emission. As frequency further increases, scattering becomes dominant and causes a decrease in brightness temperature. This accounts for the maximum in brightness temperature in the figure.
2.6 Passive Remote Sensing of a Layer of Mie Scatterers Overly-
ing a Dielectric Half-Space
For the case of Mie scatterers, the coupling coefficients (v(0), v(0')), (v(0), h(O')), (h(O), v(O')), and (h(O), h(O')) are given by [Tsang et al. 1985]
(v(O), v (0')) =
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2.6 Passive Remote Sensing of a Layer of Mie Scatterers
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Frequency (GHz)
Figure 8.2.10 Brightness temperatures as a function of frequency for q = 3(1 +iO.0053)E o , f s = 8.3 0' a = 5mm, f = 0.03, and T = 300K. The results are compared for two different sphere sizes.
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