Comparison Between Incoherent Approach and Coherent Approach in .NET

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Comparison Between Incoherent Approach and Coherent Approach
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In this section, we compare the results between the coherent model and
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the incoherent model. The incoherent model is established on the basis of conservation of energy instead of wave field and was described in Section 1. The transmission and reflection of wave intensity at boundary between layers are considered. Since the wave nature of the fields is neglected, it is an approximate method. We consider the case that the temperature is uniform at 295 K and the permittivity profile is given by
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where d is the thickness and is taken to be 10 cm. The profile from z = 0 to z = -d is discretized into 300 layers. The brightness temperatures as calculated by using coherent and incoherent models are plotted as a function of frequency in Fig. 5.3.1. We see the interference effects in the results of the coherent model, but not in that of the incoherent model. The interference effects decreases as frequency increases, and the results of the two methods approach the same value at high
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5 SCATTERING AND EMISSION BY LAYERED MEDIA
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Figure 5.3.1 Comparison of brightness temperature as a function of frequency between coherent and incoherent models for an abrupt change profile.
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Figure 5.3.2 Comparison of brightness temperature as a function of observation angle between coherent and incoherent models for an abrupt change profile.
3 Incoherent and Coherent Approach
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Figure 5.3.3 Comparison of brightness temperature as a function of observation angle
between coherent and incoherent models for continuous change profile.
frequency. The agreement at high frequency is due to less contribution from reflected waves which have large attenuation at high frequency. We also note that a TE wave shows more interference effects than a TM wave at observation angle of 45 . This is because a TE wave has larger reflectivity than a TM wave. In Fig. 5.3.2, the brightness temperature as a function of observation angle at 1 GHz is plotted. It is shown that the difference in the results by the two methods depends on the observation angle, showing larger differences at higher observation angles. This is because the reflectivity of each boundary approaches unity when the wave is incident at a large angle, particularly for a TE wave. Instead of using the abrupt change at z = -d in the permidivity profile, we next consider the case when the profile is continuous at z = -d. That is, we let Et = E( -d). However, there is still discontinuity in the -derivatives of the profile. The results calculated by the two methods are shown in Fig. 5.3.3. There is less interference compared to the results shown in Fig. 5.3.1, since more gradual change in permittivity creates less reflection. The results by coherent and incoherent models are quite close to each other except for very low frequency. It can be concluded that an incoherent model is a good approximation of the coherent model when the interference cre-
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ated by reflected waves is not important. The validity of incoherent model depends not only on the wave frequency but also on the permittivity profile and the observation angle. In general, it can be used in the cases of gradual change in permittivity profile or at high frequency.
Applications to Passive Remote Sensing of Soil
The study of microwave emission from soils is a practical problem, because it is closely related to the remote sensing of soil moisture. The thermal emission from soil is sensitive to the moisture content of soil, but less sensitive to the cloud cover and surface vegetation in the microwave frequency range, especially at longer wavelengths. This gives microwave remote sensing a favorable position compared to other techniques for soil moisture sensing from space. Soil is a mixture of dry soil and water. Dry soil is usually composed of sand, silt, and clay at various percentages for different kinds of soil. The dielectric constant of the soil-water mixture can be obtained by direct measurement or by using an empirical formula with parameters determined by experiment. There are several mixing formulas for soil-water mixture [Wang and Schmugge, 1980]. One of the commonly used formula is given as follows: