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For both lossless and lossy media, the emissivity is given by The theoretical results are illustrated for a sinusoidal surface in Figs. 3.2.3, 3.2.4, and 3.2.5 at a frequency of 1.4 GHz. The effect of the row structure on the microwave emission from a bare agricultural field has been reported [Wang et al. 1980] together with the soil moisture contents for the measured data. The periodic surface has a height h = 10 cm and a period P = 95 cm and can be approximated by a sinusoidal function. For the upper medium, we let E = Eo and /-L = /-La. In Fig. 3.2.3 we illustrate the comparison between the theoretical results and the experimental data for both the vertical and horizontal polarizations when the radiometer observation angle is along the row direction ( = 90 ). The reported soil moisture content varies from 26% by dry weight at top o to 1 cm to 21.4% at 9 to 15 cm. In the theoretical results, we take E1 = (5.5 + i1.2)E o which corresponds to a soil moisture content of approximately 18%. In the same figure, we also show the theoretical curves for the fiat surface case. It is seen that the brightness temperature for the periodic rough
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2.3 Emis&ivity and Comparison with Experiments
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Figure 3.2.3 Brightness temperature as a function of viewing angle. Radiometer observation plane is parallel to the row direction ( = 90 ). q = (5.5 + i1.2)E o
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surfaces for the horizontal polarization is higher than that for the fiat surface, whereas for the vertical polarization the brightness temperature is lower. For the fiat surface, both polarizations have the same brightness temperature value when viewed from nadir, whereas for the periodic surface, the values for the horizontal polarization are higher than the vertical polarization at near-nadir angles and become lower at larger angles of observation. In Fig. 3.2.4, the radiometer observation angles are perpendicular to the row direction ( = 0 ). The soil moisture content is 29% by dry weight at the top 0 to 5 cm and becomes drier with depth. We use El = (10 + i2)E o . We see that at near-nadir angles, as compared with the fiat surface cases, the brightness temperatures for the horizontal polarization are lower and for the vertical polarization are higher. The effect of the rough surface as compared with the fiat surface appears to bring both the horizontal and vertical polarization results closer together at higher incident angles. The case of observation plane at = 30 is illustrated in Fig. 3.2.5. In Figs. 3.2.3, 3.2.4, and 3.2.5, we observe that the TB curves for the periodic rough surface are not smoothly varying. For instance, in Fig. 3.2.4, there are kinks appearing at observation angles near 6 , 19 , 34 , and 51 0. The corresponding change in TB may be as high as 10 K. Such a phenomenon can be explained by the appearance and disappearance of Floquet modes at various threshold angles. The kinks are caused by the redistribution of the
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3 SCATTERING AND EMISSION BY A PERIODIC ROUGH SURFACE
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3 Integral Equation Approach
scattered power during the course of the disappearance and appearance of the propagating Floquet modes. For real soil surfaces, such kinks will not appear because real soil surfaces are not periodic. They have randomness superimposed on the periodic structure.