(8) T hus, "'a = "'ag + "'a an d in .NET

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(8) T hus, "'a = "'ag + "'a an d
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where "'a an "'e are a sorptIOn and extinction coefficients of the water droplets in cloud or rainfall.
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The brightness temperature for a cloud or rain layer over ocean is illustrated in Fig. 8.2.17. The permittivity of the ocean at this temperature
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Figure 8.2.17 Layer of cloud or rain on top of air layer and ocean surface. (a) Brightness temperature as a function of cloud or rain layer thickness. (b) Scattering effect Tt,. at 94 GHz for (a).
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is taken to be [Saxton and Lane, 1952]
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where f is frequency in GHz and>. is wavelength in cm. The ocean temperature is T2 = 293 K. The cloud layer is assumed to be at a height of 6 km (= ta) above the ocean surface. We examine the brightness temperature at two frequencies, 30 GHz and 94 GHz. For the purpose of illustration, the atmospheric gaseous absorption coefficients K,ag are taken to be 0.023 km- 1 and 0.108 km- 1 at 30 GHz and 94 GHz, respectively. The absorption coefficient K,ag is assumed to be independent of height, although, in reality, K,ag decreases with increasing altitude. The temperature of the air layer Ta is taken to be 293 K. In the absence of scattering, the brightness temperature of the two-layer model is given by
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TBO(3(O) =T{ 1- exp[-(K,~s) + K,ag)t sec 0] }
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r(3(0) exp [-2K,agta sec 0] { 1 - exp [_(K,~s) + K,ag)t sec 0] }
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eXP[-(h;~S) + h;ag)tsecO]
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+ f(3~e) exp[-(K,~S) + K,ag)tsece]
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2.6 Passive Remote Sensing of a Layer of Mie Scatterers
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vertieol polarization (no ,collerin'll)
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vertIcal polarization
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horizontal polorozotion (no scallerino)
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Figure 8.2.18 Brightness temperature as a function of viewing angles. Shown in dotted lines are TBO for vertical and horizontal polarizations. (a) Cloud layer of 1 km over ocean at 94 GHz. (b) Rain layer of 1 km over ocean at 94 GHz.
We first discuss the brightness temperatures as observed from nadir and plotted as a function of thickness as shown in Fig. 8.2.17a. The scattering effect is shown in Fig. 8.2.17b by plotting the change in the brightness temperature compared with the no-scattering case Tb,.{3 = TB(3 - TBO(3' We note that for small thicknesses, scattering induces brightening but at the same time it also blocks the emission from the air layer and the ocean surface. These two effects tend to cancel and result in a relatively small brightening or darkening effect. At 94 GHz, the atmospheric gaseous emission from the air layer is strong. Therefore, the scattering-induced blocking of emission is stronger than the scattering-induced brightening effect. Thus, in Fig. 8.2.17, we observe an overall darkening effect, even at small optical thickness. For large thicknesses, scattering causes darkening for both the cloud emission and the emission from the air and the ocean. These two effects reinforce each other and result in a larger darkening effect as compared with that shown in Fig. 8.2.16. In Fig. 8.2.18, the brightness temperatures are plotted as a function of viewing angle at 94 GHz. The darkening effect is evident at larger angles of
280 270 260
vertical polarization (no scotlerinll)
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Figure 8.2.19 Brightness temperature as a function of viewing angles. Shown in dotted lines are TBO for vertical and horizontal polarizations. Rain layer of 1 km over ocean at 30 GHz.
observation. In Fig. 8.2.19, we plot the brightness temperatures as a function of viewing angle at 30 GHz. At 30 GHz, the atmospheric gaseous emission is lower so that we uncover the stronger polarization dependence due to the emission from the ocean surface. The scatter-induced darkening effect is stronger at larger angles of observation. It is also larger for the vertical polarizations because the emission from the ocean surface onto the cloud layer for this polarization is stronger.