surface is smaller than that of the flat surface. That is because the Brewster angle between ground and snow is 50°. The 50°angle in snow corresponds to 35°in air by Snell's law. However, at the higher frequency of 36.5 GHz in Figure 4, volume scattering becomes important and obscures the Brewster-angle effect of the snow-ground interface. At 36.5 GHz, rough-surface brightness temperatures are lower than that of flat surface for both V-polarization and H-polarization.Figures 5 and 6 compare results of flat and rough surfaces as a function of observation angle for the case of larger grain size of diameter equal to 0.6 mm. Volume scattering becomes important at 18.7 GHz. The Brewster-angle effect of the snow-ground interface disappears. The roughness decreases the brightness temperatures.Figures 7 and 8 compare the results of flat and rough surfaces as a function of depth of snow; the grain size is also 0.6 mm. At 18.7 GHz, since the observation angle is 30°(which is less than the Brewster angle of 35°), the brightness temperatures of rough surface is smaller than flat surface for V-polarization.In Figure 8, we see that at 36.5 GHz, saturation occurs at large snow depth. Volume scattering becomes dominant and roughness has a negligible effect.
Brightness-Temperature Variations with Grain Size and Snow DepthFigures 9 and 10 show the angular variations of brightness temperatures for several grain-size diameters. The brightness temperatures decrease with increasing grain size. Emission from the ground is scattered and cannot reach the air region, thus accounting for the decrease in brightness temperatures.Figures 11 and 12 show that, for small grain size, brightness temperatures depend weakly on the thicknesses of the snow layer. For larger grain size, brightness temperatures decrease with snow depth at 18.7 GHz. For 36.5 GHz, saturation effects occur as a function of snow depth.
ACKNOWLEDGMENTSThe research presented in this paper was supported by RGC Central Allocation Grant no. 8730017 of Hong Kong and NASA of the United States. 1. C.M. Lam and A. Ishimaru, Mueller matrix calculation for a slab of random medium with
We show how power dividers can be effectively employed in the design of microwave recursive filters in strict accordance to low frequency principles. We present analytical, computer-simulated and experimental results for an active recursive band pass filter, and for a newly developed tunable recursive active filter, employing a reflection-type microwave phase shifter and implemented on a Durofd substrate in the 2.75-3.75 GHz range.
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