A numerical model was developed to simulate the power spectra, cross-spectrum, and derived functions obtainable from a coherent polarization-diversity radar. The model was used to investigate the effects of air velocity variance, radar system noise, and differential propagation on the spectral functions. Input parameters include radar elevation angle, air velocity variance, rainfall rate, propagation distance, relative receiver noise level, and the fraction of scatterers having a preferred orientation. Results of calculations of 8.6-mm wavelength backscatter are illustrated. These are compared with the functional forms obtained from theory and discussed in terms of the meteorological information derivable from them. The forms of the spectral power ratio and the cross-spectral amplitude ratio are strongly affected by air velocity variance and by receiver noise. However, it appears possible to derive a good estimate of the Doppler air velocity from the power spectra. The cross-spectral amplitude ratio may be of more general value in analysis than previously thought, because its Doppler velocity domain is greater than that of the spectral power ratio in the presence of receiver noise. The absolute error of the propagation term estimated from the cross-spectral amplitude ratio is not strongly dependent on the rainfall rate or propagation distance. However, it may be difficult to extract detailed quantitative backscatter information when significant propagation effects are present.
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