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, differential propagation, and noise on the spectral functions. Input parameters include radar wavelength, elevation angle, air velocity variance, rainfall rate, propagation distance, fraction of scatterers having a preferred orientation, and relative noise level. Results of calculations for 8.6 mm and 7.5 cm wavelengths 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 noise. However, it appears possible to derive a good estimation 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 radar system 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.