Estimating Radar Backscattering Cross Sections of Ice Crystals at Millimeter Wavelengths Using a Modified Rayleigh-Gans Theory

The database developed by Botta et al. (2013, in progress) was subsequently extended to backscattering cross sections and amplitude scattering matrices at forward direction of dendrites, plates and columns with different masses, maximum dimensions and shapes from different incident directions at X-, Ku-, Ka- and W-Band wavelengths for both h and v polarizations. The Rayleigh-Gans theory accounts for interference effects but ignores internal electric field change led by interactions between different parts of an ice crystal. Estimating the backscattering cross sections using the Rayleigh-Gans theory leads to errors that range from -3.5 dB to +2.5 dB for most of the cases in the database and are highly dependent on the incident directions and the polarization states. A modification to the Rayleigh-Gans theory was developed by estimating the internal electric field determined by the interactions between neighboring regions within an ice crystal using a physically intuitive iterative method. This modified Rayleigh-Gans theory reduced the error in estimating the backscattering cross sections to within 0.5 dB for most of the cases. The largest estimation errors occurred when the form factors from the Rayleigh-Gans theory were close to zero. The backscattering cross sections of these ice crystals were usually several orders of magnitude smaller than for other ice crystals with the same mass and size but different shapes and orientations. The errors in the two diagonal elements of the amplitude scattering matrix for forward scattering directions estimated using this modified Rayleigh-Gans theory were mostly within 5%, indicating the possibility of estimating the specific differential phase shift to within about 5% error. For the lower frequencies, i.e. Ku- and X-Bands, the form factor is always large for the crystals in the database. The errors in the backscattering cross sections estimated by the modified Rayleigh-Gans theory for these two wavelengths were always less than 5%. The computation time of this modified Rayleigh-Gans theory was thousands of times smaller than that of the exact method used to build the database. As such, it may have use as a relatively fast and accurate method for modeling radar signals from ice crystals at millimeter wavelengths.