Estimating ice particle scattering properties using a modified Rayleigh‐Gans approximation

Abstract

A modification to the Rayleigh-Gans approximation is made that includes self-interactions between different parts of an ice crystal, which both improves the accuracy of the Rayleigh-Gans approximation and extends its applicability to polarization-dependent parameters. This modified Rayleigh-Gans approximation is both efficient and reasonably accurate for particles with at least one dimension much smaller than the wavelength (e.g., dendrites at millimeter or longer wavelengths) or particles with sparse structures (e.g., low-density aggregates). Relative to the Generalized Multiparticle Mie method, backscattering reflectivities at horizontal transmit and receive polarization (HH) (Z HH ) computed with this modified Rayleigh-Gans approach are about 3 dB more accurate than with the traditional Rayleigh-Gans approximation. For realistic particle size distributions and pristine ice crystals the modified Rayleigh-Gans approach agrees with the Generalized Multiparticle Mie method to within 0.5 dB for Z HH whereas for the polarimetric radar observables differential reflectivity (Z DR ) and specific differential phase (K DP ) agreement is generally within 0.7 dB and 13%, respectively. Compared to the A-DDA code, the modified Rayleigh-Gans approximation is several to tens of times faster if scattering properties for different incident angles and particle orientations are calculated. These accuracies and computational efficiencies are sufficient to make this modified Rayleigh-Gans approach a viable alternative to the Rayleigh-Gans approximation in some applications such as millimeter to centimeter wavelength radars and to other methods that assume simpler, less accurate shapes for ice crystals. This method should not be used on materials with dielectric properties much different from ice and on compact particles much larger than the wavelength.

An accurate and computationally cheap microwave scattering method for ice aggregates: the Independent Monomer Approximation

“…It is clear that when the number of monomers in the aggregates is increased, the IMA bias in σ s remains very small, showing errors within 5%. This is comparable to the results of Lu et al (2014) who state that their modified RGA method provides improvements to RGA for dendrites and low density aggregates. Here we find that the results for aggregates of plates and columns show larger errors overall.…”

“…Tyynelä et al (2013)), but the absence of polarimetric information limits the usefulness of the method for understanding radar observables. Lu et al (2013Lu et al ( , 2014 developed the "modified RGA" method and used it to compute scattering by pristine ice crystals with dendritic, plate-like, and columnar habits, along with low-density aggregates. The method is based on extending RGA by including near-neighbour dipole interactions within a limited range of a given point.…”

Calculating the millimetre‐wave scattering phase function of snowflakes using the self‐similar Rayleigh–Gans Approximation

“…Another interesting avenue would be to extend SSRGA to represent second‐order scattering effects using an approach such as mean‐field theory (Berry and Percival, ) or a more explicit method (e.g. Acquista, ; Lu et al , ).…”

A polarimetric scattering database for non-spherical ice particles at microwave wavelengths

“…A total of 44 realizations of plates are now included in the database. Representations of branched planar crystals and plates for GMM calculations were as three layers of tiny spheres closely packed in the face-centered cubic lattice (FCC), which achieves a maximum packing factor of 74 % for an infinite lattice Lu et al, 2013Lu et al, , 2014b. Thus the radius of the tiny spheres was determined by the thickness of the planar ice crystals.…”