Modeling variability in dendritic ice crystal backscattering cross sections at millimeter wavelengths using a modified Rayleigh-Gans theory

- Significant variability exists in radar backscattering cross sections of dendrites.
- Source of variability depends upon detailed distribution of mass within dendrites.
- The Rayleigh-Gans theory (RG) captures most of the variability.
- Improving RG by estimating dendrite internal electric field leads to better result.
- Parameters are based on coherence and estimates of internal electric field strength.

Using the Generalized Multi-particle Mie-method (GMM), Botta et al. (in this issue) [7] created a database of backscattering cross sections for 412 different ice crystal dendrites at X-, Ka- and W-band wavelengths for different incident angles. The Rayleigh-Gans theory, which accounts for interference effects but ignores interactions between different parts of an ice crystal, explains much, but not all, of the variability in the database of backscattering cross sections. Differences between it and the GMM range from −3.5 dB to +2.5 dB and are highly dependent on the incident angle. To explain the residual variability a physically intuitive iterative method was developed to estimate the internal electric field within an ice crystal that accounts for interactions between the neighboring regions within it. After modifying the Rayleigh-Gans theory using this estimated internal electric field, the difference between the estimated backscattering cross sections and those from the GMM method decreased to within 0.5 dB for most of the ice crystals. The largest percentage differences occur when the form factor from the Rayleigh-Gans theory is close to zero. Both interference effects and neighbor interactions are sensitive to the morphology of ice crystals. Improvements in ice-microphysical models are necessary to predict or diagnose internal structures within ice crystals to aid in more accurate interpretation of radar returns. Observations of the morphology of ice crystals are, in turn, necessary to guide the development of such ice-microphysical models and to better understand the statistical properties of ice crystal morphologies in different environmental conditions.