A Simple Model of the Millimeter-Wave Scattering Parameters of Randomly Oriented Aggregates of Finite Cylindrical Ice Hydrometeors

Spaceborne millimeter-wave radiometric measurements offer the potential to observe snowfall at high latitudes. A spaceborne W-band cloud radar on CloudSat has been able to observe snow. There is thus a need for a relatively simple representation of millimeter-wave scattering parameters of snow that can be incorporated into algorithms to retrieve snowfall from remotely sensed millimeter-wave brightness temperature measurements and for computing the millimeter-wave backscatter phase function of randomly oriented aggregates of ice prisms or columns. The extinction coefficients, asymmetry factors, and backscatter phase functions describing scattering by randomly oriented aggregates of elongated cylinders were computed from the discrete dipole approximation. These parameters were also computed by means of a T-matrix model applied to single blunt cylinders by employing a phase delay that only depended on the frequency and the ratio of the volume to the projected area of the cylindrical aggregates. These scattering parameters were fitted by empirical analytical functions that only depended on that phase delay. This permitted consideration of numerous aggregate shapes with far less computational effort than that required by the discrete dipole approximation. The results of this analysis were applied to measurements of millimeter-wave extinction, radar reflectivity, and snow size distributions obtained during the SNOW-TWO field experiment conducted by the U.S. Army in 1984. Although the simultaneity of the various measurements was not well documented, the theoretical results fell within the range of measurement uncertainty. Model results of the extinction coefficient and asymmetry factor needed to compute 183-GHz brightness temperatures measured by the NOAA Advanced Microwave Sounding Unit-B (AMSU-B) radiometers are presented in the appendix.