Extending 94-GHz radar retrievals of ice water content beyond the Rayleigh regime

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Description

Ice crystal aggregates are characterized by a mass-dimension power-law having an exponent β of ~2 (β is also known as the fractal dimension). The wide range of possible β values poses a problem when retrieving cloud properties using radar, since β affects the scattering behavior of the particles at radar wavelengths.

The radar backscatter is weighted by the second moment of the particle size distribution (PSD) with respect to mass. When using a 94-GHz radar to retrieve the physical properties of frontal clouds (which have much larger ice particle sizes than cirrus clouds), ice particles with size parameter x considerably greater than 0.3 can often dominate the backscatter signal. Since Rayleigh scattering theory applies to x < 0.3, relationships based on Rayleigh theory that relate the Rayleigh backscatter to cloud properties are no longer valid.

To deal with this problem, we have adapted the work of Westbrook, which uses Rayleigh-Gans (RG) theory for fractal aggregates, to an ice water content-radar reflectivity (IWC-Z_e) relationship derived from Rayleigh scattering theory, thus enabling this relationship to be applied to frontal clouds using 94-GHz radar where pure Rayleigh theory is generally not applicable. The method is valid for PSD having D_avg < 3.3 mm, where D_avg is the mean ice particle size. IWC retrieval uncertainties can be reduced by estimating the PSD slope parameter λ as a function of temperature and by a priori knowledge of ice particle shape. Alternatively, λ can be estimated using a snow growth model initialized by the measured radar reflectivity and temperature near cloud top.

In addition, the commonly employed radar-lidar retrievals of IWC and effective diameter may be improved for frontal cloud conditions by using this approach.

Results from a sensitivity analysis study of IWC and Z_e (effective radar reflectivity) as function of ice microphysical properties using our RG formulation are presented. We find that the ratio Z_e/IWC is highly sensitive to the mean mass-weighted particle diameter (D_m) for D_m less than 0.02 cm, beyond which it behaves more asymptotically, becoming approximately constant for D_m > 0.06 cm. The sensitivity of Z_e/IWC is also studied as functions of β and the mass-dimension power-law pre- factor α. Our findings suggest that Z_e/IWC is more sensitive to a change in α than for β.