Sensitivity of Dual-Frequency Rain DSD Retrieval to Particles in Melting Layer for Space-borne Radars

Many dual-frequency DSD retrieval algorithms have been proposed for space-borne radars. A self-consistent backward iterative algorithm, based on non-Rayleigh scattering has been studied recently[1][2][3]. This algorithm is based on a certain DSD model of rain, for which the attenuation caused by the ice or mixed-phase particles should be extracted accurately. Any error in the attenuation correction at one of the two frequencies would affect the accuracy of the DSD retrievals for rain region. This paper examines how the DSD retrieval for rain is affected by the reflectivity correction for attenuation due to the ice or mixed-phase particles in bright band. First, a non-coalescence and non-break up (N-N) model, with an adjustable thickness and the DSD at the bottom of the melting layer is used to generated the reflectivity and specific attenuation profiles. The profiles for varying DSD (N_w from 1000 to 8000, D₀ from 1.0 mm to 1.75 mm) are used to derive the alpha and beta coefficients for k- Z relationships for different heights, for a certain thickness of the bright band. Then the k-Z relationships are incorporated in Hitschfeld-Bordan method to evaluate the two way attenuation at the two frequencies. Last, the reflectivities in rain region, considered of the attenuation correction error, are made of use of by the self-consistent backward iterative algorithm [2] to retrieve the DSD. The simulation shows that the accuracy of the attenuation correction for Ka-band, the higher frequency, is crucial for the dual-frequency iterative algorithm to correctly retrieve the DSD. While the attenuation correction error at Ku-band remain negligiblely small, the error at Ka-band could be as large as 0.47 dB, and this error would have been too large for backward iterative method to correctly retrieve the DSD. The method presented in his paper can be used to evaluate any rain DSD retrieval algorithms proposed for GPM.