Characterizing Multiband Reflectivity Obtained from Spaceborne Radars Using Nonlinear Dimensionality Reduction with Raindrop Size Distribution Parameters

Kuo et al (2004) have convincingly demonstrated theoretically that, when raindrops are assumed to be (near-)spherical, equivalent radar reflectivity factors (or Z_e) at Ku and Ka bands are mostly functions of the following raindrop size distribution (RSD) parameter: liquid water content (LWC), effective diameter (D_e=2r_e, i.e. twice of effective radius), and effective variance (v_e) in decreasing importance. They find that further details of the RSDs are not reflected in the calculated equivalent radar reflectivity factors. In physics-based rainfall retrievals, the goal is to relate the observe radar responses to raindrop size parameters in order to infer rain rate. Two pieces of observed information, e.g. Z_e at Ku and Ka bands, allow at most the reliable recovery of two RSD parameters. To retrieve all three RSD parameters and more fully resolve the uncertainty caused by v_e, an independent third (3^rd) band is needed. Thus, we investigate radar bands currently available on spaceborne assets, i.e. Ku, Ka, and W, and the functional dependence of their equivalent radar reflectivity factors on LWC, D_e, and v_e by applying nonlinear dimension reduction (NDR) techniques to RSD parameters obtained from 2DVD disdrometers during field campaigns and equivalent radar reflectivity factors calculated using corresponding RSDs. We show that, when ambiguity due to Rayleigh scattering by RSDs with small D_e is removed, relations between tri-band equivalent radar reflectivity factors and RSD parameters can be consistently found, which may then be used as relations for RSD parameter retrieval.

Kuo, K.-S., E. A. Smith, Z. Haddad, E. Im, T. Iguchi, A. Mugnai, 2004: Mathematical-physical framework for retrieval of rain DSD properties from dual-frequency Ku-Ka-band satellite radar. J. Atmos. Sci., 61(19), 2349-2369.