Overcoming discontinuity in retrieved rainfall profiles by approximating reflectivity profiles with polynomials

In the classical methodology of rainfall retrieval where rain rates and/or drop-size-distribution (DSD) parameters are retrieved range-gate by range-gate the resultant profiles are almost always noisy and non-differentiable. Spurious noises in derived quantities, such as latent heating, that depend on the derivatives of these profiles are thus further magnified. We develop a new retrieval framework in which these profiles are represented and retrieved as polynomials of distance and are therefore smooth and differentiable. We present here the methodology in the context of spaceborne radar rainfall retrieval.

For liquid precipitation Kuo et al. (2004) found that 1) both the effective reflectivity factor and the specific attenuation at a reference liquid water content (LWC), can be adequately parameterized by polynomials in effective radiusand effective variance (or, equivalently, mass-averaged diameter and shape factor) and 2) once effective radius and effective variance are fixed both effective reflectivity factor and specific attenuation scale linearly with LWC. If one assumes that the vertical profiles of LWC (normalized by the reference LWC), effective radius, and effective variance are expressible as polynomials in height the simulated reflectivity profile can also be expressed as a polynomial in height. Observed reflectivity profiles may then be decomposed into polynomials in height. By matching coefficients of the terms in the polynomials between the observed profile and those of the simulated profile a smooth rain and/or DSD profile may thus be retrieved.