Optimum Estimation of Rain Microphysical Parameters From X-Band Dual-Polarization Radar Observables

Abstract

Modern polarimetric weather radars typically provide reflectivity, differential reflectivity, and specific differential phase shift, which are used in algorithms to estimate the parameters of the rain drop size distribution (DSD), the mean drop shape, and rainfall rate. A new method is presented to minimize the parameterization error using the Rayleigh scattering limit relations multiplied with a rational polynomial function of reflectivity-weighted raindrop diameter to approximate the Mie character of scattering. A statistical relation between the shape parameter of the DSD with the median volume diameter of raindrops is derived by exploiting long-term disdrometer observations. On the basis of this relation, new optimal estimators of rain microphysical parameters and rainfall rate are developed for a wide range of rain DSDs and air temperatures using X-band scattering simulations of polarimetric radar observables. Parameterizations of radar specific path attenuation and backscattering phase shift are also developed, which do not depend on this relation. The methodology can, in principle, be applied to other weather radar frequencies. A numerical sensitivity analysis shows that calibration bias and measurement noise in radar measurements are critical factors for the total error in parameters estimation, despite the low parameterization error (less than 5%). However, for the usual errors of radar calibration and measurement noise (of the order of 1 dB, 0.2 dB, and 0.3 deg km(-1) for reflectivity, differential reflectivity, and specific differential propagation phase shift, respectively), the new parameterizations provide a reliable estimation of rain parameters (typically less than 20% error)

Retrieval of the raindrop size distribution from polarimetric radar data using double-moment normalisation

“…Z H , K dp , and Z DR were calculated for these DSDs for the MXPol stacked PPI incidence angles; temperatures of five, 10, and 15 • C; and each of four drop axis ratio functions: those of Andsager et al (1999); Brandes et al (2002); Thurai et al (2007), and that of Beard and Chuang (1987) in the form shown in Kalogiros et al (2013). Unusual records with Z DR or K dp less than or equal to zero (0.16 % of all simulated radar records) were excluded.…”

“…(9), the reflectivity-weighted mean drop axis ratio, r z , is related to a negative power of the differential reflectivity in linear units. In Kalogiros et al (2013), the reflectivity-weighted and mass-weighted drop axis ratios were assumed to be the same and differences were dealt with through fitting of qualitative relationships between radar variables. A similar approach is taken here.…”

“…X-band polarimetric weather radars are popular due to their portability, small size, and high resolution and sensitivity, but measurements at X band suffer from attenuation by heavy rain Kalogiros et al, 2013) and must be corrected (Matrosov et al, 2005;Park et al, 2005a). Several DSD-retrieval algorithms have been developed for X band (e.g.…”

“…Several DSD-retrieval algorithms have been developed for X band (e.g. Park et al, 2005b;Gorgucci et al, 2008;Anagnostou et al, 2013;Kalogiros et al, 2013), including some with integrated attenuation correction (e.g. Testud et al, 2000;Yoshikawa et al, 2014).…”

“…Testud et al, 2000;Yoshikawa et al, 2014). The selfconsistent with optimal parameterization attenuation correction and microphysics estimation (SCOP-ME) algorithm, developed through studies by Anagnostou et al (2009Anagnostou et al ( , 2010 and Kalogiros et al (2013), uses relationships calculated for the Rayleigh limit, corrected for Mie scattering at X band. It performs well compared to contemporary algorithms and disdrometer observations .…”