Polarimetric radar observations above the melting layer in winter storms reveal enhanced differential reflectivity ZDR and specific differential phase shift KDP, collocated with reduced copolar correlation coefficient ρhv; these signatures often appear as isolated “pockets.” High-resolution RHIs and vertical profiles of polarimetric variables were analyzed for a winter storm that occurred in Oklahoma on 27 January 2009, observed with the polarimetric Weather Surveillance Radar-1988 Doppler (WSR-88D) in Norman. The ZDR maximum and ρhv minimum are located within the temperature range between −10° and −15°C, whereas the KDP maximum is located just below the ZDR maximum. These signatures are coincident with reflectivity factor ZH that increases toward the ground. A simple kinematical, one-dimensional, two-moment bulk microphysical model is developed and coupled with electromagnetic scattering calculations to explain the nature of the observed polarimetric signature. The microphysics model includes nucleation, deposition, and aggregation and considers only ice-phase hydrometeors. Vertical profiles of the polarimetric radar variables (ZH, ZDR, KDP, and ρhv) were calculated using the output from the microphysical model. The base model run reproduces the general profile and magnitude of the observed ZH and ρhv and the correct shape (but not magnitude) of ZDR and KDP. Several sensitivity experiments were conducted to determine if the modeled signatures of all variables can match the observed ones. The model was incapable of matching both the observed magnitude and shape of all polarimetric variables, however. This implies that some processes not included in the model (such as secondary ice generation) are important in producing the signature.

Existing formulations assume that the correlation lengths of refractive index irregularities, generated by turbulence, are small in comparison to the Fresnel length. However, there is experimental evidence that the contrary may be true. This paper extends the existing formulations for the case where the Fresnel zone radius is comparable to or smaller than the correlation length and develops a statistical solution that embraces several echoing mechanisms. Conditions are specified under which Fraunhofer and Fresnel reflection and scatter from turbulent air can be distinguished. An integral expression for echo power is developed which shows that echo intensity depends not only on a resolution volume weighting function, but also on a more important Fresnel term. The spectral sampling function demonstrates that for resolution volumes in the antenna's far field this function is independent of the location of the resolution volume. The conditions under which the echo power is proportional to the square of the pulse width are based upon the statistical approach herein adopted for Fresnel scattering.

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We present a theoretical study of the bias in the copolar correlation coefficient (ρ hv ) caused by cross-polar radiation patterns and by unmatched horizontal and vertical copolar radiation patterns. The analysis of the bias induced by crosspolarization radiation is carried out for both modes of operation of polarimetric radars, designated as the simultaneous transmission and reception of horizontally and vertically polarized waves and the alternate transmission of horizontally and vertically polarized waves, respectively. The bias caused by unmatched horizontal and vertical copolar radiation patterns as a function of slight differences in pointing angles and beamwidths is also analyzed. In well-designed weather radars, for the purpose of hydrometeor classification, the overall acceptable bias in the copolar correlation coefficient should be less than about 0.01. The levels of crossto-copolar gain ratios for acceptable performance are indicated. Ultimately, pointing angle and beamwidth tolerances are indicated for horizontal and vertical copolar antenna patterns.