A geometric approach to characterizing and interpreting dual-polarization radar meteorological observations

The polarization state of a radar signal is fully characterized by four quantities, and is determined by measuring the signal covariances or powers in two orthogonal polarizations (e.g., H and V or RHC and LHC) and the magnitude and phase of the cross-covariance between the two polarizations. The covariance values are readily transformed to represent the polarization state geometrically in terms of its location on the Poincare sphere. The geometric representation provides a powerful way of understanding the dual polarization measurements, both conceptually and analytically. Z_DR, phi_DP, and rho_HV of horizontally oriented particles such as rain change the polarization state in orthogonal spherical directions in the Poincare space, and the changes are azimuthally symmetric about the H-V axis of the sphere. The polarization changes produced by randomly oriented or shaped particles are due to a single quantity termed the sphericity parameter and are azimuthally symmetric about the polar or LHC-RHC axis of the sphere. These and other features of the polarization changes make it relatively easy to understand the effect of transmitting different polarizations and how the resulting observations can be interpreted. Particular examples concern a) the effect of using simultaneous H and V transmissions, in the form of circular or slant 45 linear polarizations, and comparison with alternating H and V linear transmissions, and b) the use of polarization diverse measurements to objectively determine the parameters of different classes of hydrometeors.