Non-horizontally aligned particles.

Particles having a common alignment direction that is not horizontal depolarize the radar signal in the same way as horizontally aligned particles, except about an axis of symmetry ${\rm Q}^\prime$ corresponding to the alignment direction (Figure 8). For particles oriented an angle $\tau$ relative to the horizontal, ${\rm Q}^\prime$ is rotated an angle $2\tau$ away from ${\rm Q}$ in the linear polarization plane.

  

Figure 8: The polarization changes produced by non-horizontally aligned particles (see text).

Non-horizontal alignment occurs as a result of electrical forces, which orient populations of small ice crystals in the direction of the local electric field (Hendry and McCormick, 1976; Metcalf, 1995, 1997; Krehbiel et al., 1996). The alignment is detected by the effect that the ice crystals have on the propagation of the radar signal. In particular, the aligned crystals cause a differential propagation phase shift $\phi_{dp}$ between the components parallel and perpendicular to the alignment direction. Attenuation and differential attenuation are negligible, even at 3 cm wavelength, because the particles are ice-form. Backscatter effects ( $Z_{\rm DR}$or $\delta_\ell$) also appear not to be important. Rather, the backscattered signal appears to be produced by a relatively small number of larger hydrometeors (graupel or hail particles) which serve as a `detector' of the depolarization produced by the aligned ice crystals, which are otherwise invisible to the radar (Hendry and Antar, 1982).

When the depolarization is dominated by $\phi_{dp}$ the alignment direction can be simply determined from the change in the polarization state between successive range gates. From Figures 5 and 8, $\phi_{dp}$ changes are in a plane perpendicular to the ${\rm Q}^\prime$ axis, namely perpendicular to the alignment direction. The alignment direction is determined by projecting the polarization states of the successive gates onto the equatorial plane of the Poincaré sphere. A line constructed perpendicular to the projected points will be parallel to the $Q^\prime$axis. The alignment direction corresponds either to the $+Q^\prime$ axis, corresponding to an alignment angle $\tau$, or to the $-Q^\prime$ axis, corresponding to an alignment angle $(\tau + 90^\circ )$. The ambiguity is readily resolved from the direction/sign of the polarization change. The alignment directions are readily calculated by converting the covariance measurements into Stokes parameter space and using the ${\rm Q}$ and ${{\rm U}}$components to obtain $\tau$ as described above (Scott, 1999).

Electrical alignment is typically vertical or nearly vertical and is observed in the upper and middle part of storms. The electrical nature of the alignment is clearly demonstrated by the fact that it collapses at the time of a lightning discharge in the storm. Strong vertical alignment comes about only in this manner and has been found to be a good indicator of electrification. The fact that electric alignment is predominantly vertical agrees well with in-situ measurements of the electric field inside storms (e.g., Stolzenberg et al., 1998a,b).