Alignment direction observations.

Figures 15 and 16 show examples of alignment direction observations from the September 15 storm. The Figure 15 observations are from a vertical scan through the storm's northern edge. Electrical alignment caused the correlation phase $\phi$ to increase with range in the upper part of the storm (dark region, upper middle panel). From (11), this indicates a negative value of $\phi_{dp}$ and hence vertical alignment. The increase is shown by the upward-sloping green line in the range profile panel (lower right). The polarization trajectory through the region is shown in the Poincaré sphere panel (upper right). Vertically aligned particles would cause the polarization state to move horizontally to the left with increasing range. The actual motion was to the left and slightly upward, indicating that the alignment was slightly tilted from vertical. A line constructed perpendicular to the overall polarization trajectory points just to the right of the vertical polarization point (V) at the top of the circle, indicating that the alignment was at a slight positive angle with respect to vertical.

In a $Z_{\rm DR}$ display the above observations would be interpreted as a radial band of negative $Z_{\rm DR}$ values in the upper part of the storm. This is because polarization states above the ${{\rm U}}$ axis on the Poincaré projection plot have more power in V than in H. The negative $Z_{\rm DR}$ values are indicated by the downward-sloping blue line in the range profile panel. Such values are an artifact of the interpretation which arises from the assumption that the particles are horizontally oriented. Such an effect caused the positive $Z_{\rm DR}$ anomaly noted in the upper part of the storm of Figure 13; in this case the particles were aligned slightly left of vertical. Observations such as this have been considered to be an artifact of antenna sidelobes but are instead an indicator of electrical alignment that is not quite vertical.

The lower middle panel of Figure 15 shows the alignment direction values as a function of position in the storm. Nearly vertical alignment is denoted by the red and blue colors and was present in the upper part of the storm. Such regions are observed to develop and to spread in extent prior to the occurrence of a lightning discharge, and to disappear at the time of the lightning (Krehbiel et al., 1996). The lower left panel shows what is termed the depolarization rate. This is the angular rate of change of the polarization state with range; it differs from $K_{\rm dp}$ in that it refers to the overall spherical angular change rather than to just the rate of change of $\phi$. From the Poincaré sphere plot, the spherical angle changed by about $15^\circ$ over a distance of about 6 km through the alignment region, corresponding to a two-way depolarization rate of $2.5^\circ \ {\rm km}^{-1}$ ( $1.25^\circ \ {\rm km}^{-1}$ one-way). Maximum two-way depolarization rates of up to $4.5^\circ \ {\rm km}^{-1}$ were observed in the electrical alignment region (the green-yellow colors between 6.5 and 8.0 km altitude in the depolarization rate panel). These correspond to regions of significant ice crystal populations, whose presence is revealed by the electrical alignment of the crystals.

The alignment directions are sensed in a plane perpendicular to the radar scan plane and are best comprehended in the perpendicular plane, where they can be represented vectorially. Figure 16 shows such observations at several ranges from the radar. The storm and the alignment directions are seen as they would be viewed from the radar. An individual RHI scan provides only a vertical column of alignment vectors; a complete `map' of alignment directions has to be constructed from a series of contiguous RHI or PPI scans, namely from a volume scan of the storm. Since the resulting data is three-dimensional, the alignment directions can be displayed at different ranges from the radar. The figure shows the alignment directions at three ranges, 32.0, 32.4, and 33.3 km from the radar. (To avoid having to interpolate the measurements, each panel shows the alignment directions at a constant range value, corresponding to a spherical rather than a planar surface through the storm.) The background variable is the horizontal reflectivity Z_H. The inferred alignment directions are depicted by lines whose length is proportional to the depolarization rate. For simplicity of display the orientation angles are quantized into $22.5^\circ$ intervals; to accentuate the vertical alignment regions, lines within $\pm 22.5^\circ$of vertical are in black while the remainder are in magenta. A line length of one data pixel corresponds to $3 ^\circ\ {\rm km}^{-1}$ two-way depolarization rate.

The figure shows two regions of strong vertical alignment. The first was in the upper part of the tilted precipitation shaft at 9 km altitude on the left (north) side of the storm. The data of Figure 15 are from a vertical scan through the center of this region. The second vertical alignment region was at slightly lower altitude (8-9 km MSL) in the high reflectivity core. The correlation of strong electrification with precipitation at these altitudes is typical of electrical observations of storms (e.g., Krehbiel, 1986, Dye et al., 1988).

Many of the indicated alignment directions in the Figure 16 plots are apparent rather than real. The alignment directions are correctly inferred only when the polarization changes are dominated by $\phi_{dp}$ of aligned particles. This is generally not true, for example, in the rain region of the lower part of the storm. Nor does it appear to be true in much of the upper part of the storm, as evidenced by the random or otherwise unphysical nature of many of the vectors. The extent to which the alignment indications are real or are artifacts is not fully understood and needs to be further investigated.

Linearly polarized transmissions can be used to detect electrical alignment when the alignment is vertical or has a significant vertical component (e.g., Caylor and Chandrasekhar, 1996; Zrnic and Ryzhkov, 1999). The alignment is detected in the same way as in Figure 15, namely by identifying regions of radially extended, opposite polarity $\phi_{dp}$ changes. If the linear polarizations were transmitted simultaneously as a slant ${45^\circ}$signal, the polarization trajectory through a region of vertically aligned particles would be similar to that in the Poincaré projection of Figure 15 except it would be rotated by $90^\circ$ around the H-Vaxis to begin in the vicinity of the $+{45^\circ}$ polarization point, and would extend upward out of the page. Particles aligned at a ${45^\circ}$ angle would not depolarize slant ${45^\circ}$ transmissions because this is the characteristic polarization of the particles, and therefore would not be detected by such transmissions. (Similarly, a radar that transmits Hand V polarizations on alternate pulses could not detect particles oriented at a ${45^\circ}$ angle.) Simultaneous slant ${45^\circ}$ transmissions could be modified to detect ${45^\circ}$ alignment by introducing a phase shift between the H and V components to make the transmitted polarization circular, but no such modification would be possible for an an alternating pulse H-V system. The alternating pulse technique thus simulates only slant ${45^\circ}$ transmissions.

It follows from the above that horizontal and vertical linear transmissions are able to detect the presence of vertical or horizontal alignment but they cannot do more than determine the sign of the alignment direction. Circularly polarized transmissions detect all alignment directions equally well, by virtue of the fact that the depolarization is independent of the alignment direction.