Basic Observations.

Figure 12 shows observations of a relatively small but intense New Mexico storm obtained with the NMT radar. The data are from one of a number of convective cells that occurred during the passage of a vigorous frontal system through the Socorro area on September 15 (Day 258), 1998. The panels in the figure show vertical cross-sections of the various polarization variables through the center of the storm at the peak of the storm's vertical development. The horizontal reflectivity panel (Z_H, upper left) shows that 40 dBZ reflectivity extended up to 8 km altitude above ground level (AGL), and that detectable reflectivity extended to 10 km altitude. The radar itself was at 1.4 km MSL. The horizontal distance scale is in km from the radar. The lower right panel shows profiles of the polarization variables along the radial cursor. The cursor, shown in black and magenta, is at a low elevation angle ($1.6^\circ$) to pass through the rain region of the storm. The red trace in the lower right panel indicates the reflectivity values through the rain region.

The lower left panel shows the differential reflectivity of the storm (as combined with differential attenuation). Positive values are indicated by the yellow and red colors. The rain region is well delineated by the transition to positive values at and below 2 to 3 km altitude AGL. Precipitation above the transition level had neutral $Z_{\rm DR}$ values and was therefore frozen. The reflectivity in the central core indicates that the precipitation there was in the form of graupel or small hail. The hail had slightly negative $Z_{\rm DR}$ values (0 to -0.75 dB) and was therefore somewhat elongated vertically. (Similar observations have also been reported for example by Balakrishnan and Zrnic (1990a) and by Hubbert et al. (1998).) The altitude at which liquid drops started to appear was at lower altitude in the hail shaft than in the remainder of the storm, indicating that the particles were relatively large and required a longer time to melt. The variation of $Z_{\rm DR}$ with range through the rain region is shown by the blue trace in the lower right panel; the strongest $Z_{\rm DR}$ value (slightly greater than 2.0 dB) occurred at 31.5 km range, on the far right edge of the main precipitation shaft. Beyond this range, $Z_{\rm DR}$generally decreased with range due to decreasing average drop size and possibly differential attenuation.

The middle panels show $\phi_{{HV}}$ (upper) and the rate of change of $\phi_{{HV}}$with range (lower). A `zebra' color palette (Hooker et al., 1995) is used to accentuate the $\phi_{{HV}}$ changes in the upper panel. The phase difference in the upper part of the storm was close to $90^\circ$, corresponding to LHC polarization. The profile of $\phi_{{HV}}$ through the rain region is shown by the lower (green) trace in the range profile panel. The overall tendency of $\phi_{{HV}}$ to decrease with range is the result of differential propagation phase shift $\phi_{dp}$, as in (11). $\phi_{dp}$ would cause $\phi_{{HV}}$to decrease monotonically with range, however, and the fact that $\phi_{{HV}}$increased several times indicates the presence of differential phase upon backscatter $\delta_\ell$. $\delta_\ell$ occurs only when the scatterers are non-Rayleigh and is accentuated here by the relatively short wavelength of the radar (3.0 cm). As defined in (6), $\delta_\ell$ is negative for horizontally flattened drops and therefore adds to the apparent value of $\phi_{dp}$ at gates containing particles large enough to be in the non-Rayleigh regime. The presence of $\delta_\ell$ is detected only when it goes away, by virtue of an increase in $\phi_{{HV}}$ on the far side of a large-particle region (Bringi et al., 1990; Tan et al., 1991; Holt and Tan, 1992; Hubbert et al., 1993).

The specific differential phase ( $K_{\rm dp}$) results in the bottom middle panel are one-way values and were substantially affected by the $\delta_\ell$ effects. ( $K_{\rm dp}$ is often considered to represent the rate of change of differential propagation phase $\phi_{dp}$ with distance, but more generally combines this with the rate of change of $\delta_\ell$ with range.) Upon entering the strong rain region between 29 and 31 km range along the cursor path, the magnitude of $K_{\rm dp}$ was 3 to $4^\circ \ {\rm km}^{-1}$ or larger. This overestimates the propagation contribution to $K_{\rm dp}$ due to the effect of $\delta_\ell$ gradually increasing in magnitude with range, thereby make the slope of $\phi_{{HV}}$more negative (e.g., Hubbert et al., 1993). The fact that $\delta_\ell$ was important is indicated by the subsequent increase in $\phi_{{HV}}$, as discussed above. The effect of the increase was to produce large positive $K_{\rm dp}$values on the far side of the $\delta_\ell$ region, in this case between 31 and 32 km range along the cursor. $\delta_\ell$ regions are therefore indicated by a couplet of enhanced negative and positive $K_{\rm dp}$ values bracketing the $\delta_\ell$ region. The relative strength of the two components of the couplet depends on the suddenness of the the transitions. A particularly strong $\delta_\ell$ couplet occurred just above 2 km altitude between 29 and 30 km range. The values exceded $\pm 7.5^\circ \; {\rm km}^{-1}$ and are indicated by the red/white and blue-white regions at that location. Analysis of the observations shows that the $\delta_\ell$ excursion was close to $-15^\circ$. The $\delta_\ell$ region was on the front edge of the main precipitation shaft and was associated with a local maximum of $Z_{\rm DR}$at the same location. From this and from the later observations, the $\delta_\ell$- $Z_{\rm DR}$ region appeared to be in the storm inflow.

When the $\delta_\ell$ effects are removed to obtain the overall trend of $K_{\rm dp}$with range, as discussed by Hubbert et al. (1993), the average rate of change of $\phi_{dp}$ through the rain region was about $16^\circ$ over 5-6 km, or about $3^\circ \; {\rm km}^{-1}$ two-way ( $1.5^\circ \; {\rm km}^{-1}$ one-way). From the data of Oguchi (1983), this corresponds to an average rainfall rate of 35-40 mm ${\rm hr}^{-1}$ along the path.

The upper right panel shows the vertical cross-section of $\rho _{HV}$ through the storm. The correlation dropped below 0.9 in the precipitation core aloft, indicating the presence of a significant unpolarized component in the backscattered signal. Such reductions are typically considered to be caused by the random orientations of tumbling hail, and that is most likely the case here. The fact that the hail had slightly negative $Z_{\rm DR}$values, however, leaves open the possibility that some of the $\rho _{HV}$reduction could have been due to variations in the shapes of vertically elongated particles, as in (12). Reduced correlation extended all the way to the ground within the main precipitation region, which suggests that that the precipitation at lower altitudes consisted of a mixture of rain and hail. The profile of $\rho _{HV}$ through the rain region is shown by the black trace in the lower right panel. Reduced correlation also occurred at 3 km altitude on the front side of the reflectivity core, immediately above the strong $\delta_\ell$ region in that location, and in the melting layer on the far side of the core.

The fact that the correlation returned to strong values on the far side of the regions where they were reduced indicates that there was not a noticeable propagation effect in passing through the regions, and therefore that the decorrelation occurred during backscatter.