Issues Encountered When Unfolding Velocities




Spurious 0 m/s velocity gates inbetween folds:

Several issues were encountered when the unfolding of Cimarron radial velocities was begun. The first issue concerned spurious 0 m/s velocity gates that exist inbetween folds. An example of these spurious 0 m/s velocity gates is shown below in Fig. 1; they are present in the rightmost circled region and are indicated by their white color and by their position inbetween the fold. It is quite obvious from this picture that folding is occurring in this location. The presence of these 0 m/s velocities, however, can be confusing to the analyst and in more complicated folding situations could complicate manual unfolding. Moreover, these 0 m/s velocites would pose a problem to automatic unfolding routines. Even when unfolding the velocities manually, care must be takes (e.g. in Solo). This is discussed further in subsequently.

I have speculated the reason these spurious 0 m/s velocites located inbetween folds. This is my explanation at this point (1/5/99). The Cimarron radar system records velocities at integer intervals (e.g. 3, 4, 5, -10, -25 m/s, etc.). Consider the situation when the Nyquist velocity is more than half way to the next integer (e.g. Nyquist = 35.7, which is the Nyquist velocity 1for this data set). When the radar measures a value like 35.6 or -35.55, it rounds to the nearest integer: +36 or -36. In doing so, however, it produces a value beyond the Nyquist limit. In response, the system records a zero for these values. While this is only a theory, it is consistent with the presence of zeros inbetween folds. Note that when the velocity gradient is strong the likelihood of these spurious 0 m/s folds is significantly reduced (see the fold in the cyclonic region just to the southwest of the upper-left circle in Fig. 1, for example).

These spurious 0 m/s velocities dictate that care be taken when manually unfolding the velocity data. Since the middle value of these 0 m/s velocities is +/- n*Nyquist, I look for 0 m/s values within my unfolding regions, flag them, and then change them accordingly before doing forced-unfolding. Here is the series of commands I used when unfolding about +1*Nyquist:

!for-each-ray (put one-time cmds before this line clear-bad-flags
set-bad-flags when VE between -0.5 and 0.5
flagged-add of 35.6 in VE
forced-unfolding in VE around 35.6



Coherent and Errant Inbound Velocities Along Front Flank:

The coherent (green) velocites indicated in the second right-most circle in Fig. 1 appear to be errant. Although they appear to be coherent, they are not consistent with the flow. The abrupt color change relative to the gates that are more within the storm and are trusted imply that these gates are folding. Unfolding these gates, however, would result in outbound winds on the order of 58 m/s (compared to ~20 m/s outbound in the adjacent trustable data)! Inspection of the data indicates that the SNR is very low in this region (< 5 dB). In fact, the SNR is < 0.0 dB throughout much of this region. The velocity information, therefore, could be coming through the sidlobes. These data indicate that a lower threshold of 5 dB of SNR may be useful for thresholding velocity data.



Coherent and Errant Inbound Velocities In Reflectivity Notch:

Coherent but apparently errant inbound velocities are indicated in Fig. 1 in the Southwestern-most circle. These gates are roughly in the reflectivity notch of the storm (Zh is shown in Fig. 2 for reference). The velocity field in this region is trimodal, with the peaks at at -32.5 m/s, -0.5 m/s, and +33.5 m/s. Visually, the colors that stand out the most are the blues and the tans (~3-5 m/s and part of the second hump whose peak is at -0.5 m/s). If these data were unfolded about +1*Nyquist, the most sensible unfolding option, it would be trimodal with modes at +2.5 m/s, +33.5 m/s, and +70.7 m/s. This is unreasonable (on physical grounds it is not expected that the velocity field would be trimodal with that much distance between modal values). The SNR is, as it was in the region discussed immediately above, below 5 dB in this region. Velocity information may again be entering through sidelobes and high spectrum widths (not investigated) could be contributing to velocity-estimate errors.



Coherent and Errant Inbound Velocities In Reflectivity Notch:

The final region to be discussed here is the circled region at the base of the hook. A set of inbound velocites is present there. These values are peculiar. If one trusts them, then the most reasonable course is to unfold them; doing so would remove an apparent jet of inbound air (~-20 m/s) nestled between outbound air. Unfolding these values, however would result in outbound velocities of ~+50 m/s. These velocites would be flanked by winds of ~+23 m/s to the southeast and ~+10 m/s to the northwest. Inspection of rho-hv(0) shows that rho-hv(0) is incredibly low in this region (< 0.4 and oftentimes < 0.25) while SNR is ~10.0 dB (for comparision in the previous two regions rho-hv(0) >= ~0.45).

At this time I can think of two possible explanations for this feature. These velocities could be correct and the tornado could be located at this point. From the vertical continuity of the wind field in that region, however, this seems unlikely. It is more likely that this region is one of tremendous shear and that the strong turbulence and weak signal is resulting in a Doppler spectra that is nearly flat (saturated). Thus, it is very difficult for the processer to determine the mean Doppler velocity, resulting in the non-physical values (~-23 m/s) with a few realistic (~+25 m/s) values interspersed. Because some reasonable values are interspersed with unrealistic values this region is somewhat similar to the "Coherent and Errant Inbound Velocities Along Front Flank" region discussed above. Most bias and variance estimates of rho-hv(0) have depended upon perturbation analyses in which the spectrum is assumed to be Gaussian (e.g. Balakrishnan and Zrnic 1990, JAS; Liu et al. 1994, JTECH). If my supposition is correct, then the spectrum is not Gaussian and the bias in rho-hv(0) could be larger than expected for a Gaussian spectrum (note that the rho-hv(0) estimator on the Cimarron radar assumes a Gaussian spectrum and may produce large rho-hv(0) bias errors when the spectrum is non-Gaussian (Liu et al. 1994, JTECH, pp. 955)). Thus, it appears as if these velocity values are not trustable and that a threshold of 0.4 for rho-hv(0) may be useful for thresholding velocity.






FIG. 1






FIG. 2