Shawn B. Harley
National Weather Service Forecast Office
Vertically Integrated Liquid (VIL), one of the derived products produced by the Weather Surveillance Radar-1988 Doppler (WSR-88D) system, has been found to be correlated with large hail occurrence (in this paper the terms hail and large hail are used interchangeably, and refer to hail 3/4" in diameter or larger). Considerable documentation on the relationship between VIL and large hail exists (Elvander 1977; Beasley 1986; Devore et al. 1985; Kitzmiller and Briedenbach 1993; Kitzmiller et al. 1995).
The relationship between VIL and severe weather occurrence has been studied in various parts of the country. Kitzmiller et al. (1995) found that there was a strong relationship between VIL and large hail occurrence in the Southern Plains, but that the relationship in the northeast part of the country was much weaker. The purpose of this study was to examine the relationship between VIL and large hail occurrence in Indiana.
VIL values represent reflectivity data converted into equivalent liquid water values. The relationship between liquid water content and reflectivity is defined by the following equation:
where M is liquid water content (g m-3) and Z is radar reflectivity (mm6 m-3) (Greene and Clark 1972). With the WSR-88D system, values for M are derived for each 2.2 x 2.2 nautical mile grid box and then vertically integrated. The final VIL values are output in units of mass per area (kg m-2).
DATA COLLECTION AND PREPARATION
Archived level IV data from the Indianapolis WSR-88D for the period March to July 1994 was used in this study. Archived data was not available for August or September 1994. The geographic area covered in the study included that part of Indiana within 124 nautical miles of the radar site. This included all of Indiana except small parts of the southwest, northeast, and northwest corners.
Hail, 3/4 inch in diameter or larger, occurred in Indiana on 22 days during the March to July period, with 75 large hail reports listed in the preliminary Indiana Storm Data report. Because of analysis procedures and gaps in the archived data, only 17 days and 55 hail events could be used in the study.
For each hail producing thunderstorm, the maximum VIL that occurred during the 30 minute period preceding large hail was noted. For a given day, the lowest maximum VIL recorded in any such 30 minute period preceding a large hail event was termed the VIL threshold for the day. Storms which met the VIL threshold of the day, and occurred within a time frame running from about one hour before the first large hail report to about one hour after the last large hail report were included in the study.
For each of the seventeen hail days, a group of storms was thus identified for further study. Each of the identified storms was next broken down into 30 minute segments. For storms that did not produce large hail, the first 30 minute segment began when the VIL associated with the storm reached or exceeded the previously identified VIL threshold for the day. Additional 30 minute segments were then identified until a 30 minute period had passed during which the VIL of the storm remained below the VIL threshold for that day. For hail producing storms a 30 minute period preceding the hail was always used as one of the identified 30 minute segments. If the storm produced separate hail events then each hail event would be assigned its own corresponding 30 minute segment.
This procedure was carried out on each storm until a complete group of 30 minute storm segments was identified. Each 30 minute storm segment was assigned a VIL value equal to the maximum VIL that occurred during the storm segment. Note that the VIL value assigned to each segment could not be less than the VIL threshold of the day. Whether or not the 30 minute segment was associated with hail was also noted.
The final data base consisted of 256 storm segments. Fifty-five were associated with large hail, and 251 were not associated with large hail.
The VIL thresholds identified for the 17 hail days ranged from a low of 30 to a high of 70 (Figure 1). The lower VIL thresholds were noted in the spring months, with the higher values in the summer months.
Figure 1. Lowest VIL (Kg/m2) associated with hail for each hail day.
Figure 2 shows the distribution of the VIL values associated with the 55 large hail events. In the March through May period, VILs associated with large hail ranged from a low of 30 to 34, to a high of 55 to 59. In the June to July period, VILs associated with large hail ranged from a low of 40 to 44, to a high of 70+. Also note the clusters of hail events centered around VILs of 50 and 70. Only 4 of the 55 large hail events were associated with VILs of 60 to 69, while there were 17 cases of large hail associated with VILs of 70 or greater.
Figure 2. VILs (Kg/m2) associated with hail producing thunderstorms.
Figure 3 shows the distribution of the VIL values for the 256 storm segments used in the study. Remember that for any given day, the only storms examined were those that produced VIL values reaching the VIL threshold for the day. The VIL threshold was 60 or less on all but one day, and was 50 or less on all but two days. For the fifteen days where the VIL threshold was 50 or less, the number of storm segments with a maximum VIL of 50 to 59 was 87. Of these, 17, or 20 percent were associated with large hail. For the sixteen days where the VIL threshold was 60 or less, the number of storm segments with a maximum VIL of 60 to 69 was 39. Of these, 4, or 10 percent were associated with large hail. On the 17 hail days used in the study there were 35 storm segments identified with VILs of 70 or more. Seventeen, or 49 percent of the segments with VILs of 70 or more were associated with large hail. As can be seen, only storms with VILs of 70 or greater were associated with a relatively large percentage of hail events.
Figure 3. Maximum VILs (Kg/m2) associated with each of the 256 storm segments.
If VIL is to be used successfully as a large hail indicator, then a "VIL of the day" must be identified. One way used to determine the "VIL of the day" has been to wait for the first large hail event of the day, and then use the VIL associated with this event as the "VIL of the day". The idea is that once a "VIL of the day" is determined, then that value can be used to identify other severe storms.
For each of the 17 hail days in this study, the "VIL of the day" could range from the previously defined VIL threshold (the lowest VIL associated with hail on that day), up to the highest observed VIL associated with a large hail event for that same day.
Figure 4. Best possible CSIs for each hail day, and associated PODs and FARs.
To examine the usefulness of the "VIL of the day" concept in Indiana, standard warning verification statistics were employed. The statistics included Probability Of Detection (POD), False Alarm Ratio (FAR), and Critical Success Index (CSI). The probability of detection is defined as the number of warned events divided by the total number of severe events. The false alarm ratio is the number of unverified warnings divided by the total number of warnings. The critical success index combines POD and FAR into a single verification statistic where CSI = ((POD)-1 + (1-FAR)-1 -1)-1. A perfect CSI of one would indicate that warnings were issued for all severe events, and all warnings issued verified.
All possible "VIL of the day" thresholds were tested for each 30 minute storm segment. If the maximum VIL of the segment reached the warning threshold that was being tested, then that segment would be assigned a warning. If the maximum VIL of the segment did not reach the warning threshold that was being tested, then there would not be a warning assigned to that segment.
For each day a set of PODs, FARs, and CSIs was calculated, using all possible "VIL of the day" warning thresholds. The best possible CSIs, and associated PODs and FARs, for each of the 17 hail days is shown in Figure 4. The CSIs ranged from a high of 1 to a low of 0.17. The PODs associated with the best CSIs ranged from a high of 1 to a low of 0.25, and the FARs ranged from a low of 0 to a high of 0.83
Using the "VIL of the day" warning threshold that resulted in the best CSI for each day yielded a POD of one (perfect) on nine of the 17 hail days. However, the FARs associated with the best daily CSIs were unacceptably high on most days. Of the nine days with perfect PODs, two had FARs of zero, one had a FAR of 0.40, and the other six had FARs ranging from 0.50 to 0.83.
For the 17 hail days the best daily CSIs were associated with FARs of less than 0.50 on only five days. On four days the FAR was zero, on one day the FAR was 0.40, on four days the FAR ranged from 0.50 to 0.59, and on eight days the FAR was greater than 0.60. As can be seen, using only VIL (even the best possible "VIL of the Day") as a warning threshold for large hail would have resulted in over warning in Indiana in 1994.
CONCLUSIONS AND RECOMMENDATIONS
Based on 1994 data there does not seem to be a good correlation between VIL and large hail occurrence in Indiana. Using even the best possible "VIL of the Day" as a warning threshold would have yielded unacceptably high false alarm ratios on most hail days in Indiana during 1994. However, occasionally the "VIL of the Day" did work quite well in Indiana during 1994. Being able to identify on which days VIL can be useful as a large hail indicator may be the key.
As would be expected higher VILs were noted in Indiana as spring gave way to summer. Based on 1994 data it appears that VILS of 60 or greater are very unlikely prior to June. It also appears that during the summer months, VILs under 45 are unlikely to be associated with large hail.
VILs of 70+ were the only values associated with 3/4" diameter hail a relatively large percentage of the time. For the study period 49 percent of the storms with VILs of 70 or greater produced large hail.
One other interesting feature noted in the study was the clustering of hail events around VILs of 50 and 70. Very little hail activity was noted with VILs in the 60s. It appears that two separate convective regimes may be the cause of this apparent anomaly. It may be that VILs of 50 were associated with hail during "normal" and/or springtime convection, while the VILs of 70 were associated with hail when extremely warm and humid air masses covered Indiana during the summer.
While VIL alone does not appear to be a good indicator of large hail in Indiana, VIL can be used to identify the most significant storms. Future study should focus on using VIL in conjunction with other WSR-88D products, such as the Layer Composite Reflectivity Maximum. The relationship between VIL, storm top divergence, and large hail could also be examined. Future study could also focus on persistence or areal extent of high VIL values, rather than just the value itself. Finally, the relationship between VIL and severe wind occurrence also needs to be examined.
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Devore, D.R., K.L. Gallant, and C.E. Davis, 1985: The operational use of RADAP II and Doppler data: A pre-NEXRAD environment. Preprints, 14th Conf. on Severe Local Storms, Indianapolis, IN, AMS (Boston), 232-235.
Elvander, R.C., 1977: Relationships between radar parameters observed with objectively defined echoes and reported severe weather occurrences. Preprints, 10th Conf. on Severe Local Storms, Omaha, NE, AMS (Boston), 73-76.
Greene, D.R., and R.A. Clark, 1972: Vertically integrated liquid: A new analysis tool. Mon. Wea. Rev., 100, 548-552.
Kitzmiller, D.H., and J.P. Breidenbach, 1993: Probabilistic nowcasts of large hail based on volumetric reflectivity and storm environment characteristics. Preprints, 26th Int. Conf. on Radar Meteorology, Norman, OK, AMS (Boston), 157-159.
____________, W.E. McGovern, and R.E. Saffle. 1995: The WSR-88D Severe Weather Potential Algorithm. Wea. Forecasting, 10, 141-159.