SR/SSD 97-15

Technical Attachment


Timothy W. Troutman and Mark A. Rose
NWSO Nashville, Tennessee

1. Introduction

Numerous large hail events (hail diameter in or more) were studied across the Nashville County Warning Area (CWA) in middle Tennessee during 1995-1996 (encompassing two severe weather seasons) in order to determine the relationship (if any) between Vertically Integrated Liquid (VIL) and storm echo top. VIL Density (Amburn and Wolf 1996) was also computed for the 77 large hail events. Results show strong correlations which will be useful in determining a thunderstorm's potential for producing severe hail. The methodology used in deriving these comparisons is also provided in order to assist other NWS offices in developing their own VIL/echo top and hail size/VIL Density correlations.

2. Vertically Integrated Liquid and VIL Density

The vertically integrated liquid (VIL) is a function of reflectivity, and converts reflectivity data into an equivalent liquid water content value based on studies of drop-size distribution and empirical studies of reflectivity factor and liquid water content (Amburn and Wolf 1996). The general equation for VIL as used with the WSR-88D is:

VIL = 3.44 x 10-6 [(Zi + Zi+1)/2]4/7 h

which has units of kg m2. Zi and Zi+1 are radar reflectivity at the bottom and top of the layer h, whose thickness (h) is in meters.

VIL Density is simply the VIL divided by the echo top (m), multiplied by 103 (g kg-1) to express the result in units of g m-3. The importance of the VIL Density is its use in quickly identifying thunderstorms with high reflectivities relative to their height. Such thunderstorms often contain hail cores, and as the VIL Density increases, the hail core tends to be deeper, more intense, and the resulting hail sizes tend to be larger (Amburn and Wolf 1996).

3. Methodology

During the years 1995-1996, 77 severe hail events occurring within the Nashville CWA were analyzed. VILs and echo tops were gathered for each of these events and plotted so that a correlation based on the two parameters could be determined.

In order to select the echo top, the WSR-88D function was used. The echo top selected was always located on the same pixel as the maximum VIL. The echo top and VIL values used were in increments of 5 units. For instance, a VIL in the range of 45-49 kg m-2 was reported as 45 kg m-2. An echo top in the range of 35-39,000 ft was reported as 35,000 ft. Also, only storms for which severe hail was reported were used. Thus, it is unknown (as far as this study) whether large values of VIL or VIL Density may be associated with hail of less than in diameter. This study also does not consider other aspects of severe thunderstorms such as strong and damaging winds.

That severe hail events from all seasons of the year were utilized in this study explains the wide range of data. Severe hail was observed in thunderstorms with VILs as low as 15 kg m-2 and echo tops as low as 15,000 ft, and in thunderstorms with VILs as high as 80 kg m-2 and echo tops as high as 50,000 ft. A comparison was also made between hail size and VIL Density. Linear regression was used to fit a straight line to these two variables to assist in interpreting results.

Most of the cases used in this study were gathered from WSR-88D data in which VCP 21 (not VCP 11) was used. Volume Coverage Pattern 21 samples fewer elevation angles than VCP 11. Because of the gaps in the scan strategy, VCP 21 performs less thoroughly than VCP 11 in the estimation of VILs and echo tops (Federal Meteorological Handbook No. 1, Part C 1991).

Also, all hail sizes used in this study were obtained from the usual storm verification data. These data are collected to assist with warning verification and are not necessarily complete as far as supporting scientific studies. In other words, it is difficult to know with any certainty that the hail sizes reported with each event do, in fact, represent the largest hail which occurred.

4. Results

It was hypothesized that a relationship existed between VIL and echo top, and that such a relationship might be useful in determining the potential of a thunderstorm in producing severe hail. The results of this study show that not only is there a strong relationship between VIL and echo top, but a relationship between hail size and VIL Density also exists. Figure 1 shows a scatter plot of VIL vs. echo top for the 77 severe hail events used in this study. Figure 2 shows the best-fit straight line for the plotted data. These figures confirm earlier studies which indicate that, in cases of large hail, there is a strong positive correlation between echo top and VIL. Since hail size was not a variable in the figures, however, Figs. 1 and 2 do not assist in forecasting hail size or the likelihood of storm severity.

VIL Density, especially when compared with hail size, does provide useful information. A scatter plot of hail size vs. VIL Density is shown in Figure 3. For the 77 large hail cases studied, 79% of the cases had a VIL Density of at least 3.5 g m-3. Interestingly, Amburn and Wolf (1996) identified the VIL Density of 3.5 g m-3 as correctly identifying over 90% of the severe hail cases in their Oklahoma study. Also, the average VIL Density associated with in hail (the smallest of the severe categories) was 3.8 g m-3. The VIL Density of 1.6 g m-3 correctly identified all 77 severe hail events, 3.3 g m-3 identified all hail occurrences of 1.75 in and larger, and 3.6 g m-3 identified all hail occurrences of 2.75 in and larger. Furthermore, 76% of the cases which displayed VIL Densities of at least 5.0 g m-3 corresponded to hail 1.75 in and larger. And all instances of VIL Densities of at least 6.0 g m-3 corresponded to hail 1.75 in and larger.

A regression line describing this relationship was developed as well (Figure 4). This figure may be used during severe weather events as an indicator of a thunderstorm's potential for severe hail. Basically, the greater the VIL Density, the larger the hail.

5. Conclusion

The data gathered for this study show a strong correlation between VIL and echo top in storms which produce large hail. It has also been shown that a relationship between hail size and VIL Density exists. These relationships can be used operationally to assist in issuing severe thunderstorm warnings.

Two other issues must be addressed here. The first regards the radar's "cone-of-silence." Amburn and Wolf (1996) suggest that VIL Density is more effective than the VIL-of-the-day for assessing thunderstorms within a radar cone-of-silence. In addition, because thunderstorms occurring in cold air masses can produce large hail with low VILs, low-VIL thunderstorms occurring in these environments must not be ignored. Figure 1 shows this large range of VILs and echo tops associated with severe hail. As stated previously, severe hail has been documented during this study in thunderstorms with VILs as low as 15 kg m-2 and with echo tops as low as 15,000 ft. Warm season thunderstorms will usually display much higher VILs and echo tops before becoming severe.


The authors thank Scott Sharp and Darrell Massie (meteorologists) and Henry Steigerwaldt (SOO) NWSO Nashville, for their reviews of this paper. Special thanks to Steve Amburn (SOO, NWSO Tulsa) for his review and numerous suggestions.


Amburn, S., and P. Wolf, 1996: VIL Density as a Hail Indicator. 18th Conference on Severe Local Storms. San Francisco, CA, Amer. Meteor. Soc., 581-585.

Federal Meteorological Handbook 11, 1991: Doppler Radar Meteorological Observations, Part C, Office of the Federal Coordinator for Meteorological Services and Supporting Research, U.S. Department of Commerce/NOAA, Washington, D.C.