VERIFICATION OF THE WSR-88D BUILD 9.0 HAIL ALGORITHM OVER THE UPPER MIDWEST
Dan A. Baumgardt* and Corey W.
King
NOAA/National Weather Service Office
La Crosse, Wisconsin
I. INTRODUCTION
In early 1997, the WSR-88D radar algorithm used to detect hail was upgraded to include many new features documented to improve radar-based forecasts. This latest WSR-88D software build (9.0) incorporated a new Hail Detection Algorithm (HDA) which utilizes work done by Witt (1990, 1997) on the Hail Core Aloft Algorithm (HCAA) at the National Severe Storms Laboratory (NSSL). The HCAA is a reflectivity-based algorithm which uses the height of the 45 dBZ echo above the freezing level (FRZLVL) to determine the presence of hail. A large improvement in the HCAA (and thus, the Build 9.0 HDA) is the incorporation of a vertical integration of reflectivity, that is temperature weighted, as most severe hail growth has been documented to occur between the 0C and -20C levels (English 1973 and others). National Weather Service (NWS) WSR-88D radar operators now have the ability to adjust both the 0C and -20C heights in Build 9.0 marking the first time environmental thermodynamic parameters have been used by the radar.
With these vast changes to the WSR-88D HDA, it is necessary to look into the algorithm's performance to determine its reliability and ultimately improve NWS warning operations. Some of the HDA parameters investigated include Probability of Hail (POH), Probability of Severe Hail (POSH), and Maximum Expected Hail Size (MEHS). POH and POSH values were investigated to determine if guidance values for large hail could be determined. MEHS was compared to verified severe hail reports (the National Weather Service defines severe hail to be hail at least 0.75 inches in diameter) in order to determine how well the MEHS value represented truth. Several other parameters which radar meteorologists often use to determine a storm's hail potential: cell-based VIL, cell top, and both the maximum reflectivity observed and its height were also investigated. Hereafter, all hail sizes will be given as a measure of the diameter of the particle.
Studies of VIL density (Amburn and Wolf 1997, Troutman and Rose 1997), defined as grid-based VIL (VILgb , kg m-2) divided by echo top (m):
| VIL density = VILgb / echo top | (1) |
have shown a relationship between VIL density and severe hail. VIL density was also investigated in this study because of its demonstrated success in predicting severe hail.
Storm data was used to locate severe hail reports from within the NWS La Crosse county warning area (CWA) during the 1997 warm season and the spring of 1998. The NWS La Crosse CWA includes western WI, northeast Iowa, and southeastern Minnesota. The severe hail reports were correlated to their responsible storm using the La Crosse WSR-88D Archive level IV radar data. The cases chosen employed volume coverage pattern (VCP) 11 which utilizes a scan strategy of 14 slices every 5 minutes. It allows for better vertical resolution than would have been achieved under VCP 21 which completes 9 slices in a 6 minute period.
Several complexities had to be overcome in order to find hail data that could be considered "reliable". A storm and hail report were considered "correlated" if the radar identified a storm centroid within a 5 mile radius of the ground truth hail report and within 5 minutes of the report. In many instances, the product generation time from the radar correlated to within a 1 to 2 minute period of the storm report. This methodology makes the assumption that the hail size from the algorithm should always be consistent with the hail which is falling from the thunderstorm. This may not always be the case. It has been shown that as a hail core descends, the POSH and MEHS will decrease as the core approaches and passes below the FRZLVL (Klimowski et al. 1997). It is possible that by the time the hail reaches the surface, the POSH and MEHS may indicate that no severe hail is likely from the storm.
There were instances when more than one report was correlated with a single radar-identified cell or storm. In these instances, the largest of the hail reports was used. This was done to investigate the MEHS variable in the HDA algorithm. In some cases, storms lost their cell identification due to algorithm renaming and thus their cell history was lost. These storms were eliminated from the data set.
The authors also acknowledge the inherent error with hail sampling and reporting. The hail sizes in the data set are the largest reported however not necessarily the largest which the storm produced. Even with the complexities in hail research and the data set herein, the study's methodology attempted to glean useful information from the data available.
A total of 70 severe hail cases were identified and used in the study. The distribution (Fig. 1) contained the highest frequency of reports (28) at 0.75 inches followed next by 1.75 inches (19). There was a noticeable lack of reports between 1.00 and 1.75 inches, which suggests a natural tendency exists for spotters to report "golfball-sized" hail (1.75 inches) once the diameter exceeds one inch.
Fig. 1. Distribution and number of severe hail cases used in the study. For a "blow-up" of this figure, click here.
For this study, a modified VIL density (g m-3) was investigated using cell-based VIL (VILcb) and cell-based storm top (topcb), in lieu of eq. (1) used in past research:
| VILcb Density = VILcb / (Topcb * 0.3048) | (2) |
where 0.3048 is simply a conversion factor from KFt to meters. Raw VILcb density was also calculated in order to provide a value that could be easily calculated and applied by WSR-88D operators. It is defined by removing the 0.3048 conversion factor from eq. (2) and yields units of kg m-2 KFt-1. Topcb is defined by the highest 30 dBZ reflectivity height (KFt) in the identified storm while in eq. (1) echo top is defined by the highest 18.6 dBZ reflectivity height in the storm. The main advantage in using VILcb and topcb is that their values are obtained from a more sophisticated WSR-88D cell identification algorithm. Secondly, VILcb and topcb are available from one WSR-88D product: either the storm structure alphanumeric product or the composite reflectivity attribute table. Past research using VILgb density calculations used information from two products.
The mean POH and POSH for the 70 severe hail cases were approximately 92% and 68%, respectively (Table 1). When separating the 0.75 and 1.75 inch diameter cases, the mean POSH was found to be 60% and 78%. Users of the algorithm output should be aware of the large standard of deviation of nearly 25% for the POSH in these two categories. Some of the deviation can be attributed to the small sample size of 47 cases combined. However, the outlying 33% of the severe hail case population were found at POSH values below 34% and above 86%. Three severe hail cases contained a POSH of zero. Closer inspection of these three cases proved to maintain the findings of Klimowski et al. (1997) where previous radar volume scans contained higher POSH values suggesting the hail was found higher in the storm.
| POH | POSH | MEHS | Observed | MEHS-OB | Max | Cell-based | Cell-based | Cell-Based | Raw VIL | |
| Hail Size | (Bias) | Reflectivity | TOP | VIL | VIL Density | Density | ||||
| All Severe Hail Sizes | ||||||||||
| Mean | 91.55 | 68.31 | 1.38 | 1.12 | 0.25 | 62.25 | 34.62 | 48.63 | 4.59 | 1.40 |
| Standard Deviation (F) | 21.07 | 26.38 | 0.72 | 0.45 | 0.68 | 3.45 | 7.77 | 13.95 | 0.77 | 0.23 |
| 0.75" only | ||||||||||
| Mean | 88.57 | 60.00 | 1.16 | 0.75 | 0.41 | 61.64 | 32.49 | 44.61 | 4.51 | 1.38 |
| F | 21.50 | 25.91 | 0.65 | 0.00 | 0.65 | 2.99 | 8.00 | 14.81 | 0.94 | 0.29 |
| 1.75" only | ||||||||||
| Mean | 97.37 | 77.89 | 1.79 | 1.75 | 0.04 | 64.53 | 35.11 | 50.58 | 4.73 | 1.44 |
| F | 6.36 | 23.53 | 0.89 | 0.00 | 0.89 | 3.45 | 5.64 | 9.43 | 0.41 | 0.13 |
| Units | % | % | Inches | Inches | Inches | dBZ | KFt | Kg/m2 | g/m3 | Kg/m2KFt |
The distribution of the POSH when compared to the FRZLVL illustrates the behavior of the POSH to be greater than 50% for a large portion of the data when the 0C height is at or above 12,000 feet (Fig. 2). Greater variability exists in the POSH for severe hail cases when the FRZLVL is below 12,000 ft. Although beyond the scope of this study, this behavior is discussed in Witt (1997) and Klimowski et al. (1997) and defined by the HDA equations.
Fig. 2. FRZLVL (KFt MSL) versus POSH (%) for all cases. For a "blow-up" of this figure, click here.
When all cases of severe hail were considered, the MEHS overestimated hail size by 0.25 inches on average (Table 1). The authors acknowledge that the ground reports may miss the maximum size hail the storm actually produced, possibly making the MEHS prediction even closer than the statistics suggest. Figure 3 illustrates the distribution of cases which mostly lie above the "truth" line (MEHS=Observed size). The MEHS parameter yielded a mean expected hail size of 1.16 inches for the 0.75 observed hail cases; also a general overestimation. At larger sizes, the MEHS output improved, yielding a mean forecast of 1.79 inches for the 1.75 inch observed hail cases. The standard deviation is particularly troubling to operational forecasting, however, with values of 0.65 and 0.89 inches for the 0.75 and 1.75 inch observed data, respectively. The larger deviation of 0.89 inches is better depicted when the MEHS bias (MEHS-Observed) is shown graphically by hail size (Fig. 4). For hail sizes of an inch or less, the bias points clustered closer to zero (or "perfect forecast"). The range of the prevailing 67% of the cases located about the mean at 0.75 inches were predicted by the MEHS to be sized from 0.51 to 1.81 inches in diameter, which ranges from non-severe to damaging hail. The most extreme overestimation (underestimation) had an error of 2.25 (-1.25) inches on July 2, 1997 (June 20, 1997).
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| Fig 3. MEHS versus observed hail size. Darker lines indicate unity or the "perfect" forecast. Data points above (below) the unity line reflect an overestimate (underestimate) of hail size by the MEHS parameter. For a "blow-up" of this figure, click here. | Fig. 4. Observed hail size versus MEHS minus observed hail size: MEHS bias. Positive (negative) values indicate MEHS overestimation (underestimation). Dashed line represent standard deviations. For a "blow-up" of this figure, click here. |
The MEHS bias displays a definite binary distribution for severe hail cases both above and below the 12 KFt FRZLVL (Fig. 5). Above 12 KFt, no clear bias is observed and much more variability exists with values ranging from underestimates exceeding 1.00 inch to overestimates greater than 2.00 inches. Below 12 KFt, a more pronounced grouping of the cases occurs near the zero MEHS bias line. Recall a binary structure also existed in the POSH parameter across the 12 KFt FRZLVL (Fig. 2). This suggests a FRZLVL of 12 KFt has some importance on hail size and its prediction.
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| Fig. 5. Same as Fig. 4 except for FRZLVL (KFt MSL). For a "blow-up" of this figure, click here. | Fig. 6. VILcb density versus observed hail size. Numbers in the right-hand column indicate RAW VILcb density (kg/m**2 KFt**1). For a "blow-up" of this figure, click here. |
A correlation also exists between the VILcb density (RAW VILcb density) and severe hail with values of 3.5 g m-3 (1.06 kg m-2 KFt-1) and greater identifying 90% of the cases (Fig. 6). The average VILcb density (RAW VILcb density) for only 0.75 inch hail cases was 4.5 g m-3 (1.37 kg m-2 KFt-1). Above 0.88 inches in diameter, VILcb density (RAW VILcb Density) values were all between 3.9 and 6.0 g m-3 (1.19 and 1.83 kg m-2KFt-1). However, also note the variability of observed hail size for a given VILcb density can be quite large for values greater than 3.9 g m-3 (1.19 kg m-2 KFt-1). For example, a 4.2 g m-3 (1.28 kg m-2 KFt-1) value yielded observed hail of 0.75, 0.88, and 1.75 inches in diameter. Although these findings parallel the findings of Amburn and Wolf (1997) and Troutman and Rose (1997) in supporting the use of VIL density as a discriminating tool for severe hail prediction, some caution must be taken when using it to infer size.
The maximum reflectivity in the storm (dBZ) at any height (hereafter, referred to as MAXREF) was found to be at least 53 dBZ for all cases, with all but one being greater than 55 dBZ. A very tight grouping was apparent for values of MAXREF of 58-66 dBZ (not shown). MAXREF for all severe hail cases in the study contained standard deviations of only 3 dBZ, centered on a mean of about 62 dBZ. It follows that operational warning forecasters may be able to use MAXREF to streamline the warning process for severe hail. However, a significant number of low-topped convective cases were not included in this study.
Correlation coefficients were calculated for the various radar and environmental parameters in the study to compare their independent importance in determining hail size (Fig. 7). The MEHS provided the highest correlation to hail size in the study at 0.398. MAXREF was next with a coefficient of 0.388, however MAXREF height was ranked 10th out of 13. This small correlation value for the MAXREF height is explained by the large variation in the height of the storm at which the MAXREF is found (depending on cell age and type). The POSH was found to have the third highest correlation coefficient to hail size at 0.324. Although VILcb density provided some aid in determining if severe hail was possible, its correlation to predicting hail size was much less impressive.
Fig. 7. Independent correlation coefficients for given parameter versus observed hail size for all cases. MAXREF Hgt refers to the MAXREF height. MAXREF 0C (-20C) refers to MAXREF height minus the 0C (-20C) height. VIL, VIL density, and cell top are all cell-based measurements. For a "blow-up" of this figure, click here.
70 cases producing at least 0.75 inch hail were identified. WSR-88D archive level IV data for these individual storms were collected with various parameters investigated for their use in predicting severe hail in operational forecasting. Average POH, POSH, and MEHS for 0.75 inch diameter hail was found to be 89%, 60%, and 1.16 inches, respectively. The most correlated parameter, MEHS, produced a mean overestimation ( for all events) of 0.25 inches. However, variability existed in the MEHS causing a decreased usefulness operationally. VIL Density was also used in a cell-based form. Results showed it to be useful in determining whether severe hail was likely, however its correlation to severe hail size was less useful.
Hail research based on surface hail reports holds many complexities. For this study, conclusions were drawn regarding the WSR-88D HDA algorithm based on these reports. The WSR-88D HDA ground verification scores can vary due to non-meteorological events as well. As an example, MEHS was compared for two regions of the NWS La Crosse CWA where spotter activity was considered "low" and "high" (Fig. 8). It is quite obvious the MEHS output performed better in the
Fig. 8. Same as Fig. 3 except for reports from areas of "high" spotter activity reports ("X") and "low" spotter activity reports ("O"). For a "blow-up" of this figure, click here.
spotter region deemed with "high" activity. Although the authors feel the data in this study are useful to the operational warning process, using it to establish "thresholds" for warning is cautioned against.
The authors thank NWS-La Crosse MIC Glenn Lussky for his review and suggestions on this paper.
Amburn, S., and P. Wolf, 1997: VIL density as a hail indicator. Mon. Wea. Rev., 12, 473-478.
English, M., 1973: Alberta Hailstorms. Part II: Growth of large hail in the storm. Meteor. Monogr., No. 36, Amer. Meteor. Soc., 37-98.
Klimowski, B., S. Vasiloff, and A. Witt, 1997: On the nature of the WSR-88D Build 9 hail detection algorithm: part I. NOAA Technical Attachment NWS WR 97-25.
Troutman, T., and M. Rose, 1997: An examination of VIL and echo top associated with large hail in middle Tennessee. Preprints, 28th Conference on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 374-375.
Witt, A., 1990: A hail core aloft detection algorithm. Preprints, 16th Conf. On Severe Local Storms, Alberta, Amer. Meteor. Soc., 232-235.
Witt, A., 1997: NSSL Hail Core Aloft Algorithm. WATADS Software Documentation, Chapter 9.
