SEVERE LOCAL STORM AND LARGE-HAIL PROBABILITY ALGORITHMS

IN THE

SYSTEM FOR CONVECTION ANALYSIS AND NOWCASTING


David H. Kitzmiller, Michael E. Churma, and M. Thomas Filiaggi


Techniques Development Laboratory

Office of Systems Development

National Weather Service

Silver Spring, Maryland

INTRODUCTION

OBSERVATIONAL AND UPPER-AIR DATA USED IN ALGORITHM DEVELOPMENT

CREATION OF A STATISTICAL DEVELOPMENT SAMPLE

RADAR AND ENVIRONMENTAL INDICES AS PREDICTORS OF SEVERE WEATHER

PROBABILITY EQUATIONS

REGIONAL APPLICABILITY OF THE ALGORITHMS

GRAPHICAL PRESENTATION OF THE ALGORITHM OUTPUT

SKILL OF THE ALGORITHMS IN TERMS OF CATEGORICAL FORECASTS

REQUIRED INPUT PRODUCTS

DIFFERENCES BETWEEN SCAN ALGORITHMS AND WSR-88D POH AND POSH PRODUCTS

IMPLICATIONS FOR OPERATIONAL USE

1. INTRODUCTION


The System for Convection Analysis and Nowcasting (SCAN), a program for operational implementation of new or updated automatic radar interpretation techniques, has incorporated several algorithms within the Advanced Weather Interactive Processing System (AWIPS). The algorithms described below utilize data from existing radar products and from numerical weather prediction models to generate probabilities that individual thunderstorms will produce severe weather. The SCAN Severe Weather Detection algorithm (SSWD) produces the probabilities of general severe weather (strong winds and/or large hail). The SCAN Severe Hail Detection algorithm (SSHD) produces the probability of large hail ( 2 cm diameter). The probabilities are valid within a square region 44 km on a side, centered on a convective storm cell, for 30 minutes after the radar observation. Storm cell locations are taken from the Storm Track Index (STI) product.

These products are intended primarily to provide guidance to forecasters on which storms warrant closer examination for other severe weather signatures, and to monitor storm development over all of the forecast office's area of responsibility when the forecasters might be concentrating on a small subregion.

Forecasters have long known that critical values of many radar indices for severe storms change with the storm environment. In particular, shallow storms are much more likely to produce severe weather in the spring than in the summer. The new SCAN algorithms automatically incorporate information on upper-air temperature and wind vectors as well as radar data. In AWIPS these algorithms were implemented by using radar data from the vertically-integrated liquid (VIL) and composite reflectivity graphic products, and upper-air information from one or more numerical weather prediction models. Comparative verification tests indicate that the new radar-environmental severe weather algorithms can produce 10-15% fewer false alarms than does the operational WSR-88D Severe Weather Potential (SWP) algorithm, which incorporates only VIL data.

This note contains a brief summary of the development methodology behind these algorithms and their operational performance characteristics.

2. OBSERVATIONAL AND UPPER-AIR DATA USED IN ALGORITHM DEVELOPMENT


The methods used to develop SSWD and SSHD were fully documented by Kitzmiller and Breidenbach (1993, 1995). The approach was similar to that employed in the development of the currently-operational SWP algorithm (Kitzmiller et al. 1995, hereafter referred to as KMS95). In brief, a large sample of radar observations of convective storms and coincident storm environment observations was collected and then collated with nearby severe local storm reports. Equations relating severe storm occurrence (the predictand) to radar and environmental severe weather indices (the predictors) were then developed.

Because severe weather climatology varies significantly across the United States, two sets of equations were developed, one for the Central Plains states, another for the mid-Atlantic states. At the time of the development effort, these were the only regions with adequate archives of radar data.

Radar data

The radar data for the Central Plains development sample was taken from Radar Data Processor Version II (RADAP II) archives collected at Amarillo, Texas (AMA), Wichita, Kansas (ICT), and Oklahoma City, Oklahoma (OKC), between 1985 and 1991. Typically, new volumetric scans were available every 10 or 12 minutes. The RADAP II archive has been described in detail by McDonald and Saffle (1994) and by KMS95. The Plains sample contains data on over 6000 individual thunderstorms.

Radar data for the Northeast development sample was from the RADAP II unit at Binghamton, New York, (BGM) between 1988 and 1992, and from the WSR-88D unit at Sterling, Virginia, (KLWX) during 1992 and 1993. We obtained only VIL graphic images from WSR-88D; these were manually interpreted for cell locations, peak VIL values, and VIL horizontal coverage. This data sample contains data on nearly 700 storms.

As noted in KMS95, it appears that there were no systematic biases between VIL as estimated by the WSR-57 and WSR-88D networks, though there are likely to be random calibration differences among radars within either network. The use of data from multiple radars was intended to mitigate the effects of such calibration differences.

Environmental data

Upper-air conditions were derived from analyses and 6-h and 12-h forecasts of the Nested Grid Model (NGM) (Hoke et al. 1989) archived by the Techniques Development Laboratory. These data were chosen in preference to radiosonde observations because they are readily available in gridded form and represent a reasonable approximation of atmospheric conditions between rawinsonde observation times.

To objectively assign environmental conditions to individual storm cells, the environment was assumed to be constant over each 230-km radius radar umbrella, with values corresponding to those at the center. The NGM data were available from Techniques Development Laboratory archives at 6-h intervals: initial-time analyses at 0000 and 1200 UTC, and 6-h forecasts at 0600 and 1800 UTC. For radar data within one hour of an analysis or forecast valid time, the values were taken at that time. For data outside these 2-h windows, the conditions most favorable for strong convection (higher instability, humidity, wind speeds) at the bracketing valid times were used. Temperature, humidity, stability, and wind data were derived from 0000 or 1200 UTC analyses or 6-h forecasts; vertical velocity and divergence predictors were derived from 6- and 12-h forecasts (the initial fields are quasi-nondivergent).

Severe local storm reports

Reports of stron convective wind gusts (those causing damage or measured in excess of 50 kt), large hail (2 cm or greater in diameter), and tornadoes are logged by the National Severe Storms Forecast Center (NSSFC). We collated these reports with storm cell data by mapping the reports to the VIL analysis grid. For each cell, the number of all severe reports, the number of large hail reports, and the largest reported hail diameter were noted.

3. CREATION OF A STATISTICAL DEVELOPMENT SAMPLE


Only storm cells with at least two grid boxes with a VIL of 10 kg m-2 or more were considered for inclusion. Any two cells in the final dataset were separated from each other by at least 28 km, or by 45 minutes in time. Where spatial or temporal overlaps were found, only the larger cell (in terms of maximum VIL) was included. The final development dataset contains storm cell chacteristics including maximum VIL, the number of map grid boxes with VIL in excess of 10 and 20 kg m-2, and the operational SWP value.

The severe storm report log was then examined to locate any severe weather or hail events reported near the storms, and the number of associated severe storm and hail reports were recorded. A storm was considered to be severe (or a large hail producer) if at least one report (or one large hail report) occurred from 10 minutes before to 30 minutes after the nominal radar observation time. This convention should account for both events in progress and those about to develop.

These collection procedures yielded a Plains data sample of 6068 cells, of which 8% were severe and 5.5% featured large hail. The Northeast sample consisted of 668 cells, of which 20% were severe and 6% featured large hail. Thus most severe events in the Plains involved large hail, while over the Northeast, damaging wind events were predominant. These features of severe weather climatology might be due partly to physics and partly to land development patterns. Many reported wind events in the mid-Atlantic region are associated with falling trees and damage to structures. The scarcity of wind events over the Plains could be due in part to a relatively low density of construction even near population centers and to sparse forestation.

4. RADAR AND ENVIRONMENTAL INDICES AS PREDICTORS OF SEVERE WEATHER


Two-predictor histograms clearly illustrate that independent information on severe weather potential is available from both radar and environmental data, as noted earlier by Breidenbach et al. (1993). The histograms in Figs. 1-3 show the percentage of storm cells that had associated severe weather, as a function of a radar-derived storm characteristic and an environmental severe weather index. The predictor combinations shown were the optimum ones in terms of the statistical correlation between the particular predictand and the predictors.

General severe storm probability (winds and/or hail) for the Plains region is shown as a function of cell-maximum VIL (kg m-2)and freezing level height (m MSL) in Fig. 1. The dominant severe weather event in this region is large hail; thus the optimum predictor combination reflects both the intensity of the individual storm (through VIL) and the atmospheric mean temperature and temperature lapse rate (through freezing level height). Severe weather is most likely (> 60% probability) for the highest VIL values and the lowest freezing level values.

General severe storm probability for the Mid-Atlantic region is shown as a function of cell horizontal area (number of 4-km grid boxes with VIL  20 kg m-2) and 700-mb wind speed (m s-1) in Fig. 2 . In this region, where wind events predominate severe weather, it is possible that the optimum predictor combination indicates storms and general conditions likely to result in momentum transfer from middle levels of the troposphere to the ground. Larger storms (and those with higher VIL) are the ones with the most intense updrafts and downdrafts, while the environmental wind speed is a direct measure of horizontal momentum above the surface. Widespread convective wind damage is often associated with higher wind speeds aloft.

For large hail potential alone (Fig. 3) the dependence on both VIL and freezing level height is readily apparent. While this sample is from the Plains region, a similar relationship was evident in the Mid-Atlantic sample.

5. PROBABILITY EQUATIONS


Applying forward-selection linear screening regression procedures to the data sample yielded the following algebraic relationships between the available predictors and event probability:


      SSWD = -16.37 + 2.33 SVG20 + 1.02 WSPD700 + .646 MAXVIL           (1)
      

for the Mid-Atlantic region and:


      SSWD = -16.49 + .025 MAXVIL2 - .00206 (MAXVIL x FRZLVL)
      
           + .365 U-WIND500 + .341 (SFC TOTAL TOTALS)  (2)


for the Plains. Here, SVG20 is the number of 4-km grid boxes with VIL  20 kg m-2, WSPD700 is the 700-mb wind speed in m s-1, FRZLVL is the freezing level height in dm MSL, and U-WIND500 is the west-east 500-mb wind component in m s-1. The Total Totals index predictor is in C. The expression in (1) explains 18.6% of the predictand variance, and that in (2) explains 25.7%. In (2), most of the predictand variance is explained by the MAXVIL2 and MAXVIL x FRZLVL terms. The forward-selection procedure itself selected the 700-mb windspeed predictor in (1), indicating the importance of strong mid-tropospheric winds in causing strong convective wind events over the eastern United States.

The following equations were derived for probability of 2-cm hail:


      SSHD = 14.22 + .03 MAXVIL2 - .0031 (MAXVIL x FRZLVL)   (3)
 

for the Mid-Atlantic and:

 
      SSHD = -375.43 + .019 MAXVIL2 - .00619 (MAXVIL x FRZLVL)
 
           + 2.057 MAXVIL + .066 THICK1000-500            (4)
 

for the Plains. Here, THICK1000-500 is the 1000-500 mb thickness in m. The expression in (3) explains 22.4% of the predictand variance, and that in (4) explains 24.9%. The similarity between (2) and (4) reflects the dominance of hail events within the Plains sample of severe weather reports.

We have often noted that during the summer months the SSHD is significantly lower than the SSWD, as would be expected in very warm, humid environments. The SSHD and SSWD values are generally closer to each other in the spring, when storm environments are rather cool.

6. REGIONAL APPLICABILITY OF THE ALGORITHMS


Our experience in developing the large-hail probability algorithm suggests that either the Plains or Mid-Atlantic equations would serve in most of the conterminous United States.

The choice of predictors in a general severe weather probability equation depends on the dominant modes of severe weather (hail or wind), which in turn depend on regional storm climatology, surface characteristics, forestation, and extent of land development. As noted, the prime environmental predictors for the Plains equation (2) appear to be associated with hail potential, while the equation for the Mid-Atlantic (1) reflects mainly the potential for wind events. An examination of severe local storm reports between 1973 and 1994 indicated that wind events predominate east of the 85th meridion, with hail events predominating farther west. We therefore have constructed the algorithm so that the 'Mid-Atlantic' equations are used for all radar sites east of that meridion, and the 'Plains' equations are used at sites to the west of it.

In the southeastern and south-central U.S., it is possible that many wind events during the late spring and summer are driven more by local instability effects (e.g. wet microbursts) than by vertical momentum transfer. In that case, the prime environmental forcing mechanism would be low-level temperature lapse rate or theta-e lapse rate, rather than 700-mb wind speed. We plan to investigate this possibility following the collection of an adequate sample of radar observations.

7. GRAPHICAL PRESENTATION OF THE ALGORITHM OUTPUT


Probability values are listed along with with other information in a text popup box in the AWIPS Thunderstorm Product display. This box is brought up by locating a cursor over a cell identified in the SCAN Thunderstorm Product display (Smith et al. 1998). Information on storm location, velocity, VIL, reflectivity, and lightning activity then appears (Fig. 4). The SSWD value for the cell appears under "SWP" and the SSHD value under "HAIL."

To obtain the box for any identified storm cell in the Thunderstorm Product display:

1) Select Storm Cells/Site Storm Threat from the local radar menu;

2) Position the cursor over the "Thunderstorm Popup" text identifier at the lower right part of the screen, and middle click. This makes the product "editable";

3) Position the cursor within a cell circle and right-click to bring up the box for that cell.

8. SKILL OF THE ALGORITHMS IN TERMS OF CATEGORICAL FORECASTS


Though SSWD and SSHD provide probabilistic guidance, their performance is most easily evaluated by examining categorical (severe/nonsevere) forecasts based on the probabilities. Categorical forecasts are generally derived by setting some fixed threshold probability value, and forecasting all storm cells with probabilities at or above the threshold to be severe. All other cells are assumed to be nonsevere. This verification exercise is most useful when a range of possible thresholds, from low to fairly high, is examined.

The performance of these forecasts may be described by four commonly-used measures, the probability of detection (POD), false alarm ratio (FAR), bias, and critical success index (CSI) (Donaldson et al. 1975; Schaefer 1990). Let x be the number of severe events correctly forecasted to be severe, w be the number of nonsevere events correctly forecasted, z the number of nonsevere events incorrectly forecasted to be severe, and y the number of severe events incorrectly forecasted to be nonsevere. Then the following definitions apply:


      POD = x / (x + y)                      (5)  

      FAR = z / (x + z)                      (6)

      CSI = x / (x + y + z)                  (7)

      BIAS = (x + z) / (x + y)               (8)

The POD, FAR, and bias tend to decrease if the severe/nonsevere probability threshold is lowered. For rare events such as severe local storms, the CSI reaches a peak value near thresholds that yield neither too low a POD nor too high an FAR.

The performance of the severe weather and large hail algorithms in terms of these scores is shown in Figs. 5-8. The chart for the Mid-Atlantic SSWD algorithm (Fig. 5) can be interpreted as follows: If the yes/no threshold is set at 20%, then over many cases about 75% of the severe cells will be detected (POD = 0.75); 62% of the "yes" forecasts will be false alarms (FAR = 0.62); there will be about twice as many "yes" forecasts as there are severe cells (Bias = 2). The CSI at the 20% threshold is 0.32.

Similar interpretations can be made for the Plains version of SSWD (Fig. 6), and for the regional versions of SSHD (Fig. 7 and Fig. 8). Note that these scores are based on the dependent data sample. We expect that skill will be lower within a sample of new cases, that is, for any given probability threshold, the POD will be lower and the FAR higher in the new sample than in the dependent one. However, experience has shown that the scores shown here are reasonable estimates of the values achievable for independent cases.

9. REQUIRED INPUT PRODUCTS


In order for SSWD and SSHD to be generated in real time, AWIPS must ingest the following products from the WSR-88D Radar Product Generator (RPG):

VIL (product 57)

STI (Storm Track Index, product 58)

These must be included in the Routine Product Set (RPS) list.

The system also ingests numerical model input data for the upper-air conditions. These data could be from the Eta or the RUC models. When model data are unavailable, the algorithms revert to VIL-only estimates of event probability, and a warning message appears in the popup box.

10. DIFFERENCES BETWEEN SCAN ALGORITHMS AND WSR-88D POH AND POSH PRODUCTS


The POH and POSH (Witt et al. 1998) are generated within the RPG. The POH is the probability that a storm cell is producing hail of any size at any level; the POSH is the probability of large hail at the surface. The POSH algorithm is similar to that in SCAN, in that both rely on measures of upper-level reflectivity within the storm and the height of the freezing level. However, environmental data for POSH must be entered manually through the radar Unit Control Position, while SSWD and SSHD obtain environmental data automatically from within the AWIPS database. To date, no large-scale comparison has been made between POSH and SSHD.

11. IMPLICATIONS FOR OPERATIONAL USE


These techniques do not possess high absolute accuracy in identifying severe storms; that is, a high probability of detection is associated with a high false alarm rate. Thus the algorithms are intended primarily to alert forecasters to sudden or unexpected severe storm development. Other considerations, such as three-dimensional storm structure, storm motion, and real-time spotter reports must be used to decide which storms actually warrant warnings, and where the warnings should be valid. At the same time, forecasters can be confident that storms with very high SSWD values (70% or more) are very likely to be severe. Meanwhile, the vast majority of storms are assigned very low probabilities (< 5%), and these are very unlikely to be severe within the next 30 minutes.

For specification of large hail in severe weather warnings, absolute skill is again rather low. Forecasters can be confident that storms with SSHD in excess of 50% will generally produce hail shortly, and may wish to specifically mention hail as a threat in statements to the public.

We have used NGM data as a robust source of upper-air information in the development of these equations. It should be noted that the algorithms include only upper-air predictors that have a fairly broad spatial structure function, and thus do not change quickly with time.

ACKNOWLEDGEMENTS


We are indebted to Robert Saffle and Wayne McGovern, both formerly employed in the Techniques Development Laboratory, for their expertise and their support of this work. Melvina McDonald developed the RADAP II data archive used here. Manual reduction of the WSR-88D VIL graphic images was carried out expertly by Bryon Lawrence and Mary Scarzello.

REFERENCES


Breidenbach. J. P., D. H. Kitzmiller, and R. E. Saffle 1993: Joint relationships between severe local storm occurrence and radar-derived and environmental variables. Preprints 13th Conference on Weather Analysis and Forecasting, Vienna, Virginia, Amer. Meteor Soc., 588-591.

Donaldson, R. J. Jr., R. M. Dyer, and J. J. Kraus, 1975: An objective evaluator of techniques for predicting severe weather events. Preprints Ninth Conference on Severe Local Storms, Norman, Amer. Meteor. Soc., 321-326.

Hoke, J. E., N. A. Phillips, G. J. DiMego, J. J. Tucillo, and J. G. Sela, 1989: The regional analysis and forecast system of the National Meteorological Center. Wea. Forecasting, 4, 323-334.

Kitzmiller, D. H., W. E. McGovern, and R. E. Saffle, 1995: The WSR-88D Severe Weather Potential Algorithm. Wea. Forecasting, 10, 141-159.

_____, and J. P. Breidenbach, 1993: Probabilistic nowcasts of large hail based on volumetric reflectivity and storm environment characteristics. Preprints 26th International Conference on Radar Meteorology, Norman, Amer. Meteor. Soc., 157-159.

_____, and _____, 1995: Detection of severe local storm phenomena by automated interpretation of radar and storm environment data. NOAA Technical Memorandum NWS TDL 82, National Weather Service, NOAA, U.S. Department of Commerce, 33 pp. [Available from Techniques Development Laboratory, W/OSD2, National Weather Service, 1325 East West Highway, Silver Spring, Md.]

McDonald, M., and R. E. Saffle, 1994: Revised RADAP II archive data user's guide. TDL Office Note 94-2, National Weather Service, NOAA, U.S. Department of Commerce, 18 pp. [Available from Techniques Development Laboratory, W/OSD2, National Weather Service, 1325 East West Highway, Silver Spring, Md.]

Schaefer, J. T., 1990: The critical success index as an indicator of warning skill. Wea. Forecasting, 5, 570-575.

Witt, A., M. D. Eilts, G. J. Stumpf, J. T. Johnson, E. D. Mitchell, and K. W. Thomas, 1998: An enhanced hail detection algorithm for the WSR-88D. Wea. Forecasting, 13, 286-303.