On the Imprecision of Radar Signature Locations and Storm Path Forecasts

Douglas A. Speheger and Richard D. Smith

NOAA/NWS Forecast Office, Norman, Oklahoma

Final Submission January, 2006


Weather radar data are often used to determine the location and projected path of severe weather without the understanding of the limitations inherently involved with these data. This paper documents the imprecision of radar-based features by comparing locations of radar-derived circulation centers with over 90 tornadoes surveyed in the Norman Oklahoma National Weather Service county warning area, demonstrating that location errors of more than one-half mile are common, with location errors of up to 8 miles also observed. Meteorological sources of uncertainty are discussed as well as general limitations of weather radar. Both the imprecision of radar to determine where severe weather is currently occurring and the often non-linear movement and evolution of severe weather make the projection of these features difficult in both time and location. The impact of these imprecise projections to users is also discussed.

1. Introduction

Following a number of recent tornado outbreaks, including the May 3, 1999 Oklahoma/Kansas tornado outbreak, meteorologists from the National Weather Service Weather Forecast Office (WFO) in Norman and other local NOAA agencies performed numerous ground surveys of tornado damage. Since 1995, detailed ground or aerial surveys were made for over 100 tornadoes within the Norman county warning area (CWA). While comparing tornado paths from these damage surveys with the locations of radar signatures, it has been noted that there can be a distance of a few miles between the location of the radar signature and the corresponding tornado damage path. This uncertainty in the radar estimated location has significant implications on the ability to pinpoint where damaging weather is occurring, and the ability to predict the movement and locations of dangerous storms.

For several years, the broadcast media and National Weather Service Forecast Offices have expanded their use of detailed storm path forecasts (also known as pathcasts) to try and provide detailed warning information to those in the path of a tornado or severe thunderstorm. These efforts have resulted in a wide range of levels of detail in forecasts, from highly specific street-by-street forecasts of storm position and arrival times to more general estimates of location and impact times. Occasionally, these pathcasts are created or interpreted by users who might not be aware of the imprecision inherent with these projections.

2. Data and methodology

Figure 1
Figure 1
Since 1995, the WFO Norman has conducted or obtained highly detailed ground surveys of over 100 tornadoes within the Norman CWA conducted by ground surveys. Radar circulation locations were taken from the Twin Lakes, OK (KTLX), Vance AFB, OK (KVNX) and Frederick, OK (KFDR) Weather Surveillance Radar 88 Doppler (WSR-88D) radars and compared to the path of 94 of these tornadoes (see Appendix A). The radar circulation center locations were manually identified by finding the strongest gate-to-gate shear using the 0.5 degree elevation angle data. Figure 1 shows an example of the surveyed location of a violent tornado that struck the Oklahoma City metropolitan area on 8 May 2003 and the storm-relative velocity image from the KVNX radar which is approximately 100 miles to the northwest. In this case, the strongest gate-to-gate radar signature was located approximately 3 miles southeast of the damage path. For all of the tornadoes in this study, the latitude and longitude were taken from the cursor readout of the radar Principal User Processor (PUP) or the Advanced Weather Interactive Processing System (AWIPS) workstation, and these coordinates were plotted on a street map using the U.S. Census Bureauís Tiger Map web server.
Figure 2
Figure 2
The tornado paths were then drawn onto the map using the survey information. An example of surveyed tornado tracks compared to centers of radar circulation for a tornado event on 11 April 2001 is shown as Fig. 2. For this event, the location of the tornado determined by ground and aerial surveys is often displaced from the location of the strongest radar gate-to-gate shear by as much as 2 miles.

3. Results and Sources of Error

The center of circulation identified from the lowest radar elevation angle was compared to the surveyed tornado location of the 94 tornadoes, and the one-dimensional difference in distance is shown as Fig. 3. The time of the tornado at any given location is generally unknown, so it is not known where the tornado is along the track at the exact time of the radar data. Therefore, the distances shown on Fig. 3 are one dimensional distances (normal to the damage path) from the circulation center to the nearest point of the damage path. A two-dimensional distance (which includes both the distance normal to the damage path and the distance along the damage path) will be greater if the tornado is not at the closest point of the surveyed track at the time of the radar signature.
Figure 3
Figure 3

A least squares fit regression line is plotted on Fig. 3. This figure shows that the error is greater at a longer distance from the radar where the radar beam may be overshooting the low level circulation. However, even within 30 statute miles of the radar, there were a number of cases where the radar estimated location was one or two miles from the location of tornado damage. Uncertainty of two miles using radar is enough to make specific determination of a tornado location unreliable. At greater distances from the radar, the error has been as much as eight miles in the case of an F2 tornado in the Oklahoma City metropolitan area. In this extreme case, the mid-level rotation associated with the tornadic circulation had dissipated and another developing circulation was observed by the Frederick, OK radar approximately 110 miles from the storm. Fortunately, in this case, data from a closer radar were available that showed low-level rotation with the tornadic portion of the storm. Table 1 shows the mean one-dimensional distance at various ranges from the radar of the 94 tornadoes studied and the percentage of signatures that are at least one-half and one mile from the tornado location. When the radar circulation signature is over 20 miles from the radar, the distance between the radar signature and the tornado is one-half mile or greater more than 50% of the time.

Figure 4
Figure 4
The 11 April 2001 case displayed in Fig. 2 shows that although there is an approximate one to two mile error in the tornado location based on the center of radar circulation, the general direction of movement on radar is consistent with the tornado path. However, an example from a tornado outbreak on 9 October 2001, shown as Fig. 4, shows that the movement of radar circulation signatures may not always indicate the true direction of tornado movement. Radar indicated that the circulation was moving to the east-northeast, while the tornado moved to the northeast and north-northeast.

Figure 5
Figure 5
One major source of error when comparing mesocyclone locations to the tornado path is the tilt of the vortex. This can often be seen visibly below cloud base as shown in Fig. 5 where the tornadoís location at the surface can be significantly displaced from the location of the circulation at cloud base. In this photograph, the location of the tornadoís contact with the ground is estimated to be displaced about one half mile west of the location of the vortex at cloud base. The radar perspective of this tilt has been documented as early as the Union City, OK tornado in 1973 in which the tilt in elevation of the radarís tornado vortex signature (TVS) with height was consistent with the observed tilt of the tornado below cloud base and this tilt continued at elevations well above cloud base (Brown et al., 1978). Figure 6 shows the actual path and radar circulation centers for the tornado that moved through the south Oklahoma City metropolitan area on 8 May 2003. This tornado occurred between 7 and 16 miles from the Twin Lakes (KTLX) radar. Overlaid with the surveyed damage path are the manually identified circulation centers at the 0.5, 4.3, 10.0 and 14.0 degree elevation angles from the KTLX radar.
Figure 6
Figure 6
The centers of circulation at the 0.5 degree elevation angle (altitude between 300 and 1,000 feet AGL) are within about 1/4 mile of the center of the tornado damage path. But as the elevation angle is increased to 14.0 degrees (altitude between 11,500 and 20,000 feet AGL), the radar-detected circulation was up to 3 miles away from the damage path, even at close range. Most commonly, the tornado damage path was located to the south of the center of radar circulation as is shown in Figs. 2 and 6, which suggests that storm tilt can lead to discrepancies between radar circulation centers and tornado paths in situations of increasing southerly winds with elevation that are usually present during severe weather events in the Southern Plains. However, there were still a significant number of events where the tornado damage occurred to the north of the radar circulation. In some cases, there was variability even with the same tornado event. We found no systematic bias. For a given radar elevation angle, the height of the radar beam above the surface increases and the uncertainty based on the tilt of the storm increases at greater distances from the radar.
Figure 7
Figure 7
Although precise beam height is not known because the refraction of the radar beam varies with the thermodynamic properties of the atmosphere, estimates can be made using a standard atmosphere as is shown in Fig. 7 (NOAA 2004).

The width of the radar beam can also influence the location of a radar-identified circulation, and as with beam height, increases with downrange distances. On average, the WSR-88D has a beam width of 0.93 degrees, but because of the radar antenna rotation and the pulse repetition frequency, the effective beam width broadens to 1.29 degrees (Wood and Brown 1997). Therefore, at a distance of 50 miles from the radar, the effective diameter of the radar beam is 1.13 miles, and at 240 miles from the radar, it is 5.4 miles. Since the velocity signature of a circulation would be detected between two adjacent radar azimuths, depending on where the circulation happens to fall relative to the radar beams, this will lead to uncertainty on the location of the circulation of up to one-half of the beam diameter based solely on this sampling. Although the specific values listed here represent the WSR-88D radar, the issue of beam width would apply to any radar. The width of a radar beam depends on the radar wavelength and the diameter of the radar dish (Doviak and Zrnic 1984). The radar beam will be larger for smaller radar dish diameters or longer wavelengths. Similarly, the uncertainty in location along a radar radial is one-half of the length of a radar bin. Upon initial deployment of the WSR-88D, the storm relative velocity was determined using a bin length of 1 kilometer along the radial, therefore, the distance from the radar would have an uncertainty of up to 0.5 kilometer (0.31 mile). Storm-relative velocity data are now available in some circumstances with bins of 0.25 kilometers, reducing this uncertainty to 0.08 miles.

There is also an inherent limitation to the mechanical accuracy of the radar determining the azimuth. There is a maintenance check performed on the WSR-88D radars where the radar is pointed at the known azimuth and elevation of the sun to minimize this source of uncertainty. This test is performed monthly and places the radar within a +/- 0.33o tolerance. A 0.33o uncertainty in the azimuth would yield an uncertainty of 0.29 miles at a range of 50 miles, and 1.39 miles at a range of 240 miles. The actual uncertainty in azimuth is usually less than these values with radars that are properly maintained.

Figure 8
Figure 8
Non-meteorological factors contribute to the complexity of communicating the location of a threat with precision. For example, cities and towns are often defined as a single point on a radar display (such as the location of city hall, or the geographic center of the town), even though the city may cover many square miles. The interpretation of a phrase such as "6 miles southwest of Oklahoma City" is difficult when the city limits of Oklahoma City encompass 607 square miles (U.S. Census Bureau, 2000) in four different counties. The latitude/longitude coordinates initially used in the AWIPS system, and probably also used in other computer systems, were taken from the United States Census Bureauís Gazetteer files. The Census Bureau defines these coordinates as "The lat/long for each place was calculated with reference to the legal boundaries of the entity as of the 1990 census and 2000 census respectively, not to the center of a collection of buildings (like the central business district). ... The resulting point is the approximate geographic center of the polygon making up the legal entity." (U.S. Census Bureau 2002). Figure 8 shows the result for the city of Norman, OK. The city of Norman encompasses an area of 177 square miles (U.S. Census Bureau 2000) with most of the population in the western section of the city. The U.S. Census Bureau coordinates for Norman are more than 5 miles east of the downtown area and almost 12 miles east of the western city limits. As a result, the location of a tornado in downtown Norman would be described ambiguously as "5 miles west of Norman" using these coordinates. The May 3, 1999 Bridge Creek/ Oklahoma City/ Moore tornado caused F5 damage and a number of deaths within the city limits of Oklahoma City. However, its location was 9 miles from downtown Oklahoma City and the point of reference used for the city in the Census Bureauís Gazetteer files. Without manual intervention, Oklahoma City would not have been listed as being in the path of the tornado.

4. Implications for "pathcasting"

These results have obvious implications on the accuracy of storm track forecasting. Not only is there already some uncertainty in the initial location and movement of the storm based on radar signatures, the pathcast often makes a linear extrapolation of storm motion, which is often non-linear. This can lead to significant errors in the projected path.

A major source of error in pathcasts is the assumption that a certain linear motion will continue through the duration of a projection. While this will occasionally work reasonably well, there will often be deviant motion within a storm that will violate this assumption, especially with longer projections. There may also be a difference in the motion of the tornado and the parent thunderstorm. The NWS Warning Decision Training Branch cites two examples in their Tornado Warning Guidance (2002) observed by researchers during the VORTEX (Verification of the Origin of Rotation in Tornadoes Experiment) project:

Storm motion and tornado motion (direction and speed) may be significantly different. For example, on two VORTEX days (6/2/95 and 6/8/95), there were several instances where the parent thunderstorm was moving toward the northeast while the tornado was moving north. In addition, for another case, the tornado's forward movement was measured at 60 mph only to become nearly stationary before it dissipated. Be careful about issuing tornado warning locations based on the storm cell centroid motions; use the motion of the radar vortex signature, whenever available, and allow adequate room to allow for uncertain (and nonlinear) tornado motion.

Figure 9
Figure 9
Figure 9 shows an example from 3 May 1999. A supercell thunderstorm that had already produced five tornadoes began producing a sixth tornado about nine miles southeast of the town of Anadarko, OK. For three radar volume scans, the circulationís path was to the northeast at 27 mph. If a pathcast had been issued on the storm at this point using this linear motion, it might have read:

   " * The storm will be...
         2 miles southeast of Verden at 6:00 P.M.
         8 miles northwest of Chickasha at 6:15 P.M.
         5 miles northwest of Amber at 6:30 P.M.
         3 miles west of Tuttle at 6:45 P.M."

As Fig. 9 shows, the storm turned to the right and continued to produce tornadoes during this time, including the beginning of the F5 Bridge Creek/Oklahoma City/Moore Tornado (A9) as documented by Speheger et al. (2002). Not only was the center of radar circulation one mile away from where the tornado was initially producing damage west of Chickasha, this pathcast would have yielded errors of approximately 2 miles, 4.5 miles, 7 miles and 8 miles at each forecast time. In addition, tornadoes associated with this thunderstorm hit the northwest edge of the city of Chickasha, the Chickasha airport, and the southeast edge of the town of Amber despite the fact that the pathcast would have indicated the tornado would stay well to the west and north of these towns. As mesocyclones or tornadoes occlude and redevelop, additional non-linearity is observed, both in the perceived motion of radar circulations and in the tornadoes themselves. Other inaccuracies can result from radar mapping errors, and errors in radar derived speed and motion information.

Most systems used to generate storm path forecasts require the user to manually select the storm features to be tracked. This introduces the possibility that the wrong part of the storm might be selected for tracking, thus introducing additional time and location errors in the pathcast. There are many potential areas that can be identified and tracked in a severe thunderstorm (Piltz and Smith 1998), including the mesocyclone, hook echo, gust front, leading edge of the precipitation, high reflectivity cores, high reflectivity gradient, and algorithm-based feature locations. For example, there is an anecdotal account of a tornadic supercell being tracked by a meteorologist through a major metropolitan area. The storm exhibited a rather pronounced hook echo and velocity signature at low levels on radar, and spotter reports corroborated the tornadoís location. However, despite this information, the meteorologist incorrectly chose the high reflectivity core of the supercell as the basis of a tornado path projection, which in this case was seven to eight miles north of the tornado location. This forecast resulted in misinformation and confusion concerning who was in the tornadoís path.

Besides the meteorological uncertainty related to the projection of a tornado location, there is also the issue of a personís misperception of pathcast precision. A victim of the Moore tornado of 8 May 2003 mentioned in a post-storm interview, "Leroy told me they were saying on TV it would hit at 5:27, so I better get in. But it hit before then" (Patton 2003).

Researchers with the Oklahoma Department of Health also interviewed tornado survivors following the 8-9 May 2003 Oklahoma City metro tornadoes regarding the tornado warning system. A number of respondents indicated they were confused by the tornado locations and arrival times presented by the broadcast media. One respondent said the warning on television had indicated the tornado would strike in about 20 minutes, but in reality the tornado hit after only "a couple of minutes." Others responded that they felt some of the television pathcast times were inaccurate, and that they were confused by different arrival times being projected by different television stations. (R.D. Comstock 2003 personal communication)

After a tornado outbreak in Arkansas on 1 March 1997, the newspaper USA Today (1999) carried an Associated Press article describing a young woman who at 2:30 P.M. heard the warning of a tornado predicted to hit the town of Arkadelphia, AR around 2:50 P.M. She and a friend drove to her house in Arkadelphia to rescue her sister from the approaching storm.

"Comforted by the advance notice, they braved heavy winds and rain and reached home at 2:47 P.M., a minute after [italics added] the storm entered the town of Arkadelphia. Thinking they had several minutes more, [the three women] returned to the car - right on the tail of a twister concealed by the surrounding rain."

The National Weather Service warning issued at 2:14 P.M. mentioned that the tornado would reach Arkadelphia at 2:50 P.M.. The tornado continued in a generally linear motion allowing the projection to verify within 5 minutes. But this young woman perceived the forecast to have greater precision than is possible, and placed herself in danger.

Warnings and other statements might still include information on the projected movement, arrival times at certain locations, etc, while accounting for the uncertainties and imprecision inherent in the process. A warning might use a range of times for arrival to a certain area, such as the statement "this storm will impact western parts of Oklahoma City between 5:15 P.M. and 5:30 P.M." The meteorologist may also want to account for the fact that different threats exist at different locations within the same storm. This could be done with statements such as: "the leading edge of the storm, producing strong winds, heavy rain and hail, will move into the city around 4:30 P.M. The highest potential for a tornado will occur after 4:45 P.M.", or "The threat of a tornado will be highest along and just south of Interstate 44. However, large damaging hail will also be likely, especially just north of the interstate."

5. Summary

There are a number of meteorological, mechanical and mapping uncertainties inherent in radar data, and it is important for the radar and broadcast meteorologist to understand these limitations, and to give accurate information without conveying a false sense of precision. Although some of these limitations such as radar beam width can be addressed with the design of individual radar systems, other sources of uncertainty will still apply to all radars. For example, the uncertainty based on the tilt of the tornado vortex will apply to any radar system. As shown in this paper, there are limitations to current technology, and the public may perceive precision that is not available. The radar circulation signature may be some distance from where a tornado is occurring, and there is a much greater uncertainty at greater distances from the radar. Users can not use isolated cases where a radar detected a tornado location well, especially those near the radar, to demonstrate that the radar will always have this precision. When this uncertainty in a current position of a tornado is combined with the linear extrapolation of a potentially significantly non-linear event, the resulting uncertainty in projected locations and times in a pathcast can be large. The implications associated with potentially significant time and location differences in severe storm pathcasts suggest meteorologists and others involved in disseminating severe weather forecast information use caution when dealing with storm path forecasts. Warnings giving specific locations at times in the future such as the theoretical example in section 3 are especially problematic since they combine the uncertainties of both where the tornado is currently occurring and the linear extrapolation of its motion, but also give "exact" locations of the projection. Pathcasts listing approximate arrival times to or near specific locations should be used cautiously and with an understanding of the uncertainty inherent in such a projection. Frequent updates to storm information and projections are important to update the changes in the storm character or projection of movement.

Although this paper discussed tornado damage specifically, most of the limitations mentioned will also apply to detection of other phenomenon, including hail, rain and wind. Additional limitations may also exist with these features, such as displacement of rain from its apparent position on radar by low-level winds.


The authors would like to thank David Andra (NWS Norman OK), Liz Quetone, Jami Boettcher, and Andy Wood (NWS Warning Decision Training Branch), and Steve Piltz (NWS Tulsa OK) for their review and suggestions for this paper. Thanks are also extended to Dr. Alan Czarnetzki (University of Northern Iowa) and James Noel (NWS Wilmington OH) for their reviews and suggestions to improve this text.


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