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341MARCH 2005AMERICAN METEOROLOGICAL SOCIETY |

M

DO METEOROLOGISTSSUPPRESS THUNDERSTORMS?

Radar-Derived Statistics andthe Behavior of Moist Convection

BY MATTHEW D. PARKER AND JASON C. KNIEVEL

Reflectivity statistics from the WSR-88D network shed light on storms’ behavior

and reveal that meteorologists’ hometowns probably are not the weather holes

that many believe them to be.

ost meteorologists are acquainted with the no-tion of a weather hole—that is, a place that re-ceives less exciting weather than does its sur-

roundings. Exciting weather takes many forms, butwhen people use the term weather hole, they tend tomean a place that thunderstorms often barely miss, ornear which approaching storms often dissipate. For thispaper, that is the meaning we adopt.

In our experience, many meteorologists and layweather enthusiasts genuinely believe that they live inweather holes, and this belief, almost without fail,

AFFILIATIONS: PARKER—Department of Geosciences, Universityof Nebraska–Lincoln, Lincoln, Nebraska; KNIEVEL—NationalCenter for Atmospheric Research,* Boulder, Colorado*The National Center for Atmospheric Research is sponsored bythe National Science FoundationCORRESPONDING AUTHOR: Dr. Matthew Parker, 214 BesseyHall, University of Nebraska–Lincoln, Lincoln, NE68588-0340E-mail: [email protected]:10.1175/BAMS-86-3-341

In final form 23 August 2004©2005 American Meteorological Society

seems to stem from countless hours spent gazing atdisplays of radar reflectivity. We have generally pre-sumed that such people simply relish thunderstorms,are memorably disappointed whenever storms missthem, and erroneously conclude that their locations aresubject to some kind of meteorologic disfavor.

The recent availability of multiple years’ worth ofnational radar composites from the WeatherSurveillance Radar-1988 Doppler (WSR-88D) networkmakes it possible to address objectively, if notdefinitively, whether meteorologists appear to live inweather holes and whether such an appearance isphysical or artificial.

MOTIVATION. Although friendly hallway debateabout weather holes perhaps does not constitute apressing scientific problem, meteorologists’ seeminglycommon belief that they live in weather holes suggeststhat the statistical behavior of moist convection ispoorly understood. If moist convection is somewhaterratic—often dissipating, reforming, and movingnonlinearly—then an observer should expect upstreamthunderstorms to strike any single location far less fre-quently than they strike anywhere else but that singlelocation. To paraphrase Grazulis (2001) in his commen-

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tary on the probability of tornado strikes, “there” en-compasses much more area than “here” does.

Our study is an effort to satisfy our curiosity aboutrumored weather holes while simultaneously testing afew simple methods of constructing climatographiesof convective echoes using the comparatively new, andreadily available, data from the WSR-88D network. Inthe future, radar-based climatographies may prove tobe very powerful, important tools for forecasting thun-derstorms and for quantifying the risks that thunder-storms pose to society. But, before that potential is re-alized, limitations in the WSR-88D network must bebetter documented and mitigated.

BACKGROUND. Thunderstorms are defined bytheir lightning and thunder, and it was upon observa-tions of thunder that researchers based earlyclimatographies of thunderstorms in the United States(e.g., Harrington 1894; Alexander 1915; Changery 1981;Dai 2001a,b). Before 1893, precipitation had to accom-pany thunder to warrant an official thunderstormreport, but this is no longer true (Humphreys 1920).In the last few decades, lightning has been used verysuccessfully for thunderstorm climatographies, owingto the regional and national detection networksestablished starting in the 1980s (e.g., Reap 1986;Orville 1987; Reap and MacGorman 1989; Orville andHuffines 2001), and to satellite-borne instruments suchas the Lightning Image Sensor (e.g., Christian et al.1999) and Optical Transient Detector (e.g., Boccippioet al. 2001).

The remaining methods of identifying or, at least,inferring thunderstorms rely on clouds and precipita-tion as proxies for lightning and thunder. Spreadingcirrus tops of anvil clouds have been used as markersin satellite-based climatographies (e.g., Banta andSchaaf 1987). Hail has also been used, but standardNational Weather Service hail reports greatlyunderrepresent thunderstorms (Court and Griffiths1981; Witt et al. 1998) and may be biased toward se-vere thunderstorms, which are distributed differentlyfrom the total population of thunderstorms (Wallace1975). Rain, on the other hand, has proven quite use-ful for thunderstorm climatographies. Although rain-fall alone is not a reliable discriminator among con-vective modes, rainfall rate can be. Rainfall ratesinferred from radar reflectivity, in particular, are ex-tremely useful for constructing climatographies of thun-derstorms. Until recently, researchers relied primarilyon manually logged reflectivity (e.g., Byers and Braham1949; Falconer 1984; Michaels et al. 1987; Matthews andGeerts 1995). Now, in the United States at least, theWSR-88D network makes possible more automated

regional and national studies of thunderstorm distri-butions through datasets that provide excellent reso-lution and good, if not thorough, coverage (e.g.,MacKeen and Zhang 2000).

No matter the data on which they are based, virtu-ally all climatographies reveal pronounced spatial vari-ability in areas where thunderstorms occur. Not sur-prisingly, the scale of the variability follows theresolution of the data. Spatial variability consistentenough to appear in extensive climatographies mustbe due to fixed, slowly varying, or regularly recurringinfluences on moist convection. For example, mechani-cal lifting of conditionally unstable air by inclinedground (Hallenbeck 1922; Banta 1990) or by sea breezes(Frank et al. 1967; Pielke 1974) can concentrate moistconvection. Conversely, moist convection may be in-frequent over, and immediately downwind from, rela-tively cool lakes (Wilson 1977; Segal et al. 1997), as wellas beneath subsiding branches of solenoidal circula-tions (Hindman 1973; Banta and Schaaf 1987). Soilmoisture and vegetation also influence the location andtiming of moist convection, but the complexity andnonlinearity of the processes involved make the pre-cise results of those influences hard to predict (Pielke2001). Moreover, compared with many physiographicinfluences on moist convection, soil moisture and veg-etation can change quickly as, for example, irrigationand crop maturity on farms vary through the growingseason (Fowler and Helvey 1974; Stidd 1975; Mooreand Rojstaczer 2001).

Unquestionably, topography and land cover influ-ence distributions of thunderstorms. Is it also possiblethat meteorologists and other weather enthusiasts in-fluence distributions by suppressing or deflecting thun-derstorms? Such superstition seems akin to the beliefthat a community is protected from tornadoes by vir-tue of a nearby hallowed burial site (e.g., Grazulis 2001;Sobczyk 2002). Yet meteorologists and other weatherenthusiasts have insisted to us that they live in weatherholes, sometimes with the zeal usually reserved fordiscussions of politics and sports. If such suspicions arecorrect, either meteorologists do influence weather orthey have the astoundingly rotten luck of consistentlyestablishing educational programs, research institu-tions, and forecasting companies in cities where thun-derstorms just happen to be relatively infrequent. Mostlikely, these superstitious meteorologists simply mis-understand the statistical behavior of convection.

Henceforth, weather hole, or simply hole, means asite that receives disproportionately fewer thunder-storms than its surroundings receive; weather hot spot,or simply hot spot, means the converse. Objective defi-nitions follow in the next section.


TABLE 1. Twenty-eight targets selected for detailed study becauseof their prominent populations of meteorologists and their regulardistribution across the conterminous United States.

ID

ALB

ARB

BOU

CLL

CMI

CVO

DCA

FCL

GFK

GTF

HSV

IDA

LAX

LBB

Location

Albany, NY

Ann Arbor, MI

Boulder, CO

College Station, TX

Urbana–Champaign, IL

Corvalis, OR

Washington, DC

Fort Collins, CO

Grand Forks, ND

Great Falls, MT

Huntsville, AL

Idaho Falls, ID

Los Angeles, CA

Lubbock, TX

ID

LNK

MIA

MSN

OFF

ONM

OUN

RDU

RNO

SEA

SFO

SLC

TLH

TUS

UNV

Location

Lincoln, NE

Miami, FL

Madison, WI

Bellevue, NE

Socorro, NM

Norman, OK

Raleigh–Durham, NC

Reno, NV

Seattle, WA

San Francisco, CA

Salt Lake City, UT

Tallahassee, FL

Tucson, AZ

State College, PA

DATA AND METHODS. Radar. Because, judgingfrom our experience, meteorologists first begin sus-pecting that they live in weather holes while gazing withgrowing consternation at approaching and dissipatingor deviating thunderstorms onplan-position indicator (PPI) radardisplays, radar reflectivity seemedto be the most appropriate datasetfor this research.

Our analyses incorporateNOWrad™ national composites,or summaries, of WSR-88D re-flectivity data for 6 years: 1996–2000 and 2002. We omitted datafrom 2001 because they were miss-ing for 1 January to 3 May.NOWrad™ composites are prod-ucts of the Weather Systems Inter-national (WSI) Corporation. Tocreate the composites, raw data ona polar grid of 1° × 1 km from eachradar are converted to a Cartesiangrid with nominal temporal, spa-tial, and reflectivity intervals of 15min, 2 km × 2 km, and 5 dBZ. Eachpixel’s value is the largest reflectiv-ity measured in a 15-min intervalby any radar in a column above apoint, with the exception that re-flectivity from radars within230 km of a point is given priorityover reflectivity from radars be-yond 230 km. Near the center ofthe raw polar grid, where over-

sampling occurs during conversionto the Cartesian grid, the largestreflectivity is used. When a cone ofsilence above a radar is not filled byreflectivity from another radarwithin 230 km, extended-rangereflectivity from the nearest radarsis used. Automated computer algo-rithms at WSI filter bad data fromindividual WSR-88Ds and from thenational composite before a radarmeteorologist removes by handmost remaining artifacts, includinganomolous propogation echoes.NOWrad™ data cover most of theconterminous United States.

For the purposes of commen-tary in this article, we henceforth calleach echo that is > 40 dBZ a storm

element (or, more briefly, a storm) and call each 15-minradar summary a time. Other researchers have usedthe same or similar thresholds to diagnose thunder-storms and to discriminate between convective and

FIG. 1. Target sites. Three-letter identifiers mark 28 locations with largemeteorological communities, chosen for detailed study. Abbreviationsare defined in Table 1. Dots mark 50 randomly selected backgroundtargets. Targets with good radar coverage are marked in red; the restare marked in blue.

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stratiform rain (e.g., Gamache and Houze 1982;Falconer 1984; Rickenbach and Rutledge 1998). Evenso, the discrimination is imperfect because bright bandsin regions of melting stratiform precipitation can pro-duce reflectivities > 40 dBZ. However, the extent towhich this caused us to overcount thunderstorms is de-batable; for example, the commonly observed brightbands within stratiform regions of mesoscale convec-tive systems (MCSs; Biggerstaff and Houze 1993) areoften attended by lightning and thunder, which definea thunderstorm. Cold-season stratiform precipitationmay also produce bright banding. However, we foundthat almost all of the echoes > 40 dBZ in our sampleactually occurred during the warm season (March-October), so this appears to have had little effect onour results.

The appendix provides some additional commen-tary on the limitations of the NOWrad™ dataset andtheir possible impacts upon our study.

Targets. To test for weather holes and hot spots, wechose 28 target cities with notable meteorologicalcommunities (Fig. 1). Table 1 defines their abbrevia-tions. The pairs of LNK–OFF and BOU–FCL were in-cluded to examine spatial variability in storms wherethe authors reside. Reassuringly, despite some limita-tions in the radar dataset, these sites revealed basicregional consistency in the statistics that we used. Tocreate a background population of targets we used arandom number generator to determine 50 latitude–longitude pairs within the conterminous United States(dots in Fig. 1). The 50 random points were usefulbecause it was not computationally feasible to com-pute all of the statistics for every point within the ra-dar network.

Largely owing to terrain (Fig. 2), radar coverage wasincomplete at some of the targets. Therefore, we iso-lated from the 78 total targets a subset of targets withgood radar coverage (comprising 55 targets of 16 me-teorological cities and 39 random points, shown withred in Fig. 1). In making these selections, we subjec-tively defined “good coverage” to mean that fields ofthe statistics we explain in the next subsection did notexhibit any excessive abnormalities due to blocking byterrain, miscalibration, or unusually sparse distribu-tions of radars in the network.

Statistics. Most of our analyses are based on statisticscalculated from radar data over the conterminousUnited States and over several areas, centered on themiddle of each target city. Many statistics were aver-aged over a circle with a 100-km radius. We also con-sidered three square arrays representing familiar geo-

political areas. A square that is 274 km × 274 km(75076 km2) approximates the size of a typical NationalWeather Service county warning area (CWA). A squarethat is 54 km × 54 km (2916 km2) approximates the sizeof a typical county in the United States. A square thatis 14 km × 14 km (196 km2) approximates the size of amoderately large city. This last target array, the inner-most of the three, is the smallest area for which statis-tics were calculated. Points within the square arrays areidentified by their locations relative to a target pixel,which has coordinates of x = 0, y = 0.

Our statistics are calculated from several formu-las. First, for the binary “storm” variable i40, definedby

(1)

we computed the following statistics at each point inthe target array for the n times in the 6-yr sample asfollows:

(2)

which is the probability, or frequency (Wilks 1995), thatpoint (x, y) had a storm at a randomly selected time,and

(3)

which is the normalized probability that, when a stormat point (x, y) occurred, a storm at the target alsooccurred Dt later, wherein Dt, the lag time, is takenin 15-min intervals between 0 and 120 min. Hereafter,Prhit|storm (x, y, Dt = 0) is designated Prcoexistence|storm (x, y)and represents the probability that storms simulta-neously existed at some regional point and at thetarget. In order to summarize all of the informationrepresented by the two-dimensional Prhit|storm field forall other lag times, we computed the overall prob-ability that a storm at point (x, y) was followed by astorm at the target at any time during the subsequent2 h:


Finally, we also analyzed the time-lagged reflectivitycorrelation between dBZ(x, y, t) and dBZ(0, 0, t + Dt),wherein Dt was again taken in 15-min intervals be-tween 15 and 120 min. Because the lagged correlationsin dBZ essentially confirmed the results from ouranalyses of Prhit|storm, we mention them only briefly inthis article.

Statistical definitions of a weather hole and hot spot. Weconsider a weather hole to satisfy two primary criteria:it must have had markedly fewer storms than did itssurroundings, and it must have been disproportion-ately missed by approaching storms. A hot spot satis-fies the converse criteria.

The first criterion—whether a target had markedlyfewer or more storms than did its surroundings—isquantified by Prstorm. We computed Prstorm for each targetand for each pixel in its surrounding county and CWA.We then computed the following fractional differencesin each target’s Prstorm: (city – CWA)/CWA and (county– CWA)/CWA. If a good target fell within the bottomquartile of the distribution of all 55 good targets foreither fractional difference, it was deemed a potentialweather hole. The converse defines a potential hot spot.(We use the qualifier potential because the completedefinitions of a hole and hot spot are based on morethan just a single criterion.) Figure 3 summarizes thedistributions of targets’ Prstorm and fractional differencesthereof.

The second criterion, whether a target was dis-proportionately missed byapproaching storms, is quan-tified by Pranyhit|storm. We com-puted an average Pranyhit|storm

within a radius of 100 km ateach of the 55 good targets.If a target’s average value ofPranyhit|storm fell within the bot-tom or top quartile of the dis-tribution for good targets,the target was considered apotential hole or hot spot, re-spectively. Figure 4a summa-rizes the distribution of tar-gets’ Pranyhit|storm.

Both criteria were neces-sary because sites with low(or high) values of Prstorm

were not necessarily holes (or hot spots). Many siteswith very low Prstorm are simply located within regionswhere storms are unusually scarce compared to else-where in the nation. These may be dull places for a me-teorologist to live, but they are not “missed” by stormson the regional scale in any recurring way.

Because our objective definitions of holes and hotspots are somewhat arbitrary, and because the behav-ior of convection is apparently not well understood,we analyzed a few additional parameters based on thestatistics above in order to paint a richer picture of thepatterns of thunderstorms in the vicinity of the targets.The first parameter—an average of the maximumlagged correlations in dBZ (for any lag, Dt = 15 –120 min) for each pixel within 100 km of a target—measures how well preceding regional reflectivitieswere correlated with a target’s reflectivity (summarizedin Fig. 4b). This parameter was less susceptible to anypossible local biases associated with radar calibrationand coverage but was somewhat redundant withPranyhit|storm. Therefore, we present it for completeness,but generally without comment. The second param-eter is a fraction, wherein the number of storms arriv-ing from within 60° of the most common upstreamazimuth is divided by the total number of storms to hita target (summarized in Fig. 4c). This parameter mea-sures the directionality of storms’ paths to a target;values range from 0.33 for isotropic storm arrivals to1.0 for unidirectional arrivals. The third and fourth pa-

FIG. 2. Elevation (m) of topography in the conterminous United States.

(4)

346 MARCH 2005|

rameters are the aspect ratio (minoraxis divided by major axis; Fig. 4d) andarea of the region circumscribed byPrcoexistence|storm > 0.1 (summarized inFig. 5a). These two parameters re-spectively describe the relative circu-larity and the size of regions of stormi-ness at a target. Finally, the fifthparameter is the area circumscribedby Pranyhit|storm > 0.50, which is the foot-print of the region where storms weremore likely than not to be followedby a storm at a target within 2 h(summarized in Fig. 5b). This area(Pranyhit|storm > 0.50) was highly corre-lated with the 100-km mean Pranyhit|storm

(a correlation of 0.95), but is includedto help orient the reader, though with-out much additional comment.

STATISTICAL RESULTS.National storm frequency. Storms, as wehave defined them, were most fre-quent in the eastern half of the coun-try, particularly in the Southeast(Fig. 6). This distribution is grosslysimilar to the distributions of dailythunderstorm frequency found byCourt and Griffiths (1981), and to thedistribution of the mean annual den-sity of lightning flashes found byOrville and Huffines (2001). Mesos-cale structures, including distinctmaxima and minima, are clearly vis-ible in Fig. 6. Of course, some of thestructures are obviously artificial, suchas the high reflectivities that sur-rounded Wilmington, North Caro-lina (at 34°N, 78°W), and the beamblocking by terrain in southern Ari-zona and New Mexico. In the appen-dix we comment further on such ar-tifacts and their effect on studies suchas this one.

A typical target. Because it was a typi-cal target and not a hole or a hot spot,LNK serves to demonstrate the diag-nostic capabilities of our statistics.LNK was neither a local minimumnor a significant local maximum inPrstorm (Fig. 7a). LNK’s average Prstorm

was 0.332 × 10–2, which was 5.4%

FIG. 4. Box-and-whiskers plots of statistical parameters for the good tar-gets. The meanings of the boxes and whiskers are as in Fig. 3. (a) Theaverage Pranyhit|storm within a radius of 100 km at each target; (b) the av-erage of the maximum lagged correlation in dBZ for each pixel within100 km of a target; (c) the directionality of Pranyhit|storm, a fraction whereinthe number of storms arriving from within 60° of the most commonupstream azimuth is divided by the total number of storms to hit a tar-get; and (d) the aspect ratio (minor axis divided by major axis) of theregion circumscribed by the 0.1 contour in Prcoexistence|storm. All meteoro-logical targets that fall outside the middle two quartiles are labeled.

FIG. 3. Box-and-whiskers plots of statistical parameters for the goodtargets. The boxes bound the middle two quartiles of the population,with the median shown as a dark line. The whiskers span the top andbottom quartiles. (a) The target city’s average Prstorm; (b) the targetcity’s fractional difference in Prstorm: (city—CWA)/CWA; and (c) thetarget county’s fractional difference in Prstorm: (county—CWA)/CWA.Values in (a) are multiplied by 100 to match the ordinates of (b) and (c).All meteorological targets that fall outside the middle two quartiles arelabeled.


higher than that of its surrounding CWA. Both valuesplaced LNK firmly in the middle of the distribution ofgood targets (Fig. 3).

The predominant gradient in Prstorm from northwestto southeast (Fig. 7a) indicates that thunderstorms wereslightly more common in the southeastern part ofLNK’s CWA than in its northwestern part. During thesix years studied, storms within 100 km to the west-northwest, west, and west-southwest of LNK were fol-lowed within 2 h by a storm at LNK at least 60% of thetime (Fig. 7b), which puts LNK justbarely into the top quartile in termsof Pranyhit|storm (Fig. 4a). However, re-gional reflectivity was not particularlywell (nor poorly) correlated withsubsequent reflectivity at LNK (Fig. 4b;LNK’s value was 0.55).

Judging from the LNK CWA’sPranyhit|storm (shading in Fig. 7b), thun-derstorms arrived at LNK most fre-quently from the west and west-southwest, and very rarely from thesoutheast, although storm direction-ality at LNK was not extreme (Fig. 4c;LNK’s value was 0.42). The aspectratio of storms (Fig 4d; LNK’s valuewas 0.71) and the orientation of themajor axis in Prcoexistence|storm (contoursin Fig. 7b) suggest the recurrence offrontal convective bands and/orMCSs, which most frequently are ori-ented southwest–northeast.

Population-wide behavior.Among all 78 targets, eachyear the average site experi-enced a storm during 81(0.23%) of the 15-min periodswe analyzed, amounting toabout 20 h of annual stormi-ness. The median good targetexperienced about 24 h(0.27%) of storminess (Fig. 3a).The average for all pixels inthe entire U.S. radar network(Fig. 6) was between these twosample averages (0.26%, orabout 23 h of storminess). Wehave not provided plots of thespatial distribution of averagePrstorm for the subsamplepopulations because they arenearly homogeneous. Most

target cities were fairly similar to their surroundings, ascan be seen from the fairly narrow distributions of frac-tional differences, grouped around 0 in Figs. 3b,c.

Plots of average Pranyhit|storm for all 78 targets (Fig. 8a),and for the good targets only (Fig. 8b), reveal similarstructures (with similar interpretations) to those ob-served at LNK. As targets with poor radar coveragewere eliminated from the study, values of Pranyhit|storm

increased slightly (Fig. 8). The typical good target had a100-km mean Pranyhit|storm of 0.46 (Fig. 4a), meaning that

FIG. 5. Box-and-whiskers plots of statistical parameters for the good tar-gets. The meanings of the boxes and whiskers are as in Fig. 3. (a) Thearea of the region in which Pranyhit|storm > 0.50 and (b) the area of theregion in which Prcoexistence|storm > 0.10. Values in (a) are divided by 10 tomatch the ordinate of (b). All meteorological targets that fall outsidethe middle two quartiles are labeled.

FIG. 6. Storm frequency, Prstorm, over the conterminous United States. Valueshave been multiplied by 100 (and therefore are equivalent to percentages). Themean value for all points within the radar network is 0.258 × 10–2.

348 MARCH 2005|

when storms were within 100 km of some point, astorm followed within 2 h at that point slightly less thanhalf of the time. Alternately, for the typical good tar-

get, regional storms were more likely than not to hitthe target when within a 11,792 km2 area nearby andupstream (Fig. 5a).

FIG. 7. Plan views of (a) Prstorm (plotted values have been multiplied by 100 and therefore are equivalent to percentagesand (b) Pranyhit|storm (shaded) and Prcoexistence|storm (thin contours) for LNK during the 6 yr studied. LNK is in the center ofeach diagram (x = 0, y = 0). Dark contours are state boundaries. In (a) the smallest box outlines LNK’s “city,” and thelarger box outlines LNK’s “county.” The full plots encompass LNK’s “CWA.” The statistical computations are ex-plained in the text. The mean areal values of Prstorm were as follows: city, 0.332 × 10–2; county, 0.318 × 10–2; and CWA,0.315 × 10–2. The 100-km average Pranyhit|storm value was 0.54.

FIG. 8. Same as in Fig. 7b, except for (a) all 78 targets and (b) the 55 good targets. Note that the shading scales differfrom those in Fig. 7b. The 100-km average Pranyhit|storm was (a) 0.38 for all targets and (b) 0.45 for good targets.


Values both for lagged correlation in dBZ and forthe “directionality” of Pranyhit|storm had narrow distribu-tions (Figs. 4b,c), suggesting that most targets’ precipi-tation followed regional precipitation in a fairly stan-dard way and that in most places, storms arrived fromthe most climatically favored 120° sector roughly 45%of the time. However, there is great variety in stormaspect ratios among the good targets (Fig. 4d). Thefootprints of storms, or of groups of storms, were typi-cally somewhat elongated, presumably because syn-optic fronts and linear convective systems often shapedthe distribution of storms in much of the United States.However, there are several targets whose local stormi-ness appears to have been quasi circular (Fig. 4d).Notably, the storm aspect ratio was very poorly corre-lated with all of the other statistics that we computed.Therefore, even though aspect ratio provides usefulinformation about typical convective behavior in a re-gion, it does not appear to have greatly influenced ei-ther Prstorm or Pranyhit|storm for the targets in this study.Interestingly, however, the directionality of Pranyhit|storm

was moderately negatively correlated with the 100-kmmean Pranyhit|storm (a correlation of –0.63). In otherwords, targets may appear to have been weather holesif most of their storms arrived from one preferred di-rection, because those targets were often missed bystorms that did not approach from the climatically up-stream direction.

The median storm area parameter (Prcoexistence|storm> 0.1) is 1947 km2 (Fig. 5b). This value is not meant tobe taken as a literal storm size since it is an amalgam oflarge and small, linear, and circular storm elementsover a long period of time. However, it is useful as ameans of comparing targets: smaller values representthe existence of comparatively fewer large convectivesystems in a target’s vicinity. This parameter, in turn,was strongly correlated with the 100-km meanPranyhit|storm (a correlation of 0.87) and with the area ofPranyhit|storm > 0.5 (a correlation of 0.92). In other words,regions with fewer large convective systems were moreoften missed by regional storms (see, e.g., TLH, MSN,OUN, OFF, and UNV in Fig. 5).

Taken together, the parameters in Figs. 4 and 5 arequite useful for characterizing the regional behavior ofstorms. For example, MIA, although neither a hole nora hot spot, was characterized by comparatively small (Fig.5b), circular (Fig. 4d) storms, which arrived from all di-rections (Fig. 4c), rendering a very low lagged correlationin dBZ (Fig. 4b). Nevertheless, MIA’s city mean Prstorm

was the highest in the study (Fig. 3). The picture is that offrequent and seemingly disorganized small thunder-storms.

A weather hole. The lone weather hole among the 28meteorological targets was GFK (Fig. 9). In GFK’sCWA, the regional Prstorm decreased from south to north(Fig. 9a). Although it may not be obvious at first glancethat GFK’s local Prstorm was significantly lower than thatof the surrounding CWA, Fig. 9a does reveal that GFKresides within a corridor where Prstorm was low com-

FIG. 9. Same as in Fig. 7, except for GFK. Note that theshading scales differ from those in Fig. 7. The mean arealvalues of Prstorm were as follows: city, 0.111 × 10–2; county,0.120 × 10–2; and CWA, 0.135 × 10–2. The 100-km aver-age Pranyhit|storm value was 0.33.

350 MARCH 2005|

pared to points farther east and west. The actual valueof GFK’s Prstorm was 0.111 × 10–2, making it 18.4% lowerthan that of the surrounding CWA and placing it inthe bottom quartile (Fig. 3). On average, each year GFKexperienced less than 10 h of storminess. The stron-gest east–west gradient in Prstorm was approximately50–60 km west of GFK, and this corresponds to thewestern wall of the Red River Valley of the North andthe former bed of Glacial Lake Agassiz, in which GrandForks is centered (Fig. 10). Because the gradients inelevation and in Prstorm correspond so well, we infer thatthe Red River Valley is comparatively inhospitable tothunderstorms, perhaps because of local solenoidal cir-culations induced by the terrain. Notably, the gradientin Prstorm west of GFK (Fig. 9a) also roughly coincideswith the eastern edge of the Minot, North Dakota,WSR-88D radar range. We comment on this sort ofsignal further in the appendix. However, the gradientto the east of GFK does not correspond to any suchchange in radar coverage, hence, the GFK signal ap-pears to be at least partly physical.

Also defining GFK as a hole were its relatively lowvalues of Pranyhit|storm (Fig. 9b). A comparison of GFK’sPranyhit|storm to LNK’s (Fig. 7b) and to those of the goodpopulation (Fig. 8b) illustrates that although thunder-storms only a few tens of kilometers west of GFK werefollowed by storms at the target at typical rates, stormsrarely hit GFK from any other direction. This largedirectionality in Pranyhit|storm (Fig. 4c) led to the small azi-

muthally averaged values for Pranyhit|storm at GFK (Fig. 4a)and to its qualification as a hole.

Reasons for the isolated, secondary maximum inPranyhit|storm at x = –30 km, y = 120 km (Fig. 9b) are un-clear. Storms were so scarce there (Fig. 9a) that the sig-nal in Pranyhit|storm may be attributable to only a few oc-casions on which storms in the secondary maximumoccurred serendipitously within 2 h of storms at GFK,without traversing the intervening 100 km. This is con-sistent with the notion that storminess was compara-tively isolated in the GFK region (storms appeared tohave been quite circular at GFK; Fig. 4d) and coveredan area somewhat smaller than average (GFK’s stormarea statistic was 953 km2; cf. Fig. 5b). This implies asmaller proportion of storminess due to fronts and lin-ear convective systems. When episodes of organizedprecipitation are rare in a region, it is not surprisingthat the region’s storm statistics compare unfavorablywith those from most other sites.

A weather hot spot. The lone hot spot among the 28meteorologic targets was TLH (Fig. 11). In TLH’sCWA, values of Prstorm decreased southward and werelargest roughly 20 km inland from the coast. TLH lieson the northern fringe of these maxima, which werealmost certainly caused by recurring diurnal convec-tion associated with the sea-breeze front (e.g., Byersand Rodebush 1948; Frank et al. 1967). The Prstorm de-creased farther inland, especially to the northeast. Asa result, it is evident from Fig. 11a that TLH’s county(and city) mean Prstorm was relatively high comparedto values in many other parts of the CWA. The actualvalue for TLH’s county was 0.709 x 10–2, making it 8.4%higher than that of the surrounding CWA and placingit in the top quartile (Fig. 3). For this reason, TLHqualified as a potential weather hot spot. TLH’s countyhad the highest mean value for Prstorm of any target’scounty in this study, including the random targets.Every year, TLH experienced roughly 62 h of stormi-ness. The maxima in Prstorm south and southeast ofTLH illustrate an important point (Fig. 11a). Hot spotsneed not have been the single most frequent sites ofthunderstorms in their CWA areas. Although TLHwas a hot spot, other locations in its CWA were evenstormier.

TLH’s regional plot of Pranyhit|storm (Fig. 11b) is in manyways similar to that for the typical site, LNK (Fig. 7b).The major axes of maxima in Pranyhit|storm were orientedsouthwest to northeast, for example. The importantdifference is that, around TLH, high values ofPranyhit|storm covered a much larger azimuthal range. Thisis apparently because storms, or groups of storms, overTLH had comparatively large footprints (Fig. 5b), and

FIG. 10. Elevation (m) of topography near GFK (markedby white cross).


yet had very small directionality in Pranyhit|storm (Fig. 4c).In other words, consistent with the persistent sea breezefront, and the generally widespread thunderstorms thattypify summer weather in Florida (e.g., Byers andRodebush 1948), large groups of storms arrived at TLHfrom almost all directions. As a result of this, TLH’s100-km average Pranyhit|storm was in the upper quartileof good targets (Fig. 4a), which helps establish TLH asa hot spot. The area over which Pranyhit|storm > 0.5 forTLH was third largest among the 55 good points andover twice the median value (Fig. 5a). Although TLHand MIA both had very high Prstorm values and mightbe expected to be similar, TLH may have been morelike a hot spot because it was more heavily influencedby cool-season midlatitude fronts (being roughly 5° far-ther north). This would explain its more elongated,larger footprint of storminess (cf. Figs. 4d and 5b), andhence its greater regional Pranyhit|storm and lagged corre-lation in dBZ.

Our assessment of TLH as a hot spot for convec-tive weather is interesting given the claim by Lericos etal. (2002, p. 21) that “meteorologists . . . have often ob-served the apparent demise of nonsupercell squall linesas they approach the Tallahassee area.” Because ourmethods did not separate convective modes, it is pos-sible that if only squall lines were considered, TLH wasa weather hole. It is also possible that, although TLHwas a hot spot according to our criteria, meteorolo-gists’ attention is often drawn to the coast southeast

and southwest of TLH, where thunderstorms are evenmore frequent (Fig. 11a).

Interannual variability. Not only did distributions of thun-derstorms vary spatially among targets, the distribu-tions also varied temporally among years. The varia-tions were no doubt partly a response to changes inregimes of the synoptic and planetary flows that shapethe frequency and organization of convection. Theinterannual variability in the data is one measure ofthe robustness of our results.

LNK’s two most outlying years (1996 and 2000)serve as useful examples. Although a typical site over-all, LNK was a hot spot in 1996 according to our crite-ria for the 6-yr dataset. (The criteria would have beendifferent for individual years.) LNK’s Prstorm was higherthan that of areas to its southwest, west, northwest,north, and northeast (Fig. 12a), and the city was hit bya fairly high proportion of upstream storms (cf. Figs. 7band 12b), especially from the west and southwest. In2000, LNK was very nearly a hole according to our cri-teria for the 6-yr dataset. The city’s Prstorm was lowerthan in much of its CWA (e.g., the quasi-annular ringof elevated Prstorm at a radius of approximately 100 kmin Fig. 13a), and LNK had quite low upstream valuesof Pranyhit|storm in nearly all directions (cf. Figs. 7b and13b). In three of the four other years, LNK was neithera hot spot nor a hole and had statistics more similar tothe means listed in Fig. 7. In 2002, LNK was a hot spot.

FIG. 11. Same as in Fig. 7, except for TLH. Note that the shading scales differ from those in Fig. 7. The mean arealvalues of Prstorm were as follows: city, 0.692 × 10–2; county, 0.709 × 10–2; and CWA, 0.654 × 10–2. The 100-km averagePranyhit|storm value was 0.60.

352 MARCH 2005|

GFK, a hole overall, had lower values of Prstorm thanthat of its surrounding CWA in five of the six yearsand would have qualified as a hole (including thePranyhit|storm criterion) in four of the six years. GFK wasnever a hot spot. TLH, a hot spot overall, had higher

values for Prstorm than that of its surrounding CWA infive of the six years, would have qualified as a stronghot spot in one of the six years, and very nearlyqualified in three additional years. TLH was never ahole.

FIG. 12. Same as in Fig. 7, except only including data from 1996, the year in which LNK was most like a thunderstorm hotspot. The mean areal values of Prstorm were as follows: city, 0.435 × 10–2; county, 0.411 × 10–2; CWA, 0.395 × 10–2. The100-km average Pranyhit|storm value was 0.55.

FIG. 13. Same as in Fig. 7, except only including data from 2000, the year in which LNK was most like a thunderstormhole. The mean areal values of Prstorm were as follows: city, 0.225 × 10–2; county, 0.240 × 10–2; and CWA, 0.264 × 10–2.The 100-km average Pranyhit|storm value was 0.38.


In short, the regional distribution and behavior ofthunderstorms at the targets varied from year to year,such that many were hot spots or holes at certain times.However, for the 6 yr we studied, extreme periodsevened out for most such targets. Only for those thatqualified as holes and hot spots, GFK and TLH, didextreme distributions of thunderstorms tend to per-sist from year to year. Admittedly, a 6-yr dataset is rela-tively short for a thunderstorm climatography, as mosttargets’ interannual variability suggests, and our resultsshould be regarded in this context.

So, do meteorologists suppress thunderstorms? If meteo-rologists suppress thunderstorms, weather holeswould have been more common among the goodmeteorologic targets than among the good randomtargets. They were not. Given our method, at most itwould have been possible to find 13 holes and 13 hotspots among the 55 good targets. An even distributionwould then have yielded 3.8 holes and 3.8 hot spotsamong the meteorological targets, and 9.2 holes and9.2 hot spots among the random targets. Instead, wefound just one meteorological hole and one meteoro-logic hot spot, along with eight random holes and fourrandom hot spots. In other words, holes and hot spotswere less common than might be expected, and weredecidedly uncommon among meteorological commu-nities. Many of the meteorological targets exhibitedsome hole- or hot spot–like qualities, but overall theyfell fairly close to the typical values for all of the pointsthat we tested.

SUMMARY AND INTERPRETATION. Drivenby curiosity and skepticism, we tested the frequent as-sertion that meteorologists and weather enthusiastslive in weather holes—that is, places that receive lessexciting weather than do their surroundings. We lookupon this widespread superstition as an opportunityto take a small step toward improved understandingof the statistical behavior of moist convection.

Our analyses incorporated NOWrad™ nationalcomposites, or summaries, of WSR-88D reflectivitydata for 6 yr: 1996–2000 and 2002. We selected 28 tar-get cities, based on their prominent meteorologicalcommunities, and 50 random targets. We then defineda storm element (or, more briefly, a storm) as an echoof > 40 dBZ and calculated various statistics, fromwhich we defined two criteria for a weather hole. Ahole must have had markedly fewer storms than itssurroundings during the six years we studied, and itmust have been disproportionately missed by ap-proaching storms. The converse criteria defined a hotspot.

According to our data and methods, a meteor-ologist’s hometown is no more likely to be a weatherhole or hot spot than is any random place around theconterminous United States. During the entire 6 yrperiod, the lone weather hole was Grand Forks,North Dakota, and the lone hot spot was Tallahassee,Florida. During any single year, many of the targetswere holes or hot spots according to at least one crite-rion but such short-term behavior does not justifymeteorologists’ enduring superstitions that the mostexciting weather consistently misses them. Over time,very few sites were repeatedly, anomalously missedor hit by storms.

This study is by no means definitive. It is impos-sible to choose objective definitions of a hole or hotspot that are not also somewhat arbitrary. Otherequally reasonable definitions might yield slightly dif-ferent results. For example, a reviewer jokingly la-mented being “missed by the ‘best’ storms ‘on allsides’” and pointed out that some location might behit by a storm (echo > 40 dBZ) but still be missed byeven stronger echoes that were upstream or nearby.The time-lagged correlation in dBZ actually does ad-dress this and similar situations, and it is highly corre-lated to the Pranyhit|storm statistic (a correlation of 0.78).So, the 40-dBZ threshold appears to be a solid refer-ence point for the present discussion, even though thereremain other methods for constructing climatographiesthat may yield additional insight into the statistical be-havior of convective storms.

This study is also not completely categorical becausethe WSR-88D network, although a boon to research-ers and forecasters, is still an imperfect tool for diag-nosing storms (see the appendix). The network is toosparse, especially in the western United States, andterrain can perpetually hide storms in certain regions,even when a radar is nearby. Small amounts of groundclutter seem to elude quality controls, and poor cali-bration and the range dependence of reflectivity canintroduce into climatographies persistent features thatare extremely difficult to eradicate. In some sense,though, these imperfections are unimportant for ourspecific application, because the fairest evaluation ofsuperstitions about weather holes and hot spots is atest of the very dataset that seems to inspire such su-perstitions: radar reflectivity. Most of the persistentholes or hot spots in reflectivity that meteorologistsbelieve to plague their hometowns, whether physicalor artificial, simply did not appear in our analyses.

In part, the commonly held belief in weather holesseems to stem from a generally poor understandingof the statistical behavior of moist convection.Significantly, beyond its usefulness in addressing thun-

354 MARCH 2005|

derstorm holes and hot spots, a large radar reflectivitydataset allowed us to characterize the typical sizes,shapes, orientations, and temporal behaviors ofstorms, or groups of storms, in various parts of thecountry. To the extent that our limited study is repre-sentative of long-term storminess in the conterminousUnited States as a whole, our results suggest that typi-cal storms are likely to be somewhat elongated, em-phasizing the major role played by fronts and linearconvective systems; are likely to approach a locationfrom climatically favored directions less than half ofthe time; and, when within 100 km, are likely to actu-ally strike a given location less than half of the time.Departures from these median statistics then may helpexplain unique storm behaviors in certain regions, suchas the Red River Valley of the North (GFK) or south-ern Florida (MIA).

The data and methods we used together are onestep toward understanding anecdotal claims aboutweather holes and hot spots. More generally, and muchmore importantly, such data and methods may alsoprove to be very powerful tools for forecasting thun-derstorms and for quantifying the risks that thunder-storms pose to society. For many decades, research-ers have proposed and sometimes demonstrated thatclimatic statistics can be a valuable tool for meteoro-logical and hydrological forecasting (e.g., Kincer 1916;Reap and Foster 1979; Balling 1985; Matthews andGeerts 1995; Krzysztofowicz and Sigrest 1997). An ex-ample of a successful application of this sort is ModelOutput Statistics (MOS), in which statistics from ob-servations and from deterministic NWP models arecombined. In decades past, efforts to apply radar-derived statistics to forecasts of thunderstorms weresometimes problematic. For example, there were signsthat poor calibration and variations among operatorsproduced systematic biases in reflectivity from one ra-dar to another (Weiss et al. 1980), and no automated,national system existed for collecting and processingthe data. The WSR-88D network is a great improve-ment over earlier radars, notwithstanding imperfec-tions such as those mentioned above (and in theappendix).

As computational resources permit, it should proveuseful to perform these and other statistical analysesfor every point in the WSR-88D domain, in order toassess possible links between storms and local- toregional-scale terrain and land cover features. Everyday, WSR-88D databases get larger. As they do, thestatistical significance of the patterns in even small sub-sets of the data also gets larger. In the future, it shouldbe possible to construct probabilistic, short-termforecasts of thunderstorm evolution and motion by

using previous storms as analogues. In addition, a suf-ficiently large database should allow us to stratify sta-tistical forecasts by factors such as time of year, timeof day, climatic index, synoptic wind pattern, and soilmoisture.

Currently, forecasters can use a few minutes of real-time radar data to track thunderstorms and predict theirlocations. Perhaps before long, forecasters might usedecades of historical radar data not only to track ex-tant cells, but also to predict changes in those cells’strengths and motions as well as to predict where newcells will develop. Indeed, an informal feasibility studyinto precisely this capability is now underway at the Na-tional Center for Atmospheric Research. We will fol-low their progress with great anticipation.

ACKNOWLEDGEMENTS. NOWrad™ national radarcomposite data were provided by the Global HydrologyResource Center. NOWrad™ is a registered trademarkof the Weather Services International (WSI) Corporation.We appreciate comments and assistance from D. Ahijevych,W. Callahan, R. Carbone, L. Carey, C. Davis, R. Edwards,J. Gourley, R. Henson, S. Honey, T. Lane, D. Loope,R. Maddox, D. Pederson, E. Pytlak, C. Rowe, D. Thompson,R. Thompson, D. Zaras, and two anonymous reviewers,whose insightful suggestions greatly improved themanuscript.

APPENDIX: IMPERFECTIONS IN RADARDATA. Coverage and range dependence. Although theWSR-88D network provides unprecedented radar cov-erage of the conterminous United States, the cover-age is still incomplete, especially in the western thirdof the nation, where it is impossible to construct reli-able thunderstorm climatographies on any scale exceptthe local (Fig. A1). The incompleteness of the radarnetwork is reflected in some of the statistics we calcu-lated, particularly in Prstorm (Fig. 6). The fewer radarsthat scan over a target, the less likely such coarse sam-pling will observe small pockets of high reflectivity. Itmay not simply be coincidental that the lone weatherhole in our dataset, GFK, is covered by only one ra-dar, and the lone hot spot, TLH, is covered by many(Fig. A1).

This problem is compounded if the radars are far froma target because a radar’s sensitivity is a function of dis-tance to a target. Reflectivity depends on range partlybecause a tilted radar beam’s altitude depends on range.Thus, certain angles of tilt intersect the melting level andhence produce bright bands at certain ranges (Baeck andSmith 1998), and may also over- or undershoot storms’regions of maximum reflectivity. Reflectivity also dependson range because radar sample volumes are larger at


greater distances from a ra-dar, thereby failing to resolvesmall reflectivity maxima. Itis more likely that a reflec-tivity threshold will be ex-ceeded near a radar, wherethere are many small vol-umes, than far from a radar,where there are but a fewlarge volumes. Althoughthese problems of coverageand range were unavoidable,our 40-dBZ storm thresholdwas seemingly less suscep-tible to them than were lowerreflectivity thresholds (cf.Figs. A1 and A2).

Ground clutter and blocking byterrain. In the domains usedfor analysis, there are sev-eral pixels whose anomalousvalues revealed the presenceof persistent clutter (e.g., bya telecommunications an-tenna near a radar), even though WSI’s quality controlof the NOWrad™ data includes automatic, then manual,removal of most ground clutter. Excluding these pix-els had very little effect on the statistics, which wereaveraged over areas much larger than one pixel.

Beam blocking by complex terrain was much moreproblematic. Statistics for TUS are an exemplary case(Fig. A3). The primary regional radar for the TUS areais on high ground roughly 40 km southeast of the tar-get (Fig. A4). The radar beam is relatively unimpededin its observations directly over TUS, the Santa CatalinaMountains to the north-northeast of TUS, and highterrain farther to the north and northwest (Fig. A3).However, the beam is mostly blocked by the Santa RitaMountains to the radar’s southwest, the Rincon Moun-tains to its northeast, and the Whetstone and DragoonMountains to its east and southeast (cf. Figs. A3 andA4).

This beam blocking presented us with several obvi-ous difficulties. For example, it is unclear whether re-gions of very high Prstorm (e.g., at x = 15 km, y = 30 kmin Fig. A3) corresponded to virtually stationary oro-graphic thunderstorms or to ground returns from ter-rain, although the high gradients around the localminima in Pranyhit|storm at the same places suggest the lat-ter (Fig. A3). Second, owing to beam blockage, there isno information in the lee of the nearby ranges (as dis-cussed above), so that comparing TUS’s Prstorm with that

of its CWA has very little meaning. Third, owing to thepaucity of thunderstorm echoes, Pranyhit|storm in the ra-dar voids was excessively noisy and unreliable, espe-cially in the southwestern part of the Tucson CWA(Fig. A3). For these reasons, although we gained somelimited insight into the regional behavior of thunder-storms at targets with poor radar coverage, we ex-cluded them from our core analyses.

Calibration. A WSR-88D that is not well-calibrated canover- or undermeasure reflectivity compared to othernearby radars in the network. Figure 6 illustrates theeffect poor calibration can have on Prstorm. The circle ofhigh values centered on Wilmington in southern NorthCarolina is an obvious signature of an overcalibrated,or “hot,” radar. Certain configurations of cold(undercalibrated) and hot radars may have artificiallyproduced the sorts of gradients, maxima, and minimain Prstorm that we used in our first criterion for definingweather holes and hot spots. Hot and cold radars mayalso have masked real holes and hot spots. However,as with coverage and range, this problem seemed tobe mitigated somewhat by our choice of the 40-dBZstorm threshold (Fig. A2). Nevertheless, concern overthese effects is partly what motivated us to adopt thesecond criterion for holes and hot spots, that based onPranyhit|storm, which is less sensitive to poor radarcalibration.

FIG. A1. Coverage of WSR-88D radar beams at 5 km (AGL) over the contermi-nous United States, following the method of Maddox et al. (2002). Figure kindlyprovided by J. J. Gourley, National Severe Storms Laboratory, Norman, Oklahoma.

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