RadarIMPROVED SEVERE STORM WARNINGS

USING DOPPLER RADAR

Rodger A. Brown (1)and Vincent T. Wood (2)

National Severe Storms LaboratoryNorman, Oklahoma 73069

ABSTRACT

Research data collected by the National SevereStorms Laboratory's Doppler radars and operationaltests conducted during the Joint Doppler Opera­tional Project reveal the severe storm detectioncapability of lO-cm wavelength Doppler radars.Severe storm identification is based on the pres­ence of the Doppler velocity signature of a meso­cyclone -- d circulation that appears on conven­tional radar scopes as d hook echo.

Volume 8 Number 3

1. INTRODUCTION

There has been increasing discussion re­cen tly abou t r eplac ing the na tion I s agingweather radars with a network that hasDoppler capability (e.g., Grebe (3». Whyare claims being made that a Doppler radarwill do a better job than a conventionalradar in detecting severe thunderstorms?To answer this question, we need to ex­plore what has been taking place duringthe past 15 to 20 years.

We know that power scattered back to aconventional (incoherent) radar is a func­tion of the size and number concentrationof precipitation particles in the storm.A Doppler radar has the same capability -­and more. Being coherent, a Doppler radaralso is able to sense the very slight fre­quency shift (Doppler effect) caused bythe movement of precipitation particlesrelative to the radar. The frequencyshift at each location in the storm thencan be conver ted in to a Doppler velocityvalue.

It is important to note that a Doppler ra­dar senses only the component of motion inthe direction the radar is pointing. Forexample, when the radar is pointing north,only the north-south component of the windis measur ed: the eas t-wes t componen t can­not be detected. Similarly, when the ra­dar is pointing toward the northeast, thenor theas t -southwes t componen t is fullysensed while the northwest-southeast com­ponent is not sensed at all. We discusssome specific examples in the next section.

During the latter half of the 1960's, DOP­pler radar investigators noted that infor­mation about the horizontal flow fields in

thunderstorms could be deduced from singleDoppler velocity data (e.g., Easterbrook(4), Donaldson (5), peace and Brown (6),Donaldson et al. (7), Lhermitte (8»).Recognizing-,- however, that unique flowfields cannot be determined from such da­ta, Donaldson (9) proposed a set of cri­teria for helping to distinguish mesoscalevortices (mesocyclones) from regions ofazimuthal shear (that is, shear across theradar Viewing direction). In effect, thecriteria designate an azimuthal shear re­gion to be a vortex when the shear region(a) persists for at least half the timeperiod required for one vortex rotation,(b) extends vertically a distance greaterthan the shear diameter, (c) does notchange its basic pattern during a viewingdirection change of approximately 45° and(d I when the azimuthal (angular) width ofthe shear regions is in a position rela­tive to the radar where the vieWing direc­tion changes by less than 45° during a ma­jor portion of the feature's lifetime.Therefore one usually applies only theother three criteria.

2. DOPPLER VELOCITY SIGNATURES OF MESOCY­CLONES AND DIVERGENCE AREAS

We start with a discussion of single DOp­pler velocity signatures that help identi­fl'· severe thunderstorms. Two hor izontalflow fields that easily are recognizedthrough Doppler velocity ·signatures· arerotation and convergence/divergence. Ex­amples of these fields are shown in Fig.1: the basic features are zero velocity atthe center and maximum velocity (bold ar­rows) at a radius R from the center.

There are a number of different modelsthat aIle can use to describe the variation

17

Cl Vx/R (within core region, rfR) (3)

C2 VxR (within core region, r>R) (4)

2.a. Mesocyclone Signature

The inner part of the profile will be re­ferred to as the core region with R beingthe core radius. The maximum velocity,v x ' in the profile occurs at the coreradlus. Once Rand Vx are specified,the entire profile can be determined usingthe constants

of velocity with radius. We choose a sim­ple model -- called the Rank ine combinedvelocity profile (Fig. :n -- that approxi­nates the basic features observed in theatmosphere. This profile consists of twodistinct velocity (v l distr ibutions. Theinller portion of tile profile increaseslillearly with distance (r) from the center

also can bedivergence/

~he Rank ine combined prof ileused to model axisymmetric

2.b. Divergence Signature

A mesocyclone is a rotating column (10 to15 km diameter) within a severe thunder­storm that usually is associated with thestorm's updraft. Looking in the directionof storm motion, the rnesocyclone is foundon the right rear flank. Under ideal con­di tions, the mesocyclone appears as a"hook echo" on a conventional radar dis-play. If a bounded weak echo regionindicating a very strong updraft ap­pears in the radar reflectivity pattern,it usually coincides with the mesocyclone.

ro Doppler velocity because flow every­where along the line is perpendicular tothe v iewing direction. To the right ofthe line, flow is away from the radar(thin solid contours) and flow on the leftis toward the radar (thin dashed con­tours). Whereas a Doppler radar sensesnone of the flow when viewing a vortexthrough the circulation center, it sensesthe complete flow on both sides of thecenter where flow is directly toward oraway from the radar. The arrows eitherside of center represent the core radius(R) where the full value of the peak tan­gential velocity (Vt) is measured.

Therefore the single Doppler velocity sig­nature of a mesocyclone {or any vortex}has a pattern that is symmetric about theradar viewing direction and has peak val­ues (Vt) of opposite sign at the coreradius (R) either side of the circulationcenter. If the vortex is moving and/or isembedded in a uniform horizontal flowfield, the circulation no longer will becircular but the vortex signature patternwill remain unchanged; the only differencewill be that the contour lines will havedifferent values and the center contour nolonger will have a Doppler velocity valueof zero.

An example of a meso cyclone signature nearcloud base is shown in Fig. 4. During the45-rninute period ending 5 minutes beforethe data time, the storm caused extensivedamage due to very large hail, strongwinds and at least 5 short-lived torna­does. At data time, the storm was becom­ing nonsevere with heavy rain at the sur­face within the mesocyclone. NegativeDoppler velocities represent flow towardthe radar and positive velocities are flowaway; storm motion has been subtracted, sovelocities are those as seen by an obser­ver moving with the storm. The signatureis located about 80 km south-southeast ofthe Norman Doppler radar. The averageDoppler velocity value across the signa­ture of about -6 m s-l represents a com­ponent of southerly environmental windsnear cloud base.

(2 )

(1 )

velocity change isto distance from

(r > R)

(r ~ R)

Corv

In the outer portion,inversely proportionalthe center

Figure 3 shows a horizontal scan through avortex (thick circular lines) rotatingaround a vertical axis and the associatedsingle Doppler velocity pattern (thinnerlines -- lines having constant Doppler ve­locity values). A Doppler radar is as­sumed to be located a considerable dis­tance due south of the vortex center.Since a Doppler radar senses only the com­ponent of flow in the radar viewing direc­tion, the heavy dashed line represents ze-

':'he combined velocity profile origin­ally was developed to descr ibe axisymmet­ric vortices {e.g., Rankine (10). For avortex, Vt represents tangential (rota­tional) velocity and Vt represents peaktangential velocity. Since tangential ve­locity is modeled to increase linearlywith radius within the core region (r R),the core rotates like a vertical solidcylinder (having a circular horizontalcross-section). The cylinder thus repre­sents the driving force that keeps thes rrounding fluid (water or air) rotating;fluid tangential velocity changes inverse­ly with distance from the rotation center.

By analogy, a fluid vortex can be thoughtof as having a core that rotates as if itwere a solid. This nodel is a good firstapproximation for describing atmosphericvortices ranging in size from dust devilsto hurricanes. The key parameters neededto specify a vortex in nature are the coreradius and the maximum tangential veloci­ty. These two parameters form the basisfor the single Doppler velo ity signatureof a mesocyclone.

18

(9 )

Outside the core region, substituting Eqs.(2) and (4) into (5) and (6), we find that

convergence areas (Fig. Ib). In thiscase, v r epr esen ts r ad ial veloci tiesflowing directly inward toward or outwardfr om the cen ter of the model; Vr is thepeak radial velocity. Since radial veloc­ity changes at a constant rate with in­creasing radius in the core region (r! R),horizontal divergence is constant withinthe core.

v =

Volume 8

( r~ R)

Number 3

( 8 )

A model radial flow field and the corres­ponding single Doppler velocity pattern isshown in Fig. 5. Note that the divergencesignature is the same as a mesocyclonesignature that has been rotated counter­clockwise by 90 0

• Here the zero line isperpendicular to the radar viewing direc­tion because the radar does not sense mo­tion toward the left or right of the di­vergence center. Maximum flow toward andaway from the radar (short arrows) is Vrmeasured along the viewing direction thatpasses through the divergence center;these peak velocities occur at the coreradius.

An example of a divergence signature nearstorm top is found in Fig. 6. In thiscase, the radar (located above the top ofthe figure) is about 145 km north of thesignature center. The average of the DOP­pler velocity maxima (located near theclosest and farthest edges of the radarecho) is 77 m s-l. If we assume thatthe peak values should be +77 m s-l, themeasurements suggest that a-Doppler veloc­ity component of -11 m s-l -- represent­ing the component of storm motion and en­vironmental winds at the data level -- hasbeen added to the pure divergence signa­ture.

3. COMPUTATION OF VORTICITY, DIVERGENCEAND VERTICAL VELOCITY FROM SINGLE DOPPLERVELOCITY DATA

The mathematical definitions of verticalvorticity so~onent (5) and horizontal di­vergence (1:;7.\1) in an eXisymmetric coordi­nate system (e.g., Spiegel (13), pp. 153­154) are

(5 )

( r > R)

(10 )

For one who is not familiar with the im­plications of the Rankine combined veloci­ty profile, the results of Eqs. (7)-(10)may be surpr ising: vorticity and diver­gence are constant within the core regionand zero outside. Constant vorticity inthe core should be expected since the corerotates like a solid. Even though thefluid outside the core is rotating (e.g.,Fig. la), the mathematical quantity calledvorticity is zero because the tow terms inEq. (5) have the same magnit de but haveopposite signs, cancelling each other.Constant divergence within the core regionimplies uniform vertical velocity withinthe core.

3.a. Derivation of General Equations

So far, we have discussed only those situ­ations where pure vorticity (Fig. 3) orpure divergence (Fig. 5) are present. Inreality, some combination of the two quan­tities usually exist. If we assume thatthe core radii and peak velocities for thetwo quantities are equal, Eq. (7) and (8)can be modified for those situations whereboth vorticity and divergence are present.

For an orientation of the Doppler velocitypattern other than pure rotation or pureconvergence/divergence, peak Doppler ve­locity values at the core radius no longercan be labeled Vt or V. Also, ingeneral, Doppler velocity values contain acontribution from storm motion and envi­ronmental winds. So in order to obtain arepresentative peak Doppler velocity(Vd) value, a mean peak value can becomputed:

.,V

dVr-+ar

v-..!:.r (6 )

d

Vd(+) - Vd(-)----r-- (11 )

wher~ the arrow indicates a vector quanti­ty, 'V. is the vector differential operatorand ~ is the horizontal wind vector. Sub­stituting Eqs. (1) and (3) into (5) and(6), we find that within the core region

where Vd(+) is the more positive (lessnegative) peak value and Vd(-) is themore negative (less positive) peak value.

(7)

19

NationiJ1 Weather Digest

SUbstituting Eg. (11) into (7) and (8) andadding the appropriate trigonometric func­tions, we find that

2Yd cos 0~ --R--

-, .> 2Yd sin 0V V --R--

(12 )

(13 )

Uncorrected vertical velocity profiles canbe modified by adjusting the values ateach level such that w is zero at both theground and storm top. Aujustment parame­ters can be computed by adding a ver ticalvelocity error term to the right side ofEg. (16) and evaluating the equation fromthe gr ound (s torm top) to storm top(ground). Different correction develop­ments are discussed by OIBrien (16), Nel­son (17) and Ray ~ a1. (18) among others.

where represents the amount of patternrotation from the pure mesocyclone posi­tion shown in Fig. 3; counterclockwise ro­tation is positive. Cyclonic vorticity (~>

0) is a maximum when 8 -0°; anticyclonicvorticity (~(,O) reaches a peak when8=180°; divergence (V'v >0) reaches a max­imum whene =90 0

; convergence (9·iJ <0) is apeak when 6=270'.

When a vertical distribution of divergenceis available, vertical velocity (w) withinthe core region can be computed. The pro­cedure is to use the mass continuity equa­tion

3.b. Computation of vorticity, Divergenceand vertical Velocity

Applying Egs. (12) and (13) to a singleDoppler data set, Fig. 7 shows verticalprofiles of vorticity and divergence in ameso cyclone computed from single Dopplervelocity signatures. These two profilesseem to be realistic. Low-level conver-gence topped by divergence at upper levelsdenotes an updraft. Strongest vorticity(rotation) is found at storm midlevels.Had data extended to storm top, datatrends in the two curves suggest that di­vergence increases toward storm top andvorticity approaches zero.

3 ~ ~

"i+1 = 1.105263 'Ii - 1.05263 x 10 (V'V)i+0.5 (17)

Single Doppler velocity patterns associ­ated with the type of ver tical vorticityand divergence variations found in Fig. 7are presented in Fig. 8. The modeled pat­terns (with superimposed streamlines) re­flect variations -- at 3 to 5 km intervalsfrom the ground to storm top -- that com­monly are seen in mature mesocyclones. Aconvergent mesocyclone near the groundchanges to pure rotation then to a diver­gent circulation and finally to pure di­vergence near storm top.

In 1971, the National Severe Storms Labor­atory (NSSL) commissioned its first of two10-cm wavelength Doppler radars (Brown eta1. (201)). Since that time, Doppler ra­dar data have been collected annually inspringtime Oklahoma thunderstorms.

4. DOPPLER RADAR AS A SEVERE STORM SENSOR

An uncorrected vertical velocity curve al­so is shown in Fig. 7. I twas compu tedusing Eq. (16), which can be simplified to

when Az is 1.0 km and the value of the di­vergence data point at the middle of theAZ interval is used as the interval mean.computations were made to a height of 9km. Since the height of storm top was notknown, approximate procedures (e. g., Brownand Nelson (19» could not be employed toproduce an adjusted vertical velocity pro­file.

(15)

(14 )

(16 )

-----:~

H; + (kl-I - V'V) f),z

....... (J\-'V . V + az - kw = 0

vI. '-"''+1

\'1~ =,+1

\.,~ (1+ex}/(1-ex) - [(V·V). + (V·V). ] f),z/{2(1-,,})1 1 1+ I

where ~ is kAZ/2. The prime indicatesthat the vertical velocity values have notbeen cor r ected for the cumula tive effectsof errors in divergence computations. Un­corrected vertical velocities are computedthroughout storm depth by assuming that wis zero at the ground (or storm top) andevaluating Eg. (16) at successive AZ stepsuntil storm top (or the ground) isreached. Even though w should return tozero at storm top (or the ground), exper i­ence has shown that slightly erroneous di­vergence values at each A Z step can resul tin a markedly nonzero final value (e.g.,Nelson and Brown (15».

where w is computed at level i+l given wat level i and the mean value of the quan-tity in parentheses in the verticalAZ(iai+l-zi) interval. The quantityin parentheses can be expanded by assumingthat the parameters vary linearly betweenthe two levels:

where k is the logarithmic decrease ofdensity with height (can be approximatedusing a constant value of 0.1 krn- le.g., Kessler (14». Put into finite dif­ference form, Eg. (14) becomes

20

Volume 8 Number 3

By 1975, sufficient single Doppler mesocy-·clone data using Donaldson's criteria

had been collected to look at basicmesocyclone characteristics (Burgess(21)). During that five year period, 37mesocyc lones were iden t i f ied; thei r char­acteristics are summarized in Table 1.Ninety-five per cent of all mesocycloneshad severe weather reported with them and62% of the mesocyclones were associatedwith reported tornadoes.

Table 1 reveals no significant differencesbetween mesocyclones that produced torna­does and those that did not. However,there is a significant difference betweenthose mesocyclones that produce weak tor­nadoes and those that produce strong tor­nadoes. The parameter that discriminatesbetween weak and strong tornadoes is meso­cyclone tangential velocity or azimuthalshear (tangential velocity difference div­ided by core diameter -- equal to one-halfvorticity for solid rotation). Azimuthalshear associated with strong tornadoes isnearly twice that associated with allother mesocyclones. Three-quarters o~

mesocyclones producing strong tornadoeshad shear values greater than 12xlO- 3s-l, whereas only 21% of mesocycloneswith weak tornadoes and 14% of non-torna­die meso cyclones exceeded that value.

Based on these interesting research re­sults including tornado warning leadtimes of 35 minutes -- the National Weath­er Service (NWS) wanted to test the meso­cyclone identification techniques in anoperational setting (Johannessen and Kes­sler (22)). The Air Weather Service, likeNWS, was in need of replacing an agingweather radar network. So the two organi­zations joined forces with NSSL, the AirForce Geophysics Laboratory (AFGL) and theFederal Aviation Administration to formthe Joint Doppler Operational project(JDOP). NSSL's lO-em Doppler radar atNorman was chosen as the test facility(staff (23».

Table 2 summarizes the results of the JDOPoperational tests during 1977 and 1978.Compared are severe weather and tornadowarnings issued by the Oklahoma city NWSoffice with and without the benefit ofDoppler information (advisories). Conven­tional NWS warnings (without Doppler advi­sor ies) wer e based on conven t ional radar,storm spotter and public reports. Aboutone-half of the conventional NWS warningswere false alarms, whereas only 20% of themesocyclone-based warnings were not asso­ciated with repor ted damage. Of the se­vere weather and tornadoes that did occur,half of them were missed using convention­al NWS techniques and one-third were notassociated with recognized mesocyclonesignatures.

The lead time between issuance of a warn­ing (NWS) or advisory (Doppler) and theoccurrence of severe (nontornadic) weatherduring 1978 was the same for both groups.This finding suggests that severe stormradar reflectivity features become evidentat about the same time that the Dopplermesocyclone signature has satisfied andtime continuity requirements.

Tornado lead time presents a differentpicture. conventional NWS tornado warn­ings had zero lead time on the average,compared to a Doppler lead time of 22 min­utes. The problem with conventional N~~S

tornado warnings is that radar reflectiv­ity patterns do not provide many clues fordiscriminating between tornadic and non­tornadic storms. Most of the help comesfrom public reports that tornadoes are onthe ground producing negative leadtimes. But even this is not mUch help be­cause over half of the pUblic tornado re­ports received during JDOP had to be dis­counted based on damage surveys.

The 22 minute average lead time for torna­does during the JDOP operation (Table 2)is considerably less than the 35 minuteaverage based on five years of NSSL re­search results (Table I). This 13 minutediscrepancy easily can be explained. Re­search data were recorded on computertapes, so it was possible to trace a meso­cyclone signature backward in time to itsorigin. However, during the real-timeoperation, a potential mesocyclone signa­ture had to satisfy height and time conti­nuity before an advisory could be issued.The Doppler radar operated using a seriesof elevated antenna scans that took 6 min­utes to complete. Therefore a minimum of6 minutes was required to establish timecontinuity. Applying typical mesocyclonecharacteristics (such as those in ?able 1)to Donaldson's criteria, it takes nearly10 minutes for the average mesocyclone tocomplete half a rotation. Apparently asecond tilt sequence was required on theaverage -- a total of at least 12 minutes

before the height and time criteriacould be satisfied.

5. CONCLUDING COMMENTS

We have shown from both research findingsand operational tests that a single DOp­pler radar is SUfficient for detectingmesocyclones and divergence regions wi thinsevere thunderstorms. Furthermore, theaddition of single Doppler velocity signa­ture information to the conventional N\1Swarning procedure dur ing JDOP resulted inseveral dramatic improvements: (1) thepercentage of severe storms for whichwarnings were issued (= hits/(hits + mis­ses)) increased from 54 to 70%; (2) thepercentage of warnings that verified (=hits/(hits + false alarms) jumped from 46to 80%; and (3) the lead time for issuing

21

National Weather Digest

tornado warnings increased from no leadtime to over 20 minutes on the average.

Based on the success of JDOP, the threeconcerned agencies National WeatherService, Air weather service and FederalAviation Administration continue tomove forward wi th plans to jointly procurea next generation weather radar system(NEXRAD) that incorporates 10-cm Dopplercapability (Bonewitz (24». While thenearly decade-long procurement processcontinues, scientists within NWS, AFGL andNSSL are developing the many types of com­puter algorithms that will be needed tocompute and display radar derived informa­tion for the forecaster's use.

Included among the algorithms are thosedesigned to automatically detect the sig­natures discussed in this paper. The de­velopment of automated signature recogni­tions techniques, however, is complicatedby a number of practical problems and con­siderations. One problem is caused by an­tenna sidelobes, where strong reflectivityin side lobe can dominate weak reflecti­vity in the main lobe and Doppler velocityfrom the side lobe azimuth will appear asif it were measured in the main lobe.

Algorithm development for the NEXRAD DOp­pler radars has been assured by the choiceof 10-cm wavelength for the radars. Ra­dars with wavelengths of 5 cm or less havetwo serious limitations when used as se­vere storm detectors: (1) attenuatTOn ofthe radar signal and (2) limited Dopplervelocity interval. The attenuation prob­lem is so grave that a severe storm candisappear from the radar scope when anoth­er storm moves between it and the radar.Also, the far edge of a severe storm candisappear, potentially erasing an existingmesocyclone (e. g .• Allen et al. (25».

The Doppler velocity problem arises fromthe fact that, for a given range interval,the measurable Doppler velocity intervaldecreases with decreasing radar wave­length. Velocities outside the interval(that is, greater in magnitude) -fold­back into the interval as aliased veloci­ties; techniques are available to -unfold­automatically the aliased velocities(e.g., Brown et al. (26)). However, forthe more severe storms, it commonly is notpossible to unscramble real and aliasedvelocities within the limited velocity in­tervals of the shorter wavelength radars.Even at 10-cm wavelength, velocity gradi­ents within a storm can be 50 large thatit may be impossible to resolve theseproblems objectively by computer -- caus­ing false or missed signature ~ecognition.

Even though the computer will play a sig­nificant role in the signature recognitionprocess, it merely is relieving operation­al personnel of some of the more mundaneand time-consuming mon i tor ing tasks.Through the use of a jUdicious human­machine mix, the additional informationprovided by 10-cm Doppler radars shouldshow a marked improvement in the issuance,accuracy and timeliness of severe weatherand tornado warnings.

ACKNOWLEDGMENTS

We appreciate general discussions withDonald Burgess and Dr. Stephan Nelson.Thanks to Alice Adams Krentz for use ofthe data in Fig. 7 that she prepared for ayet-to-be-published report. sandraMcPherson skillfully typed the manu­scr ipt. Figures were drafted expertly byJoan Kimpel and Robert Goldsmith providedadditional timely graphics support.

~. statistics for .socyclones observed by NSSL DOppler ud.. rs fro. 1971 through1975. Proa Burgess (21J.

All Non-tornadic All Tornadic weak Tornado Strong Tornado1'71_1975 Statistics Hesocyclones Hesocyclones Mesocyclones Hesocyclones Mesocyclones

No. of Mesocyclones J7 14 23 l'peak Tangential 22.3 20.9 23.3 21.5 31.0Velocity I_ s-l) 113-42) (15-25 ) (13-42) (13-32) 120-42)

Core oh,.eter Ik.) '.7 ,., '.7 '.0 , .0t2-111 ll-ll ) (2-10 ) (4-10 ) 12-10 I

u.i_uthal Shear ••• .., •• 1 7.' 15.2110-3 S-l) 11-20J 14-171 13-201 ll-lJ) (8-20 )

vertical Extent Ik_) 7., 7., 7.7 7.3 ..,(5-13 ) (5-13 ) (5-11) 15-11 ) 18-11 )

, With severe Weather " .. 100 100 100

, with Tornadoes " 100 100 100

Tornado Lead Ti_e 3S 34 "(_in) (13-61) (13-61) (13-58)

J • range of values

22

Table 2.

Volume 8

su_cy of 1977-78 JOOP severe weather and tornado warnings. Warnings based onthe conventional National Weather Service warning syste. ace cocpared with thosebased. on ..socyclone signatures detected by Doppler radar. "Hits' are success­ful warnings, "false alacas" are wacnin')s for storas that did not becolle severeand ·.isses· represent severe stor_ for which no warnings wece issued. FrOIiStaff (2]'.

Nw:rber 3

,alae 1978 Severe 1977-78 Torn",doWarnina Systea Hits !'Iisses AlaUIS Weather Lead "'ill! Lead Ii~e

Netlond Weathec Serv ice 10. " 123 14 ain lIin(Oklahollolll City, 146\) 154\'

DOppler R",dar 70 30 11 15 .," 22 Ilin(NSSL. Noraan I (l0\) (20\'

, ,t, , , ,, , , , , ---~-'" /, , / ,

/ , " 'X, , ,, , , , , , /I . ...., I • , R ........ \, /R \ I

I • I f • ~-7-.\ • , •,

I,, , , , , , , ;, , , ,

'- , / X X"-

," " "

,- , "-\---' "-, , , ,, , I

(a) ROTATION (b) DIVERGENCE

Figure 1.Bold arrows

Hor izon tal flow fields forrepresent maximum velocities

axisymmetric (a)at core radius R.

rotation and (b) divergence.

RANKINE COMBINEDVELOCITY PROFILE

t>

>:"t: V.uo....JW>

\\\\\\\\\

\ /\/

//

//

//

//

//

RADIUS, r_

Figure 2. Rankine combined velocity profile, where peak velocity (Vx ) is at coreradius (R).

23

National Weather Digest

I' APItI", 1.72IUO CST0&' E...EVolTION

150'170' 1&0'

Figure 4. Single Doppler mesocyclone sig­nature in the Davis, OK tornadic storm on19 April 1972. Radar is located beyond

4 upper left corner of figure; flow awayfrom radar is positive, toward is nega­tive. From Burgess (11).

Figure 3. Plan view of mesocyclone model(thick curved lines) and associated singleDoppler velocity signature (thin con-tours). For a Doppler radar located duesouth of circulation, solid thin contoursrepresent flow away from radar, dashedcontours represent flow toward radar.

4

3,,,. ,, ,, ,, ,

>: , -, , I,'" , , ,

, , ,I, r ,

w , , •u 0 , ,z , ,

Ia: , ,f- , , ,

I~-l, , ,, ,

ICl,,,

, ,-2 , ,,,,,-3

,,,,

-4-2 0 2 3-4 -3 -1 1

DISTANCE IKMI

wuza:f-

~ -1Cl

-3 -2 -1 0 1DISTANCE IKMJ

2 3 4

Figure 5. Plan view of axisymmetric divergence model (thick radial lines) and associ­ated single Doppler velocity signature (thin contours). For a Doppler radar located duesouth of the divergence area, solid thin contours represent flow away from radar, dashedcontours represent flow toward radar.

24

Volume 8 NUr.lber 3

30 MAY /976/6/6 CST /4 km AGL

130 km-

140-

150-

160-

20 dBZ

~6

Figure 6. Single Doppler divergence signature near the top of the Waurika, OK tornadicstorm on 30 May 1976. Radar is located above the top of figure (180 0 azimuth directionis indicated). Measured Doppler velocities are positive for flow away from radar, nega­tive for flow toward radar. From Lemon and Burgess (12).

VERTICAL VELOCITY, m 5- 1

10-3~O=---__-.:2;.0__---.:-1.;..0 0:;....- 1:;.0__---.:2-:;.0:......._---=,30

------ ...Vert. Velocity········Vorticity ­Divergence - __ -

Figure 7. vertical profilesof vorticity, divergence anduncorrected vertical veloc­ity for the mesocyclonein the Konawa right-movingsevere storm on 29 April1978. profiles were computedfrom single Doppler velocityda ta us ing Egs. (12) , (13)and (17). Data courtesyof Alice Adams Krentz.

.......".

.KONAWA MESOCYCLONE29 APRIL 1978 I ,._-

1850 CST : /'I I•I II ,..;.~

"'If lI I

j I/

~ II I

I I,..' I

.,-/ I ...•

2

8

~ 6

~IClw 4I

15-10 -5 0 5 10

VORTICITY, DIVERGENCE, 10-3 5- 1

o L--__....L "'--__---"•.:...__-'- .J-__....J

-15

25

NatiOOdl Weather Digest

- '!. L..4~"'-"'3=L_1LJ

2............._wI......J.JDL..u..£t::jI...u...u.J2~l:.J..l3..L.L..i..J.J4

DISTANCE IKMI

- '!.L4

............._3~:L.LJ_2~.u.J_~IA..uD.....L*-lI..w::bi:!2=......3.........;~4

DISTANCE IKMJ

2 - __

3

wuzcr:f--

~ -Io

-2

-3

3

t3 Dzcr:f--

~ -Io

-2

-3

,,,

//

"""

,,,,,

//

//

","

//

/

"C

wuzcr:f--

~ -1o

wuzcr:f--

~ -Io

-3

-3

-2

-2

-I DDISTANCE

-I DDISTANCE

1IKMI

IIKMJ

2

2

3

3

Figure 8. Modeled single Doppler velocity patterns (thin contours) and equivalent hori­zontal flow fields (thick curves) at 3 to 5 km height intervals in a typical severestorm. The patterns represent (a) convergent rotation near the ground, (b) pure rota­tion at lower midlevels, (c) divergent rotation at upper midlevels, (d) pure divergencenear storm top.

26

Volume 8 Number 3

RBFBRENces AND FOOTNOTES

ERL NSSL-94,(Available

Service,

tion techniques. NOAA Tech. Hemo.Norman, Nat. Severe Storms Lab., 1-10.from National Technical InformationSpringfield, VA 22151 as PB81-152551.)

16. O'Brien. J. J., 1970: Alternate solutions tothe classical vertical velocity problem. J.~.

~., !' 197-10J.

1. Rodger A. Brown is a research meteorologist atthe National Severe Storms Laboratory. He re­ceived a B.S. degree from Antioch College, a N.S.

degree from the university of Chicago and is con­tinuing graduate studies at the University of Ok­lahoaa. His research interests are in severestorms and meso-meteorology, utilizing Doppler ra­dar as a priaary data source.

1. Vincent T. Wood is a research aeteorologist atthe National Severe Storms Laboratory. He re­ceived <1 B.A. degree from the University of St.Thomas, a N.S. degree from Texas Ao.H Universityand is continuing graduate studies at the Univer­sity of Oklahoma. His research interests are me­teorological modeling, severe storms, and mesocy­clone and tornado dynaaics.

17. Nelson, S. P., 1980: A study of hail produc­tion in a supercell storll using a Doppler derivedwind field and a numerical hail growth model.NOAA Tech. NemO. ERL NSSL-89, Norman, Nat. SevereStorms Lab., 90 pp. (Available from NationalTechnical Inforllation Service, Springfield, VA12151 as PB81-17821Q.)

J.is

Grebe, R., 1981:it worth it? Nat.

Operational Doppler radarWea. Digest, !' 48-51.

18. Ray, P. S., C.R. J. Serafin, 1980:radar obserations ofRev.; 108, 1607-1625.

L. ziegler, W. Bumgarner andSingle- and multiple-Dopplertornadic storms. Hon. Wea.

19. Brown, R. A., and S. P. Nelson, 1982: Hulti­

pIe Doppler radar derived vertical velocities inthunderstorms. Part II - Naximizing a real extentof vertical velocities. NOAA Tech. Hemo. ERLNSSL-94, Norman, Nat. Severe Storms Lab., 11-21.(Available from National Technical InformationService, Springfield, VA 22151 as PB83-15255J.

Horizontal windsevere squallSevere Local

Heteor. Soc.,

5. Donaldson, R. J .. Jr., 1967:measurement by Doppler radar in aline. PreDr~nts, Fifth Conf. onStorms (St. Louis), Boston, Amer.89-98.

4. Basterbrook, C. C., 1967: So,.e Doppler radarmeasurements of circulation patterns in convectivestorms. J. Appl. Neteor., !' 881-888.

13. Spiegel, M. R., 1959: Vector Analysis and AnIntroduction to Tensor Analysis, New York, SchaumPublishing Co., 225 pp.

10. Ri!lnkine, 'ii.J.H., 1901: A Hanual of AppliedHechanics, 16th edition. London, Charles Griff

and Company, 574, 578.

14. Kessler, E., 1969: On the distribution andcontinuity of water substance in atmospheric cir­culation. Meteor. Monoqraphs, 1£ (32), 84 pp.

8. Lhermitte, R. H., 1969: Doppler radar obser­

vation of a convective storm. Preprints, SixthConf. on Severe Local StormS (Chicago), Boston,Amer. Heteor. Soc., 119-145.

10. Brown, R. A., W. C. Bumgarner, K. C. Crawfordand D. Sirmans, 1971: Preliminary Doppler veloci­ty measurements in a developing radar hook echo.Bull. Amer. Heteor. Soc., 1!, 1186-1188.

25. Allen, R. H., D. W. Burgess and R. J. Donald­son, Jr., 1981; Attenuation problems associatedwith a 5 cm. radar. Bull. Amer. Heteor. Soc., §l..,807-810.

22. Johannessen, K., and E. Kessler, 1976: Pro­gram to develop Doppler for use in the NationalWeather Service. Prepr~nts, Seventeenth Conf. onRadar Heteor. (Seattle), Boston, Amer. Heteor.Soc., 560-561.

21. Burgess, D. w., 1976: Single Doppler radarvortex recognition: Part I Nesocyclone signa-tures. Preprints, Seventeenth Conf. on Radar He-teor. (Seattle), Boston, Amer. Neteor. Soc.,97-101.

23. Staff, NSSL, AFGL, NWS, AWS, 1979: Final re­port on the Joint Doppler Operational Project(JDOP), 1976-1978. NOAA Tech. Nemo. ERL NSSL-86,Norltan, Nat. Severe Storms Lab., 84 pp. (Avail­able from National Technical Information Service,Springfield, VA 22151 as PB80-107188/AS.)

26. BrOlin, R. A., C. R. Safford, S. P. Nelson. D.W. Burgess, W. C. Bumgarner, N. L. Weible and L.C. Fortner, 1981: Hultiple Doppler radar analysisof severe thunderstorms; Designing a generalanalysis system. NOAA- Tech. Hemo. ERL NSSL-92,Herrman, Hat. Severe Storms Lab., 21 pp. (Avail­able from National Technical Information Service,Springfield, VA 22151 as PB82-114117.)

14. Bonewitz, J. D., 1981; The NBXRAD programAn overview. preprints., Twentieth Conf. on RadarNeteor. (Boston), Boston, Amer. Heteor. Soc., 757­761.

Vortex signature rec­J. Appl. Hetaor., !'

11. Lemon, L. R., and D. W. Burgess, 1980: Mag­nitude and implications of high speed outflow atsevere storm summits. Prepr~nts, Nineteenth Conf.on Radar Heteor. (Miami), Boston, Amer. Heteor.Soc., 164-J68.

9. Donaldson, R. J., 1970:ognition by Doppler radar.661-670.

6. Peace, R. L., Jr., and R. A. Brown, 1968.:Coaparison of single and double Doppler radar ve­locity JIIeasurements in convective storms. Pre­prints, Thirteenth Radar Heteor. Conf. (Hontre-;rr,Boston, Amer. Heteor. Soc., 464-471.

7. Donaldson, R. J., Jr., G. H. Armstrong, A. C.Chllleia and H. J. Kraus, 1969: Doppler radar in­vestigation of air flow and shear within severethunderstoras. preprints, Sixth Conf. on SevereLocal Storms (Chicago), Boston, Aaer. Heteor.Soc., 146-154.

11. Burgess, D. fl., 1974: Study of a severe

right-moving thunderstorm utilizing new singleDoppler radar evidence. N. S. thesis, Dept. ofHeteorology, Univ. of Oklahoma, 77 pp.

IS. Nelson, S. P., and R. A. Brown, 1981: Ifulti­pIe Doppler radar derived vertical velocities inthunderstorms. Part I - Error analysis and solu-

27