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