OCTOBER 1994 W O O D 1207A Technique for Detecting a Tropical Cyclone Center Using a Doppler Radar VINCENT T. WOOD NO/L4, Environmental Research Laboratories, National Severe Storms Laboratory, Norman, Oklahoma (Manuscript received 30 June 1993, in final form 7 January i994) ABSTRACT A ground-based Doppler radar technique is developed for detecting a tropical cyclone center position. Accurate determination of the cyclone center position, based on Doppler velocity measurements, will become essential for the issuance of hurricane advisories, forecasts, and warnings once a network of WSR-88D Doppler radars is deployed on the United States coastlines, islands, and military bases during the 1990s. This will allow high resolution detection and tracking of hurricanes nearing land for the first time. Simulated Doppler velocity data, which were reconstructed from wind field dat~ collected by reconnaissance aircraft during Hurricanes Alicia (1983) and Gloria (1985), were used to test the concept of using ground based Doppler radar data to estimate cyclone center location. The center range and azimuth estimates of a hurricane signature were calculated from the simulated coastal Doppler radar velocity data. Prelimina.ry results indicate that the technique performed well for estimating center locations from the radar measurements compared with storm center positions determined from in situ aircraft measurements.1. Introduction Radar has been a valuable tool in tracking tropicalcyclones since the first radar observations of tropicalcyclones began in the late 1940s (Maynard 1945; Wexler 1947). Major radar networks were established inJapan and the United States in the late 1950s primarilyto track tropical cyclones. With the deployment of theWeather Surveillance Radar-1988 Doppler (WSR88D) system during the 1990s, the potential for routinely tracking tropical cyclones nearing land can berealized. Because of their Doppler velocity-measuringcapabilities, these S-band (10-cm wavelength) radarshave the potential to increase the accuracy and timeliness of hurricane advisories, forecasts, and warnings(Baynton 1979; Jorgensen 1982; Zipser et al. 1990)through improved observations of a storm center'strack and intensity. Many techniques were devised to identify and tracktropical cyclones using noncoherent radars, weathersatellites, and hurricane reconndissance missions. Sennet al. (1957) and Senn and Hiser (1959) developed atechnique that utilized a logarithmic spiral fit to therainband positions to estimate a tropical cyclone center.Sivaramakrishnan and Selvam (1966) devised a spiraloverlay technique used in conjunction with cloud photographs obtained by a weather satellite to locate a hurricane's center. Willoughby and Chelmow (1982) developed an objective procedure to estimate the dynamiccenter of a hurricane based on the flight-level wind and Corresponding author address: Vincent T. Wood, NOAA/ERL/NSSL, 1313 Halley Circle, Norman, OK 73069.D value (the departure of a selected isobaric heightfrom its value in the standard atmosphere). Timely and accurate estimates of the center positionand motion of a tropical cyclone by the WSR-88Dradar are essential for hurricane surveillance when reconnaissance aircraft and satellite estimates are unavailable or available too infrequently to provide thedesired degree of time and space continuity. Furthermore, they are among the more important parametersto be determined from the WSR-88D radars becausethey are needed as input not only to the hurricane forecasters but to tropical cyclone algorithms as well. Forexample, the tropical cyclone center position was usedby Donaldson (1991), Lee et al. (1993), and Roux( 1993 ) for diagnosis of hurricane structure. This paper describes a computer technique that detects a tropical cyclone center position based on Doppler velocity measurements. Section 2 discusses an analytical flow model that is used to simulate a singleDoppler velocity field corresponding to an idealizedtropical cyclone. Section 3 describes the concept of apattern recognition technique that is a useful tool forsingle-Doppler radar identification of atmosphericvortices such as a tropical cyclone or a thunderstormmesocyclone circulation. The computer technique incorporates azimuthal shear and velocity differencethresholds for detecting tropical cyclones and makingestimates of the center location from the radar measurements. In section 4, the technique is evaluated todetermine its ability to detect a tropical cyclone. Simulated single-Doppler velocities are reconstructed fromthe wind fields for Hurricanes Alicia (1983) and Gloria(1985), and the hurricane center positions estimatedfrom the radar are compared with in situ aircraft mea1208JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYVOLUME 11surements. Conclusions and future research problemsare discussed in section 5.2. The analytical flow model A simple analytical model (e.g., Brown and Wood1991; Wood and Brown. 1992) can be used to approx,imate the basic horizontal flow field within a tropicalCyclone vortex; the model specifies, to'a first approximation, axisymmetric velocity distributions (Hughes1952; Riehl !954, 1963; Gray. and shea 1973). According to the distributions~ tangential velocity increases linearly from a circulation center where velocityis zero to a ~core radius where the tangential velocityattains.its maximum value. Beyond the core radius,the tangential velocity decreases in a manner inverselyproportional to distance from the.circulation center:Mathematically, the x~elocity, distribution for the tangential, vt (r), wind component in the Rankine ( 1901 )combined vortex flow model is given by - Ira\x vt(r)= Vt['~ ) , (1)where Vt is the peak tangential.velocity at the core radius ~c, and r is the distance from the circulation center.The exponent X describes the radial profile of the tangential wind component: Inside the radius of maximumwind (RMW), X = -1 is often assumed. Outside theRMW,.X generally lies between 0.4 and 0.6 (Hughes1952;-Riehl 1954, 1963; Gray and Shea -1973). . The Doppler velocity component Va at slant 'rangeR is the component of the wind vector in the viewingdirection 0, from a radar. As derived by Wood andBrown (1992), the Doppler velocity value at R, 0 isgiven by = -- Sin(0 - 0c), (2) O/where r.= [Rc2 + R2', 2RcR cos(0 - Oc)] ~/2 is theradial distance from .the circulation center; Rc, Oc rep--resents the center range and azimuth, respectively, ofthe modeled flow feature from the radar; and a dimensionless aspect ratio a is defined as the ratio ofcore diameter 2re tO range Rc. Of a circulation centerfrom the radar. The procedure for generating a simulated Doppler velocity field in (2). was outlined byWood and Brown .(1992). The velocity field containssome additional simplifying assumptions. The verticalcomponent of motion is not simulated; therefore, theradar measurements, are assumed to be made at lowelevation angles. Furthermore, the simulation assumesthat the radar measurements are free of noise and thatthe radar beam has an infinitesimal width (producingperfect radar resolution at all ranges, rather than degraded resolution at far ranges).- Figure 1 depicts a horizontal scan through a modeledhurricane vortex rotating cyclonically around a verticalaxis, and the associatod single-Doppler velocity pattern 150 , ...,-30~ r , ,~ , - 140 . '",,, 10'/~ '"'~ ' / ~01 I I I ~ I 11 I' /I I I -50 -40 -$0 -20 -10 0 10 20 30 40 50 FIG. 1. Plan view of an axisymmetdc hu~cane vortex flow:(windvectors) and the co~esponding sin~e-Doppler velocity signature fora radar located 100 km south of the vomex center. The wind plottingconvention is flag, 25 m S-~; barb, 5 m s-~; and hal~barb, 2.5 m s-~.Doppler velocities are contoured. Solid cu~es represent flow awayfrom the radar (positive Doppler velocities), with the exception lhatthe zero Doppler velocity contour is the flint solid contour; dashedcu~es repre~nt flow toward the radar (negative Doppler velocltiis);The contour inte~al is 10 m s-~. The hu~cane center is indicatedby the hu~cane symbol. The dotted cimle ~u~oun~ng the hu~canecenter is the location of maximum wind s~ed.that would be measured by a Doppler radar due Southof the vortex center (Rc = 100 km, Oc= 00, a =. 0:4,in this case). The radial velocity structure of a hurricaneat low elevation angle is similar to that of a thunderstorm mesocyclone detected by a single Doppler radar(Burgess and Ray 1986; Brown and Wood 1983, 1991;Burgess and Lemon 1990), except that the hurricaneis roughly ten times larger in diameter.3. Pattern recognition technique - The pattern recognition technique used here relieson identification of the main attribute that an atmospheric phenomenon (e.g., thunderstorm mesocycloneor tropical Cyclone,circulation) produces in the Dopplervelocity field. The pattern recognition technique wasused~ for example, by Zrni~ etal. (1985) and Desrochers and Donaldson (1992) to search successive radar-viewing azimuths for increases of Doppler velocities in order to detect thunderstorm mesocycl0nes. Inthe technique, when a run of increasing velocities ends,the beginning and ending velocity data points .of therun define a shear segment, represented by curved arrows in Fig. 2. The main attributes of the shear segment,which are consolidated into-a seven-component patternvector, consist of the slant-range (R), the beginningand ending azimuth angles (0~, 0~), the beginning andOCTOBER 1994 W O O D 1209~ 430[~.~: 120g~ 1100 100~.I.I.tlJozg 90 .. 50 i i ~ ~' i ' ~ ~ ~ ~ ~ i i -50 -40 -30 -20 -10 0 10 20 30 40 50 X-DISTANCE FROM RADAR (kin) FiG. 2. Sinsle-Doppler velocity pattern o[ the hu~cane vo~cx(hcaw solid ca~cs rcprcscnfin~ the re-on of positive azimuthalDoppler shear). A cu~cd a~ow represents a shear segment. TheDoppler vclocJW contour convention and the hu~ca~e center areas in Fi~. 1. Here, F~ and F~ represent cxtreme negative a~d positiveDoppler vclociW values located at ran[c and azimuthal points (R~,8~) a~d (R~, e~), rcspcctivdy, as indicated b~ crosses.ending Doppler velocity values (Vb, Ve), and the beginning and ending times (G, te) at both ends of theshear segment. Here, beginning b and ending e subscripts refer to a clockwise radar sweep. When patternvectors are consolidated into a two-dimensional shearfeature, pattern vectors jointly provide information onthe circulation size, strength, and rotational velocity. For identifying the tropical cyclone vortex, the mostimportant parameter is the sign of the azimuthal velocity gradient. Azimuthal shear is defined here as theshear of Doppler velocities in the azimuthal direction,and for a pattern, vector, it is given by S = R(Oe - 0~) ' (3)where A V = V~ - Vo is the velocity difference and R(Oe- 0~) represents the azimuthal distance across the shearsegment. In Fig. 2, heavy solid curves to the left andright of the hurricane center represent the lines alongwhich Doppler velocity peaks occur. They are, respectively, bounded by data points (R~, 0b) and (Re, Oe).The azimuthal Doppler shear changes sign at thesepoints, thus satisfying OVa/O0 = 0. The shape of thepattern vector region is characteristic of tropical cyclones and is useful for tropical cyclone identification.a. Tropical cyclone detection The detection of a tropical cyclone vortex commences by searching for cyclonic shear (i.e., S > 0)across adjacent radials of Doppler velocity data. Thisis accomplished by identifying increasing velocities atconstant range in the clockwise azimuthal direction. Ifpositive shear exists, a pattern vector is "opened." Theprocedure continues for the next two radials, and soon until positive shear is no longer detected for thatrange and the pattern vector is "closed." Two parameters, velocity difference A V and azimuthal shear $,are then calculated, and if these quantities exceed predetermined detection thresholds, the seven-componentpattern vector is saved for further analysis, as indicatedby the curved arrows in Fig. 3a. In this example, thevelocity difference and azimuthal shear detectionthresholds are 50 m s-l and 1 m s-l km-l, respectively. At the end of an elevation scan, individual patternvectors that are oriented perpendicular to the radarbeam are then grouped together into a two-dimensionalshear feature according to their spatial proximities. Thevectors whose azimuthal extents overlap, and that areseparated in range by no more than 1 km, are combinedinto a common feature. If the total number of vectorsin a completed feature is less than a preset threshold,the feature is discarded. The next step is to determine the locations of extremeDoppler velocity values, where the maximum tangential flow at the RMW of a hurricane vortex is measured.As depicted in Fig. 2, the maximum velocities of thevortex core can easily be observed by the Doppler radaronly at the two points where tangential velocity is directed along the radar beam. As shown in the figure,the range and azimuth of the extreme negative Dopplervelocity value VN on the left side of the vortex signaturecenter, as viewed from the Doppler radar, are represented by (RN, 0N); the range and azimuth of the extreme positive velocity value Vv on the right side arerepresented by (Rv, 0v). The technique of Desrochers and Donaldson (1992)was followed for isolating the velocity maxima of acouplet. They searched for the beginning and endingvelocities for every pattern vector of a feature for thepositive and negative velocity extrema. The patternvector is included in the sample if its magnitude iswithin some velocity difference threshold /xW of themaximum velocity of all the kth pattern vectors. Thevelocity, range, and azimuth on each side of the velocitycouplet are computed as weighted averages, Z (v~)~w VN--kZW k Y~ (R)kWRN -- k for W = A ['V - I ( Vb)k -- Vmin [ ZW ' k (o~kw(4)1210 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME II150140"-' 130E,',' 1201009070 - pATTERN VECTO/: .... .-:zzzz:zzzzzzzzzzzzzzz:W=max at "'"'-~ ~ W=max at(RN, ON) , ..__~..~ (Rp,Op) W__<O ..... - ......... W__<O (R,O~) (R, Oe) 1501. , , 140[- bn. 12o ~e .......t3"~ 110~ o'" ,ooz~ 8om~ 7- w~o 60 0 i i i i ~W<_O6O -50 -40 -30 -20 -10 0 10 20'30 40 50 -60 -50 -40 -30 -20 -10 0 10 20 30 40 , '. X-DISTANCE FROM RADAR (kin) DOPPLER VELOCITY (ms" )50 60 FIG. 3. (a) The pattern vector envelope defined by preset thresholds for velocity difference and azimuthal shear. Heavy dots indicatewhere Wis maximum. (b) Profiles of the beginning and ending peak Doppler velocities along the curves shown in (a). Dashed curves areindicated for W ~< 0. Heavy dots indicate peak Doppler velocity values (Vmax, Vmi.). Other parameters are defined in the text. 2 (re)kWVe= ~: k Z (R)/,WRe- k for W--- AW-- I(Ve)~,- Vmaxl, 2w 2 (Oe)kW Op= k 2w-. k (5)where Wis confined to 0 < W~ fiW(Fig. 3). Notethat ~ Wis the difference between a ~ven velocity andthe peak value shown in Fig, 3b. The values on theleft-hand sides of (4) and (5) are the Doppler velocity~alues and vel'ocity couplet endpoint locations, whichare determined by a process that wei~ts toward thelargest Velocity values. This weighting technique fortropical cyclone parameters provides estimates of rotational velocity that generally are ~thin 3% ofvisu~lyderived estimates. Note that the dashed cu~es shownin Fig. ~3 indicate that (4) and (5) are not calculatedwhenever: W ~ 0: The number of saved pattern vectors(indicated by both S'01id and dashed cu~es in Fig. 3a)mustbe ~eater than those in which W is confined- to0 < W ~ ~ W (indicated by only the solid cu~es inthis figure). The choice 0f ~ Wdepends empirically onthe shape of the be~nning and ending Doppler velocityprofiles, which are a function 0f tropical cyclone sizeand .strength. For a ~weak iropical cyclone circulationwhose profile ~f tangential Mnd outside' the"RMW isnearly flat, AW must be as small as 3 m s-t. For anintense, mature hurricane having the steep profile oftangential wind outside the RMW, AW = 5 m s-~ issufficient, as in the example of Fig. 3b. The computation of the weighted values V, R, and 0 in (4) and(5) is sensitive to the choice of A W. The larger theA W value, the' more the weighted values depart fromtheir true values. Therefore, it is proposed that AW = 3 m s-1, for /xff < 35 m s-1, (6) /xW=5ms-~, for /x~>~35ms-t, (7)where /x~ = (Vm~x - Vmi.)/2 is the average of peakDopp!er velocity values obtained readily from the pattern vectors.b. Estimation of center location After (4) and (5) are computed, the next step is tocalculate an estimated range from the radar to Dopplervelocity peaks at N and P. Following Wood and Brown(1992), the estimated range R~r is represented by ~ Re = 2 ' (8)where (Rjv + Rv)/2 is the average of the ranges fromthe radar to an apparent signature center. Here, thecorrection factor F can be estimated from the obserw~'dangle A0 using the following relation: 0o F = sec , ~< I~01 < 180-, (9)OCTOBER 1994 W O O D 1211where /x0 = 0v - 0N is the observed azimuth angledifference between the two peak Doppler velocity values at N and P. Without the correction factor, the difference between the estimated range and the true rangefrom the radar to the center position would becomeincreasingly large as the region of maximum winds ofa large, axisymmetric circulation approached the radar,as reported by Wood and Brown (1992). The estimatedazimuth of the signature center (0E) from the radar isthe average of 0N and 0p; that is, 0e = (0N + 0p)/2.4. Test of the tropical cyclone center detection technique The technique developed in the foregoing discussionis evaluated here to determine its ability to detect atropical cyclone center. Because the Wood and Brown(1992) technique was designed for determining thecenter position of a large, axisymmetric wind circulation at a short range, it is necessary to experimentallytest the performance of the center-finding techniqueby using different ranges and viewing directions relativeto real tropical cyclone wind asymmetries.a. Simulated Doppler velocities Doppler velocity component Vd at slant range R andelevation angle q~ is the component of the three-dimensional wind vector in the viewing direction 0 fromthe radar and is given by (e.g., Doviak and Zrni6 1984,p. 262)Vd = u cosqO sin0 + v cos- cos0 + (w + Vt) sinq~, (10)where u, v, and w are, respectively, the velocity components directed eastward, northward, and upward,and Vt is the terminal fall speed (negative) of precipitation particles. The range and azimuth from the radarto a storm circulation center must be defined in orderto generate Doppler velocities. Equation (10) was usedto produce WSR-88D-like Doppler radar data simulating the scan of a ground-based Doppler radarthrough a gridded volume of hurricane wind field data.b. Hurricane Alicia Willoughby et al. (1984) analyzed in situ aircraftobservations in a moving, circular domain within 150km of the storm center of a hurricane. The storm centerposition was objectively identified from the flight-levelwinds using the technique described by Willoughbyand Chelmow (1982). Willoughby's (1985) analysiswas applied to Hurricane Alicia (1983) to reconstructthe gridded wind field from aircraft measurements atthe 850-mb level, which was evaluated on a two-dimensional array with a 5-km grid spacing. Because thegridded aircraft data were at an altitude of 1.5 km, itis assumed that the hurricane was far enough from theradar. Also the data were obtained at a 0- elevationangle, and therefore the last term on the right-handside of(10) can be ignored. A scenario is considered here in which the simulatedhurricane (Alicia) approaches a coastline, in this case,the Houston-Galveston area, where a WSR-88D system is located. This scenario is presented in Fig. 4.Given the radar site and flight-level storm center position in terms of latitude and longitude, the range andazimuth from the radar to the center position can becalculated. The low-altitude structure of the Alicia windfield at 0300 UTC 17 August 1983, 1500 UTC 17 August 1983, and 0300 UTC 18 August 1983 is, respectively, shown in Figs. 4a-c. The northwest-translatingstorm reached hurricane intensity at 0000 UTC 17August (Powell 1987). During the 24-h period beginning 3 h later, the radius of the inner wind maximumdecreased from about 40 to 20 km, and an outer windmaximum formed at a greater radius of about 100 kmfrom the storm center as Hurricane Alicia approachedthe Texas coast. Simulated Doppler velocity patterns that correspondto the Alicia wind fields are shown in Figs. 4d-f. Because a WSR-88D produces velocity data out to amaximum of 230 km (Crum and Alberty 1993), anapproaching tropical cyclone will first be seen usingonly reflectivity data (out to 460 km). The circulationcenter at 0300 UTC 17 August was beyond the 230km range; therefore, Fig. 4d does not show a coupletof closed isodops of opposite Doppler velocities. Between 0900 UTC 17 August and 0300 UTC 18 August,peak Doppler velocity values increased in magnitudeand the diameter of the couplet contracted steadily inresponse to the contraction of the inner concentric eye(Willoughby et al. 1984). Velocity difference /xV and azimuthal shear Sthresholds for the detection of tropical cyclones havenot yet been established because of the lack of data.However, such thresholds were arbitrarily determinedfor this study: 50 m s-~ for the velocity differencethreshold and 0.5 m s-~ km-~ for the azimuthal sheardetection threshold. Table 1 summarizes the tropical cyclone center positions estimated from simulated single Doppler radarand in situ aircraft measurements between 0900 UTC17 August 1983 and 0300 UTC 18 August 1983. Theaverage of peak Doppler velocity values across the hurricane vortex core diameter, denoted by ~a = (Ve- VN)/2, changed with time and is also shown in thetable. The fluctuation in ~ resulted from temporalchanges in the asymmetric structure of the tangentialwind and overall change in hurricane intensity. WhileAlicia intensified, tangential wind asymmetric patternsrotated from time to time, as can be seen in Figs. 4a-c.When a tangential wind maximum was in the frontquadrant of Alicia (Fig. 4b), the corresponding Doppler velocity pattern (Fig. 4e), as viewed from the radar,was quasi-axisymmetric. When Alicia approached theradar with its strongest winds in the left quadrant (Fig.4c), the Doppler velocity pattern was asymmetric (Fig.a ISOTACHS (m s'~) d DOPPLER VELOCITY (m s'~) % /L /b e / ',~.~. ~. ,., IAUG 1983c f ~~ 18AUG1983 ~ ~ FIG. 4. (a)-(c) Analyses of the ground-relative wind speed (m s-l) in Hurricane Alicia as itmade landfall on the Texas coast at (a) 0300 UTC 17 August 1983, (b) 1500 UTC 17 August1983, and (c) 0300 UTC 18 August 1983 (after Willoughby 1985). The contour interval is 5m s-t; the wind-plotting convention is the same as in Fig. 1. The hurricane center is indicatedby the hurricane symbol. (d)-(e) Corresponding simulated Doppler velocity patterns of theAlicia flow field relative to the current WSR-88D radar site [indicated by a solid star in panels(c) and (f)] in the Houston-Galveston area. The Doppler velocity contour convention is thesame as in Fig. 1. The heavy, dashed arc represents a 230-kin range. The solid dot represents anestimated position of the signature center from the radar; the heavy arrow centered on the soliddot represents the direction to the radar. In panels (b), (c), (e), and (f) the coastline is indicatedby heavy lines.OCTOBER 1994 W O O D 1213 TABLE 1. Average peak Doppler velocity Pa values across the core diameter, and storm center positions estimated from simulated land-based Doppler radar measurements and in situ aircraft measurements for the Hurricane Alicia case. The elevation angle was 0% Storm centerTime ~d* difference(UTC) (ms-l) Storm center* Storm center** (km) 198317 August 0900 1200 1500 1800 210018 August 0000 0300198334 27.968-N, 93.945-W 27.910-N, 94.000-W 8.438 27.907-N, 94.317-W 27.910-N, 94.330-W 1.340 27.970-N, 94.338-W 27.970-N, 94.360-W 2.144 28.062-N, 94.339-W 28.070-N, 94.360-W 2.341 28.382-N, 94.651 -W 28.370-N, 94.660-W 1.041 28.504-N, 94.638-W 28.480-N, 94.680-W 4.943 28.504-N, 94.825-W 28.500-N, 94.850-W 2.5 * Determined from simulated land-based Doppler radar measurements.** Determined from in situ aircraft measurements.4f). The decrease of ~a between 1800 and 2100 UTC,shown in Table 1, could be mistaken for a weakeninghurricane. However, from a forecasting point of view,it is important to recognize the change of closed isodopsof opposite Doppler velocities on both sides of the signature center that indicate temporal rotation of thewind asymmetric pattern relative to the radar-viewingdirection. Notice in Fig. 4d that an estimated signaturecenter was not calculated, since the Alicia circulationcenter at 0300 UTC 17 August 1983 was beyond the230-kin range associated with the Doppler velocitymode. Estimated ranges Re and azimuths 0~ of the signaturecenter of Alicia from the radar were converted intolatitudes and longitudes that were compared with stormcenter positions determined using in situ aircraft measurements and the Willoughby and Chelmow (1982)technique. The differences between center positionsestimated from simulated single Doppler radar and insitu aircraft measurements, shown in Table 1, indicatea good correlation between the estimates. At 0900 UTC17 August 1983, the difference between the center positions is somewhat large. This is due in part to theradii of the inner wind maximum on one side of theAlicia circulation center being greater than those onthe opposite side. This is a result of asymmetric convection in the inner eyewall. It may cause the cyclonecenter to move erratically some tens of kilometers ina few hours (Willoughby 1990). In this case, the disadvantage of using the center azimuth 0~ is obvious,since the Wood and Brown (1992) technique cannotbe applied to an asymmetric hurricane circulation.c. Hurricane Gloria Airborne Doppler-derived, three-dimensional radarreflectivity and wind fields of Gloria were obtained tofurther test the concept of using ground-based Dopplerradar data to estimate tropical cyclone center location.Three-dimensional analyses of these fields of the Gloriaeye were discussed in detail by Franklin et al. ( 1988,1993). The fields covered a 147 km x 147 km regioncentered on the storm circulation center position determined from the Willoughby and Chelmow (1982)technique. The gridded analysis was extended from 0.5to 14 km in altitude. The horizontal and vertical resolutions of the Doppler analysis were 3 and 0.5 km,respectively. Table 2 lists cyclone center positions with variousheights. Each center position was computed from thecenter of vorticity maximum and represents the bestcenter position in a moving vortex system, accordingto F. D. Marks Jr. of the National Oceanographic andAtmospheric Administration's (NOAA) AtlanticOceanographic and Meteorological Laboratory/Hurricane Research Division (AOML/HRD) ( 1993, personal communication). Note that the vorticity centerpositions were just to the northeast of the flight-levelmean storm center position, as indicated in Table 2.The main reason for the displacement of the vorticitycenters to the right of Gloria's track was that the centerswere earth relative for the purpose of navigation. Willoughby and Chelmow (1982) described the difference TABLE 2. Storm center positions at different heights, determinedfrom the center of maximum vorticity in a moving vortex system ofHurricane Gloria. The mean storm center position at the flight levelwas 24.568-N, 69.916-W at 0059 UTC 25 September 1985. Gloriawas moving from 148- at 4.1 m s-~ (provided by staff of AOML/HRD).Height (km) Latitude Longitude0.5 24.614-N 69.884-W1.0 24.596-N 69.884-W1.5 24.598-N 69.888-W2.0 24.591-N 69.883-W2.5 24.597-N 69.889-W3.0 24.595 -N 69.891 -W3.5 24.598-N 69,890-W4.0 24.598-N 69.890-W4.5 24.598-N 69.890-W5.0 24.618 -N 69.889-W1214 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUblE 11RADAR ARADAR BRADAR C RADAR DFIG. 5. Four different radar locations relative to theflight-level storm center position of Hurricane Gloria.are shown in Table 3. The latter positions were irtterpointed to the radar's height location of storm centerposition for the purpose of comparison with radar-estimated cyclone center positions at slant range. Thestorm center differences shown in Table 3 indicate 'thatthe center-finding technique performed well for detecting center location estimates from the radar measurements for radars A-C compared with center positions determined from in situ aircraft measurements.As viewed from radar D, differences between thesecenter location estimates were somewhat larger. Thiswas because when the radius of maximum wind wasperpendicular to radar D, and to the right of the stormcenter, it was smaller than that to the left. Again, thecenter azimuth 0E can cause problems in centering because of asymmetries in the wind field.5. Conclusions and discussionsbetween the earth- and storm-relative centers and track.The storm-relative track paralleled and lay to the rightof the earth-relative track. In the case of Gloria, it wasabout 3 km to the right in the mean overall altitudes,as shown in Table 2. Four different ranges and azimuths from the radarto the flight-level center location were selected and areshown in Fig. 5. In this case, the velocity differenceand azimuthal shear detection thresholds were chosenas 60 m s-~ and 1.0 m s-~ km-~, respectively. Asviewed from each radar location, ground-based Doppler radar-estimated cyclone center positions werecompared with objective cyclone center position, and A tropical cyclone center-finding technique for landbased Doppler radar determination of the center position in tropical cyclones approaching land has beendeveloped and applied to the wind field data collectedby reconnaissance aircraft during Hurricanes Al~cia(1983) and Gloria (1985). Preliminary results showthat the estimated locations of the hurricane vortexsignature centers from the radar compare favorablywith objective center positions determined from theWilloughby and Chelmow (1982) technique and according to Marks (1993, personal communication).Automated determination of the cyclone center position and its motion are very important for issuingtimely information. Center positions identified in s'uc TABLE 3. Storm center positions estimated from simulated land-based Doppler radar measurements and in situ aircraft measurementsfor the Hurricane Gloria case. Different radar ranges and azimuths relative to the storm center are as shown in Fig. 5. The elevation anglewas 0.5-. Height was computed from the estimated center range, which accounts for the earth's curvature. Storm ccuter Range Height differenceRadar (km) (km) Storm center* Storm center** (km) A 50 0.63 24.596-N, 69.851 -W 24.610-N, 69.884-W 3.6 100 1.44 24.613-N, 69.882-W 24.598-N, 69.888-W 1.8 150 2.61 24.605-N, 69.890-W 24.597-N, 69.889-W 0.9 200 4.08 24.593-N, 69.896-W 24,598-N, 69.890-W 0.8 B 50 0.68 24.606-N, 69.855-W 24.608-N, 69.884-W 3.0 100 1.55 24.592-N, 69.875-W 24.597-N, 69.888-W 1.4 150 2.70 24.581-N, 69.892-W 24.596-N, 69.890-W 1.7 200 4.12 24,566-N, 69.911 -W 24.598-N, 69.890-W 4.2 C 50 0.68 24.619-N, 69.882-W 24.607-N, 69.884-W 1.4 100 1.59 24.610-N, 69.873-W 24.597-N, 69.887-W 2.0 150 2.81 24.608-N, 69.865-W 24.596-N, 69.890-W 2.9 200 4.29 24.597-N, 69.867-W 24.598-N, 69.890-W 2.4 D 50 0.60 24.579-N, 69.933-W 24.610-N, 69.884-W 6.0 I00 1.45 24.561 -N, 69.944-W 24.598-N, 69.888-W 7.0 150 2.63 24.566-N, 69.947-W 24.596-N, 69.890-W 6.7 200 4.14 24.579-N, 69.941 -W 24.598 -N, 69.890-W 5.6 * Determined from simulated land-based Doppler radar measurements.** Determined from in situ aircraft measurements (Table 2) and interpolated for height.OCTOBER 1994 W O O D 1215ceeding radar volumetric scans are correlated in timeto provide a smooth storm track that could be used toforecast future center positions. In addition to centerposition calculations, the Doppler technique is valuablein determining the maximum wind speed and the radius of the maximum wind speed, which are essentialfor storm surge calculations. Although the performance of the tropical cyclonecenter-finding technique presented here is encouraging,this technique is limited by the circulation asymmetryor ellipticity of natural hurricanes, which cause problems in locating the eye center. This is a particularlytroublesome error source for calculations of center location estimates, because the Wood and Brown (1992)technique on which the current technique was basedwas designed for determining the center position of alarge, axisymmetric wind circulation. Tropical cyclonecenter-finding evaluations need to be performed overmany WSR-88D cases before greater statistical confidence in the technique's performance can be achieved. Future testing should include the study of eyewallradar reflectivity data, which will eliminate Dopplerwind information where reflectivity values are belowa threshold suitable for velocity measurements. Thepattern vectors of many hurricanes may be interruptedby regions of little or no rain, where reflectivities arebelow detection threshold. When hurricanes are viewedfrom a Doppler radar, it is critical that a couplet ofclosed contours of opposing Doppler velocities on bothsides of the eyewall reflectivity region be present forcenter position computation. If either side of the couplet is absent, the center position will not be calculated,thereby producing a gap in the track. The task of estimating a tropical cyclone center location is difficultin a situation where the precipitation in tropical stormsand weak hurricanes is organized in rainbands thatmay not encircle the storm center completely. In a reasonably symmetric storm with a closed eyewall, thestorm's center is easily identified and is a good approximation of the storm position. One aspect of the center-finding technique that needsto be improved is the magnitude of the azimuthal shearand velocity difference criteria for pattern vector identification of tropical cyclone center positions. Determination of the criteria depends upon the tropical cyclone size and strength. In different hurricanes, maximum horizontal winds occur 10-50 km from thestorm center and 0.5-1 km above the ocean surface(Burpee 1986). An observer may subjectively determine the azimuthal shear and velocity differencethresholds by obtaining low-altitude wind maximumand eye diameter estimates from hurricane reconnaissance flights or from ships and buoys that provide occasional observations of low-altitude winds. Anotherpoint to bear in mind is that the criteria need to bedifferent from those defined in a mesocyclone detectionalgorithm. This is'important, because a hurricane mesocyclone that appeared in analyses of airborne Doppler radar measurements done by Marks and Houze(1984) in the eyewall of Hurricane Debby ( 1982 ) occurred well out over the ocean. The tropical cyclonecenter-finding technique could inadvertently detect thecenter position of mesocyclones or highly localizedshear zones if the azimuthal shear and/or velocity difference criteria were improperly defined. The upperlimit of the shear and velocity difference thresholds fora mesocyelone detection algorithm have not yet beendefined and could be considered in the near future. Marks (1990) pointed out that there were discrepancies between WSR-57 reflectivity centers and windderived centers estimated from airborne Doppler observations of tropical cyclones. On the basis of a studyof Hurricane Frederic (1979), Marks found that thehurricane reflectivity-based center determined from theNational Weather Service's WSR-57 radar in Slidell,Louisiana, was different from an airborne Doppler-derived wind center. The reflectivity-derived center wasdetermined from the centroid of the oval rellectivitymaximum, whereas the wind center was observedcloser to the more intense portion of the eyewall reflectivity maximum as a result of asymmetric convection. In some tropical cyclones, the position of the windcenter with respect to the reflectivity center rotatedaround inside the eye, often in response to changes inthe position of the intense reflectivity in the eyewall,and thus caused a trochoidal oscillation in the stormtrack (e.g., Lewis and Black 1977). As suggested byMarks (1990), a combination of noncoherent and coherent radar observations may be necessary to determine storm position. Both Doppler velocity- and reflectivity-based techniques are needed to identify and track tropical cyclonecenters using the coastal WSR-88D radars because ofthe range limitations for the Doppler data. Eye centerestimates based on reflectivity patterns of the spiralrainbands and eyewalls are obtained at distances between 230 and 460 km from the radar, where Dopplervelocities are not available. At distances less than 230km, where Doppler velocities are estimated, a determination of the location of the center is obtained froma velocity-based technique. When the tropical cyclonecenter is within 230 km, the center-finding techniquesbased on both Doppler velocity and reflectivity information are needed not only to provide center locationestimates to forecasters but also to supply such important information as a trochoidal oscillation in the stormtrack and the relative orientation of the reflectivityand wind-derived centers. In the future, considerableapplications research will include the analyses of comparisons between reflectivity-derived centers andDoppler velocity-derived centers. It would be useful tounderstand how the Doppler technique compares withreflectivity-based techniques. Acknowledgments. The author appreciates the reviews of Dave Jorgensen, Rodger Brown, Mike Eilts,and Arthur Witt of the NOAA/Environmental Research Laboratory (ERL) National Severe Storms1216 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUI~:E 11Laboratory, and Ralph Donaldson of Hughes STXCorporation, who provided valued comments on themanuscript. Review by and discussions with Wen-ChauLee of the National Center for Atmospheric Researchwere especially helpful. The author 'appreciates thethorough reviews of and helpful suggestions from twoanonymous reviewers. 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