1354 MONTHLY WEATHER REVIEW VOLUMI~ 110Tropical Cyclone Movement and Surrounding Flow Relationships JOHNNY C. L. CHAN AND WILLIAM M. GRAYDepartment of Atmospheric Science, Colorado State University, Fort Collins 80525(Manuscript received 24 February 1982, in final form 30 June 1982)ABSTRACT This paper presents results of a comprehensive study of the relationship between the movement of tropicalcyclones and the large-scale circulation which surrounds them. Cyclones have been stratified by directionand speed of movement, latitude, intensity change and size (as delermined by the radius of the outermostclosed surface isobar) in three ocean basins: the northwest Pacific, the west Atlantic and the AustralianSouth Pacific region. Twenty-one different stratifications are available in the nonhwes! Pacific, 13 in thewest Atlantic and 6 in the Australian-South Pacific area. Cyclone movement and surrounding flow relationships were studied at different pressure levels and a variety of radii. Pressure-weighted layer-averageswere also analyzed in search of such relationships. Results show an important relationship between surrounding large-scale flow and tropical cyclone movement. For all stratifications, the winds in the mid-troposphere (500-700 rob) at 5-7- latitude radius fromthe cyclone center have the best correlation with cyclone movement. Tropical cyclones in the NorthernHemisphere move ---10-20- to the left of their surrounding mid-tropospheric flow at 5-7- latitude radius,and those in the Southern Hemisphere move ~ l0- to the right. It is also found that cyclones, in general,move ~ i m s-~ faster than this flow. These general relationships appear to be modified by the vertical shearof the environmental wind, the zonal component of the cyclone velocity and other characteristics of thecyclone. The mean tropospheric flow (surface to 100 rob) at 5-7- latitude radius also correlates well withcyclone movement in most cases. For cyclones embedded in an environment with relatively small verticalwind shear, the mid-tropospheric flow is as good a descriptor of cyclone motion as the mean troposphericflow. The average wind between the upper (200 mb) and lower (900 rob) troposphere also appears to correlaterea~nably well wilh cyclone movement.1. Introduction h has long been observed that the movement ofa tropical cyclone can be described, to a large extent,by the synoptic-scale flow surrounding the cyclone.These observations have led to the steering-flow theory of cyclone movement. It appears that a tropicalcyclone can be considered as a point vortex embedded in an air current such that the direction and speedof the center can be approximated by those of itssurrounding winds, or equivalently, the pressure orheight gradients across the cyclone. The pressure levelat which the speed and direction of the surroundingwinds best correlate with those of the cyclone is calledthe steering level. Based on this theory, a number of tropical cyclonetrack forecasting schemes have been developed, e.g.,Riehl and Shafer (1944), Miller and Moore (1960),Tse (1966) and Renard et al. (1973). For a detaileddescription of these methods, the reader is referredto the WlVIO Tropical Cyclone Project Report (WMO,1979). Although different forecast schemes employdifferent steering levels, it is generally accepted thatthe mid-tropospheric levels (700 and 500 mb) are thebest for predicting tropical cyclone movement. Attempts to use winds and heights at upper tropospheric0027-0644/82/! 01354-21 $09.25c 1982 American Meteorological Societylevels (see, e.g., Jordan, 1952; Miller, 1958) have notbeen as successful. No unified conclusion can bedrawn from all these schemes on the location (relativeto the cyclone center) at which one should measurethe surrounding winds or height gradients to get thebest description of cyclone movement for all classesof cyclones. This diversity exisls because the datasamples used in these studies have, in general, notbeen large and the variety of cyclone types have notbeen extensive. A more comprehensive study on the steering flowproblem is therefore necessary in order to determine:1) Which level(s) is/are the best steering level(s);2) How far from the center of the cyclone the surrounding flow best correlates with the movement ofthe cyclone; and 3) If this correlation varies among cyclones in different oceans, with different directions and speeds ofmovement, at different latitudes, of different intensities, intensity changes and sizes, etc. George and Gray (1976) established the statisticalrelationship between the movement of northwest Pacific tropical cyclones and their surrounding windsaveraged between 1-7- latitude radius from the cyOCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1355 TABLE 1. Description of stratifications of tropical cyclones inthe northwest Pacific. All cyclones under study had a maximumsustained wind speed Vmax > 18 m s-~. The number of rawinsondesoundings in each group of stratifications within the 5-7- latituderadial band is ~ 1000. CD is cyclone direction, CP is central pressure, ROCI is radius of outermost closed surface isobar averagedaround the cyclone to the nearest whole degree latitude, and Vc iscyclone speed.Stratification DescriptionLatitude: North cyclone South cycloneSpeed: Slow cyclone Moderate cyclone Fast cycloneDirection: Westward cyclone Northward cyclone Eastward cycloneIntensity: Weak cyclone Intense cyclone Very Intense cycloneIntensity change: Deepening north cyclone Deepening south cyclone Filling north cycloneFilling south cycloneSize and intensity: Small tropical storm Medium tropical storm Large tropical storm Small typhoon Medium typhoon Large typhoonLatitude of cyclone >20-NLatitude of cyclone <20-NCyclone speed V,. < 3 m s-~4ms-~ ~< V,.~<7ms-~Vc>7ms-~250-<CD~310-310-<CD~<350-350- < CD ~< 60-980 mb < CP ~< 1000 mb950 mb < CP ~< 980 mbCP < 950 mbCP decreasing at time of observation; latitude of cyclone > 20-NCP decreasing at time of observation; latitude of cyclone ~<20-NCP increasing at time of observation; latitude of cyclone >20-NCP increasing at time of observation; latitude of cyclone ~<20-N980 < CP ~< I000 mb; 1- ~< ROCI ~< 3-980 mb < CP ~< 1000 mb; 4- ~< ROCI ~< 5-980 mb < CP ~< 1000 mb; ROCI >~ 6-CP~<980mb;1-~<ROCI~<3-CP~<980mb;4- ~<ROCI~<5-CP ~< 980 mb; ROCI >~ 6-clone center. They found that over this broad radialbelt, the 500 mb winds have the strongest correlationwith the direction of cyclone movement, while the700 mb winds best correlate with cyclone speed. Gray(1977) presented a similar composite analysis of thewinds at 1-7- radius around west Atlantic tropicalcyclones. The results were in general agreement withthose obtained by George and Gray (1976). Since thearea over which the winds were averaged includesboth the cyclone circulation and part of the environmental flow, this radial belt, therefore, will not provide the best description of the relationship betweenthe movement of a cyclone and its environmental TABLE 2. AS in Table 1, except for tropical cyclones in the westAtlantic. The number of rawinsonde soundings in each group ofstratifications within the 5-7- latitude radial band is 4900.Stratification DescriptionLatitude: Region I cyclone*Region II cyclone*Speed: Slow cyclone Fast cycloneDirection: Northward cyclone Westward cycloneIntensity: Hurricane Tropical stormSize and intensity: Small tropical storm Large tropical storm Small hurricane Large hurricane north Large hurricane southLocation: latitude ~< 18-N, longitude > 45-W; or latitude < 22-N, 75-W < longtitude ~ 87-WLocation: 18-N < latitude ~< 35-N, longitude >~ 45-W except those already included in Region IVc<4ms-~V~4ms-~CD 316--45-CD 225%315-Vmax~33ms-118ms-t~ Vma~<33ms-t18 m s-~ ~ Vm~ < 33 m S-~; 1- ~< ROCI < 3-18 m s-~ < Vmax < 33 m s-~; ROCI >~ 4-V,~ax >~ 33 m s-~; 1- ~< ROCI ~< 3-Latitude of cyclones > 25-N Vm~, >~ 33 m s-t; ROCI >~ 4-Latitude of cyclones ~ 25-N Vm~, >~ 33 m s-t; ROCI >~ 4-* See Fig. 2 for a more detailed description of the regions.winds. Furthermore, due to the usual lack of upperair data around the cyclone center, it is typically impossible to apply these results to describe the movement of an individual cyclone. The present study is an extension of these two pre TABLE 3. As in Table 1, except for tropical cyclones in the Australian-South Pacific region. The number of rawinsonde soundingsin each group of stratifications within the 5-7- latitude radial bandis ~ 500.Stratification DescriptionDirection: Eastward cycloneWestward cycloneIntensity and region: All hurricanes Coral Sea hurricanes Coral Sea tropical stormWest Australian hurricaneCP ~< 990 mb; 40- ~< CD < 150-CP ~< 990 mb; 210- ~< CD < 320-CP ~< 990 mbEast of 136-E; CP ~< 980 mbEast of 136-E; 980 mb < CP < 995 mbWest of 136-E; CP ~< 980 mbMONTHLY WEATHER REVIEW VOLUME 110l~G. 1. Northwest Pacific rawinsonde stations.vious analyses. Composite wind data over an area(5-7 o latitude radius from the cyclone center) outsidethe strong inner circulation of the cyclone were correlated with cyclone movement in the west Atlantic,northwest pacific and Australian-South Pacific regions. More stratifications for both west Atlantic andnorthwest Pacific cyclones ha,~e been included to testthe validity of the conclusions in the two previousstudies. Data at individual levels, as well as meanlayer averages, were studied and compared for datasets with different characteristics. A combination ofthe winds in the lower (900 mb) and upper (200 mb)troposphere was also analyzed to more thoroughlytest the idea of using upper and lower troposphericwinds to describe and predict, cyclone movement assuggested by Chan et al. (1980). It is important totest this relationship because satellite-derived winddata at lower and upper tropospheric levels have be-.come increasingly available.2. Methodology and data stratifications Because of the scarcity of data over the oceanswhere tropical cyclones spend most of their lifetime,the only way to obtain quantitative and representativeresults is to composite data around cyclones with similar characteristics so that a more even coverage ofdata can be obtained. Although such a procedureundoubtedly smooths out features particular to individual cyclones, those characteristics that are common to all cyclones in the same stratification shouldbe isolated. In addition, random noise from the datawill be largely eliminated through the process of averaging. A more detailed description of this compositing philosophy can be found in Williams and Gray(1973), Frank (1977), Gray (1981) and other Colorado State University tropical cyclone research reports. Corrections for balloon drift and mass-balancewere made in the same way as described in thesepapers and reports.a. Stratification of the cyclones Tropical cyclones with maximum sustained windspeed (Vm~x) >~ 18 m s-1 in the northwest Pacific(1961-1970), west Atlantic (1961-1974), and Ausfralian-South Pacific (1961-1970) oceans were studied. The cyclones were stratified according to theirdirection and speed of movement, latitude, intensity,intensity change and size. These stratifications arelisted in Tables 1, 2 and 3.b. Compositing technique Wind data from rawinsonde stations shown in Figs.I (northwest' Pacific), 2 (west Atlantic) and 3 (Australian-South Pacific region) were composited aroundcyclones for the stratifications listed in Tables 1-3using the circular grid shown in Fig. 4. The center ofthe grid coincides with the cyclone center. The gridhas a radius of 15-, latitude~ with eight radial bands.Each radial band is divided into eight equal segments(octants) and numbered from 1 to 8 in a counterclockwise fashion, with Octant 1 always being in frontof the cyclone. The -+6 h (from current position) best-track positions were used to determine the direction and speedof cyclone movement. Each parameter (in this case ~ Hereafter all distances will be referred to in degrees latitude(1- latitude = 111.1 km).OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1357FIG. 2. West Atlantic rawinsonde stations.the wind components), for all soundings, fallingwithin any given grid box for a stratification is thenaveraged, This average value is assigned to the midpoint of the grid box giving 64 values of each parameter at each pressure level. The wind vectors were resolved in two coordinatesystems. The first system involves resolving each windobservation into a parallel component (Vv) along thedirection of cyclone movement and a componentnormal (VN) to this direction, as shown in Fig. 5. Thiswill be referred to as the ROTated (ROT) system. Inorder to study the environmental flow relative to thecyclone, a second coordinate system is used in whichthe speed of the cyclone Vc was subtracted from theparallel wind component (Vv) for each sounding. Thecomposite method was then applied to the differenceVv - Vc which is labeled as VvM (see Fig. 6). This willbe referred to as the MOTROT (for MOTionROTated) system. The normal component VN is thesame as in the ROT system. See George and Gray(1976) or Chart et al. (1980) for a more detailed description of these two coordinate systems.3. Relationship between the surrounding flow and the direction of tropical cyclone movement A convenient parameter to describe the relationship between the surrounding flow and the directionof movement of tropical cyclones is the differencebetween the direction of the surrounding wind andthat of the cyclone. If the ROT system is used, thisDirectional Difference (DD) is given byDD / arctan (VMVv), Vt, > 0 I ='] arctan (V~v/V~,) + 180-, V~v > O, Vv < 01 ' t. arctan (Vs/Vv) - 180-, VN < O, Vv < 0 (1)where V~ and Vv are the components of the composite wind normal and parallel to the direction ofcyclone movement. The parameter DD therefore represents the deviation of the composite wind in a particular octant and radial band from the direction ofmovement of all tropical cyclones in a particular1358 MONTHLY WEATHER REVIEW VOLUME II0FIG. 3. Australian'South Pacific region rawinsonde stations.stratification. A positive value of DD means that thecyclone is moving to the left of the composite wind. The basic assumption in the steering-flow theoryis that the vortex and its environmental circulationsdo not interact. If this is the case, the directional difference at the steering level should be approximatelythe same for cyclones with different characteristics.Under this assumption, the steering level can be determined by studying the scatter of the values of DDfor data sets in-the same ocean at each pressure level.The level and radius with the least amount of scatteris then assumed to be the steering level. Mid-tropospheric (700-500 mb) data 5-7- from the cyclonecenter appear to best satisfy this criterion. This is notsurprising, since forecasters have traditionally foundthese to be the best steering levels. To make use of this information in practice, reconnaissance flights will have to be made to measurewinds at these levels because most of the time, fewor no rawinsonde observations are available arounda cyclone. Such flights, however, are not routinelyflown. A plausible alternative may be to use 200 and/or 900 mb winds which can often be derived fromsatellite pictures. An examination of the rawinsondedata shows that the values of DD at these two levels I STORM DIRECTION OCTANT NO I 8 FIG. 4. Grid used for compositing rawinsonde data. Arrow pointsm the direction of storm motion. Outer numbers denote octants.Numbers inside grid indicate distances from the center in degreeslatitude.OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1359STORMMOTIONVECTORVpARALLEL ~ VNORMAL MOTION SYSTEM COMPONENT VECTORS FIo. 5. Parallel (Vp) and perpendicular (VN) component of awind vector showing their relation to the storm motion vector inthe ROT system.vary significantly between the different stratifications.However, if the V~v's and Vv's at these two levels areaveraged and substituted into Eq. (1), the values ofDD are quite consistent among data sets. This may.prove to be rather useful in areas where only satellitederived winds are available. In some of the track forecast schemes, layer-averaged winds are used to represent the steering current(see, e.g., Riehl and Burgner, 1950; Jordan, 1952;Miller, 1958; Sanders and Burpee, 1968). To see if'this idea would yield better results than "single-levelsteering," layer-averaged deviations (pressureweighted) have also been computed. One problem in steering flow studies is that theenvironmental flow around the cyclone might not beuniform. That is, each part of the cyclone ,may besubjected to a different current. The best way to avoidthis problem is to consider the mean surroundingflow, i.e., by relating cyclone movement to the average flow around a radial band. To calculate theradial band average of DD, the values of VN and Vpin each of the eight octants are averaged to obtainmean VN (or 17~) and mean Vv (or Vv) values. Eq.(1) is then applied using F~ and Fv to give the radialband average of DD (or DD). The value DD thereforerepresents the difference between the direction of themean wind in a particular radial band and that of thecyclone. This was done for all radial bands at eachindividual pressure level. As mentioned above, thesmallest scatter in the values of DD appears 5-7-from the cyclone center. Therefore, only data at thisradius will be presented.a. Variation with height 1) NORTHWEST PACIFIC Fig. 7 shows a plot of the 5-7- belt average windsin the ROT coordinate system at different levels forall data sets in the northwest Pacific. These windswere plotted using the values of Fs and Pp. Thedirection of cyclone movement is towards the top ofthe figure. This figure shows that for all data sets, thecyclone is moving to the left of the mean wind direction at all cyclonic levels (below 300 mb) exceptnear the boundary layer (below 900 mb). The leastvariability between data sets appears to be in the midtroposphere. More variability exists both at the anticyclonic levels (above 300 mb) and in the boundarylayer. The actual variations of the belt average deviationof (DD) with height for all the data sets in the northwest Pacific are shown in Fig. 8. A positive numbermeans, that the cyclone is moving to the left of themean wind. It can be seen that for most of the datasets, the values of DD do not vary much throughouta large portion of the troposphere. This suggests thatthe average flow around most of these cyclones doesnot have much directional wind shear in the vertical.If the values of DD at different levels are comparedamong all the data sets, the ones in the mid-troposphere (500-700 rob) show the least amount of variation. This is apparent from Fig. 8. For a detailed,quantitative comparison, the reader is referred toChan and Gray (1982). Focusing at the middle levels, some variationswithin each category of cyclones can be seen in Fig.8. Cyclones at latitudes north of 20-N seem to movemore to the left of the mean wind than those southof 20-N. Similar results have also been obtained byBrand e! al. (1981). DD values of slow-moving cyclones appear to be the largest among the speed composites. Westward-moving cyclones appear to moveless to the left of the mean wind than northward- andeastward-moving cyclones. As a cyclone increases inintensity, it seems to move more to the left of themean wind. The value of DD also appears to increasewith the size of the cyclone. Although variations exist, a general consistencybetween data sets (which have widely different characteristics) in the mid-troposphere is still remarkable.These results might suggest the general applicabilityof the steering flow theory at the middle levels. HowCYCLONEMOTIONVECTOR --, VP~vN ACTUAL WIND VECTORVpM --~--~ WIND VECTOR RELATIVETO CYCLONE MOTION ( MOTROT SYSTEM)FIG. 6. Illustration of the MOTion-ROTated (MOTROT) coordinate system.1360 MONTHLY WEATHER REVIEW VOLUME Ii0LATITUDE N of 2DeNSol 20~N~. SLOW-SPEED DIRECTION INTENSITYMODERATE FAST WESTWARD EASTWARD WE, [KINTENSEVERYINTENSEINTENSITY CHANGEDEEPENING DEEI~N of 20~N SOfFILLINGN of 20"N SIZE AND INTENSITY SMALL MEDIUM LARGEFILLING TROPICAL TROPICAL TROPICAL SMALLS of 20~N STORM STORM STORM TYPHOON IMEDIUMTYPHOON I~G. 7. 5-7- belt average winds in the ROT coordinate system at different pressure levels for all data sets in thenorthwest Pacific. The direction of cyclone movement is toward the top of the figure. Wind barbs were plotted inthe usual meteorological convention, one full barb being equivalent to 5 mever, if such a theory is correct, one would expect thevalue of DD to be near zero. While. this is true in afew stratifications, a systematic difference of ~20-exists between the mean 5-7- mid-tropospheric winddirection and the direction of cyclone movement.This suggests that the large-scale flow, though thedominant factor, is not totally responsible for thedirectional movement of the tropical cyclone. Otherfactors, which still need to be identified, must be present to provide such a systematic directional deviation. The vertical variability in the values of DD formost data. sets is also not very significant. Therefore,OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1361it appears that winds at a single-level in the mid-troposphere might be used to describe the directionalmovement of a tropical cyclone equally as well aslayer-averaged winds. More discussion of this willfollow.2) WEST ATLANTIC Fig. 9 shows the 5-7- belt average winds in theROT coordinate system for west Atlantic tropicalcyclones. The portion of the atmosphere in which the3iXLATITUDE N of 20~N Sof ~ - I - I - I - I . I _ I _ I~O~80~ - i -5 0 -5 O 5SPEEI~i SLOW MODEl ll/: i i~,~,! - ~o 0DIRECTION'E FA~ WESTWARD NORTH Rrl I I I I ,-5 0 5 -5 O $ -~ ODIRECTIONAL DEVIATION (lO1 DEGREES)INTENSITYINTEI E t o VERYINTENSE -~oo ' I 1 I -~oo I00 2OO 300~4oo& 80~ ?0~ OEEP~NING N of 20*N - I - I - I _ I - I -ooc-- I~0- -- ~ , II - 0INTENSITYD[EI~ I NGSol2 N :tCHANGE G 'N I-5 0 5 -5 0 MEDIFILIJ '~N T~S of 2 STO !I II II II II II I~ II II II II II II II IIi ~I II II II II ~ ~ ~-5 0 -5 0 5 -5 0 5 -5 0 DIRECTIONAL DEVIATION (lOI DEGREES) ISMALL TROPICAL STORM 5 I,I I ~ I SIZE AND INTENSITY/I LARG~ L TROPICAL SM~dSTORM TYPHOON: 1 I 1 I ~ ~ I I 5 -5 0 MEDIUM TYPHOON 3 1 I t ,l -$ o LARGE TYPHOON - Ioo -~oo -~oo I - ,oo~ & '~ -~oo~ i~ - ~OO I - ~ I I -~ - ~05 -5 0 5 lqo. 8. Variation with height of the 5-7- belt average wind deviation (DD, solid line) for all data sets in the northwestPacific. The zero (dashed) line represents the direction of cyclone movement. A positive value means that the cycloneis moving to the left of the 5-7- belt average wind direction.1362 MONTHLY WEATHER REVIEW VOLUME II0LATITUDESLO~SPEEDFASTJ.JIIDIRECTIONWESTWARD NORTHWARD ' ,~ -~/ ',,V .,~ \ x/ ',,,/ - ~ - -J ~J ~ ~- J i r~~, I hFIG. 9. As in Fig.INTENSITY TROPICALHURRICANE STORM _ SMALL LAI GETROPICALTROF CALSTORM ST~ RM y .,,/ .~ .~ -~ -~ ,,v7, except for west Atlantic tropical cyclones-SIZE AND INTENSITY LA~ SMALL HURRI HURRICANE SO[ ~ ~ .j ..~ ~ .4 ~ ~ ~ j ~ -3 ~LARGEHURRICANE* NORTH tO0 -.V L>O0 ,~ ,~ ~0o .~ ,.~ 400 ~ ~ 0 E ~oo ~o ~1 I0~ i -variability between data sets is small, seems to beconfined only to the mid-troposphere between 700and 500 mb. For each data set, the variation in thevertical is slightly larger, when compared with northwest Pacific tropical cyclones. Most cyclones moveeither in the same direction or to the right of themean winds below 800 mb. In the mid- to uppertroposphere, however, west Atlantic cyclones moveto the left of the mean wind, as in the northwestPacific. In the mid-troposphere the winds are, in gen-,eral, weaker than those in the northwest Pacific andthe values of DD are also smaller. These observations are more clearly shown in Fig.10. For all data sets except the westward-moving cyclones, the values of DD appear to increase withheight from the surface up to ~ 150 mb. Westward IO( 20( ~o(~mLATITUDE REGION I REGI ~1 II - ~ ~ ~- II _ _?01 . / I ~ I -5 0 -5 0'SPEED SLO~ FA:? ,I' I I I I ' I I I I I '-5 0 ~ 0DIRECTION WESTWARD NORT f'N/~ I'It 'I "5 -5 0 $ -5 0 INTENSITY I TROI ~'L ~ r, ALHURRICANE STI A ST M-5 0 5 -5 0 5 -5 0DIRECTIONAL DEVIATION (10m DEGREES) SIZELAR(TRO~I~ JSTO~ I 'I Ii~ ! ~-5 0AND INTENSITY LARGE SMI HUI~ICANE HUR~ NE SOUTH - ~ ' 1 '1 -5 0 5 -5 0 ,~HURRICANENORTH ?o0-$FIG. 10. As in Fig. 8, except for west Atlantic tropical cyclones.OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1363DIRECTION|'/~ INTENSITY AND REGION AL SEA WEST~ORAL SEA TROI~CAL /~I.ISTRAI.JAN ~ooFIG. 1 1. As in Fig. 7, except for tropical cyclones in the Australian-South Pacific region.moving cyclones tend to move in the same directionor even slightly to the right of the mean wind direction. Values of DD above 300 mb for this data setwere not plotted because the winds are very weak, asshown in Fig. 9, and directional deviations are, therefore, less well defined. Again, if the values of DD atvarious levels are compared among the data sets, theyare most consistent at the middle levels. More quantitative discussion of these observations can be foundin the report of Chan and Gray (1982). However, slight variations within each category ofcyclones in the mid-troposphere are still discerniblefrom Fig. 10. Region I (~south of 18-N) cyclonesmove less to the left of the mean winds than cyclonesin Region II (~-north of 18-N). Westward-movingcyclones have quite different values of DD thannorthward-moving cyclones. This is the same as thenorthwest Pacific, except it is more obvious for westAtlantic cyclones. The values of DD also appear toincrease slightly with the size of the cyclones. However, from a practical point of view, the differencesin the values of DD between cyclones of differentsizes may not be distinguishable. Therefore, it mightbe safe to say that the direction of cyclone movementcan be described adequately using the 5-7- meanmid-tropospheric wind, irrespective of the size of thecyclone. This is true in both the northwest Pacific andwest Atlantic. The general increase in the values of DD withheight for west Atlantic tropical cyclones, suggeststhat the cyclones are in an environment with a stronger average directional vertical wind shear than northwest Pacific cyclones. This type of shear profile wouldimply that using layer-averaged steering might be superior to us!ng single-level steering. This will be discussed in greater detail later.3) AUSTRALIAN-SOUTH PACIFIC Fig. 11 gives the 5-7- belt-averaged winds in theROT coordinate system for tropical cyclones in theAustralian-South Pacific region. At first glance, thedata appear to be very noisy. However, a closer examination shows that for data sets classified under"intensity and region," the variability among the datasets in the mid- to upper-troposphere is actually verysmall, with the cyclone moving to the right of themean wind direction above 700 mb. This is also thecase for eastward-moving cyclones. Westward-moving cyclones appear to move to the left of the meanwind at levels up to 400 mb. These variations are better illustrated in Fig. 12,which gives the 5-7- belt-average deviations (DD) atdifferent levels. The values of DD generally decreasewith height, the exact opposite of the west Atlantic.These profiles again demonstrate the existence of anaverage directional wind shear profile in the vertical.This shear appears to be stronger in the lower troposphere (below -~600 mb). With the exception ofeastward-moving cyclones, the values of DD in themid-troposphere are fairly constant among all datasets. The same type of difference in the DD profilesbetween westward and eastward-moving cyclones exists in this region as in the two Northern Hemisphereocean basins (see Figs. 8 and 10). It appears that whendirectional vertical wind shear is present (as in thewest Atlantic and Australian-South Pacific regions),this difference in directional deviations (between cyclones moving in different directions) is more obvious. One must conclude that the deviation of thecyclone direction from that of the mean wind at aDIRECTIONINTENSITY AND REGION \ I [ DIRECTIONAL DE~ATION (~ DEGREES)FIG. 12. As in Fig. 8, except for tropical cyclones in the Australian-South Pacific region.1364 MONTHLY WEATHER REVIEW VOLUME II0 given level is related to the zonal and meridional di rection of cyclone motion. 4) SUMMARY The results in this subsection show that the verticalvariation of the deviation of the cyclone directionfrom the 5-7- belt average wind direction for all threetropical regions depends on the directional verticalwind shear of the environmental winds. The leastvariability among data sets in a given ocean basinappears to be in the mid-troposphere. Most cyclonesin the Northern Hemisphere move to the left of the5-7- belt average wind (at least in the mid-troposphere) while cyclones in the Southern Hemisphere,in general, move to the right of mid-tropospheric'winds at this radius. The direction of movement ofwest Atlantic cyclones tends to deviate less to the leftof the mid-tropospheric mean wind ('-~10-) thanthose in the northwest Pacific .(--~20-). In oppositedirection but probably with similar physical agreement, cyclones in the Southern Hemisphere move tothe right of the mean winds at 600 and 500 rob. Partsof these results are Consistent with those obtained byGeorge and Gray (1976) and Brand et al. (1981) forthe northwest Pacific and those of Gray (1977) forthe west Atlantic. Such deviations appear to beslightly modified by latitude, intensity and size of thecyclone. Also, cyclones with different zonal components 6f motion have large differences in their D~values. The fact that consistent differences occur forcyclones with east and west directions of movementsuggests the possible presence of other factors in determining the direction of cyclone movement besidesthe large-scale mean surrounding flow.b. Level and layer-averages Five averages were calculated: surface to 100, 300and 500 rob; 700 to 500 rob; and the average betweenthe 200 and 900 mb levels. The first four layer integrations involve pressure-weighted averages and thelast is the arithmetic mean between the two levels.The radial band averages of the two component winds~v, I?~, were integrated or averaged to get the layeraverage (~N) and ~p). That is, for the pressureweighted averages, ( I2~) = V~v dp (P2 - P,), (2a)(2b)where p~ and P2 are the lower and upper pressurelevels of the layer. The 200 and 900 mb arithmeticaverages are defined by[~r] = V2[/~r(200 mb)+ l?~v(900 mb)], (3a) [Pp] = V2[/~(200 mb)+ /~(900 mb)]. (3b)The layer- or level-averaged directional deviation isthen calculated by substituting < ~), < l~v) or [~],[ ~v] into Eq. (1). The reason for choosing the surface to 100 mblayer-average is to test the validity of the suggestionby Sanders and Burpee (1968) that the integrated tropospheric flow is the most applicable "steering" current. Riehl and Burgner (1950) and Jordan (1952)used the surface to 300 mb mean flow as their predictor. The surface to .500 mb mean flow is calculatedfor comparison with the deeper surface to 300 mbmean flow pattern. The results in the previous subsection indicate the importance of mid-troposphericflow and hence the 700 to 500 mb mean flow wasalso calculated. To compare different layer-averages, the scatter $among the data sets is calculated. This is defined as 1 i~S = ~ (DDi- DD)2J ,where N is the total number of data sets, DDi is thevalue of DD for the data set i and DD is the meanvalue of DD for all data sets. In a sense, the value ofS is similar to the standard deviation of a sample.However, it cannot be interpreted in the same waybecause the data sets are not all independent and thevalues of DD are population means. Nevertheless,this calculation will provide a measure of the spreadof the values of DD. The larger the value of & theless "useful" will be the type of layer-average. 1) NORTHWEST PACIFIC Table 4 shows the layer-averaged values of DD fornorthwest Pacific tropical cyclones. Not much variation exists between the different pressure-weightedaverages. This small variation is also reflected in' themean for all the data sets. However, within each category, slight differences exist between data sets. Thesedifferences are consistent with those discussed in Section 3a. Cyclones south of 20-N move less to the leftof all the layer-averaged flow than those north of20-N. Slow-moving cyclones have the largest deviations in the speed category. An increase in the directional deviation is also found to correlate very wellwith an increase in cyclone intensity. The deviationalSO increases with cyclone size. The different layeraverages have approximately the same scatter amongthe data sets. The mean flow corresponding to thelayer of cyclonic flow (surface to 300 mb or surfaceto 500 rob) is slightly better than the other levels.These results again demonstrate the absence of appreciable directional wind shear in the vertical. The 200 and 900 mb average directional deviationsalso relate in a reasonable way to cyclone motion.With the exception'of the large tropical storm dataOCTOnER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1365 TABLE 4. Directional deviations between cyclone direction and direction of level- or layer-averaged 5-7- mean winds for differentcombinations of levels for northwest Pacific tropical cyclones. See text for a description of how these averages and the scatter werecalculated. ~100 mb ~si,00 mb ~si00 mb ~7500 mb 200 mb + 900 mbStratification suaa~ trace trace 00 mb AverageLatitide:North of 20-N 19 19 15 23 16South of 20-N 2 6 8 8 3Speed:Slow (1-3 m s-~) 29 27 10 30 22Moderate (4-7 m s-~) 20 20 14 23 16Fast (>7 m s-~) 12 14 15 18 9Direction:Westward (250-310-) 9 17 18 20 5Northward (310-350-) 16 17 13 23 13Eastward (350-60-) 17 16 13 19 15Intensity: ,Weak (1000-980 mb) 8 14 16 16 4Intense (950-980 mb) 16 20 18 25 9Very intense (<950 mb) 23 26 22 34 13Intensity change:Deepening north of 20-N 23 23 17 23 21Deepening south of 20-N 14 24 30 30 8Filling north of 20-N 19 20 17 23 14Filling south of 20-N 8 13 10 13 9Size and intensity:Small tropical storm 9 12 11 13 8Medium tropical storm 9 14 16 18 6Large tropical storm I 14 19 19 - 15Small typhoon 15 16 15 22 13Medium typhoon 12 15 14 18 7Large typhoon 27 29 26 31 22Mean 15 18 16 21 10Scatter 7.5 5.6 5.2 6.4 8.1set, the variation between data sets is not large. Thenegative value for the large tropical storm data set isa result of the large negative deviation at 200 mb (seeFig. 8). The reason for this is unknown. These resultssuggest that it might be possible to use winds at theselevels (derivable from satellite pictures) to describethe directional movement of tropical cyclones whenother information is not available.2) WEST ATLANTIC Table 5 indicates that the directional variabilitybetween data sets in the west Atlantic is larger thanin the northwest Pacific. The smallest variation appears to be for the surface to 300 mb and 700-500mb averages. These results again point to the existence of directional wind shear in the vertical. Whenintegrated over the lower troposphere (surface to 500mb), the shear near the boundary layer gives a largevariability among data sets. However, when the integration is made up to 300 mb or just in the midtroposphere (700-500 rob), the effect of the boundarylayer is quite small. If the upper tropospheric flow isincluded (surface to 100 mb), a large variability existsbecause of the strong shear at the upper levels. Therefore, it appears that in the west Atlantic, where directional wind shear is present in the upper and lowertroposphere, winds in either the mid-troposphere ora deep layer corresponding to the cyclonic rotationof the storm-is a better descriptor of cyclone direction. As in the northwest Pacific, small variations between data sets exist within each category. North cyclones move more to the left of the layer-averagedwinds than south cyclones. In fact, south cyclonesmove slightly to the right of the mean flow. This isalso the case for westward-moving cyclones. Thesetwo data sets (south and westward-moving) probablyinclude almost the same cyclones since cyclonessouth of 20-N usually move west-northwestward.Northward-moving cyclones, on the other hand, areusually at higher latitudes. Therefore, consistent withnorth cyclones, they move more to the left of themean wind. These results suggest the importance ofthe latitude (which relates to the Coriolis parameter)in cyclone motion. This question has been addressedin some theoretical studies (e.g., Holland, 1982;1366 MONTHLY WEATHER REVIEWTABLE 5. As in Table 4, except for west Atlantic tropical cyclones.VOLUME 110 f~,100 mb ~i00 mb fs~OOmb ' 5f7~(~:) me' 200 mb+ 900 mbStratification suaace fface race mb AverageLatitude:Region I (South) -1 -3 -7 -3 10Region II (North) 16 5 -4 7 27SpeedSlow (1-3 m s-~) 11 3 -7 4 16Fast (>3 m s-~) 14 10 7 11 18Direction:Northward (316-45 o) 27 13 . -5 13 34Westward (225-315 o) -9 -5 -2 - 1 1Intensity:Hurricane 10 3 -3 3 24Tropical storm 6 - 1 -8 2 6Size and intensity:Small tropical storm 14 9 5 10 19Large tropical storm 22 18 11 20 19Small hurricane 12 8 5 9 16Large hurricane north 22 . 21 21 23 24Large hurricane south 18 4 -12 6 34Mean 13 7 0 8 19Scatter 9.7 7.7 9.2 7.6 9.8Chan, 1982). Anthes (1982) also presented a reviewof this topic. In the intensity category, hurricanes generally move more to the left of the layer-averaged flowthan tropical storms. The deviation' also appears toincrease with cyclone size. The small (or even negative) deviation for the large hurricane south-movingdata set is probably a result of the latitude of thecyclones. Because of the shear between the upper and lowertroposphere, the 200 and 900 mb average directionaldeviations do not give as small a variability as theircounterparts in the northwest Pacific.data sets for the surface to 100' mb layer-average. Itshows the Australian cyclones move to the right ofthe 5-7- mean tropospheric wind. Because of thelarge directional vertical wind shear, a relatively largevariability exists among the different layer-averagesfor a given data set, with the exception of eastwardmoving hurricanes (see Fig. 12). Again, because ofthe strong vertical directional shear, these layer-averages show a larger variability than those in theNorthern Hemisphere ocean basins. This is also thecase for the 200 and 900 mb average directional deviation. 3) AUSTRALIAN-SOUTH PACIFIC REGION Table 6 gives the layer-averaged DD values fortropical cyclones in the Australian-South Pacific region. The striking result is the consistency among 4) SUMMARYThe mean DD values for all data sets for each levelor layer-average for the three ocean basins are shownin Table 7. They show that the mean tropospheric TABLE 6. AS in Table 4, except for tropical cyclones in the Australian-South Pacific region. ~siO0 mb fsiO0 mb J~,500 mb ~7500 mb 200 mb + 900 mbStratification ra~ rface surface 00 mb AverageDirection:Eastward (40-150-) -10 -13 -14 -17 2Westward (210-320-) -9 14 22 22 -72*Intensity and region:Hurricane -20 - 12 3 -5 -29Coral Sea hurricane -15 -7 12 -12 -15Coral Sea tropical storm -13 -2 5 -4 -23West Australian hurricane -22 -8 10 14 -36'Mean -15 -5 6 0 -29Scatter 5.3 10.0 12.0 15.2 24.9* Such a large directional difference is due to weak 900 mb winds (see Fig. ? 1). This value is therefore not well defined.OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY TABLE 7. Summary of the mean level- or layer-averaged values of DD for all data sets in each ocean basin. The corresponding scatter within each ocean basin is given in parentheses.1367 ~slOOrnb ~s~OOmb ~sl,OOmb ~7500rob 200 mb + 900 mbOcean basin ~f~ trace trace 00 mb AverageNorthwest Pacific 15 18 16 21 10 (7.5) (5.6) . (5.2) (6.4) (8.1)West Atlantic 13 7 0 8 19 (9.7) (7.7) (9.2) (7.6) (9.8)Australian-South - 15 -5 6 0 -29 Pacific region (5.3) (10.0) (12.0) (15.2) (24.9)flOW (surface to 100 mb) gives almost the same resultsfor all the three ocean basins. It seems that the meantropospheric flow, on the average, would be the bestdescriptor or predictor for direction of cyclone movement, with cyclones in the Northern Hemispheremoving to the left of this flow by '-- 15 o and those inthe Southern Hemisphere moving to the right by approximately the same amount. However, it appearsthat, for individual ocean basins, the best layer depends on the directional vertical shear 'of the environmental wind in that region. In general, the moredirectional shear there is with height, the deeper thesteering layer. When little directional shear is present,mid-tropospheric and deep layer steering are comparable. The magnitude of vertical directional shearalso affects the degree of applicability of winds at 900and 200 mb in describing the directional movementof the cyclone. It is important to note that the means in Tables4-7 are meant to provide an idea of the average deviation of the cyclone direction and that of its environmental flow. The deviation in individual cases willdiffer from the mean, although in most cases not significantly. The amount of this difference depends onthe various characteristics of the cyclone, as discussedin the previous subsection.4. Relationship between the surrounding flow and the speed of tropical cyclones In both coordinate systems described in Section2b, the winds are resolved into two components, onenormal (VN) and one parallel (Vp) to the direction ofcyclone movement. The normal component VN obviously does not contribute to the scalar speed of thecyclone. The study of the relation between the surrounding flow and the speed Vc of a cyclone thereforereduces to relating the parallel component of the windVe to Vc. If the large-scale surrounding flow is thedetermining factor in cyclone speed, as is the casewith cyclone direction, then values of Ve, relative tocyclone movement, should be approximately thesame for different data sets. The MOTROT coordinate system described in Section 2b is used for thispurpose. That is, for every wind observation, thevalue of Vp relative to the cyclone (Vpm) is calculatedfromVpM = Vp- VC.See Fig. 6 for an illustration of how this is done. Acomposite was then made using the individual valuesof Vp - Vc. The parameter VeM therefore representsthe composite relative (to the cyclone) wind component parallel to the cyclone direction. A negativevalue of Ve~4 means that the cyclone is moving fasterthan the composite wind. As in the last section, the azimuthally-averagedflow will be analyzed. The radial band average at eachpressure level and each radius is the average of theVp~ for all eight octants in that radial band, denotedby ~p~. To find the "best" steering level and radiusfor cyclone speed, the scatter of l~p~ for data sets atvarious levels and radii were calculated in the sameway described in the last section. Again, the 5-7-radial band at the mid-tropospheric levels (700 and500 mb) have the smallest scatter among data sets forall three ocean basins. Following the procedure usedin Section 3, the variation of 5-7- Vp~ with heightwill be presented, followed by level- or layer-averagedwinds.a. Variation with height 1) NORTHWEST PACIFIC Fig. 13 shows the vertical profile of 17pM at 5-7-for northwest Pacific tropical cyclones. Not muchvariation in the vertical exists for most data sets except for the data set north of 20-N, the fast-moving,eastward-moving, filling north of 20-N and large typhoon data sets. This means that, with the exceptionof these five stratifications, the other cyclones are generally embedded in an environment with relativelysmall vertical speed shear. The variation among data sets in the mid-troposphere is generally small, with ~'p~ ~-. -1 m s-~.However, within each category, slight variations arestill present. Cyclones north of 20-N tend to movewith the same speed as the mean mid-troposphericwind. Fast cyclones move slower than the 500 mb1368 MONTHLY WEATHER REVIEW VOLUME 110,. VpM (ms-') INTENSITY CHANGE - FILLING DEEPENING DEI ENING _,o,~o..s,~:,.., ,~o.,, '~ ~ '/tooI Ii ~ I - I60~80~ '5 0 5 '5'5 oJNG~O"N TI ~ICALTI = ,.I I I I'5 O $ -5 O v~ (ms-[) SIZE)M..,AL 1'1MAND INTENSITY:;GE:qCAL $ ~LL:)RM TY ~1~ i'I , iI I I I0 S '5 0 5 -5 0M J-TY ION LARGE T~ HOON-5 0 5 F~O. 13. Variation with height of the 5-7- belt average relative component of the wind parallel to cyclone direction for northwest Pacific tropical cyclones (solid line). The zero (dashed) line represents the cyclone speed. Anegativ~ value of V~,M means that the cyclone is moving faster than the 5-7- surrounding wind.mean wind while both slow and moderate speed cyclones move faster than their environmental flow(~eM < 0). Eastward-moving cyclones and those filling at latitudes north of 20-N move slower than themidtropospheric wind. All these cyclones have astrong northward and/or eastward component ofmotion. It seems, therefore, that the zonal and meridional components of cyclone motion have someeffect on the speed of the cyclone relative to it~ surrounding wind.OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1369LATITUDEREGION IREGION II I II SPEEDSLOW-5 6ST WF_.Ii'-5 0 5 -5DIRECTION \ INTENSITYHURRICANE T~-5 0 5 -5 0Vm (m sq)SMALL I [TROPICAL I TASTORM .~ ' I I II = I ~ I I-5 0 5 - 0 5SIZE AND INTENSITYRGE L:tGEicANE~ICAL S t, LL HU!DRM HUF ICANE ~ JTHI I1 t ~ I ' t I I [I II I II I !I ~I II I II II I I I I I I i I I ! I , ! ,i, ! , -5 0 5 -5 0 5FIG. 14. As in Fig. 13, except for west Atlantic tropical cyclones.IURRICANE NORTH-5 0I00 2) WEST ATLANTIC The vertical profiles of 5-7- 17e~ values for west Atlantic tropical cyclones are shown in Fig. 14. The variation with height for most data sets is not very large. Noticeable exceptions are westward- and north ward-moving cyclones, large tropical storms and large- hurricanes north of 25-N. Again, all cyclones move faster than the lower and mid-tropospheric winds (~eM < 0). Between data sets, very little difference between the values of ~e~t can be noticed, especially in the mid-troposphere. It is also of interest to note that a similar relationship between the 5-7- wind speed and the cyclone speed holds for cyclones of different sizes in both the northwest Pacific and the west Atlantic. It therefore appears that, despite the difference in the sizes of cyclones, the 5-7- surround ing flow can be used to describe the cyclone move ment. 3) AUSTRALIAN-SOUTH PACIFIC Fig. 15 shows the vertical profiles of 5-7 o l?e~t values for tropical cyclones in this region. Considerablevariation of ~2e~ with height exists for most data sets,indicating a large speed shear in the vertical. Similarto those in the Northern Hemisphere, all cyclonesmove faster than the mean wind ~in the lower troposphere (below ~600 mb). Although strong shearis present, the values of ~eM in the mid-troposphereare approximately the same among different data sets.The main exception is the eastward-moving stratification, again pointing to the importance of the zonalcomponent of cyclone motion. 4) SUMMARY The vertical profiles of ~PM at 5-7- do not showmuch variation among cyclones in the three oceanbasins, when compared to the vertical profiles of directional deviations. Exceptions arise when the cyclone is in an environment with strong 'vertical speedshear. All the data sets indicate that cyclones, in general, tend to move faster than the 5-7- mean windat the mid-troposphere. This is consistent with theresults obtained by George and Gray (1976) and Gray(1977). Slight modifications to this rule could arisewhen cyclones have a large eastward component ofmotion. If the steering flow is totally responsible forthe movement of a cyclone, one would expect ~e~to be near zero. The fact that ~e~t is mostly negative,at least in the mid-troposphere, points out the existence of other factors in the determination of thespeed of a cyclone.b. Level- or layer-averages To calculate the pressure-weighted averages ofEq.-(2b) was used with ITeM in the integrand of thenumerator instead of ~e. Similarly, the 200 and 900mb arithmetic average of PeM can be computed usingPe~ instead of 12e in Eq. (3b). Similar pressure1370 MONTHLY WEATHER REVIEW VOLUME ll0DIRECTION iNTENSITY AND REGION SEAt', /l I v~ (ms'~)FIG. 15. As in Fig. 13, except for Australian-South Pacific region tropical cyclones.weighted averages were calculated: surface to 100, 300and 500 mb, and 700 to 500 mb. The scatter amongdata sets is also computed in the way described in thelast section. 1) NORTHWEST PACIFIC Table 8 shows the four pressure-weighted layer averages and the 200 and 900 mb average PvM for allnorthwest Pacific cyclones. As with the layer-averageddirectional deviations, not much variation existsamong the different averages. This is also evidentfrom the mean for all the data sets. Slight variationswithin each category are also apparent. Cyclonessouth of 20-N move faster than the layer-averagedflow by a larger amount than those north of 20-N.The values of the integrated l~vM for eastward-movingcyclones are generally the least negative among thedirection data sets. Very intense cyclones tend tomove faster than the mean wind by~ the largestamount within the intensity category. For the sameintensity change, north cyclones have ~'v~u values lessTABLE 8. Level- and layer-averaged 5-7- ~'~,~t for a different combination of levels for northwest Pacific tropical cyclones. See text for a description of how the averages were calculated. Units: m s-~. ~.10o mb ~,300 mb fs0o mb fS00 mb 200 mb + 900 mbStratification su~fa~ su,fa~ ,'~v,face ~70o ~,b AverageLatitude:North of 20-N -0.6 - 1.0 - 1.7 -0.6 -0.6S~uth of 20-N - 1.3 - 1.6 - 1.7 - 1.5 -0.8Speed:Slow (1-3 m s-~) -0.9 -0.9 -0.9 -0.6 -0.7Moderate (4-7 m s-~) -rl.l -1.I -1.3 -0.9 -1.1Fast (>7 m s-~) -0.1 -1.3 -3.0 -0.6 ' 0.2Direction:Westward (250-310-) -2.2 -2.3 -2.4 -2.4 - 1.7Northward (310-350-) - 1.5 - 1.0 -0.8 -0.9 -2.0Eastward (350-60-) 0.2 -0.5 - 1.8 0.2 0.2Intensity:Weak (1000-980 mb) -0.8 - 1.1 - 1.6 -0.9 -0.9Intense (950-980 mb) -0.7 - 1.1 - 1.6 -0.6 -0.7Very intense (<950 mb) -1.4 -1.7 -1.9 -2.0 -0.5Intensity change:Deepening north of 20-N - 1.0 - 1.1 - 1.1 - 1.1 -0.5Deepening south of 20-N - 1.5 - 1.7 - 1.7 - 1.5 - 1.1Filling north of 20-N 0.2 -0.7 -1.9 -0. ! 0.8Filling south of 20-N - 1.9 -2.3 -2.5 -2.4 - 1.2Size and intensity:Small tropical storm - 1.3 - 1.2 - 1.5 - 1.1 - 1 ~5Medium tropical storm -0.2 -0.7 - 1.4 -0.6 -0.1Large tropical storm - 1.7 - 1.9 -2.3 - 1.9 - 1.5Small typhoon - 1.2 - 1.0 - 1.0 -0.8 - 1.4Medium typhoon -0.1 -0.4 '- 1.0 -0.3 -0.2Large typhoon -0.7 - 1.0 - 1.7 - 1.0 -0.3Mean -0.9 - 1.2 - 1.7 '- 1.0 -0.7Scatter 0.7 0.5 0.6 0.7 0.7OCTOBER 1982JOHNNY C. L. CHAN AND WILLIAM M. GRAYTABLE 9. As Table 8, except for west Atlantic tropical cyclones.1371 ~slOO mb f30o mb fsi00 mb ~soo mb 200 mb + 900 mbStratification ~face Osurface rface 00 mb AverageLatitude:Region I (south) -1.3 -0.9 -0.7 -0.7 -1.7Region II (north) -1.4 -1.3 -1.3 -1.3 -1.2Speed:Slow (1-3 m s-~) -0.5 -0.5 -0.6 -0.6 -0.3Fast (>3 m s-~) -1.7 -1.8 -2.2 -1.7 -2.0Direction:'Northward (316-45 o) - 1.4 - 1.6 -2.0 - 1.5 -0.8Westward (225-315-) -2.2 - 1.4 -0.7 - 1.3 -2.8Intensity:Hurricane 1.3 - 1.2 - 1.1 - 1.1 - 1.4Tropical storm -1.6 -1.3 -1.1 -1.1 -1.7Size and intensitySmall tropical storm - 1.4 - 1.3 - 1.4 - 1.2 - 1.2Large tropical storm - 1.4 - 1.8 -2.3 - 1.7 -0.6Small hurricane - 1.3 - 1.3 - 1.5 - 1.4 - 1.0Large hurricane north -0.6 -1.3 -2.2 -1.5 0.2Large hurricane south - 1.7 - 1.5 - 1.2 - 1.3 - 1.5Mean -1.4 -1.3 -1.4 -1.3 -1.2Scatter 0.4 0.4 0.6 0.3 0.8than those of south cyclones. This is consistent withthe results for cyclones in the latitude category. Apart from such small variations, these resultsseem to suggest that a relatively shallow layer wouldbe nearly as representative of cyclone speed as a deeplayer average. This is of course a reflection of therelatively small speed shear of the environmentalwind. The values of 200 and 900 mb average PeM arealso very consistent. This suggests that it may be possible to use the 200 and 900 mb winds to describetropical cyclone movement in the northwest Pacificwith some degree of confidence. 2) WEST ATLANTIC The layer-averaged 5-7- I2~,M values for west Atlantic tropical cyclones are shown in Table 9. Thevariations among different averages is also small formost data sets. The scatter among data sets is approximately the same for all four layer-averages. The 200 and 900 mb average Vps~ has a muchlarger scatter. This might restrict the use of this typeof data for describing the cyclone speed more in thewest Atlantic than in the northwest Pacific. Verticalwind shears in the west Atlantic are generally larger,probably due to the higher latitude of these storms. 3) AUSTRALIAN-SOUTH PACIFIC Table 10 shows the level- and layer-averaged5-7- for tropical cyclones in this region. As mentioned before, the vertical speed shear in this regionis relatively large (see Fig. 15). Therefore, a large variation among different layer-averages exists for a givendata set, as seen in Table 10. Both the surface to 500mb and the 700 to 500 mb layer-averages give extremely good consistency. The deep layer averageshave a larger spread. This is different than the layeraverage directional deviations discussed in Section 3in which the mean tropospheric flow best describe thedirectional movement of a cyclone. It appears fromFig. 15 that the speed shear is too variable amongdata sets to give a Consistent l~,~ when integratedover a deep layer. However, if the integration isthrough a shallower layer, the effect of the shearwould not be felt as much. Because of this large spread in vertical windshear, the 200 and 900 mb average !~,~ has a widescatter among data sets in this region. The possibilityof using 200 and 900 mb information for cyclonesteering in the Australian-South Pacific region is thusmore doubtful than in the northwest Pacific or thewest Atlantic. 4) SUMMARY Layer-averaged ~e~u for all data sets in each of thethree ocean basins is shown in Table 11. It can beseen that in the three ocean basins, cyclones generallymove faster than the mean 5-7- level- or layer-averaged winds. The most consistent layer-average appears to be the surface to 300 mb average. The midtropospheric average is also approximately the samebetween the three oceans. Therefore, it seems that1 3'~2 VOLUME 110 MONTHLY WEATHER REVIEWTABLE 10. AS in Table 8, except for tropical cyclones in the Australian-South Pacific region. LIO0 mb L300 mb fS00 mb L$00 mb 200 mb + 900 mbStratification ,~ ,uffa~ asurface O0 mb AverageDirection:Eastward (40-150-) 0.2 -0.8 -2.5 -0.5 1.0Westward (210-320-) -2.2 - 1.9 - 1.5 -0.6 -3.3Intensity and region:Hurricane -0.7 - 1.3 -2.1 -0.8 -0.4Coral Sea hurricane -0.8 -1.5 -2.4 -0.9 -0.7Coral Sea tropical storm -2.4 -2.1 -2.4 -1.4 -2.4West Australian hurricane -0.1 - 1.0 - 1.7 - 1.5 1.0Mean - 1.0 - 1.4 -2.1 - 1.0 -0.8Scatter 1.1 0.5 0.4 0.4 1.8what layer-average is best, depends ~ery much on thevertical wind shear profile in the environment. The200 and 900 mb average ~vM appears not to be nearlyas useful as the mean layer information.5. Summary and discussion The main conclusions of this study are: 1) The large-scale circulation is a key factor indetermining the movement Qf tropical cyclones. 2) Wind data at the mid-troposphere (700, 600and 500 rob) correlate best with both the directionand speed of cyclone movement. 3) On the average, tropical cyclones in the Northern Hemisphere moves --~ 10-20- to the left of thesurrounding mid-tropospheric winds at ~6- radiusfrom the cyclone center; an approximate oppositedirectional deviation occurs for cyclones in the Southern Hemisphere. 4) On the average, tropical cyclones move. fasterby ~ 1 m s- ~ than the surrounding mid-troposphericwinds at ~6- radius from the cyclone center. 5) Cyclones having different zonal directions ofmotion have different relationships with their 5-7-surrounding flow. 6) Deep tropospheric flow appears to be a gooddescriptor of cyclone movement; for cyclones in arelatively weak shear environment a shallow layeraverage flow is equally suitable. 7) The average wind data between the upper (200 mb) and lower (900 mb) troposphere also correlate relatively well with the direction of movement and speed but less well than the wind data at the mid troposphere or the mean layer data. Some of these same conclusions were also made by George and Gray (1976), Gray (1977) and Brand et al. (1981). Bell and Lam (1980) found that northwest Pacific tropical cyclones move, on the average, 0.9 m s-~ more northward and 3.4 m s-~ more westward compared to the geostrophic steering flow. This means that cyclones having a westward component of motion, which is normally the case, move faster than and to the left of the geostrophic flow, in qual itative agreement with the present study. From a forecasting point of view, these results im ply that a forecasting scheme based on steering flow alone would tend to predict a cyclone to move to the right of and slower than the observed track. This, in fact, was found to be the case by Kasahara (1957) using a barotropic non-divergent model. Since then, other numerical forecasts of tropical cyclone move ment based primarily on steering flow also produced- a systematic rightward deflection of the predicted tra jectory relative to the actual path and a predicted speed slower than the observed speed. See, for ex ample, Kasahara (1959, 1960), Birchfield (1960), Jones (1961, 1977),. Sanders and Burpee (1968), - Anthes and Hoke (1975), Sanders et al. (1975), Har TABLE I 1. AS in Table 7, except for level- or Jayer-averaged I?vM. L,oo,,,,, f,oom,, f*Om,, 200 tab + 900 mb ,~Ocean basin ,a~r~ Osuffacc '~sufface ' ,.b AverageNorthwest Pacific .-0.9 - 1.2 - 1.7 - 1.0 -0.7 (0.7) (0.5) (0.6) (0.7) (0.7)West Atlantic - 1.4 - 1.3 - 1.4 - 1.3 - 1.2 (0.4) (0.4) (0.6) (0.3) (0.8)Australian-South - 1.0 - 1.4 -2.1 - 1.0 -0.8Pacific region (1.1) (0.5) (0.4) (0.4) (1.8)OCTOBER 1982 JOHNNY C. L. CHAN AND WILLIAM M. GRAY 1373rison (1981). Such systematic direction and speedbiases have also been discussed by Neumann andPelissier (1981) in the analyses of operational trackforecast errors. Some of the authors have attributed such biasedrightward deflection in the predicted track to the influence of the Coriolis acceleration as discussed byRossby (1948). Birchfield ( 1961) managed to reducethe rightward bias in his model by implicitly includingan interaction between the storm vortex and its surrounding flow. He gave no physical explanation, however. Kasahara and Platzman (1963) solved a modified barotropic potential:vorticity equation whichincluded an interaction between the vortex and thesteering flow and obtained predicted directionaltracks closer to the observed ones. Theoretical studies by Rossby (1949), Adem (1956)and Kasahara and Platzman (1963) all suggest theimportance of the zonal direction of cyclone motionin determining the relation between the environmental flow and cyclone movement. Their results implya slight slow-down of vortex movement, relative tothe surrounding flow for eastward-moving cyclones,while the opposite is true for westward- and northward-moving cyclones. The findings in this paper areconsistent with these theoretical analyses. Recentstudies by Chan (1982) and Holland.(1982) also arriveat the same conclusion. They explained both the directional deviation and the difference between cyclone speed and environmental wind speed in termsof the variation of the Cofiolis parameter across thecyclone. All these theoretical and observational results pointto the fact that although the environmental flow isimportant in the determination of cyclone motion,the steering flow theory cannot completely explainthe physical processes involved in the movement oftropical cyclones. The interaction between the vortexand the environmental circulations must also be considered. More detailed observational information on therelations between tropical cyclone movement and itsenvironmental flow at individual levels and octantsare contained in Chan and Gray (1982). Acknowledgments. The authors would like to thankMr. Edwin Buzzell for his programming assistanceand Mrs. Barbara Brumit and Ms. Cindy Schrandtfor their help in manuscript preparation. We alsothank Mr. Greg Holland, Dr. Geoff Love and Mr.Grant Burton for their help with the Australian/SouthPacific region data sets. This research was supported by the Office of NavalResearch Contract N00014-C-0793, with supplementary support from the Naval Environmental Prediction Research Facility Contract N000228-81-C-H20. REFERENCESAdem, J., 1956: A series solution for the barotropic vorticity equa tion and its application in the study of atmospheric vortices. Tellus, 8, 364-371.Anthes, R. A., 1982: Tropical Cyclones: Their Evolution, Structure and Effects. Meteor, Monogr., No. 41, Amer. Meteor. 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