Classification of Surface Wind Fields of Tropical Cyclones at ...

Journal of the Meteorological Society of Japan, Vol. 85, No. 6, pp. 747--765, 2007 747

Classification of Surface Wind Fields of Tropical Cyclones at Landfall

on the Japan Main Islands

Fumiaki FUJIBE and Naoko KITABATAKE

Meteorological Research Institute, Tsukuba, Japan

(Manuscript received 4 December 2006, in final form 26 August 2007)

Abstract

A statistical study was made for surface wind fields of tropical cyclones (TCs) at landfall on the mainislands of Japan using the AMeDAS data. The analysis was performed for 70 TCs which made landfallon the southern part (south of 36�N) of the main islands during the period 1979–2004. The wind fieldwithin 200 km of each storm center was obtained by applying a composite analysis to hourly or ten-minute observations for the four hours around landfall, with the direction of storm motion as they-axis. Then the fuzzy c-means method (FCM), which is a kind of cluster analysis, was applied to classifythe wind distribution. All but one of the resulting five patterns show stronger winds on the right side ofthe center than on the left, with different degrees of right-left asymmetry and the shapes of the strongwind area. The five patterns have some differences in the preferred season, central pressure, speed anddirection of motion, and regions of landfall of storms. A supplementary analysis using the wind profilerdata, available from 2001, reveals that the right-left asymmetry is roughly explained by the storm mo-tion, although the storm-relative wind fields still have some asymmetry.

1. Introduction

From summer to autumn, Japan is occasion-ally attacked by tropical cyclones (hereafterTCs, including typhoons, severe tropicalstorms, and tropical storms, defined by maxi-mum winds of b 64 kt, 48–64 kt, and 34–48 kt, respectively). The number of TCs whichmake landfall on the four main islands of Ja-pan is 2.6/year on the 30-year average (1971–2000) according to the best track data createdby the Japan Meteorological Agency (JMA).The number of landfall amounted to ten in2004.

The basic structure of TCs is axially symmet-ric, apart from the effect of storm motion (Fu-jibe 1996), and higher-order features such aspolygonal eyewalls and mesoscale vortices

(Muramatsu 1986; Schubert et al. 1999; Kossinand Schubert 2004; Sato 2004; Mashiko 2005).There are a number of empirical formulas forwind and pressure distribution in TCs basedon axial symmetry (Kurashige 1977; Leslieand Holland 1995), with application in manyresearch fields, such as statistical and wind en-gineering studies (e.g., Fujii 1998).

However, TCs moving poleward into the mid-dle latitudes begin to deviate from symmetricfields, as a result of increasing baroclinicity ofthe environment (Jones et al. 2003; Sinclair2004; Kitabatake 2005). Many TCs hitting theJapan main islands exhibit pressure distribu-tion deviating from the symmetric pattern. Forexample, TC9119 (Mireille, 27–28 September1991) was accompanied by stronger pressuregradient behind the center than in the front inpassing western Japan, with a surge of strongwind in the left-rear quadrant (Fujibe et al.2007). The effect of orography also causesdistortion of the vortex (Yeh and Elsberry1993a, b; Lin et al. 2002). A number of studies

Corresponding author: Fumiaki Fujibe, Meteoro-logical Research Institute, Tsukuba 305-0052,Japan.E-mail: [email protected].( 2007, Meteorological Society of Japan

for TCs passing Japan have indicated morecomplicated features such as mesoscale fronts,pressure dips, and topographically intensifiedwinds (Yamamoto et al. 1963; Sakakibara et al.1985; Fujibe et al. 1995; Matsumoto and Oka-mura 1985; Fudeyasu and Hayashi 2001, 2003;Saito 1994), with large differences according tocases.

Although some statistical studies have beenmade on synoptic features of the extratropicaltransition (ET) processes of TCs (e.g., Sinclair2004), there is little statistical information ofmesoscale wind distribution in TCs passing Ja-pan. In the present study, surface temperatureand wind fields for 70 TCs during 1979–2004were analyzed using the data of the AutomatedMeteorological Data Acquisition System (AMe-DAS), which provides surface observation dataat nearly a thousand stations. The wind fieldof each TC was obtained using a compositeanalysis, in which data at different observationtimes were superimposed with respect to thestorm center, in order to achieve a high degreeof spatial resolution. Then wind patterns wereclassified using the fuzzy c-means method(FCM; Bezdek 1981; Sakawa 1989), which is amethod of cluster analysis, but allows for par-tial membership to more than one cluster. Inapplication to meteorological analysis, theFCM has been found to be suitable for obtain-ing a small number of representative patternsfrom among data with a large sample size (Fu-jibe 1989, 1999).

In Section 2, the procedure of composite anal-ysis and the FCM are described. The resultingpatterns, and their climatological features areshown in Section 3. Section 4 shows some ex-amples of these patterns, as well as the upper-level wind distribution obtained from wind pro-filers.

2. Data and procedure of analysis

2.1 DataThe spatial distribution of surface wind, tem-

perature, and precipitation was analyzed usingthe AMeDAS data for 1979–2004. The time in-terval of observation is ten minutes for the pe-riod 1994–2004, and an hour for 1979–1993.The wind data are ten-minute averages forboth periods.

The data of surface wind are highly depen-dent on observational environments and the

anemometer height, so that some adjustmentis needed in using them. The power low is oftenused to adjust the difference in anemometerheight, while more detailed inspection for eachstation is needed to standardize the effect ofsurface roughness (Kondo and Yamazawa 1986;Kondo et al. 1991). Moreover, there is somelong-term trends of wind speed arising fromchanges in observational environments (Fujibe2003). In the present analysis, the wind speeddata were adjusted using the monthly averageof daily maximum wind speed hUmaxi as

U 0i ¼

hUmax;0i

hUmax; iiUi; ð1Þ

where Ui and U 0i are the original and adjusted

wind speed at station i, respectively, andhUmax;0i is the average of hUmaxi over all thestations. In order to avoid the influence of ex-ceptionally strong wind at the typhoon attack,the largest three values in the month wereomitted in obtaining hUmaxi. This adjustmentis based on an assumption that hUmaxi shouldbe spatially uniform if the anemometer heightand local effects around the observation sitesare uniform. Although this is a very crude as-sumption, U 0 gives much smoother wind fieldsthan using the original data. The reason forusing daily maximum, rather than daily meanwind speed, is that the former is likely to bemore representative of nearly neutral stratifi-cation of the surface layer during a TC passagethan the latter, which is affected by low windspeed under strong nocturnal inversion. Thetemperature data was adjusted to the sea level,with a lapse rate of 5 Kkm�1, as done in someprevious studies (e.g., Fujibe et al. 2007).

A supplementary analysis for winds abovethe boundary layer was made using the datafrom the wind profiler network which enteredinto operation in 2001. The time resolution ofthe observation is ten minutes, and the verticalresolution is about 300 m, although there aresome missing data due to poor signal quality.The number of profiler sites was 25 in 2001,and increased to 31 by May 2003. The cubicspline functions of Akima (1970) were used tointerpolate the wind at a given mean sea level(e.g., 1.5 km high).

Figure 1 shows the distribution of AMeDASstations and wind profilers in September 2004.The networks have slightly changed after

748 Journal of the Meteorological Society of Japan Vol. 85, No. 6

deployment, although these changes are notlikely to affect the analysis described in the fol-lowing.

The tracks and central pressure of the TCswere obtained from three-hourly best trackdata prepared by the JMA. The cubic splinefunctions of Akima (1970) were applied in orderto interpolate them into smooth time series,which were used to generate data at every fiveminutes.

2.2 Case selectionOur analysis requires data points in all the

quadrants of the storm. We therefore selectsuch TCs that entered the main region of theAMeDAS network and moved inside to an ade-quate distance. For this purpose, the ‘‘main net-work region’’ was defined by a polygonal areasurrounded by coastal stations (Fig. 1), and theinward distance of the storm center from theboundary of the region, Rin, was obtained forevery five minutes during storm passage. Thecase used for analysis requires that Rin ex-ceeded 20 km within six hours of entrance tothe region. If Rin had a maximum value of>20 km within two hours of the entrance tothe region, then the time of the maximum Rin

value was defined as the base time of the anal-

ysis ðt0Þ. Otherwise, t0 was defined by the timethat Rin first exceeded 20 km.

The speed and direction of the storm motionat the time of landfall were defined from thedifference of the storm center position att0 � 2 h and t0 þ 2 h.

2.3 Method of composite analysisThe composite analysis can provide densely

distributed data in the storm as long as itsstructure is unchanged with time, while mostTCs begin to weaken after landfall. In the pres-ent study, the analysis was confined to the fourhours, from t0 � 2 h to t0 þ 2 h, in order toavoid the influence of weakening. Figure 2 com-pares the central pressures at t0 G 2 h, basedon the interpolated best track data. There issome increase of central pressure, by 3.6 hPaon the average. However, this change is muchsmaller than the scatter among cases, so thatit can be regarded to be of minor influence tothe composite analysis. For the period 1979–1993, hourly data at four observation times inthe period were used. For 1994–2004, data at24 observation times with ten minute intervalswere used.

The grids were spaced at a 5 km interval,with the origin as the storm center. The y-axis

Fig. 1. Location of AMeDAS wind stations and wind profilers in September 2004. Dashed lines indi-cate the ‘‘main network region’’, defined in Section 2.2. Areas above 300 m MSL are shaded.

December 2007 F. FUJIBE and N. KITABATAKE 749

of the grids was directed to the storm motion,since wind fields in TCs are strongly influencedby storm motion. The 5 km grid size has suffi-cient resolution to express the temperatureand wind fields observed in the AMeDAS net-work. The analysis area was defined as a circleof 200 km radius, corresponding to 5024 gridpoints. In the pattern classification (next sub-section), values at every three grids (namely,15 km intervals) were used in order to save thecomputer storage, corresponding to 556 gridpoints. The method of interpolating the valueson the grids are described in the Appendix A.For the sake of comparison, a supplementaryanalysis was made by taking the y-axis ori-ented to the north, as briefly described in theAppendix B.

Since our interest is in the relative distribu-tion of temperature and wind, their spatialmean was removed from the composite fieldsin each case. For temperature, the spatialmean was subtracted as

zgj ¼ Zgj � Zj; ð2Þ

where Zgj is temperature at grid g in the case j,and Zj is its average over the grids. For wind,

zgj ¼ Zgj/Uj; ð3Þ

where Zgj is any one of the u, v components andthe wind speed, which have been normalized inEq. (1), and Uj is the wind speed averaged overthe grids.

2.4 Smoothing with the principal componentanalysis

Before applying the FCM, the principal com-ponent analysis was used to filter out higher-order irregularities which may obscure themain features of temperature and wind distri-bution. The analysis was based on normalizedvariables

zgj ¼ wgzgj � hzgi

sg; ð4Þ

where zgj is any one of temperature, u-component, v-component, and wind speed atgrid g in the case j, hzgi and sg are the averageand standard deviation of zgj over the cases,and wg is a weight described later. If zgj is lack-ing for more than half of the total cases, zgj isnot defined. The weight wg was defined by

wg ¼ R2

r2g þ aR2

; ð5Þ

where rg is the distance from the storm center,R ¼ 200 km, and a ¼ 0:1. This weight was usedso that the central area may have a high contri-bution to the analysis. For the parameter a,analysis based on a ¼ 0:5 was made as well,for the sake of comparison (see Appendix B).

Principal components were obtained by diag-onalizing the covariance matrix generated fromzgj. The leading 15 components account for96.1% of the total variance for temperature,93.1% for u-component, 94.1% for v-component,and 94.5% for wind speed. The score was ob-tained from the least-squares condition

XN

g¼1

zgj �XMm¼1

ffiffiffiffiffiffilm

pFjmAgm

!2

! min:; ð6Þ

where Fjm is the score of the case j for the com-ponent m, Agm and lm are the eigenvector andeigenvalue of the component m, and M is thenumber of principal components (M ¼ 15, asdescribed above).

2.5 Pattern classificationThe FCM is based on the least-squares condi-

tion

Fig. 2. Central pressures of each TC att0 � 2 h and t0 þ 2 h. The dashed lineshows the linear regression. The thindotted line corresponds to y ¼ x.


XJ

j¼1

XK

k¼1

cpjk

Xs

XN

g¼1

ðzðsÞgj � bðsÞgk Þ

2

" #! min:; ð7Þ

with a restraint

XK

k¼1

cjk ¼ 1 ðfor each jÞ; ð8Þ

where bgk is the pattern of the cluster k, cjk isthe membership of the case j to the cluster k,and p is a given parameter controlling the reso-lution of clustering. The suffix s indicates anyone of u- and v-components and wind speed.The result of analysis, including temperatureor excluding wind speed in Eq. (7) will be shownin Appendix B.

The solution of Eqs. (7) and (8) is given by

cjk ¼

Xs

XN

g¼1


2

" #�1/ðp�1Þ

XK

k¼1

Xs

XN

g¼1


2

" #�1/ðp�1Þ ; ð9Þ

and

bðsÞgk ¼

XJ

j¼1

cpjkz

ðsÞgj

XJ

j¼1

cpjk

: ð10Þ

Eqs. (9) and (10) are equivalent to

cjk ¼

Xs

XMm¼1

lmðFðsÞjm � G

ðsÞmkÞ

2

" #�1/ðp�1Þ

XK

k¼1

Xs

XMm¼1

lmðFðsÞjm � G

ðsÞmkÞ

2

" #�1/ðp�1Þ ; ð11Þ

and

GðsÞmk ¼

XJ

j¼1

cpjkF

ðsÞjm

XJ

j¼1

cpjk

; ð12Þ

with

bðsÞgk ¼

XMm¼1

GðsÞmkAgm; ð13Þ

if components m > M are neglected.

Eqs. (10) and (12) can be rewritten as

bðsÞgk ¼

XJ

j¼1

cpjkz

ðsÞgj

XJ

j¼1

cpjk

; ð14Þ

where

bðsÞgk ¼ wg

bðsÞgk � hzgi

ðsÞ

sðsÞg

: ð15Þ

Eq. (14) can be applied to grid points which arenot used for classification.

Finally, the transformation in Eqs. (2) and (3)was reversed as

Bgk ¼ hZiþ bgk; ð16Þ

for temperature and

Bgk ¼ hZibgk; ð17Þ

for wind, where hZi is the average of Zj overthe cases, in order to make easier the intuitiveunderstanding of the results. The presentationin the following section is based on Bgk ob-tained in this way.

3. Results of the cluster analysis

3.1 Main features of the clustersThe number of clusters obtained from the

FCM decreases with the parameter p in Eqs.(7)–(14) (Fujibe 1989, 1999). In the presentanalysis, the number of clusters is 1 forpb 1:75, 2 for p ¼ 1:65–1.7, 3 for p ¼ 1:5–1.6,and 5 for p ¼ 1:45. Figure 3 shows the five clus-ters for p ¼ 1:45, hereafter denoted by C1–C5,and the average over all the cases. The averagepattern exhibits a cyclonic wind pattern aroundthe center, with substantially higher windspeed on the right side than on the left side.These features are commonly found in eachcluster, except for a strong wind area extendingin the left-rear quadrant in C4. In more detail,C1 and C5 have a round-shaped strong windarea around the center, with a higher degree ofconcentration in C5 than C1. In C2, the strongwind area is elongated along the direction ofstorm motion, with a higher degree of right-leftwind asymmetry than C1 and C5. The right-leftcontrast of wind speed is further enhanced inC3. In these two patterns, isotachs of 5–6 ms�1

run almost parallel to the y-axis. The pattern of


C4 is different from others with respect to thestrong winds on the left side of the center. Thehigh wind area in C4 has a V-shape surround-ing the center, with a zone of weak wind ex-tending forward slightly to the left. Figure 4shows the distribution of wind speed along thex-axis. The nearly stepwise change near x ¼ 0in C2 and C3, the left-side peak in C4, and thesharp peak at x@ 30 km in C5 reconfirm thefeatures observed in Fig. 3. It is to be notedthat wind speed has been normalized as inEqs. (3) and (17), so that there is no meaningin comparing the values of wind speed amongclusters.

In an attempt to quantify these features, thefollowing indexes were calculated for each pat-tern: (1) Radius of maximum wind speed, Rmax,defined by the distance of the position of maxi-mum wind speed form the center, (2) Windspeed ratio in 100 km/100–200 km ranges,

U100/U100a200, defined by the ratio of averagewind speed within 100 km of the center, andthat for the 100–200 km range from thecenter, (3) Right/left wind speed asymmetry,DUR-L/UR ¼ ðUR � ULÞ/UR, where UR and UL

Fig. 3. Surface wind vectors (arrows) and wind speed (isotachs in ms�1) for the five clusters, and theaverage over all the 70 cases. The y-axis is in the direction of storm motion. The cross indicates thestorm center at t0.

Fig. 4. Distribution of wind speed alongthe x-axis for each cluster.


are the average wind speed in the right and leftsemicircles (within 200 km of the center), re-spectively, and (4) The v-component ratio, v/U,defined by the ratio of average v-component(wind velocity component in the direction ofthe y-axis) and wind speed within 200 km ofthe center. The first two indexes are related tothe compactness of strong wind area, whileDUR-L/UR and v/U give the degree of right-leftasymmetry in the wind field. Table 1 lists thevalues of these indexes averaged for each pat-tern. The values of Rmax and U100/U100a200 indi-cate that the compactness is highest for C5, anddecreases in the order of C1, C2, C3, and C4.The degree of right-left asymmetry correspond-ing to DUR-L/UR and v/U is highest for C3, andalso high for C5.

Table 2 shows the pattern similarity indexbetween clusters defined by

Skh ¼

Xg

BðWSÞgk B

ðWSÞghffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

g

fBðWSÞgk g2

" # Xg

fBðWSÞgh g2

" #vuut; ð18Þ

where BðWSÞgk is the pattern of wind speed for the

cluster k. If the two patterns are identical, thenSkh ¼ 1. It can be seen that C1 and C2 have thehighest degree of similarity ðSkh ¼ 0:9933Þ tothe average pattern. There is also close similar-ity ðSkh ¼ 0:9853Þ between C2 and C3. It isoften the case that the FCM analysis yieldssome dominant clusters having a high similar-ity to one another, with some minor clusters ex-hibiting different features from others. In thisrespect, C1–C3 are regarded as ‘‘typical’’ windpatterns of TCs that hit the Japan main is-lands. On the other hand, C5 is the least sim-ilar to the average ðSkh ¼ 0:9219Þ, and has rela-tively low similarity to other four patterns.

Figure 5 shows the distribution of divergenceand vorticity of the surface wind field. The clus-ters have common features of strong conver-gence exceeding 5 � 10�5 s�1 within severaltens of kilometers of the center, which roughlyagrees with the position of maximum conver-gence. Large vorticity (>5 � 10�5 s�1) is foundmainly in front of the center. For C4, conver-gence has smoother distribution than othersand vorticity is widely spread in the front semi-circle, while the weak wind zone in the left-front quadrant coincides with a region of rela-tively large convergence (>5 � 10�5 s�1) andpositive vorticity.

Figure 6 shows the distribution of tempera-ture and rainfall intensity obtained by applyingEq. (14). Temperature is 2–3�C higher on theright side than on the left side in all the clus-ters. This is a typical feature of an early stageof ET, in which a TC tends to move northeast-ward along a baroclinic zone oriented in thenortheast-southwest direction (Sinclair 2004;north and south are reversed for the SouthernHemisphere). The right column of Table 1 liststhe index of right/left temperature difference,DTR-L ¼ TR � TL, defined by the difference ofthe average temperature in the right and leftsemicircles (within 200 km of the center). Thevalue of DTR-L is largest in C4, and relativelysmall in C2 and C3. Rainfall tends to be mostintense near or just in front of the center.More specifically, the area of intense rainfall(b8 mm/h) tends to be located on the left-frontquadrant of the center, while the largest cover-age of b 2 mm/h and b 4 mm/h areas is in theright-front quadrant except C4. The latter fea-ture is similar to the result of Shimazu (1998),who showed that the inner rain shields of ty-

Table 1 Indexes of wind and temperaturepatterns for each cluster. See text fordetails.

Rmax

(km)U100/

U100a200

DUR-L/UR v/U

DTR-L

(�C)

C1 54.0 1.34 0.37 0.15 1.87C2 57.6 1.09 0.50 0.25 1.31C3 115.8 1.00 0.59 0.37 1.56C4 199.5 0.85 0.20 0.11 2.36C5 49.1 1.53 0.57 0.29 1.69Average 57.6 1.13 0.46 0.23 1.70

Table 2 Pattern similarity index (Skh de-fined by Eq. (18)) between clusters, andbetween each cluster and the averagepattern.

C1 C2 C3 C4 C5

C1 1 0.9820 0.9734 0.9645 0.8976C2 1 0.9853 0.9458 0.9178C3 1 0.9588 0.8749C4 1 0.8153C5 1Average 0.9933 0.9933 0.9864 0.9677 0.9219


phoons in mature and early weakening stagesare most frequently found in the right-frontquadrant (or in the northeast quadrant accord-ing to the geographical coordinates). On theother hand, C4 has a region of strong precipita-tion (b4 mm/h) in the left-front quadrant, cor-responding to a zone of convergence and strongright-left temperature difference. It is to benoted, however, that rainfall distribution hasconsiderable variations among cases.

3.2 Climatology of the clustersTable 3 lists the degree of co-membership be-

tween clusters defined as

Pkh ¼

XJ

j¼1

cjkcjh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXJ

j¼1

c2jk

( ) XJ

j¼1

c2jh

( )vuut; ð19Þ

which is unity if the two clusters are equallyshared by each member. There is a co-membership of 0.86 between C2 and C3, and0.68 between C1 and C2, These high values ofPkh indicate that these clusters are shared to ahigh degree, reflecting the similarity in theirpatterns. On the other hand, Pkh is 0.5 or lessbetween C4 and others, and between C5 andothers except P15, reflecting the relative isola-

Fig. 5. Surface divergence and vorticity for each cluster. Divergence is shown in contour lines at the5 � 10�5 s�1 intervals, with dashed lines for negative values (convergence). Vorticity is shown inhatching, which shows the area above 5 � 10�5 s�1, and 10 � 10�5 s�1 with increasing tones.

Table 3 Degree of co-membership be-tween clusters [Pkh defined by Eq. (19)].

C1 C2 C3 C4 C5

C1 1 0.68 0.50 0.39 0.55C2 1 0.86 0.49 0.50C3 1 0.47 0.37C4 1 0.19C5 1


Fig. 6. Temperature and precipitation intensity for each cluster. Temperature is shown in isothermsat the 1�C interval. Precipitation is shown in hatching, which indicates the area above 2 mm/h,4 mm/h, 8 mm/h and 16 mm/h with increasing tones.

Fig. 7. Tracks of TCs having highest degree of membership to each cluster. Crosses indicate the po-sition of the center at t0. Dotted lines indicate the track of TCs described in Section 4 (Figs. 9–10).


tion of these two clusters.Figure 7 shows the tracks of TCs which have

highest membership to each cluster. There issome regional preference according to clusters.Most of the C1-type TCs make landfall on thesouthern or western Kyushu, except for somecases passing near Kii peninsula. A similarfeature is found for C4. On the other hand,most C2 storms hit the area between easternKyushu and Kii peninsula, while the majorityof C3 storms hit the Kanto plain.

Figure 8a shows the contribution of cases ineach seasonal range to each cluster calculatedfrom

hcki ¼XJ

j¼1

cjk; ð20Þ

where summation is made for TCs belonging tothe specified seasonal range. Figures 8b–dshow the contribution of cases in each range ofcentral pressure at t0, speed and direction ofmotion, respectively. As an overall feature,there is no bins that are dominated by a singlecluster, except for ENE-E moving TCs forwhich C4 is dominant. This situation impliesthat wind patterns are not determined by a sin-gle factor, but are related to various factors, indifferent ways according to cases. Nevertheless,there is some seasonality in each cluster; C1has a relatively high percentage among TCs inSeptember, and C4 in October and November,while C2 and C3 have higher frequencies insummer than autumn. For central pressure,C1 has a high contribution in intense TCs(below 970 hPa), whereas C5 shows a high per-centage in TCs above 970 hPa. The contribu-tion of C3 is higher than other clusters in fast-moving TCs (b60 km/h). Table 4 summarizesthe main features of the five clusters obtainedhere.

4. Supplementary analysis for individualcases

This section presents the wind fields in someindividual cases as examples. Then a briefanalysis is made on upper-level winds derivedfrom wind profilers and the effect of storm mo-tion. The figures in this section show the unnor-malized wind field, namely Zgj rather than zgj

in Eq. (3).Table 5 lists the membership ðcjkÞ to each

Fig. 8. Contribution of cases in eachrange of (a) season, (b) central pressureat t0, (c) speed, and (d) direction of mo-tion to each cluster.

Table 4 Main feature of the clusters.

Cluster Main feature Climatology Preferred regions

C1 High wind core near the center Intense cyclonesEarly autumn (September)

Southern-western Kyushuand Kii peninsula

C2 Right-left asymmetry Middle-late summerSlow movement

Eastern Kyushu–Shikoku

C3 Conspicuous right-left asymmetry Middle-late summerRapid movement

Mainly Kanto

C4 Strong wind region on the left sidewith low temperature

Middle-late autumn Kyushu and Kii peninsula

C5 Sharp high-wind core near the center Relatively high centralpressure


Table 5 List of TCs in 2001–2004. For each case, the cluster of highest membership is underlined.

No. NameDate oflandfall

Centralpressure

at landfall# Intensity$

Membership (%)

C1 C2 C3 C4 C5

TC0111 Pabuk 22 Aug. 982 TS 9.0 22.1 52.9 6.4 9.6TC0115 Danas 11 Sep. 970 STS 11.3 8.9 6.1 1.5 72.3TC0207 Halong 16 July 975 STS 18.4 26.7 38.7 6.7 9.5TC0221 Higos 1 Oct. 961 T 22.9 22.6 33.8 5.1 15.6TC0304 Linfa 31 May 984 STS 12.7 28.7 26.2 26.7 5.7TC0310 Etau 8 Aug. 950 T 25.0 32.0 21.1 11.4 10.4TC0404 Conson 11 June 996 TS 17.0 35.4 20.2 21.4 6.0TC0406 Dianmu 21 June 966 T 9.1 50.2 30.4 3.3 7.1TC0410 Namtheu 31 July 977 T 18.0 31.9 25.1 16.1 8.9TC0411 Malou 4 Aug. 997 TS 19.0 22.2 14.4 9.1 35.2TC0416 Chaba 30 Aug. 951 T 8.6 8.9 7.7 72.4 2.5TC0418 Songda 7 Sep. 945 T 17.4 45.7 24.7 2.3 9.9TC0421 Meari 29 Sep. 969 STS 62.2 13.8 8.4 8.3 7.3TC0422 Ma-on 9 Oct. 958 T 28.4 11.7 7.3 7.6 44.9TC0423 Tokage 20 Oct. 955 T 4.9 6.5 6.1 81.1 1.4

# The central pressure on entry to the polygonal region in Fig. 1, based on interpolation from three-hourlybest track data.$ T ¼ typhoon (max. windsb 64 kt), STS ¼ severe tropical storm (48–64 kt), and TS ¼ tropical storm (34–48 kt)

Fig. 9. Surface wind fields for each TC. Solid lines indicate wind speed, with 2 ms�1 intervals.Dashed lines indicate temperature, with 2�C intervals. Crosses indicate the position of the centerat t0.


cluster for TCs in 2001–2004. Figures 9 and 10show the wind fields for six selected cases asexamples. Five of them correspond to TCs hav-ing maximum membership to each cluster. Theremaining one is the case of TC0410 as an ex-ample of a northwest moving typhoon. We cansee that each case exhibits the main feature ofthe corresponding cluster, characterized by acompact vortex in TC0421 (C1), conspicuousright-left asymmetry in TC0406 (C2) andTC0111 (C3), the strong wind on the left sidewith weak wind region spreading forward inTC0423 (C4), and a near-center high wind corein TC0115 (C5). The case of TC0410 invariablyshows an asymmetry between the right and leftsides in spite of the different direction of motionfrom others.

Table 6 lists intense typhoons with centralpressure below 960 hPa for 1979–2000. Manyof them have high membership to C1 as alreadyseen in Fig. 8b. Figure 11 shows their windspeed distribution along the x-axis for the

upper five cases with central pressure below950 hPa, and for the next nine cases with 950–960 hPa. The upper five typhoons, which havebeen classified as either C1 or C2, dependingon the wind distribution on the left side, com-monly have a sharp peak to the right of the cen-ter. The next nine typhoons show more diversepatterns.

Figure 12 shows the wind fields at 1.5 km

Fig. 10. Distribution of wind speed alongthe x-axis for each case in Fig. 9.

Table 6 List of typhoons with central pressure below 960 hPa for 1979–2000.

No. NameDate oflandfall

Centralpressure

at landfall# Intensity

Membership (%)

C1 C2 C3 C4 C5

TC7916 Owen 30 Sep. 957 T 61.1 12.8 5.7 13.1 7.3TC8213 Ellis 27 Aug. 955 T 9.3 30.5 27.1 30.9 2.2TC8513 Pat 31 Aug. 957 T 48.8 18.7 8.8 6.3 17.4TC9019 Flo 19 Sep. 949 T 31.0 33.5 18.2 4.2 13.1TC9119 Mireille 27 Sep. 938 T 47.2 20.0 10.8 17.2 4.9TC9313 Yancy 3 Sep. 933 T 74.9 6.5 2.9 1.8 14.0TC9426 Orchid 29 Sep. 955 T 38.0 26.5 12.9 13.1 9.5TC9612 Kirk 14 Sep. 959 T 13.1 12.6 10.4 61.8 2.0TC9918 Bart 24 Sep. 941 T 54.9 9.7 3.4 1.8 30.2

Fig. 11. Distribution of wind speed alongthe x-axis for (a) five intense typhoons,and (b) nine next rank typhoons.


MSL, where the effect of surface friction is ex-pected to be negligible, obtained from the windprofiler data. The wind fields roughly show thesame feature as those of surface wind, althoughthe strong wind core near the center of TC0115is not obvious, probably because of poor hori-zontal resolution of the wind profiler network.Fujibe (1996) showed that the wind field nearthe center of a moving typhoon is given by thesummation of the gradient wind for the station-ary typhoon and the translation velocity, if fric-tion is neglected. Figure 13 shows the storm-relative wind fields obtained by subtracting thestorm motion velocity. In the relative windfield, the right-left wind speed difference islargely reduced from the original wind field, ex-cept the case of TC0423. This fact confirms thatthe storm motion is the major cause of right-leftwind asymmetry. However, the cases ofTC0406, TC0115 and TC0410 still show aslightly stronger wind on the right side than

on the left side. A similar feature is found inother TCs in summer (e.g., TC0207, TC0310,TC0411). In contrast, the storm-relative windin TC0421 and TC0423 is stronger on the leftthan on the right side. This feature is found inother TCs from September to November (e.g.,TC0221, TC0418, TC0422).

5. Summary and remarks

By applying the FCM, the wind fields of TCsat landfall on central and western Japan wereclassified into five clusters (C1–C5). All theclusters except C4 exhibit stronger winds onthe right side of the center than on the left,with different degree of right-left asymmetryand radial profiles. The patterns of C1 and C5are characterized by a strong wind core aroundthe center, while C2 and C3 have a higher de-gree of right-left asymmetry. The pattern of C4is characterized by a V-shaped strong windarea extending to the left-rear of the center,

Fig. 12. Wind field at the 2 km level for each TC. Isotachs are every 5 ms�1.


with a weak wind zone in the forward slightlyto the left. Although these patterns commonlyhave a cyclonic vortex around the center, thedistribution of vorticity and precipitation is notstrictly symmetric, indicating that the stormstructure has begun to deviate from that of atypical TC.

The right-left asymmetry in wind speed re-confirms the importance of storm motion onthe wind fields of TCs. The analysis of thewind profiler data has given a convincing evi-dence that the right-left asymmetry is roughlyexplained by the storm motion. However, thestorm-relative fields still retains some asymme-try, with stronger winds on the right side insummer and on the left side in autumn. Corre-spondingly, the right-left wind speed differencetends to be more conspicuous in summer TCsthan autumn ones.

The wind pattern of C1 is close to the tradi-tional image of mature TCs, characterized by astrong wind area concentrated near the center.

It is believed that intense, mature typhoonsgenerally have a sharp wind peak near the cen-ter. Fujii (1998) statistically showed that in-tense TCs tend to have a smaller radius of max-imum cyclostrophic wind than weak ones. Theresult of the present study agrees with that ofFujii (1998), with respect to the high C1 mem-bership of intense typhoons.

The high right-left asymmetry of C2 and C3implies the strong effect of storm motion. Infact, the high percentage of C3 in fast-movingTCs indicate the contribution of storm motionin generating the C3 pattern. However, thereare many C2 and C3 cases with low movingspeed (Fig. 8b), implying that the asymmetricwind field is not solely attributable to stormmotion, but also to other factors such as thestorm structure itself, and topographic effectsdiscussed in a later paragraph.

The V-shaped strong wind area in C4 is simi-lar to the ‘‘horseshoe-like appearance’’ often ob-served in a stage of ET (Edson 2004; Kitaba-

Fig. 13. Same as Fig. 12, but for the storm-relative wind. Isotachs are every 3 ms�1.


take 2005). As shown in Figs. 5 and 6, the weakwind zone is accompanied by convergence, posi-tive vorticity, intense precipitation and strongtemperature gradient, implying the presence ofan ana-front. The large right-left temperaturedifference, and the high moving speed of C4are also a sign of ET, corresponding to the highpercentage of C4 cases after middle autumn(October and November). It is to be noted thatthe C4 TCs can still have the intensity enoughto cause wind damage, not only on the right butalso on the left side of the center. For example,TC0423 was accompanied by peak gust exceed-ing 50 ms�1 at some stations more than100 km to the left of the track.

The pattern of C5 is characterized by com-pactness. As seen from Fig. 8b, C5 has a highmembership in relatively weak TCs, which canbe regarded to be in the mature stage but of asmall size. It is interesting that C5 has a highdegree of right-left asymmetry (DUR-L/UR andv/U in Table 1), in spite of the compact struc-ture. This can be explained by the relativelystrong effect of storm motion in comparison tothe weaker storm circulation, corresponding tothe higher central pressure than other patterns.

The regional preferences of the clusters (Fig.7) imply the importance of topographic effectson wind patterns. The high percentage of C3cases in the Kanto district may be explained interms of barrier effect of the Central Mountains(Fig. 1), where low-level air in valleys and onmountain sides is often stagnant, with a regionof strong wind over the coastal area (Harada1981; Fujibe 1990), resulting in a wind patternlike C3. Moreover, the TC track itself can be de-flected by orography (Yeh and Elsberry 1993a;Lin et al. 2002) so as to pass around the Cen-tral Mountains onto the Kanto plain. On theother hand, the high frequency of C1 and C4 insouthern and western Kyushu, and the Kii pen-insula, is likely to correspond to the land-seadisposition with coastlines on the western side,where small friction at sea surface intensifiesthe winds in the left semicircle and results insmall right-left asymmetry. However, there aremany examples in which TCs of similar trackshave different wind distributions, as TC0111and TC0115 (Fig. 9), and TC0418 and TC9119(Fujibe et al. 2007). Thus, the topographic ef-fect cannot explain all the differences amongclusters.

These discussions indicate the variety of fac-tors controlling the wind fields in TCs. It is notrarely that two cases of similar wind patternsare generated by totally different physics, suchas the ET and topographic effects. Detailed casestudies will reveal more precise features andphysical processes of TC wind fields, while ourpresent result will provide statistical guidelinesto understand the climatological meaning ofeach case.

Since our analysis is confined to TCs on land-fall in western and central Japan (south of36�N), the results correspond to a relativelyearly stage of weakening or ET. In many casesthe structure of cyclones changes rapidly afterthey make landfall and move northward, withhighly complicated wind distribution in somecases (e.g., Fujibe 1993). It requires furtheranalysis to find the climatological features ofwind fields in TCs after landfall.

Appendix A

Method of the composite analysis

The composite analysis consists of interpolat-ing the values on grid points from a series ofobservation data on the coordinates with theorigin as the storm center. The interpolationis based on the concept of Cressman’s (1959)successive correction method, but the originalmethod has been improved in that, (1) the spa-tial resolution of interpolation is dependent onthe local network density, and (2) the interpola-tion is based on a least-squares fitting of alinear function. The procedure is made up ofthe following steps.

A1.1 Definition of the local network densityThe network density around the data point i

is defined by

ri ¼

XN

j¼1

exp

�� rij

R0

� �2�

pR20

; ðA1Þ

where j is the data point (including the point iitself ), rij is the distance between the points iand j, and R0 is a given parameter correspond-ing to the radius of the area, for which ri isdefined. The present analysis is based onR0 ¼ 20 km.


A1.2 Initial guessThe initial guess at a grid point g is calcu-

lated by the least-squares condition

XN

i¼1

WigfZ�i � ðpxig þ qyig þ ZgÞg2 ! min:; ðA2Þ

where Z�i is the observation at point i, xig and

yig are the eastward and northward distancebetween the data point i and the grid point g,and p, q, and Zg are least-squares coefficientsin which Zg gives the interpolated value at thegrid point g. If there is no data point within50 km of the grid point, then Zg is left unavail-able. The weight Wig is defined by

WigðrigÞ ¼ ri exp �rir

2ig

4n

!; ðA3Þ

where r2ig ¼ x2

ig þ y2ig, and n is a given parame-

ter indicating the number of data points contri-buting to the interpolation. The effective radiusof Wig is

reff ¼

ððrigWigðrigÞdxig dyigðð

WigðrigÞdxig dyig

¼2p

ðy0

r2WðrÞdr

2p

ðy0

rWðrÞdr

¼ffiffiffiffiffiffiffin

rip

r; ðA4Þ

so that n ¼ ripr2eff .

A1.3 Successive correctionFor each data point, the difference between

the observation and the interpolated valueaveraged for the surrounding four grid points,DZ�

i was calculated. Then the correction for thegrid point g was calculated by

DZg ¼

XN

i¼1

W 0igDZ�

i

XN

i¼1

W 0ig

; ðA5Þ

with the weight

W 0igðrigÞ ¼ ri exp �

rir2ig

4n 0

!; ðA6Þ

where n 0 is a given parameter corresponding tothe number of data points contributing to cor-rection.

In obtaining the composite fields from hourlydata (1979–1993), the value n ¼ 30 was used.The successive correction was applied withn 0 ¼ 15, and then with n 0 ¼ 10. These valueswere chosen simply by trial and error so thatthe interpolated fields are not too rugged nortoo smooth. In the analysis of ten-minute data(1994–2004), which provides six times more ef-fective data points than the hourly data, valuesof n ¼ 180, n 0 ¼ 90, and n 0 ¼ 45 were used. Thevalue of n 0 in the second correction is not sixtimes of that used for the hourly data, becausen 0 ¼ 60 was found to result in too smooth fields.

Appendix B

Difference of results according to optionsin the analysis

A series of calculation was made by changingsome parameters and procedure in the analysisin order to see their influence on the classifica-tion. Table B lists the eight optional runs. Eachof these runs yields clusters having the samefeatures as C1–C5, although there are someredistribution of intermediate cases affectingthe number of clusters. As an example, Fig. Bshows the cluster similar to C4 obtained ineach run except g and h, which yielded resultsvery close to that of the main analysis. Thereis a common feature characterized by a V-shaped high wind area with a weak wind re-gion extending forward from the center. Evenin the p ¼ 1:5 case which gives only three clus-ters, a pattern similar to C4 is obtained. Thusour analysis is not sensitive to minor changesin parameters and procedure.

More detailed comparison reveals that the noadjustment run (a) tends to enhance right-leftasymmetry, with the maximum wind areashifting behind and away from the center (notshown). This feature can be attributed to thehigh wind speed observed at coastal stations,especially at small islands and capes, whichare most often located in the right-rear(southern) quadrant of the storm at landfall onthe southern coast.


In the case of the north-oriented coordinate(b), all but one cluster (including the patternshown in Fig. B) have a strong wind area onthe southeastern side, reflecting the northeast-ward motion of most TCs. However, there is an

additional cluster which has a strong wind areain the northeastern quadrant, corresponding tosome TCs moving to the northwest. This pat-tern should be mixed into others if the differ-ence of storm motion is removed. In this re-

Fig. B. Clusters corresponding to C4 obtained from modified procedures.

Table B List of modified analysis procedures.

Run Option Setting in the main analysis ModificationNumber

of clusters

a Adjustment of wind speed in Eq. (1) Applied Not applied 6b Direction of the y-axis Storm motion North 7c Radial weight in Eq. (5) a ¼ 0:1 a ¼ 0:5 6d Parameter p in the FCM p ¼ 1:45 p ¼ 1:5 3e

oVariables used forclassification in the FCM

u, v, and wind speed u and v only 5f Temperature, u, v

and wind speed$

6

g Number of principal componentsin the FCM

M ¼ 15 M ¼ 30 5

h Time interval of data for thecomposite analysis

Hourly for 1979–1993, tenminutes for 1994–2004

Hourly for the wholeperiod 1979–2004

5

$ p ¼ 1:4 is used because only three clusters are obtained for p ¼ 1:45.


spect, the coordinate based on storm motion ismore suitable for the purpose of our analysis.

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