ML19268B785
| ML19268B785 | |
| Person / Time | |
|---|---|
| Site: | 05000502 |
| Issue date: | 06/05/1979 |
| From: | Fay C WISCONSIN ELECTRIC POWER CO. |
| To: | Harold Denton, Parr O Office of Nuclear Reactor Regulation |
| References | |
| NUDOCS 7906120421 | |
| Download: ML19268B785 (31) | |
Text
{{#Wiki_filter:. O wisconsin Electric posen coursur 231 W. MICHIGAN, P.O. BOX 2046. MILWAUKEE, WI $3201 June 5, 1979 Mr. Harold R. Denton, Director Office of Nuclear Reactor Regulation U. S. NUCLEAR REGULATORY COMMISSION Washington, D. C. 20555 Attention: Mr. Olan D. Parr, Chief Light Water Reactors Branch 3 Gentlemen: DOCKET STN 50-502 REFERENCE DOCUMENT HAVEN NUCLEAR PLANT Please find enclosed a copy of Paper 24 entitled, "Toward a Universal Climatological Extrem Wind Distribution" by H. C. S. Thom. This Paper should be brought to the attention of Mr. John Goll of your Staff. Mr. Goll requested that we provide a copy of this Paper during our conference telephone call held on May 24, 1979, concerning our response to NRC Question 372.6(2.3.1). Should you have any question regarding this Paper, please contact us. Very truly yours, T: C. W. Fay Director, Nuclear Power Department Enclosure 9500M4.5 79 o e l u o ut p Qoot Sc //
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t TOWARD A UNIVERSA L - a CLIMATOLOGICAL EXTREME WIND DISTRIBUTION i , f, . H. C. S. Thom - U. S. Environmental Science Services Administration, Silver Spring, U. S. A. {
- l "O I
t' . Ab s t r ac t I e v lt was foun1 that the shape of the Trdchet extreme value wind distributton for j entratropic al storme and thunderstorms tended to approach a value of 9 as the record length , , . lacrossed. The remaining scale parameter m as found to be well cor'reI*ated with the i maximum mean monthly wind speed. This gave a method of approximating the extreme wini * , distributton to extratropic al storm areas, An exarrdnation of tropical storin extreme wind . i dastributtor.s showed them to have a quite diffe rent shape c haracteristic, The shape para. ' ,' ; rnate r tended to be meat 4. 5, half of that for extratropic al cycinnes, and the sc ale parameter l . J' tended to follow the same relationship with maximum monthly mean wind speed. In the 41 trootcal storm area of the southern North Atlantle an annual sortes of extreme winds is !,i always a comple f rom a misture of tropical and extrat*opical storms which is fitted by a I ; 3 mixed extrerre value distributton, Although the typhoon type appears to have the same distribution of extreme winds as the hurric ano type, the f requency of occurence of the
' I typhoon is much higher and n.. mixing with extr atropic al storms occurs until higher latitudes . . -
are resehed. The opprettmation procedure for extreme value statistics an typhoon areas } has not yet been completed.
. I .
t i R d sumd ; .
. ' +
Au fur et h rnesure que s'accumulent les donnees, l'on s'apergott que le II I parametre de forme <*e la courbe de Fedc het de s valeur s de pointe de la vite s se du vent pour 'j les cyclones et les orages extratropic aux tend ve rs 9. ,L.e param6t re d'dehelle re stant , s'accorde t8en avec la maximum des moyennes mensuestes de vttesses des vents. On a ainst , une mdth sour connaitre le diagramme acoroximatif des valeurs de pointe de la vitesse - { des vente ; les edgtons & cyclones extratropic aux. Un examen du diagramme des
- i valeurs de , te de la vttesse des vents de cyclone troowal a montr4 qu'il prdsentait un I, l pa ram 6tre de forme tout h f ett diff e rent. Ce de rnier avoisinalt 4. 5, soit la moitid de celui I de cyclones extratropicaux, en meme temps que le parametro d' echelle du maximum den ,
8 moyennes mensuelles de vttesses ties vents tend h outvre la meme ietation. Dans la rdgtott des c yclones troote aux au sud de !'Atlantique.Nord, une ad rie annuelle de vents aux vttes ses l de valeurs de potnte contient toujours un ec hantillonnage de eyelones troptc aux et extra. f, tropicaux et est representee par une courbe mixte des valeurs de pointe de vitesses. Lee , typhone semblent avoir la meme courbe des valeurs de pointe de vttesses des vente que les }l ouragans, mais les premiere sent beaucoup plus frsquents et ne presentent pas d'intrueton de cyclone extrattonic al as ant d' avoir atteint des latitude s elevdee, La methode , 6
- d'approumation stattstiaae des valeurs de pointe de v6tesses des vente dans lea ristons n l,-
typhone n'a pas encore ete mise au point. i 4 I I I a ., . t 9500 &246 I
. .- s'*. __,===.we.e= p. m o % =... p.e ..
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E - 670 Wind Errects on Buildings and Structrees l '
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. .) Introdoetten l}
f ! di The engineer is now f requently called upon to design against wind forces o l i Et j in many parts of the world. Only in a few areas are the necessary short du- 1 . s
! FP I ration vind speed data series available for analysis to provide rational'de'=
sign values. e present study attempts the development of approximate methods for determining design values at extratropical locations vtere only mean monthly ( vind speeds are available and for tropical storm areas where c.ean vind speed 1
- and tropical storin f requency are availabl In the letter case a mixed extreme {
l. value distribution must be employed. There is also increasing interest in the { ' 8 i
' extreme wind regime over ocean areas where such approximate methods are all
;I I the more necessary. No previous treatment of this general problem was found
{ ! I reported in the literature. l 1 3 g The Streme Utnd Dt s t ribia t en 4
.( The writer has employed the Frechet distribution (1) for fitting extreme $
k winds for a nunber of years (2), D), (4). This distribution is the second o
- type distribution considered by Fisher and Tippett (5) who developed the gen-i eral theory for asymptotic extreme value distributions. Its distribution {
{ l function is defined by the equation l r F(v) = exp - (1) .
-Y}
where F(v) is the probability of an extreme value being less than v. De is the scale parameter which scales v. and v is a parameter which defines the shape i of the distribution. The effect of variation in the shape parameter is shown
- 1
. in (2]. i The Fisher-Tippett Type I distribution function is defined by the equation i
F(x) = cxpf-exp[- (2)
] '.
1 i l i i ,
! 9500)247 3 1 ..m .. . _ . . .
" M M . We 44M 4 hhMe - T
.. . , - -., - ._ . .~ ,. - - -- .
i s v
. . .,..~.....,.tm.., .. ,. . . . . .. , , .....< .# -
h....3 - ..-
. a ,
i l ( hper 24 - Thom ,,, 671 l. . M I Bete p is the scale parameter and a is the location parameter, the Type ! g i rces distribution having a fixed shape. I ' du. If one makes an equiprobability transformation of the Type I to the . j* e'
~
de. Frechit distribution i.e., equation (2) to (1) the condition is that ' l l' ethode ' (v/pe)*Y = expi '
. U l.
E (3) , l monthly l " Taking logarithms and setting y = 1/p and a = Ins, it is readily found that ;{ ,e e d g
.s xtreme 'i s x = In v (4) in the
'_+
-i 11 so the Type I distribution is transformed to the Preche't distribution by a l; '
Sund logarithmic transformation. Thus, the logarithms of the extreme winds will j follow a Type I distribution. This results in considerable advantage since l . it is much easier and more precise to fit the Type 1. The parameter of the
. Type 1 may then be converted to the Freche't distribution by the equations [
reme l , nd Y " 1/@t (5) l 4 and , i 6
'l 0 = e" . (6) lI (1) justification for using the Frechdt distribution for extreme wind speed l was given in [2] and [3] The main basis for this was the superior fit over j ,
is tho the Type I to several hundred extreme wind data series and the aero lower . h*P* bound locations required by the wind speed variable so that small citmatic *' shown variations migSt be reflected as scale changes as is observed. Fits be che f Type I distribution occasionally result in negative speeds which nr , of couren, untion inadmissible. Recently, further justification vna provided wher it was found (2)
. f t
95005248 _ _ _ - - - - * . - -* , , - te g, nose ee%% , ,._ _ .
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= -
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1
'! 672 Wind Effects on Buildings and Structures '.
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.i that departures from everage vind level for very high speeds did not follow i*
a Caussian distribution as has been of ten assumed at lower wind speeds but followed a logarithmic Caussian distribution. Thus, a Coussian distribution , on the logarithm of speed leads to a Type I distribution on the logarithm or. 2 1 a Freche't distribut'on on the wind speed itself.
> 5 s
l ' Sbene red Senle 3tatistles. INttnerentent Ste m . 1 During the preparation of (3k it was requested that ar average shape t j f actor be computed for possible application to !!ational liighway System probles.s. !
. I Tbs value obtained and given in (3) was 9. 1.ater during the revision of (3) {
E the matter was studied further when it was found that the relatively few tropi.
' cal storms had quite dif ferent shape statistics making it desirable tu consider }
( the extratropical storms separately. hen this was done it was further observed ; that as record length increased the mean value tended toward th'e same value 9. This is shown in Figure i where the shape estimatee have been plotted for 116 {
- 1 distributt'ons of extratropical storms. The histogram on the right of the Figure shows the distribution to be skewed as would be expected. This analysis appeared I
1 i to justify the assumption of v* = 9 as a closa approximation of the shape param-eter for extratropical storms. The approximation of the scale statistic was more difficult. After trying several possibilities, it was conjectured that the extreme values would be partly ( i 1 1
/The present study and all previous studies by the writer employed the speed I
of the fastest mile of wind, the variable most readily available in the U. S. , This extreme variable is very close to the automatically recorded f astest minute. t If the extreme minute speed is observed only once per hour it has been found that 10 mph must be added to attain the approximate fastest mile or fostest minute. J , 95006249
)
l
. , . . . . . . . . . . . . . . . . ....ew.......... n a .. . .w.,.......% . . . . . . . . . . . . . . . . . . . .
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. . . . . . - . . - . ~ . . . ..
I ( , j - Paper 24 - "'h o m 673 i I* !y I 4,1 scaled by some average value governed possibly by local surface friction. s but Thus, the higher the average value the higher the extreme values. The con. l . ' #- -
"" " , y dittens along ses coasts are examples where higher everage vinds prevail and *
" ' l '
the same areas experience higher extremes. The maximum monthly everage viad l' t ! speed v was finally chosen as the independent variable which was to be asso- I s > ciated with the sample scale p* since p* ciust be sero when v = 0, the functional l; , I : hape telationship must pass through zero. Also it appeared likely that although ' l problems. the function should be montonic increasing, it should rise at a decreasing rate ' i! I g [3) es? increased. This suggested a parabola with axis on the abscissa as a log. g' = v tropt- test function which was fitted to 47 (I,0*)'s for 47 stations experiencing 4 considor extratropical storms exclusively,shown in Figure 2. The five highest pointe + ob.o ved came from records at North Atlantic Ocean Station vessels which with their high '
,gy, 9, v's helped estah11sh the function at high average vind speeds exparte:nced over Ior 1 the open ocean. The equation of the curve fitted by least s,quares is i .
me Figure i , p*, = (320.5 v + 248.7)I -15.7 . (7) ! is appeared . I
, pg,. The parabola provides a good fit to the data as sho w by correlation index '
a ! r which is 0.935 meaning that 93.5% of the variability in p* is accounted for ' - i' cr trying by variability in v through equation (7). l d be partly ,
- The hern Treeten t Wind Dis tributien. I Having estimates of p, and y the extratropical extreme vind distribution i
the speed function approximation may be expressed by the equation c U. S . .
- ont minuto. F(v) = exp"-(' 9} . (B) found 0 ,
stest minuto. Tests of the method show that it applies with very little bias over the I U. S. and over the North Atlantic Ocean. The standard deviation of errors in ' t i 9500b250
, a-.. --
.w-,%.--..-.
t ,
) ,
674 Wind Effects on Buildings and Structures 1 i
) -
approximating the 0.98 quantile or 50 year mean recurrence interval was found
; ,[,
to be 6.5 miles / hour. This gives e 0.90 confidence interval on the true quan- , tilo V(0.98) of (v(0.98) - 8.3 < v(0.98) < v(0.98) + 8.3) 1.e., the true value , of the 50 year vind will lie on this interval with probability 0.90. App 11 l _ cation to several other extretropical areas has always given reasonable result's. ' hence, there is no reason to expect at present that it would not apply in all ,', extratropical atens and to the extreme winds from all extrattnpical storms. Of course, as with any approximation the reasonableness of results in any j spplication should always be considered. I j l
$bena. Senie, end Mirtura Statis :tes Trooten! Storms, f 1,
The problem in -.r. 6 .. tropical storms is much more 4tif tevlt because ( of the great scarcity of extreme wind data. However, sufficient data vere r available in the southoru North Atlantic area [6) to give what appears to be reasonable approximations, llere nine stations provided records which could be analysed with reasonable confidence. In addition very good record and anal-ytes were available for Hong Kong [7] and some data for Mantle (8). These are l listed in Table 1. The work for the typhoon area must, however, be said to be i just beginning and hence, the qualification in the. title of this paper. Some discussion of conditions in this area, however, vill be given. which may be helpful for rougher approximations. i i
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,, . .. . . . - . . ...- e.- e* + - * ' -' -~'*'*- * * * * '****~ ~~
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Paper 24 - Thom 675 - J 6 . und TARLE I {* - uan* Distributten shape an<1 Seele statistles
; ys .
alue p* * ' n y* S(y)
~
1* Atlantic City, N. J. 8 52.2
- 40
. 2.58
- sulte, Ratteras H. C. 14 62.0 5.73 1.43 t' ,
all Wilmington. N. C. i '? 9 42.4 3.77 1.17 I Charleston, S. C. 18 46.0 5.67 1.20 8
/i' s
Miami, Fla. 22 $0.1 3.83 0.73 i Mobile, Ala. 6 35.7 4.76 1.72 . New Orleans, 1,s. 8 27.2 3.48 1.17 [ San Juan, P. R. 21 45.1 3.27 0.65 '. use ,I i Manila, P. I. 12 44.2 4.93 1.26 'l i flong Kong (32) 32 52.3 4.56 ').75 i Hong Kong (14) 14 50.9 4.36 1.10 l5 , anal, Tropical Storm Mean 4.58' f
- are Hurricane Mean 4.57
- o be Typhoon Mean 4.59 -
- t i
tome s (y*) = 0.34 1 i For tropical storms the situation with respect to the shape parameter is similst to that for extratropical storms. The y* tended to again have a skewed distribution, but this time y* was about half that for extratropical storms. As seen in Table I the y*'s tend to be less variable es the record increasee , In length. This is what would be expected if this variability were due entirely to sampling errors in the y*'s. Such variability could, of course, be partly ; i due to relationships with other variables. This was checked by attempting to relate y* to several other variables but no relationship was found. It has . ee i 95003252 o m. - ,, ___ ,.ee.e smee. e e+ ar** *e* =ee m **
- v * -
M eme egesh w e.e ee+ 4***.se w e%^ee 6 em une , o muunuse essenetmee eewemo.ne.e> *- eg Se.eme _ ennuye
. _ _. J __ _-
1 5 676 Wind Effects cn Buildir.gs and Otructures ,, .. 3 4 1*een concluded, therefore, that the variability in y* is pure shapling error relatcJ to the length cf record as with extratropical stor1r.a and tho, et. I estimate of the true value of y* is obtained f rom its arithmetic menn givea ; to Table I as 4.58 Note the close agreement of the c.ean ye's for hurricanes
.' and typhoons. Also note the similarity of liong Kong to *. anils where the i 4
; annual typhoon frequency is svice as great.
Table I also Atets the standard ueviations of the individual y*'s ; i obtained from the order statistics. It is seen that these are relatt ely ' large because y* has en inherently large variance. The standard error . the ween of y* van obtained by weighting the individus1 variances w , foA
\
to 1.s 0.34 as given in Table I. This gives a 0.90 confidence tuterval on y , of (4.14 < y < 3.02). This appears to justify the assumption of a convenient ' value of 4.5 for 3* for trcpical storse.
- At first it was t.hought that the scale of the extreme wind distribution for tropical etorins was r constant. However, further consideration which cari.e ti sough a study of the Ocean Station Vessel data, lead to the conclusion that
, the tropical storn scale must also be a function of some base wind speed param*
eter. When the scales of hurricar.es and typhoons and their ccrresponding c.axi- 8 mw:,mean ponthly wini speeds were plotted on Figure 2, they were in the see general area es the extratropical points. A refitting of the curve including these points only gave a slightly dif ferent equation p * * ./ 3 H . 5 v + J t~ . 5 19.1 . (9) i The two equations agree almost exactly up to J* = 60 mph; above this equation ; (9) eveeeds Figure 2 (equation O)) by from 1 to 2 mph up p* = 100. The correlation indes r8 wee reduced f rom 0.93 to 0.90 e non-significant decrease. 9 1
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95006253 5 I I I
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1 Paper 24 - Thom ., 677 , s-
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t The maximum mean monthly wind speeds over open veter areas in the hurricane .' tror .
. } ^'
t ; and typhoon areas, except the ette of f Suqutta in the vestern Arabian Sea, have j; , 4
..4 .e n maximum mean conthly wind speets that are generally less than 18 eph, which is -
1
,5
l canes within the portion of th,s curve well e.tablished by both types of storms. Off i;. Suqutre, a trc,pical stem area, the msxtr un mean monthly wind speed exceeds i -
- 3) eph which is f ar above spee$s for otba' tropleal storm areas. This raises ' +
some doubt as to the applicability of equation (9) for such high rean speede . y although until dif fering information is ave 11able equation (9) could be employed. -
. s, f the in atens such as portions of the Southwest pacific where all storms are , ,' , ,
und tropical the entreite vind distribution function may be rtpressed as f t av ,
.t. 5 3 T (v) - esp.*
T ' S *'. (10) t
~
nient Here $,* may be estimated f rom equation (9). No estimate of the precision of ; . o t ier. quantiles obtained from (10) is presently available. h c a. In the entire southern North Atlantic and Caribbean as vell as the fringe i } l that stees of all tropical s torm areas c.me of the annual extreme vinds are due to i , p. i l I param. extratropical s tort.s (or thundeutorms). This results in the annual extreme ; a maxi. vind population being a mixture of extreme vinds from tropical and extratropical , se sama s tems giving the mixed extreme value distribution function f t .
% ding -
C(v) = pggF (v) + pg(v) . (11) , 4 : 6 F g and F have beer, estimated above and since p
- l'E ' II ****l"* * ***i"*'* i E T (94 '
p *h*'* "T ** th* probability of an annual extreme vind being produced by a f stion tropical storm or the proportion of tropical storm extreme vinds. , he It was immediately clear that pT must be related to the number of tropical .rease, storm passages in a given area. A trial shcrved that a good correlation was f obtained between the mean number of tropical storm passages per year through a , I t 95005254 N W9W N WOW- , _ . -FW p@M.MMee W * , M 4 688 6'9 999 9 % sN 4*W mes . . . .. - t oes. ee . - = .ese e > e. e. . . . *w - _ .y- e e* +-
- i. - > - _ _ __
. ., m -
4
. 676 Wind Effects on Buildings and f,tructures t five degree square and Tp at the center uf the square. Unf ortunately, no s published c.aps of this statistic were found so Figure 3 for the southern
. llorth Atlantic was prepared f rom stor1s tracks in (6). A e.ap was also pre. l pared for the ty>boou area of the Soutbvest Facific north of the aquator but t ,
is not presented here because the typhoon regime has a dif ferent pf *h*'**** - l totic than the hurricane regime. As vill be seen below riot enecgh data were availabi r to analyre it satisf actorily.
~
When the problem of estimating p7 was first approached it was thought
-t the relatico of p7 to the e.ean annual five degree square f requency (
sight be the same in the Southwest pacific. llence, the relationship of pT to f was chosen to not only fit a logical scheme but to be capable of possible extension to the typhoon regime. Although the relationship could not be ex* . tended to this regime it still appeared desttable to keep the logical shape. The f unction employed is the logistic wht;h in this instance was required to be asymptotic tu pT = 0 andT p = 1, the limits for probability. This de= fined the coefficient of the exponential in the denominator of the logistic. I The function t defined by e t=In((1-p)/(99'464 ET )] (l2) T is then a linest function of f. This to shown in Figure 4 vith the observed points from southern North Atlantic tropical storms. The line was fitted by least squares. Transforming back to the logistic gave the equation I PT
= 1/(1 + 99 exp( 3.0 f)] . (13)
The curvo with the observed points is shown in Figure 5. The squared correlo. tion is 0.783. L 9500b255 4 .. .. .... ... . .. . . . . . . . . . . - . . ~ . . . . . . _ . - . _ -
-+ - - . - . - . .
, .. ....a.,...... . . . . . . . . *. . ~ ~ v. ~ ' * < - - ' '
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Faper Pli - Thom
- 679 {
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e ' t f While the typhoon of the Southwest Pacific is probably identical in '
. I form with the hurricare of the southern North Atlantle, its maximum mean l'I
. 3 ..
annual frequency. located at 1$N
- 130E is roughly three tim <s as large.
l _ st , If it is assumed that p =t 0.95 at riong Kong where f = 1.7 and p = 0.9999 . T
- era at P.anila where f = 3.5. the relationship for pT will be given by o .
PT " l/{ l + 9t **PI*4 II)
- II') , . ,
This relationship gives an f of 2.6 at p T= 0.999 ~ 1 Further s tudy, however.
- must be given to this approximation before it can be put forward as anything '
but a conjecture. This completes the approximations of statistica necessary ; 'ble to make equation (11) determinate. The hun t-t%t verul Fverewe Vind Dis tribut t en II For all aress for which p*, and pTcan be ettectively determined either ! 'ied . 6. by the methode given above or directly from historical data the. approximate i
- t-extreme vind distribution la given by the equation l
- . l j
G(v) = (1-PT )'*E ' **
+I T exp - . (15) f i
(12) ' Unfortunately this equation cannot be combined into a single function so !l ni that it can be inverted to solve the usunt engineering problem which is to find a speed for a preassir,ned prebability or a quantile. Hence, the distribution {l ' ,y ,l f C(v) mus t be computed for a settes of v's and interpelations made on the prob. ;, , ability, f (13) To compute F ,from the Freche.t Jistribution it is convenient te rearrango ,3,. equation (1) in the form i' in In(1/F) = y in(v/S). (16)
~
s t 95003256
. ., ,;.2.
t 680 Wind Effects on Buildir:gs and Structures 'l j Inverting (16) gives the reciprocal of F - I
) 1/F
- exp exp( y In(v/p)). (17)
~
,e Note that accordir.g to equation (16) v/D is the same for both y's. The final ,
e step is to multiply by the probability coef fielente and add. , C 1 An example follove in which I = 10 (p*, = 43 from equation (7)) and pg = 0.25: This gives the mixed distrihtien 9 C(v)=0.75exp[- J + 0.25 exp h4.5j , (18) The results are shown in Table II. I i T utt TT l Ceerutetten F.vemple
- v l I
, In(h) 9In(h) 4.5In'h) F E
0.75F E 0*2!I T C 50 0.1508 ,
-1.3574 0.6787 1.293 1.661 0.580 0.150 0.730 f0 .3331 -2.9963 -1.4991 1.051 1.250 714 .200 .914 70 4873 4.3857 2.1929 1.013 1.118 .740 .224 .964 i 60 .6208 -5.5875 2.7937 1.004 1.063 .747 .235 .982 90 .7366 6.6475 -3.3237 1.001 1.037 .749 .241 .990 100 6440 ~7.5957 -3.7975 1.000 1.023 .750 .244 .994 110 .9393 -8.4335 4.2268 1.000 1.015 .750 .246 996 120 1.0263 -9.2366 -4.6183 1.000 1.010 .750 .248 .998 !
9500<>257 i
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- s 7 Faper 281 - The:n -
681 ll .. ACT? WIJDCrPf*!$ , (gy) The writer vishes to thank Marcella D. Thom and Maurice Kasinoff for ,.,
, os doing the statistical computations and George W. Cry and Arthur Cooperman j ra1 l end his staff for assistance with tropical storm data analyses. The assist. .t I
ance of the writer's secretary. Denaire' Pyle, in assec511cs the basic data l t and in preparing the references is also appreciated. !} t
~
(18) rnrtmers .. l i (1) M. Fre"chet sur la Loi de Prcbabiliti de l'I' cart Maxiews". Ann. Soc. polonaise Math. Cracovie 6, 93 116 (1927). ' l (2) 8. C. S. nom. " Frequency of Maximum Wind Speeds", Praecedines. ASct. ! t Vol. 80, 1954, 11 pp. ji C [3] H. C. S. nom, " Distributions of Extrees Winds in the Unitad States", ,
.tevrnal strucevent Div. Pr oc . AFC3 Vol. f6. No. ST 4. April, 1960. i 0.730 (4) H. C. S. Thom, "New Distribution of Extreme Winds in the United States", . .914 -
Conference Prerrtet 411. ASCE Environmental Engineering Conference, t
.964 Dallas, Texas, Feb. 6-9, 1967 I .962 l
($) R. A. Flaher and L. H. C. Tippett " Limiting Forms of the Prcquency {;'
.990
- Distribution of the largest or Smallest Member of a Sample". h
.994 ,I Cembridee Pbit. S+e. v. 2I. , Part .2, p. 180. 192 6. j .996 (6) Coorge W. Cry. " Tropical Cyclones of the North Atlantic Ocean" U. S. j' 998 i Dept. af Connerce. Technical paper No. 55, 1965.
(7 ) C. J. Bell. " Surf ace Winds in 11ong Y.ong Typhoons". Proc .11.S . /Aa t an ' l W neher S wrna W 1961. 2 - (8) Thomas E. Thorp, "Ittgh Velocit y Winds in the It111t pires". Indiana . University Foundation Research Division. Bloomington Indiana. .
^
Tne Final Report Aug. 1962. S6 pp. 9500d258 N.WhGg D .$ g.4 N N _ _ gggggg _ __w_ .$$g gggg gggggggggg
;gg hq@@g gghS4 9 % bG
- - . ~
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i 4
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..e Ol5TRIMl0N $HAPI VS, YEAR $ & RECORD
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o
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, ere oro ee ere.m s es e e r e to sw e ete se e ene se .e e e e ,
- a e e e e
iI 1 I I I I I I I 0 10 20 30 0 0 0 $ 10 15 20 3 30
.fRt0VENCY N YEARS flGutt 1
~
/ ,
80 - 70 -
- 60 -
, e ,
e
- e og." , e'
#, $o- e ir a.*
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, VS. MAXIMUM MONTHLY 30- AVERAGE WIND SPEED 20 - (320M +N7%-15 8 10 8
1 I I I I I I I I I I I I I f I o O 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 WIND SPE ED MILLS / HOUR p 4 e b 682 95009259 I i
* = 6 . ..,,,
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l PA$$ AGES PER 5' ; l.
, , $QUAnE 190163. :
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i 8 I , OO - t ta i n l .P. , [' I I 99.46 4 P, l M t,0 10 - - < , CY t vs. TROPICAL STORM FttCUENCY i fioUtt 4 1, 30 - t
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,3 o I I I I I 1 I I I i 1 1 1 1 l l l; 00 0.1 0.20304 os 06 or os 09 t o i.i i .2 1.3 14 i.s t o 1.7 l . Mi&N ANNUAL :DIQUtNCY 08 f t0PIC AL STOtml '
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f tGUtt $
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.no _ _' I 1 1 i l l I l i I I l l oo 02 04 06 08 10 12 la 46 it 70 22 24 26 28 30
- 1. Mt AN ANNUAL f Rf QU(NCY Of taOP'C AL 5foems [j h t M3 eu. .= -w.e.. e,+ + ee - t o.e < 6 eae - s ee . u-.e as eeeemm emme . e e* .es.eens.e. ene mmeene meema m e* am en e es as e + we.mammume em ewmeme auem. . e>----
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Paper 221 ..- - j . t TOWARD A UNIVERSAL CLIMATOLOGICAL EXTREM E WIND DISTR!DUTION ! H. C. S. T hom - U. S. Environmental Science Services Administration, Silver Spring, U. S. A. M ettset l D . (e fourvt that the shape of ti.e Frec het entteme value u tnti distrit>wtion fot ' esitatrepic al eterms at d tturide r storn.s tended to .poroac h a value e,f 9 as the tec c.trf le ngth increased. 'Ite remalrang sc ale pararr.ete r u se found to be m e;l c ot're!'ated with 'ho ;, . i* enan.!rt.um rne an trenthly win:] o pee d. T He g ave a roethrx) of actitc almatie t ti c c At te rr.e wini i distributien 6n entratropic al storm areas. An en amination <>f t r e nic aJ stor m e ntr eme wtr.1 . destttbuttor;a chem ed the m to have a tujte t'iff e rent s hape c hat et te ttstle. T he s hape para. {; rneie t tended to be ricat 4. 5, half of that for ext r atrepic al c ycle.ne s, and the sc ale rearamete r 1 te nJed to f ollow the s ame r elattuethle with mau n;urti mont*J y rr.e an wind e'ar ed. li tt e t I tropic al ete rm area of the eeuthetn North Atlae.ttc an ennu.il s e tte s c.f extre ree s.itMe le AJu ays a c arrple f rom a misture e,f t retic al 34 e stratts.pic al s tatens v,*Je h is fittei by a .'l } rnLaed e st re n't v.ilue dis t ributton. Although tt e try4pn type arocar s to have tt o e arv e '
- distributic,n of est reme winds as the hur ric ane tve, the f requeric y t f M c u retste c4 t'e ,
typhooft la muc h harhe t an't no retning with e ntr at ts pic al stot tr.s oc t ut s until Idnt e t latitude s ;I are te sehed. "ite #pproximation procedure it t extrenie value statistic s an typtioon aress ' has riot g et been t empleted. L i Risumd . t Au fur et h rne eurs tlue s'acc umulerit le s donede s, l'on s' ape rpit c,ve le ( pa rambt re de forme ete la c ourhe de l' rdc het de s valeur s de pur.te de la vite s se stu vent pour !l e le s c ycic.ne s e t le s p age s ext r at ronic.ium tend ve r s 9. ,l.e pa r an.et t e d'(c helle t e nt w t s' ace crete bien avec le m.utmu ti des roovennes mensuelle s de vites ses des vetits, On a a6nst une anothode peut conn.dt te le ellag ramme anorea6matti des valeur s de potnte e la nte s se i de s sent s slana le s regnana & ciclones e xt r attepic eus. Un examen du e:lagr am.c rtes
- 1 valeur s ele pointe de la vites se ties vents ele c yclotse treett al a mont re qu'il prJr entMt un f pa t ambt r e ele f or me tout h f.tt filif e'rcht. C e t!c t nie t ag oisinait 4. S. soit la niotttd de r etut de c yclone s extratropic aux, en ml* ree te mris e,ve le par ame t re d'i c helle du e.sasimum de s I
rnoyennes mensuelles de vite s se s r:ce ve nts tend h outvte la fMme i etatinn. Dans la r e's.inti de s c yclone s troons aut au sud de Atlantique.Notr'. une seite annuelle !c vents aus wie sses de valeur s de pointe coetter.t toujours un ec hanttiliinnage sie cycletie s tropir.tus et exten. , tropic aux et e st repre sentee par une courhe entxte tie s v Jeur s de pointe sta vtte s ses. Les
^g typhons sertiblent avete la meme court,e de s valeur s de pointe de vitese e s des vente etue les
' l ouragans, mais les pretniers sont beaucoun plus f rse.uents et ne pt/sentetit pas ti'antrusion I cle c.yclorie e st r at topte al si atit d' avoir atteint de s n atuude s ele g de s, La rnetharle capptogimation stat 6suoue des valcut s ele polnle de vites se o. des vente dans les r(glone &
typhone n'a pas encore ett rnise au point. lI I 6
. \.
4 iI i ' i
, . e t
f CC) i t 95003261 . 4 1
. ,.." ..%..*t.., m .c.,, ,w ,....w , g...
, - %, ....m..,.y ,....,....m...., . . , . . ..,,.o.,,...,....
* * )
pw
. . - .r _ ,.u - -
"! J' P
I k t l Wind Ef fects en buildir.cs hnd T.,tructures ! t 670 .. 1 4 .:
-P"
. . Int rnbe t t en )
i d:
~
g The engineer is nov f requently called upon to design against vind f orces ' e o 1 ' *. { in many parts of the world. Only in e few stees are the necessary short du. 4 I ration wind speed data series evallable for analysis to provide rational de+ I E
' sign values. The present study atteepts the develcpment of approxicate retbods I
; for determining design values at extratropical locations store only mean monthly 5
vind speeds are available and for trepical stcrm ereas shere tscan vind speed and trepical storm frequency are availabl In the latter case a cixed extrete e value distribution must be etaployed. There is also increasing Interest in the { extreino vind regime over ocean arcos where such approxie. ate e.cthods are sll l the raore necessary. No previous treattnent of this general problem was found reported in the literature. l
'
- i The Te t c ~ t'l el fil e t r ibet f an The writer ha's cinployed the Frechit dis tribution (1) f er fittieg extreze vinds f or a number of yests (2 ), [3), (4). This distribution is the second lj l
g type distribution considered by Fisber and Tippett (5) who developed the gen-I cral theory for asymptotic exlrcene valt.e distributions. Its distribution j l function is defined by the equation F(v) = exp (1)
*v}
where F(v) is the probability of an extreme value being less than v. P, is the ; scale paremeter which scales v. and v is a parsecter which defines the shore .' y d of the dist ribution. The effect of vartetten in the shape parameter is shovn l
. In (n. . !
' f, The Fisher Tippett Type I distribution function is defined by the equation I
F(x)'=expfexp(* (2)
] *.
l 1
,se l 9500D262 i !,
4 -.....--.. ~.-. .- - .
. r. . ,. .
.. . . ~ . . . . . , . . . . . i . . . . . . .
. .i.........v......
.. L . - . . . . . - ...: . - . . , t i I i Paper. 24 - Thom *,, 671 l . l s i Eere pg is the scale paremeter and er is the location pareceter, the Type I s' . distribution having a fixed shape. rces du. If one r.akes an equiprotability transferr.ati">n of the Type I to the f'
. .~
de. Freche't distribution i.e., equation (2) to (1) the 'ondition is that ethods (3) lI conthly (v/p,)* Y = e xp' *[' \ 8/] . .r e d Taking logarithme end setting y = 1/f3 and u = fr$, it is readily found that f - I stremo l x = In v (4)
- n tbn i 111 so the Type 1 distributten is transf ereed to the Freche't distribution by a und togerithmic transferr.ation. Thus, the ler,atithms of the extreme vinde vill j follev e Type I distribution. This results to considerable cdyt;ntage since ,I it to ciuch easier and mere precise to fit the Type 1. The pateetter of the I a
Type I may then be converted to tt.c Treche't distribution by the equations I' treno e Y
- 1/Pg (5) l end i)
~
ren* . * *4 and . l Il (6) '. P = e" . t I (1) justification for using the Freche't distribution for extrene vind speed was given in [2] snJ [.ij The emin basis for this was the superior fit over ; le the the Type I to several hundred extreme vind data series and the r.cro lover ', '
<l h'P4 %und locations required by the vind speed variable so that small climatic 'l I! 'h " variations mir.St be reflected as scale changes as is ebaerved. Fits by the 'l .
Type I distribution occasionally result in ner.ative speeds Wich nro, of courso,
"" I I "" inadmissible. Recently, further justification was provided when it was found
- i (7) 5) .
Ii U. , 1
\..
9500b263 -
- - - - .... ... ~ . . . . _ . . . . _ .
u.~ '.- --.
...w
, . 3 L i i I 1
. I 1
- I
..( k'in;l Effects on Saildings and Structures
! 672 I
l '~ i not follow
' that departures from average vind level for very high speeds d' '
i a Caussian distribution as has been often assuced at loser vind speeds but
' t ;
f ollowed a 1cgarithmic Caussten distribution. Thus, a Caussian distribution e on the logarithm of spted lesde to a Type I distribution on the logariths or , e Frecte's distribution on the vind speed itself.
}
i l. f k si.a rao 9: ale itntistlee rettntreefent tier-e.
- 1
- During the preparation of [3k it was requested that an averate shape
?
f actor be computed for possible application to l'ational Highway Systcm problets. i I t Tto value obtained and given in [3] sas 9. Later during the revision of [3] j
)
\
the matter was studied f urther vben it was found tbst it.e relatively few tror f. l cul storus had quite different shape statistics raking it desireble tu consider , I theextratropicalstoresseparately.hhenthiswasdoneitwasfurtherobserved ; that as record length increastd the t..ean value tended toward th'e same. valco 9. 1 1 This is shovn in Picure 1 vbere the shape estimates have been plotted for 116 g
..' distributt ms of extratrepical storts. The histogtnm on the right of the Figure i
I, a shows the distribution to be skewed es would ic < xpectcJ. This analysis appeared to justify the assu-tption of * = 9 as a close approxication of the shape pern- . eter for extratrcpical storus. l-1 The approximation of the scale statistic was more difficult. After trying I sevetal possibilities. It was conjectured that ti e extreme values vould be partly ( I 1
/The present study and all previous studies by the writer ceployed the speed of the f astcet elle of vinJ. the variable most readily available in.the U. S. t This extrese variable is very close to the autecsatically secorded f astest minute. t 6
if the extremo minute speed is observed only ence por hour it has been found that 10 mph must be adJed to attain the apprcximate f astest mile or f astest minute. f 9500 264 s I l
.. , ........a. ~.
, , , , ,o
+
. ....u..... ..-.....As6.... ...... ...... - .... $ ..........w... . . . . - . . . . . . .
. , . . . .. .s - -
a . : ~ . :. . ..
.. - = * - ~ '
.. .. - * ' ~*
,,. . w. . . .
-- .s '
i ( _ . . s j .
~~
l, ]
. Paper 24 - Them 673 I t
I N'" scaled by sone average value governed postibly by local surface f riction. f ,' Thus, the higher the averete value the higher the extree.e values. The cen. , i ditions along sea coasts are exaeples where higher average vinds prevail and the spee areas experience higher extreres. The e.mxte.nn centhly everage vind . l{ speed v vas finally chosen as the independent variable which was to be asso- i!l _ e ciated with the se-ple scale $* since p* must be sero when v = 0. the functional jg i1 3,, p, relationship must pass through zero. Also it appeared likely that although
- j proble.w . the function should t e montenic increasinE. it should rise at a decreasitig rate f'! 1 esYincreated. This suge,ested a parabola with axis on the abscisse as a log = i
,g [3 ) w trcept- ical function which van fitted to 47 (I.S*)'s for 47 stations experiencing . l 1 canct006 exttt. tropical sterits exclusively.shown in Piture 2. The five hirJest points ; c.b.etved caine from records at North Atlantic Ocean Station vessels shich with their hil,h Ii
,,gg, 9, I'shelpedestabitshthe function at high average wird speeds experienced over '
.er 1 the open ocean. The equation of the curve fitted by ler.ct squares is j'
!i
- IIC'#
C*, = (320.5 v + 24 8.7)b -15.7 . (7) .. is appented , i, i} 1pc patam* The parabotn provides a good Itt to the data as shown by correlation index l I
)t t awhich is 0.935 meaning that 93.5" of the variability in D* to secounted for ' .
_ t. er trying by variability in v through equation (7). . be pntt h The T ten Trecical Wind DI.t ributien. I( i Having estinates of p, and y the extratrepiral estreme vind distribution h. I the apced " function approxtmation inny be expressed by the equation
- U. S . . 9 t .
l (B) es t ininute . F(v) = exp"-(L .I . 3 {, found Tests cf the method show that it appites with very little bias over the {. s t co t tr.inut e . I
~
U. S. and over the North Atlantic Ocean. The standard deviction of ctrote in i 9500b265
g - -. . -
} ,
1 e
} '
l 674 wird Effects en Buildirics an:1 p.ructures i 1 I approxtr.ating the 0.98 quantile or 50 year e.ean tccurrence interval var found g _f to 1>o 6.5 elles/bour. This gives a 0.5-0 confidence interval on the true quan. ; t , tile V(0.58) of (v(0.98) - 8.3 < V(0.98) < v(0.5B) + 8.3) 1.e., the true value - 1' of the 50 year vind vill lie on this interval sith probability 0.90. App 11 { cation to several other extratropical areas has always given rear 1;neble repul,ts. C
, hence. there is no reason to expect at present that it would not aFply in all extratropical arens and to the extrate winds f rem all extrattr.pical stores.
Of course, es with any erprox,utto:i the reasonableness of results in any j spp11 cation should always t,e considered.
,W wa. Senle. eM t!!veura etett ties. Tterfen1 9tarm .
. . f, The problem in respect to tropical storms is such raore difficult because (
of the great arcity of extres.e vind date. lievever, sufficient date sete available in the southern llorth Atlantic area (6) to give viot appears to be reasonable approxirntions. I!c r e n t:. stations provided records which could - 1e analyzed sith reasonable confidence. In addition very good record end anal. yses were available for llanC 1;ong [7] and son.e data for !tentle [6). These are j listed in Table I. The work for the typhoon atea must, however. be said to be just betinning and hence, the qualification in the. title of this paper. So .c discussion of conditions in this area, hovever. vill be given. which r.ay be helpful for rougher approxtr.ations. , i
. , l i
1
<- ,I s 1 9500p266 r . . ... . ..
.e e*
- M'd
- we %e s amamsent.e ..en w m. W N S. eah hM 4 ^- - -
' ^ mem bhasecumheumamDM emeD hteO A . - " ""^ei.m6*.*
r....- - - - - . -
, ,. . . , . , . . , ... . . . . .- .- - - i's- -' * "* **
, , , . . . ... . . . ~. ' - - .'
- s -
1
\
Paper 24 - The., 675 .
+ 4 I*
.md Tif1.E 1 etn-
$'l.
Distr N tfan ?N r* *~1 feata Seatteri n ?: I: r.lue a $* g* $(y) . l 2 f* Atlantic City. N. J. 8 $2.2 7.40 2.58 nits. Ratterse. N. C. 14 62.0 $.73 1.43 i til Vileirecton. N. C. 9 42.4 3.77 1.17 Charlesten. S. C. 18 46.0 $.67 1.20 8 Miami. Pla. 22 $0.1 3.63 0.73 j Mobile. Als. 6 35.7 4.76 1.72 i New Orleans. 1.a. 8 27.2 3.48 1.17 ; San Juan, P. R. 21 45.1 3.27 0.65 'I cr.o i I Kan11e. P. 1. 12 44.2 4.93 1.;6 , i a flong Konc (32) 32 $2.3 4.56 0.75 c l 11onc lions (14) 14 $0.9 4.36 1.10 I Tropical Stom Mean i
, n, g , ' .58 '
,i I
are "U" I ' 8 "' M a n 4.57 Typhoon Hean i o bo 4.59 , .,,.,,3 s(3*) = 0.34 3i I 5i e . For tropical storns the situation with respect to the shape paremeter is 1 i6 similar to that for extratropical storms. The )* tended to etain have a skeved I distribution, but this time 3* vos about half that for extrattopical stores. '
.t As seen in Tabic I the 3*'s tend to be less variable as the record increases ii in length. TSta is what would be expected if this variability vern due entirely .
to samplint. errors in the y*'s. Fuch variability could, of course. bc .ortly
- l due to relationships with other variables. This was checked by attempting to 'l .
relate 3* to several other varlebles but no relationship was found. It has - i' . I 1 6
......% y. .. - =.--.- - -.--- ~~~v*~+-"~'--m*****~**~'
- . . . ~ . . . - . . . . . . - . . . . ~ . . . ~ . . _ ~ . . . . . . _ _.... -...... .-. . . . . . - -
I 676 Wind Errects en imildir.cs and structures ; , s - t .. been concluded, therefore. that the variability in 3* is pure sc.mplic.g error # related to the length of record as with extratropical storr.s and that an
, j ,
i estin. ate of the true valve of 3* is obtair.cd f rom its arithmetic c.ean given In Table I as 4.58. Note the close agrect.eot of the c.een y*'s for hurricane,s i 2 l ' and typhoons. Also note the similarity of I!ong I:ong to Manila where the 1 1 annual typhoon f reqsency is twice as great. ,
)
Table I also Itets the standard deviations of the individual y*'s ' l obtained from the order statistics. It is seen that these are relatively I i t 9 large because y* Las an inhercutly large variance. The standard error of the ! l 1 c.een of 3* vas obtained by veighting the individual variances and was found
- 5 t o be 0.34 as given in 'Iable 1. k This gives a 0.90 conflo' ente interval en y ;
of (4 14 < y < $.02). This cppears to justify the assutption of a convenient I I value of 4.5 for 3* for tropical storms.
- k l At first it was thought that the scale cf the extrecie vir.d dis tribution
}
} for tropical storcis was a constant. Itovever. f urther consideration which can.e through a study of the Ocean Station Vessel data. Icad to the conclusion that I
the tropical storm scale must also be a function of some base vind speed poten-eter. When the scales of hurricanes and typhoons and their corresponding r.axi- 8 mum mean conthly wind speeds were plotted on Figure 2 they were in the sa:te i geoctal arca as the extrotropical points. A tefitting of the curve including these potute only gave a slightly dif ferent equation i P * * </ 34 7. 5 v + Jb4. 5 - 19.1 . (9) ( The two equatione rarec almost exactly up to p* = 60 eph; above this equation ; (9) cxceeda Figure 2 (cquation (7)) by from 1 to 2 tyh up C* = 100 Ihe I correlation inJcx r3 was reduced from 0.9) to 0.90 a non sipnific. ant decrease. t
) -
i ee 1 9500b268 g * . 1 8 .
. , - . . - . .... 4 . . . . . _ . . . . . . . . . . . . . . . . . . . . - . _ .
a
- . .. .-......:..,.. < . .c ~ . * . *' . ....--.'~ ~ .
1 3 . ._ , *
....4 . . .
F ( ,. . . Paper 24 - Tha 677 . C f', b i ror The naxim.n evean monthly vind speeds over open vater areas in the hurricane and typhoon areas, except the area of f Suqutra in the vestern Arabian Sea, have lI f ll _., n rinxicas reen conthly wind speeds that are generally less than 18 eph, which is , Il:' , * . ** ents within the portion of the curve well established by both types of stores. Off Suqutra, a tropical storn area, the naxtetem ecan monthly vind speed exceeds i 1
- 3) aph which is for above speeds for other trepical sterm areas. This raises I, .
some doubt as to the app!!cabtitty et equation (9) for such high rean speeds ! ,. . sithough until dif f ering infornation is available equation (9) could be ceployed. t c . the In aress such as ptertions of the Soutbest pacific there all storms are 8 i arid tropical entreme vind distribution function reay be expressed as [ l
' 7 F(v)=exp*{U*.
T J. (10) .
. tent
- Here it,* nny be estimated f rem equitten (9). No estimate of the prectston of i
gen quantiles cbtained frem (10) is presently r.vailable. () i
- 1 e n. In the entire southern North Atlantic and Caribbean as voll as the fringe {6 that stess of all tropical storm areas, some of tie annual extrerne vinds are due to j pnrna. ex trat ropical s tores (c r thunders tores) . This results in the annual extrene ff i c, nnxt. vind population being a mixture of extrene vinds from tropical and extratropical '
{ t some storms giving the atxed extretr.e value distribution function rding i l C(v) = p gg r (v) + p F I'}* ( } TT ; ! i l i Fg and T have been estimated above end sinco gp = 1.pg ,, it remains to es tirnste i. ; p7 vhere pt is the probability of an annunt extreme vind being produced by a stton tropical eterm or the proportion of trepical storm extreme vinds. I to It was treiediately ricar that p7 must be related to the number of tropient . I res s o . storn passages in a given area. A trial shoved that a good correlation vns g, obtained betwen the mean number of tropical storm passtRes per year through a {; -
. .. i L 9500Q269
~ - _ . . .
- s. u - .
4
. 670 Wind Effects en Itu11 dings cr.d Structures i five degree square and p T at the center uf the square. t?nf ortuna tely. no publisted z.a,.s of this statistic vere found so Figure 3 f or the southern llorth Atlantic was prepared f rom storm tracks in (6]. A c.sp was also pre.
pared for the typhoon area of the Soutbvest Facific north of the equator but is not presented hete because the typhoon regire has a dif ferent pT cha rac:t e r. f , I istic than the hurricane regire. As vill be seen belov not enc ugh data vere
\
evailsble to sr.alyze it satisf actorily. . k' hen the prc.blem of estimatingTp vas first approacted it vas thought . that the seletion of pT to the e.can aunual five degree square f requency i sight be the sr.ce in the Southhost Pacific. 11ence, the teletionship of pT to f was chosen to not only fit a logical scher.c but to be capable of pessible , extension to the typhoon regice. Although the relationship could not be ex. - tended to this zegima it sill! appeared desitt.ble to keep the logical shape. The f unction ceployed is tbc legistic shich in this instonee was required to be asymptotic to TP = 0 andTp = 1, the liraits for prc,bability. This de. fined the evef ficient of the exponential in the denominator of the legistic. I The f unction t defined by a t = in [(1*p T} /(99'4o4 TI) (12) is then a linear function of f. This is shcw in Figure 4 uith the observed points f rom southern North Atlantic tropical storms. The line vos fitted by Icest squates. Transforming back to the logistic gave the equation k p =1/[1+99exp(.3.0f)). (13) 7
- I The curvo with the observed points to shcw in Figure 5. The sqt.ated correlo.
tion is 0.783.
.. 95.0.0/2.l0 _._
, .,....a.,.,, . . . . . .. .. ..e. * .. . '
. . . . ... _.. .. ~ - ' ' ' * * * *' ~ * *
. i i .
i i . Taper 24 - Thom .- 6'I9 '" l "
.s .
I k'htle the typhoon of the Southwes t pacific is pretably identical in
- 8 f orm with the hurricane of the southern Forth Atlantic, its maximu:n mean f'si , ..
en..ual itequency, located at 15N 130E is roughly three times as large. *
~
l
- If it is assumed that p T= 0.95 at Hong Kong dere f = 1.7 and p
- 0.9999 T
er-et P.snila where f
- 3.5, the rela.tionship for pT will te given by
- 2 P
T lf( l + 99 '*E(*4'4 f)) * {l4) ' This relationship gives an i of 2.6 at pT= 0.999 ~ 1. Further study, however, j eust t e given to this approntmation befero it can be put forward as anything but a conjecture. This coopletes the epproximations of statistics necessary
- ble to make equation (11) determinate.
j pc o iu i t'n t ve m t re e rr.e ut M Dir t r t hr i m i For all areas for which p*, and p can be effectively determined either . red ,
; by the octhcdo given alovo or directly frcu histerical data the eptroximate ' '
estreme vind distribution is given by the equation C(v) = (1 pT)'*E * '^'
+IT**I* * (l$)
(12) Unf ortunately this equation cannot be coitbined into a single function so
,) that it can be inverted to solve the usual engineering prehlem which is to find f
.y a speed for a preassir.ned prebability or a quantilo, llence, the distribution '
; y C(v) eust be corruted for a series of v's and interpolations made on the prob-i ability, I '
(13) f ! TocomputoFJromtheFreche.t distribution it is convenient to rearrango } i 33, equation (1) in the form l!i e In In(1/F) = *y In(v/p). (16) 1; j . t s 1 ', ii h 0 t
- s. . . . . . . . - - _ -,g. _ ., _.c,...w-..e--.-.....--.**~~.m*
--= . . . . . . . . . . . . . . . ....a. . . . . . . , . . _ . . . . . . . . . . . . , ~ . . - - - . . - . - -
.c 680 Wind Effects en Buildings and Structures 'l loverting (16) gives the reciprocal of F
- -< j 1/F = exp exp(*y in(v/p)). *
, (17)
~
i Uote tLet according to equatico (16) vig is the ecce f or both y's. The final . 1 + 1 etep to to cultiply by the probability coeffletente end add. 1 An er.neple follove to which 5
- 10 (p*,
- 43 f rom equatico (7)) and
- l <
p 0.25: This gives the mixed distribution T 9 4.5 C(v)=0.75exp{. J+0.25exp{. ]. (13) The resulte are shown in Table II. TM Lt 11 l re r.n e n t t r.n r . . -M ., - v lu(h) 9 In(h) 4.5in(h) 0.75F g 0.25F T C 50 0.1508 1.3574 0.6707 1.293 1.661 0.5t0 0.150 0. 7J O 00 .3331 2.9963 1.4991 1.051 1.250 .714 .200 .914 70 4673 4.3857 2.1929 1.013 1.116 .74 0 .224 .964 4 80 .6208 5.5075 2.7937 1.004 1.063 . 74 7 .235 .962 SO 7366 6.6475 -3.3237 1.001 1.037 .74 9 .241 .990 100 .8440 7.5957 3.7979 1.000 1.023 .750 .244 .994 110 .9393 8.4535 4.2268 1.000 1.015 .750 .246 .996 120 1.0263 9.2366 4.6183 1.000 1.010 .750 .248 .998 1 i e t G i . ~ . . _ . . ~ - . _ . -
_ _- _,,. . , , . _ _ __ _ - . - __ -- _ . . _- y ..
.' w . u . . . . . v u . . , e - - ., . . . . -- .u .. .. : .. . , . ......;.m. .w.,
.m .. . - , , . .. o
. .....~s- , , . . . ..
f '
\ ,
/ Faper Pli TMm
- 681 ~ i I
i -- j WWITY?'IS I 6 8' (17) The writer vishes to thank Marcella D. Thom and Maurice T.asinof f for
,i doing the statistical computations and George W. Cry and Arthur Cooperr.en . .
~
nel and his staf f for assistance with tropical storts date analyses. The assist- 1 f' acce of the vriter's secretary, Denaire' Pyle, in ast.cr.bling the beste data and in preparieg the references is also stpreciated. 6 l
.~
(10) FrPrtrier, t 5 (1) H. Fre*chet, "Sur la 1.01 de Prc,babilite" de l'I' cart itaximen", Ann. Soc. l, Polonaise Math. Cracovie 6. 93 116 (1927). l (2) D. C. S. Thom, " Frequency of Mexicium Utnd Speeds", P"cc adt eca . W t. ft
- I i
Vol. 20, 1954, 11 pp. I (3) H . C . S . D ott , " Distributions of Extrees Winds in the t'ntted Statco", C I 8
.teurnal streettret Div. Prae. S'CE. Vol. 26 No. ST 4 April, 1960. !
D.730 (4) H. C. S. Thom, "New Distribution of E:strece Winds in t'e United States", f 8
.914 .
fonference Pretrier 1.11. /SCE rnvironmental Engineering Conference, ,
,964 !
Dalles, Texas. Feb. 6-9, 1967. .
.902 {
($) R. A. Fisher and L. it. C. Tippett, "1.imiting Port s of the Frequency ' i
.990 :
Distribution of the Largest er Se.allest Member of a Sernple". h ! '
.994 !- l caehrtere Phil. Sme. V. 24 titt.2, p. 180. 1926. ;j .996 1 e (6) Ceorge W. Cry, " Tropical Cyclones of the North Attentic Ocean" U. S. j '* .993 i Dept. Jf Comette T. hnical Paper No. 55, 1965. }
l i (?) C. J. Bra 11. " Surf ace Winda in Hong Kong Typhoons", frne. ti.9. /A*t an l ,
!'i
,Venther R &rm ti.*. 1961. {
(8) Thomas E. Thorp, "Iligh Velocity Winds in the Philippines" Indient ; i University Foundation Research Division, Bloemington, Indiana. ; The Final Report Aug. 1962, 06 pp. l. E i t 9330b273 : 9 - ***9 8W ' OMN -
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