Journal o f Wind Engineering and Industrial Aerodynamics, 21 (1985) 155--166 155 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

ON T H E D I R E C T I O N A L U N C E R T A I N T Y O F S T R O N G W I N D G U S T S

w.w. MORIARTY

Bureau o f Meteorology, G.P.O. Box 1289K,, Melbourne 3001 (Australia)

(Received December 14, 1985)

S u m m a r y

The width of the direction trace produced by a standard (e.g., Dines) anemograph gives rise to considerable uncertainty as to the appropriate direction for given large gusts, and a consequent uncertainty about the expected extreme gusts calculated for particular sectors. Further uncertainty is added when the calculated expected extreme gusts are ap- plied to a fairly wide area around the observing site. The magnitudes of the directional uncertainties are examined for a particular site (East Sale in Victoria, Australia), and an approach to the problem they pose is suggested, through smoothing of the directional gust data. For East Sale such smoothing greatly reduces the irregularity of the sector-to- sector variations in the estimated directional extreme gusts.

I n t r o d u c t i o n

R e c e n t l y , the re has been an increasing r e q u i r e m e n t fo r e s t ima te s o f ex- t r e m e winds fo r bui lding design to be p rov ided by d i rec t ion sec tor , and ef- for t s have been m a d e to p rov i de such da t a [1, 2 ] . However , the e s t ima tes m a d e have had to d e p e n d on wind records k e p t over pas t years . Mos t such records have been m a d e wi th au tograph ic i n s t rumen t s which , as the i r cha r t speed was s low c o m p a r e d to the t u r b u l e n t f l uc tua t ions o f wind d i rec t ion , have le f t a d i rec t ion t race cons is t ing of a b r o a d b a n d o f var iable wid th {Fig. 1). T h e wid th o f this band represen t s an u n c e r t a i n t y as to the precise direc- t ion of a r e co rd ed s t rong gust. The m a g n i t u d e o f the u n c e r t a i n t y has been discussed br ief ly fo r a pa r t i cu la r observ ing site using a Dines a n e m o g r a p h {East Sale, Vic tor ia , Aust ra l ia ) in a p rev ious p a p e r [ 3 ] . In the p re sen t p a p e r it is p r o p o s e d to cons ide r this u n c e r t a i n t y and an addi t iona l u n c e r t a i n t y which arises w h e n obse rved d i rec t iona l gusts are used to e s t ima te e x t r e m e winds fo r use over a b r o a d su r round ing area. An a p p r o a c h to o v e r c o m i n g the assoc ia ted p r o b l e m s will t h e n be suggested.

Directional uncertainties of maximum gusts at East Sale

T h e d a t a or iginal ly o b t a i n e d fo r Eas t Sale [3] were the d i rec t ion t race wid ths c o r r e s p o n d i n g to the dai ly m a x i m u m gusts in each o f e ight d i rec t ion

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Fig. 1. Sec t ion of t he Dines A n e m o g r a p h t race f rom East Sale for 26 N o v e m b e r 1978, showing the variable w i d t h of the d i rec t ion trace. The par ts of the d i rec t ion t race corre- spond ing to the th ree s t ronges t gusts are ind ica ted by dashed lines ( the re was a slight of fse t b e t w e e n t he speed and d i rec t ion traces, a t y p e of i n s t rumen ta l e r ror w h i c h appears at t imes) .

sectors on all days when these gusts were 15 m s -1 or greater. Each gust Was allocated to the direction sector corresponding to the centre of the direction trace, as has been the usual observing practice in the past. Twenty-nine years of data were included. However, it was found that for some sectors (partic- ularly nor th and northeast) there were some years with no gusts over 15 m s -1, and in such cases the present study was extended to include daily maxima over 10 m s -1. The present study also included an extra year of data {1981).

The data are not homogeneous in that no t all gusts over a set strength were included, but only daily maxima; and the gust strengths which were included varied from day to day. However, it seems likely that the sample is sufficiently large and varied to give a good representation of the direction trace widths corresponding to the stronger gusts at East Sale.

The distribution of direction trace widths found for each of the various direction sectors are set out in Table 1. Figure 2 shows the results for all directions combined in graphical form.

The typical (modal) width of the direction trace did no t vary much from one direction sector to another. In all sectors it was only slightly less than the width of the direction sector itself {45°). Thus, the uncertainty associated with the direction allocated to a particular maximum gust would in the great majori ty of cases allow the possibility that the gust should have been allo- cated to a neighbouring sector. Such uncertainties might in turn cast con- siderable doubt on the results when the data are used to estimate long-term directional extreme gusts.

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T A B L E 1

F r e q u e n c y (%) of d i r e c t i o n trace w i d t h s for s t rong daily m a x i m u m gusts at East Sale in t h e years 1 9 5 2 - - 1 9 8 1 , Daily m a x i m u m gusts for e a c h s e c t o r greater t h a n 15 m s -l are i n c l u d e d , and , w h e n there were n o s u c h gusts in a s e c t o r for a year , daily m a x i m a s t ronger t h a n 10 m s -1. T h e m o d e for e a c h s e c t o r was e s t i m a t e d graphica l ly f r o m t h e d a t a in the table

Width o f dirn. D i r e c t i o n s e c t o r trace (o) N NE E SE S SW W NW All

0--15 12.1 2.1 1.7 0.7 0.0 0.5 0.0 0.I 0.7 15--25 15.3 12.8 8.2 2.8 6.7 1.7 1.2 1.2 2.7 25--35 21.8 19.1 29.3 14.7 15.6 9.8 10.9 9.7 12.4 3 5 - - 4 5 27.4 37.6 33.6 32 .9 37 .0 38.3 34.7 37 .7 35 .4 45 - -55 9.7 22.7 16.4 21 .0 17.0 27.7 27 .4 28.1 25 .5 55 - -65 9.7 2.8 9 .5 21.7 11.1 13,3 18.8 17 .4 16.3 65 - -75 1.6 1.4 0.9 3.5 4.4 4 .2 5.2 3.2 4.1 75- -85 2.4 0.0 0.4 2.1 5.2 2.4 1.7 1.6 1.8 85--95 0.0 0.0 0.0 0.0 1.5 1.2 0.2 0.5 0.4 > 9 5 0 .0 0.7 0 .0 0.7 1.4 0.9 0.5 0.4 0.4

M o d e o f trace w i d t h (o) 38 41 38 43 40 43 43 42 42

No. o f cases 128 141 232 143 135 592 1981 741 4 0 8 9

>_ 30

z

c> 20

I 0 213 30 40 50 60 70 80 90

WIDTH OF DIRECTION TRACF (o)

Fig. 2. Frequency distribution of direction trace widths for strong gusts at East Sale. The frequencies given are the numbers of gusts having widths within five degrees of the figure in the abscissa, expressed as percentages of the overall total number of gusts. Gusts from al l d i r e c t i o n s a r e i n c l u d e d .

In Fig. 2 there is a sugges t ion o f a s e c o n d a r y m o d e near 56 °. In the results for m o s t o f the individual d irec t ion sectors there is a s imilar sugges t ion , and in the cases o f the s o u t h e a s t and nor th sec tors it is quite p r o n o u n c e d . A brief e x a m i n a t i o n o f the gusts in the s o u t h e a s t s ec tor s h o w e d a t e n d e n c y , t h o u g h n o t a m a r k e d one , for s trong gusts t o be assoc iated wi th w ide d irec t ion traces, i.e., w i th v igorous turbu lence , as m i g h t have been ant ic ipated . Thus , the s e c o n d a r y m o d e o f d irec t ion trace w i d t h s m i g h t be assoc ia ted w i t h a strong- er gioup of gusts thml the pr imary m o d e . Ap~,~t f r o m this, its impl i ca t ions have n o t been cons idered .

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Factors affecting the uncertainty of gust direction

A t the observing site The spread of the direction trace into a band of variable width is due to

the rapid variations of wind direction associated with turbulence. In the past, as already noted, it has been customary to at tr ibute the gust to the direction corresponding to the centre of the direction trace, but this may not be justifiable.

If a maximum gust of a given strength embedded in a wind from a partic- ular direction is regarded as one member of a large ensemble of such gusts, it might be expected that the directions of the gusts in the ensemble would have a statistical distribution across the recorded direction trace. If this distribution were to have a maximum near the centre of the trace, taking the centre as giving the gust direction would seem an appropriate procedure for many purposes -- although when using the gust observations for estimating directional extreme gusts it would still be necessary to keep in mind the finite probabili ty that the gust was allocated to a wrong sector. In general, however, the distribution is not known. For the case of maximum gusts in strong general wind streams, the gusts would be due to downward turbulent transport of momentum from a higher layer where the mean wind is stronger. In the southern hemisphere the wind (under turbulent conditions) usually turns anticlockwise with height so the distribution would probably be skew- ed towards the bo t tom (low azimuth angle) side of the direction trace. For thunderstorm gusts it is not clear what to expect in the way of a statistical distribution. However, thunderstorm outflows can exhibit large variations in direction over quite short distances [4] , with corresponding large differ- ences in the direction change from the preceding regional wind, so that a given gust might well correspond to any part of the recorded direction trace.

At times, the wind direction swings appreciably during the course of a strong gust. Such a gust would need to be at tr ibuted to all directions within the ambit of the swing. However, the swing would seldom cover the full width of the direction trace, so this is not likely to be an important consider- ation.

A t a different (construction) site When observed maximum gusts in particular direction sectors are used to

estimate long-term extreme values, the results are in practice applied not just to the observing site but to a considerable surrounding area, extending some- times to 100 km or more. This introduces uncertainties about the results in addition to those arising from the width of the direction trace.

For gusts embedded in strong wind streams, Wieringa [5] has remarked that station-measured values are not regionally representative, and this ap- plies to the measured direction as well as the speed. Local topography and roughness elements near the observing site are likely to influence not just the width of the direction trace, but also the distribution of strong gust direc-

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tions across the trace, and even the direction of the mean wind. Topography and roughness elements in the vicinity of the proposed construction site may have quite a different disturbing effect, and, unless the differences are ac- curately known, they will contr ibute to the uncertainty when results from the observing site are applied. The additional uncertainty would stem partly from the possible (but unknown) differences in variability of wind direction {width of direction trace), but more particularly from possible differences in the direction of the mean wind -- differences in the distribution of strong gusts across the direction trace would not add to the uncertainty already in- herent in the observing site trace width.

Some progress has been made towards removing these topography-related uncertainties. Frost et al. [6] examined the variability of wind direction (width of direction trace), and found a relationship with mean wind speed and surface roughness, but their results depended on unverified assumptions about the correlations between orthogonal velocity components , and must be regarded as giving first indications only of the real situation. Some workers have examined the effect of topography on the mean wind by using wind- tunnel models, though in the main they have considered the effects on wind speed rather than on wind direction. Baker [7] and Meroney [8] under took field measurements to investigate the reliability of such an approach, con- cluding that wind-tunnel investigations are useful when the horizontal dimensions of the topography involved are less than about 10 km, though the results must be received with a little caution. Meroney [8] found that the results for wind direction were less reliable than those for wind speed. The mathematical modelling approach is also applicable for investigations of the mean wind, but up to the present, models usable in practice have not been developed which are capable of providing reliable results in general complex terrain [9, 10] . Some interpolation methods have been developed for particular areas, and provide reasonably good results, bu t only when there are a number of observation sites in the vicinity [9] . In general, then, even when the best current knowledge is brought to bear, it is likely that some topography-related uncertainties will remain concerning the best way to infer a strong wind direction at a construction site from that at an ob- serving site. This is so especially if the two sites are widely separated and if the relevant topography is of a large scale, extending for over 10 km horizon- tally and hundreds of metres vertically.

Under strong wind conditions topographical disturbances to the mean wind direction do tend to be small, sometimes surprisingly small. This is illustrated for the Albury-Wodonga area (on the border of New South Wales and Victoria), one of the few regions where a dense network of observations is available, by Figs. 3 and 4. Thus, the problem is not as serious as it might at first appear. Nevertheless, significant site-to-site differences of mean wind direction, which would be difficult to predict, are observed. On both of the occasions shown in Figs. 3 and 4, for instance, winds measured at site G would be at tr ibuted to the wrong direction sector for use at site F or site R.

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Table 2 shows the frequencies o f s t rong winds and gales (lasting 2 h or more) observed in the d i f ferent direct ion sectors at Albury-Wodonga in the two years August 1975 to Ju ly 1977. Leaving on one side the fact tha t some sites were windier than others (which cou ld be unde r s tood in terms of their relative exposures) , there were clear indicat ions o f site-to-site differences in the direct ions preferred for s t rong winds. I f the wind measurements f rom one site, then, were to be used for calculating the direct ional wind stresses on a s t ructure at some o ther site, a l lowance wou ld have to be made for such differences. I f the observat ions at site N, for instance, were to be used in the

Fig. 3. Winds at low level measuring sites (10 m) at Albury-Wodonga at 3.00 p.m. on 25 October 1975.5.2 ~ indicates a wind in the direction of the arrow with speed 5.2 m s -1. The winds given are means over 2 h (from ref. 11).

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design of a s t ruc ture at site P, one necessary modi f i ca t ion wou ld be to ro ta te some nor thwes te r ly winds, with the gusts e m b e d d e d in them, in to the west sector. In s i tuat ions where there were no measured winds at the p roposed cons t ruc t ion site and where accurate mode l or theoret ical studies were im- pract icable or uneconomic , differences in the preferred direct ions for s t rong winds wou ld n o t be k n o w n bu t migh t be p resumed to exist, especially if the observing and cons t ruc t ion sites were a considerable distance apar t wi th dif- ferent ne ighbour ing t opog raphy . Fo r a conservative est imate o f ex t reme winds at the cons t ruc t ion site, then, it wou ld be necessary to t reat the ob-

cP I w / I

Fig. 4. Winds at low level measuring sites (10 m) at Albury-Wodonga at 3.00 pm on 4 March 1976. 5.2 t indicates a wind in the direction of the arrow with speed 5.2 m s -~. The winds given are means over 2 h (from ref. 11).

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TABLE 2

Frequency (%) of strong winds (10.8--17.1 m s -1) and of gales (17.2 m s -1 and over) by direction sector at Albury-Wodonga during the period August 1975 to July 1977. The frequencies given refer to strong winds and gales lasting 2 h or more and are expressed as percentages of all observations made at 3-h intervals (from ref. 11)

Site N NE E SE S SW W NW

A Strong winds 0.04 0.04 0.15 Gales 0.02

B Strong winds 0.15 0.05 Gales

D Strong winds 0.17 0.02 0.12 0.02 0.03 0.44 0.56 Gales 0.02 0.02 0.07

E Strong winds 0.02 0.12 0.07 0.04 Gales

F Strong winds 0.02 0.12 0.04 0.10 0.16 Gales

G Strong winds 0.02 0.02 0.03 0.36 0.09 0.24 0.14 Gales 0.03 0.02

L Strong winds 0.08 0.06 0.14 Gales

M Strong winds 0.07 0.21 0.07 Gales

N Strong winds 0.24 0.02 0.24 0.26 Gales 0.02

P Strong winds 0.41 0.39 0.09 Gales 0.03 0.02

Q Strong winds 0.02 0.02 0.08 0.04 Gales

R Strong winds 0.21 0.02 0.10 Gales

U Strong winds 0.06 0.20 0.16 Gales 0.02

s e rved gus t s as i f t h e y w e r e e m b e d d e d in w i n d s c o m i n g f r o m a n y w h e r e w i t h - in a r a n g e o f d i r e c t i o n s . T h e e f f e c t i v e u n c e r t a i n t y o f gus t d i r e c t i o n w o u l d be t h e t o t a l a n g u l a r w i d t h w h e n t h i s d i r e c t i o n r a n g e was a d d e d t o e a c h s ide o f t h e d i r e c t i o n t r a c e .

F o r t h e case o f d e s t r u c t i v e t h u n d e r s t o r m gus t s s o m e w h a t d i f f e r e n t c o n - s i d e r a t i o n s a p p l y . F u j i t a [ 4 ] , in his e x t e n s i v e s t u d i e s o f such w i n d s , f o u n d t h a t t h e y t e n d t o " f a n o u t " f r o m t h e r e g i o n w h e r e t h e d o w n d r a u g h t r e a c h e s t h e g r o u n d . O n o c c a s i o n , t h e v a r i a t i o n s in t h e d i r e c t i o n o f d e s t r u c t i v e w i n d s m a y be 90 ° o r m o r e o v e r a f ew k i l o m e t r e s , a n d v a r i a t i o n s o f 45 ° o r so a re f a i r l y c o m m o n . T h i s w o u l d i m p l y large d i f f e r e n c e s in t h e d i r e c t i o n o f a p a r t i c u l a r t h u n d e r s t o r m " g u s t " b e t w e e n t h e o b s e r v a t i o n s i t e a n d a f a i r l y c l o s e c o n s t r u c t i o n s i te . A c o n s t r u c t i o n s i te f u r t h e r a w a y w o u l d n o t e x p e r i - e n c e t h e s a m e t h u n d e r s t o r m o u t f l o w a t all . O v e r a la rge n u m b e r o f y e a r s i t m i g h t be e x p e c t e d t h a t s t r o n g t h u n d e r s t o r m d o w n d r a u g h t s o c c u r r i n g a t var i -

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ous localities in the general area would even out such differences, unless there were some topographical effect or land surface inhomogeneity which resulted in preferred localities for thunderstorm downdraughts. Usually, it would not be known whether there were such preferred localities so there is again an implied extension of the effective uncertainty of gust direction be- yond the limits of the direction trace.

Allowing for the uncertainty of gust direction

Allowance could be made for the uncertainty of gust direction by some kind of smoothing over the direction sectors. A possible approach would be to allocate particular gusts to all sectors into which the direction trace over- lapped. Each sector would have all the strong gusts to which it was "ent i t led" , although it would also have some which actually occurred in neighbouring sectors. If the annual maximum gusts in each sector were then found from the modified data and the Gumbel technique [12] applied to estimate ex- pected extreme gusts, the results should provide conservative estimates for the extreme gusts at the actual observing site. However, if the results were to be used for construction sites in a considerable area surrounding the observ- ing site, the considerations of the last section suggest that it would be advis- able to allocate each gust to an even wider range of directions. The available observations at Albury-Wodonga suggest that in such a locality a widening of 20 to 30 ° on each site of the direction trace might be suitable, but in other areas it is not clear how great the widening should be. In view of this uncertainty, and to save the very great labour involved in checking the direc- tion sectors overlapped by each strong gust, an appropriate procedure might be to regard the modal trace width (or perhaps the secondary modal width) as typical of all strong gusts and add a widening to this. Depending on the width of the direction sectors and the magnitude of the widening chosen, an ascertainable proportion of the gusts initially allocated to each sector would then also be allocated to the neighbouring sectors, and perhaps to the sectors beyond.

With the East Sale data such a procedure was adopted, the modal trace width of 42 ° being used, and the widening being taken as 24 ° . Thus the directional uncertainty became 90 ° , or 45 ° on either side of the recorded direction; and in the re-allocation each gust was given to its original sector and to both neighbouring sectors. Calculating expected extreme gusts with this modified data base was equivalent to using the original data with a sys- tem of overlapping 135 ° sectors spaced at 45 ° intervals. The expected ex- treme gusts found for 20 and 1000 year return periods are shown in Fig. 5, and compared with the gusts found using the original unmodified data base, i.e., using only the centre of the direction trace to give the direction of each observed gust. (20 and 1000 year return periods correspond roughly to the occurrence probabilities it is proposed to use for serviceability and ultimate limit state design in the new Australian design code [13] .)

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It may De seen that the results using the original unsmoothed data exhibit- ed a somewhat erratic variation from sector to sector, which was much re- duced in the results using the smoothed data. The erratic variation was su~rising in view of the topographical surroundings of the East Sale observ- ing site; in the immediate vicinity there are the mostly low buildings of the Air Force Base, and beyond them uniform flat open c o u n t ~ with only isolated farm buildings and trees extending for considerable distances in all directions. The erratic variation could be due to the sampling error associ- ated with the comparatively small number of years of data available (30 years). Such sampling errors can be quite large [14], and the smoothing procedure used might well have reduced them. However, errors arising from the uncertainty of gust direction were almost certainly present, and it seems likely that they made at least a significant contribution to the erratic varia- tion, especially as the variation was greatly reduced by a smoothing proce- dure specifically designed to combat them.

E "'d. Z "'" i w

Nw , , . .

15 20 25 30 35 40 45 50

EXPECTED EXTREME GUST IN M/S

Fig. 5. Variat ion by di rect ion sector of expec ted ex t reme gusts for re turn periods of 20 years and 1000 years at East Sale. Values calculated for each sector using only the ob- served m a x i m u m gusts in the sec tor conce rned (i.e., for which the centre of the di rect ion trace fell wi th in tha t sector) are shown (× . . . . . × ), and values calculated using the an- nual max ima of gusts which occurred in the sector conce rned or in e i ther o f the neigh- bouring sectors (i.e., using overlapping 135 ° sectors) are shown (~ ; ).

SE

S

G sw

For the sectors north, southeast and west the 1000 year return gusts esti- mated with smoothing were less than those estimated without smoothing, suggesting perhaps that the smoothing procedure is not conservative. How- ever, for these three sectors the estimates without smoothing were based on a Gumbel line with a slope considerably greater than that for global (all

165

directions combined) gusts, and were therefore probably anomalous. Anom- alies of this type, which yield estimated directional extreme gusts for long return periods greater than the estimated global gusts, will be discussed in a forthcoming paper. The anomalies may be attributed to an effect not related to directional uncertainty, but, as may be seen by comparing the data in Fig. 5 with the estimated global gusts at East Sale for return periods of 20 years and 1000 years (32.5 and 44.0 m s -1, respectively), the smoothing proce- dure described here had the side effect of reducing them.

C o n c l u s i o n

The direction trace produced by a standard anemograph has a consider- able but variable width due to the rapid turbulent variations of wind direc- tion. For the Dines anemograph at East Sale, Victoria, it was found that the frequency distribution of direction trace widths corresponding to strong gusts did not vary much from one direction sector to another, and had for each sector a well-marked mode close to 42 °.

The width of a direction trace implies an uncertainty as to the appropriate direction sectors for strong gusts, and a consequent uncertainty about the expected extreme gusts calculated for particular sectors. When the expected extreme gusts are to be used for wide areas surrounding the observing site, as is usually the case, a further uncertainty is often added due to possible systematic areal variations in the directions of strong winds.

At East Sale the directional expected extreme gusts calculated without allowing for directional uncertainty showed an irregular sector-to-sector variation. Allocation of gusts to wrong sectors seems a possible cause. When allowance was made for the uncertainty of gust direction by using a smooth- ing technique, the irregularities were greatly reduced.

Acknowledgements

This paper is published with the permission of the Director of Meteorol- ogy. The author is indebted to his colleague Ms. J.I. Templeton for her help, and in particular for writing and running the computer programs used in analysing the data. Various other colleagues made fruitful suggestions, in particular Mr. E. Jesson, various of the participants in the Workshop on Wind Engineering and Industrial Aerodynamics held at Highett, Victoria, 3--5 July 1984, and a reviewer. Thanks are due also to Mr. E. Roache, Mr. L. Jennings- Fox, and Ms. L. Kuilboer for doing the arduous work of data extraction.

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2 W.H. Melbourne, Designing for wind speed and direction, in The Structural and En- vironmental Effects of Wind on Buildings and Structures, Course Notes, Monash Uni- versity, Melbourne, 1984, Chap. 20.

3 W.W. Moriarty and J.I. Templeton, On the estimation of extreme gusts by direction sector, J. Wind Eng. Ind. Aerodyn., 13 (1983) 127--138.

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8 R.N. Meroney, Wind-tunnel simulation of the flow over hills and complex terrain, J. Ind. Aerodyn., 5 (1980) 297--321.

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12 E.J. Gumbel, Statistical theory of extreme values and some practical applications, Applied Mathematics Series No. 33, National Bureau of Standards, Washington, DC, 1954.

13 J.D. Holmes, Wind loads and limit state design, Civil Engineering Transactions, Insti- tute of Engineers of Australia, CE27, 1985, pp. 21--26.

14 C.M.L. Dorman, Extreme wind gust speeds in Australia, excluding tropical cyclones, Civil Engineering Transactions, Institute of Engineers of Australia, CE18, 1983, pp. 96--106.