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On the directional uncertainty of strong wind gusts
Journal o f Wind Engineering and Industrial Aerodynamics, 21 (1985) 155--166
155
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
ON THE DIRECTIONAL UNCERTAINTY OF STRONG WIND GUSTS
w.w. MORIARTY Bureau o f Meteorology, G.P.O. B o x 1289K,, Melbourne 3001 (Australia)
(Received December 14, 1985)
Summary 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 applied 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-tosector variations in the estimated directional extreme gusts.
Introduction R e c e n t l y , t h e r e has b e e n an increasing r e q u i r e m e n t f o r e s t i m a t e s o f ext r e m e w i n d s f o r building design t o b e p r o v i d e d b y d i r e c t i o n s e c t o r , a n d eff o r t s h a v e b e e n m a d e t o p r o v i d e such d a t a [1, 2 ] . H o w e v e r , t h e e s t i m a t e s m a d e h a v e h a d t o d e p e n d o n w i n d r e c o r d s k e p t o v e r p a s t years. M o s t such r e c o r d s h a v e b e e n m a d e w i t h a u t o g r a p h i c i n s t r u m e n t s w h i c h , as t h e i r c h a r t s p e e d was slow c o m p a r e d t o t h e t u r b u l e n t f l u c t u a t i o n s o f w i n d d i r e c t i o n , h a v e l e f t a d i r e c t i o n t r a c e c o n s i s t i n g o f a b r o a d b a n d o f variable w i d t h {Fig. 1). T h e w i d t h o f this b a n d r e p r e s e n t s a n u n c e r t a i n t y as t o t h e precise direct i o n of a r e c o r d e d s t r o n g gust. T h e m a g n i t u d e o f t h e u n c e r t a i n t y has b e e n discussed briefly f o r a p a r t i c u l a r o b s e r v i n g site using a Dines a n e m o g r a p h {East Sale, V i c t o r i a , A u s t r a l i a ) in a p r e v i o u s p a p e r [ 3 ] . In t h e p r e s e n t p a p e r it is p r o p o s e d t o c o n s i d e r this u n c e r t a i n t y a n d an a d d i t i o n a l u n c e r t a i n t y w h i c h arises w h e n o b s e r v e d d i r e c t i o n a l gusts are used t o e s t i m a t e e x t r e m e w i n d s f o r use o v e r a b r o a d s u r r o u n d i n g area. A n a p p r o a c h to o v e r c o m i n g t h e a s s o c i a t e d p r o b l e m s will t h e n b e suggested.
Directional uncertainties of maximum gusts at East Sale T h e d a t a originally o b t a i n e d f o r E a s t Sale [3] w e r e t h e d i r e c t i o n t r a c e w i d t h s c o r r e s p o n d i n g t o t h e daily m a x i m u m gusts in each o f e i g h t d i r e c t i o n
0167-6105/85/$03,30
© 1985 Elsevier Science Publishers B.V.
156
Fig. 1. S e c t i o n of t h e Dines A n e m o g r a p h trace f r o m East Sale for 26 N o v e m b e r 1 9 7 8 , s h o w i n g t h e variable w i d t h o f t h e d i r e c t i o n trace. T h e parts of t h e d i r e c t i o n trace corres p o n d i n g t o t h e t h r e e s t r o n g e s t gusts are i n d i c a t e d by d a s h e d lines ( t h e r e was a slight offset b e t w e e n t h e speed a n d d i r e c t i o n traces, a t y p e of i n s t r u m e n t a l e r r o r w h i c h appears at times).
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 f o u n d t hat for some sectors (particularly n o r t h and northeast) there were some years with no gusts over 15 m s-1, and in such cases the present study was e x t e n d e d to include daily maxima over 10 m s-1. The present study also included an extra year of data {1981). The data are n o t hom oge ne ous in that n o 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 t hat 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 f o u n d for each of the various direction sectors are set o u t in Table 1. Figure 2 shows the results for all directions co mb i ne d in graphical form. The typical (modal) width of the direction trace did n o 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 m a x i m u m gust would in the great majority of cases allow the possibility t hat the gust should have been allocated to a neighbouring sector. Such uncertainties might in turn cast considerable d o u b t on the results when the data are used t o estimate long-term directional e x t r e m e gusts.
157 TABLE 1 F r e q u e n c y (%) o f d i r e c t i o n trace w i d t h s for s t r o n g daily m a x i m u m g u s t s at E a s t Sale in t h e y e a r s 1 9 5 2 - - 1 9 8 1 , Daily m a x i m u m g u s t s f o r e a c h s e c t o r g r e a t e r t h a n 15 m s -l are i n c l u d e d , a n d , w h e n t h e r e w e r e n o s u c h g u s t s in a s e c t o r f o r a y e a r , daily m a x i m a s t r o n g e r 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 w a s e s t i m a t e d g r a p h i c a l l y f r o m t h e d a t a in t h e t a b l e W i d t h o f dirn. trace (o)
Direction sector N NE
E
SE
S
SW
W
NW
All
0--15 15--25 25--35 35--45 45--55 55--65 65--75 75--85 85--95 >95
12.1 15.3 21.8 27.4 9.7 9.7 1.6 2.4 0.0 0.0
2.1 12.8 19.1 37.6 22.7 2.8 1.4 0.0 0.0 0.7
1.7 8.2 29.3 33.6 16.4 9.5 0.9 0.4 0.0 0.0
0.7 2.8 14.7 32.9 21.0 21.7 3.5 2.1 0.0 0.7
0.0 6.7 15.6 37.0 17.0 11.1 4.4 5.2 1.5 1.4
0.5 1.7 9.8 38.3 27.7 13,3 4.2 2.4 1.2 0.9
0.0 1.2 10.9 34.7 27.4 18.8 5.2 1.7 0.2 0.5
0.I 1.2 9.7 37.7 28.1 17.4 3.2 1.6 0.5 0.4
0.7 2.7 12.4 35.4 25.5 16.3 4.1 1.8 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
128
141
232
143
135
592
1981
741
4089
No. o f cases
>_
30
z c>
20
I0
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 all d i r e c t i o n s
are included.
In Fig. 2 there is a s u g g e s t i o n o f a s e c o n d a r y m o d e near 56 °. In t h e results f o r m o s t o f t h e individual d i r e c t i o n sectors there is a similar s u g g e s t i o n , and in t h e cases o f t h e s o u t h e a s t and n o r t h s e c t o r s 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 t h e gusts in t h e s o u t h e a s t s e c t o r 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 o n e , f o r strong gusts t o be a s s o c i a t e d w i t h w i d e d i r e c t i o n traces, i.e., w i t h v i g o r o u s t u r b u l e n c e , as m i g h t have b e e n anticipated. T h u s , the s e c o n d a r y m o d e o f d i r e c t i o n trace w i d t h s m i g h t be a s s o c i a t e d w i t h a stronger gioup o f gusts thml t h e primary m o d e . Ap~,~t f r o m this, its i m p l i c a t i o n s have n o t b e e n c o n s i d e r e d .
158
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 attribute the gust to the direction corresponding to the centre of the direction trace, but this may not be justifiable. If a m a x i m u m gust of a given strength e m b e d d e d in a wind from a particular direction is regarded as one m e m b e r of a large ensemble of such gusts, it might be ex p ect ed 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 m a xi m um 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 probability that the gust was allocated to a wrong sector. In general, however, the distribution is n o t known. For the case o f m a x i m u m gusts in strong general wind streams, the gusts would be due to dow nw ard t urbul ent transport of m o m e n t u m from a higher layer where the mean wind is stronger. In the southern hemisphere the wind (under t u r b u l e n t conditions) usually turns anticlockwise with height so the distribution would probably be skewed towards the b o t t o m (low azimuth angle) side of the direction trace. For t h un d er s to r m gusts it is n o t clear what to expect in the way of a statistical distribution. However, t hunde r s t or m outflows can exhibit large variations in direction over quite short distances [ 4 ] , with corresponding large differences 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 o f a strong gust. Such a gust would need to be attributed to all directions within the ambit o f the swing. However, the swing would seldom cover the full width of the direction trace, so this is n o t likely to be an i m p o r t a n t consideration. A t a different (construction) site When observed m a xi m um gusts in particular direction sectors are used to estimate long-term e x t r e m e values, the results are in practice applied n o t just to the observing site but to a considerable surrounding area, extending sometimes to 100 km or more. This introduces uncertainties a b o u t the results in addition to those arising from the width of the direction trace. F o r gusts e m b e d d e d in strong wind streams, Wieringa [5] has remarked that station-measured values are n o t regionally representative, and this applies to the measured direction as well as the speed. Local t o p o g r a p h y and roughness elements near the observing site are likely to influence n o t just the width o f the direction trace, but also the distribution of strong gust direc-
159
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 accurately known, they will contribute 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), b u t 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 inherent 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 a b o u t 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 windtunnel models, though in the main they have considered the effects on wind speed rather than on wind direction. Baker [7] and Meroney [8] undertook field measurements to investigate the reliability of such an approach, concluding 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, b u 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 observing 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 horizontally 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 n o t 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 attributed to the wrong direction sector for use at site F or site R.
160
Table 2 shows the frequencies o f strong winds and gales (lasting 2 h o r m o r e ) observed in the d i f f e r e n t direction sectors at A l b u r y - W o d o n g a in the t w o years A u g u s t 1 9 7 5 t o J u l y 1 9 7 7 . Leaving o n one side the fact t h a t some sites were windier t h a n o t h e r s (which c o u l d be u n d e r s t o o d in terms o f their relative exposures), there were clear indications o f site-to-site differences in the directions p r e f e r r e d f o r s t r o n g winds. I f the w i n d m e a s u r e m e n t s f r o m one site, t h e n , were t o be used f o r calculating the directional w i n d stresses o n a s t r u c t u r e at some o t h e r site, allowance w o u l d have t o be m a d e for such differences. I f t h e o b s e r v a t i o n s at site N, f o r instance, were t o 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).
161 design o f a s t r u c t u r e at site P, o n e necessary m o d i f i c a t i o n w o u l d be to r o t a t e some n o r t h w e s t e r l y winds, with the gusts e m b e d d e d in t h e m , i n t o the west sector. In s i t u a t i o n s w h e r e t h e r e were n o m e a s u r e d winds at the p r o p o s e d c o n s t r u c t i o n site a n d w h e r e a c c u r a t e m o d e l or t h e o r e t i c a l studies were impracticable or u n e c o n o m i c , differences in the p r e f e r r e d d i r e c t i o n s f o r s t r o n g winds w o u l d n o t be k n o w n b u t m i g h t be p r e s u m e d t o exist, especially if the observing a n d c o n s t r u c t i o n sites were a considerable distance a p a r t w i t h diff e r e n t n e i g h b o u r i n g t o p o g r a p h y . F o r a conservative estimate o f e x t r e m e winds at the c o n s t r u c t i o n site, t h e n , it w o u l d be necessary t o t r e a t the ob-
cP Iw/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).
162 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 A B D E F G L M N P Q R U
N Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales
NE
E
SE
winds
0.04
winds
0.15
W
NW
0.04
0.15 0.02 0.05
0.03
0.44 0.02 0.07
0.56 0.07 0.04
0.17
winds
0.02
0.12 0.02 0.12
winds
0.02
0.12
0.04
0.10
0.16
winds
0.02
0.09
0.24 0.02 0.06
0.14
winds
0.36 0.03 0.08
0.14
winds
0.07
0.21
0.07
winds
0.02
0.24
0.26
0.02
0.39 0.02 0.08
0.09
winds
0.24 0.02 0.41 0.03 0.02
0.04
winds
0.21
0.02
0.10
winds
0.06
0.02
0.03
0.02
SW
winds
winds
0.02
S
0.20 0.02
0.16
s e r v e d g u s t s as if 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 g u s t d i r e c t i o n w o u l d b e the total angular width when this direction range was added to each side of the direction trace. For the case of destructive thunderstorm gusts somewhat different cons 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 s u c h w i n d s , f o u n d that they tend to "fan out" from the region where the downdraught reaches 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 b e 9 0 ° o r m o r e o v e r a f e w 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 4 5 ° o r so a r e 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 particular thunderstorm "gust" between the observation site and a fairly c l o s e c o n s t r u c t i o n s i t e . A c o n s t r u c t i o n site 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 l a r g e n u m b e r o f y e a r s it m i g h t b e 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 vari-
163 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 n o t be k n o w n whether there were such preferred localities so there is again an implied extension of the effective uncertainty of gust direction bey o n d 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 overlapped. Each sector would have all the strong gusts to which it was " e n t i t l e d " , although it would also have some which actually occurred in neighbouring sectors. If the annual m a x i m u m gusts in each sector were then f o u n d from the modified data and the Gumbel technique [12] applied to estimate expected 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 observing site, the considerations of the last section suggest that it would be advisable 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 n o t clear how great the widening should be. In view of this uncertainty, and to save the very great labour involved in checking the direction 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 system of overlapping 135 ° sectors spaced at 45 ° intervals. The expected extreme gusts f o u n d 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] .)
164 It may De seen that the results using the original u n s m o o t h e d data exhibited a somewhat erratic variation from sector to sector, which was much reduced in the results using the smoothed data. The erratic variation was su~rising in view of the topographical surroundings of the East Sale observing 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 associated 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 variation, especially as the variation was greatly reduced by a smoothing procedure specifically designed to combat them.
E
"'d.
SE
G
Z "'"
iw
S
sw
,,..
Nw
15
20
25
30
35
40
45
50
EXPECTED EXTREMEGUSTIN M/S
Fig. 5. Variation by d i r e c t i o n s e c t o r o f e x p e c t e d e x t r e m e gusts for r e t u r n periods o f 20 years a n d 1000 years at East Sale. Values calculated for each s e c t o r using o n l y the observed m a x i m u m gusts in t h e s e c t o r c o n c e r n e d (i.e., for w h i c h the c e n t r e o f the d i r e c t i o n trace fell w i t h i n t h a t s e c t o r ) are s h o w n (× . . . . . × ), and values calculated using t h e annual m a x i m a o f gusts w h i c h o c c u r r e d in t h e s e c t o r c o n c e r n e d or in either o f t h e neighb o u r i n g sectors (i.e., using overlapping 135 ° sectors) are s h o w n (~ ; ).
For the sectors north, southeast and west the 1000 year return gusts estimated with smoothing were less than those estimated w i t h o u t smoothing, suggesting perhaps that the smoothing procedure is not conservative. However, for these three sectors the estimates w i t h o u t 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. Anomalies 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 n o t 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 procedure described here had the side effect of reducing them. Conclusion
The direction trace produced by a standard anemograph has a considerable but variable width due to the rapid turbulent variations of wind direction. For the Dines anemograph at East Sale, Victoria, it was f o u n d that the frequency distribution of direction trace widths corresponding to strong gusts did n o t 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 w i t h o u t 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 smoothing technique, the irregularities were greatly reduced. Acknowledgements This paper is published with the permission of the Director of Meteorology. 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. JenningsFox, and Ms. L. Kuilboer for doing the arduous work of data extraction.
References 1 E. Simiu and J.J. Filliben, Wind direction effects on cladding and structural loads, Eng. Struct., 3 (1981) 181--186.
166 2 W.H. Melbourne, Designing for wind speed and direction, in The Structural and Environmental Effects of Wind on Buildings and Structures, Course Notes, Monash University, 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. 4 T.T. Fujita, Manual of downburst identification for Project Nimrod, SMRP Research Pap. No. 156, Department of Geophysical Sciences, University of Chicago, 1978. 5 J. Wieringa, Comment on paper by W.W. Moriarty and J.I. Templeton, J. Wind Eng. Ind. Aerodyn., 13 (1983) 157. 6 W. Frost, D. Keopf and R.E. Turner, Wind velocity directional fluctuation prediction model, J. Wind Eng. Ind. Aerodyn., 7 (1981) 311--330. 7 C.J. Baker, Determination of topographical exposure factors in complicated hilly terrain, J. Wind Eng. Ind. Aerodyn., 17 (1984) 239--249. 8 R.N. Meroney, Wind-tunnel simulation of the flow over hills and complex terrain, J. Ind. Aerodyn., 5 (1980) 297--321. 9 J.C.R. Hunt and K.J. Richards, Stratified airflow over one or two hills, Boundary Layer Meterol., 30 (1984) 223--260. 10 U. H6gstrSm and A.-S. Smedman-H6gstr6m, The wind regime in coastal areas with specific reference to results obtained from the Swedish Wind Energy Program, Boundary Layer Meterol., 30 (1984) 351--374. 11 W.W. Moriarty, Survey of low level winds and air dispersion characteristics of the A1bury-Wodonga area, Bureau of Meteorology Bull. 50, Australia Government Publishing Service, Canberra, A.C.T., 1980, pp. 14--34. 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, Institute 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.
155
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
ON THE DIRECTIONAL UNCERTAINTY OF STRONG WIND GUSTS
w.w. MORIARTY Bureau o f Meteorology, G.P.O. B o x 1289K,, Melbourne 3001 (Australia)
(Received December 14, 1985)
Summary 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 applied 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-tosector variations in the estimated directional extreme gusts.
Introduction R e c e n t l y , t h e r e has b e e n an increasing r e q u i r e m e n t f o r e s t i m a t e s o f ext r e m e w i n d s f o r building design t o b e p r o v i d e d b y d i r e c t i o n s e c t o r , a n d eff o r t s h a v e b e e n m a d e t o p r o v i d e such d a t a [1, 2 ] . H o w e v e r , t h e e s t i m a t e s m a d e h a v e h a d t o d e p e n d o n w i n d r e c o r d s k e p t o v e r p a s t years. M o s t such r e c o r d s h a v e b e e n m a d e w i t h a u t o g r a p h i c i n s t r u m e n t s w h i c h , as t h e i r c h a r t s p e e d was slow c o m p a r e d t o t h e t u r b u l e n t f l u c t u a t i o n s o f w i n d d i r e c t i o n , h a v e l e f t a d i r e c t i o n t r a c e c o n s i s t i n g o f a b r o a d b a n d o f variable w i d t h {Fig. 1). T h e w i d t h o f this b a n d r e p r e s e n t s a n u n c e r t a i n t y as t o t h e precise direct i o n of a r e c o r d e d s t r o n g gust. T h e m a g n i t u d e o f t h e u n c e r t a i n t y has b e e n discussed briefly f o r a p a r t i c u l a r o b s e r v i n g site using a Dines a n e m o g r a p h {East Sale, V i c t o r i a , A u s t r a l i a ) in a p r e v i o u s p a p e r [ 3 ] . In t h e p r e s e n t p a p e r it is p r o p o s e d t o c o n s i d e r this u n c e r t a i n t y a n d an a d d i t i o n a l u n c e r t a i n t y w h i c h arises w h e n o b s e r v e d d i r e c t i o n a l gusts are used t o e s t i m a t e e x t r e m e w i n d s f o r use o v e r a b r o a d s u r r o u n d i n g area. A n a p p r o a c h to o v e r c o m i n g t h e a s s o c i a t e d p r o b l e m s will t h e n b e suggested.
Directional uncertainties of maximum gusts at East Sale T h e d a t a originally o b t a i n e d f o r E a s t Sale [3] w e r e t h e d i r e c t i o n t r a c e w i d t h s c o r r e s p o n d i n g t o t h e daily m a x i m u m gusts in each o f e i g h t d i r e c t i o n
0167-6105/85/$03,30
© 1985 Elsevier Science Publishers B.V.
156
Fig. 1. S e c t i o n of t h e Dines A n e m o g r a p h trace f r o m East Sale for 26 N o v e m b e r 1 9 7 8 , s h o w i n g t h e variable w i d t h o f t h e d i r e c t i o n trace. T h e parts of t h e d i r e c t i o n trace corres p o n d i n g t o t h e t h r e e s t r o n g e s t gusts are i n d i c a t e d by d a s h e d lines ( t h e r e was a slight offset b e t w e e n t h e speed a n d d i r e c t i o n traces, a t y p e of i n s t r u m e n t a l e r r o r w h i c h appears at times).
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 f o u n d t hat for some sectors (particularly n o r t h and northeast) there were some years with no gusts over 15 m s-1, and in such cases the present study was e x t e n d e d to include daily maxima over 10 m s-1. The present study also included an extra year of data {1981). The data are n o t hom oge ne ous in that n o 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 t hat 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 f o u n d for each of the various direction sectors are set o u t in Table 1. Figure 2 shows the results for all directions co mb i ne d in graphical form. The typical (modal) width of the direction trace did n o 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 m a x i m u m gust would in the great majority of cases allow the possibility t hat the gust should have been allocated to a neighbouring sector. Such uncertainties might in turn cast considerable d o u b t on the results when the data are used t o estimate long-term directional e x t r e m e gusts.
157 TABLE 1 F r e q u e n c y (%) o f d i r e c t i o n trace w i d t h s for s t r o n g daily m a x i m u m g u s t s at E a s t Sale in t h e y e a r s 1 9 5 2 - - 1 9 8 1 , Daily m a x i m u m g u s t s f o r e a c h s e c t o r g r e a t e r t h a n 15 m s -l are i n c l u d e d , a n d , w h e n t h e r e w e r e n o s u c h g u s t s in a s e c t o r f o r a y e a r , daily m a x i m a s t r o n g e r 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 w a s e s t i m a t e d g r a p h i c a l l y f r o m t h e d a t a in t h e t a b l e W i d t h o f dirn. trace (o)
Direction sector N NE
E
SE
S
SW
W
NW
All
0--15 15--25 25--35 35--45 45--55 55--65 65--75 75--85 85--95 >95
12.1 15.3 21.8 27.4 9.7 9.7 1.6 2.4 0.0 0.0
2.1 12.8 19.1 37.6 22.7 2.8 1.4 0.0 0.0 0.7
1.7 8.2 29.3 33.6 16.4 9.5 0.9 0.4 0.0 0.0
0.7 2.8 14.7 32.9 21.0 21.7 3.5 2.1 0.0 0.7
0.0 6.7 15.6 37.0 17.0 11.1 4.4 5.2 1.5 1.4
0.5 1.7 9.8 38.3 27.7 13,3 4.2 2.4 1.2 0.9
0.0 1.2 10.9 34.7 27.4 18.8 5.2 1.7 0.2 0.5
0.I 1.2 9.7 37.7 28.1 17.4 3.2 1.6 0.5 0.4
0.7 2.7 12.4 35.4 25.5 16.3 4.1 1.8 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
128
141
232
143
135
592
1981
741
4089
No. o f cases
>_
30
z c>
20
I0
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 all d i r e c t i o n s
are included.
In Fig. 2 there is a s u g g e s t i o n o f a s e c o n d a r y m o d e near 56 °. In t h e results f o r m o s t o f t h e individual d i r e c t i o n sectors there is a similar s u g g e s t i o n , and in t h e cases o f t h e s o u t h e a s t and n o r t h s e c t o r s 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 t h e gusts in t h e s o u t h e a s t s e c t o r 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 o n e , f o r strong gusts t o be a s s o c i a t e d w i t h w i d e d i r e c t i o n traces, i.e., w i t h v i g o r o u s t u r b u l e n c e , as m i g h t have b e e n anticipated. T h u s , the s e c o n d a r y m o d e o f d i r e c t i o n trace w i d t h s m i g h t be a s s o c i a t e d w i t h a stronger gioup o f gusts thml t h e primary m o d e . Ap~,~t f r o m this, its i m p l i c a t i o n s have n o t b e e n c o n s i d e r e d .
158
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 attribute the gust to the direction corresponding to the centre of the direction trace, but this may not be justifiable. If a m a x i m u m gust of a given strength e m b e d d e d in a wind from a particular direction is regarded as one m e m b e r of a large ensemble of such gusts, it might be ex p ect ed 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 m a xi m um 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 probability that the gust was allocated to a wrong sector. In general, however, the distribution is n o t known. For the case o f m a x i m u m gusts in strong general wind streams, the gusts would be due to dow nw ard t urbul ent transport of m o m e n t u m from a higher layer where the mean wind is stronger. In the southern hemisphere the wind (under t u r b u l e n t conditions) usually turns anticlockwise with height so the distribution would probably be skewed towards the b o t t o m (low azimuth angle) side of the direction trace. For t h un d er s to r m gusts it is n o t clear what to expect in the way of a statistical distribution. However, t hunde r s t or m outflows can exhibit large variations in direction over quite short distances [ 4 ] , with corresponding large differences 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 o f a strong gust. Such a gust would need to be attributed to all directions within the ambit o f the swing. However, the swing would seldom cover the full width of the direction trace, so this is n o t likely to be an i m p o r t a n t consideration. A t a different (construction) site When observed m a xi m um gusts in particular direction sectors are used to estimate long-term e x t r e m e values, the results are in practice applied n o t just to the observing site but to a considerable surrounding area, extending sometimes to 100 km or more. This introduces uncertainties a b o u t the results in addition to those arising from the width of the direction trace. F o r gusts e m b e d d e d in strong wind streams, Wieringa [5] has remarked that station-measured values are n o t regionally representative, and this applies to the measured direction as well as the speed. Local t o p o g r a p h y and roughness elements near the observing site are likely to influence n o t just the width o f the direction trace, but also the distribution of strong gust direc-
159
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 accurately known, they will contribute 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), b u t 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 inherent 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 a b o u t 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 windtunnel models, though in the main they have considered the effects on wind speed rather than on wind direction. Baker [7] and Meroney [8] undertook field measurements to investigate the reliability of such an approach, concluding 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, b u 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 observing 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 horizontally 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 n o t 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 attributed to the wrong direction sector for use at site F or site R.
160
Table 2 shows the frequencies o f strong winds and gales (lasting 2 h o r m o r e ) observed in the d i f f e r e n t direction sectors at A l b u r y - W o d o n g a in the t w o years A u g u s t 1 9 7 5 t o J u l y 1 9 7 7 . Leaving o n one side the fact t h a t some sites were windier t h a n o t h e r s (which c o u l d be u n d e r s t o o d in terms o f their relative exposures), there were clear indications o f site-to-site differences in the directions p r e f e r r e d f o r s t r o n g winds. I f the w i n d m e a s u r e m e n t s f r o m one site, t h e n , were t o be used f o r calculating the directional w i n d stresses o n a s t r u c t u r e at some o t h e r site, allowance w o u l d have t o be m a d e for such differences. I f t h e o b s e r v a t i o n s at site N, f o r instance, were t o 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).
161 design o f a s t r u c t u r e at site P, o n e necessary m o d i f i c a t i o n w o u l d be to r o t a t e some n o r t h w e s t e r l y winds, with the gusts e m b e d d e d in t h e m , i n t o the west sector. In s i t u a t i o n s w h e r e t h e r e were n o m e a s u r e d winds at the p r o p o s e d c o n s t r u c t i o n site a n d w h e r e a c c u r a t e m o d e l or t h e o r e t i c a l studies were impracticable or u n e c o n o m i c , differences in the p r e f e r r e d d i r e c t i o n s f o r s t r o n g winds w o u l d n o t be k n o w n b u t m i g h t be p r e s u m e d t o exist, especially if the observing a n d c o n s t r u c t i o n sites were a considerable distance a p a r t w i t h diff e r e n t n e i g h b o u r i n g t o p o g r a p h y . F o r a conservative estimate o f e x t r e m e winds at the c o n s t r u c t i o n site, t h e n , it w o u l d be necessary t o t r e a t the ob-
cP Iw/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).
162 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 A B D E F G L M N P Q R U
N Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales Strong Gales
NE
E
SE
winds
0.04
winds
0.15
W
NW
0.04
0.15 0.02 0.05
0.03
0.44 0.02 0.07
0.56 0.07 0.04
0.17
winds
0.02
0.12 0.02 0.12
winds
0.02
0.12
0.04
0.10
0.16
winds
0.02
0.09
0.24 0.02 0.06
0.14
winds
0.36 0.03 0.08
0.14
winds
0.07
0.21
0.07
winds
0.02
0.24
0.26
0.02
0.39 0.02 0.08
0.09
winds
0.24 0.02 0.41 0.03 0.02
0.04
winds
0.21
0.02
0.10
winds
0.06
0.02
0.03
0.02
SW
winds
winds
0.02
S
0.20 0.02
0.16
s e r v e d g u s t s as if 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 g u s t d i r e c t i o n w o u l d b e the total angular width when this direction range was added to each side of the direction trace. For the case of destructive thunderstorm gusts somewhat different cons 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 s u c h w i n d s , f o u n d that they tend to "fan out" from the region where the downdraught reaches 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 b e 9 0 ° o r m o r e o v e r a f e w 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 4 5 ° o r so a r e 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 particular thunderstorm "gust" between the observation site and a fairly c l o s e c o n s t r u c t i o n s i t e . A c o n s t r u c t i o n site 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 l a r g e n u m b e r o f y e a r s it m i g h t b e 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 vari-
163 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 n o t be k n o w n whether there were such preferred localities so there is again an implied extension of the effective uncertainty of gust direction bey o n d 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 overlapped. Each sector would have all the strong gusts to which it was " e n t i t l e d " , although it would also have some which actually occurred in neighbouring sectors. If the annual m a x i m u m gusts in each sector were then f o u n d from the modified data and the Gumbel technique [12] applied to estimate expected 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 observing site, the considerations of the last section suggest that it would be advisable 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 n o t clear how great the widening should be. In view of this uncertainty, and to save the very great labour involved in checking the direction 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 system of overlapping 135 ° sectors spaced at 45 ° intervals. The expected extreme gusts f o u n d 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] .)
164 It may De seen that the results using the original u n s m o o t h e d data exhibited a somewhat erratic variation from sector to sector, which was much reduced in the results using the smoothed data. The erratic variation was su~rising in view of the topographical surroundings of the East Sale observing 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 associated 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 variation, especially as the variation was greatly reduced by a smoothing procedure specifically designed to combat them.
E
"'d.
SE
G
Z "'"
iw
S
sw
,,..
Nw
15
20
25
30
35
40
45
50
EXPECTED EXTREMEGUSTIN M/S
Fig. 5. Variation by d i r e c t i o n s e c t o r o f e x p e c t e d e x t r e m e gusts for r e t u r n periods o f 20 years a n d 1000 years at East Sale. Values calculated for each s e c t o r using o n l y the observed m a x i m u m gusts in t h e s e c t o r c o n c e r n e d (i.e., for w h i c h the c e n t r e o f the d i r e c t i o n trace fell w i t h i n t h a t s e c t o r ) are s h o w n (× . . . . . × ), and values calculated using t h e annual m a x i m a o f gusts w h i c h o c c u r r e d in t h e s e c t o r c o n c e r n e d or in either o f t h e neighb o u r i n g sectors (i.e., using overlapping 135 ° sectors) are s h o w n (~ ; ).
For the sectors north, southeast and west the 1000 year return gusts estimated with smoothing were less than those estimated w i t h o u t smoothing, suggesting perhaps that the smoothing procedure is not conservative. However, for these three sectors the estimates w i t h o u t 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. Anomalies 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 n o t 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 procedure described here had the side effect of reducing them. Conclusion
The direction trace produced by a standard anemograph has a considerable but variable width due to the rapid turbulent variations of wind direction. For the Dines anemograph at East Sale, Victoria, it was f o u n d that the frequency distribution of direction trace widths corresponding to strong gusts did n o t 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 w i t h o u t 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 smoothing technique, the irregularities were greatly reduced. Acknowledgements This paper is published with the permission of the Director of Meteorology. 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. JenningsFox, and Ms. L. Kuilboer for doing the arduous work of data extraction.
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