Full scale measurements of gust factors and turbulence intensity, and their relations in hilly terrain

JOURNALOF

ELSEVIER

Journal of Wind Engineering and Industrial Aerodynamics 61 (1996) 195-205

~ [ ~ 3

Full scale measurements of gust factors and turbulence intensity, and their relations in hilly terrain K. Harstveit Norwegian Meteorological Institute, P.O. Box 43, Blindern, N-0313 Oslo, Norway

Received 30 January 1995; revised 26 February 1996; accepted 26 February 1996

Abstract The mean wind and the maximum 1 s wind speed, together with maximum moving averages of 3, 5 and 60 s, and horizontal components of standard deviation tru and o,, are stored each 10 rain for three record levels from five exposed stations in inhomogenous and hilly terrain in Norway. The data recorded during strong winds are grouped in 10° sectors, each containing a high number of data, so the group averages should be little influenced by casual errors. It is shown that the ratio between the friction velocity and the longitudinal standard deviation, o. is varying, while the ratio between the turbulence intensity, a , / U and the gust factors is almost constant.

List of symbols Von K a r m a n s c o n s t a n t (0.41) longitudinal standard deviation transversal s t a n d a r d d e v i a t i o n vertical s t a n d a r d d e v i a t i o n

O"u

(7"v O"w k(T) =

(GF(T)-

l)/Iu

ratio n u m b e r c o m b i n i n g gust factor a n d turbulence intensity surface roughness l o n g i t u d i n a l s t a n d a r d d e v i a t i o n related to friction velocity A = au/u. wind direction D GF(T) gust factor, m a x i m u m wind speed of T [s] divided to U l o m i n I~ = O u / U l o m i n l o n g i t u d i n a l turbulence intensity Iv ~ ffv/Ulo min transversal turbulence intensity I~ -- a w / U l o rain vertical t u r b u l e n c e intensity m e a n wind speed over 10 min U l o min u, friction velocity time in seconds T ZO

0167-6105/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0 1 6 7 - 6 1 0 5 ( 9 6 ) 0 0 0 4 7 - 5

196

K. Harstveit/.I. Wind Eng. Ind. Aerodyn. 61 (1996) 195-205

Subscripts AS HaB HuN HuS V

Askoy Storebuneset Bu in Hardanger Hurum-Nils~sen Hurum Stikkvannskollen Vealos

1. Introduction There is an increasing need for estimates of the standard deviation of the wind speed, a ........ which can easily be measured by using modern data processing techniques. In Norway, long record series (20 40 yr) of average wind speed, U, usually averaged over 10 min, and maximum wind gusts of typical duration of 2-5 s, exist at some 40 airports, 10 lighthouse stations and 5 others. A full extreme value analysis of this material is going on [1]. Shorter observation series exist at many other stations. It is of general interest to couple standard deviation to the maximum deviation from the average wind speed, and in this way, give estimates of standard deviations, or, for more easy comparisons, the scaled value of turbulence intensity, I ....... = (7 . . . . . . /U10mi n around the country. Several authors E2,3] have used calculations involving surface roughness, Zo. Such a technique presumes that realistic values of Zo can be given. This may be very difficult at inhomogenous surface conditions which are typical of many places in Norway. At Vealos near Skien, there was a need for good estimates for a ....... as well as the maximum gust speed and the maximum mean wind speed, for designing new antennas at a telecommunication mast. For simplicity, only horizontal components were measured. Wind speed and wind direction were sampled with a frequency of 1 Hz. The maximum 1 s wind speed value together with maximum moving averages of 3, 5, and 60 s, and the standard deviations along and across the mean wind, a, and a,, over the average period of 10min were recorded. Unfortunately, measurements at the top of the tower, 150m above ground, failed due to bad weather conditions (icing and lightning) and signal distortions. At a smaller mast nearby, successful measurements were carried out at the 10 and 3 0 m levels at a later time. The equipment and measuring procedure were copied at two sites, for planning long suspension bridges, Askoy near Bergen, and Bu in Hardanger, and, with small modifications, at two sites at Hurum, at that time an actual locality for building a new national airport near Oslo. Three levels of measurement were installed at all sites. All the sites are located in rather complex terrain with mountains and hills. However, inhomogenous surface conditions and complex terrain are typical for Norway, and it is of general interest to find out possible relations that hold for that type of terrain.

K. Harstveit/J. Wind Eng. Ind Aerodyn. 61 (1996) 195-205

197

2. Site description and measuring procedure Five observation masts are located in Southern Norway (Table 1). Wind speed and wind direction sensors were placed at 2 (V) or 3 levels (AS-HaB-HuN-HuS). The stations are typically located in hilly terrain. The site AS is located on a headland at the southern side of a W S W - E N E fjord near Bergen. The fjord is 1 km wide, and partly wooded or near bare hills, 100-400 masl, are found at each side of the fjord. The site HaB is located at the southern side of one of the long Norwegian fiords in the western country, the Hardangerfjorden. The fjord is 1-2 km wide, running S W - N E towards the west, curving near the station, running more E - W to the east. The station is located at the edge of a rather flat headland, 100-140 masl and mostly wooded except for some farmland. The recording mast is situated on a 5 m high rock surrounded by trees of 5-10m. This fjord is surrounded by high mountains, 1000-1500 masl, and steep mountain sides, S-SE and N W - N of the station, at a distance of 1-1.5 km. The two stations on the Hurum peninsula in the Oslol]orden, HuN and HuS, are hilltop stations, some 50-100 m higher than the surroundings, except for ridges to the north. Also, other hilltops and ridges of almost the same level are found within a distance of a few kilometers. The area is wooded, except for the ridge at HuS where the trees were cut. Also close to HuN, trees were cut, but a rather dense wood is still found 50 m north of the station. The station V is a more pronounced hilltop station in wooded land near the town of Skien, but only low trees or bare ground are found at the top. The cup anemometers were of the Vaisala Type WAA 15, with a distant constant 1.5 m. The wind vanes were the Fiedrichs Wind Direction Sensor, Type 4121, having a damping ratio of 0.57 at 3 m/s and 15° deflection. A slight inaccuracy of the vane potentiometers gave clusters of measurements close to 0 ° and 360-dD, but no

Table 1 Survey of wind stations discussed in this paper. The stations were working in the main part of the periods listed Station

Position

H

Period

Sensor height above ground

(h) N Askoy-Storebuneset (AS) Hardanger-Bu (HaB) Hurum-Nilsasen (HUN) Hurum-Stikkvannskollen

E

masl

10m

18m

30m

U,D

U,D

60o24 '

5°12 '

14

1987-90

U,D

60°28 ,

6°51'

123

1988-92

U,D

59038 ,

10034'

350

1989-90

U,D

U,D

U,D

59°38 '

10032,

335

1989-90

U,D

U,D

U,D

59°14 '

9°42'

494

1989-90

U,D

U,D

(HuS) Vealos

(v)

U,D

45m

U,D

K. Harstveit/J. Wind Eng. Ind. Aerodd, n. 6l (1996) 195 205

198

measurements in between. The factory quotes dD = 2 , but it may have been somewhat larger. A couple of instruments were removed after only a few months, and new instruments were placed out, because of potentiometer errors, which gave high dD-values. All instruments were placed on cross arms south of the masts, giving possible disturbances for the northerly sector. These combined inaccuracies made the turbulence measurements invalid from that sector. The response time of the instruments made it reasonable to use a sampling frequency of 1 Hz. Higher frequency contributions to the standard deviations were thus excluded, which should be taken into consideration when using the results.

3. Results and discussion The statistics of the turbulence parameters used for further study were determined when the average wind speeds at the highest measuring levels were above certain limits. At the most exposed stations (HaB, V), the limit was set at 10 m/s, while 6 m/s was used otherwise. The number of observations was quite large, giving the possibility of a high resolution directional analysis. The compass of 360 c was divided into 36 parts, each centred around an integral multiple of 10 ~. Any sectors where few observations obviously gave biased results, were removed from the data set. This was necessary only for 9 sectors at HaB. Due to disturbances from the observation masts and inaccuracies of the wind direction potentiometer close to 360 ~, all data from sectors 34, 35, 36, 01 and 02 were removed, leaving a total of 31 (22 at HaB) 10 ° sectors for further study. The median number of observations for the 1 0 sectors satisfying the criteria above is 422, 334, 99, 566 and 107 for the five stations of Table 1. it is believed that effects due to trends are smoothed out in a large set of data, and no attempt to correct for trends was carried out. The local wind direction was used for all turbulence calculations, but the direction of the highest level was used when dividing the data into directional classes. 3.1. Surfilce c o n d i t i o n s a n d J ? i c t i o n velocity

Fig. 1 shows a plot of the friction velocity, u , . calculated from the formulae

u, -

Ka(U 2 -- U1) ln(zz/z,)

(1)

for the levell0 1 8 m a n d 1 8 3 0 m ( 1 0 30, 30- 4 5 m a t H a B , 10 30 m at V), for each 10 ~ of wind direction with more than 10 observations. Fig. 1 shows that the estimate for u, varies between the levels, which strongly suggests surface inhomogeneity, especially at AS and HaB. At V this test could not be done as there were only two record levels, however, the high value around 160" is due to the telecommunication tower and a low building influencing winds from that direction. When u, is not constant, formulae (1) is strictly not valid and the calculated values only serve as indications.

199

K. Harstveit/£ Wind Eng. Ind. Aerodyn. 61 (1996) 195-205

2.5 T 2.0 i AS

151

2.5 2

1.0

1

0.5

0.5

[15

1.0

0.5 0.0

T2.5 I + 2.0

.

,

2.5

15

0.0

i0.5

0

10 50 90 130170210250290330

10 50 90 130 170 210 250 290 330

Sector (°) 2.5

HuN

Sector (°) 2.5

2.5

2

1.5

2.5

2

2

1.5

HuS

2 1.5

1.5

1

1

1

0.5

0.5

0

0

0.5

0.5 0

0

10 50 90 130 170210250290330

10 50 90 130 170 210 250 290 330

Sector (o)

2.5

Sector (°) 2.5

-

2 V 0.5 0

1.5

!.5

Z• 30m z 3(HaB:45m) 2 : V:30m) 18m (HaB:30m;

1

[zll lore

0.5 ~

,

0

,

10 50 90 130170210250290330

A

u,(z2, zl)

A

u,(z3,z2)

Sector (°) Fig. 1. Friction velocity, u, (m s- 1) calculated from 10 min mean wind speed measurements in two height intervals from the formulae u, = xa(U2 - U1) ln(zlz~l).

At AS, even negative values were o b t a i n e d , due to overspeeding at the 18 m level in a southerly wind. At AS, for some sectors u , increases with height, while for o t h e r sectors, it decreases. T y p i c a l for A S is the shift between sea a n d l a n d surface, a n d for some sectors, accelerated wind b e l o w 30 m. At HaB, the largest values of u , are f o u n d n e a r the g r o u n d for m o s t sectors, reflecting the fact that winds c o m i n g from the l~ord o r farmland, feel the friction from the w o o d s u r r o u n d i n g the station, b u i l d i n g a new surface layer a b o v e the r o u g h e r surface. At HaB, s o m e wind sectors are missing, due to s t r o n g channelling effects n e a r the steep m o u n t a i n s . A t H u N , for n o r t h - w e s t e r l y to n o r t h e r l y winds (only 330 ° is shown due to the general inaccuracies for n o r t h e r l y wind), calculations should p e r h a p s be d o n e using

200

K. Harstveit/J. Wind Eng. Ind. Aerodyn. 61 (1996) 195-205

a zero plane displacement, d, because the lowest 5-10 m are directly shielded by the wood in that direction. With the use of appropriate d-values, the values of u, calculated for the two layers approach each other. The near zero values of u, for south-west and westerly winds, especially close to the surface, reflect acceleration at low levels. The conditions at HuS seem to be rather uniform. Westerly winds are, however, reduced at lower levels due to a steep hillside. To conclude, the logarithmic wind profile seems not to be valid for many of the wind sectors at the stations, and especially for the two stations close to fjord sides. This is due to non-homogenous surface conditions surrounding the stations. The best approximation to the logarithmic wind profile is found at HuS.

3.2. Horizontal components" of turbulence intensiO' The turbulence intensity components, I,, and l,. were calculated for each l0 min period. Table 2 shows average values of I,, and I,/I~, = au/crv. The averaging is made over all sectorial mean values, showing an average surface picture rather than a view of the situation during typical wind conditions. Typical values of I, are 0.16 0.20 (30 m) and 0.214).33 (10 m). The ratio ~r,/~,, varies between 1.02 and 1.18 which is slightly lower than most of the values reported by Panofsky and Dutton [4] (1.10 1.40). The sectorial variation for all stations is large with the standard deviation of the ratio for the 31 sector values (22 at HuB) typically 0.10 and with single sector averages between 0.8 and 1.6. This suggests that the non-uniform terrain plays a dominant role in the relationship. It is also believed that this influences the average values of a,,, making them closer to c~,.

3.3. Turbulence intensity and jkiction velocity Standard deviation a,, and friction velocity, u, have a close relationship in uniform terrain. Panofsky and Dutton [4] refer to typical values of A = a,/u, of 2.39 for flat land and more varying and higher values in rolling terrain. For the four stations with

Table 2 Along wind, 1,, and across wind 1~ components of turbulence intensity at the five stations discussed, given as averaged values for the sector 030 330' Site

Askoy Storebuneset Hardanger-Bu Hurum-Nils~sen Hurum-Stikkvannskollen Vealos Mean

45m I,,

0.17

30m I,

18m I,

0.18 0.20 0.18 0.18 0.16

0.20

0.18

0.21 0.21

10m

45m

30m

18m

10m

lu

I,/I,:

I,/1~.

I,/1,:

lu/l,:

1.08 1.08 1.07 t.10 1.18

1.07

1.02 1.18 1.05 1.09 1.18

0.23 0.33 0.28 0.25 1).21 0.26

1.05

1.10

1.07 1.10

1.10

K. Harstveit/J. Wind Eng. Ind. Aerodyn. 61 (1996) 195-205

201

14

O

I0 8 6 4

o

.

.

.

.

.

.

.

.

®

.....

ml

FII~

~'-,~ ~--,~ ~ ® ~

0.25 0.85 1.45 2.05 2.65 3.25 3.85 4.45 5.05 5.65 6.25 6.g5 7.45 8.05 8.65 9.25

A Fig. 2. V a r i a t i o n of the ratios of s t a n d a r d d e v i a t i o n tr, to the friction velocity, u , at 53 sectors of 10 ° from four stations, at n e a r l o g a r i t h m i c wind profile conditions.

three measuring levels, reasonable estimates for u. can be given, provided that the logarithmic wind profile is valid. This, however, gives no guarantee that uniform conditions occur, because equilibrium after surface changes may not be reached. On the other hand, such conditions are very common in Norway, and it is of interest to look at the behaviour of the constant A when near logarithmic conditions occur. Average 10° values from the four stations are taken as the data base. The profile is defined as near logarithmic when 1.25 > u.(z2, Zl)/U.(Z3, z2) > 0.75. This criterion is satisfied for 53 of the 115 ten degree sectors. The average value of A = A(z2) is 2.38, where A(z2) = au(Z2)/u,(z3, Z l ) . This mean value is in good accordance with Ref. [4]. However, the variation between values from different station sectors is large (Fig. 2). The few high values are found for sectors where turbulence is increased. The great number of low values should be due to high wind shear and low turbulence, which may occur just after a wind shear is established, for instance by wind split along a ridge or just on the lee-side of a ridge. The high variation shown in Fig. 2 indicates that estimates of standard deviation, and correspondingly, turbulence intensity, from modelled or measured wind shear in inhomogenous terrain using factors valid for fiat and homogenous terrain involves a high degree of inaccuracy. Correspondingly, formulas using this relation in connecting gust factors and I, [2,3] cannot give precise results in such terrain.

3.4. Turbulence intensity and gust factors For approximately normally distributed wind gusts, it is reasonable that there exists a linear connection between the maximum deviation of duration T seconds from the mean wind speed, and the standard deviation, tr,:

k(T)

----- U m a x ( T )

--

flu

Ul°min

--

G f ( T ) - 1, Iu

where G f ( T ) = Umax(Y)/Ulomin is the T second gust factor and imum moving average wind speed.

(2)

Umax(Y)

the max-

202

K. Harstveit/J. Wind Eng. Ind. Aerodyn. 6l (1996) 195-205

Fig. 3 shows sectorial averages of k(3 s) for all levels a n d stations discussed. The m e a n values of k ( T ) , T = 1, 3, 5 and 60 s for the sectors 0 3 0 - 3 3 0 ° t o g e t h e r with s t a n d a r d deviations from these mean values, are given in Table 3. As m a y be seen, the k(3 s) values are g r o u p e d a r o u n d 2.44 _+ 0.2, averaged over all stations a n d all levels. Generally, a slightly less precise connection is found for the 10 m level than for the higher levels (Table 3). The irregularities found at the 10 m level in Fig. 3, are due to s h a r p g r o u n d inhomogeneities close to the masts. At AS, in the n o r t h - e a s t e r l y sector, lowered values are found at all levels, due to a rock in that direction with a height c o m p a r a b l e with t h a t of the mast. The precision is quite high, representing only 10% relative u n c e r t a i n t y in estimates of turbulence intensity. M o r e o v e r , the average k(3 s) value varies between 2.42 a n d

3

i3

2.5

2.5

I

AS

2.5

2.5 !2

-

HaB

2 1.5

2

2

. . . . . . . . . 1.5 10 50 90 130170210250290330 '

1.5

. . . . . . ~ 1.5 10 50 90 130170210250290330

Sector (°) 3

Sector (°) 3

2.5

3

2.5

HuN

,

~ 3

2.5 ] ~

2.5

HuS 2

2

2

2

L,

1.5 10 50 90 130170210250290330

1.5J

,

Sector (°) 3 2.5 . ~

,

•

1.5

10 50 90 130170210250290330 Sector (°) 3

~

~

f

~

2.5

V 2-

2

1.5 . . . . . . . . . . 10 50 90 130170210250290330 Sector (°)

Iz3: 30m (HuB:45m) iz2: 18rn (HuB:30m) Izl: 10m

1.5 -~t---

k3

-

-~--

k2

z~

kl

Fig. 3. The ratio, ki - (U3 ~ Ulom~n}a"t between the maximum moving 3 s wind speed deviation from the mean wind, and longitudinal turbulence intensity at all directions for the stations and levels discussed.

K. Harstveit/J. Wind Eng. Ind. Aerodyn. 61 (1996) 195-205

203

Table 3 k(T )-factors (3) for T = 1, 3, 5 and 60 s for the five stations discussed, given as averaged values for the sector 030-330 °. The STD-values given in the mean rows are given as standard deviation of all sectorial means for all stations discussed (146 values) Site

Askoy-Storebuneset Hardange~Bu Hurum Nilsfisen Hurum Stikkvannskollen Vealos

45m k(1 s) Mean

45m k(1 s) STD

30m k(1 s) Mean

30m k(1 s) STD

18m k(1 s) Mean

18m k(1 s) STD

10m k(1 s) Mean

10m k(1 s) STD

0.19 0.16

0.32

0.14

2.89 2.60

2.88

2.63

2.94 2.79

0.25 0.10

2.65

0.13

2.80

0.16

Mean Site

Askoy-Storebuneset Hardanger-Bu Hurum Nilsfisen Hurum-Stikkvannskollen Vealos

2.71 45m k(3 s) Mean

45m k(3 s) STD

2.36

0.14

Mean Site

Askoy-Storebuneset Hardange~Bu Hurum-Nils~.sen Hurum-Stikkvannskollen Vealos

Askoy-Storebuneset Hardange~Bu Hurum-Nilsfisen Hurum-Stikkvannskollen Vealos Mean

30m k(3 s) Mean

30m k(3 s) STD

18m k(3 s) Mean

18m k(3 s) STD

10m k(3 s) Mean

10m k(3 s) STD

2.61 2.33 2.39 2.43 2.36

0.18 0.14 0.08 0.07 0.11

2.6l

0.18

2.4l 2.42

0.10 0.11

2.63 2.45 2.32 2.44 2.48

0.24 (;.07 0.37 0.11 0.13

2.42

0.16

2.46

0.24

45 m k(5s) Mean

45 m k(5s) STD

30 m k(5s) Mean

30 m k(5s) STD

18 m k(5s) Mean

18 m k(5s) STD

10 m k(5s) Mean

10 m k(5s) STD

0.18 0.13

0.25

0.12

2.43 2.17

2.43

2.21

2.44 2.22

0.22 0.07

2.19

0.10

2.29

0.11

Mean

Site

2.84

2.26 45 m k(60s) Mean

45 m k(60s) STD

1.16

0.04

2.32

30 m k(60s) Mean

30 m k(60s) STD

18 m k(60s) Mean

18 m k(60s) STD

10 m k(60s) Mean

10 m k(60s) STD

1.21 1.14 1.10 1.11 1.11

0.12 0.04 0.05 0.05 0.06

1.21

0.12

1.07 1.08

0.07 0.05

1.15 0.96 0.97 1.04 1.01

0.15 0.09 0.16 0.06 0.06

1.13

0.08

1.03

0.13

K. Harstveit/J.WindEng.Ind.Aerodyn.61 (1996)195-205

204 2.40

*

2.20 ~

AS

'.* HaB

'~.

2.00

•

HuN

.."

HuS

1.80 1.60

.~

V 1.40.,

i

K(3s)=2.44

1.20 ~ i /

1.00 ]

.....................

0

2

4

6

8

10

....

[3]:best fit

.......

[3]: K(3s)=2.70

l/lu Fig. 4. The variation of the 3 s gust factor, GF(3 s) with the inverse of turbulence intensity.

2.46 depending on station level, and for the 53 x 3 station levels with near logarithmic wind profiles, the value is 2.41, while 2.48 is obtained for the 62 x 3 g r o u p means in non-logarithmic conditions, but with higher standard deviations of the g r o u p means (0.25 and 0.17 resp.). Table 3 shows that all values of for each T are rather close to each other for all stations. F o r T = 1, 3 and 5 s the average values of k ( T ) are close to each other for all levels, but with a higher standard deviation for the 10 m level. F o r the 60 s period, the values are systematically lowered near the ground. This is probably a general phenomenon due to the generation of short-time gusts near the surface which increases a,. Ashcroft c o m p a r e d GF(3 s) and using data from the UK, which gave approximately k(3 s) = 2.70 (from Ref. [3], Table 3). More than 50 stations were used. However, his calculations of were based on estimates of surface roughness, z0 and the assumption A = 2.5: I, = Moreover, the gust duration of 3 s was not well-documentated. The slight deviation between 2.44 and 2.70 m a y be due to the poorer estimating technique for I, used in Ref. [3], or due to the p r o b a b l y more n o n - h o m o g e n o u s surfaces in our study. Fig. 4 illustrates the connection between GF(3 s) and a roughness parameter, The observations are well-fitted, except for few points, representing sharp inhomogeneities at H u N , and partly at AS. The small difference between this study and Ref. [3] is illustrated.

k(T)

I.,

I,

a,/U ~ Au./U ~- 1/ln(z/zo). 1/I,.

4. C o n c l u s i o n

The five wind stations discussed in this paper are all characterized by inhomogenous surroundings. Two of the stations are situated on exposed headlands at l~ord sides, while the other stations are more or less p r o n o u n c e d hilltop stations. Rather sharp surface changes and varying vegetation in several directions are typical.

K. Harstveit/J. Wind Eng. Ind. Aerodyn. 61 (1996) 195-205

205

The calculations from the mean wind speed measurements during strong wind show varying friction velocity, u. between the two lower layers (10-18 m/18-30 m or 10-30 m / 3 0 ~ 5 m) for nearly half of the wind sectors examined. F o r the 53 10 ° station sectors of near constant u, through the two layers, the ratio A between the longitudinal standard deviation, a, and u., showed much variation, and a 50% standard deviation of these sectorial averages of A was obtained. The result is as expected: In terrain where surface homogeneity is questionable, rather unprecise estimates of au may be calculated from u,. The ratio between the longitudinal standard deviation, tru and the transverse standard deviation av varies between 1.02 and 1.18, averaged over all sectors, and 1.10 when also averaged over all stations. Larger variations are found between different station sectors. The ratio between the turbulence intensity t r , / U and the gust factor deviation from 1, is rather constant, being 2.77, 2.44 and 2.30 for the 1 s measurement and the moving gust averages of 3 and 5 s respectively. These values are almost independent of measuring height and surface conditions, but very close to sharp discontinuities variations m a y occur. The standard deviations for the whole group of sectorial means are typical 10% of the mean values. For the 60 s m a x i m u m moving average gust speed, the ratio is slightly lower at the 10 m level than at the levels of 18 to 45 m, being 1.03 and 1.13, respectively In Norway, typical gusts are recorded as a m a x i m u m average over 2-5 s, but are not well-documented at all stations. This means that tr, = (0.41 _+ 0.05) × (U~ax - Ulo rain) may be a suitable equation during strong wind in most types of terrain. However, close to sharp surface disturbances, the equation may break down. In extreme gusty conditions, for instance in recirculation zones behind steep mountains, more measurements should be carried out.

Acknowledgements The author wishes to thank the National Telecommunication Authority represented by Mr. Alexander Valen for all the support to the measurements at Vealos, which was the station where the basic idea was first carried out.

References [-1] K. Harstveit and L. Andresen, Ekstremvindanalysefor kyststrekningenRogaland-Finnmark,Rap. No. KLIMA 07/94, Norwegian Meteorological Institute, Oslo (1994) (in Norwegian). [2] J. Weiringa, Gust factors over water and built-up country, Bound. Layer Meteorol. 3 (1973) 424-441. [3] J. Ashcroft, The relationship between the gust ratio, terrain roughness, gust duration and the hourly mean wind speed, J. Wind Eng. Ind. Aerodyn. 53(3) (1994) 331-355. [4] H.A. Panofsky and J.A. Dutton, Atmospheric turbulence (Wiley,New York, 1983) pp. 159 160.