The relationship between the gust ratio, terrain roughness, gust duration and the hourly mean wind speed

dOt,~NAI. OF

II

Journal of Wind Engineering and Industrial Aerodynamics 53 (1994) 331-355

ELSEVIER

The relationship between the gust ratio, terrain roughness, gust duration and the hourly mean wind speed J. A s h c r o f t Scientific Support Group, The Meteorological O~ce, Johnson House, London Road, Bracknell, Berkshire RGI2 2SY, UK

Received 14 May 1993; accepted 15 March 1994

Abstract A large volume of 1 min mean wind data is available at the United Kingdom Meteorological Office. Until recently, very little scientific use has been made of the data. This study provides up-to-date information, using this data, upon the relationships between the gust ratio, the terrain roughness and the hourly mean wind speed by gust duration. The ratio of the maximum wind averaged over a period of a few seconds, 1 and 10 min and the hourly mean is obtained after careful quality control of many hours of data for each of eight wind direction sectors at 14 Meteorological Office anemograph stations. The ratio of the peak recorded gust to the 10 rain mean wind is also derived using two alternative derivations of the 10 min mean wind. The sector median gust ratio is successfully correlated with the estimate of terrain roughness derived from the best estimate of the sector aerodynamic roughness length. The form of the gust ratio-terrain roughness dependence is very similar to previous relationships for gust averaging periods ranging from a few seconds to 10 min but the median gust ratios obtained for averaging periods of 1 and 10 min are somewhat lower than those given in previous guidance documents. The ratio of the 3 s gust and the 10 min mean wind is obtained. A comparison is made between the observed median values of the above gust ratio and various predictive relationships in the literature. The dependence of the median gust ratio upon hourly mean wind speed is obtained. The median gust ratios for gust averaging periods of 1 and 10 min averaged over the set of stations do show a statistically significant decline with increasing wind speed. The 3 s gust ratio shows a much wider range of wind speed dependence from station to station and it is not possible to confidently define a general pattern of change with wind speed.

Nomenclature d dir6o

zero p l a n e d i s p l a c e m e n t 1 min w i n d direction

Elsevier Science B.V. SSD! 0 1 6 7 - 6 1 0 5 ( 9 4 ) 0 0 0 0 9 - 3

332

dirm G6oo G6o0c 660

Gp

6~ 6~o Gpo

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

mode of 1 min wind directions in the hour ratio of maximum of 10 min mean winds (non-overlapping average) to hourly mean ratio of maximum of 10 min mean winds (moving average) to hourly mean ratio of maximum of 1 min mean winds to hourly mean ratio of peak recorded gust to hourly mean ratio of peak recorded gust to 10 min mean (non-centred mean) ratio of peak recorded gust to 10 min mean (centred mean) ratio of peak recorded gust to 10 min mean estimated from Gp and 6600

lu Kr

l L n6o RMSD

t T U600 U600c U60 Up U' Z Z0 Zg ~600,3600

turbulent intensity - the rms of wind speed fluctuations as a proportion of the hourly mean wind non-dimensional terrain roughness parameter gust wavelength maximum likely gust wavelength number of 1 min winds (non-missing) in the hour root mean square of 1 min wind directions about the modal wind direction temporal change in 1 min winds over the hour relative to the hourly mean wind averaging duration of the gust duration over which the wind is sampled 10 min mean wind (non-overlapping average) 10 min mean wind (moving average) 1 min mean wind peak recorded gust speed hourly mean wind speed the ratio In [(z - d ) / Z o ] height above ground level aerodynamic roughness length gradient wind height coefficient of variation of the 10 min mean, i.e. the ratio of the standard deviation of the 10 min wind (non-overlapping average) about the hourly mean as a proportion of the hourly mean wind

1. Introduction The Digital Anemograph Logging Equipment (DALE) is a data logging system which works in conjunction with the Meteorological Office Mark 4 or Mark 5 anemometer system [1]. The DALE has been set up to average the wind speed and direction over sequential 1 min periods and record this information on magnetic tape. At the end of every clock hour the maximum recorded gust, speed, direction and time are also placed onto the magnetic tape [1]. The I min winds and 3 s gust data (also called

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here the peak recorded gust data) have been recorded at a number of anemograph stations (mostly at civil or RAF airfields) for a number of years and this data has been processed at the Meteorological Office, Bracknell to provide the hourly mean wind speed and modal wind direction and gust information for the Meteorological Office's climatological anemograph data sets. The 1 min wind data has been archived on magnetic tape since the autumn of 1983 but very little use has been made of this data for answering enquiries or for the purpose of scientific research. Durst [2] indirectly derived relationships between the likely maximum expected gust (averaging periods of 0.5 to 600 s) and the hourly mean wind using wind observations at Cardington. These relationships were incorporated with results from Sale, Australia by Deacon [3] and have been summarized, along with the data of Shellard in Ref. [4]. There is little other summarized data available for engineers on the dependence of the gust ratio upon surface roughness. The work of Weiringa [5] contains a set of gust ratio data from various sources along with a set of data for a site in the Netherlands. The British Standards document BS8100 [6] usefully summarizes the available information on the relationship between the gust ratio and the terrain type for gust periods ranging from 1 to 600 s in both tabular and graphical form. Ref. [7] contains much valuable information on the expected dependence of short period gust ratios (1 to 12 s averages) upon terrain type and height above ground. A number of other studies, see, e.g., Refs. [8,9] have derived relationships for the probable maximum short period gust within the hour by integrating the power spectrum of the horizontal wind velocity. The large amount of DALE wind data available can, however, provide the necessary information to define empirical relationships between the maximum of a set of short period mean winds and the hourly mean wind and the dependence of the gust ratios upon the local site roughness can be studied in a consistent way. It is the aim of this work to provide information on these relationships using the DALE 1 min winds and the peak recorded gusts. Unfortunately, no recorded wind data from the DALE system is available over an averaging period between the few seconds assigned to the recorded peak gust and the 1 min mean wind. A 15 s averaging period for the DALE equipment would have been ideal, as gust ratio relationships for this averaging period would have been most useful for engineers designing larger structures, and mean winds over longer averaging periods could have been derived from these averages. In the absence of such data, we can only consider the gust ratios derived from the peak recorded gust data and winds averaged over periods of 1 rain or more.

2. Method of analysis of DALE wind data 2.1. Selection and quality control o f D A L E 1 min mean winds

The analysis was limited to the years 1988 to 1990 because of the very large volumes of 1 min wind data available and restrictions of resources. The calendar year 1990 was chosen in particular because of the strong winds experienced in January and February of that year in southern England. The location of all the currently operational DALE stations and the chosen set is shown in Fig. 1.

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The choice of stations was made on the basis of site descriptions held at the Meteorological Office and a study of the land use around the anemograph site using 1:50 000 scale Ordnance Survey maps. The intention was to choose sites which were surrounded by terrain of as wide a range of aerodynamic roughness as possible but, unfortunately, at many DALE equipped sites the roughness is quite similar, since the site consists of an airfield surrounded by flat or gently rolling country. Some DALE stations were especially chosen because the site appeared to have an above average roughness, for example, Peterhead and Gravesend anemograph stations are close to urban and industrial areas and the Eskdalemuir site is heavily forested.

SUMBURGH

J ESKDALEMUIR

,~nAUGHTON

o j m/,._....~

.7 /

•

"

f" LARKHILL

l~i

•

•

•

r'

GRAV~ND NCEUX

Fig. 1. Location of currently operational DALE stations and stations used in the study.

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

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Other sites were chosen to provide information on gust ratios over smooth terrain. The Shoeburyness site is very fiat and open in most directions looking away from the anemometer mast, being mostly marsh fiats. The Chivenor site was chosen to provide information upon the gust ratios for wind flow over estuarine mud and sand fiats. In certain sectors the Sumburgh and Benbecula sites provide information on gust ratios for onshore winds onto a low lying coast. The wind data for the DALE stations at Herstmonceux, Cranwell and Coningsby was extracted to provide information on gust factors over open countryside of varying roughness. The wind data from Heathrow and Abbotsinch, it was hoped, would be useful for defining the gust ratios in suburban areas. 2.2. Quality control of D A L E wind data

A number of routine checks were made upon the DALE data such as checks for spurious wind speeds and directions - for more detailed information see Ref. [10]. Any hour with more than two 1 min mean wind speeds or directions queried by quality control routines was rejected from the analysis. In addition, it was thought wise to reject all hours where the hourly mean wind speed was less than 6 knots because of the fact that a few knots of wind are required to start up the Mark 4 and Mark 5 cup anemometers from rest [1]. Another important consideration was pointed out by Weiringa [5]. Unless careful checks are made to ensure that the mean wind over the hour is not subject to a significant temporal trend or to sharp changes in magnitude due to, for example a frontal passage, then the gust ratio (peak short period mean relative to the sampling duration mean) will tend to be overestimated. This is because the longer period variations of the mean wind would tend to be included within the peak gust value. Since the sequence of one hours' 1 rain DALE mean wind data describes the temporal variation of the wind then some check can be made to ensure that the wind over the hour is sufficiently steady before the gust ratios are derived. The procedure adopted was to regress, for each clock hour, the 1 min winds versus time, i.e. the minute values within the hour. The slope of this linear regression over the hour gives an estimate of the temporal change in the wind. This latter value, divided by the hourly mean wind (calculated from the 1 min mean winds) must be small if the mean wind is to be regarded as steady in time. The relative slope, S of the regression of the 1 min winds to the hourly mean is defined as S = slope of regression x 60/~.

(1)

After studying a large number of hours of data at sites with varying roughness and at varying wind speeds it was decided that the critical value for rejection of the hour's data on temporal changes alone should be S > 0.25. This value would eliminate those hours with the most serious trends in the wind but would not lead to an excessive reduction in the total number of hours of data available for the analysis. To eliminate hours with large wind direction variations within the set of 1 min means a check was made on the rms of the 1 min wind directions about the modal wind direction (taken from the Meteorological Office climatological anemograph

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

336

data sets for the DALE station). The rms is given by RMSD = x/Z(dir60 - dirm)2/n60 .

(2)

The most extreme variations in inter-hourly wind direction were found to be eliminated by setting RMSD > 20 ° as a rejection criterion. Another problem, revealed by plotting a sample of time series of 1 min winds, is that of large inter-hourly variation of wind over a period of tens of minutes without any significant overall temporal variation from the start to the end of the clock hour. The method developed to check this was to calculate the standard deviation of the 10 min winds about the hourly mean wind. The 10 min mean winds were obtained by averaging the DALE 1 min winds in six successive and independent 10 min intervals from the start to the end of the clock hour. The standard deviation of the six independently derived 10 min winds about the hourly mean as a proportion of the hourly mean value was calculated, N/~"~(U600 ?]600,3600

-- fi)2/(n6o 0 --

=

1)

(3)

It is expected that this coefficient of variation would depend upon the local terrain roughness and also upon boundary layer stability, so it was not possible to predetermine a critical value for all sites and atmospheric conditions which, when exceeded, would confidently indicate unsteadiness of the mean wind. As part of the study of the variability of the 10 min mean winds at various sites [10] a number of tests were undertaken on a critical value of the coefficient of variation in order to determine acceptable values for this parameter for use in a check on the stationarity of the wind. The final value chosen was 0.15 and was a compromise, reflecting the need to check the stationarity of the wind and the need to avoid an excessive loss of data, bearing in mind the short period of data available for the study.

2.3. Calculation of gust ratios Once the stationarity check on the hourly mean wind was performed then the calculation of the gust ratios could take place. The large volume of available DALE data gives us the opportunity to directly calculate a large number of gust ratios and directly derive representative estimates from their distributions. The practice in much previous work has been to follow the procedure of Durst [2] and indirectly derive the relationship between the peak short period average wind and the 10 min or hourly mean wind by using an estimate of the standard deviation of the short period average about the longer sampling period mean and a multiplier of this which would be sufficient to define an extreme short period gust. This procedure was also followed by Weiringa [5]. In addition, in Ref. [ 10] a number of estimates of the gust ratio (peak 10 min to the hourly mean) are also made in the manner of Durst [2] using values of ?]600,3600 derived from DALE data and the values obtained were found to be in fair agreement with those obtained by Durst.

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The directly derived gust ratios are defined as follows: peak recorded gust (averaging period of a few seconds) and the hourly mean wind over the clock hour define the peak gust ratio

Gp = Up/~.

(4)

The maximum 1 min mean wind in the given clock hour is easily found and with the hourly mean wind for the same hour is used in the calculation of the 1 min gust ratio, G6o ~- U6omax/U.

(5)

The 10 min mean winds were previously calculated for use in the stationarity check and the maximum of these six consecutive values within the hour to the hourly mean wind defines the ratio G6o 0 = U6o 0 max/U.

(6)

It is possible to average the 1 min winds to form the 10 min mean in a number of ways. The above process of calculation of the 10 min mean is perfectly consistent with the standard practice of averaging in non-overlapping and independent time intervals. This averaging is usually performed over a much shorter time interval of a few seconds or tens of seconds to calculate short period mean winds within usually, a total time period of 10 min at most - see the work of Durst [2] and Deacon [3] for example. An alternative estimate of the 10 min mean wind may be obtained by a 10 min moving average running through the sequence of 1 min mean winds. Because of operational problems at the DALE stations and removal of data by quality control checks the DALE data used in the study is not a sequential and chronological set of hourly 1 min wind observations and it is not generally possible to form a moving average for a given hour which involves the use of the subsequent and preceding hour's 1 min wind data in the average. In order to use only the current hour's 1 min winds and still define a 10 min moving average for each minute through the hour, the set of 1 min values was artificially extended by 5 min before and after the hour using the mean wind of the first 5 or last 5 min of true data so that the 10 minute mean wind could be defined for each 1 min value (5 min before the given minute and 4 min after define the 10 min period). The maximum of this sequence of 10 min means relative to the hourly mean wind defines the alternative gust ratio G600c as G6ooc : U6oo . . . . /1~.

(7)

In addition, the ratio of the peak recorded gust to the 10 min mean wind was calculated. The correct 10 min mean was found by referring to the recorded time of the peak gust. Both non-centred and centred 10 min means were used, t Gp ~- Up/U6oo,

(8)

! Gpc : Ul~U6ooc.

(9)

338

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

All the above gust ratios were calculated for 8 direction sectors at each of the 14 stations. A finer division of the compass was not thought feasible due to the need to have a sufficient sample size for every sector and wind speed class. The hourly modal direction, obtainable from the Meteorological Office climatological anemograph data sets, was used to define the correct sector for those gust ratios based upon the hourly mean wind. The direction of the 10 min mean wind used in the calculation of G~ and G~,c was taken as the mode of the directions of the 1 min mean winds in the specified 10 min period. The gust ratios were further classified by the hourly mean wind speed class, namely: 6-10, 11-15, 16-20, 21-25, 26-30 and > 30 knot. The gust ratios were calculated and placed in frequency distributions by ratio class, direction class and wind speed class. F r o m these distributions the mean, mode, median and other quartiles and the standard deviation were calculated. The individual probability distributions were summed by selected wind speed classes to provide a directional gust ratio probability distribution or for all or selected wind direction sectors for selected wind speed classes to provide a distribution by wind speed alone.

3. The dependence of gust ratios upon averaging time and terrain roughness 3.1. The probability distribution of the gust ratio The frequency and probability distribution of the gust ratios G6oo, G6o and Gp, derived from the D A L E data at the Shoeburyness and Eskdalemuir sites, was studied as a number of stationarity checks were made on the hourly mean wind. There were four different stationarity checks made. Reject hour's data as non-steady if: 1. S > 0.25 or R M S D > 20 o or (S < 0.25 and ?~600,3600 > 0.15); 2. S > 0.25 or R M S D > 20 ° or (S < 0.25 and ~/600.3600 > 0.10); 3. S > 0.25 or R M S D > 20 °; 4. S > 0.10 or R M S D > 20°. The purpose of undertaking a number of alternative checks was to ascertain the sensitivity of the distributions of the gust ratios and their median values to any check made on the stationarity of the wind and the likely loss of observations when more stringent checks were made on the hourly change in mean wind, S and the limiting value of ?]600, 3600" Some examples of the probability distributions for the gust ratios G60o, G6o and Gp obtained at the Eskdalemuir and Shoeburyness sites (all sector summation) over a wide range of hourly mean speeds are shown in Figs. 2-4. Note that the gust ratio distributions obtained for all occasions when the hourly mean speed was > 6 knot will include cases when the boundary layer stability will be non-neutral. The effect of an introduction of a stationarity check when occasions of low wind speeds are included is to clearly reduce the proportion of values in the upper tail of the distribution and to sharpen the peak of the distribution, particularly for 1 and 10 min averages. There appears to be little difference between the distributions of G600 and

J. Ashcroft/J. Wind Eng. lnd. Aerodyn. 53 (1994) 331-355 0.6

ProporBon

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G600 Fig. 2. Probability distribution of the gust ratio G6oo at the Eskdalemuir site as a function of the stationarity check.

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Fig. 3. Probability distribution of the gust ratio G6o at the Shoeburyness site as a function of the

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

340 0.15]

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2.00

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Gp

Fig. 4. Probability distribution of the gust ratio Gpat the Eskdalemuir site as a function of the stationarity check.

G6o for checks 1 and 3 though the distribution of G6oois directly affected over rough terrain, with a notable loss of the upper tail of the distribution of G6oo at the Eskdalemuir site and a very severe loss of the original distribution when check 2 is applied. This loss of data was considered unacceptable as it is obviously impinging on the usual distribution of %00, 3600 appropriate to this terrain type. Check 4 gives a very similar overall probability distribution of peak gusts to that of checks 1 and 3 though it was not adopted for subsequent general use as the loss of observations was considered unacceptable. Thus checks 1 and 3 were considered suitable for use over a wide range of wind speeds. Check 1 was adopted for use in the generation of the gust ratio distributions at all sites as it incorporates some check on the temporal trend in the wind over the hour and any extreme inter-hourly wind speed variations due to longer period (and probably) larger scale lulls and gusts. It is worthwhile noting that most of the loss of data between checks 0 (all data) and check 1 is in fact achieved by the limit on the slope, S and not by the limit on the value of %oo, 3600. This can be seen by comparing the distributions for checks 1 and 3. Therefore the difficulty in deciding upon the limiting value of r/is not in practice of much significance at the vast majority of sites. The median value of the gust ratio which can be derived from the gust ratio distribution is only affected by a seemingly small amount by the introduction of a stationarity check on the wind speed. Using all occasions when the hourly mean wind speed was 11 knot or more (approximately neutral conditions) a roughly 3% reduction in the median peak gust was obtained when the type 3 stationarity check

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341

was performed upon the the DALE 1 min winds, compared to those obtained when no stationarity checks were performed. However, the variation in the gust ratio Gp, for example, over the majority of terrain types over land (according to Ref. [6]) is only 1.45-1.65 or 1.55 _+ 6.5% so the check is clearly of some importance in determining the final gust ratio estimate from DALE data. The distribution of gust ratios in occasions of high wind speeds (type 1 stationarity check) for four stations with differing terrain roughness is shown in Figs. 5 and 6 for G6o and Gp, respectively. The probability distribution of the gust ratio G6o shows a modest dependence upon the differing site terrain roughness and has a very similar form at all sites, the peak of the distribution being progressively shifted to the right as the general terrain roughness increases. The distribution of the gust ratio Gp shows a rather different shape, with a greater standard deviation and greater sensitivity to

0.4

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Fig. 5. Probability distribution of the gust ratio G6o at high wind speeds.

I

342 0.3

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331 355

Prolx~,ion

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Gp Fig. 6. Probability distribution of the gust ratio Gp at high wind speeds.

local terrain roughness. The distributions are very similar in shape at Cranwell and Shoeburyness (two sectors omitted where there were a significant number of buildings) but at Larkhill and Eskdalemuir the distributions are broader and are skewed towards higher values of the gust ratio. The much wider range of gust ratio at the Larkhill site than at the other sites reflects the considerable directional variation of roughness at the station. These distributions were derived for each wind speed class individually and these results showed that if a sufficient sample was available at the station in question, at hourly mean wind speeds above 20 knot, the introduction of stationarity checks 1-3 made very little impact on the distribution of the peak gust ratios and gust ratios averaged over longer periods. This implies that gust ratios derived from occasions of high mean wind speeds are effectively those derived in conditions of stationary winds. Therefore, if the gust ratio is required from information which is restricted to the hourly mean wind and the peak recorded gust (i.e. no stationarity check is possible) the analysis should be confined to those occasions of strong winds, i.e. hourly mean wind speed roughly 21 knot or greater (say 10 m s - i or greater) if the gust ratios are not to be overestimates. In this particular study it was not feasible to search through the whole period of archived D A L E data at every station to find those hours when the wind speed met the above suggested criterion. Because of the need to provide a sufficient body of observations in each wind direction sector for correlation of the median gust ratio with sector roughness it was found necessary to use the sector gust ratio distributions when the hourly mean wind speed within that sector was > 11 knot. This lower limit

J. Ashcroft / J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

343

to the hourly mean wind speed will unfortunately include some occasions when the boundary layer may be classified as being slightly unstable (for example, in high summer with clear skies). However, once a large body of thousands of hours of observations is brought together using the three years worth of DALE data then these cases can be expected to be only a small percentage of the total number and the median value of the gust ratio will be scarcely affected by their inclusion. Weiringa [11] suggested that gust ratios may be derived for near neutral conditions when the hourly mean wind speed, fi is > 6 m s- 1. This lower limit on the mean hourly speed is practically the same as that used here. 3.2. Dependence of the median gust ratio upon terrain roughness category 3.2.1. Estimation of aerodynamic roughness length In order to derive relationships between the median peak gust ratio and station sector roughness it is necessary to have some numerical estimate of roughness. In this study the aerodynamic roughness length Zo, or parameters dependent upon it, are correlated by sector with the median gust ratio derived from the probability distribution of the gust ratios. It is possible to derive an effective roughness length from the median gust ratio Gp using the technique of Weiringa [-11]. However this estimate would not be independent of the gust ratio itself, so this method is not used here. The sector roughness length was estimated instead from an assessment of the land use around the anemometer site using 1:50000 Ordnance Survey maps and the terrain descriptions in Section C of Part 2 of Ref. [6]. These estimates were substantiated using the roughness lengths around the DALE station calculated from digitised land use data sets available in the Meteorological Office using the technique described in Ref. [ 12]. These roughness lengths were calculated for 100 m by 100m pixels and averaged out over radial distances of 300 m in each of the eight 45 ° sectors at the 14 stations. A particular problem concerns the distance over which the roughness length should be estimated or calculated. The roughness length can be quite variable with distance within any sector and a different averaging distance will result in quite different estimates of Zo. Weiringa [11] suggested that the gust ratios at a typical anemometer height of 10 m will be influenced by terrain roughness out to a distance of roughly 3 km and will especially reflect the disturbance to the flow induced by the largest roughness elements in the path of the wind. This guideline was followed here in deriving the effective roughness length by sector from the Ordnance Survey maps. The sector average roughness lengths derived from the digitised land use data were subjectively weighted towards the higher of the values obtained for the individual 300 m sectors. The intention was to produce a value of z0 similar to that which might be obtained by applying Weiringa's technique. In the great majority of cases the subjectively assessed roughness agreed well with that derived from an assessment of the numerically calculated sector roughness but in one or two cases, for example at the Eskdalemuir site, the calculated roughness seriously disagreed with the subjective assessment, probably in this case because of additional tree plantation since the time that the land use data was obtained. In these cases, the subjectively assessed roughness length was used.

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At Aughton, Gravesend and Peterhead the anemometer height is greater than the standard 10 m above ground because of the need to clear the disturbed wind flow generated by high roughness elements in the vicinity (typically housing development). At each of these sites the zero plane displacement was estimated as 0.7 of the maximum height of buildings in the vicinity of the anemometer. The site diagrams held in the Meteorological Office were consulted for this information. This value was used to define the effective height for these sectors. If, at these sites, the sector contained no contiguous built up area, the gust and mean wind speed were reduced to 10 m above ground using the power law profile with the appropriate power being chosen from Ref. [6] according to terrain type. This adjustment resulted in a small increase in the gust ratio for the sectors in question. Where it was unclear whether a zero plane displacement should be used or whether an adjustment of the gust and mean wind to 10 m should be undertaken (because of the highly variable height of the roughness elements in the sector) then the gust ratios for the sector were not taken into consideration in the overall analysis of the data. In all cases the median gust ratio for any sector was not used if the sample size was too small. A lower limit of 50 observations was thought a reasonable choice. 3.2.2. Results of the gust ratio-terrain roughness association In order to present results compatible with the previous guidance on the terrain dependence of gust ratios as given in Ref. [6], the median peak gust ratios were plotted versus Kr, the terrain roughness parameter, which is defined as in (105/Zor) In (10/Zo) K~ = ln(105/Zo) ln(10/Zo~)"

(10)

For the reference terrain where ZOr = 0.03 m and allowing for a general height with zero plane displacement we have Kr = 2.5855 ln[(z - d)/Zo]/ln(lOS/zo).

(11)

(Note that Kr is the same as the parameter Se in Ref. [7] and most DALE stations have d = 0 and z = 10m.) The median gust ratios for the individual sectors at the 14 sites were plotted versus the sector value of Kr and the best fit line drawn in by eye. The original plot of the sector median values of the gust ratio G6o is reproduced here in Fig. 7. The scatter of the data points is in part due to the fact that sector roughness value estimates inevitably congregated around a limited number of standard values. In spite of this it is still possible to define with some confidence the line of best fit for K r > 0.7. In the highest roughness categories there are only a few gust ratio values available and the line of best fit is more uncertain. The plotted data from this study agree well with the data of Durst [2] and Deacon [3]. Standard estimates of z0 were used to describe the terrain types for the data extracted from the above studies. The line of best fit suggests a best estimate of the peak gust ratio G6o for terrain category 3 of 1.26, which is in excellent agreement with that predicted by Vellozi and Cohen, taken from Ref. [6].

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355 1.5

1.4

345

G6x X X

X

X

X

X

X X

X

X

X X

XX X X

XX X

XX X x

~(X

X

1.3

, .xX X X~

X

1!0

1!1

l

~

1.2

Key: x Dale data

1.1

•

Deacon (1965)

Durst (1960) • Velkazi and Cohen •

1.0

0.5

0!6

0!7

o!e

0!9

1!2

11.3

Kr

Fig. 7. Sector median gust ratio G6o

as

a function of the terrain roughnessparameter Kr.

The lines of best fit for the gust ratios G600, G600c, G60 and Gp drawn to the DALE data are reproduced in Fig. 8 along with the gust ratio-averaging time relationships as given in Fig. A.1 of Part 1 of Ref. [6] or equivalently Fig. C.3.2a in Part 2 of Ref. [6]. The gust ratio G60 o can be seen to be only weakly dependent upon terrain roughness. The DALE data suggests that the value of G6o o varies from 1.07 to 1.11 over the whole range of terrain roughness types found around the DALE stations. The original data of Durst and Deacon was plotted on the original working figure and was found to agree well with the DALE gust data (G6o o data only). Weiringa [5] derived a mean value of G6o o of 1.10 for open country (corresponding to Kr = 1.0) but the present results suggest a slightly lower value of 1.08 would be more appropriate. This latter value is in good agreement with that of VeUozi and Cohen, appropriate for the terrain type "open country", taken from Fig. C.3.2c in Part 2 of Ref. [6].

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

346

The sector median values of the gust G6oo¢ , derived from a 10 min moving average were similarly plotted up and the best fit line drawn through the scatter of data points. This best fit line is reproduced in Fig. 8. The values of this gust ratio are some 2 to 4% greater than the values of G6o o derived from six sequential 10 min averages. The gust ratio G600c is however lower than that predicted by the relevant curve in Fig. C.3.2a of Part 2 of Ref. [6], reproduced here in Fig. 8. It is not clear what data was used to derive the above curve in Ref. [6]; it certainly lies above the best fit line drawn to the gust ratios obtained in this study as well as those obtained in the previous studies of Durst, Deacon, Vellozi and Cohen, and Weiringa. The gust ratio derived from the DALE wind data for the 1 min average is also seen to be consistently lower than the ratio suggested by Fig. C.3.2c in Part 2 of Ref. [6] over the whole range of roughness categories. The reduction is typically 5%. It is suggested that some previous estimates of the gust ratios may have been influenced by the presence of unsteadiness in the mean wind and may have been overestimated, but this would depend upon the mean wind speed. It is possible that previous estimates of the gust ratios for winds of shorter duration than 60 s might be similarly have been overestimated but unfortunately it is not possible to provide a definitive answer to this question using the DALE data. The peak recorded gust obtained from the Meteorological Office Mark 4 or Mark 5 anemometer system does not have a fixed averaging duration; the duration decreases with increasing wind speed. The line of best fit for the observed gust ratio Gp is close to that of the 3 s duration gust ratio over most of the range of roughness.

2.2

Gust Ratio

Key:

2.1 peak , . 2.0

gust

~

"'%,%, ,, ,,

BS 8100 Dale

.....

600 MV:

10 minute moving average

600 6AV: 610 minute averages

,,

1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0

o18

01~

o18

oI~ K~

11o

1~1

112

113

Fig. 8. The gust ratio as a function of gust duration and the terrain roughness parameter K r. (Data from BS8100 are reproduced with permission of BSI. Complete copies can be obtained from BSI sales, Linford Wood, Milton Keynes M K I 4 6LE, UK.)

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

347

(The position of the curve is rather less certain for Kr < 0.7.) It is not known whether the original curve in Ref. [6-I was based on true 3 s average gust data or, as is more likely, the peak recorded gust from the anemograph system was assumed to have a 3 s duration. The peak gusts from the D A L E data (most hourly mean wind speeds in the range from 11 to 20 knot) appear to be of a very similar, if perhaps slightly shorter duration, but, according to the best fit line, greater than 1 s duration. Unfortunately, there was insufficient data available by wind direction sector at wind speeds above 20 knot to determine the form of the relationship between G v and Kr at high wind speeds when the effective averaging period of the cup anemometer system would be reduced. The results of this study can be summarized in Table 1 which, derived using D A L E data alone, gives the expected gust ratios for winds of 3, 60 and 600 s averaging period (both overlapping and non-overlapping averages) as a function of terrain category at standard height of 10 m above the zero plane. The terrain categories follow those given in Ref. [6]. 3.3. Dependence o f the ratio o f the peak gust to the 10 rain mean upon terrain roughness It is of considerable interest to relate the peak recorded gust from the D A L E data to the 10 min mean wind. This ratio has useful practical applications within the Meteorological Office as wind speeds reported from synoptic stations are averaged over a 10 min period and it is also of interest to compare the ratios derived from D A L E data with a number of predictive equations. Firstly, it is necessary to determine whether there is any consistent difference between the individual sector median values of the gust ratio Gp (non-centred 10 min mean) and the median gust ratio G~,c (centred 10 min mean). The difference between these two values was calculated for each station and sector. This was found to be very small - the median gust ratio Gp was usually greater than Gp¢ by 0.01 or 0.02. The overall mean difference over 14 stations was only 0.012 which is regarded as of no great significance for practical applications. This result suggests that in practice, the 10 min mean does not have to be accurately centred around the time of the peak gust

Table 1 Gust ratios by averaging period and terrain category at 10 m height Category Zo (m) Kr Gp G6o G6o0 G6ooc

1 0.003 1.21 1.44 1.21 1.07 1.09

2 0.01 1.11 1.49 1.23 1.07 1.10

3 0.03 1.00 1.56 1.26 1.08 1.11

4 0.10 0.86 1.66 1.31 1.09 1.12

5 0.30 0.72 1.85 1.37 1.10 1.14

Explanation of terrain categories. 1: off-seawind onto flat coastal areas; 2: level grass plains, e.g. marsh; 3: standard category: fairly level terrain-mostly open fields with a few houses and buildings; 4: fairly level terrain with more hedges,trees and villages,farm buildings; 5: many trees and hedges,or fairlylevel wooded country or more open suburban areas.

348

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

for the median gust ratio G~ to be a good estimate (error + 0.01 compared to the "true" estimate G~c). The very small difference between the two median values may be explained by the fact that the peak gust of duration 2-3 s is almost invariably occurring when the mean wind in that part of the hour is increasing and variations from minute to minute in the wind are relatively small. If the peak gust ratio (3 s gust) relative to the hourly mean wind is already known for a particular location then it is possible to derive a first estimate of the peak gust ratio relative to the 10 min mean wind by dividing Gp by the appropriate value of G6o 0 for the terrain type, which may be taken from Table 1 or Fig. 8. These predicted gust ratios were obtained by sector for each station and were correlated with the actual median values of Gp. The correlation was excellent with r = 0.994, but with a slight underestimate of the actual value. The suggested predictive equation is t

(12)

Gpe = Gp/G6oo + 0.04.

The very high correlation between Gp and Gpe is a reflection of the fact that the peak gust is almost invariably associated with the maximum 10 min wind within the hour. We choose here to present the plot of the gust ratio G'p but in this case the median gust ratios are plotted against the parameter u' = ln[(z - d)/zo] in order to facilitate a comparison with the predictive relation of Weiringa [5] and another derived from that of Cook [6]. Weiringa [5] followed the method of Durst [2] and derived the following equation to predict the value of the gust ratio Gp, G~ = 1.0 + [1.42 + 0.3 I n ( T i t - 4)]/u'.

(13)

Weiringa estimated the root mean square turbulent intensity of the wind to be 2.5u,, where u, is the shear velocity, and assumed that the logarithmic wind profile was valid, in which case the relative turbulent intensity, lu = 1.O/u'. The assumption that I , = 1.O/u' appears to be roughly true if the whole spectrum of turbulent fluctuations of periods from I to 3600 s is considered but it is not clear that this should apply to the rms fluctuations over periods: t > few seconds and T < 3600 s, i.e. to a restricted part of the spectrum. To remove the possible uncertainty in assigning the duration t for short period gusts as recorded by standard cup anemometer systems, Weiringa re-wrote T i t as the number of gusts of wavelength l relative to the likely maximum gust wavelength within the boundary layer, L ( ~ 1000 m). We then have (14)

C~ = 1.0 + E/u',

where the eccentricity, E = 1.42 + 0.3 In (lO00/l - 4). For the U K Meteorological Office anemometer systems (Mark 4 and Mark 5) Adams [13] estimated I as 84 to 97 m depending on wind speed. If we take I = 90 m we then have C~ = 1.0 + 2.0/u',

or

C~ = 1.0 + 2.01,.

(15)

This equation is plotted in Fig. 9 along with the values of G~ as determined for each sector with the value of u' based on the estimated value of Zo. The plotted data does

349

J. .4shcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355 B 2.2

I.

i Gp

2.1

Wll

2.0

CI. ~

I

1.9

I'

~ x ,

1.8

x

x x~

~

~

x

i

\

x

~ t " x~ ~x~x.' x\ x

1.7

1.6-

x

1 1.5

x %

%

%

xx

xx %x %

,

x

~

. )oc

x

x

"~ ~.

X

1.4 %

C %

1.3

'

X xB

,%,

Wl: Weidnga, L~1000 m, h,~90m

Key:

1.2

W2

"" Wl

W2: Weiringa, T = 600, t = 3 C: Cook B: Best fit to Dale data

1.1

I

1,0

I

2.0

I

3.0

I

4.0

I

5.0

I

6.0

I

7.0

I

8.0

rj I Fig. 9. The gust ratio G~,as a function of the terrain roughness parameter u'.

not agree very well with the peak gust ratios predicted by Eq. (15) - the data lies well above the predictive line over the whole range of terrain roughness. Interestingly, if we take Tit = 600/3 and use Eq. (13) directly to estimate the gust ratio the fit to the plotted data is much improved over the whole range of terrain roughness and is judged to be good for u' > 5.0. Unfortunately, the curve clearly lies above the body of observed gust ratios over rougher terrain and is not a generally satisfactory fit overall. The suggestion is that the estimates of the gust wavelengths l and L are somewhat

350

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

erroneous as the introduction of these values into Eq. (13) leads to a substantial underestimate of the gust ratio Gp. Cook [7] adapted Weiringa's equation of the form of Eq. (13) by adjusting the empirical coefficients so that the predicted gust ratio fitted a 1 s gust ratio of 1.6 over open terrain (Zo = 0.03 m) at l0 m height. Cook assumed a peak recorded gust averaging duration of 1 s. The dependence of the predicted gust ratio upon the terrain class is implicit as the turbulence intensity is specified as a function of terrain roughness. The equation is, in our notation, Gp = 1.0 + 0.42Iu ln(3600/t).

(16)

The turbulence intensity lu can be specified as a function of height in the boundary layer and terrain roughness by the relation of Deaves and Harris as quoted in Ref. [7]. This equation has been considerably simplified here to I, = 0.54/[F(u') u'] + 0.09,

(17)

where F(u') = 2.17 + 0.15u'. The above equation is applicable only for z - d <>Zo. If we substitute (17) into (16) and divide Gp by the value of G6oo appropriate to the terrain type and in addition use the small correction factor as given in Eq. (12) we can produce a predictive equation for Gpt as a function of u'. We assume t = 3 s as an effective gust averaging period for conditions when the hourly mean wind speed is from 11 to 20 knot, which covers the majority of occasions for which the gust ratio distributions were derived. The resulting equation is judged to be a good fit to the observed gusts G~ and lies very close to the best fit line drawn in by eye for u' in the range from 4 to 7.5. Over very smooth terrain the predicted gust ratio was slightly larger than the ratio suggested by the best fit line and over rough terrain the DALE data suggest a rather higher value of the gust ratio than predicted. The equation does however very satisfactorily describe the form of the non-linear dependence of the gust ratio upon the roughness parameter u' and is somewhat superior to relationships assuming an inverse dependence of turbulent intensity upon the terrain roughness parameter u'. Note that the relationship between the 3 s gust ratios and other longer period average gust ratios and terrain roughness (Fig. 8) is also of a similar form. The predicted 3 s gust ratio relative to the hourly mean as given by Eq. (16) was derived and checked against the peak gust Gp taken from the best fit line to the DALE data. This confirmed that Cook's predicted gust ratios (t = 3 s assumed) were very close to the best estimate of Gp for terrain types 2 and 3 but were underestimates over rough terrain (type 4 and especially type 5) and a small overestimate over smooth terrain (type 1). The values of G~ obtained from the line of best fit to the DALE data are shown in Table 2. An attempt was made to predict the values of G6oo and G6o as a function ofu' using Eqs. (16) and (17) but the values obtained were far too large, almost certainly because

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

351

Table 2 3 s gust to 10 min mean wind at 10 m height, by terrain category Category zo (m) u' Kr G~,

1 0.003 8.11 1.21 1.36

2 0.01 6.91 1.11 1.42

3 0.03 5.81 1.00 1.48

4 0.10 4.61 0.86 1.58

5 0.30 3.51 0.72 1.74

the computed turbulent intensity lu represents the complete spectrum of wind fluctuations and what is required is a partitioning of the turbulent intensity over the relevant part of the spectrum (600 to 3600 s or 60 to 3600 s).

4. Dependence of the median gust ratio upon the hourly mean wind speed Once the DALE data had been subject to stationarity checks it was possible to determine whether any real dependence of the gust ratio upon the hourly mean wind speed actually existed. Because of a generally insufficient sample size at high wind speeds in the individual direction sectors it was not possible to study this phenomenon as a function of terrain roughness (which is noticeably sector dependent). Instead, the median gust ratios Gp, G6o and G6o 0 obtained by summing the distributions for all eight sectors at each of the 14 study stations (wind speed class above 15 knot) were related to those in the 11-15 knot class at each station. The trend line through the arithmetic mean of the values in each wind speed class is plotted in Fig. 10. Around the mean + / - one standard deviation is plotted. Fig. 10a shows that there is a small and consistent decrease of the relative ratio of G6oo and G6ooe as wind speed increases and this is very consistent across the whole range of stations (small standard deviation). Note, however, that the gust ratio G6ooc derived from the 10 min moving average data is rather more sensitive to the increase in wind speed presumably because it much better reflects the variations in the shorter period 1 min mean wind data used to form it. Because of the small variability of the ratios within each class the small decrease in the mean ratio is statistically significant. A t-test on the difference between the mean ratio of G6o o for the 16-20 knot class to the 31-50 knot class revealed that the decline is significant at the 5 % probability level. The magnitude of the reduction is rather small. A typical decrease of G6o 0 from 16-20 knot to > 30 knot is only 1%. The gust ratio at high wind speeds ( > 30 knot) is only 1.5% less than that at 11-15 knot. This reduction is significant because the absolute value of the gust ratio G6oo is not very sensitive to terrain roughness and so there is little variation of G6oo within a wind class, i.e. between the majority of stations. This decline is doubtless related to the small decrease in the relative turbulent intensity as the mean wind speed increases 1-10]. The gust ratio at high wind speeds ( > 30 knot) is 1.5% less than the gust ratio derived using the whole body of data (wind speed > 11 knot). This correction may be used to adjust the roughness dependent gust ratios of averaging period 600 s, derived

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

352

Ratio

a)

1.000.98

0.96 0.94 Key: •

0.92

0 i

6-10

10 min sequential 10 rain moving average 11-15

i

16-20

Ratio

21-25

25-30

31-50

Mean wind (kts)

21-25

25-30

31-50

Mean wind (kts)

21-25

25-30

31-50

Mean wind (kts)

b)

1.000.98 0.96 0.94 0.92 0.90

-

6-10

I

11-15

16-20

Ratio

I

c)

1.02 1.00 0.98 0.96 0.94 0.92

6-10

I

11-15

16-20

I

Fig. 10. The variation of the gust ratio with wind speed for: (a) 10 min mean wind; (b) 1 min mean wind; (c) peak recorded gust.

for wind speeds > 11 k n o t to those appropriate to cases of hourly mean winds > 30 knot. The adjustment of the gust ratio G60oeto cases of high wind speeds is somewhat greater. The gust ratio derived for all cases of hourly mean wind speeds > 11 knot may be reduced by 2.0% to adjust it to that appropriate to conditions of very high wind speeds, i.e. to the > 30 knot class. The relative gust ratios G6o show rather greater variability within each speed class as the shorter period gusts are more sensitive to the site roughness. Nonetheless there is still a significant decline of G6o with increasing wind speed as the relative intensity of

J. Ashcroft/J. Wind Eng. lnd. Aerodyn. 53 (1994) 331-355

353

the wind fluctuations decreases. In this case the reduction of G6o is rather greater about 3% on average, as the mean wind speed increases from around 11 to 30 knot or greater. The gust ratio G6o, derived from occasions of hourly mean wind speed > 11 knot for a chosen terrain type, may be reduced by 2.5°,/0 if it is required to estimate the ratio appropriate to very high wind speeds ( > 30 knot). The variation of the ratio Gp with respect to wind speed is rather more complicated. The short period gust ratios are far more sensitive to local terrain roughness so there is rather greater variability of the relative ratio within a wind speed class due to the variability of roughness by sector at many stations and the differing terrain types encountered at the 14 stations. In addition, it is known that the response time of the anemometer decreases as the wind speed increases [1]. This may explain why the relative gust ratios appear, on average, to increase after initially decreasing (this initial decrease might be due to a reduction in the turbulent intensity with increasing wind speed). The trend of the relative ratio at some stations contradicted the mean trend. The relative gust ratio Gp at Benbecula, for example, tended to increase with increasing wind speed. This might be thought to be due to the fact that the aerodynamic roughness length of the sea surrounding much of the site increases as wind speed increases but, conversely, the gust ratios for Sumburgh did not show any such trend. It would be unwise to use the trend of the mean relative gust ratio as an indication of the wind speed dependence of the 3 s gust ratio because of the large standard deviation of the relative ratio due to the fact that individual sites can show their own particular characteristics and of course the effective averaging duration of the peak recorded gust is not constant at 3 s. Because of the inter-class variability in the relative ratio the mean ratios by wind speed class do not show any statistically significant decline from 16-20 to 26-30 knot nor is the increase in the mean relative ratio of Gp from 26-30 to > 30 knot statistically significant.

5. Conclusions The DALE 1 min wind data can provide very useful information on the dependence of the gust ratio upon the terrain roughness for averaging periods from a few seconds to 10 min and other interrelationships may be derived - for example the 3 s gust to 10 min mean ratio - but the study would have been more comprehensive if winds over averaging periods from 10 to 30 s could have been recorded by the DALE stations. It would have been then possible to provide a comprehensive assessment of the guidance in Ref. [6] on the terrain dependence of gust ratios for all gust averaging periods from a few seconds to 10 min. The results in the present study suggest that the best summary guidance given in Ref. [6] overestimates the 1 and 10 min gust ratios by roughly 5%, but the individual gust ratios of these periods obtained from the data of Durst, Deacon, Vellozi and Cohen and Weiringa are in fair agreement with the gust ratios derived from the DALE data. This work has obtained the empirical relationship between the gust ratio, averaging duration and terrain roughness using a much larger body of data than has been

354

J. Ashcroft/J. Wind Eng. Ind. Aerodyn. 53 (1994) 331-355

available previously in any one study. The data covers a wide range of terrain categories through the careful choice of stations. Though individual sector roughness length estimates may well be erroneous, once sufficient data is accumulated the general relationship between gust ratios and terrain roughness becomes clearer and a best fit line can be drawn with some confidence for the majority of terrain types, though users of the figures should note that less confidence can be placed in the trend of gust ratios when the roughness length is > 40 cm. The gust ratios provided in this study are derived in a consistent way and usefully update and augment the smaller body of quoted information on the values of the gust ratio derived from various sources as summarized, for example, in Ref. [4]. The peak gusts recorded at the Meteorological Office anemograph stations are conservatively assumed to have an effective averaging duration of 3 s. A comparison of the best fit line to the DALE peak recorded gusts with the best guidance in Ref. [6] does not lead to a revision of this assumption. In addition, a comparison of the observed peak gust to 10 min mean ratios with the gust ratio predicted from a relationship of Cook [7], assuming a gust duration of 3 s, gave good results over terrain of moderate roughness. It is therefore suggested that the peak gust duration should not be changed from its assumed value of 3 s as long as the hourly mean wind speed is roughly 11 to 20 knot. It would be worthwhile to investigate, using anemograph data, the relationship between the peak recorded gust and the hourly mean wind on occasions of very strong winds, say 30 knot or more and to compare the gust ratio-terrain roughness relationship with previous relationships given, for example, for the 1 s gust. It would be possible to further investigate the relationship of the short period gusts to the hourly mean wind by defining the hourly mean wind as the average over an hour centered around the gust time rather than the clock hour, which has been the normal practice. This would, in practice, be quite difficult with the DALE archive as there is no guarantee that, after quality control, the preceding and subsequent hours' data will remain for processing along with the data for the current clock hour. A longer period of DALE data ought to be processed to enable a sufficient body of wind observations to be made available for such a study. An important point brought out by the study is the need to undertake some check on the temporal variation of the wind before calculation of the gust ratio. The DALE 1 min winds were most useful in this respect. It is believed that the stationarity checks undertaken were most valid and very necessary. It may not always be possible to undertake such checks in the routine analysis of anemograph data but, fortunately, it appears that, when the hourly mean wind speed is greater than 20 knot, the gust ratio may be considered to be effectively free from the effects of major unsteadiness in the mean wind. References [1] Handbook of meteorological instruments, Vol 4. Wind instruments (Meteorological Office, HMSO, London, 1980). [2] C.S. Durst, Wind speeds over short periods of time, Meteorol. Mag. 89 (1960) 181-186.

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[3] E.L. Deacon, Wind gust speed: Averaging time relationship, Aust. Meteorol. Mag. 51 (1965) 11-14. [4] C.E. Hardman, N.C. Helliwell and J.S. Hopkins, Extreme winds over the United Kingdom for periods ending 1971, Climatological Memorandum no. 50A, Meteorological Office, Bracknell (1973). [5] J. Weiringa, Gust factors over water and built-up country, Bound. Layer Meteorol. 3 (1973) 424-441. [6] BS8100, Lattice towers and masts. Part 1: Code of practice for loading; Part 2: Guide to the background and use of Part 1 (British Standards Institution, London, 1986). [7] N.J. Cook, The designer's guide to wind loading of building structures, Part 1: Background, damage survey, wind data and structural classification, Building Research Establishment, Garston (1985). [8] R.R Brook and K.T. Spillane, The effect of averaging time and sample duration on estimation and measurement of maximum wind gusts, J. Appl. Meteorol. 7 (1968) 567-574. [9] M.E. Greenway, An analytical approach to wind velocity gust factors, Eng. Sci. Rep. 1241/78, Oxford University Engineering Laboratory, Oxford (1978) (unpublished). 1-10] J. Ashcroft, Report on the study of gust ratios derived from DALE data and their dependence upon averaging time, surface roughness and boundary layer stability, PSP Scientific Support Group Technical Note no. 1, Meteorological Office, Bracknell (1992). [11] J. Weiringa, An objective exposure correction method for average wind speeds measured at a sheltered location, Quart. J. R. Meteorol. Soc. 102 (1976) 241-253. [12] M. Greengrass, Surface roughness information for the calculation of local wind climatologies, Advisory Services Discussion Note no. 16, Meteorological Office, Bracknell (1989) (unpublished). [ 13] R.J. Adams, Summary of theory of Weiringa's 'exposure correction factor', Met O. 3 Internal Report, Meteorological Office, Bracknell (1984) (unpublished).