Journal of Wind Engineering and Industrial Aerodynamics, 26 (1987) 53-64 53 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

P R E D I C T I O N O F W I N D V E L O C I T Y F L U C T U A T I O N S F R O M U P S T R E A M D A T A

TIMOTHY A. REINHOLD

Applied Research Engineering Services, Inc., Raleigh, NC (U.S.A.)

DAVID J. HALCROW

Dofasco, Inc., Hamilton, Ont. (Canada)

(Received May 26, 1986)

Summary

A wind velocity prediction scheme which utilizes data from an upwind anemometer to predict the occurrence of significant lulls in the wind at a downwind test site has been developed. A computer system developed for the purpose of monitoring and predicting wind conditions calcu- lates the time for lulls in the wind to travel from the upwind prediction anemometer to the test site. The prediction scheme utilizes Taylor's hypothesis with a modification to account for the fact that, in a shear flow, significant gusts and lulls are not transported at a rate which corresponds to the measured mean velocity.

Two prediction algorithms are presented. The first algorithm provides the highest probability of successful predictions while the second provides larger prediction lead times. Data from field tests have indicated that significant gusts and lulls can persist for several hundred meters and that prediction times in excess of 1-2 min can be achieved under certain atmospheric conditions.

1. Introduction

Pred i c t i on of wind veloci t ies ove r sho r t lead t imes ( less t h a n 5 m i n ) can be of p rac t i ca l i m p o r t a n c e . P o t e n t i a l a reas of app l i ca t ion include the t a k e o f f a n d l and ing of l ight a i rc raf t , d e v e l o p m e n t of co r re l a t ions b e t w e e n wind f luc tua- t ions a n d wind loads on s t ruc tu res , p red ic t ion of wind cond i t ions for a th le t i c even t s such as h igh div ing a n d ski j um p i ng , a n d p red ic t ion of su i tab le condi- t ions for wind sens i t ive e x p e r i m e n t s which m u s t be c o n d u c t e d a t an exposed site.

A large f r ac t ion of r e sea rch c o n c e r n i n g wind p red ic t ion over sho r t lead t imes has been d i rec ted t o w a r d s a i r p o r t app l i ca t i ons [ 1, 2 ]. S ince a i r c ra f t t r a n s v e r s e severa l k i l o m e t e r s du r ing t a k e o f f a n d landing, wind m e a s u r e m e n t s a t an ane- m o m e t e r loca t ion are on ly useful for p rov id ing an ave rage r e p r e s e n t a t i o n of

0167-6105/87/$03.50 © 1987 Elsevier Science Publishers B.V.

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the general flow field. Consequently, the emphasis in research for wind predic- tion associated with airport applications has centered on determining appro- priate averaging times which will ensure that anemometer based mean and peak values are representative of the general flow field [ 2 ].

In contrast to this prediction of average wind properties, the research and development reported in this paper was motivated by the need to conduct field experiments when the actual wind speed at a test site is less than a threshold value of approximately 1.5 m s-1. The test procedure involves a countdown where various recording instruments are started and allowed to reach operat- ing status prior to the test event. Consequently, the test procedures can require lead times which may be as large as 2 min. In addition, each test requires a significant set-up time and once the test countdown sequence has proceeded beyond a certain point (nominally 30 s prior to the test event) aborting the test requires a lengthy time to reset. Thus, the objective of this research was the development of procedures which would provide a high success rate for predition of wind speed events (lulls) where: (1) the speed at the test site is below the desired threshold, and ( 2 ) the predictions can be made up to 2 min or more before the occurrence of the lull at the test site.

The prediction would be a relatively simple measurement task if significant periods of calm could be expected. However, the tests are conducted during daylight hours in the summer months at a site which generally experiences mean wind speeds in excess of the 1.5 m s -1 threshold. Consequently, it is necessary to predict the presence of temporary lulls in the wind at the test site.

2. Basis for wind prediction model

Two approaches were considered for developing the required wind predic- tion capability. The first approach utilizes present and previous values of wind speed at the site to predict future values. The second approach uses data from an upstream position and is based on Taylor's hypothesis which states that the pattern of wind fluctuations at the upstream position will be repeated at the downstream position at a time dependent upon the spacing between locations and the mean wind speed.

The first approach is similar to a visual technique employed in the past for conducting field experiments at the Defense Research Establishment Suffield (DRES) and relies on waiting for the wind speed to drop below the desired threshold at which time the countdown is initiated. If the lull lasts long enough the test is successful. If, on the other hand, the lull is short, the operator can abort the test up to 30 s before the test event.

An estimate of the reliability of a procedure based on this first approach can be obtained by considering time series models of horizontal wind speed. A time series model [3] was developed for wind speeds measured at 1 s intervals at the top of a cooling tower, 127 m above ground level. The best model for winds with speeds less than 10 m s- 1 was found to be

55

Ut=O.7744Ut_l +at (1)

where Ut is the velocity one second later than Ut_ 1 and a~ is a random value. Equation (1) indicates a very short memory time, and that there is a low

probability of successfully predicting instantaneous velocities more than a few seconds in advance. Consequently, this approach does not offer much potential for predicting whether lulls will have a sufficient duration to ensure a success- ful test. It was considered unlikely that any pattern could be extracted which would make it possible to predict, with a high confidence level, the occurrence of a lull prior to its arrival based on data from a single point.

The second approach is intuitively appealing, but its utility hinges on limits to the transport of velocity fluctuations (applicability of Taylor's hypothesis or a modified Taylor's hypothesis) at low elevations in atmospheric surface layer winds. Several studies have been conducted to investigate the transport of velocity fluctuations in shear flows [4, 5] and in the atmospheric surface layer [6-8]. It has been shown that velocity fluctuations in a boundary layer are transported at various rates which depend on the scale of the fluctuations. Generally, small scale eddies travel with the mean velocity while larger eddies travel at a faster rate [ 5-7 ].

Limits to transport distances for eddies of various sizes have not been estab- lished. However, full scale studies have demonstrated that large scale eddies can persist for distances of up to 100 m [6, 7]. Generally, eddies are trans- ported increasing distances as their scale increases and as the terrain becomes smoother [ 7 ]. Thermal instability tends to foster the formation of large scale eddies which in turn persist longer and are transported greater distances.

The actual test site is in relatively open smooth terrain and the tests are conducted during daylight hours in the summer months when thermal insta- bility of the atmosphere surface layer tends to occur. Thus, it is well suited for a prediction scheme based on Taylor's hypothesis but modified to account for the higher translation rate of the large scale fluctuations.

3. Measurement/prediction system components

A microcomputer based system was developed capable of acquiring and ana- lyzing up to 8 channels of data at frequencies of 1 Hz. The system was designed to allow measurements and recording of horizontal wind speeds and directions at four anemometer locations. In addition to the central processing unit, the system included a monitor, a printer, two floppy disk drives, an anemometer/ computer interface and four anemometers. The internal computer components included an analog to digital conversion board, a real time clock board, and a modem for transferring data from the microcomputer to another computer.

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3 140°

Fig. 1. Details of anemometer setup.

Interactive software developed for the project included programs for data acquisition, data analysis, plotting and on-line prediction of significant lulls in the wind.

4. Field investigations

During the course of the research and development reported in this paper, two field investigations were conducted near the test site. The first investiga- tion was designed to provide a test of the data acquisition system and analysis equipment and to provide data for use in assessing the potential for making reliable predictions. The preliminary investigation also allowed the authors to become familiar with the test site and its wind conditions so that reliable pre- diction schemes could be devised. The initial investigation was conducted on 3 and 4 February 1983. Once work on a prediction scheme had been completed, a second series of field tests at the site were conducted. The second investiga- tion was undertaken on 16-19 August 1983, to obtain additional data and to demonstrate and test the final version of the wind velocity prediction program.

A typical layout of three of the anemometers is illustrated in Fig. 1. Ane- mometer 3 would represent the test site with anemometer 1 being the upwind anemometer. The anemometers were aligned with the mean wind direction at

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4

m 3

2 1

0 0 I00 200 300 400 500 600 700 800 900 I000

5

3

1

0 0 100 200 300 400 500 600 700 800 900 I000

5

3

2

1[ . . . . . . . . . . . . . . . . . . i .": ' . . . . V . . . . . , 0 O lOg 200 300 400 500 600 700 800 gO0 I000

SECONDS

Fig. 2. Concurrent wind velocity records.

the beginning of each day and reoriented as required by shifting wind direc- tions throughout the day. The anemometers were lightweight and could be reoriented in 30-45 min.

Wind velocity and direction data were recorded at one second intervals for each anemometer location. Characteristics of the data recorded at the site dur- ing the first and second field investigations were significantly different. The initial investigation was completed under overcast winter conditions where it appears that inversion type conditions were present which dampened the for- mation of the large scale turbulence (gusts and lulls ). This data exhibited only small scale turbulent activity with corresponding wind lulls having durations in the 10-20 s range. The second investigation took place under clear summer skies (typical conditions for the anticipated use of the system at the DRES site). Thermal mixing was present in the atmosphere causing the formation of large scale turbulence fluctuations with many lulls exceeding 60 s.

A sample plot of wind conditions recorded during the summer field investi- gation is shown in Fig. 2. The test configuration under which the data was recorded is shown in Fig. 1.

5. Persistence and transport of eddies

The key to assessing the prediction potential is the evaluation of the corre- lation between data from upwind and downwind anemometers. The correla- tion between the upwind and downwind anemometer data was evaluated by visual inspection and by computation of space-time correlations.

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5 '

a :~ 2

I

0 o IDD ZDD aOD 40D 5D0 SOD ?DD eoo 90D IDOD 5 ~ "~ ANEMOMETER 2 - - - - ANEMOMETER I I

1

0

D 100 200 3DD 4DD 5DD B00 7D0 800 900 IDOD

5 • ANEMOMETER 3 ---- ANEMOMETER i

1

0 , . . i . . ~ . . . . t . . . . i . . , . . . . i . . . . , . . . . i . . . . i

0 IOD 2DD 3D0 400 5DO BDO 700 800 9D0 IODO

SECONDS

Fig. 3. Comparison of shifted upstream data with downstream data (shifted by travel time of mean velocity).

An initial visual evaluation of the correlation between data shown in Fig. 2 is illustrated in Fig. 3. The 1,024 s data block used in the illustration was obtained using the anemometer configuration shown in Fig. 1 on 17 August 1983. The dashed lines in Fig. 3 represent data from anemometer I which are shifted by the times required for a particle traveling with the mean velocity as calculated at the upwind anemometer (anemometer 1 ) to traverse the dis- tances between anemometer 1 and each of the downstream anemometers. Clearly, the large scale structure of the records is more highly correlated than the small scale structure.

Cross-correlation functions between anemometer 1 and each of the other anemometers are illustrated in Fig. 4. The cross-correlations have been cal- culated from the data illustrated in Fig. 2. The vertical lines on the cross- correlation functions indicate the time of the peak correlation coefficient. This time is designated as X/UE where X is the distance between anemometers and UE is the effective velocity of the wind in transporting the flow features between the anemometers. The time of the peak correlation, X/UE, was 19 s between anemometers i and 2, and 42 s between anemometers I and 3. The travel times of winds between anemometers, based on the mean wind velocity, U, at the upwind anemometer, were 34 s between anemometers I and 2, and 79 s between anemometers i and 3.

A second visual assessment of the correlation between the data shown in Fig. 2 is presented in Fig. 5. In this figure the upstream record (dashed lines) was shifted by the time corresponding to the maximum cross-correlation, X/UE.

1 .IB

.6

.4

.2

0

- .4 - . B

-. S

-1

ANEMOMETERS 1 AND 2

~ H , l l , , J TO 40 60 eO 100 SECONDS

59

1 ANEMOMETERS 1 AND 3

. 6

. 4 UK

. 2

0 ,,,~1 20 40 60 80 lOO SECONDS

- .4 -°6

- . S

-1

Fig. 4. Cross-correlation functions between wind velocity measurements at different anemometers.

Clearly, a better correlation of the large scale structure is achieved. In fact, for the major lulls the visual correlation is quite high even for the largest separa- tion where the maximum cross-correlation coefficient was 0.59.

Correlation coefficients for data recorded in the summer were generally higher than those recorded in the winter for equivalent distances between anemo- meters. Correlation coefficients based on winter winds typically fell below 0.5 for anemometer spacing greater than 50 m. Summer wind conditions, such as those shown in Fig. 2, produced coefficients as high as 0.6 for distances in excess of 150 m. At distances of 50 m summer conditions produced correlation coefficients typically in excess of 0.75. The differences between correlation coefficients based on summer and winter data are caused by the presence of thermal mixing in the atmosphere in the summer months. Higher correlations in the summer indicate that eddies persist longer, allowing greater travel time between anemometers and longer prediction intervals. A comparison of the maximum cross-correlation coefficient versus the time delay of the peak cor- relation coefficient for winter and summer conditions is shown in Fig. 6. These data indicate that correlation coefficients as high as 0.5 may be obtained for delays of up to 60 s.

60

4

3 2 1

F . . . . , . . . . , . . . . i . . . . , . . . . i . . . . , . . . . i . . . . i , , , , i . . . . i , 0

0 lOO 200 300 400 500 600 700 800 go0 lOOO 5 4 II~ A:. ANF-./,IOMETER ~ ANEMOMETER i

1

0 o 1oo 2o0 3o0 ,Do 5oo 6oo TOP Ooo Ooo Io00

5 ~ ANEMOMETER 3f) ANEMOMETER I 7 4

~z I

0 0 I O0 200 300 400 500 600 700 800 900 1 DO0

SECONDS

Fig. 5. Comparison of shifted upstremrn data with downstream data (shifted by time of peak correlation).

6. Pred ic t ion o f des ired w i n d condi t ions

Th e objective of this s tudy was to predict, up to 2 rain in advance, the occur- rence of wind velocit ies be low about 1.5 m s - 1 in order to conduct wind sensi-

I

LU u ~ Q. 8

(J

~0.6

~0.4

(.J

x

0

[] SUMMER

~ ~ _ o WINTER

n u . . . . . . . \ \ \ \ \ \ \

l l l l l ] l l l l l ] l i l i l l l l l i l i l l i l l l [ l l l l l l l J l l ! l l l t l I

20 40 60 80 I00 TIME DELAY (SECONDS)

Fig. 6. Decay of maximum cross-correlation coefficients.

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tive experiments. Successful predictions can be made if: (1) the upstream anemometer is located far enough away from the site that it takes the desired prediction time or longer for wind to travel from the upstream anemometer to the site and if the lull remains largely intact for that distance; or (2) the dis- tance between the anemometers is less than the desired prediction time but the lull is of a long enough duration that the wind speed at the site is still below the desired threshold when the test is conducted.

In order to provide for the two possible prediction methods outlined above, two schemes were developed and implemented on the computer, as branches of a single program. The prediction schemes use a correction factor based on the time associated with the peak of the cross-correlation, X/UE, between ane- mometers at the upwind location and the test site as compared with the travel time associated with the mean velocity.

The prediction routines include an initiation period where the system is "calibrated" to the test site and existing wind conditions. During this initiali- zation period, 512 s of data are simultaneously acquired from all wind velocity and direction channels. Following data acquisition, a cross-correlation is nor- mally computed between the records from the upwind and test site anemo- meters and the time associated with the peak of the cross-correlation is compared with the time associated with the distance between the anemometers divided by the mean velocity. However, at large separation distances, signifi- cant gusts or lulls are necessary in order to ensure reasonable cross-correla- tions. Thus, if large gusts or lulls are relatively rare, if may be necessary to acquire and store data several times before a suitable record is captured.

The peak of the cross-correlation function corresponds to the opt imum time delay for prediction based on the upstream data and current mean wind veloc- ity (mean value for the last 512 s of data). Given the separation distances between anemometers and the mean velocity at the upwind anemometer, a factor is calculated which relates the translation speed of large scale eddies to the mean velocity. The time delay corresponding to the peak value of the cross- correlation function is printed on the monitor screen and represents the max- imum feasible prediction lead time which can be attained for the current mean wind speed and anemometer locations (using the first prediction scheme). If the maximum possible prediction time is not sufficient for the first prediction scheme to be utilized, the location of the anemometers can be changed and the program restarted or predictions based on the second scheme can be made. The program prints a warning if the peak value of the cross-correlation func- tion is less than 0.25.

Travel time of the lull between upwind and prediction anemometers

= Correction Factor.X/U

XlUE = "X/U (2)

X/U,

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where X is the distance between upwind and prediction anemometers, Us is the velocity of the large scale structure between upwind and test site anemo- meters, UI is the mean velocity at the upwind anemometer based on an initial data block of 512 s, and U is the current mean velocity at the upwind anemometer.

If the lead time is sufficient, the first prediction sequence is initiated when the wind velocity has remained below a preset threshold velocity for 15 s. The prediction sequence is automatically aborted if the wind velocity does not remain below the threshold value for 30 s. This helps to ensure that a signifi- cant lull has been identified which may persist for the required time and dis- tance. Once the prediction scheme has been initiated, the computer calculates the estimated time of arrival of the 15 s point in the lull at the test site. The estimate is calculated using eqn. (2) which utilizes the previously determined correction factor and the present mean wind speed at the upwind anemometer. The computer waits until the time remaining for the 15 s point to reach the prediction site equals the desired prediction time before prompting the oper- ator to start the test countdown.

The probability of achieving a successful prediction using the first scheme is increased by using an intermediate anemometer which is placed between the upwind anemometer and the test site. The intermediate anemometer is located such that the time required for translation of lulls between it and the test site anemometer is greater than the minimum abort time. The computer checks to ensure that the predicted lull passes the intermediate anemometer and that it will arrive at the test site within a few seconds of the original prediction. If the lull is not detected at the intermediate anemometer, or if the new estimate of the arrival time is significantly different from the originally predicted arrival time, the operator is instructed to abort the test. If all checks are successful, the computer assumes that the test has proceeded and continues to take data for at least 15 s after the estimated time for conducting the test. It subsequently stores on floppy disk the wind data from this buffer and the preceding buffer of 256s of data so that the record of wind conditions during the test is available for subsequent analysis.

The second scheme allows predictions to be made when the transport time between the upwind location and the test site is less than the requested pre- diction time. This option is activated whenever the mean wind speed becomes so large that the requested prediction time exceeds the expected travel time between the upwind and test site anemometers. As in the first scheme, the prediction sequence is activated after the velocity has dropped below the threshold for 15 s. An abort will be indicated if the end of the lull is encountered at the upwind anemometer before a time period has elapsed which is greater than the requested prediction time minus the calculated transport time to the test site. For the abort to be successful, the calculated transport time must be greater than the minimum abort time. If not, the abort could be indicated too

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late for implementation. In order to avoid this situation, no prediction is made if the transport time is less than the minimum abort time. If the lull lasts for a sufficient time, the computer locks the prediction sequence and assumes that the test has proceeded.

The program provides for manual override of the prediction sequence at any time by aborting the countdown. All internal parameters are reset and the computer begins looking for the next significant lull to start the prediction process over again.

7. Conclusions

Based on analyses of field tests and a review of literature on the validity of Taylor's hypothesis in atmospheric boundary layer flows, a wind velocity pre- diction scheme which utilizes data from an upwind anemometer can be expected to operate successfully under certain atmospheric conditions. In addition, since the prediction process requires the identification of significant large scale lulls in the wind velocity, the chances of successful predictions for lead times of 1-2 min is much higher than would be the case for predicting values of the instan- taneous wind velocity. This is due to the fact that the large scale eddy structure of the atmospheric flow tends to persist for significantly longer times and downstream displacements than the small scale flow structure.

It has been established that large scale fluctuations move faster than the mean velocity transport rate at elevations close to the ground. Using this knowledge, it has been demonstrated from field tests that large scale eddies can remain largely unchanged over distances exceeding 150 m.

Interactive computer software for performing a wind velocity prediction function has been developed. The software uses a calculation of the cross-cor- elation function between the upwind and prediction site anemometers to deter- mine a factor which compensates for differences between the travel speed of large scale eddies and the mean wind speed.

Two prediction schemes have been implemented. When the transport time between the upwind anemometer location and the test site is greater than the required prediction time, the first scheme is implemented. When the transport time is less than the required prediction time but greater than the minimum abort time, the second scheme is implemented. If the transport time is less than the minimum abort time, then neither prediction scheme is implemented. Probabilities of successful prediction are increased for the first prediction scheme by utilizing an intermediate anemometer to check whether the desired conditions are being transported as predicted.

Acknowledgments

The work reported in this paper was carried out while the authors were employees of Morrison Hershfield Limited, Edmonton, Alberta, Canada.

The authors wish to express their appreciation to Mr. J.T. Templin of DSMA and formerly of Morrison Hershfield Ltd. for his advice and assistance in the

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p r e p a r a t i o n of th is paper . T h a n k s are also e x t e n d e d to the s t a f f o f the Defense Resea r ch E s t a b l i s h m e n t Suffield, Ra l s ton , Alber ta , unde r whose guidance the work was car r ied out. T h e work was funded by Supp ly a n d Services C a n a d a unde r c o n t r a c t 01SG,97702-R-2-5742.

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7 (1974) 309-321. 7 T. Mizuno and H.A. Panofsky, Boundary Layer Meteorol., 9 (1975) 375-380. 8 S. Berman and C.R. Sterms, Boundary Layer Meteorol., 11 (1977) 485-506.