Investigation of turbulence measurements with a continuous wave, conically scanning LiDAR. Risø-R-Report

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1 Investigation of tubulence measuements with a continuous wave, conically scanning LiDAR Risø-R-Repot Rozenn Wagne, Toben Mikkelsen, Michael Coutney Risø-R-168(EN) Mach 009

2 Autho: Rozenn Wagne, Toben Mikkelsen, Michael Coutney Title: Investigation of tubulence measuements with a continuous wave, conically scanning LiDAR Division: Wind Enegy Division Risø-R-168(EN) Mach 009 Abstact (max. 000 cha.): LIDAR systems ae getting moe and moe accuate and eliable. It has been shown many times that the mean hoizontal wind speed measued by a lida ove flat teain compaes vey well with that measued by a cup anemomete. But can a lida measue tubulence? Hee we investigate the case of a continuous wave, conically scanning Zephi lida. Fist, the wind speed standad deviation measued by such a lida gives on aveage 80% of the standad deviation measued by a cup anemomete. This diffeence is due to the spatial aveaging inheently made by a cw conically scanning lida. The spatial aveaging is done in two steps: 1) the weighted aveaging of the wind speed in the pobe volume of the lase beam; ) the aveaging of the wind speeds occuing on the cicula path descibed by the conically scanning lida. Theefoe the standad deviation measued by a lida esolves only the tubulence stuctues lage than a length scale depending on the cicle diamete and the mean wind speed (ange of magnitude: 100m). Howeve, the Zephi lida gives anothe tubulence quantity, the so-called tubulence paamete, which can esolve tubulence stuctues with a smalle length scale. In this pape, we suggest a volumetic filteing of the tubulence to epesent the effect of the spatial aveaging opeated by a lida when measuing the wind speed. We then evaluate this model by compaing the theoetical esults to expeimental data obtained with seveal Zephi systems, fo both tubulence quantities. ISSN ISBN Contact no.: Goup's own eg. no.: (Føniks PSP-element) Sponsoship: Cove : Pages: Tables: Refeences: Infomation Sevice Depatment Risø National Laboatoy fo Sustainable Enegy Technical Univesity of Denmak P.O.Box 49 DK-4000 Roskilde Denmak Telephone bibl@isoe.dtu.dk Fax

3 Contents 1 Intoduction 5 Volume aveaging: theoy..6.1 Staing lida _Pobe length aveaging..6. Conically scanning LiDAR _ Spatial aveaging ove a cicle.7 3 LiDAR tubulence measuement What can a cw conically scanning lida tell us about tubulence? Illustation with the Kaimal spectum 13 4 Expeiment Desciption of the expeiment Results.15 5 Discussion Standad deviation Radial speed vaiance Conclusions....0 Refeences 1 Appendix...3 Risø-R-168(EN) 3

4 Peface The authos gatefully acknowledge the inteesting discussions and useful data fom M Hais and C Abiven fom Natual Powe. This wok was pefomed as a task unde Wok Package 6 of the Euopean Union s Sixth Famewok Pogamme (FP6) Upwind poject. This epot is a fomal deliveable (D5) in that context. Rozenn Wagne is suppoted by the Maie Cuie ModObs Netwok MRTN-CT Risø-R-168(EN)

5 1 Intoduction LiDAR systems ae moe and moe attactive fo the wind enegy industy, because of thei ability to measue mean wind speed pofiles up to about 00m. Thei accuacy has inceased significantly ove the last 5 yeas. 10 minutes mean wind speed measued by some LiDAR systems compae now vey well with cup anemomete measuements [1]. Meanwhile anothe quantity of geat inteest fo the wind industy is the tubulence. The wind speed standad deviation measued by a emote sensing device is inheently diffeent fom the one measued by an anemomete. Indeed an anemomete measuement can be consideed as a point measuement, wheeas a LiDAR system measues ove a volume. In this pape we conside the volume aveaging effect obtained with a continuous wave (cw) QinetiQ ZephiR LiDAR. Fistly, fo such a system, the measuement at a given height is achieved by focusing the lase beam at the equied distance. The wind speed component along the lase beam (the adial speed) esults fom a weighted aveage ove the pobe volume. Sjöholm et al. [] poposed a volumetic filteing of the the tubulence to epesent the effect of aveaging within the pobe volume fo a ZephIR LiDAR. They have shown a good ageement between this model and expeimental data. Secondly, a ZephIR lida device conically scans the ai at a ate of one evolution pe second. The hoizontal wind speed esults fom the adial speeds obtained ove one o thee complete otations. Theefoe thee is an aveaging of the wind speed ove a cicula path cented above the scanning lida. In this pape we descibe the spatial aveaging opeated by a conically scanning lida when measuing the wind speed and we focus on the effects of the conical scanning. We then efine the model suggested by Mikkelsen & Jøgensen [3] and evaluate these impovements by compaing the theoetical esults to expeimental data. To ealize such a compaison, we can look at two quantities given by a ZephIR LiDAR: the wind speed standad deviation and the tubulence paamete. These two paametes give infomation on diffeent scales of tubulence. Although the fist one seems obvious, the standad deviation fom a lida is diffeent fom the coesponding standad deviation measued by a cup anemomete because of the spatial aveaging. On the othe hand the tubulence paamete is not that obvious and we futhe explain what this quantity epesents in tems of tubulence covaiances. This investigation theefoe has two main objectives: - to define and evaluate a simple model fo the filteing effect of the conical scanning; - to povide an intepetation of the standad deviation and the tubulent paamete measued by a ZephIR lida. Risø-R-168(EN) 5

6 Volume Aveaging: theoy.1 Staing LiDAR _ Pobe length aveaging The QinetiQ ZephIR lida consists of a continuous wave (cw) coaxial lase and detecto system [4]. In ode to explain the way of opeation of the system, we fist conside a LiDAR staing in one diection. It emits a cw lase adiation, and detects the Dopple shift of the signal backscatteed by the paticles convected by the ai. This Dopple shift is popotional to the adial wind speed, V, i.e. the pojection of the wind speed vecto, u = { u, v, w }, in the lase beam diection [5]. A cw lida measues the adial wind speed at a given distance by focusing the lase beam at that distance. The powe of the lase is then distibuted along the beam with a distibution that has its maximum at the focus point. The adial wind speed V () measued by a cw lida focused at a location can geneally be expessed by integation along the lase beam of the wind field u pojected in the diection of the beam: V() = ϕ().( s n u sn + n) ds n () whee is a unity vecto along the beam and ϕ s is the spatial volume aveaging function. Fo a focused cw coheent Dopple lida, the spatial volume aveaging function is given by the powe distibution along the beam which can be appoximated by a Loentzian function [6]: (1) 1 zr ϕ() s = π z + ( s ) R () whee s is the distance fom the focus point along the beam, the focus distance o ange and z R is the so-called Rayleigh length, elated to the depth of focus. The depth of focus o pobe length is geneally defined as zr. Fo the seies ZephIR lida, the Rayleigh length was estimated to be: z R = Accoding to the Loentzian function, the pobe length inceases quadatically with the focus distance. The aveaging of the wind speed ove the pobe length has the effect of a low pass filte on the wind speed powe spectum, which esults in filteing out the tubulent stuctues with a length scale smalle than the pobe length. Indeed, assuming the beam to be in the diection of the mean wind speed, the countepat in the wave-numbe domain of the line-ofsight spatial aveaging function (φ) is: z R k1 LLoentzian = e (3) whee k 1 is the wave numbe along the mean wind diection. Sjöholm et al. [] validated the effect of this filte by analysing specta fom wind speed measuements with a staing cw LiDAR and compaing them to sonic measuements. If howeve the line-of-sight of the lida does not coincidence with the mean wind diection, the atio between the volume-aveaged lida-obseved wind speed spectum and the λ 1 The theoetical value is given by zr = whee λ is the wavelength and a 0 is the adius in the telescope whee the intensity has fallen to e of π a its 0 cente value. With a standad ZephIR s optical 3 lens design a0 4 mm and hence theoetically should be zr Howeve, ou measuements have shown that the effective apetue is somewhat smalle, esulting in a best estimate fomula: z = z R 6 Risø-R-168(EN)

7 spectum of the coesponding wind speed component measued by a sonic anemomete, will in geneal then be dependant on the entie thee-dimensional stuctue of the tubulence []. In this pape we ae consideing the wind speed standad deviation (see section 3), theefoe the integal of the spectum and this does not depend on the shape of the specta. We expect that the spectum measued with a lase beam not aligned with the wind diection to have a diffeent shape but the same integal.. Conically scanning lida_ Spatial aveaging ove a cicle In ode to get a 3 dimensional wind vecto at a given height, adial wind speeds in diffeent diection ae equied. To do so the QinetiQ ZephIR lida conically scans the ai, with a fixed angle Ф=30 fom the vetical (see Figue 1), at the ate of one otation pe second. The cw lida design allows a Dopple specta acquisition fequency of 00000Hz. Each goup of consecutive 4000 Dopple specta ae aveaged (coesponding to an aveage ove 0 milliseconds o a conical segment of 7.6m when focusing at 100m) in ode to impove the signal to noise atio, afte which the Dopple peak should stand clealy above a flat shot-noise floo [7]. A adial wind speed is deduced fom each aveaged spectum by finding the peak fequency (f peak ) using the centoid method. The adial speed (v ) is diectly popotional to the peak fequency accoding to the following elation: v f peak = whee λ is the lase wavelength. Nominally, 50 adial wind speeds ae obtained λ fo each otation. Figue 1 Sketch of the conical scanning patten of the lase beam of a Zephi lida. The gay scale epesents the distibution (φ) of the powe ove the lase beam. Hee the lase focuses at 70m agl. The ed dots epesent the middle of each 7. angle ove which the Dopple specta ae aveaged. Risø-R-168(EN) 7

8 As the backscatteed signal is mixed with the oiginal signal, this lida system cannot distinguish the sign of the Dopple shift (i.e. whethe the wind comes towads the lida o goes away). Theefoe the 50 o 150 adial wind speeds as function of the azimuth angle follow a ectified cosine wave: V( θ) = Ai Cos( θ θwind ) + B (4) whee θ is the beam azimuth angle (see Figue ). We can then deduce the wind diection: θ wind, the hoizontal and vetical components of the wind speed: U = A/ Sin( Φ), w= B/ Cos(Φ) whee Φ is the conical angle. V = 7.39 CosH1.86-q wind L Figue Example of esult fom a 3-second scan. The black points ae the actual adial wind speed measuements. The ed line is the fit function (given at the top of the figue). Until sping 008, the scanning time was fixed at 3 seconds (3 otations fo one wind speed vecto). ZephiR lidas now offe the possibility to choose the scanning time of 1 second o 3 seconds (giving 50 o 150 adial wind speeds espectively). Both configuations ae consideed in this pape. The fist step of this investigation is to define a simple filte modeling the effect of the spatial aveaging due to the scanning. An effective instantaneous hoizontal aveaging length scale can be estimated as the combined esult of time lag and the cicula coveage. Fo the ZephIR lida, this means the distance coveed by the cicle of diamete D convected by the mean wind speed U. Figue 3 displays the path of the lase seen by the wind field, i.e. the path of the lase in the coodinate system attached to the wind field of mean diection the x- axis and mean speed U. 8 Risø-R-168(EN)

9 L=0.5U+D L=.5U+D md Figue 3 Path of the lase conically scanning at 50m high (then D=55m) and convected by the mean wind speed U=10m/s, fo 1 second scanning in geen and 3 seconds in blue. Fom that path we can estimate a epesentative length scale fo the filte due to the combined effect of mean wind advection and conical scanning. Theefoe, a simple effective hoizontal length scale,, epesenting an effective filteaveaging length scale fom conically scanning fo n seconds (n=1 o 3), can to a fist appoximation be modelled by: laz = D+ U( n 0.5) 1 = z+ ( n 0.5) U (5) Cos(30) = z+ ( n 0.5) U 3 whee z is the vetical distance to the gound whee the measuement is taken (see Figue 3). The conical scanning has also a low pass filte effect on the wind speed spectum. Tubulence stuctues smalle than the length scale l az cannot be effectively measued by the conically scanning lida. As the magnitude of the adial wind speed vaies with the azimuth angle following a ectified cosine function (see Figue ), the hoizontal components of tubulence ae not filteed homogeneously ove the length scale l az, see Figue 4. In the steam wise diection, the weighting function can be modeled by a ectified sine function: l az π x sin if x laz / fu ( x) = laz 0 othewise (6); The powe spectal tansfe function coesponding to (6) is obtained by nomalising and squaing the Fouie tansfom in the wave-numbe domain: L u Scan π l az π l az 1 cos k 1 cos k π laz + laz = + 4 π l az π l az k + k laz laz (7); Risø-R-168(EN) 9

10 Similaly, in the coss steam diection, the weighting function can be defined by: π x cos if x laz / fv ( x) = laz 0 othewise (8); giving in the following powe spectal tansfe function in the wave-numbe domain: L v Scan π l az π l az sin k sin k π laz + laz = + 4 π l az π l az k + k laz laz (9) In the vetical diection, all vaiation ae taken into account homogeneously (Figue 5), theefoe we can model this effect with a simple Box ca-like filte function: 1/ laz if x laz / fw( x) = 0 othewise (10) The coesponding powe spectal tansfe function in the wave-numbe domain is: L w Scan laz sin k1 ( k1) = laz k 1 (11) 10 Risø-R-168(EN)

11 Figue 4 Top left and ight: Distibution of the adial wind speed in the wind diection and the coss wind diection espectively (plan view fom top of the cone); Bottom left and ight: Weighting functions fo the wind steam component and coss steam component of tubulence espectively. Figue 5 Left: Distibution of the adial wind speed in the vetical diection; Right: Weighting function fo the vetical component of tubulence. Risø-R-168(EN) 11

12 3 Lida tubulence measuement 3.1 What can a cw conically scanning lida tell us about tubulence? A ZephIR can measue two diffeent quantities that give infomation about tubulence. The fist one is the wind speed standad deviation ove 10 minutes, of the 1 o 3 seconds hoizontal wind speeds (obtained fom the fitting of the adial speeds). Fom measuements we know that the standad deviation measued by a LiDAR usually gives only about 80% of the standad deviation given by a cup anemomete, see Figue 6. This is mainly due to the volume aveaging descibed in section. The standad deviation given by a conically scanning LiDAR does not effectively esolve the pat of the tubulence having a scale smalle than the length l az defined peviously. Figue 6 Example of egession plot of the 10 minutes wind speed standad deviation measued simultaneously by a Zephi LiDAR (3 second scan) and a cup anemomete at 40 m. The second quantity povided by a ZephIR LiDAR is the so-called tubulence paamete (TP), defined as the tubulence intensity of the adial wind speed within the scanned cicles: whee ' v π TP 1sec ' π v = u (1) 1sec is the vaiance of the adial wind speed ove 1 otation (π) (see appendix) o fo 1 second. We can define a simila quantity fo a 3 second scan, then we aveage ove 3 ' otations:. TP actually quantifies the goodness of fit of the ectified cosine function to v 6π the adial wind speeds measued ove the cicula path. This paamete contains infomation about the tubulence stuctues with a length scale smalle than l az but lage than the lase beam adial pobe length. 1 Risø-R-168(EN)

13 3. Illustation with the Kaimal spectum To evaluate the effect of spatial filteing we use the Kaimal spectum tansfomed to wave numbe space. The tansfomation between the measued fequency and the wave numbe is based on the Taylo s fozen-wave hypothesis. So that k1, max i Fi( k1) dk1 0 σ = (13) The steam-wise component of the Kaimal specta in wave numbe space is then [4]: 3 z 10 m Fu ( k1 ) = u* kz π ( ) 5/3 + s π (14) Figue 7 Steam wise component of the Kaimal spectum (black) shown as a efeence. Left: spectum filteed with the Loentzian filte (puple), spectum filteed with the scan filte (geen). Right: spectum of 10 minutes steam-wise tubulence obtained fom a cw conically scanning LiDAR (ed), tubulence spectum obtained with the high-pass filte modeling the tubulence unesolved by the conical scanning effect (blue), see equation (17).The specta shown coespond to a focus height z=30m (then the cicle diamete is 34.6m), fo a 3-second scan and z =0.0017z (z=cos(30 )). Figue 7 (left) shows the effect of each spatial filte (L Loentzian and L scan ) on the steam-wise component of the Kaimal spectum. Both kinds of spatial aveaging (ove the pobe volume and the scanning aea) act as low pass filte emoving all the small tubulence stuctues (high wave numbes). As the effect of the conical scanning is much stonge than the pobe length aveaging, the combination of both effects (ed spectum in ight-handed plot in Figue 7) esults in a low pass filte vey close to the scanning filte (geen spectum in left-handed plot in Figue 7). Fistly, Figue 7 (ight) shows also the fist component of the Kaimal spectum as a efeence. Its integal coesponds to the wind speed vaiance: k1, max u Fu( k1) dk1 0 σ = (15) Risø-R-168(EN) 13

14 Secondly, Figue 7 (ight) shows the spectum obtained afte applying the combination of both pass filtes (ed). Fo an ideal wind speed field expeiencing only hoizontal fluctuations and no vetical fluctuations, then the integation of this spectum coesponds to the vaiance measued by a cw conically scanning LiDAR : ' ZephIR u σ ( 1) 10min uzephir u Scan 1 Loentzian 1 0 u F k L ( k ) L ( k ) dk (16) = = 1 Only lage tubulence stuctues (with a length scale lage than l az ) ae left. In eality, both the hoizontal and the vetical speeds contibute to the adial wind speed and theefoe, the wind speed standad deviation obtained with a LiDAR cannot be deived fom the steamwise tubulence spectum only. Howeve, ou objective in this investigation is to make a simple model to compehend basically the spatial aveaging made by a cw conically scanning LiDAR. So we decided to make the ough assumption that the standad deviation fom the LiDAR was coming only fom the steam wise tubulence, i.e. we assume that equation (16) is also tue fo 3-D tubulence. The thid spectum (blue) showed in Figue 7 was obtained by applying the low pass filte coesponding to the Loentzian function and the high pass filte complementay to the scanning filte: ' ZephIR u u = F ( 1) (1 ( u k LScan k1)) LLoentzian ( 1) π 1 10min 0 k dk (17) This integal coesponds to the vaiance of the adial wind speed (as defined in the appendix) due to the steam-wise component of tubulence. As it is an aveage ove 1 (o 3 ) second, it coesponds to the tubulence stuctues with a length scale smalle than l az but lage than the length of the pobe length (z ). Since TP is a tubulence quantity chaacteistic of the small eddies, TP is a combination of the high wave numbe pat of the specta in all 3 dimensions: v ' ( ) ' TP u = v ZephIR π 1sec 1sec 10min ZephIR π 10min = u + v + w 4 ' ZephIR ' ZephIR ' ZephIR π 10min π 10min π 10min ' ZephIR ' ZephIR w u π 10min π 10min (18) and ae obtained as in equation (17) but with the v and w component of the tubulence spectum and with the coesponding filte definitions: v L scan w L scan and. 14 Risø-R-168(EN)

15 4 Expeiment 4.1 Desciption of the expeiment Combined lida and mast measuements wee made at Risø DTU s Test Station fo Lage Wind Tubine in Høvsøe, westen Denmak. Høvsøe is located in vey flat teain and is theefoe an ideal site to make lida measuement tests. The wind is mainly blowing fom west (fom the sea). The facility compises an intensively instumented meteoological mast. It has top mounted anemomete at 116.5m and measuing stations with both cup and 3-D ultasonic anemometes at 100m, 80m, 60m and 40m. Due to its height, intensity of instumentation and high data quality, this mast is well suited fo testing lida pofiles. Cup anemometes ae mounted on the south and sonic anemometes on the noth of the mast. To compae lida measuements to anemomete measuements we selected two wind sectos whee the anemometes ae not influenced by the mast: and The expeimental data used fo this investigation wee obtained with thee ZephiR lidas. The fist one was equipped with the standad softwae using thee seconds scanning to calculate the wind speed vecto. The two othes had an upgaded vesion of the softwae, giving the possibility of one second scanning. All lida systems wee positioned about 50m noth of the met. mast (see sketch) in ode to be fa enough fom the mast to avoid most of the mast wake effects, but also close enough to get sensible compaison with the mast instuments. The data wee selected fo ain fee peiods. Moeove, a ceilomete placed neaby the mast enables us to measue the height of the cloud base. Because Zephi LiDAR measuements can be biased by low clouds, the peiods with cloud base below 1600m wee emoved fom the data sets used fo the compaison. The fist data set (3 seconds scan) was measued in fall 007. The LiDAR was measuing at 40m, 80m, 100m, 116.5m coesponding to mast measuing height. Theefoe we could make compaison with the measuements fom the sonic anemometes at 40m, 80m, and 100m. The second data set (1 second scan) was obtained in sping 008. The lida was measuing at 60m, 80m, 100m and 116.5m. Howeve a faulty sonic anemomete at 80m pevented us fom making compaisons at that height. Theefoe we have esults at only heights: 60m and 100m. The thid dataset (1 second scan) was obtained in Febuay 009. This lida was set to measue at only one height: 80m. As tubulence measuements can be easily coupted by noise, we selected the 10 minutes peiod when the aveage numbe of points used to calculate the fit function was highe than 65% of the maximum possible numbe of points. 4. Results In ode to obseve the effect of the spatial aveaging, we look at the atio between measuements fom the two instuments: lida and anemomete. Fo both the wind speed standad deviation and the adial speed vaiance, the model is compaed to expeimental data at diffeent heights, thus we can obseve the vaiation of the effect of spatial aveaging with height. Moeove, as the length scale l az depends on the numbe of otations (n) ealized duing the scanning, we show the esults fo 1 and 3 evolutions in diffeent plots. 1) Standad deviation: Risø-R-168(EN) 15

16 Figue 8 Vaiation with height of the atio between wind speed standad deviation measued by the Zephi lida scanning fo 3 seconds (3 otations fo each wind speeds vecto) and the wind speed standad deviation measued by the cup anemomete. Compaison of the model pesented in pat 3 and expeimental data. Figue 9 Vaiation with height of the atio between wind speed standad deviation measued by the Zephi lida scanning fo 1 second (1 otation fo each wind speeds vecto) and the wind speed standad deviation measued by the cup anemomete. Compaison of the model pesented in pat 3 and expeimental data. Compaison of the wind speed standad deviation measued by a ZephIR LiDAR to cup anemometes measuements wee pefomed in seveal places, with diffeent ZephIR LiDAR units in vaious types of teain. Figue 10 sum up the esults fo 8 tests in addition to the measuements we made in Høvsøe. 16 Risø-R-168(EN)

17 Figue 10 Compaison of the atios between wind speed standad deviation measued by a ZephIR LiDAR and a cup anemomete fo 8 expeiments made in vaious types of teain (flat, flat with building, complex). The numbes displayed in the plot coesponds to the expeiment numbe and the colo to the type of teain. ) Radial speed vaiance In the follwing plots, we ae compaing the quantities: ( ) ' ' ZephIR = 1sec ZephIR 1sec = π v TP u v and ' ' sonic = v sonic 10min v 10min ' sonic ' sonic ' ( ) 3 sonic u v w 10min 10min 10min = Risø-R-168(EN) 17

18 Figue 11 Vaiation with height of the atio between adial speed vaiance measued by the Zephi lida scanning fo 3 seconds (3 otations fo each wind speeds vecto) and the adial speed vaiance measued by the 3-D sonic anemomete. Compaison of the model pesented in pat 3 and expeimental data. Figue 1 Vaiation with height of the atio between adial speed vaiance measued by the ZephIR lida scanning fo 1 second (1 otation fo each wind speeds vecto) and the adial speed vaiance measued by the 3-D sonic anemomete. Compaison of the model pesented in pat 3 and expeimental data. 18 Risø-R-168(EN)

19 5 Discussion 5.1 Standad deviation The fist obsevation we can make fom Figues 8, 9 and 10 is the wind speed standad deviation measued by a LiDAR gives on aveage about 80% of the standad deviation measued by a cup anemomete in flat teain. The expeimental data coincide with the pediction of the model, which favous the poposed model of tubulence filteing due to the spatial aveaging. Moeove it confims the fact that the volume aveaging is the main eason of the diffeence of the wind speed standad deviation between a cw conically scanning LiDAR and an anemomete. We can obseve that the atio between the standad deviation measued by the two instuments deceases with height. Indeed the aveaging volume inceases with height. Finally, the atio is geneally highe fo the LiDAR scanning fo 1second than fo the LiDAR scanning fo 3 seconds. Again, this is a diect consequence of the size of the aveaging volume which is smalle fo a one second scan than fo a thee seconds scan. 5. the adial speed vaiance The adial speed vaiance is geneally deceasing with height, see Figues 11 and 1. This is due to a combination of diffeent factos including the inceasing spatial volume of aveaging and the deceasing amount of small tubulence stuctues with height. Fo both cases (1 sec and 3 sec scanning) we get good ageements between the model and the measuements at the lowest heights (40m and 60m) but not that good at highe heights. A possible explanation is that TP depends on the goodness of fit of the ectified cosine function to the adial speed points which implies that TP also accounts fo measuement eos including noise, and not only fo tubulence. As the amount of small v tubulence stuctue deceases with height, might account fo eos and noise moe than tubulence at high heights (eo that ae not taken into account in the model). Risø-R-168(EN) 19

20 6 Conclusions We defined a volumetic filteing of the tubulence to epesent the effect of the spatial aveaging opeated by a lida when measuing the wind speed. As the objective was to undestand the pinciple of the spatial aveaging, we decided to keep the model simple, which implied that we have made some ough appoximations. Nevetheless, the aveaged expeimental data coincide elatively well with the model. This confims that the diffeence in wind speed standad deviation measued by a lida and a cup anemomete is mainly due to the spatial aveaging. In aveage, a cw conically scanning lida measues 80% of the standad deviation measued by an anemomete, because such a lida cannot esolve the tubulence stuctues with a length scale smalle than the cicle (descibed by the scanning lida) diamete appoximately. Meanwhile, the tubulence paamete given by a ZephIR lida can give some infomation about the smalle eddies. Howeve, as it also quantifies the goodness of fit of the adial wind speed when calculating the wind speed vecto, the tubulence paamete is easily coupted by noise and it should be consideed only as an aveage indicato of the high fequency tubulence. 0 Risø-R-168(EN)

21 Refeences [1] Coutney, Wagne, Lindelöw, Testing and compaison of lidas fo pofile and tubulence measuements in wind enegy, ISARS 008 poceedings [] Sjöholm et al.,time seies analysis of continuous-wave coheent Dopple Lida wind measuements, IOP Conf. Seies: Eath and Envionemtnat Science 1 (008) TM [3] Mikkelsen, Jøgensen, Tubulence measued by the ZephIR : The Effects of the Conical scanning and Loentzian Pobe Volume Filteing, IEA Meeting 51, Remote Sensing, Risø, Januay 007 [4] Smith et al., Wind lida evaluation at the Danish wind test site in Høvøse, Wind Enegy , 006 [5] Mikkelsen,Jøgensen: Measuing Tubulence with the QinetiQ ZephIR Wind Lida, Upwind pogess epot, 006 [6] Sonnenschein C M, Hoigan F A 1971 Applied Optics [7] M.Hais: Lida fo Tubine contol, NREL technical epot,006] Risø-R-168(EN) 1

22 Appendix: definition of the vaiance of the adial wind speed Refeed to a spheical coodinate system the adial wind speed can be expessed as V ( θ) = usinϕcosθ + vsinϕsinθ + wcosϕ (19) whee u, v and w ae the wind components of the instantaneous wind vecto, θ is the beams azimuth angle and ϕ the conical angle. Fo the configuation of the QinetiQ ZephIR wind lida, θ is scanning ove the inteval [0; π ] and ϕ = 30. Fom this, (10) becomes V ( θ) ucosθ vsinθ = + + w (0) We next denote the fit function to the adial speeds as function of the azimuth angle (θ), assuming that the vetical mean wind speed ove a evolution is null, as v ( θ ) = u cos θ + v sin θ (1) 1 1 _ fit π π whee π 1 denotes an aveage ove 1 full evolution ( x = xdθ π π ). By the usual Reynolds decomposition (u(t)=<u>+u ) we can now, by subtacting (13) fom (1), obtain the following expession fo the fluctuations in the adial measued wind speed component π 0 ' = _ fit v ( θ) v ( θ) v ( θ) 1 ' 1 ' 3 ' u cosθ v sinθ w = + + () whee v denotes the instantaneous adial velocity component, as function of azimuth θ. ' By squaing, and subsequently taking the aveage ove one full evolution (index π), we finally obtain ( cos( θ) sin ( θ) ) ' ' ' ' = + + π π 1 ' 1 ' 3 ' = u cos 4 ( θ) + v sin 4 ( θ) + w π π π π 4 π 1 ' 1 1 ' 1 3 ' = u + v + w 4 π 4 π 4 π v u v w ' ' ' ( u v ) 3 w = π 4 π π (3) Because of the azimuth aveaging, all of the coss covaiance tems uw ', vw, uv ' v π π will dop out. Theefoe π fo a LiDAR coesponds to the ' aveage ove 10 minutes of the quantity v ; fo a sonic anemomete it is calculated π diectly fom the 10 minutes vaiance of u, v and w.

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