Turbulence velocity profiling for high sensitivity and vertical-resolution atmospheric characterization with Stereo-SCIDAR

2.1 MB·

by  J. Osborn

MNRAS000,1–11(2016) Preprint11January2017 CompiledusingMNRASLATEXstylefilev3.0
Turbulence velocity profiling for high sensitivity and
vertical-resolution atmospheric characterisation with
Stereo-SCIDAR
J. Osborn(cid:63), T. Butterley, M. J. Townson, A. P. Reeves, T. J. Morris and R. W. Wilson
1Centre for Advanced Instrumentation, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK
7
11January2017
1
0
2
ABSTRACT

n As telescopes become larger, into the era of ∼40 m Extremely Large Telescopes, the
a high resolution vertical profile of the optical turbulence strength is critical for the
J
validation,optimisationandoperationofopticalsystems.Thevelocityofatmospheric

0 optical turbulence is an important parameter for several applications including astro-
1
nomical adaptive optics systems. Here, we compare the vertical profile of the velocity

oftheatmosphericwindaboveLaPalmabymeansofacomparisonofStereo-SCIDAR
]
M with the Global Forecast System models and nearby balloon borne radiosondes. We
use these data to validate the automated optical turbulence velocity identification
I
from the Stereo-SCIDAR instrument mounted on the 2.5 m Isaac Newton Telescope,
.
h La Palma. By comparing these data we infer that the turbulence velocity and the
p
windvelocityareconsistentandthattheautomatedturbulencevelocityidentification
-
o of the Stereo-SCIDAR is precise. The turbulence velocities can be used to increase
r the sensitivity of the turbulence strength profiles, as weaker turbulence that may be
st misinterpreted as noise can be detected with a velocity vector. The turbulence veloc-
a ities can also be used to increase the altitude resolution of a detected layer, as the
[ altitude of the velocity vectors can be identified to a greater precision than the native

resolution of the system. We also show examples of complex velocity structure within
1
v a turbulent layer caused by wind shear at the interface of atmospheric zones.
4
Key words: atmospheric effects, instrumentation: adaptive optics, methods: data
2
analysis, methods: statistical, site testing
6
2
0
.
1
0 1 INTRODUCTION 2010; Masciadri et al. 2013a; Gendron et al. 2014). This is
7 currently a challenge fot optical turbulence profiling instru-
1 Asastronomicaladaptiveoptics(AO)systemsbecomemore mentation.
: sophisticated,adetailedknowledgeofthealtitudeprofileof
v
optical turbulence, measured as the refractive index struc- The three most prevalent optical profiling techniques
i
X ture constant, Cn2(h), and velocity, is increasingly impor- in operation today are MASS (Multi Aperture Scintillation
tant. Detailed characterisation of the atmospheric turbu- System, Tokovinin & Kornilov 2007), SCIDAR (SCIntilla-
r
a lence profile permits realistic modelling, performance pre- tion Detection And Ranging, Vernin & Roddier 1973) and
diction, and real time validation and optimisation of AO SLODAR (SLOpe Detection And Ranging, Wilson 2002).
instruments. MASS is not intended as a high vertical-resolution tech-
The large number of wavefront sensor subapertures nique. It has a limited logarithmic vertical resolution and
acrosstheAOsystempupilcombinedwiththewidefieldof the high altitude response is very broad (Tokovinin & Ko-
viewmeansthatthenextgenerationof30to40mclassEx- rnilov2007).BothSLODARandSCIDARaretriangulation
tremely Large Telescopes (ELTs) will be significantly more techniques in which the atmospheric turbulence profile is
sensitive to variations in the optical turbulence profile than recovered from either the correlation of wavefront slopes in
existing 8 m class systems. These telescopes will be sensi- the case of SLODAR, or scintillation intensity patterns in
tive to variations in turbulence altitude of the order of 100 the case of SCIDAR, for two target stars with a known an-
to500m(Neicheletal.2008;Basdenetal.2010;Vidaletal. gularseparation.Generalised-SCIDAR(Fuchsetal.1994)is
adevelopmentoftheSCIDARtechniquewherethedetectors
are conjugate below the ground level in order to make the
(cid:63) Contacte-mail:[email protected] instrument sensitive to turbulence at the ground. For SLO-
(cid:13)c 2016TheAuthors
2 J. Osborn
DARtheresolutionislimitedbythedoublestarseparation increased sensitivity to weaker turbulence and can operate
andthesizeofthewavefrontsensorsubapertures.Thesub- with a larger difference in brightness of the target stars.
aperturesmustbesufficientlylarge(>5−10cm,depending In addition, the spatial cross-covariance function has only
on stellar magnitude) to provide adequate signal for cen- one covariance peak per turbulent layer. This lends itself
troidmeasurements.Toachieveaverticalturbulenceprofile toautomatedturbulencevelocityidentificationoverthefull
up to 20 km with 200 m altitude resolution, the SLODAR atmosphere (Osborn et al. 2015b).
would require 100 subapertures, with 0.08 m suparpertures Stereo-SCIDARcanusetheautomatedvelocityprofiles
this would require an 8 m telescope. with the HVR technique of (Egner & Masciadri 2007) to
The theoretical resolution for Generalised-SCIDAR measuretheopticalturbulencewithELT-scalealtituderes-
varies with the Fresnel zone size for a given altitude of the olution (100 - 500 m). In addition, the turbulence velocity
turbulence and is given by (Prieur et al. 2001), identification can be used to confirm the existence of weak
√ turbulent layers close to the noise floor of the instrument.
δh(z)=0.78 λz, (1) If a covariance peak is seen to move in the spatio-temporal
θ covariance function then we can confirm that it is real and
whereλisthewavelength,θ istheseparationofthedouble not simply noise, which would behave differently. This tur-
starandzisthepropagationdistancefromtheturbulenceto bulence could easily be ignored in the data analysis but for
the detection plane. z depends on the airmass of the obser- applications where high sensitivity is required, they could
vation(sec(θ ),whereθ ,isthezenithangle),theconjugate beimportant.However,beforethisdatacanbeusedinper-
z z
altitude of the detector plane, z , and the altitude of the formance simulations for future ELT instrumentation the
conj
turbulentlayer,h,andisgivenby,z=|hsec(θ )+z |.For automated turbulence velocity identification must be vali-
z conj
larger propagation distances the spatial scale of the inten- dated.
sity speckle patterns is larger, reducing the altitude resolu- Here,wecomparewindandturbulencevelocityprofiles
tion.ThereforethenativealtituderesolutionofGeneralised- from three sources:
SCIDAR is altitude dependent with a significantly reduced
• physical tracking measurements of balloon borne ra-
resolution for high-altitude turbulence. As with SLODAR,
diosondesviaaGlobalPositioningSystemandradiotheodo-
in order to achieve 200 m altitude resolution to 20 km with
lite.
Generalised-SCIDAR an 8 m telescope is required (Masci-
• computer model, Global Forecast System (GFS) mete-
adri et al. 2013a).
orological forecasts provided by the National Oceanic and
Egner & Masciadri (2007) proposed a way to increase
Atmospheric Administration (NOAA/NCEP 2015)
the altitude resolution of Generalised-SCIDAR based on si-
• optical remote sensing, Stereo-SCIDAR automated
multaneous turbulence velocity profiles. To implement this
wind velocity detection algorithm.
High-Vertical Resolution (HVR) mode the profiler needs to
be able to measure the vertical profile of the turbulence ve- These data sources were chosen for our comparison as
locity in addition to the strength. The approach taken is both the measured radiosonde and modelled GFS wind ve-
to track the position of the covariance peaks in the spatio- locities have been shown to provide precise estimates (for
temporalcross-covariancefunction.Usingtheframerateand example, Sarazin et al. 2011; Vernin et al. 1979; Garc´ıa-
pixelsizetheturbulencevelocitycanbeestimated.Differen- Lorenzo & Fuensalida 2006; Avila et al. 2004).
tialvelocityvectorswithinaverticalresolutionelementsig- Withthiscross-validationwe showthattheturbulence
nifydifferentturbulentlayersandcanprovideaverticalres- and the wind velocity are highly correlated, simultaneously
olution better than the native resolution of the instrument. showingthattheStereo-SCIDARturbulencevelocityispre-
Although turbulence velocity profiling has been demon- ciseandthatthenumericalmodelsofthewindvelocitycan
stratedwithSLODAR(forexampleCortesetal.2012;Gue- be used as an estimator for the turbulence velocity.
salagaetal.2014;Gilles&Ellerbroek2013andGeneralised- Inadditiontoimprovingthealtituderesolutionofopti-
SCIDAR(forexample,Prieuretal.2004;Garc´ıa-Lorenzo& calprofilersthewindvelocityverticalprofileisanimportant
Fuensalida 2006) an automated approach is difficult. parameter for astronomical Adaptive Optics (AO) applica-
Thisimprovedaltituderesolution,enabledbythehigh- tions.
vertical resolution mode, is currently of critical importance The wind velocity determines how quickly an AO
for studies for the next generation of ELTs. system must be updated. For AO systems this can be
For SLODAR, the number of subapertures in exist- parametrised by the coherence time, a measure of how long
ing systems is generally low, making it difficult to separate theturbulencecanbeassumedtobecoherent,(Greenwood
the covariance peaks even in the temporal dimension. For 1977).Thecoherencetimedefinestheupdaterateatwhich
Generalised-SCIDAR there are three covariance peaks for an AO system must function at in order to minimise resid-
each turbulent layer. This excess of signals is difficult for ual wavefront errors due to the temporal lag between the
automated systems to track. wavefront measurements and correction on the deformable
Stereo-SCIDAR (Shepherd et al. 2014; Osborn et al. mirror (DM). Higher wind speeds mean that the coherence
2013) is a Generalised-SCIDAR instrument which is de- time will be shorter and the AO system update rate will
signed to measure the vertical profile of optical turbulence have to be faster. However, the optical turbulence strength
strength and velocity in the full atmosphere. In contrast to and velocity are not constant in altitude and so to calcu-
most SCIDAR instruments, Stereo-SCIDAR uses two cam- late the coherence time we need to know the speed of the
eras, one to image the defocussed pupil of each of the two turbulence at the altitude of the turbulence. Therefore, the
target stars. By doing this the intensity of the images can vertical profile of the turbulence velocity as well as the tur-
benormalisedindependently,andhenceStereo-SCIDARhas bulencestrengthisrequiredtocalculatethecoherencetime,
MNRAS000,1–11(2016)
SCIDAR turbulence velocity profiles 3
an important parameter for both the design and real-time
operation of AO systems.
SophisticatedAOcontrollersthatmakeuseofthewind
velocityprofilecanalsobeusedtoimprovetheperformance
of AO systems. One such technique is Linear Quadratic
Gaussian (LQG) (Paschall & Anderson 1993; Kulcsa´r et al.
2006). In this case, a spatial and temporal model is used to
reconstructthewavefront.LQGhasbeentestedon-skyand
proven to provide superior AO reconstruction and control
over conventional integrators (Sivo et al. 2014; Sivo 2014).
In the case of predictive distributed Kalman filters (DKF),
Gilles & Ellerbroek (2013) show that the wind profile esti-
mation must be accurate to better than 20%.
Thewindvelocityprofilingalgorithmoutlinedaboveas-
sume”frozenflow”,i.e.thatthewavefrontdoesnotevolveas
ittraversesthetelescopefieldofview.However,theinterface
oftwozonesofatmospherewithdifferentwindvelocitiescan
Figure 1.Ifaturbulentlayeratheight,h,isilluminatedbytwo
induceavelocitydispersionintheturbulence.Althoughthe
stars of angular separation, θ, then two copies of the aberration
optical turbulence is a passive tracer of the bulk motion of
willbemadeonthegroundseparatedbyadistancehθ.Bycross
the air, a gradient of velocity between the top and the bot- correlatingeitherthecentroidpositionsfromaShack-Hartmann
tom of the turbulent zone can exist. This may not be seen wavefrontsensor(SLODAR)ortheintensitypatterns(SCIDAR)
in numerical models and probes (such as weather balloon wecantriangulatetheheightoftheturbulentlayerandtheam-
tracking)duetothediscretealtitudesampling.Opticalsys- plitudeofthecorrelationpeakcorrespondstothestrengthofthe
tems,suchasAO,aresensitivetothevelocityoftheoptical layer.
turbulence (refractive index variations) and not necessarily
the bulk velocity of the wind. It is only by comparing the
numerical models with turbulence velocities determined by
300 300
optical remote sensing means that we can understand the
250 250
differences, if any, between wind velocity, turbulence veloc-
200 200
ity and gusting. The Stereo-SCIDAR has sufficient resolu-
150 150
tiontobeabletoresolvethisandweshowexamplesofsuch
100 100
velocity dispersion.
50 50
In section 2 we describe the instrumentation used in
thisstudyandinsection3weshowcomparisonsofthewind xels) 00 50100150200250300 −00.020.000.020.040.060.080.10
and turbulence velocity measurements. Section 4 describes (piδs 300 300
the conclusions from this study.
250 250
200 200
150 150
2 INSTRUMENTATION 100 100
50 50
2.1 Stereo-SCIDAR 0 0
0 50100150200250300 −0.020.000.020.040.060.080.10
δs (pixels) Covariance (arbitrary units)
SCIDAR is a technique to profile the vertical distribution
Figure 2. Simulated 2D covariance functions (left column) and
of atmospheric turbulence by triangulation. The distance
verticalcutthrough(rightcolumn)forStereo-SCIDAR(toprow)
to a turbulent layer is estimated by measuring the spatial
andconventionalgeneralised-SCIDAR(bottomrow).Inthiscase
displacement of the scintillation patterns from two target theatmosphericsimulationcontainedsixequalstrengthturbulent
stars. The strength of the turbulence is related to the mag- layersat2kmspacingbetween0and10km,inclusive.
nitude of the covariance peak (figure 1). The technique can
beextendedbyopticallyconjugatingthedetectorstoanal-
titude below the telescope and in this way the Generalised- in the overlapping patterns, reducing the visibility of the
SCIDARcanalsobeusedtomeasuretheturbulenceatthe covariance peaks (figure 2). A vertical cut through each co-
ground (Fuchs et al. 1998). variancefunctionisshownontheright.δsisthepositionin
Stereo-SCIDARisastereoscopicversionofGeneralised- the covariance function. We see that for single camera SCI-
SCIDAR,inwhichaseparatedetectorisusedtoimageeach DARwehavetwosetsofspatiallyseparatedpeaksandone
star. The reader is referred to (Shepherd et al. 2014) for a set of overlapping peaks at the centre. For Stereo-SCIDAR
full description of Stereo-SCIDAR, including how it works we only have one set. Both plots have the same contrast
and the opto-mechanical design. scale,thecorrelationpeaksforStereo-SCIDARarelargerin
By separating the scintillation patterns onto separate magnitudethanthatofsinglecameraGeneralised-SCIDAR.
detectorsinsteadofoverlappingthemonasinglecamera(as Stereo-SCIDAR was designed, built and operated as
with traditional SCIDAR instruments) we reduce the noise partoftheCANARYproject,ademonstratorforELT-scale
in the profile estimation. This is because, in conventional AO technologies on the 4.2 m William Herschel Telescope
SCIDAR instruments, the intensity speckles lose contrast (WHT), La Palma (Morris et al. 2014; Martin et al. 2014).
MNRAS000,1–11(2016)
4 J. Osborn
For this project the Stereo-SCIDAR was operated on the verse. For the slowest layers the wind direction resolution
2.5 m Isaac Newton Telescope (INT), approximately 400 m is 10 degrees, for a typical wind speed of 10 m/s the wind
from the WHT (Osborn et al. 2015a). direction resolution is 2.5 degrees. Here, we use 5 degrees
The Stereo-SCIDAR on the INT has 100 pixels across (corresponding to 5 m/s wind speed) as a constant mea-
the 2.54 m re-imaged pupil, resulting in 2.54 cm effective surement precision of the wind direction for our analysis.
pixelsize.Theframerateis∼100Hzandtheexposuretime Figure5showsanexamplerecoveredopticalturbulence
is 2 ms to ensure that enough flux is received for full time strength and velocity profile.
coveragei.e.thatauseabletargetisalwaysvisible.Theelec- For the turbulence velocity identification we use the
tronmultiplicationgainonthedetectorsischosensuchthat frozen flow assumption, i.e. that the turbulence does not
theimagesdonotsaturatethedetectorsandusuallyoperate evolve during the time it takes to cross the pupil. To calcu-
with a peak intensity at ∼80% of the maximum saturation late the velocity we use temporal delays of -5 ms to +5 ms.
level. A dichroic beam splitter with a cutoff at 615 nm is Ithasbeenshownthatthefrozenflowhypothesisisaccurate
used to divert the red light onto a SLODAR channel for a over these short time scales (for example Sch¨ock & Spillar
dualSLODAR/SCIDARexperiment(Butterleyetal.2015). 2000; Guesalaga et al. 2014).
TheshorterwavelengthlightgoestotheStereo-SCIDARin-
strument.
2.1.1 Measuring wind velocity with Stereo-SCIDAR
2.1.2 High Vertical Resolution Mode
Inadditiontofittingthespatialcross–covariancetorecover
the optical turbulence profile, if we assume ‘frozen flow’ of Thealtituderesolution(intermsoftheminimumseparation
the turbulence then wind velocity information can also be requiredtoresolvetwolayers)ofSCIDARisaltitudedepen-
gleanedbyexaminingthespatio-temporalcross–covariance. dent and is given in equation 1. For higher altitude layers
To do this we calculate the cross–covariance function for this can be larger than 1 km.
the two pupil images with increasing temporal offsets. By In HVR mode (Egner & Masciadri 2007) the covari-
viewing the cross–covariance with increasing temporal de- ance peaks are tracked in the spatio-temporal covariance
lay we see that the covariance peaks from the turbulence function.Usingtheframerateandpixelsizetheturbulence
will traverse the covariance function with a velocity corre- velocity can be estimated as described above. The altitude
sponding to the velocity of the turbulence. Figure 3 shows of the turbulence can also be estimated by calculating the
thespatio-temporalcross–covariancefunctionsfordelaysin intersect of the peak’s trajectory with the altitude axis in
the range -2 frames up to +2 frames. In this way the ve- the spatial cross–covariance function (i.e. with no temporal
locity of the turbulent layers can be estimated optically by delay). In this way the altitude of each of the layers can be
tracking the covariance peaks through the spatio-temporal estimatedtoahigherprecisionthenthenativeprofiling. Us-
covariance function. If we add the central three frames to- ing the HVR technique, the altitude resolution is no longer
gether (b, c and d from figure 3) then it becomes easier to altitude dependent as layer altitudes can be ascertained to
see the velocity of each layer (figure 4). less than a Fresnel zone size. The HVR altitude resolution
To build a wind profile we assume frozen flow and im- is given by (Egner & Masciadri 2007),
plement a geometric algorithm. We make a least squares fit
between equi-spaced covariance peaks in adjacent frames. cos(γ)D
dh= , (2)
We then do the same for several sets of three frames (pos- θnpix
itive and negative temporal offsets) so that we can detect
layers even if they leave the scope of the cross–covariance where D is the telescope Diameter, θ is the angular sepa-
function.Todetectthevelocityofalayerwerequireittobe ration of the double stars and nnpix is the number of pixels
seeninatleasttwosetsofthreeframes,seeShepherdetal. across the pupil image. In typical conditions the altitude
(2014) for more details. resolution of the La Palma system is ∼200 m.
The wind velocity can be identified in this way by However, for Stereo-SCIDAR this has been further im-
all SCIDAR systems (Prieur et al. 2004; Garc´ıa-Lorenzo provedbyfittingthetrajectoryofthecovariancepeakinthe
& Fuensalida 2006), however the problem is simplified for spatio-temporal covariance function to sub-pixel accuracy,
Stereo-SCIDAR. All of the methods involve tracking the enablingasub-pixelestimateofthealtitude.Werecordthe
motion of the covariance peaks through the 2D covariance altitude of the peak to 1/10th of a pixel in the covariance
function, but with conventional SCIDAR systems there are function, approximately 20 m. To do this we fit all of the
three peaks for each turbulent layer making the extraction detected covariance peaks to a straight line and record the
of velocity vectors complicated to automate. altitude given by this fit. An RMSE for the fit also allows
FortheStereo-SCIDARontheINT,theestimatedwind us to judge the goodness of fit. This altitude resolution is
speed precision is ±2.5ms−1, corresponding to one pixel sufficientforELT-scaleinstrumentperformancemodelling.
movementofthecovariancepeakinoneframe.Itispossible It should be noted that a limitation of the HVR tech-
to estimate the position of the coherence peak to sub-pixel nique is that it can only separate layers if their altitudes
precision. This would increase the precision of the wind ve- and velocities are significantly distinct. It can not identify
locity estimates, but is currently not implemented. twolayersmovingwiththesamevelocitywithinthealtitude
The wind direction precision is wind speed dependent. range of the Fresnel zone size in the spatio-temporal cross-
For slow layers the angle is harder to determine due to the covariancefunction,i.e.thecovariancepeaksmustseparate
small number of pixels that the covariance peak will tra- in the spatio-temporal cross-covariance function.
MNRAS000,1–11(2016)
SCIDAR turbulence velocity profiles 5
(a) (b) (c) (d) (e)
Figure 3. Spatio–temporal cross–covariance functions of example on-sky data taken at a conjugate altitude of -2 km (inverted for
clarity). The plots show cross–covariance functions generated with temporal delays equal to 1 frame (∼10 ms) from -2 frames (a) to
+2frames(e).Thecaseofnotemporaldelayisshownin(c).Byexaminingthepositionofthesepeaksinsubsequentframesthewind
velocity(magnitudeanddirection)canbecalculated.
2.1.4 Stereo-SCIDAR example cross-covariance functions
In this section we show examples of the Stereo-SCIDAR
spatio-temporal cross–covariance functions. Figure 6 shows
anexampleoftheHVRtechnique.Inthisexampleweclearly
see two turbulent layers at a very similar altitude with a
smallangulardifferencebetweenthem.TheStereo-SCIDAR
datapipelineidentifiestwolayersseparatedby50m.Inthis
case it is likely that a zone of turbulent flow has occurred
betweentwobodiesofair.Thetemperaturegradientatthe
topandthebottomoftheturbulentzonehasgeneratedthe
changes in the refractive index and manifests as two tur-
bulent layers. This supports earlier work by, for example,
Figure 4. The sum of three consecutive spatio-temporal cross–
Coulman et al. (1995).
covarianceframes.Weshowthesumononeimagetodemonstrate
Figure7showsanothertypicalexample.Inthiscasean
the wind velocity estimation process. The arrows indicate the
arc can be seen in the spatio-temporal covariance function.
detectedlayersandvelocities.
Thissuggestsazoneofturbulencewithadispersionofwind
velocities and can be explained by a zone of turbulent flow
betweentwobodiesofairwhicharemovingwithadifference
in their direction. In this case the motion of the turbulence
Table 1.Stereo-SCIDARdatavolume is distributed between the two. The HVR Stereo-SCIDAR
pipelineisnotdesignedtoidentifythesearcsandsofitsmul-
Year Month Days HoursofData NumberofProfiles tiple independent layers to the arc. In this case it identifies
8 turbulence vectors within a 200 m altitude range.
2014 March 13-17 32.9 533
July 11-16 49.7 1421 Theexamplesinfigures6and7werechosenasclearex-
October 6-12 61.9 1966 amples to show the effects that we see regularly. In figure 8
2015 June 25-30 47.9 1854 weshowanexampleofwhatthecross–covariancefunctions
July 1 8.5 310 usually look like. It can be seen that the turbulent struc-
September 29-30 19.4 541 tureoftheatmosphereiscomplex.Weseeacombinationof
October 1-5 29.0 914 double layers and arcs at all altitudes.
Totals: 28 249.3 7539
2.2 Radiosonde
Balloon borne radiosondes are released twice daily from
Valle de Guimar, Tenerife. The launches are at 12:00 and
2.1.3 Stereo-SCIDAR Data
00:00 UT, here we only use the data from the 00:00 UT
Table1showsthevolumeofdatathathasbeencollectedby launch,i.e.onelaunchpernight.ValledeGuimar,Tenerife,
Stereo-SCIDAR on the INT. In total 249 hours of profiles is approximately 150 km from the INT on La Palma. The
have been recorded over 28 nights. The results presented launch site is also at sea level, 2330 m below the INT.
here are not meant to be representative of the La Palma The average ascension rate of the radiosonde is 300 m
site in general due to the limited data, clustered over a few per minute (NOAA 1997). This means that it will take
monthsintwosummers.Theintentionofthispaperistoval- approximately 85 minutes to probe the atmosphere up to
idatethewindvelocitymeasurementsbycross-comparisons 25km.Inthistime,assumingahighaveragehorizontalwind
of the three data sources. speedof30ms−1 theballooncoulddriftupto150kmfrom
MNRAS000,1–11(2016)
6 J. Osborn
25
20
m)
k15
e (
d
u
Altit10
5
0
20:00 22:00 00:00 02:00 04:00 06:00
25
20
m)
k15
e (
d
u
Altit10
5
0
20:00 22:00 00:00 02:00 04:00 06:00
Time (UT)
10−18 10−17 10−16 10−15
C2n (m−2/3)
Figure5.ExampleStereo-SCIDARprofilesequencefromthenightof9thOctober2014(top)andwithwindvectorsoverlaid(bottom).
Onlyasub-sampleofwindvectorsareshownforclarity.
200 200 200 200
150 150 150 150
100 100 100 100
50 50 50 50
0 0 0 0
0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200
(a) (b) (c) (d)
Figure 6. Example cross covariance function from 16th March 2014. The first three frames (a, b and c) are calculated with temporal
offsetsof-0.03s,0sand+0.03srespectively.(d)isthesumofthethreeframeswiththeturbulencevelocityvectoroverlaid.Thecolour
scaleisdifferentforeachplottoenhancevisibility.Inthisexamplethereareclearlytwolayersofturbulencewithinaverysmallaltitude
range moving with a small angular differential (approximately 10 degrees). The HVR technique can separate these layers. In this case
theautomatedscriptidentifiedtwolayersatseparatedby50metresinaltitudewithwindspeedsof25and30m/sanddirectionsof247
and259degrees.
thelaunchsite.Therefore,theradiosondeisnotprobingthe and direction is 3 m/s and 5 degrees respectively (NOAA
same line of sight as the telescope and the GFS forecast. 1997).Thealtituderesolutionoftheradiosondesisvariable
We do not expect the correlation to be perfect, however for but tends to be a few hundred metres.
higheraltitudes,awayfromanylocalsurfaceeffects,theme-
teorological conditions should be similar.
The quoted measurement precision of the wind speed
MNRAS000,1–11(2016)
SCIDAR turbulence velocity profiles 7
200 200 200 200
150 150 150 150
100 100 100 100
50 50 50 50
0 0 0 0
0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200
(a) (b) (c) (d)
Figure 7. Example cross covariance function from 17th March 2014. The first three frames (a, b and c) are calculated with temporal
offsetsof-0.03s,0sand+0.03srespectively.(d)isthesumofthethreeframeswiththerangeofthepossibleturbulencevelocityvectors
overlaid.Thecolourscaleisdifferentforeachplottoenhancevisibility.Thesearcsareoftenseeninthespatio-temporalcrosscovariance
function and show that a range of velocities can be seen within a single turbulent layer. In this case the arc covers a range of angles
of approximately 30 degrees. The Stereo-SICDAR data pipeline identified 8 independent vectors corresponding to layers within 200 m
(3050mto3350m)withaspreadof10m/s(20m/sto30m/s)and30degrees(270degreesto300degrees).
200 200 200 200 200
150 150 150 150 150
100 100 100 100 100
50 50 50 50 50
0 0 0 0 0
0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200
(a) (b) (c) (d) (e)
Figure 8. Typical example cross covariance function from 17th March 2014 showing a complex turbulence structure with arcs and
double layers occurring at all altitudes. The cross-covarinace functions are calculated with temporal offsets from -0.04 to +0.04s. The
centralframe(c)showsthecasewithnotemporaloffset.Thecolourscaleisdifferentforeachplottoenhancevisibility.
2.3 GFS beenpreviouslyusedtoprovidefreeatmosphere(abovethe
ground layer) wind velocity profiles (for example, Hagelin
TheGFSmodelfromtheNationalOceanicandAtmospheric et al. 2010, and references therein). It is known that these
Administration (NOAA/NCEP 2015) provides global fore- models can be unreliable in the lower atmosphere, where
casts of meteorological parameters, including the vertical local geography can influence the climatic parameters. The
profileofthewindspeedanddirection.TheGFSmodelhas meso-scale approach of Masciadri et al. (2013a), is able to
a horizontal resolution of 0.5 degree (55.4 km N-S, 48.2 km provide these parameters, including the ground layer, with
E-WatthelatitudeofLaPalma)for2014dataand0.25de- 2 minute temporal and 100 m spatial resolution.
gree(27.7kmN-S,24.1kmE-WatthelatitudeofLaPalma)
for 2015 onwards. The vertical resolution has 25 mb resolu-
tionfrom1000to900mbandthen50mbresolutiondownto
Here,weonlyusethewindvelocityinformationasitis
50 mb. The model is updated every six hours and provides
presentedintheGFSdatasets,nofurtherdatamanipulation
forecasts for the next 16 days in three hour time intervals.
is performed. Therefore, unlike more sophisticated models
We compare two versions of the GFS forecast, the first (theMOSEprojectforexample,Masciadrietal.2013a),we
istheforecastproducedat18:00UTfor00:00UT(GFS+6), limitourselvestothetemporalandspatialresolutionofthe
the same time as the radiosonde launch. The second fore- modelprovided.Forthisreason,itshouldalsobenotedthat
castisproducedat00:00UTforthecurrenttime(GFS+0). wearenotproposingtousetheGFSwindvelocitiesdirectly
This short time-scale forecast should be the most accurate intheAOcontroloptimisation,orforanyotherapplication,
approach, but we include the 6 hour forecast version for in- butonlytovalidatetheStereo-SCIDARmeasurementsand
terest. toshowthatthewindvelocitycanbeequatedtotheoptical
General circulation models (GCM), such as GFS, have turbulence velocity.
MNRAS000,1–11(2016)
8 J. Osborn
Table 2.Correlationvaluesforallcombinationsofdatasources Table 3. Bias and RMSE values for all combinations of data
forwindspeed,Ws,(m/s)anddirection,Wθ,(degrees). sourcesforwindspeed(m/s)anddirection(degrees).
Correlation Bias RMSE
Datasource1 Datasource2 Ws Wθ Datasource1 Datasource2 Ws Wθ Ws Wθ
(m/s) (degrees) (m/s) (degrees)
Radiosonde GFS+0 0.90 0.96
Radiosonde GFS+6 0.88 0.96 Radiosonde GFS+0 -0.1 3.5 2.2 17.0
Radiosonde SCIDAR 0.82 0.82 Radiosonde GFS+6 0.8 5.6 2.5 17.4
SCIDAR GFS+0 0.90 0.93 SCIDAR Radiosonde 0.6 -1.9 3.3 23.5
SCIDAR GFS+6 0.88 0.86 SCIDAR GFS+0 -0.8 -2.6 1.9 12.5
GFS+0 GFS+6 0.99 0.97 SCIDAR GFS+6 -0.7 -1.5 2.0 19.9
3 COMPARISONS Themeandifference,orbias,andtheroot-mean-square-
error (RMSE) in the wind velocity values are shown in ta-
For these comparisons, only Stereo-SCIDAR profiles
ble 3. The bias and RMSE values between the radiosonde
recorded between the hours of 23:30 and 00:30 UT are in-
and GFS model are consistent with those stated by Masci-
cludedtoensurethatthedatathatwecompareiswithinhalf
adri et al. (2013b) for radiosonde and ECWMF (an alter-
an hour of the radiosonde launch and GFS forecast time.
native GCM). We see a very low bias for the wind speed
Due to the flight time of the radiosonde a better correla-
∼±0.5 m/s, for all comparisons and a bias of up to ∼5 de-
tion might be found with Stereo-SCIDAR data from 00:00
grees for the wind direction.
to 01:00 UT, however the GFS forecasts are published for
The RMSE for the turbulence speed is of the same or-
00:00 UT and so we have chosen to use midnight as the
der as the measurement precision. However, the RMSE for
centreofallcomparisons.Duetothedifferentaltitudereso-
theturbulencedirectionislargerthantheexpectedmeasure-
lutionsofthethreesystemsweonlycomparemeasurements
menterror.ThiscanbeexplainedbythefactthetheStereo-
that are within 100 m in altitude of each other. The data
SCIDAR measurements given are the median velocity over
shown here is for all altitudes above the observatory level,
an hour of observations whereas the GFS and radiosonde
including the ground. If the data from the first kilometre
estimates were instantaneous. This is demonstrated by the
above the observatory is ignored no significant difference is
error bars in the figures. As the RMSE for wind speed is
seen in any of the comparisons.
low,thiswouldsuggestthatthereismorevariationindirec-
An example velocity profile for 2014/07/15 is shown in
tionoverthehour.AnotherexplanationisthattheSCIDAR
figure9.OnthisparticularnightwehavedatafromtheGFS
measures the velocity of the optical turbulence whereas the
forecast, the radiosonde and the Stereo-SCIDAR.
radiosonde and GFS give estimates of the wind velocity in
Figures10,11and12showthescatterplotsfordifferent
discretealtitudebins.Turbulentzoneswithvelocitydisper-
combinations of the data sources. The colour of the marker
sioninasmallaltituderange,asshowninsection2.1.4will
indicates the altitude of the turbulent layer. We first com-
result in a difference between the optical turbulence direc-
pare the radiosonde measurements with the GFS forecast
tion and the Radiosonde / GFS discrete wind direction re-
for our dataset to confirm that these sources agree and can
sulting in scatter in the above figures.
be used to validate the SCIDAR velocities.
We also note that outlying data points for the wind
ThelargeerrorbarsfortheSCIDARdatashowalarge
direction comparisons tend to be from low wind speed
variability in some of the wind velocity measurements. For
(<5 m/s). This is because wind direction identification of
the comparisons of the wind velocity, speed and direction,
slow turbulent layers is inherently more difficult due to the
measurements from Stereo-SCIDAR are averaged over the
fewer pixels covered by the covariance peak in the sample
one hour period. The error bars are then set to the stan-
time.
dard error of the measurements. These error bars appear
large in comparison to the quoted measurement resolution
and therefore show a large variability in some of the wind
velocity measurements. This could be due to actual wind
4 CONCLUSIONS
variabilityoverthecomparisonperiodandtoturbulentgust-
ing,aknownphenomenoninturbulentflow(Boettcheretal. We have compared the wind velocity (speed and direc-
2003). Also, note that the wind direction is wrapped in the tion) from the GFS CGM model and from balloon borne
plotsandthereforepointsinopposingcornersawayfromthe radiosonde with turbulence velocity measurements from
main trend should wrap around at 360 degrees. Stereo-SCIDAR on the INT, La Palma. As all three data
Table2showsthePearsoncorrelationvaluesfromeach sources agree with a high degree of correlation and a low
combination of data sources. The correlation for all combi- bias we can say that the wind velocity, as measured by Ra-
nationsarehigh,indicatingagoodagreementbetweeneach diosondeandGFS,isconsistentwiththeturbulencevelocity
data source. as measured by Stereo-SCIDAR.
The correlation for all of the datasets with GFS +0 is The turbulence velocity dispersion measured by the
slightly higher than that of GFS +6, and the correlation Stereo-SCIDARforsometurbulentzonesprovidesaninsight
between the GFS +0 and GFS +6 is extremely high. This into the structure within turbulent flow. The dispersion is
indicatesthatthesixhourforecastisgenerallyveryprecise. not seen by the radiosonde or the numerical model, GFS.
Only the GFS +0 data is shown in the figure 12 for clarity. We often see significant velocity dispersion and double lay-
MNRAS000,1–11(2016)
SCIDAR turbulence velocity profiles 9
35
350
GFS +0 GFS +0
GFS +6 GFS +6
30
SCIDAR 300 SCIDAR
Radiosonde Radiosonde
25 s)250
e
Windspeed (m/s)1250 d direction (degre125000
n
10 Wi100
5 50
0 0
0 5 10 15 20 25 0 5 10 15 20 25
Altitude (km) Altitude (km)
Figure 9.Anexamplevelocityprofileforwindspeed(left)anddirection(right)fromtheStereo-SCIDARontheINT,GFSmodeland
radiosondemeasurementsfor00:00UTthenightof2014/07/15.
50 25.0 25.0
350
22222222222222222225555555555555555555 mmmmmmmmmmmmmmmmmmm///////////////////sssssssssssssssssss
22.5 11111111111111111115555555555555555555 mmmmmmmmmmmmmmmmmmm///////////////////sssssssssssssssssss 22.5
300 5555555555555555555 mmmmmmmmmmmmmmmmmmm///////////////////sssssssssssssssssss
40 20.0 s) 20.0
e
m/s) 17.5 egre250 17.5
onde windspeed (2300 111025...050Altitude (km) e wind direction (d125000 111025...050Altitude (km)
dios 7.5 ond 7.5
Ra dios100
10 5.0 Ra 5.0
50
2.5 2.5
0 0.0 0 0.0
0 10 20 30 40 50 0 50 100 150 200 250 300 350
GFS windspeed (m/s) GFS wind direction (degrees)
Figure 10.Comparisonofwindspeed(left)andwinddirection(right)fromradiosondeandGFS.Thecolourindicatesthealtitudeof
theturbulence.Forthecomparisonofthedirection(right)thesizeofthepointindicatesthewindspeed.
erswhichmanifestinthecomparisonasalargeRMSEwhen profiles can then be fed into the turbulence strength pro-
compared to the measurement precision. file reduction in real-time. This makes the Stereo-SCIDAR
solution ideal for real-time support of existing and future
ThisworkvalidatestheuseoftheStereo-SCIDARreal-
astronomical adaptive optics systems. This data is imme-
timeautomatedturbulencevelocityidentificationalgorithm.
diately required for instrument modelling and development
ThisresultissignificantbecauseitjustifiestheuseofStereo-
as well as for operational support as the next generation of
SCIDAR in the high-vertical resolution mode, where differ-
sophisticated adaptive optics systems come on-line.
ential velocity vectors can be used to increase the altitude
resolution of the turbulence profiles. This is currently the
only way of achieving the same altitude resolution as the
future generation of ELTs on 1 to 2 m class telescopes.
TheautomatedalgorithmsusedbytheStereo-SCIDAR
meanthattheturbulencevelocityprofileismeasuredinreal-
time with no input from a user. The turbulence velocity
MNRAS000,1–11(2016)
10 J. Osborn
50 25.0 25.0
350
222222222222222222555555555555555555 mmmmmmmmmmmmmmmmmm//////////////////ssssssssssssssssss
22.5 111111111111111111555555555555555555 mmmmmmmmmmmmmmmmmm//////////////////ssssssssssssssssss 22.5
300 555555555555555555 mmmmmmmmmmmmmmmmmm//////////////////ssssssssssssssssss
40 20.0 s) 20.0
e
m/s) 17.5 egre250 17.5
onde windspeed (2300 111025...050Altitude (km) e wind direction (d125000 111025...050Altitude (km)
dios 7.5 ond 7.5
Ra dios100
10 5.0 Ra 5.0
50
2.5 2.5
0 0.0 0 0.0
0 10 20 30 40 50 0 50 100 150 200 250 300 350
SCIDAR windspeed (m/s) SCIDAR wind direction (degrees)
Figure 11.Comparisonofwindspeed(left)andwinddirection(right)fromradiosondeandStereo-SCIDAR.Thecolourindicatesthe
altitudeoftheturbulence.Forthecomparisonofthedirection(right)thesizeofthepointindicatesthewindspeed.
50 25.0 25.0
350
222222222222222222555555555555555555 mmmmmmmmmmmmmmmmmm//////////////////ssssssssssssssssss
22.5 111111111111111111555555555555555555 mmmmmmmmmmmmmmmmmm//////////////////ssssssssssssssssss 22.5
300 555555555555555555 mmmmmmmmmmmmmmmmmm//////////////////ssssssssssssssssss
40 20.0 20.0
s)
m/s) 17.5 egree250 17.5
S windspeed (2300 111025...050Altitude (km) nd direction (d125000 111025...050Altitude (km)
GF 7.5 S wi 7.5
F100
G
10 5.0 5.0
50
2.5 2.5
0 0.0 0 0.0
0 10 20 30 40 50 0 50 100 150 200 250 300 350
SCIDAR windspeed (m/s) SCIDAR wind direction (degrees)
Figure12.Comparisonofwindspeed(left)andwinddirection(right)fromGFSandStereo-SCIDAR.Thecolourindicatesthealtitude
oftheturbulence.Forthecomparisonofthedirection(right)thesizeofthepointindicatesthewindspeed.
ACKNOWLEDGEMENTS knowledge support from the Science and Technology Fa-
cilities Council (STFC) in the form of a PhD studentship
We are grateful to the Science and Technology Facilities (ST/K501979/1). The Stereo-SCIDAR data used in this
Committee (STFC) for financial support (grant reference project is available upon request from the authors.
ST/J001236/1). FP7/2013-2016: The research leading to
these results has received funding from the European Com-
munity’s Seventh Framework Programme (FP7/2013-2016)
under grant agreement number 312430 (OPTICON). The
REFERENCES
Isaac Newton Telescope is operated on the island of La
Palma by the Isaac Newton Group in the Spanish Ob- Avila R., Masciadri E., Vernin J., S´anchez L., 2004, PASP, 116,
servatorio del Roque de los Muchachos of the Instituto 682
de Astrofisica de Canarias. We are also grateful to the BasdenA.,MyersR.,ButterleyT.,2010,Appl.Opt.,49,G1
NOAA Earth System Research Laboratory for making the BoettcherF.,RennerC.,WaldlH.-P.,PeinkeJ.,2003,Boundary-
radiosonde and Global Forecast System (GFS) meteorolog- LayerMeteorol.,108,163
ical forecast data available on the web. MJT gratefully ac- ButterleyT.,OsbornJ.,WilsonR.,2015,J.Phys.Conf.Ser.,595
MNRAS000,1–11(2016)