Refractive-index structure parameter inthe planetary boundary layer: comparison ofmeasurements taken with a 10.6-mm coherentlidar, a 0.9-mm scintillometer, and in situ sensors

Philippe Drobinski, Alain M. Dabas, Patricia Delville, Pierre H. Flamant, Jacques Pelon,and R. Michael Hardesty

An optical technique is described that determines the path-averaged value of a refractive-index structureparameter at 10.6 mm by use of a pulsed coherent CO2 lidar in direct detection and hard-target returns.The lidar measurements are compared with measurements taken by a 0.9-mm scintillometer and tem-perature probe ~with humidity corrections!. The experimental results show good agreement for Cn

2 $

10214 m22y3. With respect to practical applications the new technique permits Cn2 lidar measurements

in a neutral meteorological situation to an unstably stratified convective boundary layer over long ranges~1 km or more!. © 1999 Optical Society of America

OCIS codes: 030.6140, 010.7060, 010.3640, 030.1640, 120.5710.

pl

if

1. Introduction

Atmospheric refractive-index turbulence ~Cn2! affects

the performance of coherent lidar through the trans-verse coherence length of the backscattered electro-magnetic field from remote targets. The transversecoherence length determines the heterodyne effi-ciency, a key parameter for the application of acoherent-lidar instrument. Because Cn

2 depends onboth temperature and humidity fluctuations in theatmosphere, it is a function of the transmitted wave-length and height of the probing beam above theground. Measurements taken at different wave-lengths with scintillometers have been shown to be ingood agreement with values derived from in situ tem-

P. Drobinski, P. Delville, and P. H. Flamant are with the Labo-ratoire de Meteorologie Dynamique, Ecole Polytechnique, Pal-aiseau Cedex F-91128, France. The e-mail address for P.Drobinski is drobi@colisa.polytechnique.fr. A. M. Dabas is withMeteo-France, Centre National de Recherches Meteorologiques,Toulouse, France. J. Pelon is with Service d’Aeronomie, Univer-site Paris VI, Paris, France. R. M. Hardesty is with the WavePropagation Laboratory, National Oceanic and Atmospheric Ad-ministration, Environmental Research Laboratory, 325 Broadway,Boulder, Colorado 80303.

Received 21 August 1998; revised manuscript received 16 No-vember 1998.

0003-6935y99y091648-09$15.00y0© 1999 Optical Society of America

1648 APPLIED OPTICS y Vol. 38, No. 9 y 20 March 1999

erature and humidity probes by use of a scalingaw.1,2

Currently the coherent-lidar technique has beenapplied in atmospheric boundary layer physics forwind and turbulence measurements.3–10 To charac-terize the sensitivity of a coherent-lidar system toturbulence conditions, it is essential to compare theexpected performance ~i.e., heterodyne efficiency as afunction of Cn

2 based on relationships presented inthe literature! with the measured actual perfor-mance. Recently a study was conducted at Labora-toire de Meteorologie Dynamique that was aimed atdeveloping a new method to determine heterodyneefficiency in the presence of turbulence from experi-mental data.11 The method requires a simultaneousestimate of the strength of the refractive-index tur-bulence characterized by Cn

2. As a matter of fact, anestimate of the refractive-index turbulence strengthwith the lidar technique would provide a long-path-averaged value of Cn

2 that is better suited for assess-ng lidar performance. The methodology proposedor retrieving Cn

2 from the backscattered opticalpower collected by coherent lidar is based on the det-rimental effect of turbulence on the transverse-fieldcoherence length. This latter parameter can be de-termined in a direct-detection mode12 by estimatingthe number of speckle cells m captured by the re-ceiver telescope. The parameter m can be deter-mined by the inverse relative root variance ~IRRV!

13

sd

i

itrod

b

cms

w

method, which relates m to the order of the chi-quare distributed probability density function of li-ar return.To validate the lidar technique, we conducted an

ntercomparison of three different types of Cn2 mea-

surement. One comparison was made directly bycoherent lidar operating at 10.6 mm in the direct-detection mode, a second by a scintillometer operat-ing in the near IR at 0.9 mm, and a third by usingrelationships between Cn

2 and temperature and hu-midity fluctuations recorded by in situ probes. Adescription of the new lidar method for estimating Cn

2

is described in this paper along with the results of anintercomparison of the three methods outlined above.The theoretical background and the IRRV method arepresented in Section 2. The various measurementsand experimental setups are described in detail in Sec-tion 3. In Section 4 we present the three data setsalong with the data analysis and intercomparison.

2. Theoretical Background

A. Number of Speckle Cells

In the direct-detection mode the electrical currentdelivered by a photodetector is proportional to thelight intensity integrated over the active area S.The light collected by the lidar receiver is backscat-tered by a large number of point targets ~i.e., aerosolparticles! randomly distributed in space so that thendividual backscattered wavelets add randomly onhe receiver ~and in practice on the detector!. Theesulting intensity pattern ~i.e., random distributionf speckle cells! is changing as a function of time bothuring a single lidar event and from shot to shot.14

Considering a single point on the photodetector andthe direct-detection mode, the probability densityfunction of the intensity can be characterized by anegative exponential distribution. When the inten-sity is integrated over the whole detector area, theprobability density function of the electrical current iecomes chi-square15:

p~i! 5mm

G~m!

im21

^i&expS2m

i^i&D , (1)

where ^i& is a statistical mean and m is the number ofspeckle cells. The number of speckles can be relatedto the spatial coherence, m~x, y! 5 ^F*~x!F~y!& ~themutual coherence function! of the backscatteredwave F~x! at the detector plane ~the vector x standsfor a point on the photodetector! through

m 5

*S

m~x, x!W~x!dx *S

m~y, y!W~y!dy

**S

um~x, y!u2W~x!W~y!dxdy

, (2)

where S is the detector area and W~x! is a weightingfunction that accounts for a possible variation in thequantum yield. Closed-form expressions can be de-rived, assuming a given geometry for the detector and

a given shape for the coherence function. For exam-ple, considering a Gaussian coherence function m~x,y! 5 exp@2pix 2 yi2y~2Sc!#, where i i is the vectornorm and

Sc 5 **S

m~x, y!dxdy (3)

is the coherence area ~i.e., the size of a speckle cell!, asquare photodetector of uniform quantum yield @Eq.~2!# is then15

m 5 HSSc

SD1y2

erfSpSSc

D1y2

2 SSc

pSDF1 2 expS2pSSc

DGJ22

.

(4)

When the Gaussian instrument model proposed byFrehlich and Kavaya16 is used, where the detectorarea is assumed to be infinite and the mutual coher-ence function of the backscattered wave has a Gauss-ian shape at the primary mirror, but afterward can bealtered by transmission through the telescope, theresponse of which is assumed to be Gaussian as well,the relationship linking m to S and Sc is12

m 5 1 1SSc

. (5)

Figure 1 shows m as a function of SySc according toEqs. ~4! and ~5!, respectively. It shows that the re-eiver geometry has a weak effect on m ~;10% atost! and that the asymptotic behaviors for large and

mall ratios SySc are identical: m ' 1 for S ,, Scand m ' SySc for S .. Sc. In the following sectionswe use Eq. ~5! instead of Eq. ~4!.

Fig. 1. Dependence of the number of speckle cells m on SySc,hich is the ratio of receiver area S to coherent area Sc, for two

different lidar geometries. The analytical equation derived byGoodman @Eq. ~4!# is shown as a solid curve ~square detector andconstant quantum yield!, and the dashed curve represents m 5 1 1SySc @Eq. ~5!# ~Gaussian detector and quantum yield!.

20 March 1999 y Vol. 38, No. 9 y APPLIED OPTICS 1649

mfrGc

Etl

w

ag

a

o

NaFid

1

B. Transverse Coherence

The coherence area Sc is basically limited by the in-strument geometry ~size and divergence of the trans-

itted laser beam, primary of the receiving telescope,ocal length, etc.! but can be further decreased byefractive-index turbulence. In the frame of theaussian instrument model it is possible to write a

losed-form equation for Sc:

Sc 5pr0

2

2, (6)

where r0 is the transverse-field coherence length12

related to the radius sB ~1ye of maximum intensity! ofthe transmitted laser beam at the target plane atrange R and the transverse-field coherence length r0by

1r0

2 5k2sB

2

4R2 11

2r02 . (7)

For spherical waves within the framework of the Kol-mogorov model for refractive-index fluctuations17

r0 5 FHk2 *0

R

Cn2~z!S1 2

zRD5y3

dzG23y5

, (8)

where k 5 2pyl and H 5 2.91. The second term inq. ~7! accounts for the degradation of coherence by

urbulence on the return path. The radius sB of theaser beam at the target plane can in turn be written

sB2 5 sB

2 12R2

k2r02 , (9)

where sB is the laser beam size at the target planewith no turbulence and the second term accounts forthe broadening of the beam shape by refractive-indexturbulence. When Eqs. ~7! and ~9! are used, theright-hand side of Eq. ~7! results in

1r0

2 51

r02 1

1r0

2 , (10)

here r0 is the transverse-field coherence length atthe target plane with no refractive-index turbulence~Cn

2 5 0 m22y3! and the second right-hand-side termccounts for cumulative turbulence effects on the out-oing and return paths.Equations ~7!–~10! assume that the effect of turbu-

lence on the outgoing and return paths is statisticallyindependent and include the square-law approxima-tion18 in which the structure function of phase pertur-bations that the optical field incurs from turbulence isapproximated by a square law instead of the 5y3 lawpredicted by theory. Since we are considering here amonostatic lidar, the assumption that turbulent effectsare independent of outgoing and return paths is ques-tionable. Indeed we should rather consider that bothpaths go through the same turbulent structures. Theeffect of turbulence on the mutual coherence of a wavepropagating to a target and back to a transceiver

650 APPLIED OPTICS y Vol. 38, No. 9 y 20 March 1999

through a frozen turbulent field has been the subject ofmany studies.16,18–23 Nearly all of the studies pre-dicted an enhanced coherence for the backscatteredfield ~compared with independent two-way propaga-tions!. A relevant result of our study is from Cliffordand Wandzura19 who numerically computed the back-scattered field coherence in frozen conditions by usinga 5y3 scaling law for the phase structure function andcompared their results with the analytical formulationone can derive with independent turbulent effects andthe square-law approximation. They concluded thatthe analytical formulation agrees with the numericalresults provided that the coherence length r0 given inEq. ~8! is doubled. Following their conclusion, in thefollowing we use a doubled coherence length r0, whichmounts to H 5 0.92 in Eq. ~8!.As a result, for horizontal propagation in the plan-

etary boundary layer and assuming for simplicity sta-tistically homogeneous turbulent conditions, theeffect of turbulence on coherence length for a single-ended monostatic lidar is given by

r0 5 ~0.118Hk2Cn2R!23y5. (11)

3. Experimental Procedure

A. Principle

The number of speckle cells onto the photodetectorcan be measured using the IRRV method13:

m 5^i&2

si2 , (12)

where si is the standard deviation of the electricalcurrent ~in the direct-detection mode!. An estimatef both ^i& and si from a time series of M lidar mea-

surements allows a direct estimate m of m:

m 5M 2 1

M 3M(k51

M

ik2

S(k51

M

ikD2 2 1421

, (13)

where ik is the value of the electrical current mea-sured, for example, at range R. The IRRV method isused for several receiving apertures Sn ~n 5 1, . . . ,

! so that a better statistical representativeness ischieved for estimating m from Eq. ~5! ~see below!.rom a practical point of view the receiving aperture

s changed when a diaphragm is used in front of theetector ~see Fig. 2!. Different m~Sn! values are cal-

culated as a function of Sn. The next step consists offitting Eq. ~5! ~in a least-squares sense! to m~Sn!,which provides us with an estimate Sc for Sc:

Sc21 5

(n51

N

@m~Sn! 2 1#Sn

(n51

N

Sn2

. (14)

The transverse-field coherence length r0 can be ob-tained by inverting Eq. ~10!, which requires r0 to be

ag

b

rvs

1rlt3t

AM

I

Etp

p

known in advance. ~This point is addressed in Sub-section 3.C.! Finally, the structure parameter Cn

2

can be estimated from r0 by using Eq. ~11!, i.e., byssuming homogeneous turbulence along the propa-ation path.

B. Uncertainty

A first-order development of Eqs. ~6!, ~10!, and ~11!that relates Sc to Cn

2 yields the following relationshipbetween the statistical uncertainties dSc and dCn

2 onoth quantities:

dCn2

Cn2 < 0.3S1 1

2r02

r02 D dSc

Sc. (15)

It shows that the accuracy of Cn2 measurements de-

pends on the level of refractive-index turbulence. Aweak turbulence condition ~r0 $ r0y=2! amplifies thedCn

2 uncertainties, whereas strong turbulence ~r0 #

0y=2! damps the effect and tends to a minimumalue of the proportionality constant of 0.3. A sen-itivity limit can be set by r0 5 r0y=2; the limit

depends on r0, which is an instrumental factor. Acondition for useful measurements is that r0, thetransverse-field coherence length at the target plane,must be as large as possible, since that results in thehighest possible coherence for the backscatteredwave. This condition makes clear why the proce-dure proposed here for measuring Cn

2 is based on acoherent lidar system even though the ultimate goalis a measurement of the backscattered power.

The relative accuracy of the Sc measurement de-pends on the accuracy of the least-squares fit of Eq.~5! and therefore on the accuracy of m~Sn!. Since

ym~Sn! is the relative variance of the electrical cur-ent, its standard deviation is '~2yM!1y2 ~valid forarge M!. A first-order expansion then shows thathe accuracy of m~Sn! is '~2yM!1y2m~Sn!. For M 500, for example, it turns out that the relative uncer-ainty of m~Sn! is '8%.

The statistical uncertainty of Sc can be investi-gated by using Eq. ~14!. Assuming that dSc ,, Sc,we can show that

^dSc2&

^Sc&2 <

(n51

N

Sn2^dm~Sn!

2&

H(n51

N

Sn@m~Sn! 2 1#J2 . (16)

s long as the standard deviation of m~Sn! is '~2y!1y2m~Sn!, it turns out that Eq. ~16! depends on the

single parameter SnySc:

^dSc2&

^Sc&2 <

2M

(n51

N

~SnySc!2~1 1 SnySc!

2

F(n51

N

~SnySc!2G2 . (17)

t can be shown that

(n51

N11

~SnySc!2~1 1 SnySc!

2

F(n51

N11

~SnySc!2G2 #

(n51

N

~SnySc!2~1 1 SnySc!

2

F(n51

N

~SnySc!2G2 .

(18)

xpressions ~17! and ~18! show the need to increasehe number of lidar shots M and the number of dia-hragms N to provide an accurate estimate of Sc.

C. Experimental Setup

Figure 2 is a schematic of the coherent TE CO2 lidar.The output energy is 300 mJypulse for an ;3-mspulse duration at 2 Hz. The TE CO2 laser cavity ismade of a grating and a super-Gaussian output cou-pler. The emitted and the backscattered light aretransmitted and collected by a 17-cm-diameter afocaloff-axis Cassegrain telescope ~magnification 73!.The backscattered light is then detected by a liquid-nitrogen-cooled cadmium–mercury–telluride photo-voltaic detector supplied by SAT ~Type A4!. The

hotodetector active area ~300 mm in diameter! ismatched to the first ring of the Airy disk of the returnsignal.

We varied the active area by using a diaphragm infront of the photodetector, from 4 mm to as large as 20mm ~Ø 5 4, 6, 8, 10, 12.5, 15, 17.5, and 20 mm!corresponding to sensitive areas ranging from ;3% to;70% of the original area. For each Cn

2 measure-ment the number of speckle cells at target range Rwas estimated from M 5 300 lidar returns for theeight diaphragms, so one measurement correspondedto ;20 min.

The coherence radius r0 ~the coherence length of

Fig. 2. Schematic of TE CO2 lidar.

20 March 1999 y Vol. 38, No. 9 y APPLIED OPTICS 1651

fsFt

ar

tt

dst

siat

4

1

received light with no turbulence! was determinedrom numerical computations. The transmitted la-er beam was propagated to target range R by use ofresnel integrals.24 Figure 3 shows the results ofhe numerical simulation: Figure 3~a! shows the

beam shape in the near field, whereas Fig. 3~b! showsthe beam shape in the far field at range R. In thislatter case the beam shape is Gaussian25 with 1yeradius, sB 5 9.2 cm, corresponding to a coherenceradius r0 5 62 mm or a coherence area Sc

0 5 6000mm2. ~Superscript 0 represents no turbulence.!

When Eqs. ~5!, ~6!, ~10!, and ~11! and relation ~15!re used, it is possible to evaluate the relative accu-acy of Cn

2 measurements as a function of Cn2. The

result is in Fig. 4. A relative error of 100% isreached for Cn

2 ' 10214 m22y3. We consider thisvalue to be a sensitivity limit of the present experi-

Fig. 3. Simulated laser beam shapes ~a! in the near field and ~b!at target range R 5 1690 m in the far field. The beam shape isuper-Gaussian in the near field, whereas at range R 5 1690 m its Gaussian with a 1ye intensity radius of 9.2 cm. ~a! The circlesre measurements of the true beam shape, and the solid curve ishe best fit; ~b! the circles result from the computations, and the

solid curve is the best fit.

Fig. 4. Expected relative accuracy for lidar Cn2 measurements as

a function of the true atmospheric Cn2 according to the experimen-

tal setup.

652 APPLIED OPTICS y Vol. 38, No. 9 y 20 March 1999

mental setup. For Cn2 ' 10213 m22y3 the relative

uncertainty is ;7.5% and even less than 2% for Cn2 $

7.0 3 10213 m22y3.An example of m~Sn! measurements is in Fig. 5

together with the best fit of Eq. ~5!. There appearso be good agreement between experimental data andhe fitted curve. The Cn

2 measurement derivedfrom the best fit is 1.7 3 10213 m22y3. According toFig. 4 the relative uncertainty is then ;4.5%.

4. Validation

A. Field Deployment

The validation of the method was conducted througha comparison of the Cn

2 values retrieved by use of10.6-mm coherent lidar in the direct-detection modewith measurements taken from a 0.9-mm scintillom-eter loaned by the National Oceanic and AtmosphericAdministration ~NOAA!yETL ~Ref. 26!, and values

erived from in situ temperature and humidity sen-ors. The experiment was conducted at the Labora-oire de Meteorologie Dynamique located ;25 km

south of Paris. The validation experiment was con-ducted in late spring and early summer 1997.

The lidar beam propagated quasi-horizontally onthe surface layer ~10 m above the ground! to a hardtarget located at range R 5 1690 m. The propaga-tion took place over various surfaces with a largeproportion of grassy surface ~;70%!.

Temperature and humidity measurements wererecorded simultaneously with two in situ sensors. Acapacitive probe measuring the relative humidityand an associated Pt-resistance-wire temperatureprobe were mounted on a 3-m mast placed on the roofof the building sheltering the lidar. Relative humid-ity and temperature ~T in kelvins! led to an absolutehumidity ~Q in kilograms per cubic meter!. The fre-

Fig. 5. Example of lidar measurement. With the circles are dis-played the numbers of speckles m measured for the various aper-tures or sensitive areas Sn. The solid curve is the best fit of m~S!5 1 1 SySc, providing an estimate of the coherence area Sc of 2430mm2 corresponding to Cn

2 5 1.7 3 10213 m22y3. According to Fig.the relative uncertainty is then ;4.5%.

fr

am

t

ssf~~ s

quency response of both sensors was ;1 Hz. Therefractive-index structure parameter Cn

2 was com-puted by using temperature and humidity measure-ments from27

Cn2 5 AT

2CT2 1 2AQ AT CTQ 1 AQ

2CQ2. (19)

For each experiment the temporal power spectra,ST~ f ! and SQ~ f !, of T and Q and their cospectraSTQ~ f ! were computed every 5 min ~ f is the timerequency!. We then calculated the structure pa-ameters, CT

2, CQ2, and CTQ, for each time segment

by averaging values at four different frequencieswithin the inertial subrange, using27,28

CT2 5 13.62ST~ f ! fS f

UD2y3

,

CQ2 5 13.62SQ~ f ! fS f

UD2y3

,

CTQ 5 13.62STQ~ f ! fS f

UD2y3

, (20)

where U is the mean wind velocity measured by a cupnemometer mounted on a 10-m mast near the 3-mast. Analytical expressions for AT and AQ were

derived for the two measurement wavelengths,1,2 i.e.,0.9 and 10.6 mm. A value for Cn

2 was computedevery 5 min.

The scintillometer was located ;200 m east of thelidar. The transmitter and the receiver were sepa-rated by 260 m over a grassy area at 2 m above theground. The scintillometer measured the path-averaged value of the refractive-index structure pa-rameter Cn

2 and the crosswind. The domain ofoperation ranged from Cn

2 5 10212 m22y3 down to

Fig. 6. Measurements collected on 17 June 1997: ~a! visible so-lar insolation; ~b! Cn

2 measurements. Lidar measurements arehown by circles. The thick solid curve is for a NOAA 0.9-mmcintillometer. The dotted and thin solid curves were derivedrom in situ ~temperature and humidity! measurements at 0.9 mmdotted curve! ~compared with scintillometer data! and at 10.6 mmthin solid curve! ~compared with lidar data!.

10216 m22y3. The measurement was derived fromhe log-amplitude variance of the irradiance sx

2:

Cn2 5 4.48sx

2D7y3L23, (21)

where D is the transmitter and the receiver aperturediameter and L is the path length. The measure-ments were recorded every ;15 s. Cn

2 measure-ments were further corrected for altitude dependence,assuming a scaling law with the height for an unstablesurface layer29 }z24y3.

B. Results

Scintillometer measurements were available from 21April 1997 to 17 June 1997, whereas the in situ sen-sors were operational from 17 June 1997. Simulta-neous measurements of Cn

2 by the three differenttechniques were available on one day, 17 June 1997only. Figure 6~a! shows the solar insolation, and

Fig. 7. Measurements collected on 23 April 1997: ~a! visiblesolar insolation; ~b! Cn

2 measurements. Circles, lidar measure-ments; thick solid curve, NOAA 0.9-mm scintillometer measure-ments.

Fig. 8. Scatter diagram of the scintillometer and in situ Cn2 mea-

urements versus lidar measurements.

20 March 1999 y Vol. 38, No. 9 y APPLIED OPTICS 1653

s1tc

at~bn

r

s

Table 1. C 2 Measurement and Accuracy for Different Atmospheric Conditions

1

Fig. 6~b! shows the Cn2 measurements taken by

10.6-mm coherent lidar, the 0.9-mm scintillometer,and the in situ sensors on 17 June 1997. The dotsrepresent the lidar measurements, the thick curvethe scintillometer, and the thin and dotted curves theCn

2 values retrieved from Eq. ~19! and in situ mea-urements of temperature and humidity, for 0.9 and0.6 mm, respectively. Conditions were cloudy inhe morning, then clear until ;1330 UTC, and thenloudy again for the rest of the day. As expected, Cn

2

varied with the solar insolation @Fig. 6~a!#. We sawgood agreement between the various measurementsand noted that Cn

2 values from in situ measurementst 0.9 and 10.6 mm were very close ~#20%!. Theerm AT

2CT2 for sensible heat contribution is in Eq.

19!, dominant over the terms of latent heat contri-ution, 2AQATCTQ and AQ

2CQ2, the latter term being

egligible at moderate to high values of Cn2.30

Figure 7 for 23 April 1997 is similar to Fig. 6. InFig. 7 the lidar and the scintillometer measurements

Fig. 9. Scatter diagram of the scintillometer and in situ Cn2 mea-

urements versus lidar measurements. Cn2 measurements are

averaged over the whole observation time period.

n

Date~1997!

Time~UTC!

Solar Insolation~W m22!

Lat 1

21 April 1236–1448 ;480 7.522 April 1254–1330 ;210 5.323 April 1230–1306 ;720 16.8

1312–1445 ;600 8.926 May 1206–1324 ;790 13.3

27 May 0824–0942 ;664 7.91224–1400 ;823 8.5

28 May 0730–0900 ;500 8.417 June 1230–1330 ;200 4.418 June 0730–1130 ;752 12.7

1930–2100 ;0 2.9

654 APPLIED OPTICS y Vol. 38, No. 9 y 20 March 1999

on a sunny day are compared, leading to higher val-ues of Cn

2 than for 17 June 1997: Cn2 ' 10213

m22y3. Cn2 decreased with the solar insolation from

3.0 3 10213 m22y3 at 1230 UTC, when the solar in-solation was '750 W m22, to 8.0 3 10214–1.1 3 10213

m22y3 at 1500 UTC, when the solar insolation was'500 W m22. We noted good agreement betweenthe two remote sensors on 23 April 1997. As can beseen in Figs. 6 and 7, both the scintillometer and thein situ measurements show larger fluctuations thanthe lidar, mainly owing to the different integrationtimes required by the various instruments for com-puting one value of Cn

2. The larger fluctuationscould also be due to broken cloud cover that makesthe solar insolation at a single point fluctuate in timemore than average over a long path.30

Figure 8 shows a scatterplot of the scintillometerand in situ Cn

2 measurements versus lidar measure-ments. The circles show 10.6-mm coherent lidar com-pared with 0.9-mm scintillometer measurements,whereas asterisks and pluses show 10.6-mm coherentlidar compared with in situ measurements at 0.9 and10.6 mm, respectively. Figure 8 shows a nonsignifi-cative bias according to the fact that reliable lidar Cn

2

measurements correspond to Cn2 $ 10214 m22y3. The

ms error of the Cn2 difference between the lidar mea-

surements and the scintillometer and in situ measure-ments is '3.0 3 10214 m22y3. The error accountsmainly for scatter that is due to different path averag-ing or integration time, different locations on the site,a different atmospheric probed volume, differentheights, etc. During the experimental time periodthe Cn

2 values were high enough to provide accurateand reliable lidar estimates. Because the experimentwas conducted for various atmospheric conditions,from a neutral atmosphere to an unstably stratifiedconvective boundary layer, the coherent lidar allowsmeasurement of Cn

2 in most meteorological conditionsof interest over optical paths of a few kilometers.

In Table 1 we summarize experiments conductedon several days, listing and comparing the daily av-erages of the various Cn

2 measurements. All the

Cn2 ~10214 m22y3!

mScintillometer

at 0.9 mmIn Situ at

0.9 mmIn Situ at10.6 mm

.4! 6.1 ~60.6! — —

.4! 3.0 ~60.5! — —

.4!9.1 ~61.2! — —

.4! 7.6 ~60.9! — —

.3!9.3 ~61.3! — —

.4! 6.5 ~62.6! — —

.4! 6.3 ~60.7! — —

.4! 7.1 ~62.2! — —

.4! 3.3 ~60.3! 2.2 ~60.6! 2.8 ~60.7!

.4! — 8.1 ~61.3! 10.9 ~61.3!

.5! — 1.0 ~60.3! 1.1 ~60.3!

idar0.6 m

~60~60

~60~60

~60~60~60~60~60~60~60

1

cs

srF

rf

m

Ni

8. R. M. Banta, L. D. Olivier, P. H. Gudiksen, and R. Lange,

individual measurements are then plotted in Fig. 9.There is good agreement between the three sensorsfor Cn

2 ranging from ;10215 m22y3 to ;10212 m22y3

with negligible bias of ;2.2 3 10215 m22y3 and rmserror of ;1.1 3 10214 m22y3. At higher than 4.0 30214 m22y3 the lidar estimates are reliable to within

an accuracy of better than ;20%.

5. Conclusion

We have proposed and validated a new method formeasuring refractive-index turbulence with 10.6-mmoherent lidar in the direct-detection mode. Wehow that the method is reliable for Cn

2 $ 10214

m22y3. A careful calibration of the system, i.e., theize of the transmitted beam at the target plane, isequired. This calibration was done here by aresnel diffraction approximation.24 The experi-

mental results show good agreement among the10.6-mm coherent lidar, in situ measurements, and a0.9-mm scintillometer for neutral to unstable meteo-ological conditions. The results show the potentialor coherent lidar to retrieve Cn

2 values during thedaytime when the refractive-index turbulence is ofthe order or larger than 10214 m22y3, over an opticalpath of a few kilometers. The results also show thatduring high-turbulence episodes both the coherentlidar ~10.6 mm! and the scintillometer ~0.9 mm! are

ainly sensible to CT2.

The authors are greatly indebted to L. Menenger,R. Oriel, C. Boitel, B. Romand, and C. Loth for helpduring the experiment. Special thanks go to R. G.Frehlich and M. J. Kavaya for fruitful discussionsand J. H. Churnside and H. Bravo for the loan of thescintillometer. This research was conducted at theLaboratoire de Meteorologie Dynamique du Centre

ational de la Recherche Scientifique. P. Drobinskis supported by Centre National d’Etudes Spatiales

~CNES! and Alcatel ~formerly Aerospatiale Cannes!.

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