Global distribution of CT2 at altitudes 30–50 km from

space-borne observations of stellar scintillation

Alexandre S. Gurvich, Viktoria F. F. Sofieva, Francis Dalaudier

To cite this version:

Alexandre S. Gurvich, Viktoria F. F. Sofieva, Francis Dalaudier. Global distribution of CT2 ataltitudes 30–50 km from space-borne observations of stellar scintillation. Geophysical ResearchLetters, American Geophysical Union, 2007, 34 (24), pp.L24813. <10.1029/2007GL031134>.<hal-00201348>

HAL Id: hal-00201348

https://hal.archives-ouvertes.fr/hal-00201348

Submitted on 17 Feb 2016

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

Global distribution of CT2 at altitudes 30–50 km from space-borne

observations of stellar scintillation

A. S. Gurvich,1 V. F. Sofieva,2 and F. Dalaudier3

Received 26 June 2007; revised 14 September 2007; accepted 12 November 2007; published 28 December 2007.

[1] Locally isotropic turbulence in the stratosphereconsists of isolated sporadic patches with random values oftemperature structure characteristic CT

2. Stellar scintillationsmeasured aboard GOMOS/ENVISAT through the Earthatmosphere provided the first global distribution of theeffective characteristic CT,eff

2 averaged along sounding ray.For zonal mean, the largest values are achieved in winterpolar regions. This observed intense turbulence is probablyrelated to the polar night jet. Relatively weak turbulence isobserved at low latitudes. Turbulence intensity map isshown for altitude 42 km in the latitude band ±35�, where themaxima follow the sub-solar latitude, with enhancementslocated mainly over continents. Turbulence enhancementsare not related with orography. Despite a noticeablecorrelation with typical regions of deep convection, theoverall distribution of CT,eff

2 displays a more complicatedstructure. Analyzed data suggest that the main turbulencesources, at altitudes�40 km, are instabilities of stratosphericcirculation and gravity wave breaking. Citation: Gurvich,

A. S., V. F. Sofieva, and F. Dalaudier (2007), Global distribution

of CT2 at altitudes 30–50 km from space-borne observations of

stellar scintillation, Geophys. Res. Lett., 34, L24813, doi:10.1029/

2007GL031134.

1. Introduction

[2] Breaking of internal gravity waves (IGW) and insta-bilities of different kind (e.g., shear instability, convectiveinstability etc.) generate turbulence in the stratosphere.Turbulence constitutes the last stage of kinetic energydissipation into heat through molecular diffusion. Phillips[1967] has shown that turbulence in the stable stratosphereconsists of isolated sporadic patches. These patches seem totake the form of ‘‘pancakes’’ whose horizontal length scaleis much larger than the vertical one. Radar returns visualizethese patches [Atlas, 1965]. Because of flatness of turbulentpatches, they appear as turbulent layers in balloon sound-ings [Coulman et al., 1995]. Nowadays, there are nosystematic observational data of turbulence at altitudes30–50 km. These altitudes are not accessible for airplaneexploration. Routine radiosondes usually reach a little higherthan 30 km. Rocket soundings [Lubken, 1997] usually giveinformation about the atmosphere above 60 km. Radiooccultation technique provides reliable data below 30 km[Gorbunov, 2002]. Radar returns cannot usually be ob-served for altitudes 30–50 km.

[3] Information about air density irregularities for thesealtitudes are available from lidar studies [Wilson et al.,1991; Whiteway and Carswell, 1995; Sica and Russell,1999]. However, lidar data are rare and they are boundedto a specific location. Air temperature irregularities withvertical scales larger than few kilometres are studied byusing observations of infrared [Eckermann and Preusse,1999] and microwave [Wu and Waters, 1996] emissions.[4] Using satellite measurements of stellar scintillation is

an alternative approach that allows remote sensing of small-scale processes, with scales down to fractions of meter, inthe stratosphere [Gurvich, 2002]. This approach is based onthe theory of scintillations developed by Tatarskii [1971]. Itconnects scintillation spectra with spectra of air densityirregularities. Waves and turbulence create irregularities ofair refractivity dn, which are proportional to fluctuations ofair density dr. When a star is observed on board a satellite,stellar flux passed through the atmosphere exhibits scintil-lation caused by these fluctuations. Analyses of scintillationmeasurements on board the MIR station allowed the re-trieval of parameters of IGW and turbulence spectra[Gurvich and Kan, 2003a, 2003b]. However, the man-controlled photometer on board MIR allowed only a smallnumber of observations in the latitude band ±60�. Thescintillation measurements became available with globalcoverage since the launch of Envisat satellite in 2002. TheGOMOS (Global Ozone Monitoring by Occultation ofStars) instrument on board ENVISAT is equipped withtwo fast photometers (FP) operating at blue (470–520 nm)and red (650–700 nm) wavelengths l with the samplingfrequency fs = 1 kHz (http://envisat.esa.int/instruments/gomos). Analysis of coherency spectra of the GOMOS scin-tillation data [Gurvich et al., 2005] has shown the presenceof stratospheric layers with large intensity of isotropicturbulence. The analysis of scintillation variance for twoseasons of year 2003 is presented by Sofieva et al. [2007a].[5] In this paper, we present the first global and seasonal

distribution of the structure characteristic CT2 of isotropic

turbulence at altitudes 30–50 km obtained from scintillationmeasurements by GOMOS FP in 2003.

2. Model and Processing

[6] Observed scintillation is the result of light wavesdiffraction on refractivity irregularities dn that are propor-tional to irregularities of air density [Tatarskii, 1971]. Themain contribution to energy of turbulent scintillations comesfrom irregularities of light field with scales smaller than afew tens of meters [Gurvich and Kan, 2003a, 2003b]. Thescintillations caused by IGW have larger scales and can beseparated from small-scale turbulent scintillation by spectralanalysis. Ignoring turbulent fluctuations of pressure, turbu-

GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L24813, doi:10.1029/2007GL031134, 2007

1A. M. Oboukhov Institute of Atmospheric Physics, Moscow, Russia.2Earth Observation, Finnish Meteorological Institute, Helsinki, Finland.3Service d’Aeronomie du CNRS, Verrieres-le-Buisson, France.

Copyright 2007 by the American Geophysical Union.0094-8276/07/2007GL031134

L24813 1 of 6

lent irregularities dn are connected with temperature irreg-ularities dT: dn = �(hni/hTi)dT, where hni and hTi are themean refractivity and temperature at a given altitude.Propagation of light waves through the stratosphere con-taining turbulent patches can be considered as propagationthrough a random media with variable parameters.[7] Let us assume that temperature irregularities in tur-

bulent patches have the Kolmogorov’s 3D spectrum:FT (k) =0.033 CT

2k�11/3 exp(�k2/km2 ), with parameters: CT

2, the struc-ture characteristic, and km, the wave number correspondingto the inner scale. We assume that sizes of turbulent patchesare random, as well as parameters CT

2 and km in them. Hence3D spectrum of dn in a patch is

Fn kð Þ ¼ 0:033hni2hTi�2C2Tk

�11=3 exp �k2=k2m

� �: ð1Þ

Mean refractivity hn(h)i decreases almost exponentiallywith altitude h, with the atmospheric scale height H0(h).Therefore the region of main interaction between lightwaves and dn is located around the perigee of a soundingray. Horizontal size LA of this region is a few hundreds ofkilometers; the ray can cross many patches. Satelliteobservations are performed at a large distance L (L � LA)from the ray perigee. For GOMOS, L = 3200 km.Integrating 2D scintillation spectra [Tatarskii, 1971, equa-tions (4.48) and (5.48)], we calculate the variance sI2 ofisotropic scintillation in the observation plane:

s2I ¼

2:25

cos 5p=12ð Þ k7=60 L5=6

Zray

dxC2n xð ÞW�5=3

1þW 4� �5=12

cos 5atan W 2� �

=6� �

� 1h i

;

C2n xð Þ ¼ hn h0ð Þi2

hT h0ð Þi2exp � x2

REH0

� �C2T xð Þ;

W ¼ km xð ÞffiffiffiffiffiffiffiffiffiffiffiL=k0;

pk0 ¼

2pl

where x is the coordinate along ray, x = 0 and x = Lcorrespond to the ray perigee point and to the observationplane, respectively, RE is the Earth radius. Turbulentfluctuations of temperature significantly exceed that ofpressure dT/hTi � dP/hpi; this is taken into account in (2).[8] If the inner scale of turbulence km

�1 is much smallerthan Fresnel scale Fr =

ffiffiffiffiffiffiffiffiffiffiL=k0

p(equivalently W � 1),

Equation (2) can be transformed to:

s2I ¼ 2:25k

7=60 L5=6LA

hn h0ð Þi2

hT h0ð Þi2C2T ;eff ;

C2T ;eff ¼ L�1

A

Z1

�1

dx exp � x2

REH0

� �C2T xð Þ

The parameter CT,eff2 is CT

2 averaged along a ray with theweight function LA

�1 exp(�x2/REH0) determining the effec-tive region of interaction between the light wave and theturbulent atmosphere. Its horizontal size is LA =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffipREH0

p.

[9] Equations (2) and (3) give an opportunity for esti-mating CT,eff

2 from space-borne observations of stellarscintillation. However, modest sampling frequency ofGOMOS photometers does not allow estimating km fromthe scintillation data, thus real values of W are uncertain.Previous space-born observations of stellar scintillation

[Gurvich and Kan, 2003b] have shown that values of 1/kmdo not exceed 0.6m at altitudes 30 50 km, themean of 1/kmis � 0.2 0.3 m. Since

ffiffiffiffiffiffiffiffiffiffiL=k0

p= 0.59 m for the red FP,

we can assume W > 1 along the ray. The influence of theparameter W on sI

2 in equation (2) is described by a smoothmonotonous function g(W) = cos�1(5p/12)W�5/3[(1 +W4)5/12 cos(5atan(W2)/6) � 1], g(1) = 1, g(1) = 0.228.According to the mean-value theorem, the use of a constantvalue g(Weff) = 0.7, which corresponds to the effective valueof 1/km = 0.21 m, introduces an uncertainty less than 50%in the resulting sI

2.[10] Scintillations are recorded along a spacecraft trajec-

tory with the integration time tS = fS�1. The scale of time

averaging is tSu (u is the projection of the satellite velocityon the observation plane), while the typical scintillationscale on the observation plane is max (1/km, Fr) [Tatarskii,1971]. In GOMOS observations tSu > max (1/km, Fr), thusthe variance of recorded isotropic scintillation biso

2 is smallerthan sI

2 defined by (2) by a factor G. The effect of temporalsmoothing is estimated by using the above cited equations(4.48) and (5.48) from Tatarskii [1971] and assumingCT2(x) = CT,eff

2 and W = Weff = const. This results in theapproximation G = 1.63 [(ut)2 k0/L]

�0.485 [g(Weff)]�0.39.

The accuracy of this approximation is better than 1 2 %for possible values of turbulence parameters, 3.4 km/s < u <6.5 km/s and Weff > 1. Finally, we obtain biso

2 :

b2iso ¼ 2:25k

7=60 L5=6LAhn h0ð Þi2hT h0ð Þi�2

G ut=ffiffiffiffiffiffiffiffiffiffiffiL=k0;

pWeff

�g Weffð ÞC2

T ;eff ð4Þ

The above equations are derived for monochromaticradiation and without refractive dilution. The impact ofrefractive dilution and averaging over wavelength band ofthe FP optical filter [Dalaudier et al., 2001] are notsignificant at altitudes above 30 km compared to uncertaintyof km discussed above. The equation (4) is the base fordetermination of CT

2 from space-borne observations ofstellar scintillation. We leave out the subscript ‘‘eff’’hereafter for short. The above results are based on thetheory of weak scintillations i.e. when sI

2 < 1. In case ofstrong scintillation, it is very difficult to separate scintilla-tions caused by turbulence and IGW. In our analysis, weconsider the altitude range above 30 km, where the weakscintillation assumption is valid [Gurvich and Kan, 2003a].[11] biso

2 can be determined from GOMOS scintillationsby using the technique described in detail by Sofieva et al.[2007a]. This technique uses the fact that scintillationspectra at wave numbers larger than the inverse of IGW’sinner scale are defined mainly by the turbulent component.The scintillation spectrum of the turbulent component isnearly flat in the wave number range available fromGOMOS measurements [Tatarskii, 1971; Sofieva et al.,2007b]. This allows separating the IGW and turbulentcontributions from the observed scintillation variance andthus computing biso

2 (for details and illustration of thismethod, see Sofieva et al. [2007a, section 2 and Figure 3]).Known biso

2 , CT2 is determined using (4).

3. Results and Discussion

[12] Locations of dark-limb occultations of 30 brighteststars in 2003 selected for analysis are shown in Figure 1.

ð3Þ

ð2Þ

L24813 GURVICH ET AL.: GLOBAL DISTRIBUTION OF CT2 L24813

2 of 6

The observed structure of latitude bands is the consequenceof the non-uniform distribution of the brightest stars. Thered photometer measurements are used for CT

2 computation,as they are less affected by absorption and scattering in theatmosphere. The profiles of CT

2 are computed for eachindividual occultation. The coverage by bright stars is notsufficient for obtaining monthly global maps (as can be seenin Figure 1), therefore we restricted ourselves by consider-ing seasonal distributions. For producing plots of zonalmean CT

2, the data are averaged in latitudinal bins distributedin accordance with available data: the centers of the bins areassigned to the characteristic latitudes corresponding tooccultation series. The width of latitudinal bins is mostly�10�, but it ranges from 5� to 30�. The median values ofCT

2 at each altitude are used for the construction of Figure 2due to robust properties of the median estimates of highlyvariable dataset.[13] Figure 2 shows the distribution of zonal median CT

2

in four seasons of 2003 obtained from observations indicatedin Figure 1. First of all, large variations of CT

2 can be noticed:the range of possible values of CT

2 covers more than twoorders of magnitude, from 3 � 10�5 to 6 � 10�3 K2m�2/3.The value of CT

2 has a clear physical sense. It equals to thevariance of the temperature difference in two points at thedistance of one meter. The largest CT

2 values are observed in

the boundary layer [Tatarskii, 1971], where values of CT2

vary depending on insolation, wind velocity, underlyingsurface and so on. Values of CT

2 usually decrease withaltitude in the troposphere [Gavrilov et al., 2005; Zink etal., 2004]. Typical values for the lower stratosphere (below30 km) may cover more than two orders of magnitude.Above 30 km and up to 70 km, there exists scanty dataobtained from spacecraft scintillation observations [Gurvichand Kan, 2003a, 2003b]. They show the definite increase ofCT2 with altitude from some units of 10�4 to some units

10�3, with scattering about one order of magnitude at 30 50 km, for different locations and observation time. In themesosphere, Lubken [1992] reported the values of thestructure characteristic of relative refractivity fluctuationsCn2 at altitudes 84–85 km, as obtained from rocket sound-

ings. The corresponding CT2 values are �10�1 K2 m�2/3.

[14] Values of CT2 shown in Figure 2 are within the range

of the values given by Gavrilov et al. [2005], Zink et al.[2004], and Lubken [1992, 1997]. Wide range of CT

2

variation explains the data scattering of Gurvich and Kan[2003a, 2003b]. The maps for Jan–Feb–Dec and Jun–Jul–Aug are almost mirror-symmetric. The largest values of CT

2

are observed above 40 45 km in polar winter in bothhemispheres; they are especially large in the SouthernHemisphere. The strong turbulence here is probably related

Figure 1. Location of the selected occultations in four seasons of year 2003.

L24813 GURVICH ET AL.: GLOBAL DISTRIBUTION OF CT2 L24813

3 of 6

to the polar night jet [Holton, 2004]. Based on the simpli-fied spectral analysis, Sofieva et al. [2007a] suggested thatthe strong turbulence at winter polar stratosphere might berelated with breaking IGW in the polar night jet. Severalprevious observational studies [Duck et al., 1998, 2001;Jiang and Wu, 2001] also pointed out that the gravity wavesshould break in the polar night jet at altitudes close tostratopause, in order to explain the thermal balance in thepolar vortex area. Local enhancement of turbulence at theedge of the polar vortex during the sudden stratosphericwarming in December 2003 (which also contributes to thedistribution shown in Figure 2) is discussed by Sofieva et al.[2007b]. The plot for Sep–Oct–Nov shows enhancementsat high latitudes, in both hemispheres. However, taking intoaccount that in SH the measurements were carried outmainly in September, while in NH they were performed inNovember (Figure 1), these enhancements are most proba-bly related to the remaining (beginning) of the polar vortex.This is confirmed, in particular, by the distribution of CT

2 inMar–Apr–May. The major part of occultations were carriedout in April, and the distribution of CT

2 has smaller varia-tions. In addition to the noted peculiarities at polar latitudes,modest enhancements in zonal mean turbulence around20�S in March–May and some smaller ones around 20�Nin June–August are observed.

[15] Figure 3 shows the geographical distribution of CT2 in

the layer about 3 km thick (vertical resolution) centered ataltitude �42 km, between 35N and 35S. We selected thisaltitude, because the previous consideration of GOMOSscintillation data [Gurvich et al., 2005] has shown thatturbulence is observed more clearly on the IGW backgroundat these altitudes. Turbulence intensity is smaller in thiszone than in polar regions and, in average, it has apronounced zonal structure. The plots of Figure 3 showthat the average values of CT

2 follow the sub-solar latitudelike main distinctive feature of general circulation of themiddle atmosphere [Holton, 2004]. At the same time,almost all of the local enhancements are over continents(except for that one over Western Pacific in June–Septem-ber). Many of CT

2 enhancements seen in Figure 3 correspondwell to the typical regions of deep convection, e.g., Africa,South America and Indonesia in Dec, Jan–March, regionsof Indian and American monsoons and of North African dryconvection in June–September [Jiang et al., 2004]. Manysimilarities can be found between enhancements in CT

2

shown in Figure 3 and local maxima of temperaturevariances at �38 km obtained from MLS data [Jiang etal., 2004, Figure 4]. In spite of the large difference in spatialscales (many hundreds times), it is possible to assume thatthe observed enhancements in CT

2 correspond to the last step(before molecular diffusion) of breakdown of temperature

Figure 2. Zonal averaged CT2(K2 m�2/3) in four seasons of 2003, logarithmic color scale.

L24813 GURVICH ET AL.: GLOBAL DISTRIBUTION OF CT2 L24813

4 of 6

irregularities observed by MLS and interpreted as IGW.However, this question requires a deeper analysis and isbeyond the scope of this paper.[16] Turbulence in the stratosphere results not only from

IGW breaking but also from different kind of instabilities[Staquet and Sommeria, 2002], therefore the distribution ofCT2 has a more complicated structure: some of local maxima

of CT2 (e.g. over Western Brazil and over Australia in Jun–

Sep) do not correspond either to typical regions of convec-tion or to mountain GW.[17] No systematic increase of CT

2 over large mountainrange such as Himalaya, Andes and Sierra Nevada isobserved in seasonal average distributions shown inFigure 3. Probably mountain waves are too long fortransformation into small scale turbulence observed byscintillation at 42 km.

4. Summary

[18] Analysis of GOMOS stellar scintillation observa-tions gave the first estimation of global distribution of CT

2

at altitudes 30–50 km for four seasons. The values of zonalmean CT

2 increase with the altitude, as a rule. The largest CT2

values are achieved in polar regions in winter, where theymay reach 0.006 K2m�2/3 in SH, i.e. the values, which arecomparable with those observed in the turbulent boundarylayer. It can be assumed that this observed intense turbu-lence is related to the polar night jet.

[19] Relatively low turbulence is observed at low lat-itudes. Minimal values of CT

2 are less than 10�4 K2m�2/3

there. The average turbulence intensity at altitudes �42 kmfollows the solstice, with enhancements located mainly overcontinents. Turbulence enhancements in tropical regions arenot related with orography. Despite a good correlation withtypical regions of deep convection, the overall distributionof CT

2 displays a more complicated structure. These pecu-liarities of CT

2 fields and the observed zonal structure inturbulence distribution indicate that the main turbulencesources are instabilities of general stratospheric circulationof different kind and IGW breaking induced by theseinstabilities.

[20] Acknowledgments. The authors thank ESA, ACRI-ST and theGOMOS team for the GOMOS data. The work of AG was supported byRFBR grant 06-05-64357. The work of VS was supported by the Academyof Finland.

ReferencesAtlas, D. (1965), Angels in focus, J. Res. Natl. Bur. Stand., Sect. D, 69,871–875.

Coulman, C. E., J. Vernin, and A. Fuchs (1995), Optical seeing—Mechanismof formation of thin turbulent laminae in the atmosphere, Appl. Opt., 34,5461–5474.

Dalaudier, F., V. Kan, and A. S. Gurvich (2001), Chromatic refraction withglobal ozone monitoring by occultations of stars. I. Description andscintillation correction, Appl. Opt., 40, 866–877.

Duck, T. J., J. A. Whiteway, and A. I. Carswell (1998), Lidar observationsof gravity wave activity and Arctic stratospheric vortex core warming,Geophys. Res. Lett., 25(15), 2813–2816.

Figure 3. CT2(K2 m�2/3) at 42 km for (top) Jan–March, Dec. and for (bottom) June–Sept., logarithmic color scale. The

data are averaged in 5� � 10� latitude-longitude bins and a three-point smoothing is applied to the obtained fields. In orderto make these maps more contrasting, the color scale covers one decade only.

L24813 GURVICH ET AL.: GLOBAL DISTRIBUTION OF CT2 L24813

5 of 6

Duck, T. J., J. A. Whiteway, and A. I. Carswell (2001), The gravity wave-Arctic stratospheric vortex interaction, J. Atmos. Sci., 58, 3581–3596.

Eckermann, S. D., and P. Preusse (1999), Global measurements of strato-spheric mountain waves from space, Science, 286, 1534–1537.

Gavrilov, N. M., H. Luce, M. Crochet, F. Dalaudier, and S. Fukao (2005),Turbulence parameter estimations from high-resolution balloon tempera-ture measurements of the MUTSI-2000 campaign, Ann. Geophys., 23,2401–2413.

Gorbunov, M. E. (2002), Ionospheric correction and statistical optimizationof radio occultation data, Radio Sci., 37(5), 1084, doi:10.1029/2000RS002370.

Gurvich, A. S. (2002), Parameters of turbulence and internal waves and thedissipation of kinetic energy in the stratosphere based on space observa-tions, Dokl. Earth Sci., 385(5), 599–603.

Gurvich, A. S., and V. Kan (2003a), Structure of air density irregularities inthe stratosphere from spacecraft observations of stellar scintillation,1. Three-dimensional spectrum model and recovery of its parameters,Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., 39, 300–310.

Gurvich, A. S., and V. Kan (2003b), Structure of air density irregularities inthe stratosphere from spacecraft observations of stellar scintillation,2. Characteristic scales, structure characteristics, and kinetic energy dis-sipation, Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., 39, 311–321.

Gurvich, A. S., F. Dalaudier, and V. F. Sofieva (2005), Study of strato-spheric air density irregularities based on two-wavelength observation ofstellar scintillation by Global Ozone Monitoring by Occultation of Stars(GOMOS) on Envisat, J. Geophys. Res., 110, D11110, doi:10.1029/2004JD005536.

Holton, J. R. (2004), An Introduction to Dynamic Meteorology, Int. Geo-phys., vol. 88, 4th ed., Elsevier, New York.

Jiang, J. H., and D. L. Wu (2001), UARS MLS observations of gravitywaves associated with the arctic winter stratospheric vortex, Geophys.Res. Lett., 28, 527–530.

Jiang, J. H., B. Wang, K. Goya, K. Hocke, S. D. Eckermann, J. Ma, D. L.Wu, and W. G. Read (2004), Geographical distribution and interseasonalvariability of tropical deep convection: UARS MLS observations andanalyses, J. Geophys. Res., 109, D03111, doi:10.1029/2003JD003756.

Lubken, F.-J. (1992), On the extraction of turbulent parameters from atmo-spheric density fluctuations, J. Geophys. Res., 97, 20,385–20,395.

Lubken, F. J. (1997), Annual variation of turbulent energy dissipation ratesat high latitude as determined by in situ measurements of neutral densityfluctuations, J. Geophys. Res., 102, 13,441–13,456.

Phillips, O. M. (1967), The generation of clear-air turbulence by the de-gradation of internal waves, in Atmospheric Turbulence and Radio WavePropagation, edited by A. M. Yaglom and V. I. Tatarsky, pp. 130–136,Nauka, Moscow.

Sica, R. J., and A. T. Russell (1999), How many waves are in the gravitywave spectrum?, Geophys. Res. Lett., 26, 3617–3620.

Sofieva, V. F., et al. (2007a), Global analysis of scintillation variance:Indication of gravity wave breaking in the polar winter upper strato-sphere, Geophys. Res. Lett., 34, L03812, doi:10.1029/2006GL028132.

Sofieva, V. F., A. S. Gurvich, F. Dalaudier, and V. Kan (2007b), Recon-struction of internal gravity wave and turbulence parameters in the strato-sphere using GOMOS scintillation measurements, J. Geophys. Res., 112,D12113, doi:10.1029/2006JD007483.

Staquet, C., and J. Sommeria (2002), Internal gravity waves: From instabil-ities to turbulence, Annu. Rev. Fluid Mech., 34, 559–593.

Tatarskii, V. I. (1971), The Effects of the Turbulent Atmosphere on WavePropagation, 417 pp., U. S. Dep. of Commer., Springfield, Va.

Whiteway, J. A., and A. I. Carswell (1995), Lidar observations of gravitywave activity in the upper stratosphere over Toronto, J. Geophys. Res.,100, 14,113–14,124.

Wilson, R., M.-L. Chanin, and A. Hauchecorne (1991), Gravity waves inthe middle atmosphere observed by Rayleigh lidar: 2. Climatology,J. Geophys. Res., 96, 5169–5183.

Wu, D. L., and J. W. Waters (1996), Satellite observations of atmosphericvariances: A possible indication of gravity waves, Geophys. Res. Lett.,23, 3631–3634.

Zink, F., R. A. Vincent, E. Murphy, and O. Cote (2004), Comparison ofradar and in situ measurements of atmospheric turbulence, J. Geophys.Res., 109, D11108, doi:10.1029/2003JD003991.

�����������������������F. Dalaudier, Service d’Aeronomie du CNRS, F-91371 Verrieres-le-

Buisson Cedex, France.A. S. Gurvich, A. M. Oboukhov Institute of Atmospheric Physics,

Pyzhevsky 3, Moscow, 119017, Russia.V. F. Sofieva, Earth Observation, Finnish Meteorological Institute, P.O.

Box 503, Helsinki, FIN-00101, Finland.

L24813 GURVICH ET AL.: GLOBAL DISTRIBUTION OF CT2 L24813

6 of 6