Gravity waves in the middle atmosphere observed by Rayleigh lidar: 1. Case studies

JOURNAL OF GEOPHYSICAL GRAVITY WAVES RESEARCH, VOL. 96, NO. D3, PAGES 5153-5167, MARCH 20, 1991 IN THE MIDDLE ATMOSPHERE OBSERVED BY RAYLEIGH LIDAR 1. CASE STUDIES R. Wilson, M. L. Chanin, and A. Hauchecorne Service D'Atronomie du CNRS, Verrieres le Buisson,France Abstract. Densityandtemperature mesoscale fluctuations asobservedin the stratosphere andmesosphere by meansof two Rayleighlidarswith highresolutionin time (15 min) and space(300 m), have beenanalyzedin someparticularcases correspondingto different seasonalconditions.These case studiesarecharacteristic of recurrentlyobservedpatternsand thusprovidea descriptionof the mesoscalefluctuationfield in the middleatmosphere. The spatial,temporal,andspectral characteristics of the fluctuations are described and discussed in the framework of the gravity wave interpretation. Dominantwave modeswith largeperiodand largevertical wavelength(inertia-gravitywaves)are frequentlyobserved in the stratosphereand lower mesosphere.These lowfrequencymodesare not generallyobservedabove50- to 55km altitude,suggestinga strongdampingof suchwavesin the mesosphere. The vertical growth of potentialenergy densityindicatesthat the wave motionsare generallynot conservativein the middle atmosphere.The gravity waves amplitude appears too small to produce convective instabilities in the stratosphere.On the contrary, the amplitude of the fluctuations is close to the convective saturation limit deduced from the linear theory for wavelengths up to 3-5 km in thelowermesosphere, andup to 6-8 km above 60 km altitude.Furthermore,convectively instablelayers,which can persistfor periodslongerthan 1 hour,havebeenfrequentlyobserved in themesosphere. 1. Introduction It nowappears fmuly established thatgravitywavesplaya major role in the momentumand thermal budgetof the mesosphere[Lindzen, 1981; Holton, 1982; Fritts, 1984; Garcia and Solomon,1985]. Dissipationprocesses,which induce a convergenceof the vertical fluxes of horizontal momentumand energy,lead to an accelerationof the mean flow, and to the productionof turbulence.The momentum convergence due to wavedissipationinducesthereversalof the verticalmeanwind gradient,thusa meridionalflow and thereforethe mesospheric temperature distributionknownto befar fromradiativeequilibrium[MurgatroydandSingleton, 1961]. More recently, it has been suggestedthat gravity wavesalsoplay an importantrole in the momentumbudget of the stratosphere [Miyaharaet al., 1986, Palmeret al., 1986]. The mean flow acceleration and turbulent diffusion inducedby thewavesaturation havebeenfarstparameterized by Lindzen[ 1981] in the frameworkof the lineartheoryof gravitywave.The wave saturation refersto thoseprocesses limiting the amplitudeof the waves due to instabilities arisingfrom the large amplitudeof the fluctuations(for a review see Fritts [1984] and Fritts and Rastogi [1985]). Despitethe successencounteredby the linear theory,the involvedschemeof the wave-meanflow interactionappears to berelativelysimpleandrequiresimportanttheoreticaland observational efforts in order to be better understood and parameterized.Numerousquestionsremain: what are the typical energy levels of the gravity wave field in the stratosphere and mesosphere? What is the vertical energy growthrate of the waves?Is therea significantseasonalor geographicalvariability of the wave activity?What are the dominantdissipativeprocesses:convectiveor dynamical instabilitiesor otherprocesses This paperwill bringelements of answers for some of these issues. Up to the present,mostof the mesoscalefluctuationsdata in the middleatmosphere havebeenobtainedby usingradar techniques,rocketssounding,or balloon-borneinstruments. The horizontalandverticalwind fluctuations areobservedby radarbothin the troposphere andlowerstratosphere [Balsley and Garello, 1985; Fritts et al., 1988] and in the upper mesosphere [Vincent, 1984; Meek et al., 1985; Vincent and Fritts, 1987] but radars are blind in part of the middle atmosphere.Rocket data, on the other hand, have allowed the studyof wind and temperaturefluctuationsin the 20- to 65-km altituderangefrom a largenumberof rocketranges [Hirota, 1984; Hirota and Niki, 1985; Hass and Meyer, 1987], but the data are obtained in a sporadicmanner. Balloonborneinstruments give accessto thefine structure of the fluctuation field [Barat, 1982; Cot and Barat, 1986], the Papernumber90JD02231. altituderangebeinglimited to about25 km. Rayleighlidar offers the unique feature of high resolution routine measurements of the densityor temperaturefluctuations,in the 30- to 75-km altituderange, where radarsand in situ measurements are not possible and rocket soundings sporadic. The use of lidar in this height range thus complements to the othertechniquesandhasnow provedto be quitepowerfulto measurethe mesoscale fluctuationsin the middle atmosphere.Preliminaryresultswere reported duringthe early phaseof the developmentof this technique 0148-0227/91/90JD-02231$05.00 [Chanin and Hauchecorne,1981, 1984; Shibataet al., 1986, Copyright 1991bytheAmerican Geophysical Union. 5153 5154 Wilsonet al.: Gravitywavesobservedby RayleighLidar, 1 1988] and from a relatively low performance system [Gardner et al., 1989]. The purpose of this paper is to pressure estimated at height Zsup from the CIRA 1986 describe and to discuss the main features of the mesoscale Thereare now two operatinglidar stationsin the southof France, located in two sites different with respect to orography: theObservatoire deHauteProvence(OHP) in the foothillsof theAlps (44øN,6øE)andthe Centred'Essaisdes Landes at Biscarosse(BIS) on the Atlantic Coast (44øN, 1øW). Routinemeasurements havebeenperformedon clear nightssinceJune1981at OHP andsinceMarch 1986at BIS. High spatialandtemporalresolutiondataallow the studyof gravitywavemotionswith 300 m verticalintegration and 15 min integrationtime. A very large data base has been acquired:it consistsof about100 nightsa year, eachnight duration lasting between 3 and 14 hours,i.e. more than 10,000 verticaldensityprofries,in an altituderangewhich hasbeenthusfar barelyexplored. Only a part of these nights, about 100, have been individuallystudiedin greatdetails.From this limited but alreadylarge numberof casestudies,it appearsthat some wavepatternsare very frequentlyobserved.The few cases presentedhere are characteristicof recurrentobservations and thus provide a meaningfuldescriptionof the gravity wavefield in the middleatmosphere. Theseparticularcases fluctuation field from observations obtained by two performingRayleighlidars.The fluctuations are interpreted in the frameworkof the gravitywave theory.Casestudies, characteristicof recurrentlyobservedwave patterns,are analyzed,thusprovidinga descriptionof the wave field in the stratosphereand mesosphere.A climatologicalstudy, performedover a large data set, is reportedin a separate paper. This paperis organizedas follows.In the secondsection the databaseand the relevantparametersare described.The differentdataprocessingmethods,giving accessto various wave features, are reviewed in section 3. From typical particularcasesthe main characteristics of the gravitywave field in the middle atmosphereare describedin section4: dominant modes, vertical anisotropyof the wave field, spectralenergydensityversusverticalwavenumber,vertical growth of energy density per unit mass. The frequent occurrenceof unstablelapserate in the mesosphereis also shown. The results and conclusions are summarized in section 5. model. have 2. The Data Base The backscatteredlight from a pulsedlaser beam sent verticallyinto the atmosphere, providedthat Mie scattering couldbe neglected(i.e., above30 km) andin the absenceof any resonantline, is due to Rayleighscatteringfrom neutral molecules and is thus proportional to the atmospheric density. The uncertaintyon the density measurementis simplyrelatedto the numberof receivedphotons,n(z), and dependsuponthe spatialandtemporalintegrationof thelidar signal.The statisticof receivedphotonsbeing a Gaussian function (asymptoticlimit of a Poissondistribution)the standarddeviation of the density measurementis simply proportional ton(z) -1/2. As described in earlier publications[Hauchecorneand Chanin, 1980; Chanin and Hauchecorne,1984], the absolute temperature profilecanbe deducedfrom therelativedensity measurements by assumingthe hydrostaticequilibrium, applyingtheidealgaslaw andfittingthetemperature profile with an atmospheric model(CosparInternational Reference Atmosphere(CIRA), 1986) at the upper altitudeof the measurement. Thisupperlimitaltitude, Zsup, isdefined asthe heightwhere the relative statisticalerror on the density reaches15%, typically about80 to 85 km for a temporal integrationof 15 min. The temperature T(zi)in a layerof thickness Az centeredon thealtitudezi is givenby T(zi) = giAz (1) )) RLn(1 +pigiaz/(P(zsup) +zw Lpzgzaz z=zi wherePi andgi are respectivelythe densityand the Earth acceleration at altitudezi, R theair constant andP(zsup) the been selected either because measurements were obtained simultaneouslyat both sites (May 29, 1986; December 17, 1987) or becausethey correspondto long measurement periods(August7, 1985 at OHP, January28, 1989 at BIS). In a single case,on May 29 at BIS, wind measurements from tracked rocketsondes were obtained simultaneously with the temperaturemeasurements from Rayleighlidar. Let us brieflydescribetheparameters of interestfor wave studieswhicharemadeavailableby Rayleighlidar.It should be firstrecalledthat,with regardsto gravitywavemotions,it is equivalentto considerthe densityor the temperature relative fluctuations (the pressureperturbationsbeing negligible) provided that the vertical scalesof the fluctuations arenotmuchlargerthantheatmospheric density scaleheight,Hp. The relativedensityfluctuations, P'/Po,are estimatedas the first orderperturbation termof thevertical profileof log(p).Therelativeperturbations of density (P'/Po) ortemperature (T'/To)areextracted bysubtracting fromthe raw vertical profile (or from its logarithm) a smoothed profileor a third-order polynomial fit. The smoothed profile is obtainedby applyinga finite impulseresponsefilter, symmetricand nonrecursive, the so-calleddiscreteprolate spheroidal filter(DPSF)[Mathews et al., 1983].Examples of temperaturevertical profiles, resulting from 15-min integrationtime and 1-kmverticalresolution,are givenin Figure 1. The shadedareacorrespond to plus or minus1 standarddeviation.The relativeuncertaintyfor suchspatial andtemporalresolution,whichcouldvary from onenightto another depending upon the laser power and upon the atmospheric transmission, is typicallyaround0.2% at 30 kin, 1% at 55 km, and 5% at 70 km. Vertical profilesof relative temperature perturbations corresponding to the temperature profilesshownin Figure1 areplottedin Figure2. Wilsonet al.:Gravitywavesobserved by RayleighLidar,1 Mean 75' 5155 Tem')erature 70 65 [ •o 'ID 50 40 22•:2i0 I )/'it'>r[ • t"I / [ OHP 7 AUG1985 )::!9 0:,4 ß L ii , Temperoture (K) Fig. 1. Temperature profilesobtainedby Rayleighlidar on August7, 1985, at OHP. The temporal resolution is 15 min, the vertical resolution is 1 km. Relative Temperature OHP 7 AUGl•g5 Pertubations (T'/To) (g) Fig.2. Relativefluctuations of temperature corresponding to thetemperature profilesshownin Figure1. The perturbations areextractedby removinga smoothed profile(DPS filter, cutoffwavenumber1/12000 m-1) From the mean densityor temperatureprofilesdeduced from a low-passfiltering of the data, the static stability characterized by the local Brunt-Viiisiiliifrequency,N(z), is givenby $2(z)=_ g(po•Z 1•p- -•2 •z+-$Cs)=T•o C•) (2) where g istheEarthacceleration, Csthesound velocity, Cp the air specificheat at constantpressure,and z the vertical coordinate. Density or temperaturefluctuationsare associatedwith verticaldisplacement of the atmospheric fluid andtherefore are related to the available potential energy of the fluctuations. Indeed,for a verticaldisplacement relativeto an equilibrium position,•, thepotential energyperunitmass, Ep, is givenby g2 '1"2 >=•1(N•)2<(p')2>___ <(•oo) > (3) Ep =•1N2<•2 Po •1(N) wherebracketsindicatea spatialor temporalaverage. The temporal characteristicsof the temperature (or density) fluctuations are obtained from the successive verticalprofilesof the perturbations whichgive the apparent frequencyof thewave,o. Indeed,it is notpossibleto directly estimate from ground based measurementsthe intrinsic frequency,co(z),in the referenceframeof the meanflow, as it dependsuponthe meanwind velocity,u(z), the horizontal wavenumberkh, andtherelativedirectionof propagation of the wave with respectto the meanflow: co(z)= 0- kh. u(z) (4) 3. Data Processing The distribution of gravitywaveenergyas a functionof altitude, time, vertical wave number,and (apparent) frequency is described by means of various dataprocessing 5156 Wilsonet al.: Gravitywavesobservedby RayleighLidar, 1 methodswhich are being presentedhere. Each of these methodsgivesaccessto differentwaveparameters in several altitudeand spectralranges.The grossfeaturesof the wave field, i.e., the vertical and temporalscalesof the dominant wavemodes,are viewedby time-heightperturbation plots. The spectralenergydistributionis givenby the verticaland frequencyspectra,whereasthe spatial (vertical) energy distributionis estimatedby a complexdemodulation of the perturbation profilesin severalwavelengthbands.For each of thesemethods, thedefinitionof theperturbation termswill be slightlydifferentasdescribedbelow. Fromdimensional arguments, it hasbeenshownby Dewan averageduponthe individualspectra(resultingfrom 15-min integratedprofiles) obtainedfor a given day. It has been verified that the noise of the lidar signal due to the uncertaintyon the photon counting has a white spectral response.The white noiselevel is evaluatedin the high wave numberportionof the meanPSD (wherethe signal-to-noise x:atio is low),thatis to say,forwavelengths smaller than! andGood[1986]thatthepowerspectral density(PSD)of the relativedensity(or temperature) fluctuations of a saturated km andis subtracted from theraw spectrum.The uncertainty on theraw powerspectrum,estimatedin the standardway, is proportionalto the estimatedPSD. However,becauseof the variablesignal-to-noiseratio versuswave number(the noise being subtracted),the uncertaintyon the resultingpower spectrumshouldbe proportionalto the signal-to-noise ratio. The relative uncertainty on the resulting PSD is thus assumed to be of the form gravity wavefieldis proportional to N4/(g2m3). The perturbed densities arethus normalized as(g•2)(p7Po) in orderto providea comparison betweenthe verticalspectra obtainedin variouslocations,times,andheightranges,with respectto the saturation limit. In orderto reduceedgeeffects a Welchwindowis appliedto the spatialseries.The power spectrum,estimatedby a simpleFourier transform,is then normalizedto the raw variance.The daily meanspectrumis A(S(k)-B) 1 S(k) (5) S(k)-B nsl/2S(k)-B whereS(k) is the powerspectraldensityof the raw data,B the whitenoiselevel, andns the numberof spectraover whichtheaverageis performed. 65 60- 6O • 50 .•=• ß• 45 .< 40 40- 35 :3O 18 19 2.0 œ1 a2. a3 Tin-ie 0 I 2. 3 4 5 6 { H) T'/To I .•ovE I 0.0:35• 0_025"-•--.'• 0.015• o 005 [•3 -0.005 [•3 -0.015 [---] -0.0•5 ':;i• -0.035 • -0.045 ':'• BELOW o,o45 0.045 0.035 0.035 0,015 0.005 -0.005 -0•015 -0 0..25 -0.035 --0.045 21 22_, 23 o Tinge I 2, { H) Fig. 3. Time-heightcontoursof temperature relativeperturbations, on (a) January28, 1989, at BIS; (b) May 29, 1986, at OHP; (c) August 7, 1985, at OHP; and(d) December17, 1987, at BIS. 3 Wilsonet al.: Gravitywavesobservedby RayleighLidar, 1 Spectralanalysisas a functionof vertical wave numberis performed in threealtituderanges: theupperstratosphere (30 to 45 km), the lowermesosphere (45 to 60 km), andthe 55to 70-kmheightrange.The potentialenergydensityperunit massis estimatedby integratingthePSD oververticalwave numbers between 1/15and1/0.6km-1,subtracting thenoise variance andscaling bytheaveraged value ofN2. 5157 changesignificantly in theheightrangeunderstudy.For the demodulationanalysisthe perturbationterm is definedas (g/N)(p'/po), the varianceof which is twice the available potentialenergy.As for the spectralanalysis,thenoiselevel is estimatedby estimatingthe meanvarianceof shortscale fluctuations, smaller than 1 km, and is removed from the raw variance. The uncertainty on the resulting variance is evaluated in the same way as for the spectral analysis (equation(5)). functionof verticalwavenumberand(apparent) frequency. The spectraland demodulationanalysesare performed A frequency Fouriertransform is applieduponthesuccessive from densityprofiles which are simply proportionalto the verticalwavenumberspectragivinga qualitativeinsightinto lidar signal (i.e., the number of backscatteredphotons), the temporal characteristicsof the fluctuations.The 2D whereastemperature profilesresultfrom a differentiationof spectrum shows,for eachwavenumber,thephaseevolution the densityprofiles.Indeed, the white noiselevel is better of the successiveFourier Transformsof the density defined from the density data, becauseit could be biased perturbations profiles.The zerofrequencyterm represents from the temperaturedataowingto the differentiationandto on the pressureat the topof theprofile. thepowerspectrum of thefluctuations with periodslonger theinitial assumption In any case,whethertemperatureor densityfluctuationsare than the measurement duration,suchfluctuationsbeing used for such analyses the results are not significantly verticallyresolved.The integration of the2D spectrum over frequenciesgives of coursethe power spectrumversus different,providedthattheyareobtainedfar enoughfrom the topof theprofile,asis the casein thisstudy. verticalwavenumber.According to therelativesignof the The time evolution of the density fluctuations are described by a two dimensional (2D) spectralanalysisas a frequency andwavenumbertermsof thephase,expressed as exp(mz+ cot),the upwardand downwardverticalphase velocitiescan be identified.Providedthat co<<N(asit is the case in this study), the dispersion relation of a monochromatic gravitywave is 4. Gravity Wave Characteristics The main features of the gravity wave field in the stratosphere and mesosphere, as observedby two Rayleigh lidars at mid-latitude, are now describedfrom a few selected o,)2 =f2+N2kh 2 m2 (6) where f is the inertial frequency,kh and m being the horizontaland vertical wave numbers,respectively.The verticalgroupvelocity,Cg,is thus ;9o• o• 4.1. A DominantGravityWave Mode in the Stratosphere f2 Cg-3m-m(1-•) cases,characteristicof recurrentlyobservedwave patterns. The presenceof dominantlow-frequencywave modesin the stratosphere, the potentialenergydistributionversusvertical wave number,apparentfrequencyand altitude,and finally thefrequentoccurrence of convectivelyinstablelayersin the mesosphere will be shown. (7) The verticalgroupvelocity,Cg,andtheverticalphase velocity,Cz (=co/m),arethusin opposite direction.Therefore the energy flux of a wave the vertical phasevelocity of which propagatesdownward is directed upward. Even thoughthe result couldbe biased,owing to the frequency Dopplershift, an observedrecurrentbehaviorwouldbe a clearindicationof a verticalasymmetryof thewavefield. A complexdemodulationof the densityprofilesis also performedin threewavelengthbandscenteredat 6, 5, and4 km. The purposeof the complexdemodulation is to estimate the variationof the varianceversusaltitudein a givenwave numberband of the wave spectrum.The spatial seriesis multiplied by exp(-imc) before applyinga low-passfilter (DPSF), thereforeprovidingthe varianceof the fluctuations in a spectralband centeredon rnc. The spectralwidth is a function of the cutoff wave number of the filter. The used Most often,a dominantoscillatorymodeis observedin the stratosphere andlower mesosphere. This dominantmodehas a large apparentperiodrangingtypically from 6 hoursto infinity, a downwardphasevelocity, and a large vertical wavelength,from 5 to 10 km. Examplesof time-height contoursof relative temperatureperturbations are shownin Figure3. Thesedata havebeenobtainedduringdifferent seasons andthusin variousmeanflow conditions: January 28, 1989, at BIS; August7, 1985, at OHP; May 29, 1986, and December 17, 1987, at both sites. From these four examples,which illustratea recurrentpattern,a dominant oscillationof severalkilometers'vertical wavelengthand severalhours'periodcan be clearlyidentified.Excepton August 7 (Figure 3c), this low-frequencymode seemsto disorganize andto disappear in thelowermesosphere, above 55 or 60 km altitude.The temperatureperturbationplot, shownin Figure 3d, for the measurements of December17, averageof the varianceover the threeneighboringspectral intervals(partiallyoverlapping)will be presented, takinginto 1987, at BIS, exhibitsa somewhatmore complexpattern which probablyresultsfrom the superposition of several largeamplitudeoscillatorymodes. In a single case,on May 29, 1986, at Biscarosse,wind account the fact that the vertical measurements, obtained from tracked rocketsonde, were DPS filter has a cutoff wave numberat 1/10 Km-1. An scales of the waves could 5158 Wilsonet al.:Gravitywavesobserved byRayleigh Lidar,1 collectedon the site simultaneously with the lidar Thereforethe amplitudesof the temperatureand wind measurements. The time-heightplot of the temperature perturbationsare alsorelatedto to. The directionof the wave fluctuations as well as thehorizontal windperturbation propagation is estimated, assuming a quasi-monochromatic profile (Figure 4) showsthe presenceof a dominant wave,by determining analytically themajoraxisorientation oscillatory modein thestratosphere andlowermesosphere of the wind elliptical hodograph[Kundu, 1976; Cot and between 35-and55-kinaltitude with6-to12-kin wavelength Barat, 1986]. The direction towards which the wave androughly10hours'period.Thezonalandmeridional wind components havea roughlyconstant phaselagupto 55 km altitude.Abovethisheightthepatternis somewhat more complicated, resulting probably fromwavesuperposition. In thissingle opportunity it hasbeenpossible toclearly identify a gravitywavefromthepolarization relationships, i.e.,the relationships between thedifferentperturbed variables. From theWKBsolutions of thelinearized perturbations equations, propagatesis found to be closeto-0.8 tad (anticlockwise from east). The propagationdirectionof the wave with respectto themeanflow (directedtowardswest-south West) makeanangleof roughly•/3 (anticlockwise). Figure5 shows thehorizontal windfluctuations projected in the directionof the wave propagationand in the perpendicular directionjust as thenormalized temperature perturbations (g/N)(T'/To) between 33and 50-km altitude. the horizontal wind fluctuations in the direction toward The fluctuations are extracted by a band pass filtering (cutoff whichthewaveis travelling, U', andin theperpendicular wavelengths at 3 and 12 km) of the vertical profiles. The direction, V', andthetemperature relative fluctuations, T'/To, phase relationships between the two horizontal wind of a monochromatic gravitywavearerelatedasfollows: componentsare consistentwith the polarizationrelations (equation(8a)). The temperature fluctuationsare about180ø V'=-i fU'=(1-to2/N2.•1/2 (•) outof phasewithV' between 33 and50 km (equation (8b)). Below and abovetheseheightsthe phaserelationship (8a) betweenthe temperatureandwind fluctuationsdo not seem U'=-i(11to2]N2.,•l/2 f2-'•2'! NK (•----o) (8b) consistent withthepolarization relationships (equation (8a), (8b)), suggesting a superposition of otherwavemodes.An inertia-gravity waveis thusclearlyidentifiedoverabouttwo where i=x/-1, theother notations being defined aspreviously.verticalwavelengths,eventhoughotherwave modesare Theinertial frequency, f, isclose to2n/17hours '1 at44øN. probably superimposed.The main characteristicsof this inertio-gravity wave, as deduced from the wind and temperaturemeasurements over two verticalwavelengths, The windperturbations perpendicular to thedirectionof the wave propagation,V', is 180ø out of phasewith the temperature fluctuations andin quadrature withU' (equation aresummarized in Table1. Thehorizontal windhodograph (8a)),U'andT' being ofcourse inquadrature (equation (8b)). (Figure 6) shows a clockwise rotation of the wind vector Theratio,U7V',isproportional totheintrinsic frequency, to. RELATIVE •O -"':"' '" •: FLUCTUATIONS ":-".• ' ' " •: '" OF TEMPERATURE '•-"•z--•.•] .................. • ..... 6 0 '-•: ' •; -%> •. ' - WIND FLUCTUATIONS .................................... •' •. •.• .......... (a) • ' "--' ..•c:• ',:•-•_•--.:, 29MAY 1986•sz'""'•½/••- 20:29- 1:15 •5o• with altitude(thusan upwardenergyflux). The ratio f/to, ,' [-•-•' • 60 ...... ...... • • 55 •-•' %46 I AaOVE 0.045 ....**.•• 0.035- 0.045 38*' •-- •-0.005- 0.005 32 • -0.015 --0.005 •,:• -0.035 -0.025 --o.o15 --0.025 ::;':•-0.045 --0.035 •:.• BELOW -0.045 •';" ' •t ' .... ••'.... I 4o o k:' ,•,,- 2z ' 23" ' Time(H) 0 ' Wind In•ensi[y BIS22:55 (M/S) ZonalWind ........ Meridional Fig.4. Time-height conto•s of(a)•e tem•rature relative fluctuations obse•ed byRayleigh lidar•d (b) ß e hofizon•windfluctuations ob•• from•ack• r•ketsonde onMay29,1986,atBIS. Wind Wilson et al.: Gravity wavesobservedby RayleighLidar, 1 W & T 5159 closeto 0.75, indicatesan intrinsicperiodof theorderof 13 hours. The horizontal wavelength, deducedfrom the FLUCTIIATIONS 5O dispersion relationship (equation (6)), shouldbe therefore 48 close to 1500-2000 km. The vertical phase velocity, as observedfrom the temperature fluctuations(Figure4), is directed downwards (roughly -0.2 to-0.4 m s'l), as expected fora wavewitha positive intrinsic horizontal phase velocity (equation(7)). Note also that the wave pattern observed the samedayat OHP (Figure3b), 550 km eastof BIS, is quite similarabove40 km altitude: it showsa verticalwavelength of 6 to 8 km anda downwardphase velocity ofabout -0.3ms'1. Theverticalcomponent of theperturbation velocity,w', as well asthemeridionalcomponent, v', arerelatedto thezonal windcomponent [Gossard andHooke,1975]by 36 W'=kh2 1 ')U' - •- (1+ia.tg(x)' (9a) 34 v'=(1iatg(x) ) u' + ia.tg(x) BIS g9 MAY 86 THETA--0.8 rad where x is the angle defining the directionof the wave propagation(anticlockwise from east),tg(x)=l/k,1 andk beingthe meridionalandzonalwavenumberrespectively, anda=f/t0.Followingthe methoddescribedby Eckermann U 22:55 V ........ (9b) T Fig. 5. Verticalprofilesof thehorizontal windfluctuations and Vincent [1989], the vertical fluxes of the zonal and meridional horizontal momentum (<u'w'> and <v'w'>, (projected in thedirection of thewavepropagation andin the perpendiculardirection) and normalized temperature respectively)are written fluctuations (g/N)(T'/To)obtained witha bandpassfilter kh <U'W'> = - -- <u'v'> msin•(1-a 2) centered on 6 km between 33- and 50-km altitude. Table1. TheInertia-Gravity WaveCharacteristics Observed onMay 29, 1986,at BIS From 33 to 39 km Polarization f/co Directionfrom east,rad Verticalwavelength, km Horizontal wavelength, km 0.78 -0.82 6 1640 From 39 to 49 km 0.73 -0.75 10 2208 Momentum flux,N m-2 po<U'W'> po<V'W'> 2.47x10 -5 - 2.17x 10-5 0.67x10 -5 - 0.63x 10-5 Induced acceleration, m s-1d-1 -1/poA/Az(po<u'w'>) -1/poA/Az (po <v'w'> ) Vertical group velocity, ms-1 4.lx10 -2 - 3.6x 10-2 0.49x10 -1 1.02x10 -1 Horizontal group velocity, ms-1 Kinetic energy density, j kg-1 Potential energy density, j kg-1 Total energy density, j kg-1 Vertical energy flux, j m-2s-1 34.8 4.2 1.9 6.1 2.18x10 -3 50.0 12.1 5.6 17.7 4.26x10 -3 Horizontal energy flux,j m-2s-1 1.55 2.1 (10a) 5160 Wilsonet al.- Gravitywavesobserved by RayleighLidar, 1 HODOGRAPE <V'W'> -- kh <U'V'> mcosx(1-a 2) --i (10b) the bracketsdenotingherea verticalaverage.On insertingin theserelations the inferred values for f/co,kdm, <u'v'>, and % and the atmosphericdensityPo(CIRA, 1986), the mean values for po<U'W'> and po<V'W'> can be estimated [Eckermann acceleration evaluated • and Vincent, between 33- 1989]. The wave-induced and 50-kin from these momentum altitude have been fluxes estimations. These valuesare reportedin Table 1. Even thoughvery small, the orderof magnitudeof the inducedaccelerationwas foundto be nearlythe samein the zonalandmeridionaldirection.The wave-inducedaccelerationis in a directionoppositeto the zonal componentof the mean flow (eastward)and in the samedirectionthanthe (weak) meridionalcomponentof the -3 mean flow (southward). 4.2. The VerticalAnisotropyof theWave Field Zonal Wind (rn/s) BIS 29 MAY 86 22:55 Fig. 6. Hodograph of the horizontal wind fluctuations between33- (indicatedby x) and50-km altitude.The wind vectoris turningclockwise. BIS 28 JAN 30--45 PERIOD (H) 89 --2 --4-• • 4 OHP 2 !a) km I StEp/PrEp = 0.45 O.4 I [•] r--] 11.811.4- 3 PERIOD (H) 86 -,• • 30-45 km 10.4 10.1 9.7 B[LOW ,.•UpEp/DnEp =2.33 (rn3s) 4 Z• ';:--• li.t- n.4 02 5 • DEE] 0.1 8 10.7 10.4 9.7 • 07 AUG 30-45 85 StEp/PrEp = 0.26 UpEp/DnEp = 2.72 -z - km ' PERIOD (H) -• • •' - , 4 -r.!.... :-' - (b) /A,:%:."':-":-4 Z 9.7- 10.3 10.0 • 1o.o9.4 • -- 0.7 0J. -- 0.4 BIgLOW 0.1 •?:":::•i ..... :!::!?!':ij? !:.:i?,,/(;>.,:: .':.,,.... ,,, , ....• 8 "::::,. 'AM:'"':::.L', FREQUENCY(i/H) z *-- (t-• BIS 17 DEC 87 .,\•'/ • -• • ] ,-,';•m:.• :--• ....... . ............................ PERIOD (H) 30-45 km •le • • o3 • •R•u•cY • • • 0.:• '• . 7•:::.;{,• -•/:•x_•.,•-__--:: •:,_:.. ,] StEp/PrEp = 0.44 0• •8 .,• 0.3 O/n) •• --.,:.,•._ ?- ::---:• [--• _?•.:.:.- .... 0.4 lO.6- 10.G •.o.s- t• 'e •-0.4-o'.• o.o oa0.4o.• •u•c• .• StEp/PrEp= 0.37 m 12.1 11.8 z OHP MAY A•OVS .•...• 1•.4-12.8 • 29 0.4 '" UpEp/DnEp = 1.50 From most of the case studiesperformed,the observed inertia-gravitywaves exhibit a downwardvertical phase velocity of the order of a few tens of centimentersper second.Four examplesof two-dimensional spectra,function of vertical wave number,m, and apparentfrequency,o, resulting from density measurements in the upper stratosphere(30-45 km), are shown in Figure 7. The • •- .• •0.? - •.• •.• '-'• to.o-to.3 o.• o.• o.• 01•) Fig. 7. Two dimensional spectra,functionof the verticalwavenumberandapparentfrequency, of the densityfluctuations in thestratosphere (30-45km). Theratiosof upwardto downward propagating energy (UpEp/DnEp)andof stationary to propagating energy(StEp/PrEp) areindicated. (a) BIS, January 28, 1989; (b) OHP, May 29, 1986;(c) OHP, August7, 1985;(d) BIS, December17, 1987. Wilsonet al.:Gravitywavesobserved by RayleighLidar,1 dominant low-frequency andlow wavenumberwavemodes are easilyidentifiedfrom eachof theseexamples.On December17, a low-frequency modewitha relativelysmall verticalwavelength (3 km)is observed whereas fortheother casestheverticalwavelengthof the dominantmoderanges between5 and 8 km. The frequencyterm of the phase (expressed asexp(mz+ (•t) with(•>0)of thisdominant wave modesis generallypositive.It impliesa downward vertical phasevelocity,indicativeof an upwardenergyflux. The energyratioof thefluctuations withupwards anddownwards verticalphasevelocityrespectively isreported in Figure(7). This ratio rangesbetween1.5 and 2.7. The PSDsof the fluctuationswith vertical phase velocities propagating upwardanddownward (resulting froman integration over the positiveand negativefrequencies, respectively) are shown in Figure8. A verticalasymmetry of thewavefieldis observed, 65 to 80 % of theenergycontentof theprogressive waves(i.e.,resolvedfrequencies) havingdownward vertical phasevelocity. 5161 about0.3-0.4 in the stratosphere to 0.1 in the mesosphere. Thisfrequently observed featuresuggests thatthewaves should haverelatively higherfrequencies in themesosphere thanin the stratosphere. It appears frommostcasestudies thattheverticalphase velocityof thedominant inertia-gravity wavesobserved in the upper stratosphere and lower mesosphere is very generally directed downward. Above50- or 55-kmaltitude the lower-frequencywaves frequentlyseempartially dissipated. A verticalasymmetry of the wavefield (for verticalscalesbetween1 and 15 km) is generallyobserved, mostpartof the waveshavingdownward verticalphase velocityindicating anupwards energyflux.Sucha vertical asymmetry of thewavefieldhasbeenobserved in thisheight rangefrom rocket soundings[Hirota and Niki, 1985, EckermannandVincent, 1989].Thesefindingsarebasically in agreement withtheresultsshownabove,suggesting that mostpartof thewavesaregenerated below30-kmaltitude, in thetroposphere andlowerstratosphere. The two-dimensionalspectraresultingfrom density measurements in themesosphere, from 55 to 70 km (Figure 9), showthat the dominantwavemodeshave somewhat 4.3. The PowerSpectralDensity higherfrequencies thanat lowerlevel.Theenergyratioof the stationarywaves (unresolvedfrequencies)to the progressive waves(resolved frequencies) decreases from Before discussingthe resultsconcerningthe density fluctuationPSDs, we first briefly recall someof the main resultson the gravity wave saturationtheory.Numerous WAVELENGTH(KM) WAVELENGTH(KM) 1,2 9 9 9• f; 5 4 3 ? 2 5 4 S 2 t • toTM ld ø • 6 •o• m lo c• lo -4•0 -$• --S.0 • 10• a• 10 a. 10 -4• -3,4 •.6 Up Ep= 4.8 J/kg Dn Ep= $.• J/kg •w.• ......... DOWNWARD •ER•Y Up Ep= 1.8 J/kg Dn Ep= 0.8 J/kg 9 8 Y 8 5 4 -•4 ......... DOWNWARD •N•RGY WAVELENGTH (KM) WAVELENGTH • -3.8 LOGWAVEN•MBER hOG W•NLrM•E• S • 9 8 ? O 5 4 S Fig.8. ThePSDversus vertical wave number ofthefluctuations forwhich thevertical phase velocity propagates downward (i.e.,upward energy flux)andupward (i.e.downward energy flux)obtained by integrating the2Dspectra overthepositive andnegative frequencies, respectively. (a)BIS,January 28, 1989;(b)OHP,May29,1986;(c)OHP,August 7, 1985;(d)BIS,December 17,1987. 5162 Wilsonet al.:Gravitywavesobserved by Rayleigh Lidar,1 BIS 28 JAN PERIOD(H) 89 55-70 kin ß -. StEp/PrEp = 0.O7 UpEp/DnEp = 0.72 I ABOVE • '• {2_9 -4-6 6 4 .... • UpEp/DnEp =1.02 13.2 Lz .6 {2.9 {2-3 {2.0 {2.6 {2.3 11.5 , • • ii-8 • ii8-{2.0 11.2 -2 13.4 :.• 13.2 - 13.4 • • PERIOD(H) -4•8 86 4 2 -'• ............ !............ ,(a) SIS17DEC 87 ...- • •..... %,• ,"i:ff•.•,•;. ,55-70km ' , ' •'• StEp/PrEp =0.13 - it.5 iO 9 - ii.2 BELOW la6- ta.8 .' • {2.•{2., 10.9 -0.8•.6-0.4-0.a 0.0 0.a 0.4 0.6 0.8 vr•u•nc• -0.8-0.6 •.4-0.a (l/•) 0 0.g 0.4 0.• 0.8 v•u•ncv (l/•) Fig. 9. Two dimensional spectraresultingfrom densitymeasurements in the mesosphere (55-70 km) performedon (a) January28, 1989, and(b) December17, 1987, at BIS. experimental evidencesindicatea largesimilarityin both shapeand amplitudeof the mesoscalefluctuationPSDs as a functionof wave numberand frequencyin the middle atmosphere [Dewanet al., 1984;BalsleyandGarello, 1985; Nastrom and Gage, 1985; Smith et al., 1987; Hass and Meyer, 1987; Sidi et al., 1988; Fritts et al., 1988]. It hasbeen WAVELENGTH 12 9 8 7 6 5 suggested by Van Zandt [1982] that the observedmesoscale fluctuationsspectraare due, as in the ocean [Garrett and Munk, 1975], to a randomsuperposition of gravitywaves, theso-called"universal spectrum." The shapeandmagnitude of the wind and temperature fluctuations PSDs versus verticalwave numberare thoughtto be the consequence of (KM) 4 WA':ELET,IGTH 3 2 I 12 td ø 9 •- 10 • 10 m " '- -30,4-5km •- I 10 < I I EP= 11 6 1 + 0_8l/kg -4.0 -3.8 -3.6 6 5 (KM) 4 I 3 I { tO8 • lo ? • 1o El:'= 3. + 03 /kg -3.8 -3.6 -3.4 (KM) WAVELENGTH 2 12 9 8 7 6 5 4 I.KM) 3 I(d)II't,-.., 1..•1 II ""- HP 07 UG 85 • I { • 2 I I I3o-.45km . "'-. -,1 -3.2 (CY, M) 3HP -... "-' k to •,HP 2.9 MAY86 30-.45 km LOG WAVENUMBER -"'•- I { -...... •.•II1 • -4.0 3 2 I I "['- (CY 4 5 I "'""' -3.4 WAVELENGTH 6 1o I LOG WAVENUMBER 7 (b) i '"' •111B i 8 II I 1.[ I I I - 1otø (a) ! I 9 17 DEC 87 i_o --.• 1o8- • •'--._ .. 1o8 i2:: r.... cc • to 7 ' ! t ' c. I i ½ ..t_ 1o .. .o •o I ' •I -4 0 -3 8 -3 ( LGG WAvENUMEElq -3 4 (CY :M) -3 2 IIII I o i . , . / 10 -4 0 --3.8 -3.6 LOG WAVENuMBER -3 4 -3 2 ICY: M) Fig.10.PSD versus vertical wave number ofthenormalized density perturbations g/N2(p'/po) intheupper stratosphere (30-45km). Thespectra areplottedupto thelargerwavenumbers for whichthesignal-to-noise ratiois largerthanunity.(a) BIS, January 28, 1989;(b) OHP,May 29, 1986;(c) OHP, August7, 1985;(d) OHP, December 17, 1987. Wilsonet al.'Gravitywavesobserved byRayleigh Lidar,1 the saturationprocesses[Dewan and Good, 1986]: the convectiveand/ordynamicalinstabilitiesinducedby large amplitudewaves acts to limit this amplitudeto an upper value related to the vertical wave number. With these assumptions, the relative density (or temperature) fluctuations PSD versus vertical wave number of a saturated 5163 the upper stratosphere are 1 or 2 ordersof magnitudeless than the1/2m 3limitforvertical wavelengths between 1and 15 km (1/200<•x<1/20, i.e., much below the expectedvalue for saturated waves). The standard deviation of the temperaturefluctuationsappearsto be too small (between 1.5 and 2.5 øK) to produceconvectiveinstabilitiesin the upperstratosphere. Excepton January28, 1989, the power wave field is scaled as spectra arenotscaled asm'3in thelowwavenumber partof N4 FST'/To,p,/po(m)• c• 2 3 (11) gm where• is a proportionalityfactorrangingbetween1/2 and 1/20, dependingupon the spectralwidth of the saturated the spectrum(i.e., for wavelengthlargerthan2-3 km). The spectralindex(thepowerdependency of the spectrumversus vertical wave number) ranges between -2 and +1. The potential energy density per unit mass, estimated by integratingthe PSD over wave numbers,varies within a wave field [Dewan and Good, 1986; Smith et al., 1987, Sidi factor of 6,ranging between 2 and12Jkg'1.It appears from et al. 1988]. This estimateof the powerspectraof saturated densityfluctuationsdoes not dependupon the frequency distribution of the waves owing to the assumptionof convectiveinstabilitiesastheonly saturation mechanism. thesefew examplesthatthepotentialenergydensityis larger duringwinter than duringother seasons. This resultwill be confumedfrom the statisticalstudy. The PSD of the normalizeddensity fluctuationsin the lower mesosphere (45 to 60 km) increaseswith altitudefor all wave numbers(Figure 1la). The power spectraof the densityfluctuationsappearto be compatiblewith the spectral limit (11) for vertical wavelengthssmallerthan 3 or 4 km (1/10<a< 1/4). For largerverticalscalefluctuationsthe PSDs PSDs versus vertical wave number of the normalized densityfluctuationsin the upperstratosphere (30-45 km) are shown in Figure 10. With the chosennormalization,the straight line1/2m 3 indicates thespectral limit(11)with a=l/2. An importantvariabilityin the spectralshapeand magnitude is observed from a day to another in the accessible spectraldomain.The densityfluctuations PSDsin WAVELENGTH 12 9 B 7 6 5 are much smaller than the saturationlimit (11) (a< 1/20), the spectral index being also larger than -3. The standard WAVELENGTH (I_-M) 4 3 l()tø I I I i I I I I {I I 12 I I I I O I'I I 8 7 I 6 I .5 I 4 I (I-IM) 3 2 I I I . 101ø 45- 60 km ""' 3HP 07 AUG8.5 E --.... 4.5--60km _L_ [- -' lo •_ii13 • 10 rf., 2; • 108-- . • 10 8 ffi a• 107 EP= 19 I ñ 2,8 J kg -4 0 -3 8 -3 6 -:3 4 LOG WAVENUMBER WAVELEIIGTH 12 9 8 7 6 5 4 EP= 9.,I :t: 1.7 J/kg I0 -3 2 -4 0 iotO • II I I [ I I I I I -3 6 WAVELENGTH (KM } :1 2 I - -3 8 •IS -3.4 -3.2 LOG WAVENUMBER (CY/M) (CY/M) 12 I I • .-. ' • c• • 7 I55-70 28 lat.[ I 9 I '1,. 8 I 7 I 6 I õ I 4 I (KM) 3 2 I I , 1olO 89 " 3HP 07 AUG 55-.70 • lo a. 1o .. (b) , • ,•: ¸ 7 EP= 8,3 ñ /2.2 J ¸ a• -4 0 -3 ,q -3 6 LOG WAVEHUMBER -3 4 (CY -3 6 _ EP= 60. • + 12.5 J/'kg 1o 2 l•l) -4 0 -3 8 -3 6 LOG WAVEHUMBER -3 4 -3.2 (CY/M) Fig. 11. PSD versusverticalwavenumberof thenormalized densityperturbation (a) in thelower mesosphere (45-60kin) and(b) in themiddlemesosphere (55-70km). 85 km 5164 Wilsonet al.: Gravitywavesobservedby RayleighLidar, 1 deviationof the temperature fluctuations is of theorderof 2ø to 3 øK,thepotentialenergydensityperunitmassincreasing by a factor 2 to 5 from the upperstratosphere to the lower mesosphere. The fact that the densityPSDs are not scaledas between 10 and 20 km. Using the WKB solutionsof the linearized perturbationsequations,the potential energy density,Ep(z), of a conservativemonochromaticgravity wave should be scaled as N4 fromthestratosphere tothemesosphere (asN4 decreases by abouta factor of 2 to 3) seemsto indicatethat the wave field is not convectively saturated(i.e., saturatedthrough inducedconvectiveinstabilities)in the stratosphere. Normalized density fluctuations PSDs in the middle mesosphere (55 to 70 km), on January28 andAugust7, are shown in Figure 1lb. At these heights, waves amplitude reachthe saturationlimit as definedin equation(11) (et• 1/2) strongly suggestingthat the wave field is convectively saturatedabove60 km altitudefor wavelengthsup to 6 km. The spectralindex seemsto be consistent,within the error bars,with a -3 slopefor wavelengths between6 and2-3 km. Furthermore, the standard deviation of the temperature fluctuationsrangingbetween3ø and 5 øK, appearsto be large enoughto induceconvectiveinstabilitiesin an height rangewherethe temperature gradientis negative. The normalizeddensityfluctuationsPSDs, interpretedin the frameworkof the gravity wave saturationtheory, thus indicatethat the wave field is not convectivelysaturatedin the upper stratosphere(30-45 km) within the accessible spectraldomain(from 1- to 15-km verticalwavelength).As the altitudeincreases,the power spectraldensityincreases for all wave numbers,reachinga spectrallimit close to N4/292m 3inthemiddle mesosphere. It strongly suggests that gravity waves reach saturation inducing convective instabilitiesfor vertical wavelengthsup to 6 km. A growth from the stratosphere to the mesosphereof a mean temperaturePSD has also beenobservedby Shibataet al. [ 1988] from 13 Rayleighlidar profiles.Thesefindingsseem to be in contradictionwith those of Smith et al. [1987] and Tsuda et al. [1989], who have shown from in situ and MST radar measurements, that the horizontal wind PSDs are scaled byN2in thesaturated range fromthestratosphere to the mesosphere. This may indicate that dynamical instabilities (Kelvin-Helmoltz instabilities) are the main saturationprocesses in the stratosphere wherelow frequency waves appearsdominantand where the amplitudeof the density fluctuations seemsto be small comparedto any convective saturation limit. Nevertheless, no firm conclusionscan be reachedfrom the densitymeasurements alone. 4.4. The Potential Energy Density Versus Altitude The available potential energy density per unit mass (Figures 10 and 11) increasessignificantlyfrom the upper stratosphere, whereit is a few joulesper kilogramme,to the N Ep(z) o•I exp(z•p) (12) wherez is theheight,Hp thedensityscaleheight,and• the mean horizontalwind. Thereforea backgroundwind shearcanbethecauseof largedeparture from anexponential growthparticularlyif the intrinsicphasespeedof the wave, c-u--(•-, is small. The potentialenergydensitiesversusaltitude,asobserved on January28 andDecember17 at BIS andon May 29 and August7 at OHP, deducedby a complexdemodulation of the signalaveragedover threewavelengthbands(centered on 6, 5 and 4 km), are plottedin Figure 12. The energy densityis plottedup to the altitudewherethe signal-to-noise ratio is lessthan unity. The noisevariance(dottedline in Figure 12), which is subtractedfrom the raw variance, increaseswith altitude as the density scale height. An increaseof energydensityis generallyobservedfrom the stratosphere to the mesosphere.However,therateof energy growthvariesconsiderably fromonecaseto theother.In two cases(January28 and December17) the energydensityis almostconstantin the stratosphere whereasin anotherone (August7) the growthis exponential with a scaleheightof the order of the density scaleheight. A minimum in the variance is observedin some casesabove the stratopause level (January28). This variancedecreasecouldbe due to the dampingof the inertia-gravitywavesoften observedat that level (Figure 3a). An energy growth is quasisystematically observedin the mesosphere at leastup to 65 km. In a few cases,ason August7, theenergyscaleheightis close to the density scale height in the stratosphereand mesosphere. From these selected case studies, on cannot clearly concludeaboutthe energydensityscaleheightas the energy growthis highly variablewith altitude.This variabilitymay be due to wind shears and/or dissipative processes. Nevertheless, the smallenergygrowthfrequentlyobserved in the stratosphereseems to indicate that the waves are dissipatedat theseheights.BecausethePSDsof thedensity fluctuationsdo not appearcharacteristicof a convectively saturatedwave field (section4.3), this suggestthat the waves are dissipatedthroughdynamical instabilitiesor any other processes. Conclusionson the verticalgrowthof the waves will be furtherachievedfrom the statisticalstudyon a large number of cases. middlemesosphere, whereit reaches some10j kg'1. The 4.5. Convective instabilities energydensityper unit massgrowsroughlyby a factor2 of to 4 over about two atmosphericscale heights(the exact valuesfor the casespresentedhere are given in Figure 10 and 11). The vertical scaleheightof the energydensityper unit mass, Hi• (=Az/ln{Ep(z+Az)/Ep(z)}), thus ranges The powerspectraof the normalizeddensityfluctuations and the inferred standarddeviation of the temperature fluctuationsboth suggestthat convectiveinstabilitiesmay occur in the mesospheredue to large waves amplitudes. Wilsonet al.: Gravitywavesobserved by RayleighLidar, 1 • 7o • 5165 () 70 •1•65 6o "0 55 "13 55 •iil-ii õo • • 50 ß• 45 /?t/H 40 40 35 log Potential •nergy log Potential Energy (J/Kg) BIS OHP E8 JAN 89 17:52-18:13 70 • ,• E9 MAY 86 g0: 51:31 (d) 7o , t . ,'0 55 ß'• -P-I 50 45 35 log Potential Energy (J/Kg) log Potential Energy (J/Kg) OHP 07 AUG 85 gg:343:89 BIS 17 DEC 87 ;gO:45-;g;g:13 Fig. 12. Availablepotentialenergydensityper unit massversusaltitudededucedby a complex demodulation of thesignalaveraged in threewavelength bands(centered on 6, 5, and4 km).Thenoise level,deduced by demodulation on shortscalefluctuations (smaller than1 km)is plottedfor comparison (dashed line).Thevariance of thefluctuations is plottedup to thealtitudewherethesignal-to-noise ratiois largerthanunity.(a) BIS, January 28, 1989;(b) OHP,May 29, 1986;(c) OHP,August7, 1985;(d) BIS, December 17, 1987. Vertical temperatureprofiles deduced from 1 hour integrationtime (in order to reducethe uncertainty), observedduringthe night of January28, 1989; May 29, 1986; December 17, 1987, at BIS; and August7, 1985, at gravity wave breaking [Hauchecorneet al., 1987; Hauchecorneand Maillard, 1990]. 5. Conclusions OHP are plotted in Figure 13. Vertical gradientsof temperature closeto theadiabatic lapserate(roughly -10ø km'l) areobserved in themesosphere independently of the seasons,during winter (January28, December17), in summer(August7), and in equinoctialconditions(i.e., in weak wind conditionsas on May 29). Theseconvectively unstable layersareobserved eitherjustabovethestratopause level(May29) or athigherlevels.Fromcomparing Figures3 and13,theunstable layersarefrequently produced abovethe altitude where the dominant wave amplitude reachesa maximum(asonJanuary28, May 29 andAugust7). Above this level, the dominantmodeappearsto be disorganized. Suchinstabilitiesseemthus clearly inducedby the large ampiit,,de. c}fthe waves. On January28, just abovethe adiabaticlapserate, a mesospheric temperature inversion occurs.Thoseare frequentlyobservedin the mesosphere abovelargetemperature gradientandarelikely inducedby Densityand temperature fluctuations, observedin the stratosphere andmesosphere by meansof Rayleighlidars with highspatialandtemporalresolution (15 min and300 m), havebeenanalyzedin someparticularcasesin various seasonal conditions. These selected cases are characteristic of tipicallyobservedwavepatterns. 1. The presence of a dominantfluctuating modeof large period, typically 10 hours period, and large vertical wavelength, from5 to 10 km,is verygenerally observed in the stratosphere and lower mesosphere. In a singlecase, when simultaneouswind and temperature measurements have beenperformed,an inertia-gravitywave has been clearlyidentified.The frequencies of thewavefield seemto be relatively higher in the mesospherethan in the stratosphere, suggesting a strongdampingof the lowerfrequencywavesin thelowermesosphere. Wilsonetal.:Gravitywavesobserved byRayleigh Lidar,1 5166 8O -• õo ()•IF ) 17 DD' 87 / <• / II ,½ , Temperoture(K) Fig. 13. Verticaltemperature profiles,resultingfrom 1-hourintegrationtime of the signal,observedon January 28, 1989;May 29, 1986;andDecember17, 1987at BIS andonAugust7, 1985,at OHP. 2. The verticalscaleheightof thepotentialenergyis most often larger than the densityscaleheight, generallylarger than 10 km. Nevertheless,in a few casesthe energy scale heightis closeto thedensityscaleheight.The energydensity growthis generally,but not systematically, smallerin the upperstratosphere andlowermesosphere, thanabove55 km. Sucha changein the energyscaleheightaccordingto the altitude domain could be due partially to the mean wind reversalin the mesosphere. 3. If the gravity wave field doesnot appearto produce convectiveinstabilitiesin the stratosphere, the amplitudeof the density(or temperature)fluctuationsis consistentwith the convective saturation limit of the linear theory for wavelengths up to 3 or 4 km in the lowermesosphere, andup to 6 km above 60 km altitude. Furthermore, convective unstablelayers,whichcouldpersistoverperiodslargerthan one hour,are currenfiyobselwedin the mesosphere. Becauseof the day-to-dayvariabilityof the wavesenergy density(whichreaches a factorof 5 in thestratosphere, and1 orderof magnitudein the mesosphere) a largedata setmust be analyzedin order to give a generalview of the wave activity in this height range. This is the subjectof the companion paperwhichwill describe anddiscuss thegravity wave climatology from the large data set obtained by Rayleighlidarsat the two sites. 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