DTIC ADA530433: Properties of the Average Distribution of Equatorial Kelvin Waves Investigated with the GROGRAT Ray Tracer

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Atmos. Chem. Phys.,9,7973–7995,2009
Atmospheric
www.atmos-chem-phys.net/9/7973/2009/
Chemistry
©Author(s)2009. Thisworkisdistributedunder
theCreativeCommonsAttribution3.0License. and Physics
Properties of the average distribution of equatorial Kelvin waves
investigated with the GROGRAT ray tracer
M.Ern1,H.-K.Cho2,P.Preusse1,andS.D.Eckermann3
1InstituteofChemistryandDynamicsoftheGeosphere(ICG-1),ForschungszentrumJu¨lich,Ju¨lich,Germany
2DepartmentofAtmosphericSciences,YonseiUniversity,Seoul,Korea
3E.O.HulburtCenter,NavalResearchLaboratory,WashingtonD.C.,USA
Received: 16March2009–PublishedinAtmos. Chem. Phys.Discuss.: 11June2009
Revised: 20August2009–Accepted: 10October2009–Published: 23October2009
Abstract. Kelvinwavesexcitedbytroposphericconvection Salby, 1994; Pires et al., 1997; Straub and Kiladis, 2003;
are considered to be one of the main drivers of the strato- Lindzen, 2003; Randel and Wu, 2005). Therefore spectral
spheric quasi-biennial oscillation (QBO). In this paper we signatures of Kelvin waves can be found in tropospheric
combine several measured data sets with the Gravity wave space-time spectra of, for example, outgoing longwave ra-
Regional Or Global RAy Tracer (GROGRAT) in order to diation(OLR)orrainrates(e.g.,WheelerandKiladis,1999;
study the forcing and vertical propagation of Kelvin waves. StraubandKiladis,2003;Choetal.,2004). Theseparame-
Launch distributions for the ray tracer at tropospheric al- ters are linked to the latent heat released in convective sys-
titudes are deduced from space-time spectra of European temswhichisthesourceprocessofthewavegeneration(e.g.,
CentreforMedium-RangeWeatherForecasts(ECMWF)op- SalbyandGarcia,1987;BergmanandSalby,1994;Ricciar-
erational analyses, as well as outgoing longwave radiation dulliandGarcia,2000).
(OLR) and rainfall data measured by the Tropical Rainfall Kelvin waves can propagate vertically into the strato-
Measuring Mission (TRMM) satellite. The resulting strato- sphere. While the wave signal observed in the troposphere
sphericKelvinwavespectraarecomparedtoECMWFopera- islocatedatrelativelyslowphasespeedsandmostlydirectly
tionalanalysesandtemperaturemeasurementsoftheSound- coupledtotheconvectivesystems,Kelvinwavesobservedin
ing of the Atmosphere using Broadband Emission Radiom- thestratospherearedominatedby“free”wavemodes,which
etry(SABER)satelliteinstrument. Questionsaddressedare: are excited by deep convection in the troposphere but not
the relative importance of source variability versus wind longerlinkedwiththespace-timepatternsoftheconvective
modulation, the relative importance of radiative and turbu- forcing (Randel and Wu, 2005; Ern et al., 2008; Kiladis et
lent damping versus wave breaking, and the minimum alti- al.,2009).
tudewherefreelypropagatingwavesdominatethespectrum. IthasbeendemonstratedbySalbyandGarcia(1987)how
theatmosphericresponseinthenearfield(directlyatthetop
oftheheatingsourceprocesses)isgenerated.Ithasalsobeen
shownbyGarciaandSalby(1987)howthespectraofequa-
1 Introduction
torial waves are changing in the far field: with increasing
Kelvin waves are the most prominent global scale equato- altitudethespectrumisshiftedtowardshigherphasespeeds
riallytrappedwavemodeinatmospherictemperatures(e.g., duetowavedampingprocesses.
Tindalletal.,2006a).Theyaresymmetricwithrespecttothe Kelvinwavesplayanimportantroleinthedynamicsofthe
Equator,trappedatlatitudesbetweenabout20◦Sand20◦N equatorialatmosphere. Togetherwithotherequatorialwave
inthestratosphereandtraveleastward. modesandabroadspectrumofgravitywaves(GWs)Kelvin
Like the other equatorially trapped planetary scale wave wavesareoneofthemaindriversofthequasi-biennialoscil-
modes (e.g., equatorial Rossby or Rossby-gravity waves) lation(QBO)oftheequatorialzonalwindinthestratosphere
Kelvinwavesareforcedinthetropicaltropospherebydeep (Hitchman and Leovy, 1988; Dunkerton, 1997; Baldwin et
convection (e.g., Salby and Garcia, 1987; Bergman and al.,2001).Manyprocessesinatmosphericchemistryanddy-
namicsinthestratosphereandmesosphere(evenathighlati-
tudes)aremodulatedorinfluencedbytheQBO,showingthe
Correspondenceto: M.Ern importanceofthedrivingequatorialwavemodeslikeKelvin
([email protected]) waves(Baldwinetal.,2001).
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Properties of the average distribution of equatorial Kelvin waves
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investigated with the GROGRAT ray tracer
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14. ABSTRACT
Kelvin waves excited by tropospheric convection are considered to be one of the main drivers of the
stratospheric quasi-biennial oscillation (QBO). In this paper we combine several measured data sets with
the Gravity wave Regional Or Global RAy Tracer (GROGRAT) in order to study the forcing and vertical
propagation of Kelvin waves. Launch distributions for the ray tracer at tropospheric altitudes are deduced
from space-time spectra of European Centre for Medium-RangeWeather Forecasts (ECMWF) operational
analyses, as well as outgoing longwave radiation (OLR) and rainfall data measured by the Tropical
Rainfall Measuring Mission (TRMM) satellite. The resulting stratospheric Kelvin wave spectra are
compared to ECMWF operational analyses and temperature measurements of the Sounding of the
Atmosphere using Broadband Emission Radiometry (SABER) satellite instrument. Questions addressed
are the relative importance of source variability versus wind modulation, the relative importance of
radiative and turbulent damping versus wave breaking, and the minimum altitude where freely
propagating waves dominate the spectrum.
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7974 M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT
Further processes Kelvin waves are important for are the partially realistic convective forcing (Ricciardulli and Gar-
mean upwelling observed in the equatorial region (e.g., Se- cia, 2000; Horinouchi et al., 2003). Highly idealized simu-
meniuk and Shepherd, 2001) as well as mixing processes lationswhichassumeforinstanceonlyasinglewavenumber
both vertically (e.g., Fujiwara et al., 1998; Fujiwara and 1Kelvin wave and a continuous omnipresent forcing were
Takahashi, 2001) and across the subtropical mixing bar- justified in terms of thought experiments. In addition, only
rier,whichismorestableduringQBOeasterlyphases(e.g., little was known about the spectrum of Kelvin waves and
Shuckburgh et al., 2001). In addition, they play an impor- its temporal variations. However, improved satellite sen-
tant role for the dehydration of the tropical tropopause re- sors recently provide these information for the troposphere
gion (e.g., Fujiwara et al., 2001; Zhou and Holton, 2002; (e.g., Wheeler and Kiladis, 1999; Straub and Kiladis, 2003;
HatsushikaandYamazaki,2003;EguchiandShiotani,2004; Cho et al., 2004) as well as for the stratosphere (Ern et al.,
JensenandPfister,2004;Immleretal.,2008). 2008; Alexander et al., 2008) and the mesosphere (Garcia
Because Kelvin waves interact with the QBO winds et al., 2005; Ern et al., 2009). In our work we additionally
Kelvin wave activity itself is modulated by the QBO. En- use European Centre for Medium-Range Weather Forecasts
hanced Kelvin wave activity is observed during QBO west- (ECMWF)analyseswhichassimilatetroposphericmeasure-
ward phases when the propagation conditions are favorable mentsofconvectionandrainratesandhavebeenvalidatedto
for eastward traveling waves. According to conventional wellrepresentalsothestratosphericKelvinwaveamplitudes
wisdom Kelvin waves are subjected to enhanced radiative (Ernetal.,2008)andalsoKelvinwavefluxesandzonalwind
damping when they approach the zonal wind reversal from forcinghavebeenfoundtobeingoodagreementwithmea-
westward to eastward wind, and accordingly transfer mo- surements(ErnandPreusse,2009).
mentumtothebackgroundwindthuscontributingtothere- FordrivingtheQBOorthetropicalupwellingweneedto
versalofthezonalwinddirection(e.g.HoltonandLindzen, knowthewaveforcing,i.e.theverticalderivativeofthemo-
1972;CampbellandShepherd,2005a,b). mentum flux. This means that even data sets displaying on
In contrast, GWs are assumed to transfer momentum average roughly the same Kelvin wave amplitudes can pro-
by either absorption at critical levels (e.g., Lindzen and duce different forcing if the vertical gradients differ. In ad-
Holton, 1968; Campbell and Shepherd, 2005a,b) or break- dition,theinteractionbetweenwavesandbackgroundwinds
ing on reaching their saturation amplitudes (e.g., Campbell is non-linear in nature. Therefore both the intermittency of
and Shepherd, 2005a,b). Therefore GW parameterizations the wave sources and the details of the interaction with the
(e.g.,Hines,1997a;AlexanderandDunkerton,1999;Warner backgroundwindareimportant.
andMcIntyre,2001)donottakeintoaccountradiativedamp- Inordertointerpretallmeasurementsavailableforthetro-
ing. However,inthetropicsKelvinwavesandgravitywaves posphere and the stratosphere in a synergetic approach we
sharethesamedispersionrelation usetheGravitywaveRegionalOrGlobalRAyTracer(GRO-
GRAT) model. GROGRAT calculates the upward propaga-
ωˆ =−Nk/m, (1) tionofwavesaccordingtotheraytracingequationsandcon-
serveswaveactiondensityalongtheraypath.Inaddition,the
withωˆ theintrinsicfrequencyofthewave, N thebuoyancy
modelincludesdissipationofwaveamplitudesthroughwave
frequency, k thehorizontal, andmtheverticalwavenumber
breaking (wave saturation) due to convective and dynam-
ofthewave.I.e.,KelvinwavesareinprincipalGWsconfined
ical instabilities (Fritts and Rastogi, 1985), vertical scale-
to the tropics by the Coriolis force. The only difference is
dependent infrared radiative damping (Zhu, 1993), and cli-
theirhorizontalwavelengthandhencetheirgroupvelocity
matologicalbackgroundverticaldiffusivities(fordetailssee
∂ωˆ Nk kcˆ2 Marks and Eckermann, 1995, and Eckermann and Marks,
cgz = ∂m = m2 = Nh, (2) 1997). In the GROGRAT model we have complete control
over these dissipative processes and can perform model ex-
which is for waves of the same horizontal phase speed perimentsinvestigatingtheinfluenceofthevariousdamping
cˆh=ωˆ/k proportionaltothehorizontalwavenumberk. This mechanisms. Inaddition,wecanfreelyvarythelaunchdis-
means that for long horizontal wavelength GWs radiative tributionandlaunchaltitudeofthewaves.
forcingmustbeimportantand,ontheotherhand,thatwave We first describe the space-time analysis and the set-up
saturation could become important for higher wavenumber of the GROGRAT model in Sect. 2. In Sect. 3 we will in-
Kelvinwaves. vestigatetheimportanceofradiativeandturbulentdamping
StudiesontheQBOanditsdrivingbydifferentequatorial fortheinteractionoftheKelvinwaveswiththezonalback-
wave modes were either highly idealized (e.g. Lindzen and ground winds. In Sects. 4 and 5 we will study the impact
Holton,1968;HoltonandLindzen,1972;Dunkerton,1997; of different source spectra and launch altitudes on the dis-
CampbellandShepherd,2005a,b)orwerebasedoncomplex tribution of Kelvin waves observed in the stratosphere. In
generalcirculationmodel(GCM)simulations(Horinouchiet addition, the influence of seasonal variations in the tropo-
al.,2003;Giorgettaetal.,2006;Mayretal.,2007)providing sphericKelvinwavesourceonthestratosphericvariabilityis
little insight in the detailed mechanisms and based on only demonstrated. TheresultsaresummarizedinSect.6
Atmos. Chem. Phys.,9,7973–7995,2009 www.atmos-chem-phys.net/9/7973/2009/
M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT 7975
2 Method: Kelvin wave spectra and simulation with data field 9(λ,8,t) can be written as sum of its symmet-
GROGRAT ric9 (λ,8,t)anditsanti-symmetric9 (λ,8,t)parts
symm anti
(λ: longitude,8: latitude,t: time):
2.1 TheoryofequatorialKelvinwaves
9(λ,8,t)= 1(9(λ,8,t)+9(λ,−8,t))
2
A theoretical description of planetary scale equatorial wave +1(9(λ,8,t)−9(λ,−8,t)) (6)
modes was first given by Matsuno (1966) who derived the 2
properties of the different equatorially trapped wave types =:9symm(λ,8,t)+9anti(λ,8,t)
from solutions of the shallow-water model on an equatorial
Inasimilarwayalsosymmetricandantisymmetricspace-
betaplane. timeFourierspectra9ˆ (k,ω;8)and9ˆ (k,ω;8)can
symm anti
Oneimportantparameteristhesocalledequivalentdepth
be calculated for every latitude 8. Both symmetric and an-
h . The equivalent depth is connected with the vertical
e tisymmetric components have to be treated independently.
wavenumber m as given in Eq. (3) (e.g., Wu et al., 2000;
This method has been used in several studies based on tro-
Lindzen,2003):
pospheric(e.g.,WheelerandKiladis,1999;Choetal.,2004)
! aswellasstratosphericdata(e.g.,Ernetal.,2008;Alexander
N2 1
m2 = − (3) etal.,2008).
gh 4H2
e This technique has the advantage that the different wave
modes can be separated more easily. In addition, in sym-
with N the buoyancy frequency, g the gravity acceleration,
metric and antisymmetric spectra the background noise due
andH thepressurescaleheight.
to non-resolved waves is lower than it would be in a “full”
One of the most prominent global scale equatorial wave
Fourierspectrum containingallspectral contributions. This
modesareKelvinwaves. ThedispersionrelationforKelvin
isthecasebecausethebackgroundvariancesaresplitupinto
wavesisgivenby:
a symmetric and an antisymmetric background, each lower
ωˆ =−pgh k ≈−Nk/m (4) than the background of the “full” spectrum. Usually both
e
symmetricandantisymmetricspectraareaveragedoveralat-
with ωˆ the intrinsic frequency of the wave, and k the zonal itudeintervalcenteredattheEquatortofurtherincreasethe
wavenumber. From Eq. (4) we see that the phase speed signaltonoiseratioofthesinglespectralcomponents.
ωˆ/k of a Kelvin wave is directly coupled with the equiva- InourstudywefollowthemethoddescribedinErnetal.
lent depth. Under the assumption of zero background wind (2008). But since our paper is focused on Kelvin waves
equivalentdepthsof8,90and2000mcorrespondtointrinsic alone,wewillonlytreatsymmetricspectraandpositivefre-
phase speeds of 9, 30, and 140m/s (see Eq. 4) and vertical quencies(i.e.,eastwardpropagatingwaves).
wavelengths of about 3, 9 and 50km in the stratosphere, or Like in Ern et al. (2008) and Ern and Preusse (2009) we
about 6, 19 and 100km in the troposphere due to the lower use residual ECMWF analysis temperatures gridded down
buoyancyfrequencyN there(seeEq.3). to9◦ resolutioninlongitudefromoriginally1◦,resultingin
Itshouldbenotedthatthefrequenciesωthatareobserved a maximum zonal wavenumber of 20 that can be resolved.
bysatelliteinstrumentsandmostotherobservingsystemsare Theoriginalresolutionof1◦ meridionallyhasbeenretained
ground based (Eulerian) frequencies. These frequencies re- unchangedandspace-timespectraarecalculatedforeachlat-
main unchanged in cases of non-zerobackground windand itude in 1◦ steps. Frequencies up to 2cycles/day can be re-
spectralfeaturesingroundbasedfrequency/zonalwavenum- solvedsincetheECMWFanalysesareavailableevery6hat
ber spectra like in our paper are not Doppler shifted. On 00:00, 06:00, 12:00, and 18:00 GMT. The symmetric spec-
theotherhandintrinsicwavefrequenciesωˆ willbeDoppler trausedinourworkaremeridionalaveragesoverthespectra
shiftedincaseofnon-zerobackgroundwindaccordingto: calculatedatthelatitudesfrom15◦Sto15◦N.TheECMWF
datasetisgivenonasetofpressurelevelswhichweconvert
ωˆ =ω − ku¯ (5)
topressurealtitudesusingaconstantscaleheightof7km.
with k the horizontal wavenumber and u¯ the background In Sects. 3, 4, and 5 we also use Kelvin wave variances
derived from Sounding of the Atmosphere using Broad-
wind. Alsotheverticalwavelengthofthewavesconsidered
band Emission Radiometry (SABER) temperature space-
willbeDopplershifted. Amoredetaileddiscussioncan,for
timespectraasareference. TheSABERinstrumentonboard
example,befoundinErnetal.(2008).
the Thermosphere Ionosphere Mesosphere Energetics and
2.2 Space-timespectraofKelvinwaves Dynamics(TIMED)satellitemeasurestemperaturesandsev-
eraltracegasesfromthetropopauseregiontoabove100km
Equatorially trapped global scale wave modes are either (e.g.,Mlynczak,1997;Russelletal.,1999;Yeeetal.,2003).
symmetric or antisymmetric with respect to the Equator. Like in Ern et al. (2008) we use version 1.06 temperature
Therefore often measured or modeled data fields are di- data,andthespace-timespectraarecalculatedfromresidual
videdintosymmetricandantisymmetriccomponents. Every temperatures and averaged over the latitudes from 12◦S to
www.atmos-chem-phys.net/9/7973/2009/ Atmos. Chem. Phys.,9,7973–7995,2009
7976 M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT
12◦N in 4◦ steps, according to the horizontal sampling dis- c the speed of sound, and γ=1.4 the adiabatic coefficient.
s
tance of about 500km along the satellite track. Due to the ForaderivationofEq.(7)seeAppendixA.
orbit geometry of the TIMED satellite zonal wavenumbers This transformation of temperature amplitudes into
upto6–7andfrequenciesupto1cycle/daycanberesolved pseudozonalwindamplitudescanbedoneforbothECMWF
bytheasynopticsampling. TheSABERdatausedaregiven and SABER temperature spectra, and in the following all
onfixedgeometricaltitudesfrom15kmtoabove100kmin ECMWF and SABER spectra shown are spectra of pseudo
1-km steps. This is somewhat better than the vertical res- zonalwindamplitudesandwavevariancesshownarepseudo
olution given by the instantaneous vertical field-of-view of windvariancescalculatedfromthesespectra.
about2km. Thesepseudozonalwindspectracandirectlyserveasin-
DifferentfromErnetal.(2008)ouranalysiswillbebased put for the GROGRAT ray tracer. For each of the indepen-
onnon-overlappingtimewindowsof36daysfortheFourier dentspectralgridpointswecancalculatetherequiredground
analysis of ECMWF and SABER temperatures because in basedphasespeedfromthegivenzonalwavenumberandfre-
Sect.5wewanttodirectlycomparetoresultsbasedonspace- quency.ThespectralamplitudesoftheFourierspectracanbe
time spectra calculated from OLR and rainfall rates mea- directlytakenaslaunchamplitudesfortheraytracer.
suredbytheTropicalRainfallMeasuringMission(TRMM) Inourstudyweonlyuselatitudinallyaveragedspectraand
satellite which were calculated using 96-day time windows areonlyinterestedintheglobalaverageevolutionofKelvin
stepped forward in 36-day steps (Cho et al., 2004). The waves. For this reason, and also to be consistent with our
center times of the 36-day windows were chosen to exactly sourcespectra,GROGRATisruninanECMWFbackground
matchthecentertimesofthe96-daywindows. atmosphere (temperature and winds) averaged over the 36-
day time-windows of the Fourier analysis and over the lati-
2.3 SimulationofKelvinwavespectrawithGROGRAT tuderange15◦S–15◦N.Inaddition,sinceweconsideronly
latitudinallyaveragedglobalscalewaves,inGROGRATwe
For the initialization of a GROGRAT ray tracer model run
allowonlyverticalpropagationofthewaves.
severalinputparametershavetobeprovided. First,thewind
Thismeansthatdifferentfromthegeneralraytracingap-
amplitude and propagation direction, as well as the ground
proach no horizontal propagation or refraction are included
basedphasespeedofthewaveω/khavetobespecified.Sec-
inoursimulations.Fortheverticalpropagation,however,we
ond,anatmosphericbackgroundprofilehastobedefined.
stillrelyontheraytracingapproach,andtheverticalevolu-
Because Kelvin waves have no meridional wind compo-
tion of the vertical group velocity and the propagation time
nent we need only zonal wind amplitudes and the propaga-
arecrucialfortheamountofradiativeandturbulentdamping
tiondirectionwillalwaysbeeastward.
takingeffect,andhence,whetherwavesaturationisreached.
Eventhoughoneoftherequiredinputparametersisawind
Andwealsomakeuseofthewellestablishedalgorithmsde-
amplitude,inourstudywewillmainlyrelyonECMWFtem-
velopedfortheGROGRATraytracer.
peraturespectra.OnereasonisthattheECMWFtemperature
Theuseofthesealgorithmsisofgreatpracticalvaluesince
spectraweredirectlyvalidatedwithmeasuredSABERtem-
by using the GROGRAT ray tracer we have full control on
perature spectra by Ern et al. (2008) and Ern and Preusse
the wave dissipation processes. In our simulation wave sat-
(2009),whereasthequalityofECMWFwindspectrahasnot
uration due to both static and dynamic instabilities are in-
beenvalidatedbymeasurementssofar. Therearesomeindi-
cludedviaaschemebasedontheworkbyFrittsandRastogi
cationsthatECMWFzonalwindspectraarelessreliableand
(1985). For low frequency waves like in our case the satu-
lesssuitedfortheanalysisofKelvinwaves(seeSect.4). In
ration amplitudes are the same as for the more generalized
particular,intemperaturespectratheKelvinwavesignalwill
approachdescribedbyMarksandEckermann(1995)which
be the by far most prominent spectral component and less
is based on the work by Hines (1988). In addition, vertical
contaminated by other waves than in wind spectra (see also
scale-dependentinfraredradiativedamping(Zhu,1993),and
Tindalletal.,2006a,b). Anotherreasonisthatwealsowant
climatologicalbackgroundverticaldiffusivitiesareincluded
to use SABER temperature spectra or derived Kelvin wave
in the GROGRAT model (for details see Marks and Ecker-
variancesforcomparisonwiththeresultsofoursimulations
mann,1995,andEckermannandMarks,1997).
inSects.3,4,and5.
Itshouldbenotedthatthewaveamplitudecalculationfor
Thereforewechoosetocalculatepseudozonalwindspec-
gravity waves used in GROGRAT may be used as a first
trafromthetemperaturespectrawhichcaneasilybedonevia
order approximation to simulate the vertical propagation of
thepolarizationrelationsforKelvinwavesusingthefollow-
planetary-scale Kelvin waves. However large scale effects
ingequation:
like 2d flow effects, critical layers in latitudinal shear etc.
s
(cid:12)(cid:12)k(cid:12)(cid:12)|T0|. (cid:20)γ 1 (cid:21)2 (cid:20)Nk(cid:21)2 are not covered and require different concepts. In addition,
|u˜|=(cid:12) (cid:12) − + (7) theconceptoflocalizedwavepacketsusedforgravitywaves
(cid:12)ωˆ(cid:12) T c2 2gH gωˆ
s makesnosenseforplanetaryscalewaves.
Hereu˜isthezonalwindamplitudeoftheKelvinwave,T0the Itshouldalsobestatedclearlythatwemakeseveralsim-
temperature amplitude, and T the background temperature, plificationsthatallowonlyinafirstorderapproachtostudy
Atmos. Chem. Phys.,9,7973–7995,2009 www.atmos-chem-phys.net/9/7973/2009/
M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT 7977
thebasicmechanismsoftheaverageglobalKevinwavedis- Veryhighamplitudescanbefoundatlowfrequenciesand
tributionanditsinteractionwiththeQBO.Forexample,we onlyathigheraltitudesthelobe-shapedspectralfeaturedue
assume a zonal background wind that is uniform, in both toKelvinwavesknownfromobservationsinthestratosphere
zonal and meridional coordinates within the analyzed lat- (e.g., Ern et al., 2008) starts to develop. For comparison
itudinal range, and also the global distribution of Kelvin alsothelinesforequivalentdepths8,90,and2000m(values
waves is assumed to be uniform in our simulations (both given assume zero background wind) are shown as straight
at the source level and also above). However, it is known lines through the origin. These lines correspond to ground
that the global distribution of Kelvin waves is not uniform basedphasespeedsω/kofabout9,30,and140m/s.
in the troposphere (for example, due to the Walker circu- SpectralsignaturesofKelvinwavesinthetroposphereare
lation) and this will affect the distribution of stratospheric usually found in a spectral band between the lines of 8 and
Kelvin waves propagating both eastward and upward from 90m equivalent depth (Wheeler and Kiladis, 1999). The
the troposphere (e.g., Suzuki and Shiotani, 2008; Kawatani higherupinthestratospherethemorethisspectralfeatureis
et al., 2009). Non-uniform distributions of Kelvin waves in shifted towards higher phase speeds. This shift can be seen
thestratospherehavebeenfound,forexample,byAlexander in Fig. 2a–c showing symmetric pseudo zonal wind spectra
et al. (2008) or Ern et al. (2008). Another effect that is ne- calculatedfromECMWFtemperaturespectralamplitudesin
glectedisthatKelvinwavescanhaveameridionalwindcom- thestratosphereatthealtitudes21.1km(a),30.0km(b),and
ponent in a sheared background wind (see Imamura, 2006, 40.8km(c).
andreferencestherein). The stratospheric ECMWF spectra shown in Fig. 2a–c
Nevertheless,althoughneglectingthoseeffectswillintro- were validated by comparison with SABER measurements
duce some bias in the results of our simulations this will (seeErnetal.,2008)andcanthereforebetakenasreference
likely not affect the key findings of our study, which are forourGROGRATsimulations
ratherofqualitativethanofquantitativenature.
3.2 Vertical evolution of simulated GROGRAT spectra
withstandardsettings
3 The role of wave saturation, radiative and turbulent
damping for the vertical evolution of Kelvin wave The same spectra as in Fig. 2a–c were simulated with
spectra the GROGRAT ray tracer using the method described in
Sect. 2.3. The 5-year average spectrum shown in Fig. 1e
The importance of radiative damping for the dissipation of
is taken as constant source distribution at 16.9km altitude
Kelvin waves has been pointed out by Holton and Lindzen
(about the tropopause height in the tropics). In this and in
(1972) already some years after the discovery of Kelvin
allothersimulationsweuseanECMWFbackgroundatmo-
wavesintheatmospherebyWallaceandKousky(1968).
sphere which is different for each of the 36-day time win-
The GROGRAT ray tracer calculates both saturated and
dowsofouranalysis,butaveragedinlongitude,thelatitude
unsaturated wave amplitudes. A comparison of saturated
rangeused,andthewholetimewindow(seeSect.2.3).
andunsaturatedamplitudesallowstostudytheroleofwave
ThespectraresultingfromaGROGRATsimulationbased
breaking. Inaddition,thephysicalprocessesofradiativeand
on the GROGRAT standard settings were averaged over
turbulent wave damping can be switched on or off. These
the period January 2002–November 2006 and are shown in
optionswillbeusedtoinvestigatetheroleofwavedamping
Fig. 2d–f. It can be seen that indeed the lobe-shaped spec-
andbreakingfortheobservedshiftoftheKelvinwavespec-
tral feature develops in the stratosphere even though only
tralsignaturestowardshigherphasespeedswithaltitude.
weakly indicated in the source distribution (Fig. 1e). Part
ofthewavecomponentsatlowphasespeedaredampedand
3.1 VerticalevolutionofECMWFspectra
dissipate near critical levels while the amplitudes of higher
In our studies ECMWF space-time spectra are used both phase speed waves grow with altitude due to decreasing at-
as spectral source distributions and as references for GRO- mospheric density and become visible. This explains the
GRAT simulations. Figure 1 shows symmetric ECMWF lobe-shaped structure of the Kelvin wave spectral peak as
pseudo zonal wind spectra averaged over the whole 5-year wellastheshifttowardshigherphasespeedswithaltitude.
period (January 2002–November 2006) considered in our Shape and amplitudes of this spectral feature are about
study at different altitudes from about 4.9 to 18.7km in the the same as in the ECMWF spectra given as a reference in
troposphereandlowerstratosphere.PleasenotethatinFig.1 Fig.2a–c. Onlyatthehighestaltitudeof40.8kmtheGRO-
not the full spectral range covered by the ECMWF data set GRATsimulationshowssomehighbiasathighfrequencies,
is shown (see Sect. 2.2). These spectra will also be used as maybeindicatingthatthelineardissipationprocessesparam-
source distribution in Sect. 4.3 and the spectrum shown in eterized in GROGRAT are not strong enough. Indications
Fig.1ewillbeusedbelow. thatalsononlinearprocessescanbeinvolvedinthedissipa-
tion of gravity waves, in particular in the process of wave
breaking, has been shown, for example, by Achatz (2007).
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7978 M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT
ECMWF (average source spectra)
(a) (b) (c)
ECMWF zonal wind spectral amplitudes ECMWF zonal wind spectral amplitudes ECMWF zonal wind spectral amplitudes
Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ]
1.00 1.00 1.00
20 20 20
z=4.9 km z=8.5 km z=11.4 km
18 18 18
16 16 16
0.75 0.75 0.75
ay] 2000 m 14 ay] 2000 m 14 ay] 2000 m 14
d d d
s/ s/ s/
cle 12 cle 12 cle 12
y y y
cy [c0.50 90 m 10 cy [c0.50 90 m 10 cy [c0.50 90 m 10
n n n
e e e
u 8 u 8 u 8
q q q
e e e
fr 6 fr 6 fr 6
0.25 0.25 0.25
4 4 4
8 m 8 m 8 m
2 2 2
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
zonal wavenumber zonal wavenumber zonal wavenumber
(d) (e) (f)
ECMWF zonal wind spectral amplitudes ECMWF zonal wind spectral amplitudes ECMWF zonal wind spectral amplitudes
Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ]
1.00 1.00 1.00
20 20 20
z=13.9 km z=16.9 km z=18.7 km
18 18 18
16 16 16
0.75 0.75 0.75
ay] 2000 m 14 ay] 2000 m 14 ay] 2000 m 14
d d d
s/ s/ s/
cle 12 cle 12 cle 12
y y y
cy [c0.50 90 m 10 cy [c0.50 90 m 10 cy [c0.50 90 m 10
n n n
e e e
u 8 u 8 u 8
q q q
e e e
fr 6 fr 6 fr 6
0.25 0.25 0.25
4 4 4
8 m 8 m 8 m
2 2 2
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
zonal wavenumber zonal wavenumber zonal wavenumber
Fig.1.ECMWFpseudozonalwindspectraaveragedovertheperiodJanuary2002–November2006forthealtitudes4.9km(a),8.5km(b),
11.4km(c),13.9km(d),16.9km(e),and18.7km(f).Alsogivenarethelinesforequivalentdepthshe=8,90,and2000m,correspondingto
groundbasedphasespeedsof9,30,and140m/s.
The role of wave saturation for Kelvin waves will therefore the amplitude limit critical for the onset of wave breaking
bediscussedinthenextsubsection. couldalsobereachedbyasuperpositionofdifferentwaves.
Thereforewemakeanothercross-checkwhetherthecritical
3.3 Theroleofwavebreaking amplitudelimitisreallyneverreached.
Investigation of ECMWF analysis pseudo zonal wind
Amplitudelimitscriticalforwavebreakingareneverreached spectra shows that in the altitude range of about 20–50km
inoursimulations. Thiscanbeseenbycomparingsaturated about4spectralcomponentsarerequiredtodescribe50%of
and unsaturated GROGRAT amplitudes, which are always thetotalvarianceduetoKelvinwavesforequivalentdepths
exactly the same. This means that wave dissipation takes between8and2000m. Theseresultswereobtainedfromthe
placeonlybyradiativeandturbulentdampingaswellascrit- single (not time-averaged) spectra calculated in the 36-day
icallevelfiltering. time windows mentioned above. About 10 spectral compo-
GROGRAT does not support the superposition of differ- nentsarerequiredtodescribeabout80%oftheKelvinwave
ent waves and as a consequence different spectral compo- variances.
nentsaretreatedindependentlyinoursimulations. However,
Atmos. Chem. Phys.,9,7973–7995,2009 www.atmos-chem-phys.net/9/7973/2009/
M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT 7979
ECMWF (reference)
(a) (b) (c)
ECMWF zonal wind spectral amplitudes ECMWF zonal wind spectral amplitudes ECMWF zonal wind spectral amplitudes
Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ]
1.00 1.00 1.00
20 20 20
z=21 km z=30 km z=41 km
18 18 18
16 16 16
0.75 0.75 0.75
ay] 2000 m 14 ay] 2000 m 14 ay] 2000 m 14
d d d
s/ s/ s/
cle 12 cle 12 cle 12
y y y
cy [c0.50 90 m 10 cy [c0.50 90 m 10 cy [c0.50 90 m 10
n n n
ue 8 ue 8 ue 8
q q q
e e e
fr 6 fr 6 fr 6
0.25 0.25 0.25
4 4 4
8 m 8 m 8 m
2 2 2
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
zonal wavenumber zonal wavenumber zonal wavenumber
GROGRAT (constant launch spectrum)
(d) (e) (f)
GROGRAT zonal wind spectral amplitudes GROGRAT zonal wind spectral amplitudes GROGRAT zonal wind spectral amplitudes
Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ]
1.00 1.00 1.00
20 20 20
z=21 km z=30 km z=41 km
18 18 18
16 16 16
0.75 0.75 0.75
ay] 2000 m 14 ay] 2000 m 14 ay] 2000 m 14
d d d
s/ s/ s/
cle 12 cle 12 cle 12
y y y
cy [c0.50 90 m 10 cy [c0.50 90 m 10 cy [c0.50 90 m 10
n n n
ue 8 ue 8 ue 8
q q q
e e e
fr 6 fr 6 fr 6
0.25 0.25 0.25
4 4 4
8 m 8 m 8 m
2 2 2
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
zonal wavenumber zonal wavenumber zonal wavenumber
GROGRAT (constant launch spectrum, no damping)
(g) (h) (i)
GROGRAT zonal wind spectral amplitudes GROGRAT zonal wind spectral amplitudes GROGRAT zonal wind spectral amplitudes
Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ] Uamp [ (m/s)/waveno/cpd ]
1.00 1.00 1.00
20 20 20
z=21 km z=30 km z=41 km
18 18 18
16 16 16
0.75 0.75 0.75
ay] 2000 m 14 ay] 2000 m 14 ay] 2000 m 14
d d d
s/ s/ s/
cle 12 cle 12 cle 12
y y y
cy [c0.50 90 m 10 cy [c0.50 90 m 10 cy [c0.50 90 m 10
n n n
ue 8 ue 8 ue 8
q q q
e e e
fr 6 fr 6 fr 6
0.25 0.25 0.25
4 4 4
8 m 8 m 8 m
2 2 2
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
zonal wavenumber zonal wavenumber zonal wavenumber
Fig.2. ECMWFpseudozonalwindspectraaveragedovertheperiodJanuary2002–November2006forthealtitudes21.1km(a),30.0km
(b),and40.8km(c).AlsoshownthesamespectrasimulatedwithGROGRATusingstandardsettings(d)–(f)andwithradiativeandturbulent
dampingswitchedoffinGROGRAT(g)–(i).
www.atmos-chem-phys.net/9/7973/2009/ Atmos. Chem. Phys.,9,7973–7995,2009
7980 M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT
Therefore we checked whether critical amplitude limits shortly after launch vertical wavelengths shorter than about
are still not reached if the source amplitudes of the GRO- 5km are removed from the space-time spectra and the re-
GRAT simulations are multiplied by a factor of 10. In this sults filtered for vertical wavelengths longer than 5km and
way also the possibility of constructive wave superposition results without vertical wavelength filtering are almost the
ofthedifferentrelevantspectralcomponentsistakenintoac- same. This means that all Kelvin waves contained in our
count. This is a very conservative assumption because dif- GROGRATsimulationsshouldalsobecontainedinECMWF
ferent spectral components more likely will have different or be visible for SABER, and the calculated Kelvin wave
phasesanddifferentgroundbasedphasespeedssothatthere variances can be directly compared because about the same
will be an averaging effect at a given altitude. In spite of verticalwavelengthrangesarecoveredbythedifferentdata
this conservative assumption the critical amplitude limit is sets.
stillnotreachedintherelevantaltituderangefromabout20–
50km. The amplitudes are well below the amplitude limit 3.5 Radiativeversusturbulentdamping
critical for wave breaking, indicating that the assumptions
made in our simulations do not influence the results shown Wealsoinvestigatedtherelativeimportanceofradiativeand
and that radiative and turbulent damping are the most im- turbulent damping. Kelvin wave pseudo zonal wind vari-
portant wave dissipation processes for Kelvin waves in the anceswerecalculatedbyintegratingoverthepowerspectra
consideredaltituderange. forwavenumbers1–6betweenthelinesofequivalentdepths
of8and2000mforKelvinwavesandfrequencieslowerthan
3.4 Somecross-checksrelevantforthespectralshape 0.4cycles/day (see also Sect. 4). The so obtained variance
altitudeprofilesforeach36-daywindowwerethenaveraged
3.4.1 Vertical evolution of simulated GROGRAT spec- overthewholeperiodJanuary2002–November2006.
trawithdampingswitched-off The resulting average profiles are shown in Fig. 3. As
a reference the variances obtained directly from space-time
Figure 2g–i shows the same spectra as in Fig. 2d–f but re-
spectra of ECMWF operational analyses (black solid line)
sultingfromaGROGRATsimulationwithradiativeandtur-
and SABER measurements (black dashed line) are given.
bulent damping switched off. We still find some kind of
Also given are integrated and then averaged variances re-
lobe-shaped spectral peak because the waves with the low-
sultingfromGROGRATsimulationsbasedontime-varying
estphasespeedsalsostallverticallynearcriticallevels. But
ECMWFsourcespectraat16.9kmsourcealtitudewithfull
withincreasingaltitudetheamplitudeofthespectralpeakbe-
dampingswitchedon(greendotted),radiativedampingonly
comesunrealisticallyhigh,andat40.8kmaltitudethepeakis
(bluedotted),andnodampingatall(reddotted).
toobroad,coveringatoolargezonalwavenumberrangeand
Obviouslythesimulationincludingbothradiativeandtur-
extendingtowardstoohighfrequencies.Althoughtheampli-
bulent damping (green dotted) closely follows the ECMWF
tudesarenolongerdampedcriticalamplitudelimitsarenot
andSABERreferencecurves.Thereissomelowbiasaround
reachedandwavebreakingdoesnottakeeffect.
the source altitude because GROGRAT does not propagate
upward very low phase speed spectral components of the
3.4.2 Time-varyingsourcespectra
ECMWFsourcespectra,whichareremovedinthesimulated
GROGRATspectradirectlyafterlaunch. Theseredpartsof
BothGROGRATsimulations(withwavedampingswitched
the source spectra are caused partly by very short vertical
on as well as off) were also carried out with time-varying
wavelengthKelvinwaveswhicharenotimportantathigher
ECMWF source spectra: for each of the 36-day time-
altitudes,andpartlybyrednoiseduetounorganizedconvec-
windows the corresponding ECMWF spectrum at 16.9km
tion. In addition, there is also some high bias above 45km
altitudewastakenassourcespectrum, insteadofthe5-year
altitude, which is however removed if the source altitude is
average ECMWF spectrum. However, also for this simula-
chosenhigherthan20km(notshown).
tionbasedonthosetime-varyingECMWFsourcespectrathe
One possible reason for the reduction of this high bias at
simulated 5-year average spectra at 21.1, 30.0, and 40.8km
high altitudes could be that the higher the source altitude
altitude almost look the same as in Fig. 2d–i and are not
is chosen the more “noise” in the source spectra caused by
shown.
non-Kelvin wave contributions is removed. If such “noise”
3.4.3 Compatibilityofverticalwavelengthranges is located at higher phase speeds it can grow considerably
withaltitudewithoutbeingdissipatedinoursimulation. For
Another cross-check was made, whether visibility filtering sourcealtitudesabove20kmthis“noise”islikelysmalland
oftheGROGRATsimulationsisrequiredtoremoveKelvin thebiasathighaltitudeswillbereduced.
waves with vertical wavelengths too short to be contained Variances resulting from the GROGRAT simulation with
in the ECMWF analyses, or too short to be visible by the radiativedampingonly(bluedotted)areonlyslightlyhigher
SABER satellite instrument, since these two data sets will than for the full damping case (green dotted). If also ra-
be used as a reference in Sects. 4 and 5. However, already diative damping is switched off (red dotted) variances are
Atmos. Chem. Phys.,9,7973–7995,2009 www.atmos-chem-phys.net/9/7973/2009/
M.Ernetal.: TheaverageKelvinwavedistributionstudiedwithGROGRAT 7981
50 bers available for SABER) between the lines of equivalent
depthsof8and2000mforKelvinwaves. Onlyfrequencies
lowerthan0.4cpdwereusedtoavoidcontaminationbywave
modesotherthanKelvinwaves(forexample,inertia-gravity
40
waves,orquasi-two-daywaves).
Kelvin wave pseudo zonal wind variances for ECMWF
analysesareshowninFig.4aandforSABERmeasurements
m] 30
in Fig. 4b. The ECMWF and SABER pseudo zonal wind
k
e [ variances are very similar in the altitude range 21–41km.
d
u This is valid not only for integrated variances but also for
altit 20 single spectral components (Ern et al., 2008). Therefore
bothaltitude-timedistributionsofpseudowindvariancescan
serveasreferencesforGROGRATsimulations.
10 For comparison Fig. 4c shows ECMWF zonal wind vari-
ances derived from the original zonal wind data. In the
altitude range 20–35km ECMWF zonal wind spectra and
pseudozonalwindspectraareingoodagreement. Therefore
0
0 5 10 15 20 also original zonal wind variances and pseudo zonal wind
zonal wind variance [m²/s²] variances(obtainedbyintegratingoverthesameKelvinwave
band) are almost the same in the altitude range 20–35km.
Fig. 3. Altitude profiles of Kelvin wave pseudo zonal wind vari- AthigheraltitudestheoriginalECMWFKelvinwavezonal
ancesobtainedbyintegratingoverthepowerspectraforwavenum-
windvariancesare,however,highbiasedwithrespecttothe
bers1–6(therangeofwavenumbersavailableforSABER)between
pseudo zonal wind variances (this can be over a factor of 2
the lines of equivalent depths of 8 and 2000m for Kelvin waves
at 45km altitude). This hints at some imperfections of the
and frequencies lower than 0.4cycles/day and then averaged over
modelwindsathigheraltitudeswherefew(ifany)observa-
thewholeperiodJanuary2002–November2006. Shownarevari-
tionalwinddataentertheECMWFoperationalanalyses.
ances from ECMWF operational analyses (black solid line) and
fromSABERmeasurements(blackdashedline)asreferences(see Also at altitudes below the tropopause the original
alsoFig.4).Alsoshownareintegratedandthenaveragedvariances ECMWFKelvinwavezonalwindvariancesaremuchhigher
obtainedfromGROGRATsimulationswithtime-varyingECMWF than the Kelvin wave pseudo zonal wind variances derived
sourcespectraat16.9kmsourcealtitudewiththefollowingsetups: from the temperature spectra. This is likely due to non-
(1)fulldamping(radiativeandturbulent)switchedon(greendot- Kelvin wave contributions adding additional “noise” in the
ted),(2)radiativedampingonly(bluedotted),and(3)nodamping windspectrasothatwecannotseparatetheKelvinwavesig-
atall(reddotted).Fordetailsseetext.
nalfromtheoverallnoise.Thisconfirmsourchoicetocalcu-
latepseudozonalwindspectraforoursimulationsbecausein
thetemperaturespectraKelvinwavesaremuchmoredomi-
considerably higher than in the full damping case. This in-
nantthaninthewindspectraandtheKelvinwavesignalcan
dicates that for Kelvin waves the main damping process is
beextractedmucheasier.
radiative damping, and turbulent damping plays only a mi-
AnotherreasonwhywechoosetouseECMWFtempera-
norrole.
ture spectra for our simulations is that sometimes ECMWF
zonalwindspectracontainartifacts.Forexample,sometimes
thereareenhancedspectralcontributionsatzonalwavenum-
4 GROGRAT simulation of Kelvin wave variances
ber one, extending over all frequencies from 0–1cpd. This
basedonECMWFsourcespectra
clearlyartificialeffectisnotseeninthetemperaturespectra
4.1 Consistency check with stratospheric ECMWF whicharethereforebelievedtobemorereliable.
sourcedistribution The Kelvin wave pseudo zonal wind variances shown in
Fig. 4a and b should therefore be a reliable reference for
One method to derive temperature variances due to Kelvin our simulations with the GROGRAT ray tracer. And since
wavesistointegrateoverthespectralbandcharacteristicfor in the stratosphere the ECMWF temperature spectral distri-
this kind of waves (see Ern et al., 2008). In a similar way butionhasbeenvalidatedbycomparisonwithSABERmea-
variances are derived from pseudo zonal wind spectra cal- surements, we expect the reference distributions shown in
culatedviathepolarizationrelationsforKelvinwavesfrom Fig.4aandbtobereproduced,iftheGROGRATsourcedis-
ECMWF and SABER temperature spectra. The spectral tributionitselfislocatedinthestratosphere–i.e.,inthealti-
band we use has already been introduced in Sect. 3.5: the tuderangevalidatedwithSABER.Inaddition,sourcespec-
zonal wind variances were obtained by integrating over the tra in the upper troposphere and above are located at alti-
powerspectraforwavenumbers1–6(therangeofwavenum- tudeshigherthantheKelvinwavesourceprocesses,andthe
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