DTIC ADA526975: Space-Based Measurements of Stratospheric Mountain Waves by CRISTA. 1. Sensitivity, Analysis Method, and a Case Study

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JOURNAL OF GEOPHYSICAL RESEARCH, VOL.107,NO. D23,8178,doi:10.1029/2001JD000699, 2002
Space-based measurements of stratospheric mountain waves
by CRISTA
1. Sensitivity, analysis method, and a case study
Peter Preusse,1,2 Andreas Do¨rnbrack,3 Stephen D. Eckermann,4 Martin Riese,1,2
Bernd Schaeler,1 Julio T. Bacmeister,5 Dave Broutman,6 and Klaus U. Grossmann1
Received29March2001;revised27August2001;accepted28August2001;published25September2002.
[1] The Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA)
instrument measured stratospheric temperatures and trace species concentrations with
high precision and spatial resolution during two missions. The measuring technique is
infraredlimb-soundingofopticallythinemissions.Inageneralapproach,weinvestigatethe
applicabilityofthetechniquetomeasuregravitywaves(GWs)intheretrievedtemperature
data.ItisshownthatGWswithwavelengthsoftheorderof100–200kmhorizontallycan
be detected. The results are applicable to any instrument using the same technique. We
discussadditionalconstraintsinherenttotheCRISTAinstrument.Theverticalfieldofview
andtheinfluenceofthesamplingandretrievalimplythatwaveswithverticalwavelengths
(cid:1)3–5 km or larger can be retrieved. Global distributions of GW fluctuations were
extracted from temperature data measured by CRISTA using Maximum Entropy Method
(MEM) and Harmonic Analysis (HA), yielding height profiles of vertical wavelength and
peak amplitude for fluctuations in each scanned profile. The method is discussed and
comparedtoFouriertransformanalysesandstandarddeviations.Analysisofdatafromthe
first mission reveals large GWamplitudes in the stratosphere over southernmost South
America. These waves obey the dispersion relation for linear two-dimensional mountain
waves (MWs). The horizontal structure on 6 November 1994 is compared to temperature
fields calculated by the Pennsylvania State University (PSU)/National Center for
Atmospheric Research (NCAR) mesoscale model (MM5). It is demonstrated that precise
knowledge of the instrument’s sensitivity is essential. Particularly good agreement is
found at the southern tip of South America where the MM5 accurately reproduces the
amplitudesandphasesofalarge-scalewavewith400kmhorizontalwavelength.Targeted
ray-tracing simulations allow us to interpret some of the observed wave features. A
companionpaperwilldiscussMWsonaglobalscaleandestimatesthefractionthatMWs
contributetothetotalGWenergy(Preusseetal.,inpreparation,2002). INDEXTERMS:3334
MeteorologyandAtmosphericDynamics:Middleatmospheredynamics(0341,0342);3360Meteorology
andAtmosphericDynamics:Remotesensing;3384MeteorologyandAtmosphericDynamics:Wavesandtides
Citation: Preusse,P.,A.Do¨rnbrack,S.D.Eckermann,M.Riese,B.Schaeler,J.T.Bacmeister,D.Broutman,andK.U.Grossmann,
Space-basedmeasurementsofstratosphericmountainwavesbyCRISTA,1.Sensitivity,analysismethod,andacasestudy,J.Geophys.
Res., 107(D23),8178,doi:10.1029/2001JD000699,2002.
1. Introduction lower altitudes, GWs propagate upwards into the strato-
sphere and mesosphere where they deposit momentum and
[2] Gravity waves (GWs) are important for the middle energy when breaking. Therefore GWs strongly influence
atmosphere dynamics and composition. Originating from
theglobalcirculationandarethoughttobeamajorcauseof
global-scale oscillations such as the Quasi Biennial Oscil-
1DepartmentofPhysics,WuppertalUniversity,Wuppertal,Germany. lation(QBO)[Dunkerton,1997,andreferencestherein]and
2NowatICG-I,ForschungszentrumJu¨lich,Ju¨lich,Germany. theSemiannual Oscillation (SAO)[e.g.,Mayretal.,1998].
3Institutfu¨rPhysikder Atmospha¨re, DeutschesZentrumfu¨rLuftund
Raumfahrt(DLR),Oberpfaffenhofen,Germany. [3] However, most current global circulation models are
4E.O.HulburtCenterforSpaceResearch,NavalResearchLaboratory, not able to explicitly resolve GWs because of the coarse
Washington,DistrictofColumbia,USA. spatialresolutionofthemodels.Evenmodelswhichcanbe
5GoddardEarthSciencesandTechnologyCenter(GEST),Universityof run for case studies with sufficient resolution to resolve
Maryland,BaltimoreCounty(UMBC),Baltimore,Maryland,USA. GWs have to parameterize GWs for long-term runs due to
6AlsoatComputationalPhysicsInc.,Springfield,Virginia,USA.
computing constraints. The importance of a good represen-
tation of GWs to obtain realistic global circulation, mean
Copyright2002bytheAmericanGeophysicalUnion.
0148-0227/02/2001JD000699$09.00 wind and temperature structures as well as QBO and SAO
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Space-based measurements of stratospheric mountain waves by CRISTA
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1. Sensitivity, analysis method, and a case study
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CRI 6-2 PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1
patternshasbeenhighlightedbymanyauthors[e.g.,Boville, [8] IncaseoftheLIMSandtheCRISTAinstrumentGW
1995; Manzini et al.,1997; Manzini and McFarlane,1998; dataareinferredfromopticallythinemissionlimbmeasure-
McLandress, 1998]. ments. Other instruments using the same technique are the
[4] A fundamental question in this context is what and Cryogenic Limb Array Etalon Spectrometer (CLAES)
where the major wave sources are. Waves excited by flow [Roche et al., 1993] and the SABER (Sounding of the
over mountains (mountain waves, MWs), have zero phase AtmosphereusingBroadbandEmissionRadiometry)instru-
speeds relative to the ground (at least as long as the wind ment [Mertens et al., 2001]. In addition, the upcoming
speeddoesnotchangestronglywithtime)incontrasttoGWs mission of the High-Resolution Dynamics Limb Sounder
from other sources such as convection. Because nonoro- (HIRDLS) on board the Earth Observing System Chem
graphic GWs have different impacts on the synoptic-scale (EOS-Chem) satellite will provide similar global measure-
dynamics,theyarecommonlytreatedbydifferentparameter- mentsatarateof(cid:1)8000profilesadaywithglobalcoverage
ization schemes [Boville, 1995; Manzini and McFarlane, [Barnett et al., 1998]. The high spatial resolution of these
1998]. Thus there is interest in determining the sources of dataoughttomakethisinstrumentverywellsuitedforGW
observedGWsandinestimatingthefractionthatorographic studies.
GWs contribute to the total GW flux entering the middle [9] This paper provides a detailed assessment of GW
atmosphereonglobalscale[NastromandFritts,1992]. fluctuations (and MWs in particular) observed in temper-
[5] Breaking GWs not only deposit momentum but also ature data acquired by CRISTA infrared limb scan obser-
induceturbulenceandthusenhanceturbulent mixinginthe vations. Many of the results, however, are general and
atmosphere.Thisinfluencesthechemicalcompositionespe- should apply to other instruments, such as HIRDLS. To
cially in the upper mesosphere where wave breaking is interpret GW patterns in data from such instruments, a
intense[GarciaandSolomon,1985;Summersetal.,1997]. detailed knowledge of the sensitivity to different horizontal
[6] FurthermoreGWsmightplayanimportantroleinthe andverticalwavelengthsisessential.Insection2wederive
ozone depletion in the Arctic winter and spring. While ananalyticalapproximationforthesensitivityofCRISTAto
temperaturesintheArcticonglobalscalesnormallyremain GWs and compare this to numerical results derived from
too warm to form polar stratospheric clouds (PSC) and high spatial resolution radiative transfer calculations. We
thereby activate chlorine radicals, temperatures may drop demonstrate that a two-dimensional consideration of ray
locallybelowthefrostpointinthepresenceofstrongMWs paths through the GW structures is imperative. The results
as observed in the lee of the Scandinavian mountains provethatCRISTAcandetectwaveswithhorizontalwave-
[Do¨rnbrack et al., 1999]. Given the high number of length larger than 100–200 km.
mountain ridges at high latitudes in the northern hemi- [10] Insection3wedescribetheCRISTAexperiment,data
sphere, such events should occur rather frequently and acquisition and analysis. The analysis of GWs in acquired
thereforebeasignificantsourceofPSCsonsynopticscales temperatures employs a combination of Maximum Entropy
[Carslaw et al., 1999a, 1999b; Do¨rnbrack et al., 2001; Method(MEM)andHarmonicAnalysis(HA),whichiswell
Do¨rnbrack and Leutbecher, 2001]. suitedfortheanalysisofmonochromaticwavesofarbitrary
[7] In recent decades most observational studies of GWs wavelength.Theresultsarecomparedtothoseobtainedfrom
have used ground-based data from a limited number of Fourier transformation and to standard deviations, which
locations [e.g., Fritts, 1984; Tsuda et al., 1991; Eckermann highlight the characteristics of the various approaches and
etal.,1995;AllenandVincent,1995].Evenlargecoordinated theadvantagesaffordedbytheMEM/HAanalysis.
networksofground-basedandinsitumeasurements,suchas [11] Insection 4, we combine CRISTA data andanalysis
thePlanetaryScaleMesopauseObservingSystem(PSMOS) toisolateenhancedGWtemperatureamplitudesobservedin
and the Stratospheric Processes And their Role in Climate thestratosphere oversouthernSouthAmericainNovember
(SPARC)programs,stillcannotprovidetrueglobalcoverage. 1994. The high spatial resolution in all three dimensions
Global coverage is now provided by a rapidly increasing provided by CRISTA [Offermann et al., 1999; Riese et al.,
number ofGW studies from satellites. Todate,GW signals 1999; Grossmann et al., 2002] allows us to investigate the
havebeenanalyzedonglobalscalesusingtemperaturedata three-dimensional structure of the GWs. These investiga-
acquired by the Limb Infrared Monitor of the Stratosphere tions are supported by state-of-the-art meteorological non-
(LIMS)[Fetzer,1990;FetzerandGille,1994,1996],63GHz linear mesoscale model simulations that act to ‘‘hindcast’’
limb radiances measured by the Microwave Limb Sounder wave activity here, as well as targeted GW ray-tracing
(MLS) [Wu and Waters, 1996a, 1996b, 1997; McLandress studies. The detailed comparisons underline the necessity
etal.,2000;JiangandWu,2001],temperaturedatafromthe to estimate the sensitivity of the limb-sounding technique
Cryogenic Infrared Spectrometers and Telescopes for the for understanding the observed GW structures.
Atmosphere (CRISTA) [Eckermann and Preusse, 1999;
Preusseetal.,1999,2000],andtemperatureretrievalsfrom
2. GW Sensitivity Estimation for an Infrared
the meteorological programfor theGlobal Positioning Sys-
Limb Sounder
tem (GPS/MET) [Tsuda et al.,2000; Nastrom et al.,2000].
In addition, in the upper mesosphere/lower thermosphere [12] For the interpretation of GW data obtained from
datafromtheWindImagingInterferometer (WINDII) were satelliteinstruments,detailedknowledgeoftheinstrument’s
investigated for GWs [Wang et al., 2000a, 2000b, 2001a, sensitivity to disturbances of different horizontal and verti-
2001b]. GWs have also been investigated in saturated radi- calwavelengthsisessential[Alexander,1998;Preusseetal.,
ances taken by the SPIRIT-3 radiometer on board the Mid- 2000].WuandWaters[1997]andMcLandressetal.[2000]
courseSpaceExperiment(MSX)satellitefortwocasestudies provided such an analysis for saturated radiances measured
[Dewanetal.,1998;Picardetal.,1998]. by the Microwave Limb Sounder (MLS) on the UARS
PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1 CRI 6 - 3
local horizontal viewsfromtheorbitpositiondownwardthroughtheatmos-
pheric limb. The instrument measures the limb radiance,
tangent point produced by emission and reabsorption along the ray path.
ray path
The mathematical description of this radiative transfer is
tangent height CRISTA given for example by Gordley et al. [1994]. Vertical
distributions are obtained by scanning the beam up and
down in the atmosphere.
[14] Figure 2 shows the viewing geometry of a limb-
sounding instrument projected onto a simulated GW
R temperature oscillation. Since we use a Cartesian x–z
Earth
coordinate system, the curvature of the Earth’s surface
now shows up in form of a curved ray path. If we assume
that the atmosphere is optically thin, we can neglect self-
absorption in the atmosphere and in this case the intensity
Earth center measured by the satellite is the sum of all emissions along
the ray path. Atmospheric densities increase as we follow
Figure 1. Measuring geometry of the limb sounder. Two the ray path downward. For emitters with constant mixing
rays with different tangent heights are shown. These are ratio profiles (e.g., CO ), density increases proportionally
2
obtained by tilting the primary mirror of the instrument. as the total air density. Thus, the radiance emitted from a
small section along the ray is proportional to the atmos-
pheric density multiplied by the blackbody radiance for the
corresponding atmospheric temperature. This emitted radi-
satellite. For optically thin conditions one might estimate
ance is depicted in the upper panel of Figure 2 by the
an instrument’s sensitivity to different vertical scales of
Gaussian curve and shows the weighting that has to be
GWs based on the vertical weighting function [Fetzer,
applied to an atmospheric temperature fluctuation in order
1990]. Simply speaking, the weighting function defines
to obtain the temperature fluctuation detected by the
how much of the observed radiation stems from which
satellite (cf. (1)).
partoftheatmosphere.Oneoftenestimates thevisibilityof
a small-scale disturbance by convolving the disturbance [15] ThetworaypathsshownintheleftpanelofFigure2
reachtheirlowestaltitudeatthetangentpointatx=500km,
field with the weighting function (this will be discussed
wheretheweightingfunctionpeaks.Alsogivenintheupper
later in this section in more detail). To estimate the sensi-
panel is a horizontal projection of the wave oscillation,
tivity to different horizontal wavelengths l , one would
x showing the horizontal wavelength. As discussed above, a
analogously invoke the horizontal weighting function,
convolution of this wave structure with the weighting
which is approximately Gaussian. This gives an amplitude
function would lead to a nearly complete smearing out of
sensitivity
the wave. However, we can observe that the ray path is
A
SA;1DðlxÞ¼A ¼e(cid:5)2p2s2=l2x ð1Þ
0
where A is the amplitude of the atmospheric wave
0
perturbation, A is the retrieved amplitude, l is the
x
horizontal wavelength along the limb direction and s is
the width of the horizontal weighting function with typical
values of (cid:1)200 km. Following (1), a limb sounder has
less than 5% sensitivity to a 500 km wavelength GW and
shorter waves would vanish completely due to smearing
along the ray path. Reasonable sensitivity is found only
for horizontal wavelengths longer than (cid:1)800 km. This low
sensitivity is in obvious contradiction to the mesoscale
horizontal structures seen in temperature data from the
LIMS and the CRISTA instruments [Fetzer, 1990; Fetzer
and Gille, 1994; Eckermann and Preusse, 1999; Preusse
et al., 2001b] indicating that (1) does not adequately
describe the sensitivity of these instruments to GWs. Thus,
here we consider a two-dimensional geometry and Figure2. Viewinggeometryofalimbsoundingprojected
generalize the results to three dimensions at the end of throughasimulatedGW.Rightpanelshowsthetemperature
the section. profile used as model input (dashed) and the modeled
profile at the tangent point (x = 500 km; solid line). The
2.1. Limb-Sounding Technique two-dimensional temperature fluctuations and two limb ray
[13] The limb-sounding technique has been described in paths are shown in the left panel. Top panel gives the
detailelsewhere[e.g.,BaileyandGille,1986;Gordleyetal., weighting function along a ray path and the horizontal
1994;Marshalletal.,1994;Riese,1994;Rieseetal.,1999] waveshape in temperature for the bottom altitude. For
and is depicted schematically in Figure 1. The satellite details, see text.
CRI 6-4 PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1
partlycoalignedalongtheslopingphasefrontoftheGWat limb ray s
x = 200–400 km. In addition the phase does not change z
X
greatlybetween x=400kmandthetangentpoint.Thus,to t z
l
theleftofthetangentpointallraysectionswithlargeweight
have about the same phase. On the right, phases change
rapidly and no net signal can be expected due to averaging h
along this limb segment. Thus, the phase seen between x = t h
l
200kmandx=500kmwilldominatetheradianceattributed R
to this tangent height. Considering other tangent heights, Earth
different phases will be emphasized and a vertical wave φ
oscillation is measured by the satellite instrument.
2.2. Analytical Solution of the Radiative Transfer
[16] We can quantify all this by solving the radiative Earth center
transfer equations analytically given relevant simplifica-
tions. The analytical solution not only provides a better Figure 3. Geometry of a single ray path. With varying
understandingoftheradiativetransferandthesensitivityto distance s from the tangent point the altitude zl of the ray
GWs, but also avoids numerical errors due to grid spacing. above the Earth’s surface and the distance to the Earth’s
Thusitcanbeusedforcrosscheckingtheresultsfromafull centerhl=REarth+zlchanges.Tangentheightzt,s,andzlcan
numericalmodelofthemeasurementandretrievalaswillbe beall connected bytrigonometric functions in f (see text).
doneinsection2.3.Theanalyticalsolutionwewilldevelop
uses the following assumptions: p
ffiffiffiffiffiffiffiffiffi
1. TheblackbodyradianceB(T)canbelinearlyexpanded and we obtain s¼ HRE. Choosing H = 6.5 km and RE =
in the temperature Tusingafirst order Taylor series. 6350 km we get s ’ 200 km, which we have used to
2. The wavelength region considered isopticallythin. evaluate (1).
3. The background atmosphere isisothermal. [18] We now calculate the deviation of the intensity
4. The waveamplituderemains constant with altitude. emitted from a sinusoidally perturbed atmosphere from
[17] We first consider the radiance emitted along the ray the intensity for the background atmosphere by applying
path. For an optically thin atmosphere we can neglect self- the weighting function.Inthis step we alsolinearly expand
absorption and the limb radiance becomes theblackbodyradiationasafunctionoftemperature,which
requires small deviations from the mean temperature
Z 1
I ¼ (cid:3)ðsÞBðTðsÞÞds; ð2Þ Z 1
(cid:5)1 (cid:1)IðztÞ/ WðsÞ AsinðksþmzþyðztÞÞds; ð6Þ
(cid:5)1
wheresisthecoordinatealongtheraypath.Theemissivity
(cid:3) along a small part of the ray is directly proportional to with A being the temperature amplitude and k = 2p/lx and
the total atmospheric density r. Since the density in an m = 2p/lz being the horizontal and vertical wave numbers,
isothermal atmosphere is given by r = r e(cid:5)z/H we can respectively.Thus,aftermakingtheapproximationx’sthe
0
rewrite this equation as only but important difference between (6) and the assump-
tionsleadingto(1)isthat(6)contains aheightdependence
Z 1 mz(s). This height dependence z(s) is defined by the
I (cid:1) r0e(cid:5)z=HBðTðsÞÞds: ð3Þ constraintthattheairvolumesconsideredliealongthelimb
(cid:5)1 ray.Thedependenceofthewavephaseontangentheightis
ThusW=e(cid:5)z/Histheweightwhichhastobeappliedtoany expressed by the phase y(zt) = mzt + y0. For simplicity we
assume here y = 0 and use (4) to replace z by s and use
atmospheric temperature perturbation to be considered. We 0
additiontheoremstoextractyfromtheintegral.Inaddition,
nowexpressthisweightingfunctionintermsofahorizontal
we omit integrals of antisymmetric functions
weighting function by replacing z by s: Figure 3 shows the
geometryofasingletangentray.IncontrasttoFigure2,here
thecoordinatesisastraightlineandthecoordinatexfollows (cid:1)IðztÞ/
t=hehlEsainrthf’s’cuhrlvfat=urxe.aFnrdomhtF¼ighulrceo3sfwe’obhtla(cid:2)i1n(cid:5)th12efre2l(cid:3)atwiohnesres AcosðmztÞR(cid:5)11cosðksÞsin(cid:6)m2sR2E(cid:7)exp(cid:6)(cid:5)2Hs2RE(cid:7)ds
hl = RE + zl is the distance from the Earth’s center to the þAsinðmzÞR1 cosðksÞcos(cid:6)m s2 (cid:7)exp(cid:6)(cid:5) s2 (cid:7)ds ð7Þ
consideredrayelementandh =R +z isthedistancetothe t (cid:5)1 2RE 2HRE
t E t
tangent point. Since z =z (cid:5) z we get:
l t Ananalyticalsolutionfortheseintegralsexists[Gradshteyn
and Ryzhik, 1994]. The relative radiance sensitivity is
s2 s2
z’ ’ : ð4Þ obtained by dividing the intensity variation (cid:1)I(zt) by the
2hl 2RE mean intensity I(zt) and the atmospheric amplitude A. We
therefore normalize to the weight
Our weight takes the shape of aGaussian
Z 1 (cid:8) s2 (cid:9) pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
exp (cid:5) ds¼ p2HR ; ð8Þ
WðsÞ¼e(cid:5)s2=ð2HREÞ ð5Þ (cid:5)1 2HRE E
PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1 CRI 6 - 5
a) wherea=m/2R =p/(lR ),b=k=2p/l andc=1/(2HR ).
E z E x E
In order to simulate the CRISTA temperature retrieval we
[email protected]
B@T
a mean atmospheric temperature of 230 K. The phase shift
betweentheatmosphericwaveintemperatureandthewave
in the limb radiances is
1 (cid:6)a(cid:7) ab2
(cid:1)y¼ arctan (cid:5) : ð10Þ
2 c 4ðc2þa2Þ
[19] SA,2D(H, k, m) is plotted in Figure 4a for a constant
b) value of H = 6.5 km. We find that in general short vertical
wavelengths are suppressed by the radiative transfer. How-
ever, an ‘‘idealized’’ retrieval would recover all these
degradationsinthevertical,givenaninfinitesignal-to-noise
ratio of the instrument. We first want to approximate an
idealized retrieval, which does not further degrade the
measured signals in the vertical, because this allows us to
separatethedifferentconstraintsmoreclearly.Furthermore,
it allows the retrieval step width to be changed easily (see
below). Some retrieval algorithms take into account hori-
zontal gradients of the background atmosphere. However,
the fine-scale horizontal variations of a mesoscale GW
cannot be taken into account in the retrieval process
c)
particularly when the viewing direction is not aligned with
the flight vector. Thus, the retrieval will recover the wave
structure as if it were measured in the absence of any
horizontalstructure,i.e.,forinfinitehorizontalwavelengths.
We can therefore approximate the retrieval by dividing
S (H, k, m) by S (H, k = 0, m).
A,2D A,2D
[20] Applying this ‘‘idealized’’ retrieval we obtain
Figure 4b. From this figure we can already see some im-
portantfeatures.Forverticalwavelengthsaround10kmthe
limb sounder has reasonable sensitivity (0.35), even for
wavelengths around 200 km. This is much better than the
1Destimationsfrom(1).Wealsoseethatforshorthorizon-
tal wavelengths (<1000 km) the sensitivity at long vertical
Figure 4. Estimated sensitivity of an infrared limb wavelengthsisdiminished.Thisisanimportantpointforthe
sounder as obtained using an analytical approach. Panel intercomparison of satellite climatologies [Preusse et al.,
(a) shows the radiance amplitudes as percentage deviations 2000]. It also explains the low sensitivity predicted by (1).
from the total radiance corresponding to an atmospheric Setting a = 0 in (9) we get (1). Thus, the one-dimensional
oscillation with a 1 K temperature amplitude. Panel (b) considerationisgivenbyS (H,k,m=0)in(9).Figure2
A,2D
gives the ratio of retrieved and atmospheric temperature forthiscasewouldshowverticallyalignedphasefrontsand
amplitude for an ‘‘idealized’’ retrieval without any restric- the limb ray can never be oriented parallel to the phase
tions from the instrument. Panel (c) takes sampling effects fronts. Thus the one-dimensional estimation (1) is a worst
intoaccount.ThesameratioasgiveninPanel(b)isshown, case, which is never found in reality.
but as expected for a 3 km step-width onion-peeling [21] From Figure 4b we would expect to see GWs with
retrieval. The plots are based on analytical expressions shortverticalwavelengthsbest.However,thiswasobtained
derived in the text. The contour spacing is 0.1 in Panel (a) assuming an ‘‘idealized retrieval’’, whereas real retrievals
and 0.05 in Panels (b) and (c). have additional limitations. The smallest resolvable vertical
scale visible in the CRISTA data is limited by the vertical
samplingandtheretrievalprocess.Duringthefirstflightin
November 1994, CRISTA sampled with a vertical resolu-
andtakeintoaccountafactor 1@Bstemmingfromthelinear
B@T tion of 1.5 km [Riese et al., 1999]. However, except for
expansion ofthe blackbodyradiation. Wefinallyobtainthe
somespecialobservationalmodes,wehavedividedthedata
sensitivity of the total ray radiance to a sinusoidal
setintotwosubsetsof3.0kmverticalstepwidth,whichare
perturbation in the atmosphere:
retrieved separately and reemerged afterward [Riese et al.,
1999]. Since a simple onion-peeling scheme is used for the
retrieval [Riese, 1994; Riese et al., 1999], temperature and
S ðH;k;mÞ¼ 1 @Br4 ffiffiffiffiffifficffiffi2ffiffiffiffiffiffiffi exp(cid:8)(cid:5) cb2 (cid:9); ð9Þ trace-gasmixingratiosareinterpolatedlinearlybetweenthe
A;2D B @T c2þa2 4ðc2þa2Þ altitudesconsidered.Thus,theretrievallinearlyinterpolates
CRI 6-6 PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1
throughout any altitude structure which is smaller than the data extrapolated to the ground and to about 80 km. The
retrieval step width of 3.0 km. extrapolation to 80 km was necessary for the forward
[22] We simulate this in the analytical approach by radiance calculations.
applying a boxcar filter of the size of the retrieval step [25] The primary model output is a perturbed potential
width(cid:1)z.Thesmoothinginherentintheretrievalprocessis temperaturefield,whereastheradiativetransfercalculations
then given by are based on temperatures, pressures and trace gases on a
geometric altitude grid.
lpffi2ffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(cid:8)ffiffiffiffi2ffiffipffiffiffi(cid:1)ffiffiffiffizffiffi(cid:9)ffiffiffi [26] Therefore the atmosphere is rebuilt hydrostatically
RðlÞ¼ z 1(cid:5)cos : ð11Þ from the perturbed potential temperature field and temper-
z 2p(cid:1)z l
z atureandpressureareevaluated.Theresultsarestoredona
gridof10kminthehorizontaland500minthevertical.It
Applying this ‘‘cut off’’ due to the retrieval step to our should be noted that ozone, which is the most important
‘‘idealizedretrieved’’sensitivityfieldyieldsFigure4c.This interferingtracespeciesintheretrievalprocess,isperturbed
results in a realistic decrease in sensitivity at short vertical by the wave also.
wavelengths. [27] From this model atmosphere we obtain altitude
profiles of limb radiances as would be measured by
2.3. High Spatial Resolution Radiative Transfer
CRISTAwiththeuseofradiativetransfercalculationsbased
Calculations
on the BANDPAK radiance model [Marshall et al., 1994;
[23] The analytical approach is based on several approx- Gordley et al., 1994]. Every combination of horizontal and
imations which may limit the general applicability of the
vertical wavelength had to be simulated individually. For
results. A more general approach is provided here by a
eachprofilewedefineaverticalgridoftangentheightswith
numerical modeling that is divided into three steps. In the
a spacing of 200 m, oversampling the 1.5 km vertical
first step a representative background atmosphere is per-
sampling of the CRISTA instrument. This allows us to
turbed using a linear two-dimensional (2D) GWoscillation
convolve the radiances resulting from an infinitesimally
based on WKB theory. Next radiative transfer simulations
thin ray path with the vertical field of view of the CRISTA
throughout the model atmosphere are performed leading to
instrument.Foreachraypathcalculation,theatmosphereis
vertical radiance profiles such as those measured by
divided into 100 layers. These layers define the spatial
CRISTA. (The simulations are idealized in a sense that
resolutionoftheradiativetransfercalculations.Thevertical
instrumental error sources such as radiance errors or noise
spacingofthelayersisdenseimmediatelyabovethetangent
arenottakenintoaccount.)Thesimulatedinputamplitudes
height and increases with altitude. This means highest
are chosen to be typically a few Kelvin and will be easily
spatial resolution is obtained where the weighting function
identified by the MEM/HA given a reasonable sensitivity
peaks. A fine vertical resolution of the layers is especially
value. The third step involves retrieval and data analysis,
important for short horizontal wavelengths l , because in
which are performed following the CRISTA standard data x
this case the phase of the wave changes rapidly in the x-
evaluation.
direction,butclosetothetangentpointtheheightoftheray
[24] The model used is a two-dimensional, linear WKB pathvariesslowlywithx(seeFigure2).Itturnedoutthatin
model for MWs [Schoeberl, 1985]. Horizontal wavelength
somecasesaverticalresolutionofaround30misnecessary
and altitude profiles of wind speed and potential temper-
for the layers immediately above the tangent point. At the
ature are input to the model. For our calculations we have
altitude of each layer the exact position of the ray path is
chosen a wind profile that is constant with altitude. The
determinedandthesimulatedatmosphericparametersgiven
value ofthe horizontal wind speed U sets the vertical wave
bythe2Dmodelareinterpolatedtotheseraypositions.For
number m
these radiative transfer calculations none of the approxima-
tions necessary for the analytical approach are made.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(cid:8)N(cid:9)2 1 [28] The simulated radiance profiles are retrieved using
jmj¼ U (cid:5)k2(cid:5)4H2; ð12Þ the standard CRISTA retrieval algorithms, including all
smoothing procedures [Riese et al., 1999]. Finally the
retrievedtemperatureprofilesareanalyzedforGWsemploy-
whereNisthebuoyancyfrequency,kisthehorizontalwave
ing the MEM/HA method described in section 3. The
number and H is the scale height. The bottom layer of
resulting amplitudes and wavelengths can be compared to
potentialtemperaturefollowsthesurfacetopography,which
the input values. To determine the amplitude sensitivity the
hereissinusoidal.Forallotheraltitudesthedisplacementof
output of the simulated retrieval is compared to profiles
theisentropesiscalculatedaccordingtolinearwavetheory.
obtained by vertical sections throughout the GW model
Amplitude growth with altitude follows the WKB relation
outputat the tangentpoint.
[e.g., Lindzen, 1981]
sffiffiffiffiffiffiffiffiffiffi 2.4. Results of the Numerical Simulations
mð0Þ
w^ðzÞ¼w^ð0Þ ez=2H ð13Þ [29] Visual inspection of simulated altitude profiles
mðzÞ revealsaphaseshiftbetweenthewavesignaturesintemper-
atures extracted directly from the 2D-model solution and
where w^ is the vertical velocity amplitude. In addition, those obtained by simulated radiative transfer and retrieval.
calculationswereperformedwherethedensitystratification These phase shifts df(z) depend on the background atmos-
term ez/2H was omitted. The background potential tempera- phere and hence on the altitude. This can be noted from
ture is taken from a zonal mean cross section of CRISTA (10), where (cid:1)y depends on the scale height H via c.
PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1 CRI 6 - 7
Figure 5. Scatterplot of retrieved versus theoretical vertical wavelength. The solid line indicates a
perfect retrieval ofthevertical wavelength. Theobserved scatterofthesingular points asretrieved from
simulatedCRISTAprofilesisduetoradiativetransfereffectsandtheanalysismethod.Thescattergivesa
good indication of the precision of the vertical wavelength retrieved from real CRISTA measurements.
To demonstrate the way in which height dependent phase estimateoftheprecisionoftheverticalwavelengthretrieved
shiftscanaltertheverticalwavelength,weconsiderasinus- from CRISTA temperatures.
oidalwaveinasingleretrievedprofileT0=T^ sin(mz+f+ [31] GW simulationswere performed forconstantampli-
df(z)) = T^ sin y, with f being the phase at z = 0. For tudesandamplitudesgrowingexponentiallywithheight.In
example, if the phase shift df(z) in a certain altitude range the real atmosphere both cases are likely to be observed.
decreases, the total phase y of the wave changes more Exponential growth is expected where GWs propagate
slowlythanwewouldexpectfromtheverticalwavenumber conservatively without interaction with the background
m. This results in an apparently longer vertical wavelength flow. A constant amplitude reflects the classical case
in the retrieved temperatures and by the same token an described by Lindzen [1981], where GWs are breaking and
increasing phase shift results in a shorter wavelength. This retain their saturation amplitude. It should further be noted
variation of the vertical wavelength is shown in Figure 5. that even in the case of exponential growth the amplitude
Theverticalwavelengthdeducedfromtheretrievedtemper- increaseswithtwicethescaleheightofthedensitydecrease.
atures is compared to the input wavelength from (12). We Thus,theweightalongtheraypathdecreasesfasterthanthe
find a scatter of (cid:1)20% in retrieved wavelengths. wave amplitude increases and the total contribution to the
[30] The simulations employed to produce Figure 5 are measured radiance decreases exponentially with altitude.
based on a zonal mean background atmosphere and there- Results from growing amplitude as well as constant ampli-
fore embody realistic geographical variations. In addition, tudesimulationsareshowninFigure6.Panel(a)reproduces
the same method as used here is also used to determine the Figure 4c. Panels (b) and (c) show results for constant
vertical wavelength of GWs observed in real flight profiles amplitude and exponentially increasing amplitude waves,
(see section 3). Thus, the scatter observed in Figure 5 respectively.Thevaluesofthenumericalsimulationsarean
represents physical effects from the radiative transfer as average over altitudes of 25–60 km and 13 latitude bins.
well as influences of the analysis method and is a good This average increases the statistical significance of the
CRI 6-8 PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1
a) numerical modeling (Panels (b) and (c)) reveal an ‘‘island’’
ofhighsensitivityatl (cid:13)350kmandl (cid:13)6–8kmvertical
x z
wavelength, which is not found in the analytical solution.
For horizontal wavelengths between 300 and 800 km,
Panels (b) and (c) agree reasonably and exhibit only weak
dependence on the horizontal wavelength. Thus, a one-
dimensional sensitivity function averaged over the 300–
800 km horizontal wavelength range and depending solely
on the vertical wavelength is representative of the waves
contained in the residual temperatures. This is an impor-
tant point, because it allows us to correct amplitudes
retrieved from CRISTA measurements for visibility effects
noted in Figures 4 and 6 [see also Preusse et al., 2000].
This would not be possible if a strong dependence on
b) horizontal wavelength was present, since it is often diffi-
cult to deduce the horizontal wavelengths as will be seen
in section 4. We will discuss in section 3.3 to what extent
the assumption is valid that horizontal wavelengths are
shorter than 1000 km.
[32] It should be noted that there is an artificial back-
ground of relatively high sensitivity (0.2) at very short
horizontal wavelengths. This is spurious and due to a
vertical spacing of the forward calculations that is still
too coarse. Inspection of single profiles indicated that the
altitude layering has to be even finer than the 30 m
spacing we have used for these simulations. Here the
analytical approach, which is not restricted by numerical
errors and grid spacing, supports the finding of vanishing
c) sensitivity to the very short horizontal scales less than
about 200 km. For longer horizontal wavelengths the
numerical modeling can be expected to yield reliable
results.
[33] So far we have discussed sensitivity variations
versus wavelength. However, an important question is
whether the observational technique itself can cause artifi-
cial geographical structures in the observed GW variances.
Thus, we now keep the horizontal and vertical wavelength
fixedbyaveragingallvaluesinaboxofl =300–800km
x
and l = 8–12 km. Figure 7a plots these values versus
z
latitude and altitude. A second wavelength box of l =
x
300–800kmandl =15–20km resultsin the distribution
z
shown in Figure 7b. It should be noted that the MEM/HA
Figure 6. Estimated sensitivity of retrieved CRISTA method results in wave amplitudes which are independent
temperatures to GWoscillations. Radiative transfer as well ofthe phase ofthe waverelative tothe analysis interval. In
asretrievaleffectsareincluded.Panel(a)reproducesFigure addition, the average of l = 300–800 km and different
x
4c. Panels (b) and (c) show the results of the numerical vertical wavelengths is also an average over different
simulations with constant GW amplitudes and amplitudes phases of the waves. The observed structures are therefore
growing exponentially with altitude, respectively. All three reliable and not due to a specific phase choice made when
figures exhibit the same salient features, particularly the initializing the simulations. The observed geographical
strong decrease of sensitivity at around 200 km horizontal dependence is small for the short vertical wavelengths
wavelength and the decreased sensitivity to long vertical (Panel a) and varies by up to ±30% for the longer vertical
wavelength for a given horizontal wavelength. Panels (b) wavelengths shown in Panel (b). However, this higher
and (c) are very similar in the horizontal wavelength range value corresponds to about 2 dB for squared amplitudes
from 300 to 800 km, allowing us to deduce a one- and we will show in section 3 and the companion paper
dimensional correction factor, which can be applied to (Preusse et al., in preparation, 2002) that these variations
measured CRISTA data. are small compared to the observed geophysical variations
of GW variances.
[34] One last point is whether there are changes in
givenvalues.Thethreepanelshavethesamesalientfeatures, the phase of the observed waves. The analytical ap-
specifically astrong decrease ofsensitivity at l (cid:13) 200km proach indicates that the radiative transfer (10) as well as
x
andadecreaseofsensitivityatlongverticalwavelengthsfor the retrieval induce phase shifts. These are expected
a given horizontal wavelength. The results of the full mostly where the radiance sensitivity is small, namely for
PREUSSEETAL.:STRATOSPHERICMOUNTAINWAVEMEASUREMENTSBYCRISTA,1 CRI 6 - 9
λ = 8-12 km 180
a) z
g]
e
120 hift [d
s
e
s
a
60 ph
s
b
a
0
λ = 15-20 km Figure 8. Phase shift due to the radiative transfer. The
b) z values are mostly small except for wavelengths, for which
the small sensitivities have been found in Figure 6.
[36] We can assume that the case where the LOS is
coaligned with the horizontal wave vector is the exception
and that nonzero view angles a frequently occur. Thus, a
fraction of the atmospheric waves with horizontal wave-
lengths between 100 km and 200 km is observed by the
limb viewer. How large this fraction is may depend on a
possible general preference of the wave propagation direc-
tionand the actual view direction ofthe instrument. Thisis
discussed in some detail in section 4. However, for very
Figure7. Dependenceofthesensitivityonthelocationof
large view angles a this relation may not hold any longer
the measurement. Short vertical wavelengths (l = 8–
z
because this would assume infinite plane horizontal wave
12 km) given in Panel (a) depend only weakly on altitude
fronts.
and are nearly independent of latitude. The geographical
dependence of the longer vertical wavelengths (l = 15– [37] Employing the one-dimensional correction function
z
[Preusse et al., 2000] one can rescale the measured GW
20km) is stronger.However,asshownin sections 3and5,
amplitudes to estimate the ‘‘true’’ atmospheric amplitudes
the observed variations in GWactivity are much stronger.
of mesoscale GWs with vertical wavelengths l ^ 5 km.
z
The decrease of sensitivity at the short horizontal wave-
short vertical and short horizontal wavelengths (compare
Figures 4 and 6). Results from numerical simulations are
shown in Figure 8, which plots the absolute values of the
phase differences between 2D-model wave input and
retrieved temperature profiles. These phase shifts are small
for most combinations of horizontal and vertical wave-
length. The phase shifts therefore do not prevent us from
deriving horizontal wave structures from the CRISTA
temperature data.
2.5. Generalization to Three Dimensions
[35] The sensitivity estimates shown in Figures 4 and 6
are based on two-dimensional radiative transfer calcula-
tions. However, the real atmosphere is three dimensional
and it is likely that the instrument views waves at various
angles. This is illustrated in Figure 9, which shows the
horizontal projectionofalimbrayandthehorizontalphase
frontsofaGW.Thehorizontalwavelengthalongthelineof
sight (LOS) is a factor 1/(cos a) larger than the real
horizontal wavelength l . Thus, for waves viewed at an
x
angle a to the phase fronts we have to scale the x-axes of
Figures 4 and 6 by cos(a). Taking a = 60(cid:10) as an example, Figure 9. Horizontal projection of an arbitrarily oriented
the shortest horizontal wavelength l for which the sensi- GW and the line of sight (LOS). Instead of viewing
x
tivityislargerthan0.5isnow100–120kminsteadof200– perpendicular to the wave fronts (gray shading), there is an
240 km in the two-dimensional calculations (Figures 6b angle a between the line of sight and the horizontal wave
and 6c), which tacitly assume a = 0. vector~k.