DTIC ADA523741: Fourier-Ray Modeling of Short-Wavelength Trapped Lee Waves Observed in Infrared Satellite Imagery Near Jan Mayen

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2830 MONTHLY WEATHER REVIEW VOLUME134
Fourier-Ray Modeling of Short-Wavelength Trapped Lee Waves Observed in Infrared
Satellite Imagery near Jan Mayen
STEPHEN D. ECKERMANN
E.O.HulburtCenterforSpaceResearch,NavalResearchLaboratory,Washington,D.C.
DAVE BROUTMAN AND JUN MA
ComputationalPhysics,Inc.,Springfield,Virginia
JOHN LINDEMAN
SchoolofComputationalSciences,GeorgeMasonUniversity,Fairfax,Virginia
(Manuscriptreceived12July2005,infinalform20January2006)
ABSTRACT
A time-dependent generalization of a Fourier-ray method is presented and tested for fast numerical
computationofhigh-resolutionnonhydrostaticmountain-wavefields.Themethodisusedtomodelmoun-
tainwavesfromJanMayenon25January2000,aperiodwhenwavelikecloudbandingwasobservedlong
distances downstream of the island by the Advanced Very High Resolution Radiometer Version 3
(AVHRR-3).Surfaceweatherpatternsshowintensifyingsurfacegeostrophicwindsovertheislandat1200
UTCcausedbyrapideastwardpassageofacompactlowpressuresystem.The1200UTCwindprofilesover
theislandincreasewithheighttoajetmaximumof(cid:1)60–70ms(cid:2)1,yieldingScorerparametersthatindicate
verticaltrappingofanyshortwavelengthmountainwaves.SeparateFourier-raysolutionswerecomputed
usinghigh-resolutionJanMayenorographyand1200UTCverticalprofilesofwindsandtemperaturesover
theislandfromaradiosondesoundingandananalysissystem.Theradiosonde-basedsimulationsproduce
apurelydivergingtrappedwavesolutionthatreproducesthesalientfeaturesintheAVHRR-3imagery.
Differencesinsimulatedwavepatternsgovernedbytheradiosondeandanalysisprofilesareexplainedin
termsofresonantmodesandarecorroboratedbyspatialray-grouptrajectoriescomputedforwavenumbers
along the resonant mode curves. Output from a nonlinear Lipps–Hemler orographic flow model also
compareswellwiththeFourier-raysolutionhorizontally.Differencesinverticalcrosssectionsareascribed
totheFourier-raymodel’scurrentomissionoftunnelingoftrappedwaveenergythroughevanescentlayers.
1. Introduction al. 1998; Fueglistaler et al. 2003). These influences
sometimes take the form of spectacular wave-banded
When suitable environmental conditions exist, flow
cloud displays that are visible from space (e.g., Fritz
over mountains generates quasi-stationary gravity
1965;GjevikandMarthinsen1978;BurroughsandLar-
wavesthatcanpropagateobliquelyawayfromthepar-
son 1979; Sharman and Wurtele 1983; Mitchell et al.
entorography.Thesewavescanhaveimportanteffects
1990;Worthington2001).Mountainwavesgrowinam-
on other atmospheric processes. Air parcels advected
plitude with altitude and can break, generating drag
throughthesewavesexperiencerapidlyoscillatingadia-
forcesthataffectthesynoptic-scalecirculationandtur-
batic cooling and heating that can have strong net in-
bulence that mixes chemical species (e.g., Kim et al.
fluences on cloud physics and associated chemistry in
2003).
both the troposphere and stratosphere (e.g., Jensen et
In addition to these atmospheric effects, mountain
waves present hazards to aviation. Severe structural
damage and injuries to passengers and crew can occur
Corresponding author address: Stephen D. Eckermann, E. O.
when aircraft fly through severe clear-air turbulence
HulburtCenterforSpaceResearch,NavalResearchLaboratory,
(CAT) produced by mountain-wave breaking (e.g.,
Code7646,Washington,DC20375.
E-mail:[email protected] Bacmeisteretal.1994;Ralphetal.1997;deVilliersand
©2006AmericanMeteorologicalSociety
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Fourier-Ray Modeling of Short-Wavelength Trapped Lee Waves
5b. GRANT NUMBER
Observed in Infrared Satellite Imagery near Jan Mayen
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6. AUTHOR(S) 5d. PROJECT NUMBER
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OCTOBER2006 ECKERMANN ET AL. 2831
van Heerden 2001). Furthermore, sudden changes in validated globally using new data from stratospheric
flight altitude caused by mountain waves, either researchsatellites(EckermannandPreusse1999;Jiang
through wave-induced CAT and/or short-wavelength et al. 2002, 2004), as well as regionally using various
verticalwavedisplacements,arealsoanimportantissue suborbital measurements (e.g., Hertzog et al. 2002;
given recent enaction of reduced vertical separation Eckermann et al. 2006). MWFM forecasts of strato-
minima (RVSM) for commercial air traffic. The large- sphericmountain-waveturbulencewereutilizedexten-
amplitude mountain-wave event over Colorado docu- sivelybytheU.S.AirForceduringOperationsEndur-
mented by Lilly (1978) provides a vivid illustration of ing Freedom and Iraqi Freedom (Eckermann 2002),
bothofthesehazards,causingacommericalairlinerto andsince2004MWFM-2hasbeenrunoperationallyat
drop (cid:1)4000 ft in a little over 1 min while simulta- the Air Force Weather Agency. MWFM-2 hindcasts
neously undergoing severe airframe buffeting due to have also been used in a variety of research applica-
wave-induced CAT. tions,suchastheroleofmountainwavesinaccelerating
Thus, mountain wave events are important to fore- ozone loss chemistry in the Arctic winter stratosphere
cast, yet the spatial scales of these waves and the sub- (e.g.,Carslawetal.1999;Pierceetal.2003;Svendsenet
wavelengthinstabilitiesthatleadtobreaking,drag,and al. 2005; Mann et al. 2005).
turbulence generation are generally too short for op- Thus,raymethodsarenowanacceptedapproachto
erationalnumericalweatherprediction(NWP)models forecasting mountain waves (Eckermann et al. 2004).
to resolve fully (e.g., Benoit et al. 2002; Smith 2004). Yet the current MWFM ray algorithms still contain a
For example, subgrid-scale gravity wave drag must be numberofsignificantsimplificationsandshortcomings.
parameterized in NWP and climate models (e.g., Kim First, they use a one-dimensional height-dependent
et al. 2003). Until operational NWP model resolutions formforthewaveactionequationthatdoesnotinclude
improve, alternative forecasting algorithms for moun- the effects of horizontal geometrical spreading of the
tain waves must be developed. rays on the wave amplitude evolution (e.g., Shutts
Ongoingeffortsinthisareahavebeenundertakenat 1998).Second,theyuseaspatialformulationfortheray
the Naval Research Laboratory for over a decade in solutions, which leads to caustic singularities that are
developing the MountainWave Forecast Model not practical to correct (e.g., Broutman et al. 2001,
(MWFM; Eckermann et al. 2004, 2006). Instead of 2002, 2004). Third, they use idealized ridge databases
simulating the fully nonlinear discretized Navier– for their source functions that do not capture the full
Stokes equations, as in a traditional NWP model, the spectrum of waves radiated by flow over realistic to-
MWFM approach uses ray methods to simulate the pography.
generation, propagation and breakdown of mountain To fully explore and exploit the capabilities of ray
waves within the large-scale environment specified by methods for mountain-wave forecasting, over the past
operationalNWPmodeloutput.Sinceraysolutionsare several years we have progressively developed im-
easytointerpret,computationallyfast,andvalidwithin proved ray algorithms that reduce or eliminate these
a broad variety of atmospheric environments, they are andotherweaknessesinthecurrentMWFMrayequa-
attractive as potential forecasting algorithms. tions (Broutman et al. 2001, 2002, 2003, 2004, 2006).
The first version of the MWFM (MWFM-1) tested Thishasledtoanewrayalgorithmthatwerefertohere
theseideasusingahydrostatictwo-dimensionalspatial- astheFourier-raymethod,becauseitinvolvesFourier-
rayformulation(Bacmeisteretal.1994).TheMWFM-2 synthesized (rather than spatially synthesized) ray so-
was extended to use three-dimensional spatial-ray lutions. The method has recently been reviewed inter
equations governed by a nonhydrostatic dispersion re- aliabyBroutmanetal.(2004)andtheversionofitthat
lation including rotation (Eckermann and Preusse we use here is described in section 2a.
1999). Both models employ an idealized ridge decom- This method shows promise as a potential next-
position of the earth’s topography to define the major generation dynamical ray core for the MWFM, since
terrain features relevant for generation of waves near the idealized solutions derived to date alleviate or
thesurface.MWFMforecastshavebeenusedforover eliminate all of the aforementioned weaknesses of the
adecadenowtodirectNationalAeronauticsandSpace correspondingspatialraysolutions.Specifically,theal-
Administration (NASA) research aircraft away from gorithm incorporates arbritrary topographic forcing at
hazardousmountain-wave-inducedturbulenceandinto the lower boundary, models both trapped and free-
regionswherenonbreakingwavesgeneratecloud,tasks propagating waves, includes horizontal geometric
forwhichithasrepeatedlyshownskill(e.g.,Bacmeister spreading in its wave action solutions, and systemati-
et al. 1994; Eckermann et al. 2004, 2006). MWFM-2 cally corrects the caustic singularities found in spatial-
hindcasts of stratospheric wave amplitudes have been raysolutions.Todate,however,wehaveappliedthese
2832 MONTHLY WEATHER REVIEW VOLUME134
FIG.1.Three-dimensionalshadedsurfaceplotoftopographicelevationfortheisland
ofJanMayenfromtheGTOPO30digitalelevationdatabase.Allthreelengthdimen-
sions(inkm)aswellaslongitudesandlatitudesaredisplayed.
newalgorithmsonlytoidealizedmountain-waveprob- forced by flow over Mount Beerenberg that radiated
lemsthatuseanalyticalfunctionsfortheobstacleshape into much larger atmospheric volumes downstream.
and background wind profile. Such waves present an excellent test case for our new
Herewetakeournextstepinassessingthepotential algorithm’sverticalreflectionandhigh-resolutionfore-
oftheFourier-raymethodforforecastingbyextending casting capabilities, since Jan Mayen’s topography
and applying these algorithms to a more realistic case would not be adequately resolved by current opera-
study. The major extensions here are incorporation of tional NWP systems. Our results here are used to
realistic topography and real background wind and benchmarktheinitialperformanceofthisnewraycode
temperature profiles from both radiosonde observa- and to target areas for further development for future
tions and a meteorological analysis issued by a data forecasting applications.
assimilation system. We concentrate here on nondissi-
pative wave solutions, deferring developments in esti-
matinglocationsofwave-inducedCATtolaterstudies. 2. Models
Our modeling focuses on Jan Mayen (71°N, 8.4°W),
a. The Fourier-ray model
a small island in the North Atlantic whose topography
is dominated to the north by Mount Beerenberg, a Our primary tool is a flexible numerical implemen-
quasi-circular volcanic mountain of width (cid:1)5–10 km tation of a Fourier-ray method. The name “Fourier
andapeakelevationof(cid:1)2270m(seeFig.1).Weseek ray”referstoFourier-synthesizedraysolutions:thatis,
to “hindcast” wavelike patterns observed over the is- theraysolutionsarecomputedinaFourierdomainand
landinsatellitecloudimageryon25January2000.Pre- thensuperimposedbyinverseFouriertransformtogive
vious analysis and linear modeling of some earlier sat- a spatial solution. The method is described in Brout-
ellite cloud images over Jan Mayen (Gjevik and Mar- manetal.(2002,2003,2006).Duringearlierstagesofits
thinsen1978;SimardandPeltier1982)associatedcloud development, different names were used for the same
bandingherewiththree-dimensionaltrappedleewaves basicmethod(e.g.,Maslov’smethod,asimplifiedFou-
OCTOBER2006 ECKERMANN ET AL. 2833
rier method). The reasons for the name changes are Fourierdomainfortheverticalvelocityassociatedwith
discussed in Broutman et al. (2006). the mountain waves. The corresponding spatial solu-
The ray solution in the Fourier domain is expressed tion w(x, y, z, t) is obtained by inverse Fourier trans-
asafunctionofk,l,z,t,wherekandlarethehorizontal form:
(cid:1) (cid:1)
wavenumbers,zisheight,andtistime.Theadvantage
(cid:3) (cid:3)
of solving in the Fourier domain is that k and l are w(cid:5)x,y,z,t(cid:7)(cid:4) w˜(cid:5)k,l,z,t(cid:7)ei(cid:5)kx(cid:6)ly(cid:7)dkdl.
constant along the ray in a horizontally uniform back- (cid:2)(cid:3) (cid:2)(cid:3)
ground, as assumed here. Along with a simple ray-
(cid:5)2(cid:7)
based treatment of the time dependence of the solu-
tions(Broutmanetal.2006),theproblemiseffectively TheFourier-raysolutionforw˜(k,l,z,t)isgiveninthe
reducedtoaone-dimensionalcalculationinz.Thisisa appendix, based on derivations in Broutman et al.
major simplification for numerical ray tracing, espe- (2006).Weemphasizethatw(x,y,z,t)isnotthesame
cially for the wave amplitude calculations and the cor- as the spatial-ray solution for the vertical velocity,
rection of caustics. whichisobtainedfromthestationaryphaselimitofthe
Broutman et al. (2002, 2003) derived steady-state inverse Fourier transform in (2). The distinction is im-
Fourier-ray solutions for hydrostatic and nonhydro- portant because the stationary phase approximation,
static waves, respectively. Wave transience was incor- butnotw,breaksdownatcausticsinthespatialdomain
poratedintotheFourier-raymethodbyBroutmanetal. (see, e.g., Shutts 1998; Broutman et al. 2001).
(2006). We use that transient formulation here to aid This Fourier-ray code ingests arbitrary vertical pro-
directcomparisonswithoutputfromnonlinearnumeri- files of wind and temperature, which are interpolated
cal models at finite times. Besides being helpful for ontoaverticalgridsufficientlyfinetoevaluatethefol-
estimating setup times for the wave field, the transient lowing phase integrals accurately:
(cid:1) (cid:1) (cid:1)
formulation has two computational advantages. First,
z zt z
there are no resonant singularities in the transient so- mdz, mdz, |m|dz, (cid:5)3(cid:7)
lutionforthetrappedwaves,asthereareinthesteady- 0 z zt
statesolution.(Thesteady-statesingularitiescanbere-
wherez istheheightoftheturningpointforagiven(k,
moved by adding a small imaginary component to the t
l). The first integral is used for vertically propagating
wavenumber or frequency, but this artificially damps
waves,thesecondintegralisusedforverticallytrapped
wave amplitudes. The Fourier-ray solutions presented
waves at heights below their turning point z, and the
here are nondissipative.) Second, the transient wave t
third integral is used for vertically trapped waves at
field is more limited in spatial extent than the steady-
heights above their turning point (see the appendix).
state solution, which is the longtime limit of the tran-
Anabsolutevalueappearsinthethirdintegralbecause
sient solution. The transient solution can thus be rep-
m is imaginary above z. These integrals are computed
resented with fewer computational grid points. t
herenumericallybythetrapezoidalrule,usingaverti-
We consider linear three-dimensional mountain
calgridsize(cid:8)z(cid:4)0.25km.Comparisonswithsolutions
wavesradiatedfromrealistictopographyintoarbitrary
using smaller (cid:8)z showed that this grid size was ad-
vertical profiles of winds and stability. The mountain
equate.
wavesarestationary,withzerofrequency((cid:3)(cid:4)0)rela-
The code uses a finite Fourier-series approximation
tive to the ground. For a horizontal background wind
to the inverse Fourier transform (2). In the cases pre-
U(cid:4)(U,V,0),theintrinsicfrequencyis(cid:3)ˆ (cid:4)(cid:3)(cid:2)k·U(cid:4)
sentedhere,512wavenumbervalueswerechosenfork
(cid:2)kU (cid:2) lV, where k (cid:4) (k, l, m) is the wavenumber
andl,correspondingtoaspatialgridof1024by1024in
vector. The background wind and buoyancy frequency
x and y, and a horizontal grid spacing of (cid:8)x (cid:4) (cid:8)y (cid:4)
N are assumed to depend on height but not on hori-
1 km.
zontal position or time.
Theraytracingperformedhereisbasedonagravity
b. Nonlinear orographic flow model
wave dispersion relation of the form
To assess more rigorously the accuracy of the Fou-
(cid:1)ˆ (cid:4)k N(cid:2)(cid:5)k2(cid:6)m2(cid:7)1(cid:2)2, (cid:5)1(cid:7) rier-ray solutions to follow, we also performed some
h h
companionsimulationsusingafullynonlinearnumeri-
where k (cid:4) (k2 (cid:6) l2)1/2. We ignore the effects of the cal model. The model in question solves the incom-
h
earth’srotationandcompressibilityin(1)forsimplicity: pressible nonlinear Navier–Stokes equations over to-
they are included in other versions of the code. pographyusingtheLipps–Hemleranelasticapproxima-
We define w˜(k, l, z, t) to be the ray solution in the tion(LippsandHemler1982;NanceandDurran1994).
2834 MONTHLY WEATHER REVIEW VOLUME134
The model uses terrain-following coordinates (Gal-
Chen and Somerville 1975), a centered second-order
spatial discretization, and a modified leapfrog time-
steppingscheme(Rees1988).Itwasrunhereonastag-
geredArakawaCgridof256pointsineachhorizontal
directionand32pointsinthevertical,withagridspac-
ing of 1 km in all directions and a time step of 4 s. A
free-slip (frictionless) lower boundary condition was
used.Toabsorbwavesatheights(cid:4)20km,weimposed
Rayleighdampingwitharatecoefficientthatincreased
linearlyfromzeroat20kmaltitudeto410(cid:2)3s(cid:2)1atthe
32-km upper boundary. To minimize reflections from
the lateral boundaries, a radiative scheme was used
(Miranda and James 1992) as well as some linearly in-
creasingviscousdampingwithina10-km-wideregionat
each side boundary. Away from these upper and side
boundaries,theonlydiabatictermswereaRichardson-
number-dependent first-order turbulent closure
scheme(Lilly1962)andasmallamountoffourth-order
diffusion to suppress grid-scale noise (hyperviscosity
coefficient of 107 m4s(cid:2)1).
c. Topography
Topographic elevations h(x, y) for Jan Mayen were
obtained from the United States Geological Survey
(USGS) GTOPO30 database. This global dataset of
digital terrain elevation has 30 arc s resolution, corre-
sponding roughly to 1-km spatial resolution, which we
interpolated linearly to our horizontal grid spacing of
1(cid:9)1km2usingDelaunaytriangulationandfullspheri-
cal to Cartesian transformations. This model topogra- FIG.2.Topographicelevationcontoursh(x,y)forJanMayen.
phyforJanMayenisplottedinFig.2aandcanbeused (a) The unsmoothed topography interpolated to 1 km (cid:9) 1 km
in the 1 km (cid:9) 1 km Fourier-ray model runs. resolution (as in Fig. 1). (b) The topography after five-point
For the 1 km (cid:9) 1 km Lipps–Hemler model runs, smoothing. The contour interval is 100 m, and the maximum
heightofthesmallerpeaktothelowerleftintheplotsis567m
however, this 1 km (cid:9) 1 km topography must be
(unsmoothed)and359m(smoothed).
smoothed to reduce the potential for unphysical four-
point gridpoint noise in the simulations (see, e.g.,
ingsatellite.Ithassixchannels:threethermalinfrared
DaviesandBrown2001).Weachievethisusingatwo-
(IR) channels and three other channels in the visible
dimensionalfive-pointrunningaverage,andtheresults
and near IR. The system acquires radiances with a
are shown in Fig. 2b. In the Fourier-ray model runs
20.32-cm-diameter telescope that scans cross track us-
shown here we also use this smoothed topography to
ing a continuously rotating mirror. The telescope’s in-
facilitate more direct comparisons with the Lipps–
stantaneous field of view (IFOV) is 0.0745°, corre-
Hemler model output.
sponding to surface footprint diameters across track
and along track of 1.1 km (cid:9) 1.1 km at nadir and 6.2
3. Observational data km (cid:9) 2.3 km at the far off-nadir positions. For each
scan,2048samplesareacquiredatoff-nadiranglesbe-
a. Advanced Very High Resolution Radiometer
tween(cid:10)55.37°crosstrackofthesubsatellitepoint,cor-
Version 3
responding to a total horizontal swath distance at the
The Advanced Very High Resolution Radiometer surface of (cid:1)2900 km. For further technical details, see
Version 3 (AVHRR-3) is a cross-scanning passive ra- section 4.1.1 of Kidder and Vonder Haar (1995) and
diometer, first deployed on the National Oceanic and section3.1andappendixJ.1ofGoodrumetal.(2000).
Atmospheric Administration (NOAA-15) polar-orbit- This intrinsic data resolution, known as local area
OCTOBER2006 ECKERMANN ET AL. 2835
coverage(LAC),istoodensetobecontinuouslystored 4. Jan Mayen wave clouds of 25 January 2000
and telemetered to ground stations. Thus, LAC data
a. AVHRR-3 observations
can only be received at certain scheduled times. Con-
tinuous monitoring at all other times is provided by Figure 3 plots a chronological sequence of selected
global area coverage (GAC) data, which are onboard AVHRR-3channel-5((cid:1)11.5–12.5(cid:11)m)radianceson25
averages of a reduced subset of the raw LAC data as January 2000. The data have been reinterpolated to
describedinsection10.2.1ofKidderandVonderHaar Cartesian coordinates (x being east–west), with the is-
(1995) and section 3.1.3.2 of Goodrum et al. (2000). landofJanMayencenteredatx(cid:4)y(cid:4)0oneachmap
SurfacefootprintdiametersforGACdataare(cid:1)4(cid:9)3.3 anditscoastlineplottedineachpanel.Weuseonlythe
km2 at nadir. thermalIRdatasinceJanMayenisinpolarnightatthis
Datafromeachchannelareconvertedonboardinto time of year.
10-bitbinaryearthscenecountsC priortobeingtele- At (cid:1)1140 UTC, Fig. 3a shows that the island was
E
metered to ground stations. Earth scene radiances R obscuredbyclouddecks.Around3hlaterat1500UTC
E
arederivedusingthenonlinearradiancecorrectionfor- these clouds have been advected to the east to reveal
evidence of mountain-wave banding of lower-level
mula,
clouds: at this time we have both conventional GAC
data (Fig. 3b) and high-resolution LAC data (Fig. 3c).
R (cid:4)a (cid:6)a C (cid:6)a C2, (cid:5)4(cid:7)
E 0 1 E 2 E TheLACimageshowscloudbandingsuperficiallycon-
sistent with a purely diverging three-dimensional ship
where a0, a1, and a2 are regression coefficients derived mountain-wave pattern (Sharman and Wurtele 1983)
from prelaunch calibration data (Walton et al. 1998). emanatingfromJanMayen,thoughonlyone“arm”of
thisV-shapedpatternisfullyvisible,theotherstillbe-
ing partially obscured by overlying cloud decks.
b. Radiosonde data
Around90minlaterat1630UTC,GACradiancesin
AmeteorologicalstationonJanMayenlaunchesra- Fig. 3d again show a diverging wavelike cloud pattern.
diosondesat0000and1200UTCeachday:seeFig.1of Though this is a lower-resolution image than the LAC
Gjevik and Marthinsen (1978) for its precise location imageinFig.3c,itprovidesourleast-obscuredimageof
on the island. Here we use winds and temperatures thefullwavepattern.Infactthiswavepatternextends
acquired from the 1200 UTC sounding on 25 January farther downstream in this image than might be sug-
2000 in our model simulations, which we reinterpolate gested by the limited domain plotted in Fig. 3d.
onto a high vertical resolution grid, vertically smooth Figure 3e plots another AVHRR-3 GAC image ac-
usingarunningaverageof2-kmwidth,thenreinterpo- quired roughly 2 h later at (cid:1)1820 UTC. Upper-level
late again onto the models’ vertical grids. While we cloud decks have moved in and partially obscured the
assume here that these data approximate the true ver- wavepattern.Nonetheless,westillseeevidenceofthe
ticalprofileovertheislandatthistime,theactualbal- lower(southward)armofthedivergingwavepatternin
loontrajectoryisoblique:givenatypicalascentvelocity the bottom half of the image.
of 5 ms(cid:2)1 (e.g., Lane et al. 2000), passive advection Figure3fandasequenceoflaterimages(notshown)
calculations based on radiosonde winds for this day donotshowevidenceofbandedcloudsdownstreamof
place the balloon (cid:1)100 km downstream by the time it Jan Mayen. While some, like Fig. 3f, are heavily im-
reached 10-km altitude. pacted by obscuring cloud layers, the weight of evi-
dencefromtheseimagessuggeststhatthebandedwave
clouds have disappeared at these later times.
c. Meteorological analyses
Thus, from the AVHRR-3 channel-5 IR imagery in
Toprovidesomecrossvalidationforthemodelruns, Fig. 3, we deduce an approximate 6-h duration of this
we also use profiles of winds and temperatures at the apparentJanMayenwaveevent,lastingfrom(cid:1)1200to
closestgridpointtoJanMayenfromthe12-hourlyMet 1800 UTC. The role of high-cloud decks in obscuring
Office (UKMO) 3.75° (cid:9) 2.5° analyses (Swinbank and the wave banding patterns also indicates that the
O’Neill 1994). To define surface weather patterns, we banded wave clouds occur in the lower or midtropo-
use6-hourlyanalyzedmeansealevelpressures(MSLP) sphere.
from the National Centers for Environmental Predic-
b. Synoptic surface meteorology
tion–National Center for Atmospheric Research
(NCEP–NCAR) 2.5° (cid:9) 2.5° reanalyses (Kalnay et al. Figure 4 plots 6-hourly NCEP–NCAR reanalyzed
1996). MSLPinabroadregioncenteredoverJanMayenfrom
2836 MONTHLY WEATHER REVIEW VOLUME134
FIG.3.(a)–(f)ChronologicaltimesequenceofAVHRR-3channel-5earthsceneradianceimageson25Jan2000centeredatx(cid:4)
y(cid:4)0overJanMayen,whosecoastlineisoutlinedineachpanel.AllimagesareGACdata,exceptfor(c),whichisLACdata.
OCTOBER2006 ECKERMANN ET AL. 2837
FIG.4.MSLP(inhPa)derivedfromNCEP–NCARreanalysisfieldsat(a)0600,(b)1200,(c)1800UTC25Jan2000,and(d)0000
UTC26Jan2000.JanMayenisplottedasthetinyislandcoastlinenearthecenterofeachmapat71°N,8°W.
0600 UTC on 25 January to 0000 UTC on 26 January. weaken and be replaced by weaker northerly flow as
Weseerapideastwardpassageofacompactlowpres- the low moves farther eastward. This is confirmed by
sure cell across the domain. As the core of this low the isobars at 0000 UTC in Fig. 4d.
passed to the north of Jan Mayen at (cid:1)1200 UTC, Fig. Thus, the appearance of cloud banding from 1200
4bshowsthatitproducedenhancedsurfacegeostrophic to 1800 UTC in the AVHRR-3 radiances in Fig. 3
westerlies across Mount Beerenberg. These surface correlateswithaperiodofenhancedsurfacewesterlies
westerliespersistoverJanMayenat1800UTC,though across Mount Beerenberg (and hence enhanced po-
theisobarsinFig.4crevealthatthecoreofthelowhas tential for mountain-wave forcing) accompanying the
nowpassedwelltotheeastoftheisland,andthatsur- eastward passage of a polar low to the north of Jan
facewesterlyflowacrossMountBeerenbergisaboutto Mayen.
2838 MONTHLY WEATHER REVIEW VOLUME134
FIG.5.HorizontalwindprofileoverJanMayenat1200UTC25Jan2000fromaroutine
radiosondesoundingfromtheisland(black)andfromtheUKMOanalyzedwindsforthisday
andtimeinitsnearest3.75°(cid:9)2.5°gridbox(gray).Solidlinesshowthree-dimensionalwind
profiles,dashedlinesshowvarioustwo-dimensionalprojections.Bothprofilesweresmoothed
byfirstinterpolatingtherawprofiledataontoahigher-resolutionregularheightgridandthen
smoothingusinga2-kmslidingverticalaverage.
c. Meteorological profiles over Jan Mayen at rameter is a two-dimensional term in which the hori-
1200 UTC zontal wavenumber vectors and the wind vector are
coaligned. For three-dimensional problems, a range of
Figure5plotsthethree-dimensionalhorizontalwind
angles for the horizontal wavenumber vector exist and
profile over Jan Mayen from the routine 1200 UTC
the wind vector can rotate with altitude, and thus no
radiosonde ascent on 25 January (solid curve), as well
unique Scorer parameter exists. Some insights can be
as the nearest gridbox 1200 UTC profile from the
gained, however, by studying a generalized form for
UKMO analysis. The radiosonde profiles verify the
three-dimensional problems,
presenceofstrongnear-westerlysurface-levelwindsin-
ferredfromFig.4b,withspeeds(cid:1)30ms(cid:2)1.Thesewind
speedsincreasewithaltitudetoajetmaximumof(cid:1)70 (cid:1)2(cid:5)z,(cid:5)(cid:7)(cid:4)N2(cid:5)z(cid:7)(cid:2) U˜zz , (cid:5)5(cid:7)
ms(cid:2)1 near 10-km altitude. This maximum is nearer 55 U˜ 2(cid:5)z(cid:7) U˜(cid:5)z(cid:7)
ms(cid:2)1 in the UKMO profile.
To produce mountain-wave activity so far down- whereN(z)isthebackgroundbuoyancyfrequencypro-
stream of Jan Mayen in Fig. 3, it is likely that these file, U˜(z) (cid:4) U (z) cos[(cid:12)(z) (cid:2) (cid:13)] is the profile of the
tot
waveswereverticallytrapped(e.g.,SimardandPeltier component of the wind vector U (cos (cid:12), sin (cid:12)) pro-
tot
1982).StronglyshearedwindprofileslikethoseinFig. jected along a given horizontal wavenumber vector’s
5 are one way to produce the vertical wave reflection direction (cid:13)(cid:4) arctan (l/k), U˜ is the curvature in this
zz
required for trapping. To assess this, we compute pro- projected component wind profile, and U (z) (cid:4)
tot
files of the Scorer parameter. The standard Scorer pa- [U2(z)(cid:6)V2(z)]1/2.Anequivalentexpressionisutilized