雷达测量的边界层饱和山区波振幅的影响

ORIGINALPAPER

Radarmeasurementoftheeffectofboundary-layersaturationonmountain-waveamplitude

RichardM.Worthington

Received:21September2008/Accepted:19June2009/Publishedonline:7July2009ÓSpringer-Verlag2009

AbstractMeso-Strato-Troposphereandweatherradarsareusedtoshowtheeffectofsaturatedairnearthegroundonmountainwavesinthetroposphereandlowerstrato-sphere,at52.4°N,4.0°W.Mountainwavesareobservedabovescatteredprecipitation;however,long-termobser-vationsconfirmherethatwaveamplitudeisreducedaboveextensiveprecipitation,aspredictedfromnumericalmod-els.Ceilometermeasurementsofaveragecloudbasenearthemountaintopssuggestthatsaturatedaircouldbereducingthegenerationofmountainwaves,inadditiontotrappingorabsorbingwaves.

1Introduction

Oneprocessinvolvedinorographicprecipitation(Banta1990;Roe2005;RotunnoandHouze2007)isitsinterac-tionwithmountainwaves.Mountain-waveamplitudeispredictedtobereducedabovesaturatedair(DurranandKlemp1982,1983;Richardetal.1987)orprecipitation

¨ngl2006).However,fallingthroughunsaturatedair(Za

therehavebeenfewlong-termmeasurementstocheckthisprediction,andreducedstabilityofsaturatedaircouldhaveoppositeeffects:allowingairflowoverinsteadofaroundmountains(Buzzietal.1998;RotunnoandFerretti2001);ordowndraftsinprecipitationcouldreduceflowseparationfrommountainsandforcelargeramplitudewavesabove(Corby1957,Sect.14,21).Mountainwavescanalsocause

R.M.Worthington(&)

InstituteofMathematicalandPhysicalSciences,UniversityofWales,Aberystwyth,UKe-mail:rmw092001@yahoo.com

variationsofprecipitationrate(Bruintjesetal.1994;Reinkingetal.2000;BradyandWaldstreicher2001;Gaffinetal.2003).

ThisstudyusesseveralyearsofdatafromweatherandMeso-Strato-Troposphere(MST)radar.Weatherradargivesanindicationofboundary-layersaturationcontinu-ously,overawidearea.DataarefromaC-bandnetworkoftheUKMetOffice(3-hourlyforJune–August1999,December1999–June2000,July2001–January2003,andquarter-hourlysinceFebruary2003),suppliedassurfaceprecipitationratewith393kmresolution,correctedforbrightband,anomalouspropagation,groundclutterandorographicenhancementbelowtheradarbeams(Harrisonetal.2000).

MSTradarisoneofthefewmethodstomeasurecon-tinuouslytheverticalwindvelocity,w;large-amplitudeslowlyvaryingwnotfromconvectionusuallyindicatesmountain-waveactivity.Dataarefromthe46.5MHzAb-erystwythveryhighfrequencyradar,located52.42°N,4.00°W.wismeasuredwithaverticalbeam(w0),ormeanofradialvelocitiesinsymmetricbeampairs6°off-vertical(w6).Heightresolutionis300mandminimumheight1.7km.MSTradarechoesfromprecipitationinsteadofclearairinthelowestfewkilometresareavoidedusingechopeaktracking,outlierremoval,andlimitsonvertical-beamspectralwidth.Prichardetal.(1995)andWor-thingtonandThomas(1996)showearliermeasurementsofmountainwavesusingthesameMSTradar.Cloud-baseheightisalsomeasuredevery1minattheMSTradarsiteusingaVaisalaLD40ceilometer.

Section2showstwocasestudiesontheoccurrenceofmountainwavesabovedifferenttypesofprecipitation.Section3checksiftherearesimilarresultsfromlargeramountsofdata.Section4discussespossibleexplanations,andotherfactorsaffectingtheresults.

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Fig.1Horizontalmapsofsurfaceprecipitationratefromweatherradarfortwocasestudies,(a–d)23February2002and(e–h)20September2004.TheMSTradarlocation(52.42°N,4.00°W)ismarked9,ina1009100km2arearotatedtopointupwindintheboundary-layerwinddirection(Sect.3),asusedforFig.3.aSmoothedcontoursoflandheight200m(thinner,innercontours400m)abovesealevel,andelocationsofsurfaceweatherstationsR.M.Worthington

(a)(b)(c)(d)(e)(f)(g)(h)2Casestudiesofmountainwaveresponseabovedifferentprecipitationtypes2.1Convectiveprecipitationlines,23February2002Figures1a–dand2ashowalong-windprecipitationandcloudlinesabovemountains,explainableasconvectiverolls(BrowningandBryant1975;Kirshbaumetal.2007).Abovetheconvectiverolls,Fig.2bshowsbandsofupwardanddownwardw,tensofcentimetrespersecond,forover15h.Non-zerowinthefreetroposphereabovemountainsisoftenassociatedwithweathersystemsandthunderstorms¨steretal.1998).However,Fig.2bshowsavertical(Ru

wavelengthofseveralkilometres,over[360°phase,withthewavelengthdecreasinginthestratosphere,whicharecharacteristicsofverticallypropagatingmountainwaves.Therearemountainsfor*100kmhorizontaldistanceina180°sectortonorth–east–southoftheMSTradarlocation,withmountaintops*15kmeastoftheradarasshowninFig.1a.Foranywinddirectioninthenorth–west–southsector,theradarisatleast5kmdownwindofthecoastwithlowhillsreaching[100mabovesealevel,startingnearthecoast(e.g.Fig.1ofWorthington1999b).Thebackgroundwindisnorth-westerlyon23February2002,*11ms-1atthesurfaceto[60ms-1at9kmheight.1TheMSTradaristhereforeontheupwindslope,andnot

1locatedcompletelyupwindofthemountainsandmountainwaves.

Tocheckifverticalwavelengthkzofwisreasonableformountainwaves,thiscanbeestimatedasine.g.Prichardetal.(1995,Fig.7)andWorthingtonetal.(2001,Fig.8f)usingaWentzel-Kramer-Brillouin-Jefferiesmodel.Thecomparisonisformountainwavesthatareoccurringdespite,orbeforeandafter,precipitationevents.wataheighth,

0h1Zpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

wðhÞ/sin@N2ðzÞ=U2ðzÞÀk2dzþ/A

0

Height-timeplotsofhorizontalwindvectorsareavailableonthe

datasetwebsitehttp://badc.nerc.ac.uk/browse/badc/mst/plots/st-mode/2002/02/.

¨isa¨la¨frequency,U(z)wherezisheight,N(z)Brunt-Va

horizontalwindspeed,khorizontalwavenumber,and/aphaseoffset.Foruntrappedmountainwavesreachingthestratosphere,thehydrostaticassumptioncanbeused(Shutts1992,Fig.9)withk=0.U(z)andtropopauseheightof*9kmaremeasuredbyMSTradar;typicallyN*0.01s-1forthetroposphereand0.02s-1forthelowerstratosphere;and/isadjustedsothephaseofw(h)ispatthelowestheight,*9km,whereaprofileofwtime-averaged0–15hfromFig.2bcrosseszero,goingnegative.Heightseparationsbetweenlevelswherewcrosseszerogivemeasuredand(predicted)kzof10(12)kmfor*9–14kmheight,decreasingto7(6)kmfor*14–17kmheight,asexpectedbecauseofdecreasingwindspeedabovethejetstreamwindmaximum.Zero-crossinglevelsaremarkedonFig.2b.Anotherprobablezerocrossinginthelowertroposphereisbelowtheheightrangemeasured

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Radarmeasurementoftheeffectofboundary-layersaturationFig.2aNOAA–16AVHRR(advancedveryhighresolution(a)radiometer)channel2imageforthesameareaasFig.1.b,cHeight–timeplotsfromMSTradarofverticalwindwmeasuredusingaverticalradarbeam.Timeisinhoursafter0000UTC,andpositivewisupward.Dotsbelow(b,c)aremeasurementtimesofFigs.1a–h,2a.Horizontallinesshowaveragezero-crossingheightsfortimeintervalsmentionedinSects.2.1and2.2byMSTradar.UsingNfrommodeltemperatureprofilesathttp://www.ready.noaa.gov/ready/amet.htmlgenerallygivessimilarresults.Figure2bappearsconsistentwithmountainwaves,asfoundinothereventsandaboveotherprecipitationformssuchasconvectivecells.2.2Stratiformorographicprecipitation,

20September2004

Figures1e–hshowweatherradarimagesofaprecipitationbandbeforeacoldfront.ItsfrontedgereachestheMSTradar*0000UTC,anditcrossestheMSTradarby*0330UTC,followedbymorepatchyprecipitation.Precipitationrateincreasesoverthemountainsalthoughthiscouldbeoccurringbelowtheweatherradarbeams(Harrisonetal.2000).Surfacewindis*10ms-1south-westerly,andMSTradarmeasurescontinuouswesterlywindinthelowertroposphereastheprecipitationbandmovesover.

Figure2cshowsupwardanddownwardwalternatingwithheightuntil*0–2hbefore0000UTC,andagainafter*0300–0400UTC.AsinSect.2.1,measuredand(pre-dicted)kzaresimilar:18(19)and7(7)kmat6–2hbefore0000UTC;17(20)and6(6)kmat0400–0600UTC;25(23)and7(8)kmat0600–1200UTC.Tropopauseheightis*11.5km,andmaximumwindspeedis*55ms-1at9–12kmheight.Thesmallerkzvaluesareinthelowerstratosphere,whereNisincreased.Smallregionsofdownwardwbelow4kmat0100UTCareprecipitationechoinsteadofclear-airecho,withinabackgroundofupwardtroposphericwduringprecipitation(GageandNastrom1985).However,thelarge-scaleoscillationsofwwithheightareabsentwhiletheprecipitationbandisabovetheMSTradar.Theregionofmountain-waveactivitycouldhypotheticallyhaveshiftedslightlydownwindoftheMSTradarat*0000–0300UTC;or,Fig.2ccouldbeshowingalullinmountain-waveactivityinthetroposphereandlowerstratosphere,aboveextensiveprecipitation.

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(b)(c)3Climatologyofmountain-waveamplitudeaboveprecipitationLong-termMSTandweatherradardataareusednexttocheckifmountain-waveamplitudeisgenerallyreducedaboveextensiveprecipitation,assuggestedfromSect.2.2.Over110,000weatherradarimagesduringJune1999–February2007arecategorisedfor‘percentageprecipita-tion’—thepercentageofpixelswithnon-zeroprecipitationrateina1009100km2area,aroundandupwindoftheMSTradarasinFig.1,tocoverlikelymountain-wavesourceregions.Percentageprecipitation(e.g.dry,scatteredorextensiveprecipitation)isusedratherthanprecipitationrates,whichvarywithboundary-layerwindspeed(Hilletal.1981).The1009100km2ispositionedwiththeMSTradar10kminfromthecentreofoneedgetoincludethevicinityoftheradar,andthenrotatedabouttheradarlocationtopointupwindintheboundary-layerwinddirection(estimatedfrommeansurfacewinddirectionplus15°clockwise).Resultsaresimilarusingafixed1009100km2centredontheMSTradar.Percentageprecipitationis19,28,15,14%forFig.1a–dand77,96,96,51%forFig.1e–h.

Magnitudeofverticalwind,|w|,isusedasanindicatorofmountain-waveactivity(Ecklundetal.1982;Prichard

etal.1995;Cacciaetal.1997;Re

´chouetal.1999).Con-vectionandmergedclear-air/precipitationechoesareidentifiedforremovalbasedonvelocityoutliers,orverti-cal-beamspectralwidth(correctedforbeambroadening)[1ms-1.Toreduceeffectsofshort-periodgravitywaves,wprofilesaretime-averagedfor30mincentredonweatherradartimes.

Theaveragesurfacewindvectorisobtainedfromupto17synopticweatherstationsaroundtheMSTradar(Fig.1e),givingthesynopticsurfacewindacrossthemountainsforhigherwindspeedscausingmountainwaves.Hourlysurfacewindsareinterpolatedlinearlyto

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32R.M.Worthington

measurementtimesofweatherradar.Horizontalwindat*2km(1.7–2.3km)heightfromMSTradarisalsoused,althoughthisisapointmeasurement,oftenwithinthemountain-wavepatternwithpossiblecorrelationtothewvariations.Figure3displaysresultsbinnedinto36°and1ms-1(or2.5ms-1)intervals,giving10910arrays,for0–25,25–50,50–75,75–100%precipitation.SomeregionsofinterestinFig.3areneardatagapscausedbylowprecipitationfore.g.northerlytoeasterlywinddirections.However,thedataforeachshadedpixelareindependentofotherpixels.Heights1.7–2.3,4–7and12–15kmarechosentocontaindifferenttrappedanduntrappedmountain-wavecomponents,withvarioushori-zontalandverticalwavelengths,andforhighsignal-noiseratiofromMSTradar.

Fig.3Vertical-windmagnitudejwjfromMSTradarata–h1.7–2.3km,i–m4–7km,andn–r12–15kmheight,asafunctionofhorizontalwindspeedanddirection,andpercentageprecipitation(Sect.3)0–25%,25–50%,50–75%and75–100%.a–d,i–rUseaveragesurfacewindfromsitesinFig.1e,and(e–h)usewindat*2kmheightfromMSTradar.Winddirectionsareindegreesclockwisefromnorth(0°,90°,180°,270°windfromnorth,east,south,west).Pixelswithnodataorcontaininglessthanthreemeasurementsaremarked.Increaseofjwjwithwindspeedisgreatestintheareashownwithdottedlines,whentheMSTradarisdownwindofhighergroundForsurfacewindspeedsnearzero,jwjincreasesslightlyfromFig.3atod,whichcouldbecausedbye.g.someremainingconvection,precipitationechoes,orothergrav-itywavesindisturbed,wetweather.However,jwjinFig.3ashowsmuchmoreincreaseasafunctionofwindspeed,forallwinddirections.Thegreatestincreaseisfor*300°–180°wind,markedwithdottedlines,forwhichtherearehighermountainslocateddirectlyupwind(Prichardetal.1995)orupwindandlaterally(VosperandWorthington2002)fromtheMSTradar.

Aspercentageprecipitationincreases,theincreaseofjwjwithwindspeedbecomesless,e.g.comparingmarkedregionsofFig.3a,d.Resultsaresimilarusing:jwjfromsymmetric6°beams,jw6j;insteadofverticalbeam,jw0j;(MSTradarsignal-noiseratioisoftenhigherforw0than

(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(m)(n)(p)(q)(r)123

Radarmeasurementoftheeffectofboundary-layersaturation33

w6,however,w0couldunderreadmountain-waveampli-tude(Worthingtonetal.2001),andalsofordifferenttimeofdayoryear.Stronghorizontalwindspeedshigherinthetropospherecancausemountain-wavetrapping,butwindspeedsaresimilarwhenplottedinsteadofwinFig.3.InFig.3n,|w|islessfor0–180°windthaninFig.3a,e,i,consistentwithremovalofmountainwavesbycriticallayers,aseasterlywindoftenrotatesorpassesnearzerobetweengroundand12–15kmheight(WorthingtonandThomas1996,Figs.10,11).Overall,thelong-termmea-surementsinFig.3indicatereducedmountain-waveamplitudeaboveasaturatedboundarylayer,assuggestedinthecasestudyofSect.2.2,showninFig.2c.

4Discussion

VariationsofjwjwithpercentageprecipitationinFig.3areassumedtorefertomountainwavesandnotothergravitywaves.Figure4,therefore,checksanotherwavecharac-teristic,horizontalwavevectorazimuthmeasuredbyMSTradar(Worthington1999a);waveazimuthnear90°tothewindwouldbeinconsistentwithmountainwavesbecauseofcriticallayerabsorption.Measurementsarefor5–15kmheightand30mintimeintervalswithjwj[0:05msÀ1andazimutherror\\25°.InFig.4c,arandom23%ofdatapointsareplottedsothatthenumberofpointsfor0–10%precipitationisthesameasinFig.4a,b;then,thedecreasingnumberofpointsaspercentageprecipitationincreasesinFig.4a,bcanbecompareddirectlywithFig.4c.DespitethisdecreaseinFig.4a,b,theaveragehorizontalwavevectorremainsbetweenthesurfaceand2-kmwinddirections,consistentwithmountainwaves(Worthington1999b,2006).

Effectsofboundary-layersaturationcoulddependalsoonstability.Precipitationtypecanbecategorisedasstrat-iformorconvectivefromtheformofweatherradarechoes(Steineretal.1995;YuterandHouze1997;Waltherand

Bennartz2006).Also,correlationofprecipitationdistri-butiontolandheightcouldberelevant,assomestandingwavescanbecausedbyfixedvariationsofboundary-layerstructure(MalkusandStern1953;Mauritsenetal.2005;ColleandYuter2007).Worthington(2002,2006)showsexampleswherefair-weatherconvectioncanvaryinphaseandevencontributetotheforcingofmountainwaves.However,jwjappearstobereducedgenerally,forcon-vective,stratiform,orographicandnon-orographiccate-goriesofweather-radardatawith[50%precipitation(notshown).

MechanismsfortheeffectofsaturatedaironmountainwavesincludeamodifiedScorerparameter(l2)profilesothat(DurranandKlemp1982;DoyleandSmith2003),(a)wavesaremoreverticallypropagatingandwaveamplitudeincreasesinthetroposphere;or(b)saturatedaircanincreasewavetrappinginunsaturatedairbelow,orbeaneutral‘sponge’layerabsorbingwaves;or(c)condition-allyunstableairnearthegroundcanresultinconvectioninsteadofwaves.Theheightofsaturatedairabovemountainscouldinfluencewhether(b)or(c)explainsreducedmountain-waveamplitude.Clouddowntothemountainsurfacewouldsuggest(c)insteadof(b);how-ever,weatherradarcouldbemeasuringprecipitationfall-ingthroughunsaturatedairwithincreasedl2belowcloud.SurfacehumidityattheMSTradarsite,50mabovesealevel,isunsaturatedat81,88,91,93%forFig.1e–h,andonaverage79,82,84,85%forFig.3a–d,whereasmountaintopsafewhundredmetresabovesealevelcanbewithinprecipitatingcloud.

Cloud-baseheightcanbecomparedmorequantitativelytomountainheightusingaceilometerattheMSTradarsitesinceAugust2005.Thisreplacessomeheightinformationmissingfromtheavailableweatherradardata,andshowsapossibleheightregionforthemechanismreducingjwj;althoughnotthemechanismitself.Figure5showsdistri-butionsoflowestcloudbaseheightfor0–25,25–50,50–75,75–100%precipitationcategoriesasinFig.3.Also,no

(a)(b)(c)Fig.4DifferencesofmountainwaveandwindazimuthsmeasuredbyMSTradarasafunctionofpercentageprecipitation.Greydotsshowmediandifferencesfor0–10,10–20,…,90–100%.Waveazimuthreferstohorizontalwavevectormeasuredclockwisefromnorthandpointingupwind123

34Fig.5Heightdistributionoflowestcloudbase(notcloudheight),measuredAugust2005–February2007byceilometerco-locatedwiththeMSTradar,countedin100mheightintervalsandsmoothedwitha3-pointrunningmean;also,distributionoflandheightina1509150km2areacentredontheMSTradar.Withincreasingpercentageprecipitation,cloudbasedistributionshiftsdownwardtonearorbelowthemountaintopscloudisreportedfor33,5,1,0%ofmeasurementsinthesecategories.Cloudbaseheightfallsto*500masper-centageprecipitationincreases,sotheheightgapbetweenmountainsandsaturatedairmaybesmallenoughforprocess(c),althoughsomegravitywavescanbetrappedinheightintervalsofonlytensofmetres(Duynkerke1991).Mountain-waveamplitudecanbecomparedalsotocloudamountforanyeffectofreducedstabilityinsatu-ratedairwithoutprecipitation.Figure3acanbedividedintodatawithcloudandnocloudreportedfromceilometer;however,theresultsaresimilar,maybebecauseofmea-suringthincloudlayerswithlesseffectonmountainwaves.

5Conclusions

Mountainwavesareobservedinandabovepatchypre-cipitationusingMSTradar.However,thewaveamplitudeisreducedaboveextensiveprecipitation—despitepossiblemaskingeffectsofconvection,convectionwaves,synopticverticalmotion,orprecipitationechoesincreasingthemeasuredverticalvelocities.

Reducedmountain-waveamplitudeisconsistentwithpredictionsofnumericalmodels,e.g.DurranandKlemp

(1982),Za

¨ngl(2006),althoughwithoutprovingwhichofthepossiblemechanismsareoccurring.

Cloudbasesaretypicallynearthemountaintopsinextensiveprecipitation,soeffectsofsaturatedairon

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R.M.Worthington

mountain-waveamplitudecouldoccurat,notonlyabove,thewavelaunchingheight.

AcknowledgmentsWeatherradarandsurfacewinddataarefromtheMetOfficeandBritishAtmosphericDataCentre;NERCMSTradarandceilometerdatafromBADC;andtheNOAAAVHRRimagefromtheNERCSatelliteReceivingStation,DundeeUniversity.

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