Joint Variations of Temperature and Water Vapor ... - Semantic Scholar
GEOPHYSICAL RESEARCH LETTERS, VOL. 28, NO. 13, PAGES 2613-2616, JULY 1, 2001
Joint variations of temperature and water vapor over the midlatitude
continents
DouglasG. Cripe andDavidA. Randall Department of Atmospheric Science,ColoradoStateUniversity,FortCollins,Colorado
Abstract. We haveusedwarm-season datafromtheAtmospheric stateof the atmosphere. The approximationis usefulwhen the RadiationMeasurement (ARM) Program's Southern GreatPlains adjustment time scalefor the convection is significantly shorter siteto investigate thejointvariabilityof thetemperature andmois- thanthe time scaleon whichthe atmospheric stateis evolving. turesoundings, andtheirrelationship to thevariabilityof thegen- ObviouslyQE is favoredif the atmospheric stateis evolving eralizedconvectiveavailablepotentialenergy(GCAPE). The slowly, and converselythe QE approximationbreaksdown for actualtemperature andhumiditysoundings varytogether in sucha rapidlyevolvingatmosphericstates. way as to producevariationsof the GCAPE which are far smaller As discussed by AS andRandallet al. (1997), a key prediction thanthosewhichwouldoccurif therelativehumidityvariedwhile of the QE hypothesis is thattheobservedCAPE shouldbe "small" thetemperature soundingwasfixed,or viceversa. comparedto that whichwouldoccurif convectioncouldsomehow be suppressed so that non-convective processes couldhavetheir way with thesounding. The key pointis that,according to theQE 1. Introduction hypothesis, the convection consumes the CAPE (almost)as rapidly as non-convective processesgenerateCAPE. Even when Cumulusconvection converts thepotentialenergyof a dry-stat- thereis a steadysupplyof CAPE throughsurfaceheatingand ically-stable meanstateintothekineticenergyof theconvection. evaporation, large-scale lifting,etc.,theCAPE actuallyseenin the In orderfor sucha conversion to be possible,a portionof the sounding neverincreases verymuch(according to theQE hypothpotentialenergyof themeanstatemustbe "available,"i.e. convec- esis),because theconvection responds veryquicklyandconsumes tiveavailable potential energy(CAPE)mustexist;a sounding for theCAPE asfastasit is generated. It is thispredicted"smallness" whichtheCAPEispositiveis saidto beconditionally unstable. of theCAPEthatis usedto testtheQE hypothesis in thepresent Broadlyspeaking, conditionally unstable soundings arechar- study. acterizedby high moisturecontents,necessarily concentrated at The CAPE is a functionalof the temperature andwatervapor lower levels,and by relativelysteep(but dry staticallystable) soundings. Broadlyspeaking,the CAPE can be increasedby lapserates.A givensounding canbe alestabilized, in thesenseof steepening thelapserateof temperature, and/orby increasing the conditionalinstability,by increasingits moisturecontent,by watervaporcontentof the column.Accordingto the QE hypothewarmingat low levels,or by coolingaloft.Convection feedsback sis,thetemperature andwatervaporsoundings changewith time by drying the columnthroughprecipitation, warmingaloft in sucha way thattheCAPE is relativelyinvariant.For example, throughlatentheatreleaseandupwardenergytransport, andcool- the QE hypothesis suggests that a steepening of the lapserate ing nearthesurfaceasa resultof convective-scale, precipitation- shouldbe accompanied by a dryingof thecolumn.It followsthat drivendowndraftsand the attendantevaporation of rainwater. oneway to testthe QE hypothesisagainstobservations is to assess Throughthesefeedbacks, convection tendsto reducethe CAPE, the extentto which changesin the temperatureand moisture by converting it intoconvective kineticenergy,whichis thendis- soundings producemutuallycancelling changes in theCAPE. sipatedand/orradiatedawayin theformof gravitywaves. Most studiesof thethermodynamic structure of the convective Manabeet al, (1965), Arakawa(1969), andArakawaandSchu- atmosphere havebeenbasedon tropicaloceanicsoundings. This bert(1974;hereafter AS) proposed thattheintensity of convection is understandable, becausethe widespread convectionover the is approximately that requiredto consumethe CAPE (or more tropicaloceansis veryimportantfor thegeneralcirculation of the precisely thecloudworkfunctions associated witha spectrum of atmosphere. Nevertheless, thereis muchto be gainedby investicloudtypes)asrapidlyasit is generated by non-convective pro- gatingtheproperties of conditionally unstable soundings overthe cesses(alsoseeEmanuelet al., 1994,andRandallet al., 1997). midlatitudecontinents,and this is especiallytrue for studies Manylarge-scale atmospheric circulation modelstodayusecumu- aimedat evaluatingthe QE hypothesis. Both temperature and
lus parameterizations in whichthe strengthof the convectivemoisture
are much more variable over the midlatitude continents
activityis determinedby makinguse of someversionof this thantheyare overthe tropicaloceans,permitting, in principle, "CAPE quasiequilibrium" hypothesis,hereaftercalled the QE muchlargervariationsof the CAPE. The reasonsfor thisarewell hypothesis. Becausethe QE hypothesis canbe usedto determine established. Most obviously,the daytimesurfacesensibleand the strengthof the convection,it is often describedas the "clo- latentheatfluxesoverthecontinents aremuchstronger thanthose sure"of theconvection parameterization. over the oceans. In addition, large-scale-dynamical effects As explained by AS, theQE closureis expected to be a useful stronglylimit temperature excursions in the tropics,relativeto approximation whenthe statisticalpropertiesof the convective middle latitudes.In the tropics,the smallnessof the Coriolis cloudfield can respondor "adjust"rapidlyto variationsin the parameter leadsto veryflat temperature andsurfacepressure distributions (Charney,1963).The largerCoriolisparameter of middle latitudespermitsthe sharperhorizontalpressure gradients Copyright2001 by theAmericanGeophysical Union. associated with moredramatichorizontaltemperature gradients. Paper number2001GL012909 As a result,thehorizontal advection of temperature playsa much 0094-8276/01/2001 GL012909505.00 strongerrole in midlatitudes thanit doesin the tropics,andthe 2613
temporalvariabilityof temperatureis muchlargerin midlatitudes thanin the tropics.Moisturefluctuationsalsotendto be stronger in midlatitudes.Examplesof the tendenciesof temperatureand moisturedueto horizontaladvectionare shownin Fig. 3 of Randall andCripe(1999), for bothmidlatitudeandtropicalcases.The contrastbetweenthetropicsandmiddlelatitudesis very apparent in their figure. In summary,the convectiveregimesof the midlatitudecontinentsin the warm seasonprovidevery usefulopportunities for testingthe QE hypothesis. Theseopportunities haverarely been takenadvantage of, up to now.Kao andOgura(1987), Grell et al. (1991), and Wu (1993) reportedobservationaltestsof the QE hypothesis with midlatitudecontinentaldata.All of thesestudies providedsupportfor theQE hypothesis, butmuchfurtherinvestigationis needed. In this paperwe reportthe use of warm-season data from the OklahomaARM site (ARM is the AtmosphericRadiationMeasurements programsponsored by the U.S. Departmentof Energy) to test the QE hypothesisin a new way. To date,mostobservationaltestsof the QE hypothesis, whetherin thetropicsor midlatitudes,have involvedcomplexanalysesof the tendencies of the CAPE dueto variousprocesses, notablyincludingthe difficult-toobservelarge-scaleverticalmotion.In contrast,the newapproach reportedhereis very simple,andwe hopethatits simplicityadds to its utility.A preliminarytestof this approachwasreportedby Randallet al. (1997; seetheir Fig. 2). Section2 of this paperprovidessomebackground on the versionof the CAPE usedin our study.Section3 describesthe data used.Section4 presentsour results.Section5 givesa concluding
3.Data
We haveuseddatafrom the AtmosphericRadiationMeasurement(ARM) SouthernGreatPlains(SGP) site,locatedin northcentralOklahomaand south-central Kansas.Data are gathered dailyat the SGPsiteby variousautomated instruments andsensors.In addition,severalintensiveobservation periods(lOPs) are heldeachyear,eachlastingthreeto four weeks.Duringan IOP, radiosondes are launchedevery3 hours,from a locationat the centerof the site and alsofrom 4 positionsaroundits perimeter (seeFigure1 in thepaperof RandallandCripe,1999).Thesoundingsusedin thisstudywerecollectedduringsevenARM lOPs: April 1995, July 1995, April 1996, July 1996, July 1997, May 1998, and July 1999. Precipitationdata for each lOP were obtainedfrom the OklahomaState Universitymesonetsystem. RandallandCripe (1999) andGhanet al. (2000) presentfurther discussion of the ARM SGP data.
4. GCAPE variability
DuringeachlOP, boththetemperature andwatervaporsoundingsundergolargefluctuations. The GCAPE alsovariesconsiderably. As discussedearlier, the QE hypothesisstatesthat the temperature and water-vaporsoundings vary togetherin sucha way as to preventlargevaluesof the GCAPE from occurring.In otherwords,the QE hypothesisstatesthat the temperatureand water-vapor profilesevolvetogetherin sucha way thatthe values of the GCAPE which are actuallyobservedare systematically smallerthanthosewhichwouldoccurif thegivensetof temperature profiles(over an lOP, say) were randomlypairedwith the discussion. givensetof water-vapor profiles.We decidedto pursuethisideaas a testof the QE hypothesis. 2. GCAPE A practicalissueis thatrandompairingsof observed tempera. ture and water vapor soundingscan lead to relativehumidities A key variablein our analysisis the "generalizedCAPE" or whichgreatlyexceed100%.To avoidthis,we canrandomlypair GCAPE,whichwasintroduced by RandallandWang(1992;hereobservedtemperature soundings with observedrelativehumidity after RW; also see Wang and Randall, 1994). The GCAPE is (RH) soundings from the sameIOP. definedusingLorenz's(1978, 1979) conceptof Moist Available A furtherpracticalproblemis thatexhaustively_ pairingN temEnergy (MAE). Briefly, Lorenz showedthat, with a suitably perature profiles with N RH profiles produces N 2 pairs -- easily definedmoistenthalpy,the sumof the totalmoistenthalpyof the reachingtensof thousands of pairsfor a typicalIOP withbetween atmosphere (denotedby H) and the total kinetic energyof the one and two hundredsoundings. To avoidthis, we modify our atmosphere (denotedby K) is invariantunderbothdry adiabatic strategyby pairingthe lOP.averagedRH profilewith the ensem. andmoistadiabaticfrictionlessprocesses, i.e. ble of temperature profilesfor the lOP; thisprocedure yieldsjust N pairsof temperature andhumiditysoundings. H + K = constant. (1) In summary,we carryoutthefollowingsteps: 1. AcquireN soundings of temperature and water-vaporfrom Supposethat the massof the atmosphere is reversiblyrear-
rangedso as to minimizeH, i.e. H-• Hmin. The differencean IOP. 2. Computethe time-sequenceof N GCAPEs from theseN between H andHmin represents themaximum possible kinetic energythat can be realizedthroughadiabaticfrictionlesspro- soundings. 3. ComputetheobservedlOP-averagedRH at eachlevel. 4. Using each of the observedN temperatureprofiles,conMAE is a generalization of the conceptof availablepotential structa "hypothetical" water-vaporprofilefromtheobserved temenergy,whichwasintroduced by Lorenz(1955). RH profile. As discussed by RW,theMAE present in a conditionally unsta- peratureprofileandthelOP-averaged 5. ComputeN"hypothetical"GCAPEsfromtheobservedtemble sounding is the GCAPEof thatsounding. The GCAPEis the water-vapor profiles. maximumamountof kineticenergythatcanbegenerated by con- peratureprofilesandthehypothetical 6. Make a scatterdiagramby pairingthe resultsof Step5 with vectionthroughconversion from the nonkineticenergyof the time. Sucha diasounding,via adiabaticfrictionlessprocesses. The GCAPE is a the resultsof Step2, for the sameobservation cesses;Lorenz (1978) identifiedthis differenceas the MAE. The
more general concept that the conventional CAPE, in two
gram showsthe effectsof RH variationson the GCAPE. If RH
respects. First,the GCAPE can be computed withoutassuming variationshaveno effecton the GCAPE, all pointswill fall along thattheconvective updraftsoriginateat anyparticularlevel.This the diagonal.If RH variationsaffect the GCAPE randomly,the is importantfor the datausedin this study,becauseit was col- hypotheticalGCAPE will be largerthan the actualGC APE as lectedin a regimefor whichconvection is knownto originatealoft often as it is smaller. If the scatterdiagram showsthat the on some occasions.Second, the GCAPE takes into account the observedGCAPE is systematically smallerthanthe hypothetical workdonein makingthedry staticallystableenvironment subside GCAPE, this is evidencefor GCAPE QE, becauseit showsthat aroundthemoistascending air.A methodto compute theGCAPE the observedjoint variationsof the temperatureand moisture soundingsare correlatedin such a way that variationsof the is described by RW.
2615
SCM Results Using April 1995 SGP lOP Dataset (20 April - 7 May 1995) Observed Observed
Moisture
and Computed
Fields based on Fixed, Temporal
sounding
Mean RH
Observed Temperature
Sounding
200300-
I
1000½) I
2
3
4
5
6
7
Computed
8
9
10
11
12
13
14
15
16
17
18
10000I 2 3 4 5 6 7 8 9 101112131415161718
Moisture Sounding
Computed Temperature
Sound ing
20o
I
• . •,,•
.../••' .
,
I 700
10000I 2 3 4
I
Time (Oays since 00 UTC 20 April 1996)
Contour•
In g
'
2
3
4
Tim
•
6
7
8
(Days eince •
Cont•
9
10
11
12
13
14
UTC 20 April 1•5)
n
Plate1. Thetoppanelsshowtheobserved time-pressure distributions of thewatervapormixingratio(left) andthetemperature (right). Thebottomleft panelshowsthetime-pressure distribution of thewatervapormixingratiocomputed by usingtheobserved time-varyingtemperature andthetime-averaged relativehumidityat eachlevel.The bottomrightpanelshowsthetime-pressure distribution of temperature computed by usingtheobserved time-varying watervapormixingratioandthetime-averaged relativehumidityat each level.
GCAPE are suppressed relativeto thosewhich would occurif the
variationson the GCAPE duringtimeswhenconvection is (presumably)activeand thuscapableof affectingthe stateof the atmosphere. Theresultspresented in Fig. 1 showthatbothsetsof hypotheticalsoundings yieldGCAPEslargerthanthoseobserved in thevast majorityof cases,and smallerthanthoseobservedin very few cases.This meansthatthe observed variationsof the RH profile perature profiles. 1Wecould thenpairtheN hypothetical tempera-overwhelminglytendto reducethe GCAPE belowthe valuesthat tureprofileswiththecorresponding observed water-vapor profiles it wouldtakeif theRH profilewerefixedto thelOP-averaged proto computea secondsetof hypothetical GCAPEs,in analogyto file. Our results show much more than that the observed variations Step5 above,and of coursewe couldthenmakea secondscatter in the RH profileaffectthe CAPE; they showthat the observed diagramby pairingthe observed GCAPEsof Step2 with the sec- variations in theRH profilesystematically reducetheCAPE. ondsetof hypothetical GCAPEs.We haveactuallyfollowedboth The'results could easily have come outdifferently, such thatthe RH remainedconstantat eachlevel.Conversely, if the observed valuesof the GCAPE are on the wholecomparable to or larger thanthehypothetical ones,thisis evidenceagainstGCAPEQE. Note, however,that Step 4 is arbitraryin the sensethat we couldjust as well usethe observed water-vapor profilestogether withthelOP-average RH profilesto compute N hypothetical tem-
approaches, as discussed below.
hypothetical GCAPE wassmallerthantheobserved asoftenasit Plate 1 showsan exampleof the observed and hypothetical was larger.This did not happen,and a physicalexplanationis temperature andwater-vapor profiles,asfunctions of time,for one needed.The QE hypothesisprovidessuchan explanation.We particularlOP (April 1995).In the lowertroposphere, the hypo- thereforeinterpretour resultsas strongly supportingthe QE theticalmoisture plotbearsa resemblance to theobserved temper- hypothesis. atureplot,andvice versa.
Fig. 1 showsthe scatterdiagrams(seeStep6 above)for all seven lOPs combined. The GCAPE obtained from the observed
soundings is plottedalongthe ordinate.The abscissas represent the GCAPEsobtainedfrom the observedwater-vaporprofiles pairedwith the hypothetical temperature profiles(the top pair of panels)andthoseobtained fromtheobserved temperature profiles pairedwiththehypothetical moisture soundings (thebottompair of panels).Resultsfor all dataare shownon the left-handsideof
We have checkedthe influenceof the diurnal cycle on our resultsin two ways. First, we have repeatedour calculationsfor
eachof eightlocaltimesof day.In thesecalculations, theaverage relativehumiditieswerecomputedseparately for eachlocaltime. In addition,we haverepeatedour calculations usingdaily mean soundings. The figuresare omittedheredue to spacelimitations, but all cases,the resultsobtainedare consistentwith the discus-
sionandconclusions givenabove.
Fig. 1. On theright-hand sidewe showtheresultsfor onlythose soundings obtainedat the endsof three-hourperiodswith an 5. Summary and conclusions
observed precipitation rateof at least1 mmday 'l. Wereferto
We haveusedmidlatitudetemperature andwatervaporsoundtheseastheprecipitation-constrained soundings. Fortheprecipitaings to investigate the variability of the GCAPE. The testrequires tion-constrained results, weaveraged theRH overonlytheprecipandmoisturesoundings andpreitation-constrained soundings.The resultsobtainedwith the onlya timeseriesof temperature precipitation-constrained soundings focuson the effectsof RH cipitationrate.Our resultsshowthatthe observedGCAPE is often smallerthanandrarelylargerthanhypothetical GCAPEsobtained by fixing the relativehumidity at its observedtime-averaged 1. An iterativeproceduremustbe usedto determinethesehypothetical value, at each level, and usingeitherthe observedtemperature temperatureprofiles soundingor the observedwater vapor sounding.We interpret
2616
CRIPE AND RANDALL: TEMPERATURE AND WATER VAPOR OVER THE MIDLATITUDE CONTINENTS Results with Observed Moisture and Hypothetical Temperature
Resultswith ObservedTemperatureand HypotheticalMoisture
ii i i I I I II
I
I
I
i
I I I bq I I I..,I I L.,I I 1.,1 I I .-1 I I I I I I I I I I I
I I I 0
200
400
600
800
1000
1200
1400
1600
0
200
400
600
800
L•11
iii.,1
I I I 1000
I I I
I I I
I I I I I I
I I I I I I I
I I I I I I I
II II II II II II II
I I I
I I I
I I I
II II II
1200
1400
1600
HypotheticalGCAPE(J kg4),preclpfiltered
HypotheticalGCAPE(J kg4)
Figure 1. Scatterdiagrams for all sevenIOPscombined. TheGCAPEcomputed fromtheobserved soundings is plottedalongtheordinatein eachpanel.Theabscissas represent theGCAPEscomputed fromthehypothetical temperature profilesandobserved water-vapor profiles(thetoppairof panels)andthosecomputed fromthehypothetical moisture andobserved temperature soundings (thebottom pairof panels).All resultsareshownontheleft-handside.On theright-hand sidewe showtheresultsfor onlythose"precipitation-con-
strained" soundings obtained attheends ofthree-hour periods withanobserved precipitation rateofatleast 1mmday '1.Forthecalculationsshownontheright,we averaged theRH overonlytheprecipitation-constrained soundings.
theseresultsas stronglysupportingthe hypothesisof GCAPE Kao, C.-Y. J., andY. Ogura, Responseof cumuluscloudsto large-scale parameterization. J. Atmos.Sci., quasi-equilibrium, whichis closelyrelatedto closureassumptions forcingusingthe Arakawa-Schubert 44, 2437-2458, 1987. usedin cumulusparameterizations. Lorenz, E. N., Availablepotentialenergyand the maintenanceof the Our QE test has beenperformedusingmidlatitudedata.The generalcirculation.Tellus,7, 157-167,1955. testwouldbe difficultto performusingtropicaldatabecausethe Lorenz, E. N., Available energy and the maintenanceof a moist circulation,Tellus,30, 15-31, 1978. observedtropicaltemperaturevariationsare so small. Acknowledgements. This research was supportedby the U.S. Departmentof Energy'sARM Program,throughgrantnumberDE-FG0395ER61968to ColoradoStateUniversity.Ric Cederwalland JonYio of the LawrenceLivermoreNational Laboratoryprovidedthe data. Prof. Akio Arakawaof UCLA madevaluablecomments on themanuscript. We thankthe anonymous reviewersfor their comments.
References Arakawa, A., Parameterizationof cumulusconvection.Proc. WMO/IUGG
Lorenz,E. N., Numericalevaluationof moistavailableenergy,Tellus,31, 230-235, 1979.
Manabe,S., J. Smagorinsky, andR. F. Strickler,Simulated climatology of a generalcirculationmodelwith a hydrologiccycle.Mon. Wea.Rev., 93, 769-798, 1965.
Ogura,Y., andC.-Y. J. Kao, Numericalsimulationof a tropicalmesoscale convectivesystemusing the Arakawa-Schubert parameterization. J. Atmos.Sci., 44, 2459-2476, 1987.
Randall,D. A., D.-M. Pan,andP. Ding, Quasiequilibrium. In ThePhysics and Parameterization of Moist AtmosphericConvection,R. K. Smith (ed.), Kluwer AcademicPublishers,printedin The Netherlands.pp. 359-385, 1997.
Randall,D. A., and D. G. Cripe, Altemativemethodsfor specificationof Syrup.on Numerical WeatherPrediction,Tokyo, 26 November-4 observedforcingin single-columnmodelsandcloudsystemmodels,J. December,1968,JapanMeteor.Agency,IV, 8, 1-6, 1969. Geophys. Res.,103, 24, 527-24,545,1999. Arakawa, A., and W. H. Schubert, Interaction of a cumulus cloud Randall,D. A., andJ. Wang,The moistavailableenergyof a conditionally ensemblewith the large-scaleenvironment,Part I. J. Atmos.Sci., 31, unstableatmosphere, J. Atmos.Sci., 49, 240-255, 1992. 674-701, 1974. Wang,J., andD. A. Randall,The moistavailableenergyof a conditionally Charney,J. G., A noteon large-scalemotionsin the tropics.J..Atmos.Sci., unstableatmosphere, PartII: furtheranalysisof GATE data.J. Atmos.
20, 607-609, 1963. Sci., .51,703-710, 1994. Emanuel, K. A., J. D. Neelin, and C. S. Bretherton,On large-scale Wu, X., Effects of cumulusensembleand mesoscalestratiformcloudsin circulationsin convectingatmospheres. Quart. J. Roy. Meteor. Soc., midlatitudeconvectivesystems.J. Atmos.Sci., 50, 2496-2518, 1993ø 120, 111!-1143, 1994. Ghan, S. J., D. A. Randall,K.-M. Xu, R. Cederwall,D. G. Cripe, J. J. Hack, S. Iacobellis,S. Klein, S. Krueger,U. Lohmann,J. Pedretti,A.
Robock,L. Rotstayn,R. Somerville,G. Stenchikov, Y. Sud,G. Walker, S. Xie, J. Yio, and M. Zhang,An intercomparison of singlecolumn model simulations of summertime midlatitude continental convection.
J. Geophys.Res.,105, 2091-2124, 2000. Grell, G. A., Y.-H. Kuo and R. J. Pasch,Semiprognostic testsof cumulus parameterization schemesin the middlelatitudes.Mon. Wea.Rev.,119, 5-31, 1991.
(Received January 23,2001' revised April5, 2001'accepted April 7, 2001.)
Joint variations of temperature and water vapor over the midlatitude
continents
DouglasG. Cripe andDavidA. Randall Department of Atmospheric Science,ColoradoStateUniversity,FortCollins,Colorado
Abstract. We haveusedwarm-season datafromtheAtmospheric stateof the atmosphere. The approximationis usefulwhen the RadiationMeasurement (ARM) Program's Southern GreatPlains adjustment time scalefor the convection is significantly shorter siteto investigate thejointvariabilityof thetemperature andmois- thanthe time scaleon whichthe atmospheric stateis evolving. turesoundings, andtheirrelationship to thevariabilityof thegen- ObviouslyQE is favoredif the atmospheric stateis evolving eralizedconvectiveavailablepotentialenergy(GCAPE). The slowly, and converselythe QE approximationbreaksdown for actualtemperature andhumiditysoundings varytogether in sucha rapidlyevolvingatmosphericstates. way as to producevariationsof the GCAPE which are far smaller As discussed by AS andRandallet al. (1997), a key prediction thanthosewhichwouldoccurif therelativehumidityvariedwhile of the QE hypothesis is thattheobservedCAPE shouldbe "small" thetemperature soundingwasfixed,or viceversa. comparedto that whichwouldoccurif convectioncouldsomehow be suppressed so that non-convective processes couldhavetheir way with thesounding. The key pointis that,according to theQE 1. Introduction hypothesis, the convection consumes the CAPE (almost)as rapidly as non-convective processesgenerateCAPE. Even when Cumulusconvection converts thepotentialenergyof a dry-stat- thereis a steadysupplyof CAPE throughsurfaceheatingand ically-stable meanstateintothekineticenergyof theconvection. evaporation, large-scale lifting,etc.,theCAPE actuallyseenin the In orderfor sucha conversion to be possible,a portionof the sounding neverincreases verymuch(according to theQE hypothpotentialenergyof themeanstatemustbe "available,"i.e. convec- esis),because theconvection responds veryquicklyandconsumes tiveavailable potential energy(CAPE)mustexist;a sounding for theCAPE asfastasit is generated. It is thispredicted"smallness" whichtheCAPEispositiveis saidto beconditionally unstable. of theCAPEthatis usedto testtheQE hypothesis in thepresent Broadlyspeaking, conditionally unstable soundings arechar- study. acterizedby high moisturecontents,necessarily concentrated at The CAPE is a functionalof the temperature andwatervapor lower levels,and by relativelysteep(but dry staticallystable) soundings. Broadlyspeaking,the CAPE can be increasedby lapserates.A givensounding canbe alestabilized, in thesenseof steepening thelapserateof temperature, and/orby increasing the conditionalinstability,by increasingits moisturecontent,by watervaporcontentof the column.Accordingto the QE hypothewarmingat low levels,or by coolingaloft.Convection feedsback sis,thetemperature andwatervaporsoundings changewith time by drying the columnthroughprecipitation, warmingaloft in sucha way thattheCAPE is relativelyinvariant.For example, throughlatentheatreleaseandupwardenergytransport, andcool- the QE hypothesis suggests that a steepening of the lapserate ing nearthesurfaceasa resultof convective-scale, precipitation- shouldbe accompanied by a dryingof thecolumn.It followsthat drivendowndraftsand the attendantevaporation of rainwater. oneway to testthe QE hypothesisagainstobservations is to assess Throughthesefeedbacks, convection tendsto reducethe CAPE, the extentto which changesin the temperatureand moisture by converting it intoconvective kineticenergy,whichis thendis- soundings producemutuallycancelling changes in theCAPE. sipatedand/orradiatedawayin theformof gravitywaves. Most studiesof thethermodynamic structure of the convective Manabeet al, (1965), Arakawa(1969), andArakawaandSchu- atmosphere havebeenbasedon tropicaloceanicsoundings. This bert(1974;hereafter AS) proposed thattheintensity of convection is understandable, becausethe widespread convectionover the is approximately that requiredto consumethe CAPE (or more tropicaloceansis veryimportantfor thegeneralcirculation of the precisely thecloudworkfunctions associated witha spectrum of atmosphere. Nevertheless, thereis muchto be gainedby investicloudtypes)asrapidlyasit is generated by non-convective pro- gatingtheproperties of conditionally unstable soundings overthe cesses(alsoseeEmanuelet al., 1994,andRandallet al., 1997). midlatitudecontinents,and this is especiallytrue for studies Manylarge-scale atmospheric circulation modelstodayusecumu- aimedat evaluatingthe QE hypothesis. Both temperature and
lus parameterizations in whichthe strengthof the convectivemoisture
are much more variable over the midlatitude continents
activityis determinedby makinguse of someversionof this thantheyare overthe tropicaloceans,permitting, in principle, "CAPE quasiequilibrium" hypothesis,hereaftercalled the QE muchlargervariationsof the CAPE. The reasonsfor thisarewell hypothesis. Becausethe QE hypothesis canbe usedto determine established. Most obviously,the daytimesurfacesensibleand the strengthof the convection,it is often describedas the "clo- latentheatfluxesoverthecontinents aremuchstronger thanthose sure"of theconvection parameterization. over the oceans. In addition, large-scale-dynamical effects As explained by AS, theQE closureis expected to be a useful stronglylimit temperature excursions in the tropics,relativeto approximation whenthe statisticalpropertiesof the convective middle latitudes.In the tropics,the smallnessof the Coriolis cloudfield can respondor "adjust"rapidlyto variationsin the parameter leadsto veryflat temperature andsurfacepressure distributions (Charney,1963).The largerCoriolisparameter of middle latitudespermitsthe sharperhorizontalpressure gradients Copyright2001 by theAmericanGeophysical Union. associated with moredramatichorizontaltemperature gradients. Paper number2001GL012909 As a result,thehorizontal advection of temperature playsa much 0094-8276/01/2001 GL012909505.00 strongerrole in midlatitudes thanit doesin the tropics,andthe 2613
temporalvariabilityof temperatureis muchlargerin midlatitudes thanin the tropics.Moisturefluctuationsalsotendto be stronger in midlatitudes.Examplesof the tendenciesof temperatureand moisturedueto horizontaladvectionare shownin Fig. 3 of Randall andCripe(1999), for bothmidlatitudeandtropicalcases.The contrastbetweenthetropicsandmiddlelatitudesis very apparent in their figure. In summary,the convectiveregimesof the midlatitudecontinentsin the warm seasonprovidevery usefulopportunities for testingthe QE hypothesis. Theseopportunities haverarely been takenadvantage of, up to now.Kao andOgura(1987), Grell et al. (1991), and Wu (1993) reportedobservationaltestsof the QE hypothesis with midlatitudecontinentaldata.All of thesestudies providedsupportfor theQE hypothesis, butmuchfurtherinvestigationis needed. In this paperwe reportthe use of warm-season data from the OklahomaARM site (ARM is the AtmosphericRadiationMeasurements programsponsored by the U.S. Departmentof Energy) to test the QE hypothesisin a new way. To date,mostobservationaltestsof the QE hypothesis, whetherin thetropicsor midlatitudes,have involvedcomplexanalysesof the tendencies of the CAPE dueto variousprocesses, notablyincludingthe difficult-toobservelarge-scaleverticalmotion.In contrast,the newapproach reportedhereis very simple,andwe hopethatits simplicityadds to its utility.A preliminarytestof this approachwasreportedby Randallet al. (1997; seetheir Fig. 2). Section2 of this paperprovidessomebackground on the versionof the CAPE usedin our study.Section3 describesthe data used.Section4 presentsour results.Section5 givesa concluding
3.Data
We haveuseddatafrom the AtmosphericRadiationMeasurement(ARM) SouthernGreatPlains(SGP) site,locatedin northcentralOklahomaand south-central Kansas.Data are gathered dailyat the SGPsiteby variousautomated instruments andsensors.In addition,severalintensiveobservation periods(lOPs) are heldeachyear,eachlastingthreeto four weeks.Duringan IOP, radiosondes are launchedevery3 hours,from a locationat the centerof the site and alsofrom 4 positionsaroundits perimeter (seeFigure1 in thepaperof RandallandCripe,1999).Thesoundingsusedin thisstudywerecollectedduringsevenARM lOPs: April 1995, July 1995, April 1996, July 1996, July 1997, May 1998, and July 1999. Precipitationdata for each lOP were obtainedfrom the OklahomaState Universitymesonetsystem. RandallandCripe (1999) andGhanet al. (2000) presentfurther discussion of the ARM SGP data.
4. GCAPE variability
DuringeachlOP, boththetemperature andwatervaporsoundingsundergolargefluctuations. The GCAPE alsovariesconsiderably. As discussedearlier, the QE hypothesisstatesthat the temperature and water-vaporsoundings vary togetherin sucha way as to preventlargevaluesof the GCAPE from occurring.In otherwords,the QE hypothesisstatesthat the temperatureand water-vapor profilesevolvetogetherin sucha way thatthe values of the GCAPE which are actuallyobservedare systematically smallerthanthosewhichwouldoccurif thegivensetof temperature profiles(over an lOP, say) were randomlypairedwith the discussion. givensetof water-vapor profiles.We decidedto pursuethisideaas a testof the QE hypothesis. 2. GCAPE A practicalissueis thatrandompairingsof observed tempera. ture and water vapor soundingscan lead to relativehumidities A key variablein our analysisis the "generalizedCAPE" or whichgreatlyexceed100%.To avoidthis,we canrandomlypair GCAPE,whichwasintroduced by RandallandWang(1992;hereobservedtemperature soundings with observedrelativehumidity after RW; also see Wang and Randall, 1994). The GCAPE is (RH) soundings from the sameIOP. definedusingLorenz's(1978, 1979) conceptof Moist Available A furtherpracticalproblemis thatexhaustively_ pairingN temEnergy (MAE). Briefly, Lorenz showedthat, with a suitably perature profiles with N RH profiles produces N 2 pairs -- easily definedmoistenthalpy,the sumof the totalmoistenthalpyof the reachingtensof thousands of pairsfor a typicalIOP withbetween atmosphere (denotedby H) and the total kinetic energyof the one and two hundredsoundings. To avoidthis, we modify our atmosphere (denotedby K) is invariantunderbothdry adiabatic strategyby pairingthe lOP.averagedRH profilewith the ensem. andmoistadiabaticfrictionlessprocesses, i.e. ble of temperature profilesfor the lOP; thisprocedure yieldsjust N pairsof temperature andhumiditysoundings. H + K = constant. (1) In summary,we carryoutthefollowingsteps: 1. AcquireN soundings of temperature and water-vaporfrom Supposethat the massof the atmosphere is reversiblyrear-
rangedso as to minimizeH, i.e. H-• Hmin. The differencean IOP. 2. Computethe time-sequenceof N GCAPEs from theseN between H andHmin represents themaximum possible kinetic energythat can be realizedthroughadiabaticfrictionlesspro- soundings. 3. ComputetheobservedlOP-averagedRH at eachlevel. 4. Using each of the observedN temperatureprofiles,conMAE is a generalization of the conceptof availablepotential structa "hypothetical" water-vaporprofilefromtheobserved temenergy,whichwasintroduced by Lorenz(1955). RH profile. As discussed by RW,theMAE present in a conditionally unsta- peratureprofileandthelOP-averaged 5. ComputeN"hypothetical"GCAPEsfromtheobservedtemble sounding is the GCAPEof thatsounding. The GCAPEis the water-vapor profiles. maximumamountof kineticenergythatcanbegenerated by con- peratureprofilesandthehypothetical 6. Make a scatterdiagramby pairingthe resultsof Step5 with vectionthroughconversion from the nonkineticenergyof the time. Sucha diasounding,via adiabaticfrictionlessprocesses. The GCAPE is a the resultsof Step2, for the sameobservation cesses;Lorenz (1978) identifiedthis differenceas the MAE. The
more general concept that the conventional CAPE, in two
gram showsthe effectsof RH variationson the GCAPE. If RH
respects. First,the GCAPE can be computed withoutassuming variationshaveno effecton the GCAPE, all pointswill fall along thattheconvective updraftsoriginateat anyparticularlevel.This the diagonal.If RH variationsaffect the GCAPE randomly,the is importantfor the datausedin this study,becauseit was col- hypotheticalGCAPE will be largerthan the actualGC APE as lectedin a regimefor whichconvection is knownto originatealoft often as it is smaller. If the scatterdiagram showsthat the on some occasions.Second, the GCAPE takes into account the observedGCAPE is systematically smallerthanthe hypothetical workdonein makingthedry staticallystableenvironment subside GCAPE, this is evidencefor GCAPE QE, becauseit showsthat aroundthemoistascending air.A methodto compute theGCAPE the observedjoint variationsof the temperatureand moisture soundingsare correlatedin such a way that variationsof the is described by RW.
2615
SCM Results Using April 1995 SGP lOP Dataset (20 April - 7 May 1995) Observed Observed
Moisture
and Computed
Fields based on Fixed, Temporal
sounding
Mean RH
Observed Temperature
Sounding
200300-
I
1000½) I
2
3
4
5
6
7
Computed
8
9
10
11
12
13
14
15
16
17
18
10000I 2 3 4 5 6 7 8 9 101112131415161718
Moisture Sounding
Computed Temperature
Sound ing
20o
I
• . •,,•
.../••' .
,
I 700
10000I 2 3 4
I
Time (Oays since 00 UTC 20 April 1996)
Contour•
In g
'
2
3
4
Tim
•
6
7
8
(Days eince •
Cont•
9
10
11
12
13
14
UTC 20 April 1•5)
n
Plate1. Thetoppanelsshowtheobserved time-pressure distributions of thewatervapormixingratio(left) andthetemperature (right). Thebottomleft panelshowsthetime-pressure distribution of thewatervapormixingratiocomputed by usingtheobserved time-varyingtemperature andthetime-averaged relativehumidityat eachlevel.The bottomrightpanelshowsthetime-pressure distribution of temperature computed by usingtheobserved time-varying watervapormixingratioandthetime-averaged relativehumidityat each level.
GCAPE are suppressed relativeto thosewhich would occurif the
variationson the GCAPE duringtimeswhenconvection is (presumably)activeand thuscapableof affectingthe stateof the atmosphere. Theresultspresented in Fig. 1 showthatbothsetsof hypotheticalsoundings yieldGCAPEslargerthanthoseobserved in thevast majorityof cases,and smallerthanthoseobservedin very few cases.This meansthatthe observed variationsof the RH profile perature profiles. 1Wecould thenpairtheN hypothetical tempera-overwhelminglytendto reducethe GCAPE belowthe valuesthat tureprofileswiththecorresponding observed water-vapor profiles it wouldtakeif theRH profilewerefixedto thelOP-averaged proto computea secondsetof hypothetical GCAPEs,in analogyto file. Our results show much more than that the observed variations Step5 above,and of coursewe couldthenmakea secondscatter in the RH profileaffectthe CAPE; they showthat the observed diagramby pairingthe observed GCAPEsof Step2 with the sec- variations in theRH profilesystematically reducetheCAPE. ondsetof hypothetical GCAPEs.We haveactuallyfollowedboth The'results could easily have come outdifferently, such thatthe RH remainedconstantat eachlevel.Conversely, if the observed valuesof the GCAPE are on the wholecomparable to or larger thanthehypothetical ones,thisis evidenceagainstGCAPEQE. Note, however,that Step 4 is arbitraryin the sensethat we couldjust as well usethe observed water-vapor profilestogether withthelOP-average RH profilesto compute N hypothetical tem-
approaches, as discussed below.
hypothetical GCAPE wassmallerthantheobserved asoftenasit Plate 1 showsan exampleof the observed and hypothetical was larger.This did not happen,and a physicalexplanationis temperature andwater-vapor profiles,asfunctions of time,for one needed.The QE hypothesisprovidessuchan explanation.We particularlOP (April 1995).In the lowertroposphere, the hypo- thereforeinterpretour resultsas strongly supportingthe QE theticalmoisture plotbearsa resemblance to theobserved temper- hypothesis. atureplot,andvice versa.
Fig. 1 showsthe scatterdiagrams(seeStep6 above)for all seven lOPs combined. The GCAPE obtained from the observed
soundings is plottedalongthe ordinate.The abscissas represent the GCAPEsobtainedfrom the observedwater-vaporprofiles pairedwith the hypothetical temperature profiles(the top pair of panels)andthoseobtained fromtheobserved temperature profiles pairedwiththehypothetical moisture soundings (thebottompair of panels).Resultsfor all dataare shownon the left-handsideof
We have checkedthe influenceof the diurnal cycle on our resultsin two ways. First, we have repeatedour calculationsfor
eachof eightlocaltimesof day.In thesecalculations, theaverage relativehumiditieswerecomputedseparately for eachlocaltime. In addition,we haverepeatedour calculations usingdaily mean soundings. The figuresare omittedheredue to spacelimitations, but all cases,the resultsobtainedare consistentwith the discus-
sionandconclusions givenabove.
Fig. 1. On theright-hand sidewe showtheresultsfor onlythose soundings obtainedat the endsof three-hourperiodswith an 5. Summary and conclusions
observed precipitation rateof at least1 mmday 'l. Wereferto
We haveusedmidlatitudetemperature andwatervaporsoundtheseastheprecipitation-constrained soundings. Fortheprecipitaings to investigate the variability of the GCAPE. The testrequires tion-constrained results, weaveraged theRH overonlytheprecipandmoisturesoundings andpreitation-constrained soundings.The resultsobtainedwith the onlya timeseriesof temperature precipitation-constrained soundings focuson the effectsof RH cipitationrate.Our resultsshowthatthe observedGCAPE is often smallerthanandrarelylargerthanhypothetical GCAPEsobtained by fixing the relativehumidity at its observedtime-averaged 1. An iterativeproceduremustbe usedto determinethesehypothetical value, at each level, and usingeitherthe observedtemperature temperatureprofiles soundingor the observedwater vapor sounding.We interpret
2616
CRIPE AND RANDALL: TEMPERATURE AND WATER VAPOR OVER THE MIDLATITUDE CONTINENTS Results with Observed Moisture and Hypothetical Temperature
Resultswith ObservedTemperatureand HypotheticalMoisture
ii i i I I I II
I
I
I
i
I I I bq I I I..,I I L.,I I 1.,1 I I .-1 I I I I I I I I I I I
I I I 0
200
400
600
800
1000
1200
1400
1600
0
200
400
600
800
L•11
iii.,1
I I I 1000
I I I
I I I
I I I I I I
I I I I I I I
I I I I I I I
II II II II II II II
I I I
I I I
I I I
II II II
1200
1400
1600
HypotheticalGCAPE(J kg4),preclpfiltered
HypotheticalGCAPE(J kg4)
Figure 1. Scatterdiagrams for all sevenIOPscombined. TheGCAPEcomputed fromtheobserved soundings is plottedalongtheordinatein eachpanel.Theabscissas represent theGCAPEscomputed fromthehypothetical temperature profilesandobserved water-vapor profiles(thetoppairof panels)andthosecomputed fromthehypothetical moisture andobserved temperature soundings (thebottom pairof panels).All resultsareshownontheleft-handside.On theright-hand sidewe showtheresultsfor onlythose"precipitation-con-
strained" soundings obtained attheends ofthree-hour periods withanobserved precipitation rateofatleast 1mmday '1.Forthecalculationsshownontheright,we averaged theRH overonlytheprecipitation-constrained soundings.
theseresultsas stronglysupportingthe hypothesisof GCAPE Kao, C.-Y. J., andY. Ogura, Responseof cumuluscloudsto large-scale parameterization. J. Atmos.Sci., quasi-equilibrium, whichis closelyrelatedto closureassumptions forcingusingthe Arakawa-Schubert 44, 2437-2458, 1987. usedin cumulusparameterizations. Lorenz, E. N., Availablepotentialenergyand the maintenanceof the Our QE test has beenperformedusingmidlatitudedata.The generalcirculation.Tellus,7, 157-167,1955. testwouldbe difficultto performusingtropicaldatabecausethe Lorenz, E. N., Available energy and the maintenanceof a moist circulation,Tellus,30, 15-31, 1978. observedtropicaltemperaturevariationsare so small. Acknowledgements. This research was supportedby the U.S. Departmentof Energy'sARM Program,throughgrantnumberDE-FG0395ER61968to ColoradoStateUniversity.Ric Cederwalland JonYio of the LawrenceLivermoreNational Laboratoryprovidedthe data. Prof. Akio Arakawaof UCLA madevaluablecomments on themanuscript. We thankthe anonymous reviewersfor their comments.
References Arakawa, A., Parameterizationof cumulusconvection.Proc. WMO/IUGG
Lorenz,E. N., Numericalevaluationof moistavailableenergy,Tellus,31, 230-235, 1979.
Manabe,S., J. Smagorinsky, andR. F. Strickler,Simulated climatology of a generalcirculationmodelwith a hydrologiccycle.Mon. Wea.Rev., 93, 769-798, 1965.
Ogura,Y., andC.-Y. J. Kao, Numericalsimulationof a tropicalmesoscale convectivesystemusing the Arakawa-Schubert parameterization. J. Atmos.Sci., 44, 2459-2476, 1987.
Randall,D. A., D.-M. Pan,andP. Ding, Quasiequilibrium. In ThePhysics and Parameterization of Moist AtmosphericConvection,R. K. Smith (ed.), Kluwer AcademicPublishers,printedin The Netherlands.pp. 359-385, 1997.
Randall,D. A., and D. G. Cripe, Altemativemethodsfor specificationof Syrup.on Numerical WeatherPrediction,Tokyo, 26 November-4 observedforcingin single-columnmodelsandcloudsystemmodels,J. December,1968,JapanMeteor.Agency,IV, 8, 1-6, 1969. Geophys. Res.,103, 24, 527-24,545,1999. Arakawa, A., and W. H. Schubert, Interaction of a cumulus cloud Randall,D. A., andJ. Wang,The moistavailableenergyof a conditionally ensemblewith the large-scaleenvironment,Part I. J. Atmos.Sci., 31, unstableatmosphere, J. Atmos.Sci., 49, 240-255, 1992. 674-701, 1974. Wang,J., andD. A. Randall,The moistavailableenergyof a conditionally Charney,J. G., A noteon large-scalemotionsin the tropics.J..Atmos.Sci., unstableatmosphere, PartII: furtheranalysisof GATE data.J. Atmos.
20, 607-609, 1963. Sci., .51,703-710, 1994. Emanuel, K. A., J. D. Neelin, and C. S. Bretherton,On large-scale Wu, X., Effects of cumulusensembleand mesoscalestratiformcloudsin circulationsin convectingatmospheres. Quart. J. Roy. Meteor. Soc., midlatitudeconvectivesystems.J. Atmos.Sci., 50, 2496-2518, 1993ø 120, 111!-1143, 1994. Ghan, S. J., D. A. Randall,K.-M. Xu, R. Cederwall,D. G. Cripe, J. J. Hack, S. Iacobellis,S. Klein, S. Krueger,U. Lohmann,J. Pedretti,A.
Robock,L. Rotstayn,R. Somerville,G. Stenchikov, Y. Sud,G. Walker, S. Xie, J. Yio, and M. Zhang,An intercomparison of singlecolumn model simulations of summertime midlatitude continental convection.
J. Geophys.Res.,105, 2091-2124, 2000. Grell, G. A., Y.-H. Kuo and R. J. Pasch,Semiprognostic testsof cumulus parameterization schemesin the middlelatitudes.Mon. Wea.Rev.,119, 5-31, 1991.
(Received January 23,2001' revised April5, 2001'accepted April 7, 2001.)
