Thermohaline Circulation(THC) in the North Atlantic Ocean: the 2-box model of Stommel (1961)

Transcription

1 The following is from a lab project in Earth 202: Modeling the Earth System, taught by Dave Bice and Jim Kasting at Penn State University. Prior to this exercise, we spend a week talking about ocean circulation, the controls on seawater density, and some of the details of deep currents based on exploring datasets from the IRI/LDEO data library ( We also spend time going over the Younger Dryas and the D-O events and their implications Then, the students build the model, using the recipe included here. Heating and Cooling Thermohaline Circulation(THC) in the North Atlantic Ocean: the 2-box model of Stommel (96) Evaporation HOT increases salinity Temperature: T e and Salinity: S e High Salinity Equatorial Box Surface Flow Deep Flow Q/2 The mixing (Q) between the boxes is a function of the density difference, which in turn is relatd to the temperature and salinity differences (delt and dels in the model). Q/2 Freshwater Input decreases salinity COLD Temperature: T p and Salinity: S p Low Salinity Polar Box Heating and Cooling This is the temperature difference between the two boxes it varies from 0 to and is set up so that it tries to return to a value of, the equilibrium temperature difference, Teq. delt is decreased by mixing between the two boxes, which is represented by Q R is the ratio of the effect of salinity over the effect of temperature on seawater density R 2 Highly Simplified STELLA Model of the THC del T.5 The time units here are scaled to what is called the diffusional timescale of the system -- about 200 yrs heat exchange (Teq-del_T)-(del_T*Q) /5 lambda Teq Teq is the T difference the system would evolve to if Q=0. abs((r*del_s)-del_t) delrho Q delrho/lambda this is the flow between the boxes /6 delta This is the salinity difference between the two boxes it varies from 0 to and is set up so that it tries to return to a value of (but more slowly than the temp, as controlled by delta). The dels is decreased by mixing between the two boxes (Q)..5 del S salinity exchange Seq delta*(seq-del_s)-q*del_s Seq is the S difference the system would evolve to if Q=0; the return to this value is slowed by delta, because salinity diffuses more slowly than heat

2 ExperimentswiththeThermohalineCirculationModel ConstructaSTELLAmodelofStommel sthcsystemfollowingthedesignprovided. Besurethatyourflowsarebiflowswiththeopenarrowspointingtowardsthe reservoirs.setthemodeltorunfrom0to5(timeunitsarescaledtothe diffusionaltimescaleofthesystem,whichisthoughttobeabout200years),with DT=0.0,usingtheRunge Kutta2method.Hereiswhatyourmodeloutputshould looklike(notethati vegotthedeltanddelsplottedonthesamescale): : del T 2: del S 3: Q : 2: 3:. 3. : 2: 3: : 2: 3: Page Years*200 :6 PM Sun, Feb 2, 200 Untitled Ifyougetresultslikethis,thenyourmodelisreadytoexperimentwith.Ifyoudon t gettheseresults,gobackandcheckthemodelconstructioncarefully. Noticethatthesystemisnotinsteadystatetobeginwith,butthatitfindsasteady stateafterabout5or6timeunits.theevolutionofthesystemintothesteadystate iscomplex thesalinitydifferenceovershootsthefinalsteadystatevalueandthe temperaturedifferenceinitiallyheadsoffinthewrongdirectionandthenitalso overshootsthefinalsteadystatevalue.q,whichyoucanthinkofasrepresenting thecombinedgulfstreamandnadwflows,initiallystartsoffverystrongandthen declinesto0attwopointsbeforeeventuallyreachingasteadyvalue.qhereis designedsothatitcannotbelessthan0 itisameasureofthemagnitudeofflow andnotthedirectionofflow.notethatwhenq=0,bothdeltanddelsincrease theywillapproachtheteqandseqvalues.highvaluesofqmeanstrongmixing betweenthepolarandtropicalportionsoftheoceanandthiswilltendtomaketheir temperaturesandsalinitiesmoresimilar,thusmakingdeltanddelsbelower.a highqvaluealsomeansstrongtransportofheatfromthetropicstothepolar region.

3 Experiments.Varyinginitialreservoirvalues. a)changethedelsinitialvaluefrom0.5to0.beforerunningthemodel,takenoteof thesteadystatevaluesofdels,delt,andqfromyourfirstmodelrun.then,makea predictionabouthowthereservoirswillbegintochangeatfirstandwheretheywill endupattheendoftherun willthesystemreturntothesamesteadystate?run themodelandseewhathappens,thendescribetheresults. b)nowwewillexploreawiderrangeofinitialvaluestobetterunderstandthe steadystatesofthissystem.gotothesensispecswindow,fromtherunmenuand sendbothreservoirsovertotheselectedcolumn.makeruns,andhavedelsstart at0andendatanddeltgofromto0;besuretohitthesetbuttonafteryou definethestartingandendingvalues.thensetupagraphtoviewtheresults makeitacomparativescatterplot,withdelsonthexaxisanddeltontheyaxis. MakesuretheRunSpecsaresettorunfrom0to5timeunitswithaDT=0.0. Thenrunthemodelandseewhathappens.Youcanwatchthetrajectoryofeachrun byfollowingthedots theymovefastwhenthesystemisnotinsteadystate,but theybecomestationarywhenasteadystateisachieved.soifthereisonesteady state,alldotswillconvergeonasinglespot;iftherearemultiplesteadystates,then you llseemorethanoneconvergence.theseconvergences,alsoknownas attractors,canbethoughtofassimilartotopographicdepressions imaginea topographicsurfacewithsomepeaksandsomedepressions(seeschematic illustrationbelow) thedepressionsrepresentconditionswherethetwoflowsin ourmodelarebothzero.ifyoutossabunchofmarblesontothissmoothsurface, theywilltendtofindtheirwaytothedepressions,andtheinitialstartingpointof themarbledetermineswhichdepressionitendsupin.

4 Now,studytheresultsofthesemodelrunsandfindouthowmanysteadystates thereareforthissystem(youmaywanttomodifyyoursensitivityspecsabitto covermoreofthespaceinthedelsvs.deltplot)andthenreportthedelt,dels coordinatesofthesteadystates. Hereiswhattheysee: c)characterizethesteadystatesbylookingatthemagnitudeofq,theexchangeflow betweenthetwooceanicboxes.highqwouldmeanavigorousgulfstream NADW

5 system,whichwouldbeassociatedwithlotsofheattransportfromtheequatorto thepoles. Experiments2and3tobedoneashomework,duenextFriday. 2.Changesintemperature. Whatwillhappentothissystemiftheclimatewarms?Howcanwemodifythe systemtorepresentawarmerclimate?asyoumayknow,therecentclimatechange hasbeencharacterizedbygreaterwarmingathighlatitudes,whichtendstoreduce thegradientfromthepolestotheequator.inourmodel,thetemperaturedifference betweenthepolarandequatorialregionsisrepresentedbythedeltreservoir.the valueormagnitudeofdeltisafunctionoftwothings thedensity drivenmixing thattendstoevenoutthetemperaturedifference(reducingdelt)andtheclimatecontrolledtemperaturedifference(teqinourmodel),whichissetto.ifwe reduceteq,thatwilltendtodrivethesystemtoalowerdeltvalue. So,setTeqequaltotimeandmakeitagraphicalfunctionoftime.Maketheupper limitandthelowerlimit0.5(anythinglowerwouldbetooextreme).setthetime axistogofrom0to30sothatwecanmakethechangeinteqafterthesystemhas gottenintoasteadystate(itwouldbehardtounderstandtheeffectofthechange duringtheadjustmenttosteadystate).so,afterabout8timeunits,maketeqstep downtoalowervalueandthenhaveitremainatthatvalueforabriefperiodoftime andthenreturnitto.therearetwoquestionstoanswerhere: a)workingwiththeinitialdeltanddelssettingsof0.5,howdoesthesystem respondtodifferentmagnitudesanddurationsoftheexcursionofteq?doesthe systemalwaysbouncebacktotheoriginalsteadystate,orcanitgetknockedinto theothersteadystate?ifitdoesgetknockedintoanothersteadystate,isitoneof thesamesteadystatesthatwefoundearlier,byjustchangingtheinitialvaluesof thereservoirswithouttamperingwithteq?ingeneral,describehowthischange affectsthemagnitudeofdels,delt,andq.thiswillrequiresomecarefulanalysisof themodelparameters,butdoyourbesttoexplainwhythesystembehavesthisway. b)withthetworeservoirsinitiallysetto0.5,thesystemwouldfindoneoftwo steadystates,andwe vebeentamperingwiththatsteadystate.now,let sdothe samekindoftamperingwiththeothersteadystate.howdoesitreacttotheperiods ofdecreasedteq?isthissteadystatemoresensitiveorlesssensitivetoteq changesthantheothersteadystate?

6 3.Freshwaterpulses. RecallfromlecturesthattheYoungerDryasisbelievedtohavebeentriggeredbya changeofstateinthethcduetoapulseoffreshwateraddedtothenorthatlantic. Cessi(994)figuredoutthatthepulseofwater,inStommel smodelwould representafluxof0.2delsunitsforaperiodofbetween3 5timeunits.Findaway tomodifyyourmodeltosimulatethisfreshwaterpulse youwanttoaddtothe delsreservoirforalimitedperiodoftime,andyouwanttoimposethisonthe steadystateconditionthatrepresentsthewarmer(highqandlowdelt)ofthetwo steadystates. a)showhowyoumakethischangetoyourmodel(makeasketch,orprintoutthe alteredmodel),andthencarryouttheexperiment.doesthispulseknockthe systemintothecolderofthetwosteadystates?inotherwords,doesitstayinthat otherstateevenafterthepulseoffreshwaterhasended?again,delveintotheinner workingsofthemodeltounderstandwhatisgoingon. b)whatistheminimummagnitudeanddurationoffreshwaterpulsethatisneeded toknockthesystemintotheothersteadystate?