ss brown 入门文章

ss brown 入门文章 Applicability of the steady state approximationto theinterpretationof atmosphericobservations of NO3and N2O5Steven S.Brown,1Harald Stark,1and A.R.Ravishankara1,2NOAA,Aeronomy Laboratory,Boulder,Colorado,USAReceived13Januaryxx;revised14Aprilxx;aepted27Mayxx;published5Septemberxx.1This paperexamines the conditions underwhich a steady state analysis is valid formodelingNO3and N2O5chemistry in the atmosphere.The conclusionse from asimple box model analysis that considersa limitednumber ofreactions between NO2,O3,NO3,N2O5and thepresumed sinks for the latter two.The applicability of the steady statedependson the strength of the sinks for NO3and N2O5,the concentration of NO2,andthe ambienttemperature.Under cleanconditions,weak sinks for NO3prevent the systemfrom passingthrough the induction periodduring the time betweensunset andsunrise,thus keeping the system out of steady state.Under polluted(i.e.,large NO2concentrations)or coldconditions,the presence of anequilibrium betweenNO3and N2O5markedly slowsthe approach to steady state even thoughthe twospecies areclose to equilibrium.Thetime requiredto approachequilibrium betweenNO2,NO3,and N2O5is nota goodmeasure of thetime requiredto achievea steady state amongthese pounds.The paperconsidersthe conditionsfor whichsteady statemay be valid and outlines amethod foridentificationof individualsinks for NO3and N2O5from observedconcentrationmeasurements for the steady state case.I NDEXT ERMS:0317Atmospheric CompositionandStructure:Chemical kiicand photochemicalproperties;0345Atmospheric Compositionand Structure:Pollutionurban andregional (0305);0365Atmospheric Compositionand Structure:Troposphereposition andchemistry;K EYWORDS:nitrate radical,dinitrogen pentoxide,steady stateCitation:Brown,S.S.,H.Stark,and A.R.Ravishankara,Applicability of the steady state approximationto theinterpretation ofatmosphericobservations of NO3and N2O5,J.Geophys.Res.,108(D17),4539,doi:10.1029/xxJD003407,xx.1.Introduction2The steady state approximation is ananalysis -monly appliedto calculateatmospheric positionandinterpret measuredabundances ofparticular pounds.Ites from the assumption that the rates ofproduction andlossof a pound areroughly inbalance,such that thetime rate of its concentration change is smallin parisontoits ratesof formation(source term)and removal(sinkterm).The continuityequation for the concentration,C,of aspeciesin agiven volumeof airis asfollowssee,e.g.,Ravishankara andLovejoy,1994.dCdt?P?L?F?1?Here,P standsfor thelocal production rate,L for the locallossrate andF for the flux of the poundin thespecifiedvolume.Because chemicalchanges associatedwith the poundsof interestfor thispaper,namely NO3and N2O5,are likelyto berapid relativeto transport,we willassumethat theflux termsare smallin parisontoproduction and loss.Presuming that the totalloss can berepresented bya first-order process,the lossterm inequation (1)bees L=k0C=C/t,where kis thetotalfirst-order ratecoefficient for the lossof C,and t isthus itsatmospheric lifetime.t?CP?dC=dt?2?For first-order lossprocess suchas gas-phase reactionswithsink poundsthat arein excessconcentration,photolysis,etc.,tisequal to the inverse of the sum of the individualpseudofirst-order reactionrate constants,i.e.,t=1/?k i0.Asnoted above,the steady state approximationassumes thatthetime rate of concentration changeisnegligible,i.e.,dC/dt?0.In this case,the atmosphericlifetime,t,beesthe steady state lifetime(also referredto as the steady stateturnover lifetime),t SS,and has a simpleform.t SS?CP?1Pk0i?3?3Under steady state,the first-order lossrate coefficientfor apoundin the atmosphere may be obtainedfrom ameasurement of itsconcentration andproduction rate.Thismethod ismonly usedto inferthe strengths of sinks forreactive pounds(e.g.,OH,NO3).In orderfor a steadyJOURNAL OFGEOPHYSICAL RESEARCH,VOL.108,NO.D17,4539,doi:10.1029/xxJD003407,xx1Also atCooperative Institutefor Researchin theEnvironmentalSciences,University ofColorado,Boulder,Colorado,USA.2Also atDepartment ofChemistry andBiochemistry,University ofColorado,Boulder,Colorado,USA.Copyrightxxby theAmerican GeophysicalUnion.0148-0227/03/xxJD003407$09.00ACH6-1state analysis to bevalid,the effective first-order rateconstant for the sink reaction must greatlyexceed thatforthe source reaction(presuming thatboth canbe definedasfirst-order processes),and the reactionmusthave proceededfor a periodseveral timeslonger than the inductiontimedetermined by the inverseof therate constantfor the sinkreaction.In otherwords,the unitlessproduct of the first-order sink rate constantand thetime toobservation(i.e.,thetime sinceinitiation of the reaction),k sink?t obs,must bemuchlarger than unitySteinfeld etal.,1989;Wayne,2000.4The case of nitrate radical,NO3,a naturallyourringnitrogen oxide,is interestingwith respectto steady states.Its chemistryhas beenthe subjectof considerableinterestover thelast twodecades,since theoriginal demonstrationof its existencein theatmosphereNoxon etal.,1978;Plattand Perner,1980.Because it is readilyphotolyzed byvisiblelight(l635nm)Wayne etal.,1991and becauseof its rapidreaction withnitric oxideDeMore etal.,1997,generally adaytime species,nitrateradicalis essentiallyabsentduring daylighthours andonly buildsto appreciableconcentrationsat night.Even thenit typicallyours atmixing ratios ofonly afew parts per trillion(pptv)as aresultofitsreactivity andits relativelyslow formationrate.Thus NO3would appearto bean idealcandidate foranalysisvia the steady state approximation.Indeed,numer-ous previous studies havetaken advantageof theseproper-ties of NO3to drawconclusions aboutits sinkchemistryfrom observationsofitsatmospheric abundance.The situ-ation isplicated,however,by thepresenceof theequilibrium betweenNO3,NO2and dinitrogenpentoxide,N2O5(see reactions(R1)(R4)below).A steady state inNO3depends notonly onits formation andloss,but alsoonits conversionto andreformation fromN2O5,and theatmosphericsinks for thelatter.Although theinfluence ofN2O5sinks onapparent steady state NO3lifetimes has beenconsidered in the pastAllan etal.,1999;Atkinson etal.,1986;Geyer etal.,xxa,xxb;Heintz etal.,1996;Martinez etal.,2000;Mihelcic etal.,1993;Platt etal.,xx;Platt andHeintz,1994;Platt andJanssen,1994;Smith etal.,1995,the effect of the equilibrium betweenNO3and N2O5on the applicabilityof the steady stateapproximation hasnot,to thebest ofour knowledge,beenexplored todate.We note that theeffectof the strengthofsinks for NO3on the steady state approximation has beenexamined previouslyand that there havebeen previousparisonsbetweenNO3concentrations predictedby amodelusing the steady state approximation and NO3concentration measurementsAllan etal.,2000.This paperexamines the validityof steady states forthe NO3and N2O5system usinga simpleboxmodelandoutlinesthe specificfactorsthat influencetheapplicabilityof this approximationin theatmosphere.It alsopares modelcalculationsto sampledata ofrecent,simultaneous NO3and N2O5measurements.2.Steady Statesin NO3and N2O55The chemistryof the NO3and N2O5system israthersimple andhasbeenpreviously consideredin somedetail.This sectionoutlines ourdevelopment of the analysisofNO3and N2O5observations usingthe steady stateapprox-imation.Several otherrecent studieshave reachedsimilarconclusionsAllan etal.,1999;Geyer etal.,xxa,xxb;Heintz etal.,1996;Martinez etal.,2000;Mihelcic etal.,1993;Platt andHeintz,1994;Platt andJanssen,1994,although eachdevelopment isslightly different.The sim-plest reactionscheme arisesfrom theassumption thattheloss reactions for eitherNO3or N2O5canbesummed toforma single,effective sink reaction for each pound.The sourcefor NO3is thereaction of NO2with O3,and thesourcefor N2O5is thefurther reactionof NO3with NO2.The latterreaction formsa reversibleequilibrium.The fivereactionsof importancein theabsence ofsunlight and NOare asfollows:NO2?O3!NO3?O2k1?R1?NO3?NO2?M!N2O5?M k2?R2?N2O5?M!NO3?NO2?M k20?R20?NO3?X!products k x?R3?N2O5?Y!products k y?R4?The bimolecularrate constant,k1,corresponds to the NO3source reaction,while k2is atermolecular rate constant fortheformation ofN2O5.The unimolecular(at constantpressure)rateconstant,k20,is forthermal depositionofN2O5.Here wehave followedthe previouslyestablishedconventionsee,e.g.,Atkinson etal.,1986in labelingasingle,unspecified sink for NO3asXand asimilarsingle,unspecifiedYasasink for N2O5.The rateconstants,k xand k y,are effective,pseudo-first-order rateconstants foreachof thesereactions andare thesums of thefirst-order rate constantsforthe irreversibleremoval ofthesespecies.Important atmosphericsinks for NO3in thenocturnalatmosphere includegas phasereactions withhydrocarbons,particularly thoseof biogenicorigin,andsulfur pounds,in particulardimethyl sulfide,DMS.Uptake inclouds ordeposition to the groundmay alsobeimportant processesunder someconditions.The dominantsinkfor N2O5is hydrolysis,most likelyon thesurface ofaerosolbut possiblyalso in the gasphase,to formnitric acid.6To arriveat asteady statefor NO3and N2O5,oneassumes thatthetimerateof change in their concentrationsis approximately zero.From thescheme in reactions(R1)(R4),the differentialconcentrations of the twopoundsare asfollows.dNO3?dt?k1O3?NO2?k20N2O5?k2NO2?NO3?k xNO3?4?dN2O5?dt?k2NO2?NO3?k20N2O5?k yN2O5?5?Assuming asteady statein N2O5,i.e.,dN2O5/dt?0inequation (5),the sinkforN2O5is approximately equal to theACH6-2BROWN ETAL.:NO3AND N2O5STEADY STATESdifference between itsformationandloss due to theequilibrium with NO3.k yN2O5?k2NO2?NO3?k20N2O5?6?The right hand side of equation (6)is zeroif there isastrictequilibrium betweenNO3,NO2and N2O5.However,as wewillsee below,these twoterms canbe relativelylarge andnearlyequal,allowing the system to be closeto equilibriumwhilestill allowingthe lefthand sideto benonzero.Assuming asteady statein NO3,i.e.,dNO3/dt?0,followed bysubstitution ofequation (6)into equation (4),gives thefollowing relationship.k1O3?NO2?k xNO3?k yN2O5?0?7?In otherwords,thesumofthesink reactionsfor NO3andN2O5approximately balancethe sourcefrom thereaction ofNO2with O3.There arethree approachesto solvingequation (7),as outlinedbelow.2.1.Negligible SinksforN2O57The simplestapproach is to assumethatthesink forN2O5is small,i.e.,thatthethird termin equation (7)may beneglected.This assumptiongives theresult outlinedin theintroduction,and providesa usefuldefinition forthe steadystate lifetime of NO3,t SS(NO3).t SSNO3?NO3?k1O3?NO2?k?1x?8?In thiscase,the quotientofthe NO3concentration andsourcestrength isa validmeasureofthe strengthofthesinkreaction(s)for NO3.We notethatthecenter ofequation (8)will serveas the definition ofthe steady state NO3lifetimethroughout theremainder ofthe manuscript,even thoughtheequality on the right hand sidedoes notalways hold.Inother words,the expressionis whatthe lifetimewould beifsteady statewere valid.2.2.Negligible Sinksfor NO38Many previousstudies ofthe NO3and N2O5systemhave focusedprimarily onthe analysisofthe steady statelifetimefor NO3because therehasbeenno meansofdirectly measuringthe concentrationofN2O5(at leastinthe troposphere).However,thereisan analogousrelation-ship toequation (8)forthe N2O5lifetime thates fromtheassumptionthatthe NO3sinks are small pared tothose forN2O5,i.e.,that onemay neglectthe secondterm inequation (7).This assumptionmay applyunder conditionswhereN2O5maybereadily hydrolyzed(e.g.,humid saltspray,wet aerosol)but wherebiogenic hydrocarbonandsulfur loadingare low.In thiscase,solution ofequation (7)gives ameasurementoftheratecoefficient forN2O5removal,k y,from thedefined steady state lifetimefor thispound,as shownbelow.t SSN2O5?N2O5?k1O3?NO2?k?1y?9?2.3.Nonzero Sinksfor BothNO3and N2O59The mostgeneral situationinthe atmosphereisthatthesinks for both NO3and N2O5are non-negligible.In thiscase,the relationshipbetween thesteady state lifetimes foreitherNO3orN2O5and theirsink rate coefficients beeonlyslightly moreplicated,provided that NO3and N2O5areapproximately inequilibrium witheach other.While thisassumptionwould appeartobein directconflict withequation (6)if thesinkforN2O5is non-zero,the NO3andN2O5concentrations donot in fact deviatevery stronglyfromequilibrium underconditions wheresteady state isapproximately correct.We willreturn to the validityof thisassumptionin thefollowing section.From reactions(R2)and(R20),the equilibriumconcentrationofN2O5isN2O5=K eq(T)NO2NO3.Substitution into equation (7)gives amore general expression forthe NO3steady statelifetime.t SSNO3?NO3?k1O3?NO2?k x?k yK eq NO2?1?10?Note thatthedefinitionoftheNO3steady statelifetime herein terms ofitsconcentrationand sourcestrength is the sameasequation (8),but itsinterpretation interms ofthe sinkchemistrydiffers.Equation (10)suggests that a plotoft SS(NO3)?1against K eq(T)NO2should givea straightlinewhose slopeand interceptare theeffectivefirst-order lossratecoefficients forN2O5and NO3,respectively.It isthereforepossible tomeasure the individual contributionsfromeach sinkfrom the same dataset providedthat thesteady state approximation isvalidand thatthe sinks forNO3and N2O5are relativelyconstant withrespect tovariationsin temperatureandNO2.The nextsectiondemonstrates theapplication of this approach to fielddatafor NO3and N2O5.Previous analysesAllan etal.,1999;Geyer etal.,xxa,xxb;Heintz etal.,1996;Martinez etal.,2000;Platt andHeintz,1994have evaluatedan inversedependencebetween tss(NO3)andNO2to qualitativelyassessthe importanceof heterogeneoushydrolysis ofN2O5(see below).Platt andJanssen1994have deter-mined lossrateconstantsfrom alinear fitto asimilarplot.Equation (10)shows that,in thecase wheresteadystate isvalid,itispossible toextract quantitativevalues forboth NO3and N2O5sinks byconsidering thevariation oftss(NO3)withthe product,K eq(T)NO2,rather than theNO2concentration alone.10Justasequation (9)istheN2O5analogofequation (8),one arrivesat amoregeneralexpression fortheN2O5steadystate lifetime intermsof sinkratecoefficientsby substitutionofthe equilibriumNO3concentration,NO3=N2O5/(Keq(T)NO2),intoequation (7).The resultis analogoustoequation (10).t SSN2O5?N2O5?k1O3?NO2?k y?k xK eqNO2?1?11?3.Box ModelSimulations11A boxmodel analysisdemonstrates theconditionsunder whichsteady state isavalid assumptionfor charac-terizing NO3and N2O5in theatmosphere.The modelusedthe sameset ofreactions definedabove(reactions(R1)(R4)for NO3and N2O5chemistry.Concentrations ofNO3and N2O5came fromnumerical integrationof equations (4)BROWN ETAL.:NO3AND N2O5STEADY STATESACH6-3and (5).The timestep,using rectangularintegration,wasfixed at1s andmodel outputswere averagedto producedataat1minute intervals.Variation ofthe integrationtimestep from0.25s did not affectthe results,nor didthe useofdifferent integrationschemes suchastheRunge-Kuttamethod.Thus errorfrom thenumerical integrationwasnegligible.Model concentrations ofNO2and O3also variedaordingto reactions(R1)and(R2).No additionalreactionsfor NO2,O3,NO3and N2O5were included.Themodel alsodidnotinclude effectsduetodilution ormixing.Initial concentrations ofNO3and N2O5were setto zero,while thosefor NO2and O3were nonzeroand arbitrary.Thus the model assumedan instantaneoussunset in whichNO3and N2O5concentrations were initially negligible.Despite itssimplicity,themodeldoes allowfor generalconclusionsabout steadystates inNO3and N2O5,even ifitdoes notaurately representother chemistryor dynamicsofthe real atmosphere.12The toppanel of Figure1shows atwelve hourmodelrun forconcentrations ofNO3,N2O5,NO2and O3at afixedtemperature of285K.The NO2and O3concentrations areexpressedas mixing ratios inunits ofpartsperbillion byvolume(ppbv)at standardpressure,while theNO3andN2O5concentrations arein pptvunits.The initialO3mixingratio is arbitrarily setto30ppbv,while thatfor NO2is10ppbv,characteristic of a pollutedair mass.We havechosenthese conditionsbecause thedeviations fromsteadystate for NO3and N2O5are mostobvious forlarge concen-trationsofNO2.(The discussionbelow examinesthe effectoflower NO2concentrations.)The simulation in Figure1examinesthesimple casein whichsinks forN2O5arenegligible.Aordingly,k yis setto zero.The sinkforNO3isarbitrarilychosen ask x=3.3?10?3s?1,or k x?1=5min,a valuethat isrepresentative ofdata fromfieldmeasurements and would beconsistent withmodest loadingofbiogenic species(e.g.,120pptv DMS,or190pptvisoprene,or20pptv a-pineneSeinfeld andPandis,1998).The lowertwo panelsin thefigure showthe timerateofchangefor both NO3and N2O5,i.e.,dNO3/dt anddN2O5/dt from equations (4)and (5).The solid line ineachis the total.The middlepanel shows theindividualcontri-butions todNO3/dt fromreactions(R1),(R2)and(R20),and(R3)individually,i.e.,the sourcereaction,the differencein the termsthat makeup the equilibrium,and thesink.Thecontributions todN2O5/dt inthe lower panel includetheequilibrium and thesink(reaction(R4).Because theN2O5sink iszero in this simulation,the totalin dN2O5/dt isequalto thecontribution from theequilibrium in reaction(R2).13A cursoryglance atthetotaldNO3/dt inthe centerpanelshows thatthesteadystate approximationappears tobevalid for this radical,since itsconcentrationchangeisnearly alwayszero.The sameis nottrue,however,forN2O5.The differential,dN2O5/dt inthe lowerpanel,remains nonzero throughout the simulation(except,ofcourse,where itinstantaneously crossesthrough zero)andis alwayslarger thanor parableto thesink term,k x?NO3from thecenter panel.Since thesteadystateexpres-sionfornegligible N2O5sinks in equation (8)requires thatthesteadystatebevalidforbothNO3and N2O5(i.e.,bothequations (4)and (5)must beapproximately zero),a steadystate analysis is,infact,invalid forboth poundsunderthese conditions.Figure2illustrates thispoint bypar-ingthesteadystatelifetime definedinequation (8)to theinverse