GEOPHYSICALRESEARCHLETTERS, VOL. 24, NO. 18, PAGES2299-2302,SEPTEMBER 15, 1997
Dependence
of ozoneproductiononNO and hydrocarbons
in the
troposphere
LawrenceI. Kleinman,PeterH. Daum, JaiH. Lee, Yin-Nan Lee, Linda J.Nunnermacker,
Stephen
R. Springston,
andLeonardNewman
Environmental
Chemistry
Division,Department
of AppliedScience,
Brookhaven
NationalLaboratory,
Upton,NY 11973
JudithWeinstein-Lloyd
Chemistry/Physics
Department,
SUNY/OldWestbury,Old Westbury,
NY 11568
Sanford Sillman
Department
of Atmospheric,
Oceanic,
andSpace
Sciences,
University
of Michigan,
AnnArbor,MI 48109
Abstract. An expression
for theproduction
rateof 03, P(O3), is
derivedbasedon a radicalbudgetequationapplicableto low and
high NOx conditions. Differentiationof this equationwith
respectto NO or hydrocarbons
(HC) gives an approximate
analyticformulain whichthe relativesensitivityof P(O3) to
changes
in NO or HC depends
onlyon the fractionof radicals
which are removedby reactionswith NOx. This formula is
tested by comparisonwith results from a photochemical
calculationdriven by trace gas observationsfrom the 1995
Southern Oxidants Study (SOS) campaign in Nashville,
Tennessee.
Introduction
P(O3) from SteadyState Calculations- Nashville
During the summerof 1995, the SOS conducteda field
campaignin the Nashville- Mid Tennessee
regiondirectedat
understanding
the processes
responsible
for elevated03 levels.
As part of this programthe DOE G-1 aircraftflew 17 flights,
mainly in the Nashville metropolitan area. Measurements
included
03, NO,NO2,PAN,NOy,CO,hydrocarbons
(analyzed
at York University, 1995), HCHO, H202, andorganicperoxides.
All instrumentsusedfor the presentstudyhave been described
in conjunctionwith previous field campaigns[Daum et al.,
1996;Lee et al., 1996; Weinstein-Lloyd
et al., 1996].
For the purposeof illustratingthe two approaches
of calculat-
ing P(O3) and its derivatives,we rely on datacollectedduring
two
flights in which the Nashville urbanplume was sampled.
Early experiencewith photochemicalsmogin Los Angeles
These
flights were conductedin the late morning and early
and other large urban areas led to the conclusionthat O3
afternoon of 7/15 and 7/18 with most of the data collected in the
productionduringhigh O3 episodeswasHC limitedandthatHC
emissionreductionswere the most effective way of controlling boundarylayerat an altitudeof about500 m. Samplingwasalso
between1700 and2800 m on 7/15.
03. In recentyearstherehas beena rethinkingof the ozone donein the free troposphere,
Measurements
on
7/15
were
conductedunder stagnationcondicontrolproblemand an increasedawarenessthat NOx is often
reaching120 ppb. On 7/18, there
the limiting factor,especiallyin non-urbanregions[Sillman, tionswith 03 concentrations
1990, 1993; NRC, 1991]. While the optimum strategyfor was well definedflow with 55 ppb 03 upwind of the city and
controlling03 is still a matter of debate,it is clear is that the about80 ppb downwind. A wide rangeof chemicalconcentraoccurrenceof NO x limited and hydrocarbonlimited conditions tions were encounteredon these2 days;NOx varied from 0.1
at differenttimesandplaceswill haveto be takeninto account. ppbabovetheboundarylayerto 32 ppbin a powerplantplume,
The sensitivityof P(O3) to changesin NO and HC is calcu- and isoprenevaried from below detectionlimit (2 ppt) to 3.3
latedin this studyin two ways. First, from a steadystatephoto- ppb.
chemical
modeldrivenby tracegasconcentrations
observed Steady state calculationssimilar to those describedin
duringtheMiddle Tennessee
SouthernOxidantsStudy. Second, Kleinmanet al. [ 1997] were performedusingas input the trace
that were measuredcoincidentwith 13
from a radical budgetequation. The latter approachrelies on gas concentrations
sampleson 7/15 and 15 sampleson 7/18. HCHO
argumentsand approximations
from Sillman (1995), extended hydrocarbon
hereto yield an analyticformulathat explicitlygivesthe sensitivity of P(O3) to NO and HC. In this approximateformula,
whetherP(O3) is NO x or HC limited is determinedsolelyby the
primary pathwayfor removingfree radicals,a result which
agreeswith qualitativedescriptions
of 03 production[e.g.,NRC,
1991]. As Sillman [1995] has notedthe radicalremovalpathway also controlsthe value of one combinationof "indicator
species",
namely[peroxide]/[HNO3].
was not available on 7/18; the correlationbetween HCHO and
03 as determinedfrom the other flights was used instead.
Photolysisrate constantswere calculatedfrom an Eppley UV
radiometerand a radiativetransferprogram[Madronich, 1987]
aspreviouslydescribed[Kleinmanet al., 1995]. In the calculations,the concentration
of 03, NO, CO, hydrocarbons,
HCHO,
H202, andROOH are constrained
to their observedvalues. A
steadystateconcentration
of PAN is assumed.Concentrations
of methylvinylketoneandmethacrolein
areestimated
io be250
Copyright1997by theAmericanGeophysical
Union.
and 110% of isoprene,respectively,basedon an equilibrium
mixturegoverned
by OH reactions.The calculations
yield the
Papernumber97GL02279.
concentrations
of fastreactingspeciesincludingOH, HO2, RO2,
0094-8534/97/97GL-02279505.00
andNO2 thatarein equilibrium
withthemeasured
andestimated
2299
2300
KLEINMAN
ET AL.: DEPENDENCE OF OZONE PRODUCTION
ON NO AND HYDROCARBONS
mix of stablecompounds.Rate informationsuchas P(O3) and
the fractionof radicalsremovedby differentprocessesare also
dlnP.(O3)/dln[HC
], 718
0.5
calculated.
Effects of changingNO or hydrocarbonsare determinedby
takingthe differencebetweena basecasecalculationandonein
which the concentrationof NO or HC is incrementedby 10%
and thenheld fixed. The HC incrementis appliedto CH4 and
I
-0.5
shorttime period (5 minutes)that is allowed for the systemto
respondto the incrementedNO or HC, a new equilibrium is
-1.0
,
,
5
,
I
10
• /,/
,
15 30
35
0.8
1.0
NOx (ppb)
(a)
are used to deter-
theeffectof a hypothetical
instantaneous
change
in [NO]or
,
0
but the slowerreactingspeciesdo not havea chanceto respond.
mine relative sensitivities, dlnP(O3)/dln[NO]
and
dlnP(O3)/dln[HC]. A value of 1 for thesequantitiesmeansthat
an n% changein the concentrationof NO or HC yields an n%
changein P(O3). Theserelative sensitivitiesare a measureof
dlnP(O3)/dln[NO
] 715
/•
dlnP(O Ifi[NO],718
reachedby the fastreactingspecies,OH, HO2, RO2, andNO2
(asverifiedby examiningthetime dependence
of thesespecies),
calculations
"-a
C],715
CO aswell asanthropogenic
andbiogenic
hydrocarbons.
in the
The base case and incremented
/
•
ß
.:,<. o.5
[HC]. They are useful in understandingthe processof 03
formation and its dependenceon precursorsbut shouldnot be
confusedwith descriptors
of emissionchanges,i.e., d[O3]/dENo
or d[O3]/dEHc,which provide the changein 03 concentration -• -0.5
dueto an emissionschangeat someupwindpoint.
The calculationsindicatethat P(O3) is close to zero at low
•') 0.0
NOxandincreases
toa maximum
valueof about30 (14)ppbh-I
asNOx increasesto about 14 (4) ppb on 7/15 (7/18). A further
increasein NOx causesP(O3) to decrease,a result Which is
attributed
totheeffects
ofNOxasaninhibitor
of freeradical
chemistryat highNOx concentration
[seee.g., NRC, 1991].
The dependence
of dlnP(O3)/dln[NO]and dlnP(O3)/dln[HC]
onNOx is shownin Figure1a. As NOx levelsincreasethereis a
tendencyfor an increasedsensitivity.to HC and a decreased
sensitivity
toNO,culminating
ina negative
sensitivity
toNOat
the highestNOx levels. Ozone productionis said to be NO x
limited at low [NOx] where dlnP(O3)/dln[NO] >
dlnP(O3)/dln[HC]. At high [NOx], dlnP(O3)/dln[HC] >
dlnP(O3)/dln[NO],and03 productionis HC limited. similar
curvesdepictthe response
of 03 concentration
to changesin NO
and HC emissionrates [see e.g., Cardelino and Chameides,
1995].
In Figure 1b we plot the relativesensitivitiesthat are shown
-1.0
0.0
0.2
(b)
0.4
0.6
LN/Q
Figure 1. The relativesensitivityof 0 3 productionrateto [NO]
and [HC], dlnP(O3)/din[NO]and dlnP(O3)/dln[HC],as a
functionof (a) NO x and (b) the fractionof radicalsremovedby
reactionswith NO or NO2, LN/Q. P(O3) is definedby (1) and
doesnot includedestructionprocesses.Symbolson panel (a)
are resultsfrom steadystatemodelcalculationsas identifiedin
figure. Thinlinesarea quadratic
fit to datapointsil!ustrating
that differentfits are obtainedfor 7/15 and 7/18. Open symbols
in panel(b) are the samesensitivities
as/shownin panel(a), but
plottedas a functionof the calculatedprocessvariable,LN/Q.
Analytic formula without organic nitrate (16-17) is shown by
solid line. Shadedsymbolsare•from (14-15) and differ from
solidline by the organicnitrateterm.
ß
in Figure1a asa function
of thefractionof radicals
whichare
lost by reactionsof the type Radical+NOx -• products. This
fraction, denotedas LN/Q, is calculatedfor each sampleas the
ratio of the loss rate from R+NOx reactions,LN, to the total
radicalproductionrate, Q. BecausePAN is assumedto be in
steadystate,it doesnot contributeto Q as a radicalsourceor to
L N as a radical sink. A comparisonof Figures l a and lb
indicates that there is significantly less scatter when the
independentvariable is LN/Q. This result is shownbelow to
follow from analytic expressions in which the relative
sensitivitiesof P(O3) dependon LN/Q but not on NO or NOx
alone.
RO2 + NO ---)(1-6) NO2 + t5organic
nitrate+ (1<5)RO
(R2)
Ozone is producedwith nearly a 100% yield from the subsequentphotolysisof NO2 andreactionof O atomwith 02. The
03 productionratecanthereforebe expressed
as
P(O3)- kt([HO2]+[RO2])[NO
]
(1)
wherekt is a weightedaveragerateconstant
for (R1) and(R2)
which can be defined to take into account nitrate formation in
(R2), i.e.,
kt = kI([HO2]/([HO2+RO2])
-I-(1-•) k2 [RO2]/([HO2+RO2])(2)
Equation(1) forms the basisfor many observationalbased
studieson ozone production[see e.g., Ridley et al., 1992;
P(O3) from Radical Budget
The only significantchemicalsourceof ozonein the troposphereis from the reactionof peroxyradicalswith NO, producing NO2.
HO2 + NO --) NO2 + OH
(R1)
Kleinman
et al., 1995]. We will usethisequation
alongwitha
radicalbudget
equation
forperoxY
radicalconcentration
in order
to determineP(O3)aridits sensitivityto changesin NO andHC.
Our startingpoint is a statementthat the productionrate for
radicals(oddhydr6gen= OH + HO2 + RO2), Q, mustequalthe
sum of radical sinks:
KLEINMAN ET AL.' DEPENDENCE OF OZONE PRODUCTION ON NO AND HYDROCARBONS
Q= 2k3[HO2]
2+ 2k4[HO2][RO2]
+ LR+ LN
(3)
k3 andk4 arerateconstants
for thereactions,
2 HO2 --• H202 + 02
(R3)
HO2 + RO2 --• ROOH+ 0 2
(R4)
The first 2 termsin (3) thereforerepresentlossof radicalsdueto
productionof H202 and organicperoxides. L R represents
all
otherradical- radicalreactionsincludingOH+HO 2 and RO2 +
R'O2. LN includes all radical loss reactions between free
radicalsand NO or NO2 includingOH+NO 2 • HNO3 and
whereHOx cyclingis inefficient,in thosecasesLN/Q is near
zero and a poorapproximation
to this term can be tolerated.
Substituting
(10) into(9) andassuming
thatNO is proportional
toNO2 (i.e.,[NO]=•O2]/T) andthendifferentiating,
yields,
LN = (7k5/k6)([NO]/[HC])P(03)
+ 8'P(O3)
(12)
[HC]dLN/d[HC
] = LN(dlnP(O3)/dln[HC
] - 1) + 6'P(O3)
(13)
Substituting
(12-13) into (7-8) yields,
dlnP(O3) 1 - 3/2 LN/Q + 1/2 6'P(O3)/Q
givethetotalperoxyradicalconcentration:
dln[NO]
1 - 1/2 LN/Q
(14)
(4)
wherekeffis an effectiverateconstantfor peroxideformation,
keff= k3(1-oc)
2+ k4(1-oc
) oc
(11)
[NO]dLN/d•O] = LN(l+dlnP(O3)/dln[NO])
- 6'P(O3)
RO2+NO• organicnitrate.Equation
(3) canbere-arranged
to
[HO2]
+ [RO2]
= (Q- LR- LN)l/2/(2keff)
1/2
2301
(5)
oc= [RO2]/([HO2]+ [RO2])
Substituting
(4) into (1) gives
P(O3)
= kt/(2kcff)l/2(Q-LR-Ls)l/2[NO] (6)
In previousstudieswe haveevaluated03 production
ratesusing
(6) underlow NO x conditions
wherethetermLN canbe ignored
[Kleinmanet al., 1995, 1997]. In thisstudywe includethisterm
as we are interestedin a wide range of conditionsextending
dlnP(O3) 1/2LN/Q - 1/2 6'P(O3)/Q
dln[HC]
1 - 1/2 LN/Q
(15)
In many cases,as explicitly illustratedbelow, formationof
organicnitratecanbe ignored.A particularlysimpleexpression
resultswhich givesthe sensitivityof P(O3) with respectto NO
andHC in termsof a singleindependent
variable,LN/Q:
dlnP(O3) 1 - 3/2 LN/Q
dln[NO]
1 - 1/2 LN/Q
dlnP(O3)
1/2 LN/Q
dln[HC]
1 - 1/2 LN/Q
(16)
(17)
from low to highNOx. As in the low NOx casewe will ignore
thetermLR asbeingsmallcompared
with peroxideformation.
The mechanistic
significance
of LN/Q is thatit distinguishes
low
Relative
sensitivities
(i.e.,
dlnP/dln[NO]
NOx statesin whichradicalsareremovedby formingperoxides
([NO]/P)dP/d[NO]) are obtainedby differentiating(6) with fromhighNOx statesin whichradicalsareremovedby reactions
respectto [NO] or [HC]'
with NOx [Sillman,1990;Kleinman;1991, 1994]. As discussed
by Sillman [1995], the correspondence
betweenlow and high
dlnP(O3)
1/2 [NO] dLN/d[NO]
NOx statesand the productionof peroxidesor HNO3 as the
= l(7)
din[NO]
Q- L$
primaryphotochemical
endproductservesasthebasisfor using
the ratio [peroxide]/[HNO3]as an indicator for whether 03
production
is NOx or HC limited. Note, however,the different
dlnP(O3) -1/2 [HC] dLN/d[HC]
=
(8)
time scales. LN/Q gives sensitivitiesat the presentmoment,
dln[HC]
Q- L N
The dependence
of Q on [NO] and [HC] is zero becausethe
radicalprecursors
(mainly 03 and HCHO) are constrained
to
their observedvaluesand thereforedon'tchangewith a change
in NO or HC. The dependence
of kt andkeffon NO andHC is
generallysmallandhasbeenignored.
while the indicatorratio reflectsthe pasthistoryof an air mass.
In Figure lb we compare dlnP(O3)/dln[NO] and
dlnP(O3)/dln[HC]from (16-17) with the corresponding
quantities determinedfrom steadystatesimulationsof the Nashville
dataset. On a qualitativelevelwe seethattheanalyticformulas
capturethe significantfeaturesin the Nashville calculations.
The key to using(7) and(8) is to find a goodapproximation Equations(16-17) showa curve- crossingat exactlyLN/Q =
for dLN/d[NO] and dLN/d[HC]. First,we notethat,as in the 1/2, which separatesNO from HC limited conditions. This
steadystatecalculation,PAN is assumed
to be in equilibrium, result,whichwaspreviouslyfoundby Sillman[ 1995],is seento
and is neither a sourceor sink for radicals. Thus, radical loss is
due mainly to production of HNO3 and organic nitrate
be a goodapproximation
to theNashvilledatapoints. At the
curvecrossing,NO and HC reductionsare equallyeffectivein
reducingP(O3). However,therelativesensitivities
havea value
of 1/3 indicatingthat neitherreductionis particularlyeffective.
LN = P(HNO3)+ P(RONO2)
= ks[OH][NO2]
+ 8'P(O3) (9) At LN/Q = 2/3, thereis a zero crossingof dlnP(O3)/dln[NO],
wherek5 is therateconstant
for OH+NO2 -->HNO3 andproduc- closeto what the Nashville data shows. Figure lb also shows
from (14-15) with the organicnitratetermcalcution of RONO2 hasbeenwrittenin termsof an averagenitrate the sensitivities
yield, 8', using(R2). Accordingto Sillman[1990],therateof lated from the steadystatebox model. The differencebetween
the
03 productioncanbe approximated
by the rate at which OH the shadedsymbolsand solidcurvein Figure lb represents
effectof organicnitratewhichis seento be small,in spiteof the
reactswith hydrocarbons
(includingCO):
presenceof morethan 3 ppb of isoprene(with 8' = 0.15) in
P(O3)= k6[OH][HC]
(10) severalsamples.A comparisonbetweenthe openand shaded
symbols indicates that including organic nitrate generally
wherek6 is an effectiverate constantfor OH+hy•ocarbon •
H02 or RO2. Although(10) doesnot applyto cleansituations improvesthe agreementbetweentheoreticaland calculated
(RONO2):
2302
KLEINMAN ET AL.' DEPENDENCE OF OZONE PRODUCTION ON NO AND HYDROCARBONS
sensitivities.Sillman [1995] has discussedthe effectsof PAN
on the NO-HC transition point. He arrives at the criteria
P(HNO3) -- 2 P(Peroxide),where "P" is productionrate. This
reducesto L•q/Q- 1/2 if P(PAN) - 0 andgivesL•q/Q> 1/2 if
P(PAN) > 0. This resultalsofollowsfrom (11)-(15) if P(PAN)
replaces;5'P(O3).
Kleinman, L.I., Seasonal dependenceof boundary layer peroxide
concentration:
The low andhighNOx regimes,J. Geophys.
Res.,96,
20,721-20,733, 199I.
Kleinman,L.I., Low and high NOx troposphericphotochemistry,
J.
Geophys.Res.,99, 16,831-16,838,1994.
Kleinman,L, Y.-N. Lee, S.R. Springston,J.H. Lee, L. Nunnermacker,J.
Weinstein-Lloyd, X. Zhou, and L. Newman, Peroxy radical
concentration
Conclusion
A radical budget equation for 03 productionrate yields
realisticsensitivitiesto changesin NO and HC underboth low
andhighNOx conditionsasjudgedby a comparison
with steady
statemodel resultsfrom the SOS field campaignin Nashville,
TN. The mostimportantfactorin determiningthe sensitivityof
P(O3) to NO andHC is the fractionof radicalsthat are removed
by reactionsof thetype Radical+ NOx --) products,a resultthat
agrees with the use of the "indicator species" ratio,
[peroxide]/[HNO3],to diagnoseNOx andHC limitedconditions
[Sillman, 1995]. A crossoverfrom NO to HC sensitiveconditionsoccurswhen 1/2 of radicalsare removedby R+NOx. NO
is counter-productiveto 03 productionwhen more than 2/3 of
radicals are removed by reactionswith NOx. Although the
presentstudyis concerned
with the dependence
of P(O3) on NO
and HC, not the dependenceof [03] on emissions,it is likely
thatthe two problemsare linkedas [03] is dueto 03 production
over the pasthistoryof an air parcel. It thereforeseemsworthwhile to investigate whether the insensitivity of P(O3) to
changesin NO andHC over a wide rangeof LN/Q, contributes
significantlyto the problemof controllingpeak 03
concentrations.
and ozone
formation
rate at a rural
site in the
southeastern
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relatedcompounds
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R.B. Chatefield,
J.G.Walega,R.E. Shetter,
M.A.
Carroll, and D.D. Montzka, Measurements and model
simulationsof the photostationary
stateduring the Mauna Loa
ObservatoryExperiment:Implicationsfor radicalconcentrations
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Kleinman,Measurement
of peroxidesandrelatedspeciesin the 1993
Acknowledgments. We thank the pilots and flight crew from PNL
North AtlanticregionalExperiment,d. Geophys.
Res.,101, 29,081for a job well done. We gratefullyacknowledgethe manycontributions
29,090, 1996.
of P. Klotz of BNL andC. BerkowitzandV. Morrisof PNL in collecting
York University, Centre for AtmosphericChemistry, Principal
and reducingthe data. This studybenefittedin many ways from the
Investigator,D. Hastie,HydrocarbonAnalysisfor "SouthernOxidant
framework that was providedby the SouthernOxidants Study. We
Study1995"CanisterSamplesCollectedby Brookhaven
National
gratefullyacknowledgethe AtmosphericChemistryProgramwithin the
Laboratory,1995.
Office of Health and EnvironmentalResearchof DOE for providingthe
G-I aircraft. Supportfor instrumentdevelopment,participationin the
Nashville experiment,and subsequentdata analysiswas from DOE and
EPA. L. Kleinmangratefullyacknowledges
supportfrom R. Dennisof
P. H. Daum, L. I. Kleinman, J. H. Lee, Y.-N. Lee, L. Newman, L. J.
EPA for work on observationalbased analysis. This researchwas
S. R. Springston,
EnvironmentalChemistryDivision,
performed under sponsorshipof the U.S. DOE under contracts Nunnermacker,
DE-AC02-76CH00016.
Departmentof Applied Science,BrookhavenNational Laboratory,
Upton, NY 11973. (e-mail: phdaum•bnl.gov; kleinman•bnl.gov;
jaihlee•bnl.gov;ynlee•bnl.gov;newman•bnl.gov;lindan•bnl.gov;
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