JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D12, 10.1029/2001JD000932, 2002
Ozone production rates as a function of NOx abundances and HOx
production rates in the Nashville urban plume
J. A. Thornton,1 P. J. Wooldridge,1 R. C. Cohen,1,2,3 M. Martinez,4 H. Harder,4
W. H. Brune,4 E. J. Williams,5,6 J. M. Roberts,5,6 F. C. Fehsenfeld,5,6 S. R. Hall,7
R. E. Shetter,7 B. P. Wert,7 and A. Fried7
Received 6 June 2001; revised 14 September 2001; accepted 14 October 2001; published 22 June 2002.
[1] Tropospheric O3 concentrations are functions of the chain lengths of NOx (NOx NO
+ NO2) and HOx (HOx OH + HO2 + RO2) radical catalytic cycles. For a fixed HOx
source at low NOx concentrations, kinetic models indicate the rate of O3 production
increases linearly with increases in NOx concentrations (NOx limited). At higher NOx
concentrations, kinetic models predict ozone production rates decrease with increasing
NOx (NOx saturated). We present observations of NO, NO2, O3, OH, HO2, H2CO, actinic
flux, and temperature obtained during the 1999 Southern Oxidant Study from June 15 to
July 15, 1999, at Cornelia Fort Airpark, Nashville, Tennessee. The observations are used
to evaluate the instantaneous ozone production rate (PO3) as a function of NO abundances
and the primary HOx production rate (PHOx). These observations provide quantitative
evidence for the response of PO3 to NOx. For high PHOx (0.5 < PHOx < 0.7 ppt/s), O3
production at this site increases linearly with NO to 500 ppt. PO3 levels out in the range
500–1000 ppt NO and decreases for NO above 1000 ppt. An analysis along chemical
coordinates indicates that models of chemistry controlling peroxy radical abundances, and
consequently PO3, have a large error in the rate or product yield of the RO2 + HO2 reaction
for the classes of RO2 that predominate in Nashville. Photochemical models and our
measurements can be forced into agreement if the product of the branching ratio and rate
constant for organic peroxide formation, via RO2 + HO2 ! ROOH + O2, is reduced by a
factor of 3–12. Alternatively, these peroxides could be rapidly photolyzed under
atmospheric conditions making them at best a temporary HOx reservoir. This result
implies that O3 production in or near urban areas with similar hydrocarbon reactivity and
HOx production rates may be NOx saturated more often than current models
suggest.
INDEX TERMS: 0317 Atmospheric Composition and Structure: Chemical kinetic and
photochemical properties; 0345 Atmospheric Composition and Structure: Pollution – urban and regional
(0305); 0365 Atmospheric Composition and Structure: Troposphere – composition and chemistry; 0368
Atmospheric Composition and Structure: Troposphere – constituent transport and chemistry; KEYWORDS:
Ozone, NO2, peroxy radicals, Nashville, OH, HO2
1. Introduction
[2] Photochemical O3 production is a complex function
of nitrogen oxide (NOx NO + NO2) and hydrogen radical
1
Department of Chemistry; University of California, Berkeley,
California, USA.
2
Department of Earth and Planetary Science, University of California,
Berkeley, California, USA.
3
Energy and Environment Technologies Division, Lawrence Berkeley
National Laboratory, Berkeley, California, USA.
4
Department of Meteorology, Pennsylvania State University, University
Park, Pennyslvania, USA.
5
Aeronomy Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado, USA.
6
CIRES/University of Colorado, Boulder, Colorado, USA.
7
Atmospheric Chemistry Division, National Center for Atmospheric
Research, Boulder, Colorado, USA.
(HOx OH + HO2 + RO2) abundances, and of the
partitioning of NO x between NO and NO2 and HO x
between OH, HO2, and RO2 [National Research Council,
1991]. Ozone production is initiated by reactions that
produce HOx. The production rate of new hydrogen radicals, PHOx, occurs primarily via O3 and H2CO photolysis:
ðR2Þ
O3 þ hn ! O 1 D þ O2 ;
O 1 D þ H2 O ! 2OH;
ðR3Þ
O 1 D þ N2 ; O2 ! O 3 P þ N2 ; O2 ;
ðR1Þ
ðR4aÞ
H2 CO þ hn ðþ 2O2 Þ ! 2HO2 þ CO;
ðR4bÞ
H2 CO þ hn ! H2 þ CO:
Other sources of hydrogen radicals include photolysis of
H2O2 and HONO. The OH produced in (R2) usually leads
Copyright 2002 by the American Geophysical Union.
0148-0227/02/2001JD000932$09.00
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THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
to the production of peroxy radicals (RO2) via the oxidation
of VOC by OH in reactions (R5) and (R6). RO2 then
oxidize NO to NO2 in reaction (R7a) leading to the
production of O3 in reactions (R8) and (R9):
ðR5Þ
RH þ OH ! R þ H2 O;
ðR6Þ
R þ O2 ðþMÞ ! RO2 ;
ðR7aÞ
RO2 þ NO ! RO þ NO2 ;
ðR8Þ
NO2 þ hn ! NO þ O 3 P ;
ðR9Þ
O 3 P þ O2 ðþMÞ ! O3 :
The alkoxy radical product (RO) of the RO2 + NO reaction
usually reacts rapidly to produce HO2 which then oxidizes
NO, regenerating OH and producing a second NO2
molecule:
ðR10Þ
RO þ O2 ! R0 O þ HO2
ðR11Þ
HO2 þ NO ! NO2 þ OH:
Net ðR5ÞðR11Þ :
RH þ 4O2 ! R0 O þ 2O3 þ H2 O:
In most cases, the aldehyde or ketone product (R0O) of
the net reaction continues to be oxidized in the same
manner yielding more than two O3 molecules per VOC
emitted.
[3] The rate-determining step in the chain propagation is
usually oxidation of NO by HO2 and RO2 in reactions
(R7a) and (R11). Under conditions of high peroxy radical
(HO2 + RO2) abundances and low NOx the steady state
concentration of peroxy radicals is insensitive to variation
in NOx because the primary chain terminating reactions of
the HOx catalytic cycle are the HOx + HOx reactions:
ðR12Þ
OH þ HO2 ! H2 O þ O2 ;
ðR13Þ
HO2 þ HO2 ðþ MÞ ! H2 O2 þ O2 ;
ðR14Þ
HO2 þ RO2 ! ROOH þ O2 ;
O3 production in this chemical regime is said to be NOxlimited and the O3 production rate increases approximately
linearly with NOx. Reactions of HOx with NOx lead to chain
termination of both the HOx and NOx catalytic cycles
through nitric acid and alkyl nitrate formation:
ðR15Þ
OH þ NO2 ðþ MÞ ! HNO3 ;
ðR7bÞ
RO2 þ NO ðþ MÞ ! RONO2 :
At some point, as NOx increases, these termination steps
become faster than the HOx – HOxreactions (R12) – (R14). In
this regime, O3 production slows, decreasing with increasing NOx. O3 production in this high NOx regime is said to
be NOx-saturated (or VOC-limited).
[4] In addition to the role of NOx as a control over the
abundance of peroxy radicals, PO3 is affected by the rate of
HO2 and RO2 production. The role of PHOx in the balance
between NOx-limited and NOx-saturated O3 production is
illustrated by considering a constant NOx level. As PHOx
increases, the rate of OH + RH increases. It follows that
organic peroxy and hydroperoxy radical concentrations
increase with resulting increases in O3 production rates.
As PHOx increases, the corresponding increase in peroxy
radicals enhances the relative importance of HOx – HOx
catalytic chain termination steps in reactions (R12) – (R14)
over the competing HOx – NOx reactions because the rates
of HOx – HOx reactions increase as the square of HOx
concentrations. This in turn shifts the peak O3 production
rate, which by definition occurs at the crossover between
NOx-limited and NOx-saturated behavior, to higher levels
of NOx. Of course, in the polluted boundary layer the issue
is still more complicated because the assumption of constant
NOx does not hold. Increases in HOx abundance can
accelerate the removal of NOx by conversion to the longlived reservoirs HNO3 and organic nitrates. In the upper
troposphere, Jaegle et al. [1998, 2001] show that PHOx and
NOx are strongly correlated, making it challenging to obtain
observations over a range of NOx at a fixed PHOx or vice
versa.
[5] The crossover point between NOx-limited and NOxsaturated regimes remains important from both a regulatory standpoint and as a test of our understanding of the
chemistry controlling O3 production. Regulatory concerns
have focused on whether NOx-saturated inner cities will
have higher ozone concentrations if modest NOx controls
are enacted [e.g., Cardelino and Chameides, 1990].
Analyses of atmospheric models have focused on identifying observable quantities that can be used to indicate
whether ozone concentrations at a particular location
result from NOx-limited or NOx-saturated photochemistry
[Sillman, 1995; Kleinman et al., 1997; Sillman et al.,
1997; Tonnesen and Dennis, 2000a, 2000b; Trainer et al.,
2000].
[6] In this article, we use in situ measurements of NO2,
NO, OH, HO2, O3, H2CO, actinic flux, relative humidity,
and temperature made at Cornelia Fort Airpark (CFA), 8 km
NE of downtown Nashville, Tennessee, during the 1999
Southern Oxidants Study (SOS 99) to quantify instantaneous O3 production rates and to empirically evaluate the
influence of NOx and PHOx on O3 production rates. We
examine the crossover point between NOx-limited and NOxsaturated regimes, and we use chemical coordinates [Cohen
et al., 2000; Lanzendorf et al., 2001] to evaluate the relative
accuracy of the catalytic chain termination steps in current
photochemical models.
2. Measurements
[7] Continuous in situ measurements of NO2, NO, O3,
OH, HO2, H2CO, actinic flux, relative humidity, and temperature were made during SOS 99 at CFA. These data and an
extensive suite of observations of other chemical and physical parameters may be obtained by contacting the individual
investigators. A contact list is available at http://www.al.
noaa.gov/WWWHD/pubdocs/SOS/SOS99.html. Observations were made 10 –12 m above the ground from a 12-m
walkup tower. These measurements were collected at rates
between 0.03 and 1 Hz. The analysis presented here uses
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
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7-3
measurements were made using tunable diode laser absorption spectroscopy [Fried et al., 1998]. Spectrally resolved
measurements of the downwelling solar actinic flux spanning a wavelength region from 280 to 420 nm were made
using a 2p dome coupled by optical fibers to a monochromator. The downwelling actinic flux measurements together
with an in situ measurement of the upwelling radiation were
used to calculate the photolytic rate constants used here
[Shetter and Muller, 1999]. The upwelling radiation was
consistent with an albedo of 4%. Relative humidity and
temperature were measured using a commercial probe
(Campbell Scientific).
[9] Figure 1 shows measured and derived species versus
fractional day of the year for a typical day (July 9, 1999) at
Cornelia Fort Airpark. O3 peaks at 60 ppb on this day. The
maximum and minimum peak O3 concentrations observed
during the study were 110 and 30 ppb, respectively. The
sum total peroxy radical concentrations ([HO2 + RO2]PSS,
triangles) were derived from the NOx-steady state equations
as described below. Water vapor mixing ratios, plotted in
parts per thousand (ppth) in Figure 1, were calculated from
measured temperature and relative humidity and ranged
from 10 to 30 ppth during the course of the study.
[10] Table 1 shows the measurement method and accuracy (1s) for each species used in this analysis. Throughout
our analysis we average over enough observations that
precision errors from the instrumentation can be neglected.
We focus our analysis on daytime data by excluding data
where JNO2 < 5 105 s1. Reaction rate constants are
calculated point by point as functions of temperature, total
number density, and where necessary, water vapor number
density.
3. Instantaneous O3 Production Rate
Figure 1. Measured and derived species are plotted
versus time for 9 July 1999, a typical day at Cornelia
Fort Airpark. NO2 (squares), NO (circles), and O3
(triangles) measurements are plotted in ppb. JNO2 (thick
black line, left axis, s1) and JO3 ! O1D (gray line, right
axis, s1) are derived from solar actinic flux measurements.
[HO2 + RO2]PSS (triangles, ppt) are derived from the NOxsteady state assumption, and OH (small squares, 5-min
running average, ppt) and HO2 were measured by LIF.
H2CO (squares) and PAN (circles) measurements are
plotted in ppb. Temperature (squares) is in degrees celsius
and the calculated water mixing ratio (circles) is in parts
per thousand (ppth).
1-min averages of the data with the exception of OH
concentrations. A five-point running average of the 1-min
OH data is used here. The measurements were synchronized
in time using temporal structures observed in the measured
NO2/NO ratio and JNO2.
[8] NO2 measurements were made using laser-induced
fluorescence (LIF) [Thornton et al., 2000], NO was measured by an NO-O3-chemiluminescence instrument [Williams
et al., 1998], and O3 was measured by UV absorbance
[Ridley et al., 1992a]. OH was measured directly by LIF
and HO2 was converted to OH by NO followed by LIF
detection of the resulting OH [Mather et al., 1997]. H2CO
[11] NO and NO2 rapidly interconvert in reactions that
form a null catalytic cycle and in reactions that catalytically produce O3. In the null cycle, O3 oxidizes NO to
NO2, and photolysis of NO2 in reaction (R8) is followed
by reaction (R9) to regenerate an O3 molecule with a yield
near unity:
ðR16Þ
NO þ O3 ! NO2 þ O2 ;
ðR8Þ
NO2 þ hn ! NO þ O 3 P ;
ðR9Þ
O 3 PÞ þ O2 ðþMÞ ! O3 :
The rate constants for reactions of HO2 and RO2 with NO to
produce NO2 are nearly 1000 times faster than the rate
constant of NO with O3. Although HO2 and RO2
concentrations are 1000 times lower than O3 concentrations, these reactions provide a mechanism for the
production of O3:
ðR11Þ
NO þ HO2 ! NO2 þ OH;
ðR7aÞ
NO þ RO2 ! NO2 þ RO;
ðR8Þ
NO2 þ hv ! NO þ Oð3 PÞ;
ðR9Þ
Oð3 PÞ þ O2 ðþMÞ þ O3 ;
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THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
Table 1. Continuous, in Situ, Ground-Based Measurements of NO2, NO, O3, OH, HO2, H2CO, and Solar Actinic Flux Made From June
15 to July 15, 1999, at Cornelia Fort Airpark, Nashville, Tennessee as Part of the SOS99 Campaigna
Species
Method
Accuracy, % , 1s
References
NO2
NO
O3
OH
HO2
H2CO
Solar actinic flux
laser-induced fluorescence (LIF)
O3-chemiluminescence
UV-absorbance
LIF
NO titration/OH LIF
tunable diode laser absorption spectroscopy
spectral radiometer
5
4
5
20
20
10
5
Thornton et al. [2000]
Williams et al. [1998]
Ridley et al. [1992a]
Mather et al. [1997]
Mather et al. [997]
Fried et al. [1998]
Shetter and Muller [1999]
a
Observations were made at 11 m above ground on a 12-m walkup tower. The measurement method and total uncertainty (1s) for each species are
presented.
The gross rate of new O3 produced by this mechanism,
PO3, is
PO3 ¼
kHO2þNO ½HO2 þ
X
!
kRiO2þNO ½Ri O2 ½NO
ð1Þ
processes involved are NO2 photolysis and the reaction of
NO with O3:
PO3 ¼ JNO2 ½NO2 kNOþO3 ½NO½O3 ð4Þ
i
where kHO2+NO is the rate constant for reaction of HO2 with
NO in reaction (R11), and the sum is over the suite of
organic peroxy radicals with R group Ri and the associated
rate constants kRiO2+NO for reaction (R7a). In the absence of
fresh NOx emissions or rapid NOx removal a photochemical steady state between NO and NO2 is rapidly established
(t 100 s). The sum total peroxy radical concentration,
[HO2 + RO2]PSS, can be inferred using the steady state
equation:
keff ½HO2 þ RO2 PSS ½NO þ kNOþO3 ½NO½O3 ¼ JNO2 ½NO2 ð2Þ
where keff is an effective rate constant for the reactions of
HO2 with NO and of RO2 with NO, kNO+O3 is the rate
constant for reaction of NO with O3 in reaction (R16), and
JNO2 is the rate constant for NO2 photolysis in reaction
(R8). This inference assumes the chemistry described
above is complete. The subscript PSS (photostationary
state) is used here to distinguish inferred quantities from
direct in situ observations. Reactions of NO with most
organic peroxy radicals to yield NO2 have been shown to
occur at similar rates to those with HO2 [Atkinson, 1994;
DeMore et al., 1997]. In this analysis we assume
keff = kHO2+NO. Note that the derived product keff [HO2 +
RO2]PSS is expected to be more accurate than the absolute
sum peroxy radical concentrations. At CFA, there were
mea-surements of HO2 but not of RO2. We use the
difference between the measured HO2 and the calculated
sum total peroxy radical concentrations to estimate the
amount of RO2:
½RO2 PSS ¼ ½HO2 þ RO2 PSS ½HO2 OBS :
ð3Þ
Typical [RO2]PSS/[HO2]OBS at CFA ranged between 0 and
2 with extremes of approximately 1 and 4.
[12] Although some of our conclusions depend on the
estimates of RO2 from equations (2) and (3), PO3 can be
derived from the observations without any assumptions
about reactions of HO2 or RO2 so long as the only other
[13] Observations and equations (1) – (4) have been used to
infer RO2 radical abundances and to estimate instantaneous
ozone production rates for a range of urban, rural, and remote
environs [Kelly et al., 1980; Parrish et al., 1986; Ridley et al.,
1992b; Cantrell et al., 1993a; Kleinman et al., 1995; Carpenter et al., 1998; Frost et al., 1998; Patz et al., 2000]. Figure
2a shows the calculated PO3 plotted versus time of day, and
Figure 2b shows the calculated PO3 at CFA for three consecutive days, June 25– 27, 1999. PO3 inferred from equation (4)
peaks in the afternoon and reaches zero in the early morning
and late evening as the two terms become nearly equivalent.
Negative PO3 is often observed during the period of 0600–
0900 local standard time (LST). This could indicate that the
air sampled during this time of the day was frequently not in
steady state or that other processes not included in equation
(4) and involving NOx or O3 take place at a rate sufficient to
change the photostationary state. There is also day-to-day and
minute-to-minute variation in the magnitude of PO3 because
of cloud cover and changes in VOC, NOx, and O3 abundances. Some of the variation is due to noise in the measurements.
Averaging over the large data set eliminates the importance of
instrument noise in our analysis.
[14] The steady state assumption is not valid in the
following situations: (1) when measurements are made close
to NOx sources such that a steady state is not achieved prior
to sampling the air mass because of insufficient reaction
time, (2) when there are fast changes in actinic flux, and (3)
when the air sampled is sufficiently inhomogeneous so that
mixing drives NO and NO2 out of steady state in an air mass.
Cornelia Fort Airpark is nearly 2 km from a major freeway
and 8 km from downtown Nashville. These are the closest
large NOx sources. The time for a well-mixed air mass to
reach CFA from these sources is at least 10 min for an
average wind speed in the range of 1 – 4 m/s. This is several
NOx lifetimes and consequently, with respect to time for
chemistry to occur downwind of sources, the NOx partitioning in air masses observed at Cornelia Fort should usually be
in a steady state. Small NOx sources such as emissions from
the surface could perturb the NOx partitioning from steady
state, leading to PO3 and [HO2 + RO2]PSS that are biased
high compared to the true values. To investigate the magnitude of this potential bias at CFA, we assume that the
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
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Figure 2. (a) One-minuted averaged PO3 calculated using equation (4) plotted versus hour of day
(local standard time). All of the data obtained at CFA is shown. (b) Three consecutive days, 25– 27
June 1999, of PO3 versus time.
observed NO concentrations are a combination of NO that is
in steady state and NO that is freshly emitted from the
surface, i.e., [NO]OBS = [NO]PSS + [NO]Surf. A typical
nighttime value of [NO]OBS at CFA is 20 ppt. If this is
entirely due to NO emitted from the surface (i.e., [NO]Surf
= 20 ppt), and if the source strength is constant over a
24-hour period, we estimate that our derived PO3 and
[HO2 + RO2]PSS are biased high by 5%. The size of this
bias scales nearly linearly with increasing estimates of NO
concentrations that are not in steady state. Propagating a 5%
change in PO3 or [HO2 + RO2]PSS through our analysis has a
negligible effect on the conclusions of this paper.
[15] During the daytime, NOx at Cornelia Fort was
typically 1 – 5 ppb. On occasions, NOx rose above 15 ppb,
and these high NOx points are correlated with negative PO3.
The arrival of these plumes is also strongly correlated with
times when gradients in NOx and O3 were larger than 10%/
min. NO2 production in these plumes through reaction of
HO2 with NO was positive. At NOx greater than 25 ppb,
where the steady state calculation yields [HO2 + RO2]PSS
less than 3 ppt, the [HO2]OBS is often significantly larger
than [HO2 + RO2]PSS. The high NOx points were primarily
observed in the morning, possibly before solar heating
could begin to effect vigorous turbulence in the boundary
layer. Therefore high NOx seems to be a reasonable indicator for mixing of heterogeneous air masses causing NOx
to be out of photostationary state. As we are relying on the
accuracy of the photostationary state equation for our
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THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
conclusions, we exclude data where NOx > 15 ppb from
further analysis. Choosing a cutoff of NOx less than 15 ppb
is somewhat arbitrary, excluding data above either 10 or 20
ppb does not significantly alter our conclusions. All data
used in the analyses presented from here on have been
subjected to the two selection criteria: JNO2 > 5 105 s1
and NOx < 15 ppb. Other selection criteria, when noted, are
always used in addition to these two. For the available PO3
data calculated from equation (4), the JNO2 selection criteria
removes 2175 points (15) and the 15 ppb criteria eliminates another 2317 points (20% of the data that remains
after the JNO2 filter). We also impose an additional filter to
the PO3 data to remove extreme outliers by requiring each
point be within 3 standard deviations from the mean at that
time of day. This filter excludes an additional 102 points
(1%) from the PO3 data.
[16] The accuracy of PO3 calculated using equation (4)
depends on the accuracy of the products: J NO2 [NO 2 ]
and k NO+O3 [NO][O 3 ]. The accuracy of the product
kNO+O3 [NO][O3] is estimated to be ±12%, assuming systematic errors in the measurements (see Table 1) and rate constant
[DeMore et al., 1997] add in quadrature. Prior studies have
implicated the accuracy of NO2 measurements as the largest
source of error in PO3 calculated from equation (4) [e.g.,
Frost et al., 1998]. The SOS 99 campaign included three
different techniques for measuring NO2: laser-induced fluorescence [Thornton et al., 2000], photolysis-chemiluminescence [Williams et al., 1998], and differential optical
absorption spectroscopy [Alicke et al., 2000]. All three
methods agreed to within ±5% (1s) on average over the
entire campaign [Wooldridge et al., 2000]. The LIF NO2
measurements used here are therefore thought to be accurate
to 5%. The uncertainty in the J value is dominated by
uncertainty in the cross-section and quantum yield (±20%
[DeMore et al., 1997]). The accuracy of the product
JNO2[NO2] is estimated to be ±21% (1s). The maximum
systematic uncertainty in the derived PO3 is therefore ±32%.
[17] The systematic error in the difference JNO2[NO2] kNO+O3[NO][O3] can be reduced by forcing reasonable
behavior at sunset as described below. In the evening at
high solar zenith angles, the rate of O3 production at CFA
drops to near zero as JNO2[NO2] kNO+O3[NO][O3] and the
product kNO+O3[NO][O3] is typically 5 – 10 times higher
than kHO2+NO[NO][HO2]. For this high solar zenith angle
data we require that the fractional conversion of NO to NO2
by organic peroxy radicals be on average greater than or
equal to zero:
kHO2þRO2 ½RO2 ½NO
0:
kHO2þRO2 ½RO2 ½NO þ kHO2þNO ½HO2 ½NO þ kNOþO3 ½O3 ½NO
ð5Þ
This constraint is equivalent to requiring [HO2 + RO2]PSS to
be at least equal to [HO2]OBS (see equation (3)) on average
during the morning and evening, and it couples all of the
systematic errors together. We find that a negative bias in the
inferred peroxy radical concentration is present at high solar
zenith angles unless we increase the product JNO2[NO2] by
11%, decrease the product kNO+O3[NO][O3] by 11% or make
an equivalent change in a combination of the two terms. This
adjustment is well within the uncertainty in the rate constants
and measurements. We extend this adjustment to the entire
data set by increasing JNO2 by 11%. The PO3 data plotted in
Figure 2 include this adjustment to JNO2.
[18] PO3 is usually the difference between two large
numbers with consequent high uncertainty in any individual
value. While the random uncertainty in individual PO3
values can be averaged away, the average value of PO3
carries the effects of any systematic errors in the terms
JNO2[NO2] or kNO+O3[NO][O3]. To reduce the influence of
these systematic errors we focus on the derivatives of PO3
with respect to PHOx and NO. These derivatives do not
completely eliminate the effects of systematic errors. For
example, the largest term in PHOx is the measured O3
concentration and PO3 depends directly on NO. Nevertheless, the effect of measurement error is damped by
focusing on the derivatives because systematic errors in
the measurements are additive or multiplicative constants
which at most shift PO3 with respect to NO or PHOx but do
not change the functional form of the derivative @PO3/@NO
or @PO3/@PHOx. We also observe a systematic error due to a
breakdown the photostationary state assumption that is
correlated with NO. If our cutoff of 15 ppb NOx is not
low enough, our conclusions could be biased at high NOx.
4. PO3 Dependence on PHOx and NO
[19] We take the total primary HOx radical production
rate to be the sum of the O3 and formaldehyde photolysis
channels leading to OH or HO2 via reactions (R1) – (R3) and
(R4a). The total production rate for primary HOx radicals,
PHOx, at CFA is
PHOx ¼ 2JO3!O1 D ½O3 k2 ½H2 O
þ 2 JH2CO ½H2 CO
k2 ½H2 O þ k3 ½N2 þ O2 ð6Þ
where JO3!O1D and JH2CO are the photolytic rates constants
for reactions (R1) and (R4a), respectively, and k2 and k3 are
the rate constants for reactions (R2) and (R3), respectively.
JO3 and JH2CO derived from solar actinic flux measurements,
and measurements of O3, H2CO, relative humidity, and
temperature are used to calculate PHOx explicitly. Values for
PHOx ranged from 0 to greater than 1 ppt/s.
[20] During the peak of solar radiation at CFA the
photolysis of O3 in reactions (R1) – (R3) comprised 70%
on average of PHOx. We assume peroxyacyl nitrate (PAN)
was not a net source of peroxy radicals at CFA. Its time rate
of change was small compared to its lifetime with respect to
thermal decomposition (25 min at 300 K, 760 Torr), and
thus PAN was most likely in thermal equilibrium with NO2
and the peroxyacyl radical. Furthermore, the reaction of the
peroxyacyl radical (PA) with NO2 to reform PAN is on
average 2 times faster than the reaction PA + NO ! NO2 +
products under typical midday conditions at CFA. The rate
of PA + NO to yield NO2 corresponds to 5 – 10% of the
total [HO2 + RO2]PSS + NO ! NO2 inferred from equation
(2). Measurements of HONO [Alicke et al., 2000] at CFA
show that over most of the day this term is small. The large
concentrations of HONO coincide with the early morning
rush hour traffic during the period where we most often
observe NOx to be greater than 15 ppb. H2O2 and larger
aldehyde (C2 – C9 straight-chain aldehydes) photolysis
together are typically 15% of the major HOx sources
included in our analysis. These processes become a larger
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
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7-7
Figure 3. (a) The averaged (solid circles) and the raw (open squares) PO3 from the high PHOx regime
plotted versus [NO]. (b) Averaged PO3 plotted versus [NO] at CFA. PO3 data were placed into three
PHOx bins: high (0.5 < PHOx < 0.7 ppt/s, circles), moderate (0.2 < PHOx < 0.3 ppt/s, squares), and low
(0.03 < PHOx < 0.07 ppt/s, triangles), and then averaged as a function of NO. All three PHOx regimes
demonstrate the expected generic dependence on NO, PO3 increases linearly with NO for low NO
(<600 ppt NO), and then PO3 becomes independent of NO for high NO (>600 ppt NO). The crossover
point between NOx-limited and NOx-saturated O3 production occurs at different levels of NO in the
three PHOx regimes.
fraction in the late afternoon when PHOx is small. However,
there are not enough measurements of HONO, H2O2 or
larger aldehydes during the day to include them in this
analysis. Because we focus on high PHOx, omitting these
processes does not affect our conclusions.
[21] The PO3 data shown in Figure 3 are the data from
Figure 2a separated into a high (0.5 < PHOx < 0.7 ppt/s),
moderate (0.2 < PHOx < 0.3 ppt/s), and low (0.03 < PHOx
< 0.07 ppt/s) PHOx regime. These bins are representative of
the range of the observations. Observations at other values
of PHOx are consistent with the data shown here. In the
moderate and low PHOx bins we also restrict our analysis
to times later than 0900 LST so that we have an accurate
estimate of PO3 and PHOx. Consequently, we remove 93
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7-8
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
points (8%) from the moderate PHOx bin and 350 points
(37%) from the low PHOx bin. This time of day selection
does not change the number of points in the high PHOx bin
as all PHOx data greater than 0.5 ppt/s occurred after 0900
LST. The potential for the exclusion of data to bias our
conclusions is a concern. In this respect, the high PHOx
data are the most reliable, and both the raw and averaged
PO3 data in this regime are shown in Figure 3a. Of the
1018 observations where PHOx ranges between 0.5 and 0.7
ppt/s (subject to the requirement JNO2 > 5 105 s1) the
additional selection criteria (NOx < 15 ppb and PO3 within
3-sigma of the mean) remove another 15 points from the
analysis. Also, the lack of specific information about H2O2
or HONO contributions to PHOx, and the influence of PAN
are all minimized for this data because of the large
contribution of O(1 D) + H2O to PHOx.
[22] The data in each of the PHOx regimes were averaged into bins of NO concentrations ranging in size from
10 ppt at the lowest NO concentrations to 250 ppt at the
highest NO levels. Points are shown where five or more
observations were available prior to averaging. In the high
PHOx regime (circles), PO3 increases approximately linearly with NO at an average slope of 0.008 molecule O3
(molecule NO)1 s1 between 100 and 500 ppt, becoming
independent of NO over the range of 750– 1100 ppt. At
still higher NO, PO3 begins to decrease. In the moderate
(squares) and low (triangles) PHOx regimes, PO3 increases
with NO less steeply at slopes of 0.005 molecule O3
(molecule NO)1 s1 and 0.004 molecule O3 (molecule
NO)1 s1, and becomes independent of NO at 400 and
200 ppt, respectively.
[23] Qualitatively, the expected dependence of PO3 on
PHOx and NO is demonstrated in Figure 3:
1. For fixed PHOx, PO3 increases, levels, and then (most
clearly at high PHOx) decreases as NOx increases.
2. For fixed NOx, ozone production rates increase with
PHOx.
3. The NO concentration where PO3 stops increasing
linearly with NO shifts to higher NO as PHOx increases.
These features of the role of NO x and PHOx on O3
production have been demonstrated directly from measurements made in the upper troposphere [Jaegle et al., 1998;
Wennberg et al., 1998; Jaegle et al., 1999]. The observations we show in Figure 3 are the first to separate NOx and
HOx influences under the high NOx and VOC regime of an
urban setting and the first to illustrate a complete PO3 versus
NOx curve at a single value of PHOx.
reactions (R13) and (R14) represents the most important
self-loss pathway with OH + HO2 typically contributing
less than 10% of the HOx self-loss during the daytime.
Chain terminating RO2 cross reactions are too slow to be
important at CFA. Organic hydroperoxide formation, RO2 +
HO2 ! ROOH, often dominates the HOx loss because
kHO2+RO2 is approximately twice kHO2 + HO2 and RO2/HO2
is often greater than 2. We estimate that the fraction of HOx
loss due to surface deposition at CFA is less than 2% of the
total loss assuming deposition velocities for OH, HO2, and
RO2 to be 5 cm/s and a 1-km boundary layer height. We
omit surface deposition of HOx from further analysis.
Under high NOx conditions the reactions removing NOx,
specifically nitric acid and alkyl nitrate formation in reactions (R15) and (R7b), become the dominant sinks for free
radicals. Assuming a 3% yield for (R7b) relative to (R7a) +
(R7b), and using the rate constant kHO2+NO, the rate of alkyl
nitrate formation at CFA under high NOx conditions is
15% of the rate of OH + NO2 in reaction (R15). Low NOx
concentrations (<2 ppb) occur simultaneously with high
RO2 mixing ratios (50 ppt) at CFA. Under low NOx
conditions we calculate alkyl nitrate formation approaches
the rate of nitric acid formation. Other mixed HOx-NOx
reactions such as OH + HNO3 and OH + HNO4 are too
slow to be important under the conditions observed at CFA.
[25] To assess the accuracy of current models, we note
that HOx loss, LHOx, is a sum of the termination rates
described above:
LHOx ¼ HHLoss þ NHLoss;
ð7Þ
where HHLoss represents HOx self reactions and NHLoss
represents the HOx-NOx reactions:
HHLoss ¼ 2kHO2þHO2 ½HO2 2 þ2kRO2þHO2 ½HO2 ½RO2 þ 2kHO2þOH ½HO2 ½OH;
NHLoss ¼ kOHþNO2 ½OH½NO2 þ a kRO2þNO ½RO2 ½NO:
ð8Þ
ð9Þ
We illustrate the predicted behavior of this chemical system
with a simple model. Assuming HOx is in steady state and
neglecting the unique role of RO2, PHOx can be approximated as
PHOx ¼ LHOx ¼ 2kHO2þHO2 ½HO2 2 þkOHþNO2 ½OH½NO2 ð10Þ
and PO3 as
5. NOx Limited Versus NOx Saturated PO3
[24] For a single value of PHOx the crossover point
between NOx-limited and NOx-saturated behavior corresponds to a unique NO concentration where @PO3/@NO = 0
The position of the crossover point between NOx-limited
and NOx-saturated photochemistry is an extremely sensitive
test of our understanding of the response of O3 photochemistry to NOx and HOx. Models that do not accurately
predict its location with respect to NOx will likely predict
the incorrect sign of the change in PO3 due to hypothetical
changes in future NOx and VOC emissions. Under low NOx
conditions, HOx self-reactions (R12) – (R14) are the dominant chain termination. At CFA, peroxide formation in
PO3 ¼ kHO2þNO ½NO½HO2 :
ð11Þ
This model is similar to that described by Kleinman et al.
[1997] and many others. To calculate the HO2 concentration
as a function of NO, we assume a fixed NO2/NO ratio of 7
and let the HOx partitioning between OH and HO2 be
controlled by the reactions of HO2 and OH with O3, the
reaction of OH with CO and the reaction of HO2 with NO.
The NO2/NO ratio approximates midday values observed at
CFA. We use O3 = 75 ppb and CO = 4500 ppb. This high
CO mixing ratio mimics the effects of the wide array of
hydrocarbons observed at CFA in the sense that it increases
the HO2/OH ratio in the model to approximately the
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
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7-9
Table 2. Rate Constants Used for the Reactions Involved in the Two Models of LHOx Presented in Figures 6 and 7
Chain Terminating Reaction
OH + HO2 ! H2O + O2
HO2 + HO2 ! H2O2 + O2
HO2 + RO2 ! ROOH + O2
RO2 + NO ! RONO2
OH + NO2 ! HNO3
Rate Constant For Figure 6a
10 (a)
1.1 10
6.1 1012 (a)
1.0 1011 (b)
0
9.0 1012 (c)
Rate Constant For Figure 7a
1.1 1010
6.1 1012
(.08)*1.0 1011
(0.03)*8.1 1012 (a)
9.0 1012
a
The rate constant for RO2 + NO is that recommend for HO2 + NO(a). All rate constants in the table are estimated for 298 K, 760 Torr, and for the case of
HO2 + HO2 for 2% [H2O]. Units are cm3 s1, estimated for 298 K, 760 Torr, and for the case of HO2 + HO2, for 2% [H2O]. Throughout the analysis we
use measured temperature and relative humidity to calculate each rate constant explicitly as functions of temperature, pressure, and water vapor. See
references for temperature and pressure dependences used in the analysis: a, DeMore et al. [1997]; b, Atkinson [1994]; and c, Sander et al. [2000].
[HO2 + RO2]PSS/[OH] ratio observed at CFA. Rate
constants used in the model are from Sander et al. 2000,
and references therein) (see Table 2). Figure 4 shows the
model results from a calculation where PHOx = 0.6 ppt/s.
PO3 (circles, ppt/s, divided by a scale factor of 5) and [HO2]
(down triangles, ppt, divided by a scale factor of 100) are
shown as symbols. PO3 in the model increases linearly at
low NO, begins to slow at 700 ppt, peaks at 1125 ppt, and
beyond 1250 ppt PO3 decreases with further increases in
NO. Solid lines show the initial slope of PO3 and the
fractional loss of HOx due to HHLoss through H2O2
formation (black curve) and the fractional loss due to
NHLoss through HNO3 formation (gray curve). The
modeled HHLoss and NHLoss curves are equal at 900
ppt NO, which is 25% below the 1125 ppt NO value where
@PO3/@NO = 0. We examined a wide range of CO
concentrations, varied kHO2+HO2 by a factor of 10 in the
model, and increased PHOx to 1.2 ppt/s and found that the
difference between the point where HHLoss = NHLoss and
the peak PO3 in the model ranged from 17 to 27%. Allowing
the CO concentration to increase proportionally with an
increase in NO shifted the NO concentration where
HHLoss = NHLoss to 30% lower than the position of
the peak PO3. However, although there is some expectation
that hydrocarbon and NOx sources are proportional to one
another, there is no evidence that hydrocarbons and NO
concentrations increased proportionally at CFA, and we
therefore use a difference of 25% as a guide. Models with
lower HO2 or kHO2+HO2 exhibit PO3 curves that peak at lower
NO. The model does not explicitly treat RO2, consequently,
its predictions should only be considered illustrative and
they should not be expected to accurately reproduce both the
amplitude and position of the peak PO3 in the observations.
[26] Figure 3a shows the PO3 data (open squares) for the
high PHOx regime at CFA plotted versus NO concentrations
along with the averaged data (solid circles). The data are
noisy, making it difficult to exactly specify the NO concentration where @PO3/@NO = 0. However, the basic shape
is similar to that of the simple model. PO3 increases at low
NO up to 600 ppt. Beyond 1100 ppt, a decrease clearly
emerges. This decrease is due to a decrease in inferred RO2.
The contribution of the HO2 + NO reaction to PO3
Figure 4. Modeled PO3 (circles, ppt/s), [HO2] (down triangles, ppt), HHLoss/LHOx (thick black curve),
and NHLoss/LHOx (thick gray curve) plotted versus [NO] for a calculation where PHOx = 0.6 ppt/s. See
text for description of model. O3 was fixed at 75 ppb and CO at 60 * O3. The NO2/NO ratio was held
constant at 7. PO3 is plotted here reduced by a factor of 5, and [HO2] is plotted reduced by a factor of 100.
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THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
Figure 5. HOx loss rates divided into two categories, HOx-HOx (HHLoss) and HOx-NOx (NHLoss)
reactions. The two fractions, HHLoss/LHOx (open squares) and NHLoss/LHOx (gray triangles) are plotted
versus [NO] for the high (0.5 < PHOx < 0.7 ppt/s) PHOx observations. The two fractions represent the
contributions of peroxide formation and nitric acid formation, respectively, to the total free radical loss
rate, LHOx. PO3 (solid circles) for the same PHOx regime from Figure 3a are shown here divided by a scale
factor of 7.
increases approximately linearly from 1 ppt/s at 150 ppt
NO to 3.5 ppt/s at 500 ppt NO. Between 500 and 1000 ppt
NO, PO3 from the reaction of HO2 + NO increases more
slowly to 4 ppt/s. At higher NO the rate of HO2 + NO is
essentially constant while total PO3 is decreasing. Within
the noise of the measurements the inferred PO3 we present
in Figure 3 is always higher than that calculated directly
from HO2 and NO measurements. The maximum in PO3 as
shown in Figure 3 occurs approximately at 800– 1000 ppt
NO. Therefore, using Figure 4 as a guide, we expect
the point where HHLoss = NHLoss to be in the range of
600 –750 ppt NO.
[27] A complete evaluation of the HHLoss and NHLoss
terms requires an explicit treatment of the RO2 chemistry
that we omitted from the simple model. We evaluate the
balance between HHLoss and NHLoss using observations
of NO2 and NO, of OH and HO2, and the inferred RO2
concentrations in equations (2) and (3). There are few
measurements of rate constants for reactions between HO2
and RO2 (kRO2+HO2) for R larger than 3 carbons [e.g.,
Villenave and Lesclaux, 2001] and even fewer quantitative
studies of product yields. We use the rate constant
recommended by Atkinson [1994] for generic RO 2
(kRO2+HO2 1 1011 cm3 s1 at 298 K) and an
ROOH yield of unity. The rate constants for the HO2 +
HO2 in reaction (R13) and OH + NO2 in reaction (R15)
reactions were taken from DeMore et al. [1997] and
Sander et al. [2000], respectively, and we include the
H2O dependence of the HO2 + HO2 reaction (kHO2+HO2 6.1 1012 cm3 s1 and kOH+NO2 9 1012 cm3
s1 at 298 K, 760 Torr, 2% water vapor). The yield of
alkyl nitrate formation via reaction (R7b), a, is defined as
k7b/(k7a + k7b). To demonstrate the ability of our approach
to discern small errors in the photochemical model, we
initially set a to zero. Figure 5 shows the two fractions
HHLoss/LHOx and NHLoss/LHOx plotted versus NO for
the high PHOx regime (0.5 < PHOx < 0.7 ppt/s) as well as
PO3 from the same PHOx regime now scaled by a factor
of 7. The data obtained at CFA included air where
HHLoss (open squares) is the primary HOx sink and air
where NHLoss (gray triangles) is the primary sink.
Consequently, the data provides separate and distinct
information on the accuracy of models in both regimes.
If the model represented by equations (8) and (9), if our
derived PO3 are accurate, and if the calculations shown in
Figure 4 are a reasonable guide, the range of NO
concentrations at which the two loss rates are equal
should correspond to 25% lower NO than where the peak
in PO3 is observed. This crossover should occur at
600– 750 ppt. For the high PHOx range shown in Figure
5 the HHLoss is equal to the NHLoss at 1000 ppt. This
is not unambiguously inconsistent with the data, but it is
at the high end of the 600 – 750 ppt range for the
crossover derived from Figure 3 and 4. To investigate
and quantify the similarities and differences in the model
and measurement descriptions of the functional dependence of PO3 on NOx and PHOx, we examine the HOx
balance along chemical coordinates.
6. Chemical Coordinates
[28] In recent papers, Cohen et al. [2000] and Lanzendorf
et al. [2001] have proposed that chemical coordinates
provide a means to systematically organize a large ensemble
of measurements. These papers discuss how chemical
coordinates can be used to identify the information content
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
of a suite of measurements and suggest they are especially
well suited to determining the rates of fast photochemical
reactions by comparison of a large ensemble of atmospheric
observations with highly constrained models. Chemical
coordinates also serve the purpose of turning attention away
from geophysical variables and long-lived chemical species
that play no direct role in the chemistry on the timescale of
interest and aid in comparing models across gradients of
specific components of a reaction set. In recent examples we
showed that an ensemble of stratospheric measurements are
capable of (1) reducing the estimated uncertainty in the rates
of reactions controlling partitioning of NOx and NOy, and of
NO and NO2 [Cohen et al., 2000], (2) indicating that the
current recommendations for some of the key reactions
controlling the portioning of OH and HO2 are likely in error
at low temperatures [Lanzendorf et al., 2001], and (3) confirming the mechanism for NOx control over the partitioning
of chlorine between ClO and ClONO2 [Stimpfle et al., 1999].
[29] Here, we seek to determine whether the discrepancy
between the modeled and observed crossover between NOxlimited and NOx-saturated ozone production is a significant
error and if so to determine if it arises from modeled
peroxide formation rates that are too fast, nitric acid and
alkyl nitrate formation rates that are too slow, or some
combination of the two. We compare PHOx and LHOx using
the following set of chemical coordinates: (1) the primary
HOx production rate (PHOx), (2) HHLoss, (3) the contribution of organic peroxide formation in reaction (R14) to the
total loss rate, FHO2+RO2, and (4) the contribution of nitric
acid formation in reaction (R15) to the total loss rate,
FOH+NO2, where
FHO2þRO2 ¼
2kHO2þRO2 ½HO2 ½RO2 ;
LHOx
ð12Þ
kOHþRO2 ½OH½NO2 :
LHOx
ð13Þ
FOHþNO2 ¼
The values of FHO2+RO2 and FOH+NO2 range from 0 to 1.
If, for example, data are available where either coordinate,
Fx = 1, then those measurements were made under
conditions where the process x is the sole reaction
controlling HOx loss in the model. Comparison of models
and measurements at that point in the chemical coordinates
is a direct measure of an error in the rate of that process or
an indication that a process not represented by the model is
important. Conversely, data obtained where Fx = 0 contain
no information about the accuracy of process x in the model.
The primary HOx production rate, PHOx, does not isolate a
single variable in the same sense; however, this coordinate
helps to indicate missing chemistry not included in the
model and to provide a general picture of the accuracy of
the model over a range of the production and loss processes.
[30] Under typical daytime conditions the HOx lifetime is
10. Thus HOx is always expected to be in steady state. If
the chemistry included in our description of PHOx and LHOx
is correct, and if we are only limited by random noise in the
measurements, we expect a plot of PHOx/LHOx versus any
chemical coordinates to be scattered about the number 1
with a slope equal to zero. Systematic measurement errors
are expected to lead to systematic shifts in the agreement of
PHOx and LHOx but not, to first order, in the slope of
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7 - 11
PHOx/LHOx versus chemical coordinates. Furthermore,
focusing on FHO2+RO2, FOH+NO2, and HHLoss/LHOx reduces
the importance of systematic errors because these quantities
represent the importance of individual HOx loss processes
relative to a total loss rate that includes the rate of each
individual process. Figure 6 shows four panels containing
plots of PHOx/LHOx versus the chemical coordinates described above. In all panels we required [RO2]PSS to be
greater than 10% of [HO2]OBS and [HO2]OBS to be greater
than 0 ppt to minimize the influence of noise from our PSS
calculations. These two selections exclude 53 points from
data where PHOx is greater than 0.5 ppt/s (9% of the data,
Figure 6b– 6d).
[31] Figure 6a shows PHOx/LHOx versus PHOx including
data with PHOx > 0.1 ppt/s and an additional filter to exclude
points prior to 0900 LST. This filter acts to minimize the
role of other potentially large morning HOx sources such as
HONO and excludes 233 points (10% of the data for PHOx >
0.1 ppt/s) from the data where PHOx is between 0.1 and
0.5 ppt/s. The data in Figure 6a are shown as different
symbols above and below 0.5 ppt/s. The large squares are
averages over data in bins with widths of 0.1 ppt/s. The bars
represent the standard deviation of the data used in the
average. The data show no evidence of a trend in the quality
of agreement versus PHOx. Over a decade in the rate of PHOx
the quantity PHOx/LHOx is nearly constant at an average
value of 0.6. At still lower PHOx than shown in Figure 6a,
PHOx/LHOx decreases, indicating that the model is missing
an important source of HOx at higher solar zenith angles.
This discrepancy is due in part to omitting the photolysis
of H2O2 and aldehydes (C2 and larger) as well as PAN
decomposition in our PHOx calculation. However, there
may also be other missing sources. To avoid confusing the
different errors, we focus our analysis on the high PHOx
regime where O3 and formaldehyde photolysis terms are
large and where PHOx/LHOx is largely independent of
PHOx.
[32] In Figure 6b, PHOx/LHOx is plotted versus the
fraction HHLoss/LHOx. PHOx/LHOx is anticorrelated with
the importance of HOx-HOx reactions to the total HOx loss.
When the HOx-HOx reactions dominate the total HOx loss
(HHLoss/LHOx 0.95), PHOx/LHOx approaches 0.25. A
linear fit to the averaged data gives the line, PHOx/LHOx
= 1.24 0.91*HHLoss/L HOx , R 2 = 0.96. We have
excluded the point at HHLoss/LHOx = 0.1 in this fit.
Including this point degrades the quality of the fit yielding
a slope of 0.53 and an R2 of 0.60. The steep slope shown
in Figure 6 implies errors in the HOx budget are strongly
correlated with the relative importance of the HOx-HOx
reactions.
[33] In Figure 6c, PHOx/LHOx is plotted versus the fractional contribution of organic peroxide formation to the
total HOx loss rate, FHO2+RO2. Figure 6c shows that most of
the model-measurement discrepancy correlated with HOx
self-reactions indicated by Figure 6b is specifically associated with the RO2 + HO2 reaction. PHOx/LHOx is scattered
1 when the contribution of organic peroxide formation to
LHOx is negligible (i.e., FHO2+RO2 0). It is significantly
less than 1 when LHOx is dominated by organic peroxide
formation ranging from 0.25 to 0.33, where FHO2+RO2 =
0.80. If we assume a linear model, we find PHOx/LHOx =
0.940.83*F HO2+RO2 , R 2 = 0.97. Extrapolating to
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THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
Figure 6. (a – d) PHOx/LHOx calculated using 1-min averaged observations plotted versus (a) the
primary HOx production rate, PHOx, (b) the fraction of HOx-HOx reactions, HHLoss/LHOx, (c) the
fractional contribution of organic peroxide formation to LHOx, FHO2+RO2, and versus (d) the fractional
contribution of nitric acid formation to LHOx, FOH+NO2. Figure 6a shows PHOx/LHOx over both a
moderate (0.1 < PHOx < 0.5 ppt/s, small open squares) and a high PHOx (>0.5 ppts, triangles) regime.
In Figures 6b– 6d, only data from the high PHOx (PHOx > 0.5 ppt/s) regime is shown. The large squares are
unweighted averages of PHOx/LHOx over the moderate (open, Figure 6a only) and high (solid) PHOx
regimes. The error bars represent the 1s deviation of the data used in the average. A linear regression (solid
line) of the averaged data is shown for each panel. In Figures 6c and 6d, two additional lines (dashed) are
shown representing the minimum and maximum slopes allowed by the 1s variation of the data.
FHO2+RO2 = 1 gives PHOx/LHOx = 0.11. This extrapolation
suggests that the sink of HOx to form organic peroxides is
10 times too fast in the model. As a range of estimates for
the model-measurement differences, we show two dashed
lines in Figure 6c that are the maximum and minimum
slopes that bound one standard deviation of the data. These
lines indicate modeling the high PHOx data set requires the
rate of HOx chain termination by HO2 + RO2 to be reduced
by a factor between 3 and 12.
[34] Figure 6d shows the results of a similar analysis
along the FOH+NO2 coordinate. In this model, because we set
a, the yield of alkyl nitrate formation, to zero, FOH+NO2 is
the exact complement of HHLoss/LHOx shown in Figure 6b.
When FOH+NO2 approaches 1, the linear regression implies
that LHOx may be too slow by 25% indicating either that
modeled HNO3 formation is too slow or that other loss
processes involving HOx and NOx, such as alkyl nitrate
formation, may be important.
[35] There are number of possible errors that could cause
the model-measurement discrepancies identified above.
Errors in the measured [HO2], the [RO2]PSS, the rate
constants, or some combination of these three, could be
responsible. However, the uncertainty in the measured
[HO2] (±20%) and the inferred [RO2] (±56%) are too small
to have much effect, and uncertainties in [HO2] and
[RO2]PSS are anticorrelated. A systematic reduction in
[HO 2 ] leads to a systematic increase in the inferred
[RO2]PSS and vice versa. Another possibility is that the
increase in JNO2 that we use to reduce the systematic biases
in our analysis is too high. If instead we do not make an
11% adjustment to compensate for net negative [RO2]PSS in
the early morning and late evening, the chemical coordinate
plots look nearly identical with a mean error of about a
factor of 7 instead of a factor of 9 upon extrapolation to
FHO2+RO2 = 1. Furthermore, if we neglect the 11% adjustment in JNO2[NO2] and systematically increase the product
JNO2[NO2] by 21% (the maximum uncertainty), Figure 6c
looks nearly identical with FHO2+RO2 extending to 0.9. A
systematic decrease of JNO2[NO2] by 21% reduces the range
of FHO2+RO2 by nearly a factor 2, and PHOx/LHOx decreases
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
with FHO2+RO2 nearly twice as fast. However, we note that
this systematic reduction of JNO2[NO2] also produces
unphysical [HO2 + RO2]PSS where this quantity is smaller
than the measured [HO2]OBS 84% of the time.
[36] The possible errors in reactant concentrations noted
above are either unrealistic or do not approach the factor of
3 – 12 required to bring the model and measurements into
agreement where HO2 + RO2 is the dominant HOx sink. In
what follows we focus on errors in the model representation
of HOx loss processes. We note here that an alternate
solution would be to infer an error in the HOx production
rate that is correlated with the abundance of RO2 or the rate
of the RO2 + HO2 reaction. However, such an error seems
less likely, and we have been unable to identify a candidate
source molecule that has a strong correlation with the
observed RO2.
[37] The chemical coordinates indicate a large error in the
loss reactions at low NOx and indicate the possibility of an
error at high NOx. Because the HNO3 formation reaction
has been extensively revisited in recent laboratory studies
and because we deliberately set a = 0 when alkyl nitrate
yields are known to be significant, we think it more likely
that the source of the potential error at high NOx is due to
omitting alkyl nitrate formation. It is possible that a fraction
of this error may be due to net peroxynitrate formation, via
RO2 + NO2; however, we assume this term is small and
omit it from the analysis. At low NOx, there is an apparent
error associated with the HOx sink through the RO2 + HO2
reaction. The rate of this reaction is probably accurate to
within a factor of 2 or 3, although there are few direct
measurements for complex organic peroxy radicals. The
products for the reaction of RO2 + HO2 are even less
characterized than the rate coefficient. We propose that a
fraction of the reaction products are free radicals, via RO2 +
HO2 ! RO + OH + O2 for example, as opposed to a free
radical chain terminator such as ROOH. We note that a
functional equivalent to this hypothesis is that if the organic
hydroperoxide is formed as the product, it is rapidly
photylzed to produce free radicals on a timescale of 1 hour.
Although this hypothesis is not supported by some smog
chamber data [Miyoshi et al., 1994], the error we observe at
low NOx is most likely a combination of errors in the rate
constant for RO2 + HO2 and the branching ratio for ROOH
production via this reaction for the types of RO2 at CFA. We
define the parameter g that represents the change in overall
rate of RO2 + HO2 ! ROOH (where ROOH is presumed to
be long-lived).
[38] We optimized (brought as close to 0 as possible) the
slope of PHOx/LHOx versus the two coordinates FOH+NO2
and FRO2+HO2 by adjusting the parameters a and g. We find
that the optimum solution has g of between 0 and 0.15 and
a between 0.01 and 0.15. Because the role of alkyl nitrate
formation is unimportant at low NOx where RO2 + HO2 is
the dominant sink of HOx, the optimum choice of g is
independent of the optimum rate of alkyl nitrate formation.
In the rest of this analysis we set g to 0.08, which is the
smallest value allowed by the range of data in the linear
regression of PHOx/LHOx versus FHO2+RO2 for high PHOx.
We emphasize that g is an empirical parameter that represents the change in the product of the effective rate constant
kHO2+RO2 and the branching ratio leading to ROOH formation. For example, a value of 0.08 for g could be
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7 - 13
achieved by a factor of 4 reduction in the effective rate
constant together with a factor of 3 reduction in the ROOH
formation branching ratio. An alkyl nitrate yield of 3%,
minimized the slope of PHOx/LHOx versus the chemical
coordinates and brings the ratio PHOx/LHOx closer to 1 at
high NOx. However, this parameter is not precisely constrained by the observations and our assumed linear model,
and a wide range in the alkyl nitrate yield (1 – 15%) is
consistent with the measurements.
[39] In Figure 7 we show PHOx/LHOx plotted versus the
chemical coordinates PHOx HHLoss/LHOx, FRO2+HO2, and
FOH+NO2, using the optimized model developed above.
Table 2 summarizes the reactions and corresponding rate
constants and branching ratios used to generate both
Figure 5 and Figure 6. Figure 7a shows that the adjusted
model does significantly improve PHOx/LHOx in the high
PHOx data and clarifies the presence of a growing bias at
the lowest PHOx, which, as we indicated, is possibly due to
H2O2 or HONO photolysis and/or PAN decomposition. As
in Figure 6, we continue to focus on data where PHOx is
greater than 0.5 ppt/s in Figure 7b– 7d. In Figure 7b we
show the fraction of the total HOx loss that is due to the
HOx-HOx reactions, HHLoss/LHOx, in Figure 7c, we show
the data versus the fraction of HO2 + RO2 that leads to
ROOH production, and in Figure 7d, we show the data
versus the fraction of loss via the reaction of OH with
NO2. Note that the range in Figure 7c, 0 – 0.2, is greatly
reduced compared to that in Figure 6 of 0 – 1. In all four
coordinates, PHOx/LHOx is on average closer to 1 with a slope
closer to zero than shown in Figure 6. Linear regressions of
PHOx/LHOx versus HHLoss/LHOx and versus FOH + NO2 yield
slopes of 0.3 (R2 =0.86) and 0.24 (R2 = 0.76), respectively,
each nearly a factor of 3 smaller than those shown in Figure 6.
We have excluded the same points from these fits as in
Figure 6 (at HHLoss/LHOx 0.1 and at FOH+NO2 0.8) as
they continue to degrade the fit. Including these points
yields slopes of 0.08 (R2 = 0.058) and 0.106 (R2 = 0.179)
versus HHLoss/LHOx and FOH+NO2, respectively.
[40] We show the fractions HHLoss/LHOx and NHLoss/
LHOx versus NO for the revised model in Figure 8. Again,
we include PO3 (solid circles) divided by a scale factor of
7. The data are restricted to the narrow high PHOx range
(0.5 < PHOx < 0.7 ppt/s). The two fractions cross 0.5 as
early as 400 ppt NO and stay even for NO as high as 700
ppt. This result is more consistent with the start of the
crossover region beginning at 600 ppt observed in the
PO3 data. The correspondence of the NOx-limited/NOxsaturated crossover point arrived at by two largely independent analyses lends additional support for our suggestion that the rate of HO2 + RO2 ! ROOH + O2 is much
smaller than current recommendations.
7. Discussion
[41] The photostationary state (PSS) assumption that we
used to infer PO3 is frequently used to examine instantaneous O3 production rates in equation (4) and to infer
peroxy radical levels in equations (2) and (3). Surprisingly,
to our knowledge, there is no other data set that has shown
the rate of instantaneous ozone production over the full
range from NOx limited to NOx saturated behavior. Perhaps
the lack of attention to PO3 derived from the PSS analysis
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7 - 14
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
Figure 7. (a –d) PHOx/LHOx plotted versus the same chemical coordinates as in Figure 6 where LHOx
has been modified to include alkyl nitrate formation (3%; yield) and an HO2 + RO2 ! ROOH rate
that is a factor of 12 slower. (a) PHOx/LHOx over both a moderate (0.1 < PHOx < 0.5 ppt/s, small
open squares) and a high PHOx (>0.5 ppts, triangles) regime. (b – d) Only data from the high PHOx
(PHOx > 0.5 ppt/s) regime are shown. The large squares are averages of PHOx/LHOx for the moderate
(open squares) and high (solid squares) PHOx regimes. Linear regressions for the high PHOx averaged
data are shown in all panels.
arises from discomfort with using this approach in urban
and continental settings where discrepancies between
measured [HO 2 + RO 2 ] and PSS-derived [HO 2 +
RO2]PSS have been observed. These discrepancies likely
have a chemical explanation in either the RO2 measurements or in the analyses of RO2 + HO2 at low NOx
(where RO2 + HO2 ! ROOH + O2) is important. For
example, where O3, HO2, CH3O2, ClO, and BrO are the
dominant oxidants of NO, such as in the remote troposphere or the stratosphere, the photostationary state
kinetics have been shown to be accurate to better than
20% [e.g., Ridley et al., 1992b; Volz-Thomas et al., 1997;
Cohen et al., 2000].
[42] In regions with high hydrocarbon abundances, significant discrepancies in the PSS method have been
observed. Peroxy radicals calculated from equation (2) are
higher than measured [RO2 + HO2] by factors of 2 – 3
[Cantrell et al., 1993a; Volz-Thomas et al., 1997; Carpenter
et al., 1998]. Explanations for this discrepancy include the
propagation of experimental uncertainty [Cantrell et al.,
1993a; Baumann et al., 2000], inaccurate measurements of
the species used in equations (2) and (3) [Frost et al., 1998;
Baumann et al., 2000], or the deviation from a steady state in
the atmosphere [e.g., Calvert and Stockwell, 1983]. Whatever the reason for these discrepancies, we believe the shape
of the curves derived in this study and shown in Figure 3: the
presence of an initial slope that is linear in NOx, a region
where the slope decreases to near zero, and a turnover at high
NOx cannot be caused by experimental error.
[43] The results we present here add to a growing list of
discrepancies observed in the HOx budget under low NOx
conditions [e.g., McKeen et al., 1997; Stevens, 1997;
Faloona et al., 2000]. The observed discrepancies in the
various studies are not linked by an obvious error, and while
they may not be directly comparable, they point to a critical
lack of understanding of the HOx budget at low NOx.
Stevens [1997] and McKeen et al. [1997] report significant
differences between observations and model calculated
magnitudes of OH, HO2, and RO2 concentrations and also
in the partitioning between these HOx species during the
Tropospheric OH Photochemistry Experiment. At low NOx
the observationally constrained model employed by Stevens
[1997] calculates HO2/OH and RO2/HO2 that are higher by
factors of 3 – 4 and 4 – 15, respectively, than those observed.
McKeen et al. [1997] report that a similar model overestimates OH concentrations by a factor of 6 – 8, while
THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
Figure 8. PO3, HHLoss and NHLoss, as for Figure 5 with
an alkyl nitrate yield of 3% and a rate/yield of RO2 + HO2
! ROOH + O2 reduced by a factor of 12.
underestimating HO2 concentrations by more than a factor
of 3 – 4. Similarly, Faloona et al. [2000] present results from
the upper troposphere and lowermost stratosphere that show
model calculations of HO2 concentrations were often lower
than those observed. They use a 0-D stationary state box
model and a diel steady state model both constrained with
observations and show that the discrepancies between the
measured and modeled HO2 concentrations are strongly
correlated with measured NOx concentrations [Faloona et
al., 2000]. The model errors that our analysis points to are in
the chain termination steps of the HOx-NOx catalytic cycle
and substantially modify HOx partitioning at low NOx.
Analysis of HOx partitioning over a range of chemical
conditions by using combined data sets should provide
further insight. For example, the HO2 measured in Nashville
and used for this study decreases more slowly with NO than
does the RO2 inferred from equations (2) and (3). Consequently, PO3 calculated from equation (4) increases with
NO up to 800 ppt NO, decreasing for NO > 1100 ppt,
while PO3 from the reaction of HO2 + NO increases for NO
up to 1000 ppt and is nearly constant at higher NO.
[44] Comparison of our results to those from the ROSE
study in rural Alabama is particularly interesting because of
similarities in VOC abundance and PHOx. Frost et al.
[1998], and Trainer et al. [2000] compare O3 production
rates at Kinterbish, Alabama, calculated by four different
approaches: (1) the photostationary state assumption, see
equation (3) used here, (2) directly from PO3 = keff [HO2 +
RO2]MEAS [NO] using measurements of sum total peroxy
radicals made with the chemical amplifier technique [Cantrell et al., 1993b], (3) from a radical budget analysis in
which peroxy radicals are calculated such that PHOx = LHOx,
and (4) from a photochemical box model using inputs of
measured O3, NO, NO2, HNO3, CO, VOCs, temperature,
relative humidity, and JNO2. Trainer et al. examine the
results as a function of NOx and report PO3 data averaged
over the entire Kinterbish campaign. In their analysis,
Trainer et al. select data where JNO2 > 0.005 s1. Using
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7 - 15
the PSS method, they calculate O3 production rates as high
as 4 (±1, 1s) ppt/s at 1.5 ppb of NOx. There is no
observation of a crossover point, i.e., a deviation of PO3
from a linear increase with NOx, in this data. The 1s
standard deviation of the data arises primarily from atmospheric variation and not from noise in the measurements.
Applying the same J value selection criteria to the CFA data
selects a range of PHOx from 0.05 to 1 ppt/s. We calculate
peak O3 production rates of 7 (±3, 1s) ppt/s at 4 – 5 ppb
NOx. At a NOx concentration of 1.5 ppb, PO3 at CFA is 4
(±1.5, 1s) ppt/s, similar to that of Kinterbish. Both data sets
exhibit the same slope of PO3 versus NOx at low NOx (when
filtered identically).
[45] The photochemical box model and radical budget
method employed by Frost et al., and Trainer et al., yield O3
production rates that are more than a factor of 2 slower than
those they calculate using the photostationary state method.
These two models predict a crossover point between NOxlimited and NOx-saturated regimes near 7 ppb NOx. Frost
et al. [1998] note that their model and radical budget results
depend strongly on the choice of a peroxide formation rate
constant and that this is a significant uncertainty. If the
model is revised as we suggest, the predicted crossover
point for Kinterbish would move to lower NOx but not so
low as to conflict with the absence of a crossover in the
Kinterbish data set. Since both PHOx and PO3 versus NOx at
moderate to high PHOx were similar at CFA and Kinterbish
[Frost et al., 1998], it is likely that the crossover point in
Kinterbish would also be similar to that observed at CFA,
4– 5 ppb NOx (600– 800 ppt NO). This is above the highest
NOx observed at Kinterbish.
[46] An alternative approach to evaluating PO3 has been
developed by Kleinman [2000]. They have examined NOxlimited and NOx-saturated O3 production chemistry by
evaluating estimates of the rates of the competing chain
termination steps (HHLoss and NHLoss). Their method
uses an effective rate constant for total peroxide formation
and does not separate the contributions from the reactions
HO2 + HO2 and RO2 + HO2 [Kleinman et al., 1997]. For
example, Daum et al. [2000], apply this method to calculate
PO3 using a box model constrained with data observed on
two separate days in the Nashville urban plume during the
1995 Southern Oxidants Study. At low NOx their model
calculated that PO3 increases linearly with NOx and at 4
ppb of NOx, the calculated PO3 becomes independent of
NOx. For a typical NO2 to NO ratio of 7 this crossover point
is relatively close to the one we derive directly from
observations at CFA. This agreement is somewhat surprising given the large error we identify in current estimates of
organic peroxide formation.
[47] The factor of 10 reduction rate of HO2 + RO2 !
ROOH + O2 that we propose is a large change in models.
However, the rate constant for this class of reactions is not
well known for species with complicated organic moieties
such as the isoprene derivatives [Lee et al., 2000], and we
calculate isoprene-RO2 radicals are more than 40% of the
total at CFA. Current measurements and structure reactivity
estimates are described by Lesclaux [1997] and Wallington
et al. [1997] and measurements for overall rate constants
for secondary and tertiary RO2 range from 2 1012 to
2 1011 at 298 K, 760 Torr [Lesclaux, 1997]. If the rate
constant for isoprene-RO2 is at the lower end of this range,
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THORNTON ET AL.: PO3 DEPENDENCE ON [NOX] AND PHOx
then our suggestion for reducing g can be interpreted as
primarily a reduction in the rate constant used in models.
If, on the other hand, the rate constant is at the high end of
the range then g must be interpreted as a branching ratio
between ROOH and radical products. There are few
product studies for this class of reaction. The yields of
organic peroxides in these studies are usually observed to
be near unity [e.g., Rowley et al., 1992a, 1992b; Tuazon et
al., 1998], a result that clearly conflicts with our interpretation of the CFA data. These laboratory results could be
reconciled with our interpretation if the peroxides observed
are not a primary product of the initial reaction to form an
isoprene-ROOH but are produced by subsequent cycles of
RO2 + HO2 in the equilibrium reaction mixture to yield
ROOH from smaller, less complex RO2. Alternatively,
these peroxides could be rapidly photolyzed under atmospheric conditions making them at best a temporary HOx
reservoir.
8. Conclusions
[48] In situ observations of NO, NO2, O3, OH, HO2, H2CO,
actinic flux, relative humidity, and temperature are used to
separate the NOx and HOx influences on urban O3 production.
Instantaneous ozone production rates calculated using the
photostationary state assumption exhibit NOx-limited and
NOx-saturated behavior over three different ranges of primary
HOx radical production rates. The fastest HOx production
rates yield the fastest O3 production rates. The peak in O3
production and the crossover between NOx-limited and NOxsaturated behavior shifts to higher NOx abundances with
increases in PHOx. HOx partitioning between RO2 and HO2
is an important and poorly understood factor controlling the
NOx dependence of PO3. Further studies of the NOx dependence of this partitioning are necessary.
[49] We compare the observed crossover point to a model
of the chain termination processes using current recommendations for the yield of peroxides from the reaction RO2 +
HO2 ! ROOH + O2. This model predicts a crossover point
at NO mixing ratio higher than we observe. A chemical
coordinate approach to evaluating the accuracy of the
modeled fast photochemistry provides a strong indication
that the model and measurements are inconsistent because
of some error in the representation of the processes associated with the RO2 + HO2 reaction. Our analysis suggests
that any combination of slowing the rate of RO2 + HO2 or
reducing the yield of ROOH from this reaction that reduces
the effective rate of chain termination by about a factor of
10 will improve model representations of HOx. Even if this
reaction is correctly represented in current models, using the
adjusted RO2 + HO2 rate we recommend is likely to account
for some alternate process not captured in current models
(such as rapid photolysis of ROOH) and to be a better
representation of atmospheric observations.
[50] These results have significant implications for strategies to reduce urban and regional ozone concentrations.
Models that incorporate organic peroxide formation rates
that are faster than those that occur in the atmosphere will
predict crossover points between NOx-limited and NOxsaturated O3 production that are too high in NOx. These
models will underestimate the NOx reduction required to
reduce O3 concentrations in regions that are presently NOx
saturated. However, simply extending our results to predictions of the response of the atmosphere to changes in
emissions should be made with caution because of the
difference between net O3 production rates or O3 concentrations and the instantaneous gross PO3 we present in this
paper. Many modeling studies have invoked observationbased indicators to examine instantaneous O3 production, to
discern NOx-limited and NOx-saturated conditions in net
ozone formation, and to study the sensitivity of O3 concentrations to changes in NOx emissions [Sillman, 1995; Kleinman et al., 1997; Sillman et al., 1997; Tonnesen and Dennis,
2000aTonnesen and Dennis, 2000b]. Understanding the low
NOx implications of our analysis of instantaneous PO3 for
the integrated behavior of O3 should be a focus of future
chemical studies as well as for regulatory studies aimed at
guiding reductions in NOx emissions.
[51] Acknowledgments. Observations in Nashville, Tennessee, were
supported by NOAA Office of Global Programs. Joel Thornton gratefully
acknowledges support from a NASA Earth Systems Science Fellowship
NASA grant NGT5-30219.
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R. C. Cohen, J. A. Thornton, and P. J. Wooldridge, Department of
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