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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D05303, doi:10.1029/2007JD009236, 2008
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Assessing known pathways for HO2 loss in aqueous atmospheric
aerosols: Regional and global impacts on tropospheric oxidants
Joel A. Thornton,1 Lyatt Jaeglé,1 and V. Faye McNeill1
Received 30 July 2007; revised 30 July 2007; accepted 4 December 2007; published 4 March 2008.
[1] We present a study of the potential importance of known reaction pathways for HO2
loss in atmospheric aerosols. As a baseline case, we calculate the reaction
probability for HO2 loss by its self-reaction in aqueous particles. Detailed calculations
assessed the effects of aerosol pH, temperature, particle size, and aqueous phase diffusion
limitations on the rate of HO2 loss by this process. An algebraic parameterization of
the reaction probability, g HO2, due to self-reaction is valid for aerosol pH < 6 and the
existence of a homogeneous gas-phase HOx source greater than 1 105 molec cm3 s1.
In this formulation g HO2 depends strongly on particle phase, size, pH and temperature;
the latter causing g HO2 > 0.1 in the upper troposphere and g HO2 < 0.01 in the extra-polar
lower troposphere. We contrast the self-reaction pathway with catalytic oxidation by
dissolved Cu ions. Using IMPROVE network data we assess the atmospheric importance
and uncertainties associated with the Cu pathway. Simulations of tropospheric
chemistry were performed using the GEOS-Chem global chemical transport model with
different parameterizations of g HO2. Relative to simulations where g HO2 = 0 for all
aerosol types, assuming that only the aqueous-phase self-reaction proceeds on pollution
and sea salt particles causes global annual mean differences in surface OH, HO2, and
H2O2 of 1, 2, and +2%, respectively. These minor effects of heterogeneous loss are
significantly different from a simulation assuming g HO2 = 0.2 on all particles, as is
currently recommended, with implications for predictions of regional HOx levels,
ozone production rates and their sensitivity to NOx.
Citation: Thornton, J. A., L. Jaeglé, and V. F. McNeill (2008), Assessing known pathways for HO2 loss in aqueous atmospheric
aerosols: Regional and global impacts on tropospheric oxidants, J. Geophys. Res., 113, D05303, doi:10.1029/2007JD009236.
1. Introduction
[2] The odd hydrogen radicals, OH and HO2 (HOx OH + HO2), play a central role in the oxidative chemistry of
the troposphere. Coupled catalytic cycles involving HOx and
nitrogen oxide radicals (NOx NO + NO2) are responsible
for the degradation of trace species emitted to the troposphere
and ultimately control the production rate of tropospheric O3
on local and global scales [Logan et al., 1981]. Processes that
remove HOx radicals terminate these catalytic cycles. Our
ability to predict changes in the oxidative capacity of the
troposphere and regional air quality therefore requires a
detailed understanding of HOx loss processes.
[3] A number of homogeneous gas-phase reactions have
been identified and well quantified as important HOx
removal pathways, but the heterogeneous and multiphase
chemistry of HOx radicals has received comparatively little
attention. Global and regional modeling studies show that
the loss of HO2 to aerosols presents a potentially important
1
Department of Atmospheric Sciences, University of Washington,
Seattle, Washington, USA.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2007JD009236$09.00
HOx sink throughout the troposphere [Meilinger et al.,
2001; Tie et al., 2001, 2005; Martin et al., 2003; Tang et
al., 2003; Lamarque et al., 2005]. In addition, reaction of
HO2 on aerosol particles, cloud droplets, or cirrus particles
has often been invoked to explain differences between
photochemical model predictions and in situ observations
of HOx radicals and reservoir concentrations both in the
upper and lower troposphere [Cantrell et al., 1996; Brune et
al., 1999; Jaegle et al., 2000; Olson et al., 2004; Sommariva
et al., 2004; de Reus et al., 2005]. In spite of these potential
impacts of HO2 heterogeneous chemistry, there remains
significant uncertainty both in the loss rate of HO2 to
atmospheric aerosols under conditions relevant to the troposphere, and in the sensitivity of HOx and O3 abundances
to such a loss process.
[4] The loss rate of a gas-phase species due to uptake and
reaction in an aerosol particle is the convolution of several
processes operating in series or parallel: 1) diffusion of the
gas-phase species to the aerosol surface, 2) mass accommodation of the gas-phase species into the aerosol bulk, 3)
reaction directly at the surface, and 4) diffusion and reaction
throughout the aerosol bulk. Most global models of atmospheric chemistry do not explicitly treat these individual
processes. Instead, models parameterize the uptake process
by defining a reaction probability, g. The loss rate of X due
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D05303
THORNTON ET AL.: HO2 HETEROGENEOUS CHEMISTRY
to aerosols in this context is, to a good approximation, given
by equation (1)
dXg
rp
4 1
þ
AXg
¼ dt
Dg
gw
ð1Þ
where rp is particle radius (cm), Dg is the gas-phase
diffusion coefficient (cm2), w is the mean molecular speed
of X (cm s1), A is the aerosol surface area density (cm2 per
cm3 of air), and Xg is the number density of X (molec
cm3). This formulation allows gas-aerosol reactions to be
incorporated into standard gas-phase chemical mechanisms
as an additional pseudo first order process, and requires an
estimate of g and knowledge of the aerosol size distribution.
[5] In the first study of HO2 reactivity on laboratory
generated aerosol particles, Mozurkewich et al. [1987]
demonstrated that the catalytic oxidation of HO2 in solution
by dissolved Cu ions could be rapid enough that g HO2 > 0.2.
This study also demonstrated that g HO2 was a strong
function of the Cu ion molality, with Cu below 103 molal
having almost no effect on HO2 and nearly complete
titration of HO2 for Cu above 103 molal. While other
transition metal ions such as Fe can promote similar
chemistry, the rate constants for Fe ions and the soluble
fraction of Fe in ambient particles are smaller than that for
Cu, and thus it has typically been assumed that Cu is the
most atmospherically important in this regard.
[6] Recently, Thornton and Abbatt [2005] presented
measurements of HO2 uptake to aqueous sub-micron sulfuric acid and ammonium sulfate aerosols with and without
Cu ions. The results suggest that the net reactive uptake of
HO2 to aqueous sulfate aerosols without Cu ions proceeds
via relatively well-known aqueous-phase chemistry which
consists of dissolved HO2 reacting with its conjugate base,
O
2 , and generally assumed to produce H2O2 under all
conditions. The reaction rate is second-order in dissolved
HO2, and strongly dependent on temperature, pH, and
aerosol volume. If these characteristics of HO2 reactivity
are valid for actual atmospheric aerosols, then depending on
the availability of free Cu (or Fe) ions, g HO2 will vary over
many orders of magnitude for variations in HO2 number
density, aerosol size, pH, and temperature typical of the
troposphere. A single value for g HO2 would thus not
accurately represent the loss rate of HO2 to aerosols,
especially on a regional scale.
[7] In this paper, we put forth three main points that are
based on a synthesis of previous laboratory and field
experiments and their application to the global atmosphere.
First, we demonstrate the significant range of g HO2 on
aqueous aerosol in the troposphere based on known aqueous
HOx-only chemistry, which can be expected to occur in
aqueous atmospheric aerosols in the absence of significant
transition metal ions (TMI). IMPROVE Network [Malm et
al., 1994] composition data suggest that Cu-induced HOx
loss at the mass accommodation limit to fine mode particles
may not be a common occurrence. Second, based on a
kinetic model with mass transport limitations, we suggest
that previous laboratory measurements of HO2 reactive
uptake to aqueous aerosols without Cu ions are consistent
with the HO2 self-reaction mechanism, though the relevant
data set is very small. Third, using the GEOS-Chem global
D05303
chemical transport model and formulations for g HO2 based
on the assumptions of aqueous aerosol particles and one of
two possible mechanisms (HO2 self-reaction or TMI chemistry), we illustrate that the choice of g HO2 significantly
impacts surface layer oxidant levels but that both mechanisms likely yield the same result in the mid-to-upper
troposphere. We conclude with recommendations for future
laboratory and field studies to help resolve significant
limitations to our understanding of HO2 heterogeneous
chemistry, including the dependence on HO2 concentrations, aerosol phase state (solid vs. liquid), aerosol pH, and
the aerosol concentration of free aqueous TMI.
2. Methods
2.1. Mechanism of HO2 Self-Reaction in Aqueous
Aerosols
[8] Our mechanism for HO2 loss in aqueous aerosol
without TMI is given by the five reactions below:
HO2ðgÞ $ HO2ðaqÞ
ðrapid mass accommodationÞ
HO2ðaqÞ $ Hþ
ðaqÞ þ O2ðaqÞ
ðR1Þ
ðKeq Þ
HO2ðaqÞ þ HO2ðaqÞ ! H2 O2ðaqÞ þ O2ðaqÞ
HO2ðaqÞ þ O
2ðaqÞ ðþ H2 OðliqÞ Þ ! H2 O2ðaqÞ þ O2ðaqÞ þ OHðaqÞ
ðR2Þ
ðR3Þ O
2ðaqÞ þ O3ðaqÞ ðþ H2 OðliqÞ Þ ! OHðaqÞ þ OHðaqÞ þ 2O2
Mass accommodation of HO2(g) into the aerosol is followed
by the pH-determined partitioning between HO2(aq) and its
conjugate base O
2(aq). Measurements of the mass accommodation coefficient, aHO2, i.e., the probability that HO2(g)
will be taken up into a surface layer of the aerosol bulk
given a collision, have been made on a range of acidic and
pH-neutral aqueous surfaces and suggest that aHO2 > 0.2
[Mozurkewich et al., 1987; Hanson et al., 1992; Cooper and
Abbatt, 1996; Thornton and Abbatt, 2005], and likely that
aHO2 > 0.5 apparently independent of pH [Thornton and
Abbatt, 2005]. The solubility and reactivity of HO2 in
aqueous media are pH dependent given that HO2 is a weak
acid with a room temperature pKa of 4.7 [Jacob, 2000,
and references therein]. In aqueous solutions with pH > 4,
the solubility of HO2 is enhanced due to its dissociation
thereby decreasing the evaporative flux of HO2(g) out of the
solution. To account for this enhanced solubility an effective
Henry’s law constant is defined
Keq
Heff ¼ HHO2 1 þ þ
½H ð2Þ
where HHO2 is the physical Henry’s law constant, estimated
to be about 3900 M atm1 [Golden et al., 1990; Hanson et
al., 1992] at 298 K. For pH = 5, Heff is 1.2 104 M atm1
at 298 K, but increases exponentially with decreasing
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THORNTON ET AL.: HO2 HETEROGENEOUS CHEMISTRY
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Table 1. Temperature Dependent Parameters Used in the
Calculations of g HO2a
Parameter
A
B
298 K Value
Keq
k1
k2
k3
HHO2
HO3
DaqO3
DaqHO2
DgHO2
DgO3
NA
2.4 (9)
1.6 (10)
2.4 (11)
9.4 (6)
1.7 (2)
2 (2)
see text
NA
2.36 (3)
1.51 (3)
1.51 (3)
5.92 (3)
2.33 (3)
2.2 (3)
see text
00
00
2.1 (5)
8.6 (5)
1 (8)
1.5 (9)
3.93 (3)
1.7 (2)
1.3 (5)
1 (5)
0.25
0.1
00
00
a
Values are of the form A*exp[B/T], where entries are read as 2.4 (9) =
2.4 109. Units for each parameter are in the text.
temperature (see below). Table 1 summarizes the chemical
and physical parameters used in this work.
[9] Throughout this study, we assume that the only loss
pathways for HO2 in aqueous aerosols without TMI are
reactions R1 – R3. Our reasoning is based on the agreement
between the observed loss rate of HO2 in the presence of pH
5 (NH4)2SO4 aerosol and that predicted using known rate
constants for reactions R1 and R2 [Thornton and Abbatt,
2005]. Reactions R1 – R3 were found to be the most
important loss pathways for HO2 in a cloud chemistry
model which considered over 50 other aqueous phase
reactions [Jacob, 1986]. The rate constants for reactions
R1 – R3 are, respectively, k1 = 8.6 105 M1 s1, k2 = 1 108 M1 s1 [Bielski et al., 1985], and k3 = 1.5 109 M1
s1 [Sehested et al., 1983; Buhler et al., 1984]. For R1 and
R2, an effective second-order rate constant can be defined
based on the relative partitioning of HO2(aq) and O
2(aq),
keff
K
k1 þ ½H þeq k2
aq
¼ 2
Keq
1 þ ½H þ ð3Þ
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2.2. An Expression for g HO2 Due to HO2-Only
Chemistry
[11] If the overall mass transfer rate due to reactive loss in
the aerosol is not significantly limited by aqueous-phase
diffusion, calculation of net reactive uptake for a secondorder reaction becomes relatively straightforward. As detailed in Appendix A, to determine the magnitude of
aqueous-phase diffusion limitations, we numerically solved
the steady state diffusion equations for both HO2 and O3
with reactive loss rates calculated from the kinetic equations
dictated by reactions R1– R3. The calculations spanned a
range of aerosol sizes, T, pH, and HO2/O3 concentrations.
[12] For a given aerosol pH, the aqueous HO2 chemistry
is most sensitive to changes in temperature. Table 1 summarizes the temperature dependences used for most parameters in all calculations. It should be stressed that the
temperature dependence of many of these parameters are
not known, or have not been confirmed experimentally
below about 270 K. By far the most important temperature
dependence is that prescribed to HHO2. HHO2 and HO3 are
calculated as functions of temperature following recommendations of Hanson et al. [1992] and Gershenzon et al.
[2001], respectively. The Daq for O3 is calculated based
on the expression presented by Johnson and Davis [1996],
while that for O
2 (I) is calculated following the approach of
Klassen et al. [1998]
O
Daq2 ðT Þ
O T *Daq2 298
¼
vðT Þ
5
2
where *DO
aq is the diffusion constant at 298 K (1 10
2 1
cm s ) [Schwartz, 1984]. The temperature dependent
solution viscosity, n(T), is determined by an exponential fit
to the data of Hallett [1963] for water.
vðT Þ ¼ 1:09 108 expð0:068T Þ þ 0:873
aq
and the effective rate of aqueous HOx loss is calculated as
2keff[O2(I)]2 with [O2(I)] = [HO2(aq)] + [O
2(aq)]. We also
assume that the reaction product, H2O2 fully partitions to
the gas-phase. While there is evidence that H2O2 partitions
to atmospheric aerosol particles more favorably than
Henry’s Law suggests [Hasson and Paulson, 2003], this
aspect is beyond the scope of this work.
[10] Large uncertainties in the application of this mechanism arise from an incomplete knowledge of atmospheric
aerosol pH, aerosol phase state, and of HO2 reactivity on
mineral dust and aerosol organic matter at typical relative
humidity (RH) values. Few regional and global models
calculate aerosol pH or phase state and thus it is beneficial
to know the degree to which such factors could impact
heterogeneous chemistry parameterizations used in such
models. To our knowledge, no laboratory studies exist to
provide constraints on the reactivity of HO2 on mineral dust
at ambient RH. The reaction of HO2 with soot has indirectly
been estimated to have g HO2 0.05 [Saathoff et al., 2001],
but no information exists for HO2 reaction on organic
aerosols. A particle need not be aqueous for HO2 to react
on it, and the aqueous mechanism discussed herein would
become less important if a fast (g HO2 > 0.05) surface
reaction existed, which at this time, has not been demonstrated experimentally.
ð4Þ
ð5Þ
We assume an activation energy of 4.7 kcal mol1 for R1,
and 3 kcal mol1 as an estimate for reactions R2 and R3
[Jacob, 2000, and references therein]. Gas-phase diffusion
constants are calculated as a function of temperature and
pressure, using values of 0.25 cm2 s1 and 0.1 cm2 s1 for
HO2 [Mozurkewich et al., 1987] and O3 [Gershenzon et al.,
2001], respectively, at 298 K and 1 atm.
[13] Solutions to the diffusion equation with second-order
reactive loss demonstrated that for a majority of conditions,
reaction of O2(I) is slow compared to aqueous-phase
diffusion through sub-10 mm droplets, implying that mass
transport limitations within the aerosol bulk are often
negligible. In addition, we found that R3 is also negligible
under most conditions. These points are especially true for
aerosol pH 5. In the absence of aqueous-phase mass
transport limitations and reaction R3, the difference between
the rate of HO2 entering the aerosol and the rate of that
evaporating must equal the rate of reactions R1 and R2
throughout the aerosol volume, which is expressed in
equation (6):
3 of 15
2
2NAV keff ½O
NAV ½O
3
2 ðIÞ
2 ðIÞ
¼ kmt ½HO2ðgÞ 1000
1000Heff RT rp
ð6Þ
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THORNTON ET AL.: HO2 HETEROGENEOUS CHEMISTRY
Here, [HO2(g)] is the gas-phase number density of HO2. The
right hand side of equation (6) is directly related to that of
equation (A1), see Appendix A, except the surface
concentration of O
2 (I) is assumed to be equal to the bulk
concentration. Dividing both sides of equation (6) by the
gross HO2-aerosol collision frequency and assuming
[HO2(g)] and [O
2 (I)] are related by Henry’s Law in the
absence of a radial concentration gradient, g HO2 is given by
equation (7).
1
1
3wNA
¼ HO þ
g HO2
a 2
8000ðHeff RT Þ2 keff ½HO2ðgÞ rp
ð7Þ
The timescale to achieve steady state, given a constant
source, is relatively short (minutes or less) for typical rp,
liquid volume fractions, and an a = 1. As will be discussed
in section 3, this expression is not necessarily valid for
conditions when HO2 uptake is driven entirely by solubility
as is the case for aerosol pH > 6, nor for conditions where
significant levels of free TMI are present.
[14] Reaction R3 can be incorporated into equation (6) as
an additional term first-order in [O
2 (I)]. The net effect of
R3 is to lower the steady state concentration of O
2 (I)
thereby increasing g HO2, but the magnitude of this effect
depends on the radial concentration profile of O3, which in
turn depends O
2 (I) requiring an iterative approach. While
we developed such an approach, reaction R3 generally has
little effect on g HO2 unless the ratio of [HO2(g)]/[O3(g)] falls
to less than 1 105 in which case, including reaction R3
can increase g HO2 by factors of 2 – 10. Such low [HO2(g)]/
[O3(g)] ratios occur only in polar winter or at twilight when
[HO2(g)] is extremely low and thus when losses have little
impact on the diurnal average of HOx radicals. The effect of
R3 is also pH dependent since only O
2(aq) participates, and
therefore R3 becomes less important as pH decreases. We
note, however, that reaction R3 may be a significant source
of the OH radical in fresh (pH 7) aqueous sea salt particles
as it is in cloud drops [Jacob]. We calculated a production
rate of OH(aq) from reaction R3 that was 0.1 to 100 times the
gross uptake rate of gas-phase OH(g) to pH 7 sea salt
particles >5 mm in diameter when assuming aHO2 = 1 and
[OH(g)] 1 106 molec cm3.
[15] In summary, neglecting aqueous phase mass transport limitations of O2(I) and reaction R3 yields g HO2
which are within 15– 20% of those calculated by solving
the full set of diffusion equations (Appendix A) for the
majority of tropospheric conditions and for aerosol particles
less than 20 mm in diameter with pH < 5.5.
2.3. Assessing the Role of Copper Chemistry
[16] Free Cu(I) or Cu(II), and to a lesser extent, Fe(II) or
Fe(III) ions can catalytically destroy HO2(aq) or O
2(aq).
Given that the solubility of particulate iron tends to be
1 – 10% and that iron ions have smaller rate constants by a
factor of 10– 100 toward reaction with O2(I) [see, e.g.,
Deguillaume et al., 2005], we focus here on Cu as an
aerosol sink of HO2. Mozurkewich et al. [1987] found that
the molality of Cu2+
(aq) in 130 nm aqueous aerosol particles
had to exceed 103 moles kg1 before significant HO2
loss was observed. For the aerosol compositions and RH
(74%) used in this pioneering study, a Cu(II) molality of
103 moles kg1 corresponds to a Cu solute mass fraction
D05303
of 1.5 104. Above these levels of Cu, g HO2 increases
rapidly to become greater than 0.2 [Mozurkewich et al.,
1987; Hanson et al., 1992; Cooper and Abbatt, 1996;
Thornton and Abbatt, 2005]. The speciation of Cu(I) and
Cu(II) in ambient aerosol particles is not well known and we
assume all copper, regardless of oxidation sate, is available
for reaction.
[17] Typical rainwater and cloud concentrations of Cu are
109 – 106 moles kg1 [Sedlak et al., 1997; Kieber et al.,
2004], with soluble fractions typically ranging from 1 – 50%.
Such measurements, especially the soluble fraction, likely
cannot be extrapolated to aerosol particles where water
volumes are several orders of magnitude different and solute
mass may be the same. Thus while aerosol levels of free
aqueous Cu could easily approach 104 – 101 moles kg1
given the large differences in cloud droplet (10 mm) and
aerosol particle (0.2 mm) volumes, this would require that
no other compositional or phase changes occur between
saturated and sub-saturated regimes.
[18] Relatively little is known about the global distribution of Cu solute mass fraction in fine mode aerosol
particles and its distribution within a given aerosol population. What is known in this regard typically comes from
filter-based measurements of Cu mass fraction relative to
the bulk sample mass integrated over size and time. Using
such information to calculate typical heterogeneous reaction
rates is problematic because the reactivity of Cu toward
HO2 in ambient particles is highly uncertain. Cu (and other
TMI) may be chemically bound in the highly ionic, organicrich matrix [e.g., Christl and Kretzschmar, 2001; Kieber et
al., 2004; Shank et al., 2004] or the measured Cu mass may
have been confined to a small number of particles that
represent only a fraction of the available aerosol surface
area. Both possibilities potentially reduce the effect of Cu
on gas-phase HO2 loss. Olsson et al. [2007] determined that
more than 95% of Cu is chemically bound to dissolved
organic matter in solid municipal waste, and organic acids
were important ligands. Atmospheric aerosols will be rich in
organic acids and other ligands such as humic-like material.
In addition, much of atmospheric Cu in remote regions may
be contained in dust particles, which might have only very
thin aqueous coatings. Single particle composition measurements, made by the PALMS instrument in pollution plumes
off the northeastern coast of the U.S., show that more than
85% of the particles detected contained copper well less
than 1 part in a thousand [Murphy, 2007]. These measurements suggest that the extrapolation of Cu mass fractions
determined from filter samples to a value that represents the
average Cu mass fraction of an entire ambient aerosol
population is non-trivial and subject to a number of simplifying assumptions.
[19] We have examined data from the IMPROVE Network [Malm et al., 1994] obtained across the United States
to develop a more quantitative estimate as to the prevalence
of fine mode Cu as a HOx sink. The Cu data shown in
Figure 1 is a compilation of measurements made at 197
different locations in the United States during the period
from 1988 – 2004. Not all sites operated during the entire
period, and site elevations range from sea level to 3.8 km
above sea level. More information on this data set is
available elsewhere (see: http://vista.cira.colostate.edu/
improve/). In Figure 1, we show the normalized cumulative
4 of 15
D05303
THORNTON ET AL.: HO2 HETEROGENEOUS CHEMISTRY
D05303
[1987, Figure 5]. A threshold is clearly evident in their data:
HO2 does not react efficiently in 130 nm diameter
aqueous aerosols containing a Cu solute mass fraction less
than 1 –2 104. This threshold is likely due, in part, to a
reacto-diffusive length scale for the Cu-catalyzed chemistry.
The two vertical lines reflect the different functional behavior observed for HO2 reactivity in Cu-doped LiNO3 and
NH4HSO4 particles. The difference in Cu thresholds between the two particle types is not well understood, but
could be due to different Henry’s law constants of HO2 or
different rate constants for Cu-catalyzed reactions.
[22] The effect of Cu or other transition metal ions (TMI)
on g HO2 can be calculated theoretically using a similar
approach outlined in equations (6) and (7), substituting
the rate constant for reaction of O
2 (I) with the TMI and
accounting for aqueous phase mass transfer limitations [see,
e.g., Hanson et al., 1994].
Figure 1. The normalized cumulative frequency distribution of fine-mode Cu mass fraction, determined from the
entire IMPROVE Network data set, is plotted versus Cu
mass fraction (solid line). The dashed vertical lines
correspond to the threshold Cu solute mass fractions where
HO2 loss to aqueous aerosols became detectable in
laboratory experiments (see text).
frequency distribution of the measured Cu fine mode mass
fraction (solid line). The distribution shows that for 90% of
the observations, the Cu mass fraction is less than 3 104
across the surface layer of the U.S., and that for 50% of the
observations, the mass fraction is less than 8 105 (i.e.,
the median). The mean of all Cu mass fraction measurements from all IMPROVE sites is 1.8 104 with a
standard deviation of 7 104.
[20] IMPROVE sites with the highest number of reported
Cu mass fractions greater than 3 104 tended to be in the
Southwest U.S., such as in Arizona (Petrified Forest,
Chiricahua National Monument, and Tonto National Monument). These results suggest either a mineral dust influence
or the impact of U.S. Cu smelting operations nearby, which,
as of 2002, took place only at three locations: two in
Arizona and one in Utah [Feliciano and González, 2003].
A significant number of sites across the U.S. occasionally
reported values greater than 3 104, giving rise to the
large variance in day-to-day values. In the Northeast U.S.,
typical mean CU mass fractions ranged from 8 105 to
2 104 consistent with the single particle measurements
made by the PALMS in the outflow from this region
[Murphy, 2007]. Binning the IMPROVE data from all sites
by month yields monthly median mass fractions that reach a
maximum in the winter months (1 104) and a minimum
in the summer months (6.5 105). However, individual
locations can show the opposite annual cycle, such as
Mauna Loa, with median Cu mass fractions maximizing
in summer (3.5 105) and reaching minimums well below
the detection limit of 1 105 during winter.
[21] The dashed vertical lines in Figure 1 correspond to
estimates of when the HO2 reaction probability begins to
show a dependence on the Cu solute mass fraction in 65 nm
aqueous particles based on the data of Mozurkewich et al.
1
1
w
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ þ
g
a
Heff RT k I Daq Q
ð8Þ
In equation (8), kI is the pseudo-first-order rate constant
equal to kIITMI[TMI] where kIITMI is the second order aqueous
phase reaction rate constant for O
2 (I) + TMI. The parameter
Q accounts for aqueous-phase diffusion limitations which
can lead to concentration gradients of the reactants within
an aerosol particle effectively slowing the volume averaged
reaction rate, and is given by
sffiffiffiffiffiffiffiffi
1
kI
Q ¼ cothðqÞ ; q ¼ rp
Daq
q
ð9Þ
2+
The rate constant for the reaction of O
2(aq) with Cu(aq) is
reported as 1 109 M1 s1 while the rate for HO2(aq) +
8
1 1
s in dilute aqueous solutions
Cu2+
(aq) is about 1 10 M
[Rabani et al., 1973]. These rate constants yield a g HO2
from equation (8) that is limited only by mass accommodation for [Cu] > 1 106 moles kg1 in 130 nm diameter
particles, a result which is not supported by the work of
Mozurkewich et al. [1987] that showed [Cu] must be greater
than 1 103 moles kg1. The above parameterization
can capture the observed threshold behavior of HO2 loss
versus [Cu] fairly well with a value of kIIcu < 1 105 M1 s1.
We note that reaction probabilities versus a range in aerosol
Cu concentrations were not reported by Mozurkewich et al.
[1987], they reported a relative change in HO2 signal for one
interaction time. Thus we cannot be more quantitative
without direct experimental determinations of g HO2 as a
function of Cu and particle size, but when such experimental
data exists, equations (7) – (9) could be coupled to yield a
single parameterization that accounts for both the HO2 selfreaction and Cu catalyzed reactions. This parameterization
would be useful if and when size-resolved aqueous-phase
concentrations of free Cu ions in ambient particles are
known.
[23] Connecting the IMPROVE network mass fraction
data to the ‘‘solute mass fraction’’ as a function of aerosol
surface area at ambient relative humidity is non-trivial
because: 1) filter based measurements smooth out temporal
changes in Cu abundance, 2) the extrapolation depends on
knowing the particle phase, 3) the typical partitioning of Cu
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with respect to aerosol surface area is rarely known, and 4)
assumptions about Cu solubility and water volumes across
the distribution are required. Nonetheless, the IMPROVE
Network data suggest that more than 50% of the time, fine
mode aerosols in the surface layer over the U.S. do not
contain enough Cu to drive HO2 reaction probabilities to be
mass accommodation limited in 200 nm or smaller sized
particles. Extrapolating to an average molality of 1 103
moles/kg yields g HO2 0.06 for rp 100 nm, pH = 5, and
T = 290 K. This estimate implicitly assumes all measured
Cu is in a free aqueous state and evenly distributed by
surface area, and that the threshold behavior observed in the
laboratory [Mozurkewich et al., 1987] is atmospherically
relevant and can be modeled by a reacto-diffusive length
correction. If a fraction f of Cu is chemically bound in a
form unreactive toward HO2 such as in mineral dust or
complexed to organic ligands, then the appropriate x axis
values for the probability distribution (solid line) in Figure 1
would be lower by a factor of (1 f ), lowering the potential
for catalyzing gas-phase HO2 loss.
2.4. Geos-Chem
[24] We use the GEOS-Chem global 3-D model of
aerosol-oxidant chemistry [Bey et al., 2001; Park et al.,
2003, 2004] driven by meteorological fields from the
NASA Goddard Earth Observing System (GEOS-3) with
a horizontal resolution of 4° latitude 5° longitude and
30 vertical levels. The simulations presented here are for the
year 2001 using model version v7.03.03 (http://www-as.
harvard.edu/chemistry/trop/geos). The GEOS-Chem aerosol
simulation includes the sulfate-nitrate-ammonium system
[Park et al., 2004], organic carbon (OC) and elemental
carbon (EC) aerosols [Park et al., 2003], sea salt aerosol
[Alexander et al., 2005], and soil dust [Fairlie et al., 2007].
The aerosol and oxidant (ozone-NOx-hydrocarbon) chemistry are coupled through formation of sulfate and nitrate,
heterogeneous chemistry [Jacob, 2000], and aerosol effects
of photolysis rates [Martin et al., 2003].
[25] We present three simulations conducted with the
GEOS-Chem model. Our first simulation assumes a uniform
g HO2 = 0.2 for all aerosol types, following the recommendations of [Jacob, 2000] and constitutes a surrogate for
significant TMI induced chemistry. In a second simulation
we use equation (7) to calculate g HO2 due only to the HO2self reactions, neglecting the role of TMI-induced chemistry. This form is assumed for all aerosols except mineral
dust, for which we keep g HO2 = 0.2, due to a lack of
experimental results and to account for the possibility that
processed dust may have an aqueous coating into which
some TMI dissolves. A final simulation assumes g HO2 = 0
for all aerosols. In all simulations, the assumed form of the
HO2 heterogeneous reaction is HO2(g) ! 0.5 H2O2(g).
3. Results and Discussion
[26] We first examine the effects of treating HO2 loss to
aerosols as being determined solely by the aqueous-phase
self-reaction mechanism presented in sections 2.1 and 2.2.
We discuss the validity of the parameterization given by
equation (7) for HO2 loss in the absence of Cu, and then
compare the effects of including or neglecting Cu chemistry
in global simulations of HOx.
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3.1. Comparison of the Self-Reaction Mechanism
With Laboratory Measurements
[27] Confidence that the aqueous-phase HO2 self-reaction
mechanism used in this work is valid for many atmospheric
conditions comes primarily from its consistency with recent
laboratory studies of HO2 loss to aqueous sulfate aerosol
[Thornton and Abbatt, 2005]. Only a few laboratory studies
of HO2 loss to liquid systems exist for further comparison.
Cooper and Abbatt [1996] examined the loss of HO2 to
super-cooled sulfuric acid films (T 223 K) and found
first-order loss of HO2 with a g HO2 0.055. Hanson et al.
[1992] measured HO2 loss to super-cooled sulfuric acid
films (T 249 K) and cold pure H2O films (T 274 K),
also finding first-order loss of HO2 with g HO2 > 0.05 and
g HO2 > 0.01, respectively. Gershenzon et al. [1995]
obtained similar results using cooled sulfuric acid films
(T 243 K). Gas-phase diffusion limitations in these
experiments allow only lower-limits to be measured. Our
mechanism predicts g HO2 > 0.1 using the experimental
conditions of Cooper and Abbatt [1996] and Hanson et
al. [1992] for [HO2(g)] above their reported detection limits
(i.e., for HO2(g) > 3 108 molec cm3) when assuming a
particle radius of 0.2 mm to mimic the film thicknesses in
those experiments. The observed first-order loss of HO2 in
these two sets of experiments implies that perhaps our
mechanism, in which second-order kinetics are expected, is
not appropriate. However, apparent first-order kinetics could
result from gas-phase diffusion limitations and a high reactivity at the wall due to the relatively thick films (
0.2 mm)
and high initial HO2(g) (>3 1010 molec cm3). A detailed
model of these coated wall flow tube experiments that
accounts for diffusion limitations to the walls and reactivity
in the coating volume is required for a more quantitative
comparison.
[28] In the only other experiment using sub-micron aqueous aerosol particles, Mozurkewich et al. [1987] did not
report a g HO2 for aqueous NH3HSO4 or LiNO3 aerosols
without Cu, because virtually no reaction of HO2 at 1 109 molec cm3 occurred over the 30 s interaction time.
Our mechanism predicts g HO2 < 0.005 for their conditions
without Cu and thus no observable reaction would be
expected if this were the case. At the present time,
however, the amount of experimental data on the reactive
uptake of HO2 to aerosol particles is far too small to make
any strong conclusions about the true reaction mechanism
that would occur under atmospheric conditions.
3.2. Effects of T, [HO2], and Particle Radius
[29] The basic behavior predicted by the coupled mass
transport and aqueous phase chemistry models (section 2.2
and Appendix A) is illustrated in Figure 2. When the steady
state reaction probability is 0.1, it increases linearly with
HO2 number density and particle radius, and it increases
exponentially with decreasing temperature. This behavior is
apparent from inspection of equation (7) and noting that
when the value of g HO2 < 0.1, the second term on the right
hand side must be dominating g HO2 because aHO2 = 1. Thus
neglecting the first term on the right hand side of (7) makes
g HO2 proportional to [HO2(g)], rp, and (Heff)2. The latter
increases exponentially with inverse temperature.
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Figure 2. Behavior of g HO2 calculated using equation (7). (A) g HO2 plotted as a function of temperature
for three different particle radii, a constant [HO2] of 1 108 molec cm-3 and pH = 5. (B) g HO2 plotted as a
function of [HO2] for three different particle radii, a constant temperature of 288 K and pH = 5. (C) g HO2
plotted as function of pH for three different particle radii, a constant temperature of 288 K, and [HO2] of
1 108 molec cm3. See text and Figure 2 for details regarding validity of each calculation.
3.3. Effect of pH and Reactive Versus Solubility
Driven Uptake
[30] Over the pH range of 3 – 6, g HO2 calculated from
equation (7) increases with increasing pH as shown in panel
C of Figure 2. This pH dependence arises from the equilibrium partitioning between HO2 and its conjugate base
O
2 , which affects Heff and keff. At low pH, R1 is dominant
but it is slow. As pH increases, both the contribution of R2
to the total rate and the total rate increase. At pH 5, the
total loss rate for HO2 maximizes because the product
[HO2(aq)][O
2(aq)] is at a maximum. The total reaction rate
(mainly due to R2) decreases with further increases in
pH > 5. However, the reaction probability continues to
increase with pH greater than 5, even though the reactive
flux is decreasing. We interpret this behavior as being due to
the fact that the reactive flux decreases more slowly than the
volatilization flux, which is also decreasing above pH 5
because of enhanced solubility. This behavior is not a valid
representation of net HOx-loss in a closed system. That is,
for systems where gas-phase sources of HOx are near zero,
or are smaller than the volatilization flux from the condensed-phase, the reaction probability formulation presented here will over estimate the true multiphase loss of
HO2.
[31] To assess when solubility driven uptake invalidates
our net reaction probability formulation, we compared the
output of a coupled gas-aqueous phase model of HOx
chemistry to that of a model including only gas-phase
chemistry and our reaction probability formulation,
equation (7), to calculate the loss of HO2 in the condensed
phase. In the coupled gas-aqueous phase model, volatilization from the condensed phase is a source of gas-phase
HO2, while accommodation limited mass transfer of HO2
from the gas-phase is the source of aqueous HO2 ([O2(I)]).
Selected results from the comparison over a range of
conditions are shown in Figure 3. We examined the behavior of the two approaches as a function of particle size, total
particle volume, pH, T, and of a homogeneous gas-phase
source of HO2 (PHOx). In all cases the reaction probability
formulation either overestimated the net loss of HO2 or
showed no difference in behavior. The invalidity of the
reaction probability formulation increases as the volatilization flux grows in importance, which occurs with increasing
particle volume, increasing pH, decreasing temperature, and
decreasing PHOx. In the context of heterogeneous loss of
HOx, an open system would be one in which PHOx is larger
than any flux from the condensed phase as might be
expected in a diffuse plume of aerosol particles. A thick
cloud is likely closer to a closed system in that PHOx would
likely be small due to reduced actinic flux within the cloud
while the condensed phase volume density is large thereby
increasing the importance of the volatilization flux as a
source of gas-phase HO2.
[32] Panel A of Figure 3 shows the results of both models
for two conditions: PHOx = 0 (triangles) and PHOx = 1 105
molec cm3 s1 (squares). In the coupled gas-aqueous
chemistry model (open symbols) and the reaction probability formulation (filled symbols), rp = 10 mm, Np 100 cm3,
pH = 5, and T = 250 K. At long times, it is clear that in a
closed system the reaction probability formulation will
overestimate the HO2 number density (by at least a factor
of 10). In Panel B, conditions are largely the same as for
Panel A, except pH = 8. Clearly, for the closed system and
high pH, the reaction probability formulation is invalid.
However, note that in both Panels A and B where the
condensed phase volumes approach that of a cloud and not a
diffuse aerosol population, a moderate HOx production rate
(PHOx = 1 105 molec cm3 s1) causes both models to
agree because the volatilization flux from the condensed
phase is small compared to the external HOx source. The
point being that for typical aerosol particle volumes and
realistic HOx production rates, the reaction probability
formulation will likely be accurate even for high pH, even
though it is technically an upper-limit estimate of HO2 loss
by aqueous-phase processing. The results in Panel C are
from calculations using rp = 0.2 mm, Np 1 104 cm3, pH =
5, and T = 250 K. The two approaches agree regardless of
whether PHOx is 0 or 1 105 molec cm3 s1. Panel D
shows results from similar conditions as in Panel C but for
pH = 8. From the results in Panels C and D, it is clear the
reaction probability formulation remains invalid for PHOx =
0, although much less so compared to the large particle
volumes in Panel B. The impact of solubility driven uptake
on gas-phase HO2 can easily be accounted for in a global
model by assuming gas-particle equilibrium is rapidly
achieved as is the case shown in Figure 3.
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Figure 3. In each panel, the time evolution of [HO2(g)] is shown as predicted from a coupled gasaqueous model (open symbols) which accounts for the volatilization flux from the condensed phase, and
from a gas-phase only model using the reaction probability formulation (equation (7) -filled symbols).
Panel A shows results for a closed system (PHOx = 0; triangles) and an open system (PHOx = 1 105
molec cm3 s1; squares). The calculations assume rp = 10 mm, Np = 100 cm3, pH = 5, T = 250 K.
Panel B shows model outputs in the same format as A, but for conditions: rp = 10 mm, Np = 1000 cm3,
pH = 8, and T = 275 K. Model outputs in the same format as A, are shown in Panels C and D where pH =
5 and 8, respectively; rp = 0.2 mm, Np = 10,000 cm3, and T = 250 K for all runs shown in C and D. Plots
in all panels contain open and filled triangles and squares. If not visible, the symbol pairs (open or filled)
lie on top of each other.
[33] To assess the potential importance of reactive uptake,
we chose a uniform aerosol pH of 5 for our GEOS-chem
model calculations, which is where equation (7) predicts the
largest reaction probabilities and is most valid. This choice
is meant to produce upper limit effects. Typical tropospheric
aerosol pH range between 2 and 5 [Keene et al., 2004].
Fresh sea salt aerosol particles have a pH 8, and aged
aerosols generally can have a pH lower than 4 in regions
deficient in ammonia, thereby creating a large possible
range in the reactivity of HO2. Below a pH of 3, g HO2 in
the absence of Cu becomes too low to be important as a
HOx sink except for the coldest conditions (T < 240 K) and/
or the largest droplets (rp 10 mm). Above pH 5, g HO2
calculated from equation (7) greatly increases, but care must
be taken in the use of this equation under such conditions; in
particular, the volatilization flux from the condensed phase
must be small compared to other gas-phase sources of HO2
for our formulation to be valid.
3.4. Atmospheric Implications
[34] We begin our discussion of the GEOS-Chem model
results with the predicted total aerosol surface area concentrations (mm2 cm3) for January and July shown in
Figure 4. Sulfate aerosols dominate in the northern midlat-
itudes near industrial centers, exceeding 250 mm2 cm3 at
the surface. Mineral dust aerosols dominate the surface area
concentration in the regions downwind of the Sahara and
Gobi deserts, reaching annual average values exceeding
150 mm2 cm3 over the equatorial Atlantic. Organic carbon
(OC) is a dominant source of aerosol surface area over
biomass burning regions in South America and Africa.
Sea salt aerosols are most important in the high latitude
oceans during winter, with maximum contributions reaching 75 mm2 cm3. Black carbon (BC) surface area can
reach values exceeding 150 mm2 cm3 in regions of
significant industrial activity (NE U.S., Europe, and SE
Asia) or over biomass burning regions primarily in Africa.
However, annual means in these regions are typically less
than 100 mm2 cm3. Total surface area concentrations are
much lower aloft than at the surface (as expected by the
depositional and precipitation sinks) with sulfate becoming
the dominant source of aerosol surface area in the model
above 4 km (Figure 4, bottom panels).
3.5. Simulations Assuming Aqueous-Phase Self
Reaction Only
[35] In one set of simulations, we use equation (7) to
calculate g HO2 for each aerosol type (except dust for which
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Figure 4. Total aerosol surface area (mm2/cm3) calculated by the GEOS-Chem model for the months of
January (left) and July (center), and for the annual mean (left). The top panels show the distribution at the
surface, while the bottom panels are zonal means.
we assume g HO2 = 0.2), and then calculate the mean
reaction probability weighted by the respective aerosol
surface areas. Figure 5 shows surface and zonal mean
distributions of the resulting weighted reaction probability,
w_g HO2, for January and July. The strong inverse depen-
dence of g HO2 on temperature (Figure 1b), and the dependence on HO2 concentrations (Figure 1c) account for most
of the variations in w_g HO2 as a function of altitude,
latitude, and season. Low w_g HO2 values (<0.05) dominate
the lower troposphere, and increase to values >0.1 in the
Figure 5. Global distribution of g HO2 calculated with the GEOS-Chem-model. The reaction
probabilities are calculated using equation (7) for sulfate, organic carbon, black carbon, and sea-salt
aerosols. For dust aerosol, we assume g HO2 = 0.2. The resulting reaction probabilities for each grid box
are weighted by the relative aerosol surface area. Top panels: surface distribution of g HO2, for January
(left), July (middle), and annual mean (right). Bottom panels: zonal mean. Contour intervals are 0.01,
0.02, 0.05, 0.1, 0.2, 0.3.
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cold upper troposphere (Figure 5, bottom panels). At the
surface, the lowest values of w_g HO2 are in the Tropics
(
0.001 – 0.005, except for regions dominated by dust over
and downwind of the Sahara and Gobi deserts), increasing
to values larger than 0.1 at the colder high latitudes. In polar
regions, it is unlikely that the aerosols are neutralized to pH
5, so these values are likely to be upper limits. Over
continents near industrial and biomass burning regions,
smaller particles (sulfate, OC, BC) dominate the surface
area and thus result in lower w_g HO2 compared to remote
oceanic regions where larger sea-salt particles are the main
aerosols. For example, over the NE United States w_g HO2
<0.001, while over the Pacific or Atlantic Oceans at the
same latitude, w_g HO2 >0.01.
3.6. Effect of Reaction Probability Parameterizations
on Simulated HOx, H2O2 and O3
[36] Previous global modeling studies have considered
the impact of HO2 loss to aerosols on the abundance of
oxidants [Dentener et al., 1996; Tie et al., 2001, 2005;
Martin et al., 2003] compared to no loss to aerosols. These
previous studies used g HO2 = 0.1– 0.5, essentially the same
as assuming Cu catalyzed chemistry or some unknown
efficient surface chemistry, and found significant effects.
Dentener et al. [1996] examined the effect of HO2 uptake
on mineral dust (g HO2 = 0.1), finding a 10% decrease in
surface HO2 concentrations in dust source regions. Tie et al.
[2001] calculates that uptake of HO2 on sulfate aerosols
(g HO2 = 0.2) results in a decrease in HOx concentrations in
June by more than 10% are northern mid- and highlatitudes. Using the GEOS-Chem model, Martin et al.
[2003] report that aerosol uptake of HO2 (g HO2 = 0.2)
accounts for 10– 40% of total HOx loss in the boundary
layer over polluted continental regions, and for more than
70% over tropical biomass burning regions.
[37] The left panels in Figure 6 show the effect of
including heterogeneous HO2 uptake on OH, HO2, and
H2O2 concentrations using our new g HO2 formulation,
equation (7), which accounts for the aqueous-phase self
reaction but neglects Cu chemistry. The right panels in
Figure 6 assume a uniform g HO2 = 0.2 for all aerosol types
and conditions. For the uniform g HO2 case, the largest
effects of HO2 uptake are in northern hemisphere lower
troposphere corresponding to the highest aerosol loadings.
Consistent with previous studies, we find decreases in HO2
and OH of 10– 20% in that region. Locally HO2 concentrations can decrease by 25– 50% over industrial regions
and mineral dust regions (Figure 7). As we assume that
H2O2 is the sole product of HO2 loss to aerosols, its
concentrations increase by 20– 30% in the northern hemisphere lower troposphere, on average (Figure 6). Regionally
the increases exceed 30% (Figure 7). The global annual
average surface concentrations changes for OH, HO2, and
H2O2 are -7%, -12%, and +15%, respectively. The effects
on calculated O3 concentrations at the surface are smaller:
1% average decrease globally, with up to a 5% decrease in
heavily polluted or dust source regions. In the upper
troposphere, H2O2 concentrations increase by 5 – 10%. Indeed in that region, HO2 uptake is a small sink for HOx, but
it can be a strong source of H2O2 [Jaegle et al., 2000].
[38] We also ran a GEOS-chem simulation where g HO2 =
1 (not shown) on all particle types to mimic the possibility
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that enough soluble Cu exists on all particle types to make
HO2 loss on aerosol particles mass accommodation limited
[Thornton and Abbatt, 2005]. Such conditions decrease
HO2 and OH in the lower most layer of the model by more
than 50% and more than 30%, respectively, across most of
the land area in the northern hemisphere relative to a
simulation where g HO2 = 0. Over the same regions, H2O2
in the g HO2 = 1 simulation is more than 50% higher than the
g HO2 = 0 simulation.
[39] When g HO2 is calculated by equation (7) (left panels
in Figure 6 and Figure 7), we find a much smaller effect,
with only 2– 5% decreases in HOx and H2O2 concentrations
in the lower troposphere northern hemisphere. The smaller
effect is consistent with small values predicted for g HO2
(<0.05) in the lower troposphere by equation (7) (Figure 5).
Regions affected by mineral dust (for which we assume
g HO2 = 0.2), display the largest changes, with more than
10% decreases in HOx concentrations. Global annual mean
differences in surface OH, HO2, and H2O2 concentrations
are 1, 3, and +4%, respectively. If we further assume
that g HO2 = 0 on dust then the global annual mean differences in surface OH, HO2, and H2O2 concentrations are
even smaller at 1, 2, and +2%, respectively. Above 6 km
altitude, our calculated g HO2 becomes greater than 0.1,
resulting in a 5 – 10% increase in H2O2 at those altitudes.
3.7. Reaction Probability Parameterizations and
Observations of HOx, H2O2, and O3
[40] The aqueous HO2-only mechanism used here is
consistent with observations of HOx made in the upper
troposphere, where a g HO2 0.1 was inferred [Jaegle et al.,
2000]. Additionally, Hudman et al. [2007] compare GEOSChem simulations, where g HO2 = 0.2 for all particle types,
to H2O2 observations obtained over N. America. Their
model results are unbiased relative to the observations in
the free troposphere, but the model overestimates H2O2
concentrations below 3 km by 30% (see their Figure 3).
Our HO2-only formulation for g HO2 leads to a decrease in
model calculated H2O2 relative to the g HO2 = 0.2 simulation, by 15– 25% over the INTEX-A region in July (see our
Figure 7), and thus our formulation would reduce the model
overestimate of observed H2O2 they report. Similarly,
Sauvage et al. [2007] find that assuming g HO2 = 0 on
biomass burning aerosols systematically increases modeled
O3 over tropical biomass burning regions by 5 – 7 ppbv
relative to a simulation with g HO2 = 0.2. The g HO2 = 0
condition improves the consistency of their simulation with
the in situ O3 profiles.
[41] The HO2-only mechanism is inconsistent with some
surface observations which have inferred a g HO2 between
0.1– 1 by comparison of HO2 measurements with photochemical box models. For example, Cantrell et al. [1996]
inferred a g HO2 of 0.1– 1 from measurements of HO2 made
using the chemical amplifier technique at Mauna Loa.
Recently, including an aerosol loss of HO2 with g HO2 = 1
in an observationally constrained steady state model led to
improved agreement between model predictions and HO2
measurements made during the SOAPEX-2 and NAMBLEX campaigns [Sommariva et al., 2004; Haggerstone
et al., 2005; Smith et al., 2006; Sommariva et al., 2006].
These latter results are intriguing in that often, the best
measurement-model agreement was achieved with g HO2 = 1
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Figure 6. Annual mean change (percent) due to the inclusion heterogeneous reaction of HO2 relative to a
simulation with g HO2 = 0. Left panels: Effect of our new g HO2 formulation. Right panels: Effect of a uniform
g HO2 = 0.2 for all aerosols. Top: HO2 concentrations (contour lines are 30,20,15,10,5,2,1,
0%). Middle: Effect on OH concentrations (contour lines: 20,15,10,5,2,1, 0%). Bottom: Effect
on H2O2 concentrations (0, 1, 2, 4, 6, 8, 10, 15, 20, 25, 30%).
whereas g HO2 = 0.1 was not sufficient. Gas-phase diffusion
limits the reaction rate on particles larger than about 1 mm,
thus these modeling results imply that the inferred heterogeneous loss of HO2 is most important on sub-micron
particles. However, a correlation between the model-
measurement discrepancies and measured aerosol surface
area are either non-existent or not analyzed in most of these
studies and so implicating heterogeneous chemistry is
highly speculative. All three of these experiments took
place in, or were heavily influenced by, the marine bound-
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Figure 7. Annual mean change (in percent) in calculated surface concentrations of HO2, OH, and H2O2
for a simulation with our new g HO2 formulation relative to a simulation with a uniform g HO2 = 0.2 for all
aerosol types. Results for the months of January (left panels) and July (right panels) are shown.
ary layer. In fact, at Mauna Loa, aerosol chemistry was
inferred as being most important during upslope events
where the influence of marine air would be strongest. The
HO2-only aqueous mechanism analyzed here does not
predict a g HO2 as large as 0.1 on sub-micron particles for
the conditions of any of these campaigns, unless the
accumulation mode aerosols were dominated by fresh sea
salt particles with a pH 7 – 8 and had not reached
equilibrium with HO2(g). The Cu catalyzed mechanism is
a possibility but the IMPROVE network data show Cu mass
fractions at Mauna Loa are often below the detection limit
of 1 105. A final possibility is that the gas-phase
mechanisms used in these box models are incomplete,
e.g., by neglecting halogen chemistry. If the inferred HO2
loss can be shown to be correlated to aerosol surface area,
then either a direct surface reaction or an unrecognized
condensed phase reaction in the accumulation mode aerosol
particles becomes a possibility. Correlations with size and
composition would then be helpful in elucidating the
mechanism.
4. Conclusions and Recommendations
[42] Our modeling results add to a growing body of
evidence that shows the heterogeneous loss of HO2 to
aerosol particles can significantly affect regional and global
oxidant levels with consequences for prediction of ozone
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abundance, the nonlinear chemistry that connects HOx and
NOx, and trace gas lifetimes. This work and previous
studies suggest that heterogeneous loss of HO2 becomes
important to the composition and chemistry of the troposphere when g HO2 > 0.05. The loss of HO2 to aerosols via
known HO2-only aqueous phase chemistry will not be
important in the lower troposphere except in highly localized regions where aerosols are aqueous, largely neutralized, and temperatures are low. On the other hand,
neutralized deliquesced aerosols in the mid to upper troposphere should present an important HOx sink if the surface
area exceeds about 5 mm2/cm3. A number of recent studies
comparing model predictions to observations of HOx, H2O2,
and O3 made throughout the troposphere are consistent with
a g HO2 that the HO2-only formulation would predict [Jaegle
et al., 2000; Ren et al., 2006; Hudman et al., 2007; Sauvage
et al., 2007]. However, for box models to match HO2
measurements made in the marine boundary layer, g HO2
must be 0.1 on accumulation mode particles. Such a large
g HO2 would not be predicted with the HO2-only mechanism
for this region.
[43] The largest issues restricting accurate modeling of
HO2 loss to aerosols via the chemistry presented here are a
poor knowledge or parameterization of: 1) aerosol pH, 2)
aerosol concentrations of free aqueous Cu or Fe, and 3) the
reactivity HO2 (or O
2 ) with particulate organic matter and
mineral dust. IMPROVE Network data together with one
set of laboratory measurements of HO2 loss versus aerosol
Cu concentrations indicate that HOx loss catalyzed by fine
mode aerosol Cu does not often reach the mass accommodation limit in the lower troposphere over many regions of
U.S. However, the mechanism is likely operational to some
degree depending on proximity to Cu sources or aerosol
processes not yet represented in most global models (e.g.,
dust processing). The potential importance of HO2 loss to
aerosols demands that future laboratory measurements and
field studies of this process continue. Laboratory kinetic
experiments should assess the reactivity of HO2 on aged
mineral dust and other aerosol surfaces as a function of RH,
HO2 and TMI concentrations, and size. Otherwise, interpretations may be plagued by possible surface saturation
effects or by irrelevant surface-to-volume ratios.
[44] A more refined approach to the inclusion of HO2
reactions on aerosols is required for many global chemical
transport models in order to better account for the spatial
and aerosol composition dependent chemistry. Ideally models will eventually include online multiphase modules that
track aerosol phase state and size resolved aerosol pH and
TMI concentrations, but many global models lack such
modules or such modules remain too computationally
expensive. Thus we conclude with a simplified set of
recommendations, the goals of which are to grossly capture
the average behavior expected within a typical spatial
domain of models that treat aerosols as external mixtures
of carbonaceous, anthropogenic sulfate, sea salt and mineral
dust particles similar to GEOS-Chem. In the mid-to-upper
troposphere (> 4 km) or cold regions (T < 265 K), we
expect the major limitations to the rate of HO2 reaction on
aerosols are the pH and size. We therefore recommend using
the HO2-only parameterization which predicts average g HO2
0.1– 0.3 for the aerosol distributions in GEOS-Chem (see
Figure 5). We expect TMI in sea salt or carbonaceous
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particles, such as those from biomass burning, are complexed to ligands and/or exist at a concentration too low to
catalyze HO2 loss efficiently [e.g., Shank et al., 2004, and
references therein], and so we recommend using the HO2only parameterization. To account for anthropogenic Cu
emissions, we extrapolate fine-mode Cu mass fractions
measured in near surface air over the U.S. to a continental
average Cu molality (
0.5– 1 103) and use equation (8)
constrained by the data of Mozurkewich et al. [1987]. This
approach is subject to large errors due to spatial differences
in Cu sources, unknown Cu distributions within an aerosol
population, its neglect of Cu-ligands, and its reliance on a
single set of laboratory measurements. These estimates
suggest g HO2 between 0.04– 0.1 can be used for fine-mode
pollution aerosols (e.g., rp 100– 200 nm) in the boundary
layer. If such particles are deemed to have pH < 5 or
substantial Cu-ligands, the g HO2 would be lower. Mineral
dust particles present a major unknown, and we very
tentatively suggest g HO2 0.1 to account for the potential
of TMI induced chemistry to occur in a thin aqueous surface
layer. The above recommendations are for global models
with limited multiphase and aerosol particle schemes and
are of course limited by only a few experimental studies.
Regional models should assess the role of copper and other
TMI for their location of interest.
Appendix A
[45] The net reactive uptake rate, FR, of a gas-phase
species X to an aerosol of radius, rp, is required to calculate
g. FR, the aqueous phase reaction rate (per particle volume),
is defined as the difference between the gross condensation
rate of X into the aerosol, and the evaporative rate out. In
the free molecular regime, FR is given by equation (A1) in
units of molec cm2 s1,
FR ¼ kmt Xg NAV
3
X *aq
1000Heff RT
rp
ðA1Þ
where X(aq)
* is the steady state concentration (M) of X at
the aerosol surface, Heff is the effective Henry’s law
constant (M atm1), R is the universal gas constant (atm
L mol1 K1), T is temperature (K), NAV is Avagadro’s
number (mol1) and kmt is the rate constant for interfacial
mass transport in the free molecular regime in units of
cm s1
kmt ¼
aw
4
ðA2Þ
Once FR is known, g is obtained by normalizing the
reactive flux to the gas-aerosol collision flux.
g ¼
4FR
wXg
ðA3Þ
Gas-phase diffusion limitations are then accounted for by
using equation (1) to calculate the net uptake rate.
[46] Aqueous-phase diffusion and reaction may create
significant concentration gradients of reactants within the
aerosol bulk. In the case of HOx-only chemistry, we must
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THORNTON ET AL.: HO2 HETEROGENEOUS CHEMISTRY
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consider the aqueous-phase concentration profiles of total
dissolved HO2, [O
2 (I)], where [O2 (I)] [HO2(aq)] +
[O2(aq)], and also of [O3(aq)]. The aqueous-phase diffusion
limitations of O
2 (I) are small for most conditions examined
here, but those of O3(aq) can be significant for rp > 1 mm.
Thus in the first of two approaches, we solved the coupled
steady state diffusion equations for O
2 (I) and O3(aq) to
obtain a value for [O
2 (I)*], from which a calculation of
the net reactive flux and g HO2 are possible. Note that this
approach to calculating g HO2 neglects any surface-only
reactions, which in the laboratory experiments have not
been observed to be important given the consistency with
bulk kinetics [Thornton and Abbatt, 2005].
[47] The general form of the steady state aqueous-phase
diffusion equation for species X, with and aqueous-phase
diffusion constant, DXaq chemical production, PX(r), and
loss, LX(r), is
0 ¼ DXaq
1 d
2 dXaq
LX ðrÞ þ PX ðrÞ
r
dr
r2 dr
ðA4Þ
where r is the distance from the center of the droplet. We
neglect chemical production of O
2 (I) and O3 within the
aerosol bulk so that P(r) = 0. On the basis of the above
mechanism, the two diffusion equations for O
2 (I) and O3
are coupled through a term in L(r), which becomes for
O
2 (I) and O3, respectively:
2
LO2 ðrÞ ¼ 2keff ½O
2 ðIÞ þ k3 fO2 ½O2 ðIÞ½O3ðaqÞ LO3 ðrÞ ¼ k3 fO2 ½O
2 ðIÞ½O3ðaqÞ ðA5Þ
ðA6Þ
In equations (A5) and (A6), fO2 is the pH-determined
fraction of O
2 (I) that is O2(aq) only, not HO2(aq) as
determined by the acid dissociation constant, Keq. If loss
of X is first-order in Xaq, equation (A4) is readily solved
analytically [see, e.g., Jacob, 1986]. In our case, reactions
R1 and R2 are both second order in O
2 (I). Given the wide
range of environmental conditions to be examined, we
chose to solve the set diffusion equations numerically
without forcing pseudo first order behavior, subject to the
following boundary conditions:
dXaq
¼ 0
dr r ¼ 0
DXaq
dXaq
dr
¼ kmt
r ¼ rp
1000Xg
X a*q
NAV
Heff RT
ðA7Þ
ðA8Þ
Equation (A7) is due to an assumed spherical symmetry,
and equation (A8) requires that the aqueous-phase diffusive
flux at the gas-aerosol interface be equal to that determined
by the difference between molecules entering and evaporating from the interface. Equations (A4) – (A8) form a
complete description of the mass transport and aqueousphase chemistry of HO2 subject to the self-reaction
mechanism.
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[48] Acknowledgments. This work was supported in part by grants
from NASA Office of Earth Science NIP/03-0000-0025 and NSF-ATM0633897.
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